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A stella model for integrated algal biofuel production and wastewater treatment

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Title:
A stella model for integrated algal biofuel production and wastewater treatment
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Book
Language:
English
Creator:
Cormier, Ivy
Publisher:
University of South Florida
Place of Publication:
Tampa, Fla
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Subjects

Subjects / Keywords:
Mass balance
Carbon dioxide
Algae economics
Nitrogen
Phosphorous
Monod kinetics
Dissertations, Academic -- Civil & Environmental Eng -- Masters -- USF   ( lcsh )
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non-fiction   ( marcgt )

Notes

Abstract:
ABSTRACT: Based on a municipal wastewater treatment plant (WWTP) in Tampa, FL, a dynamic multiple-systems model was developed on the STELLA software platform to explore algae biomass production in wastewater by incorporating two photobioreactors into the WWTP's treatment train. Using a mass balance approach, the model examined the synergy through algal growth and substrate removal kinetics, as well as macroeconomic-level analyses of algal biomass conversion to biodiesel, biogas, or fertilizer. A sensitivity analysis showed that biomass production is highly dependent on Monod variables and harvesting regime, and profitability was sensitive to processing costs, market prices of products, and energy environment. The model demonstrated that adequate nutrients and carbon dioxide are available in the plant's influent to sustain algal growth. Biogas and fertilizer production were found to be profitable, but biodiesel was not, due to high processing costs under current technologies. Useful in determining the growth potential on a macro-level, the model is a tool for identifying focus areas for bench and pilot scale testing.
Thesis:
Thesis (MSES)--University of South Florida, 2010.
Bibliography:
Includes bibliographical references.
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Mode of access: World Wide Web.
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System requirements: World Wide Web browser and PDF reader.
Statement of Responsibility:
by Ivy Cormier.
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Title from PDF of title page.
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Document formatted into pages; contains X pages.

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University of South Florida
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usfldc doi - E14-SFE0004707
usfldc handle - e14.4707
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SFS0028014:00001


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A STELLA Model for Integrated Algal Biofuel Production and Wastewater Treatment by Ivy Cormier A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Engineering Science Department of Civil and Environmental Engineering College of Engineering University of South Florida Majo r Professor: Daniel Yeh, Ph.D. Piet Lens, Ph.D. Qiong Zhang, Ph.D. Date of Approval: October 1 8 2010 Keywords: mass balance, carbon dioxide, algae economics, nitrogen, phosphorous, Monod kinetics Copyright 2010 Ivy Cormier

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Acknowledgements I would like to express my utmost gratitude to those who have listened to, supported, helped, and pushed me throughout the design and implementation of this project. Although I have had countless influences while conducting this research, I would like to e xplicitly thank the following: Dr. Daniel Yeh for his continued support, advice, and ideas; committee members Dr. Piet Lens and Dr. Qiong Zhang for their insightful comments ; the Hillsborough County Health Department for their support and flexibility; Miss Caryssa Joustra for her expertise; Miss Ana Lucia Prieto for her insight and patience; Mr. Robert Bair for his opinions, humor, and input on economic variables; Mr. Timothy Ware from the Howard F. Curren Advanced Wastewater Treatment Plant for providing plant data; and my friends and family who have endured long discussions regarding algae and biofuel.

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i Table of Contents List of Tables ................................ ................................ ................................ ........ i v List of Figures ................................ ................................ ................................ ..... v i i i v List of Acrony ms ................................ ................................ ................................ x i v vi Abstract ....... ................................ ................................ ................................ ....... x v vii Chapter One: Introduction ................................ ................................ .................... 1 1 Chapter Two: Background ................................ ................................ .................... 3 3 Background of Wastewater Treatment Plant Case Study .......................... 3 Shortcomings of Conventional Wastewater Treatment .............................. 5 Basic Wastewater Treatment ................................ ................................ ..... 7 3 Carbon Removal ................................ ................................ ............. 8 5 Nitrogen Removal ................................ ................................ ........... 8 6 Phosphorous Removal ................................ ................................ .... 9 6 Algae and Wastewater Treatment ................................ ................. 10 7 Algal Biology ................................ ................................ ............................ 11 9 Autotrophy ................................ ................................ ..................... 1 3 11 Heterotrophy ................................ ................................ ................. 1 4 13 Mixotrophy ................................ ................................ .................... 1 5 14 Synergy of Wastewater Treatment and Algae Cultivation ........................ 1 6 14 Environment a l Conditions Affecting Growth ................................ ............. 1 7 14 Light ................................ ................................ .............................. 1 7 15 Temperature ................................ ................................ ................. 18 16 pH ................................ ................................ ................................ 19 17 Nutrient Input ................................ ................................ ................. 20 18 Lipid Production ................................ ................................ ............ 2 3 21 Carbon Dioxide Retrieval ................................ .............................. 25 23 Oxygen and Chemical Demand Reduction ................................ ... 2 6 Secondary Use of Algal Biomass ................................ ............................. 26 24 Biodiesel ................................ ................................ ....................... 2 7 25 Biogas ................................ ................................ ........................... 28 27 Fertilizer ................................ ................................ ........................ 2 9 27 Summary of Background ................................ ................................ ......... 30 28

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ii C hapter Three: Model Framework ................................ ................................ ...... 31 29 General Model Background ................................ ................................ ..... 31 29 Stella Software ................................ ................................ ......................... 3 2 30 Conceptual Approach ................................ ................................ .............. 34 31 Practical Approach ................................ ................................ ................... 3 5 31 Wastewater Framework ................................ ................................ ........... 3 6 Water Balance ................................ ................................ ............... 38 Carbon Balance ................................ ................................ ............ 4 1 Nitrogen Balance ................................ ................................ ........... 4 7 Phosphorous Balance ................................ ................................ ... 50 Algae Growth Framework ................................ ................................ ........ 5 3 Maximum and Ca lculated Specific Growth Rate ........................... 5 5 Algae Growth ................................ ................................ ................ 5 9 Determining Substrate Utilization Rate and Yield Coefficient ....... 61 Determining Substrate Removal via Biomass Assimilation ........... 6 4 Hydraulic R etention Time in Algae Basins ................................ .... 6 8 Solids Retention Time ................................ ................................ ... 6 8 Algae Production Costs & Benefits Calculations ................................ ...... 6 9 Benefits of Reduced Aeration ................................ ....................... 7 1 Reduced Chemical Additives ................................ ........................ 7 3 Biomass Prod ucti on Costs ................................ ............................ 7 4 Biomass Harvesting Costs ................................ ............................ 7 5 Secondary Product Calculations ................................ .............................. 7 5 Biodiesel Calculations ................................ ................................ ... 76 Biogas Calculations ................................ ................................ ....... 80 Fertilizer Calculations ................................ ................................ .... 8 6 32 34 Chapter F our : Sensitivity Analysis ................................ ................................ ...... 90 45 Wastewater Variables ................................ ................................ .............. 90 Wastewater Influent Characteristics ................................ .............. 90 Other Wastewater Parameters ................................ ...................... 94 Algae Growth Variables ................................ ................................ ........... 95 Specific Growth Rate and Harvest Waste Rate ............................ 95 Half Saturation Constants ................................ ............................. 9 8 Yield Coefficient ................................ ................................ .......... 100 Economic Variables ................................ ................................ ............... 101 Cost Savings from Reduced Aeration ................................ ......... 101 Cost Savings from Reduced Chemical Addition .......................... 102 Biodiesel ................................ ................................ ..................... 103 Biogas ................................ ................................ ......................... 106 Fertilizer ................................ ................................ ...................... 107 Chapter Five : Results ................................ ................................ ....................... 109 Potential Biomass Production at HFCAWTP ................................ ......... 110 Economic Viability ................................ ................................ .................. 1 17

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iii Chapter Six: Conclusions and Future Research ................................ ............... 12 4 Conclusions ................................ ................................ ........................... 1 24 Future Research ................................ ................................ .................... 126 List of References ................................ ................................ ............................ 1 30 Bibliography ................................ ................................ ................................ .... 1 3 7 Appendices ................................ ................................ ................................ .... 138 Appendix A: List of Variables ................................ ................................ 1 39 Appendix B: List of Equations ................................ ................................ 1 8 6 Appendix C: Extra Figures ................................ ................................ ..... 204 About the Author ................................ ................................ ...................... End Page #

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iv List of Tables Table 1 Varying lipid content per cell dry weight among algae species reported in different studies ................................ ............................... 2 5 Table 2 List of nutrient groups tracked within the mod el and their associated species ................................ ................................ ............ 3 6 Table 3. Calculated yield coefficients for determination of q t .......................... 6 4 Table 4. Concentration ranges of influent ammonia, soluble phosphorous, and carbon dioxide selected for wastewater characteristics sensitivity analysis. ................................ ................... 9 1 Table 5. Trial matrix for varying influe nt wastewater characteristics. .............. 9 1 Table 6. Simulation parameters for case studies at HFCAWTP. .................. 1 1 1 Table 7. Parameter settings for economic viability analysis ......................... 119 Table 8. Potential profits under best, average, and worst case scenario condit i ons per kg of algae produced ................................ .............. 120 Table A1. List of variables in the water balance framework. ........................... 1 39 Table A2. List of equations i n the water balance framework .......................... 140 Table A3 List of variables within water loss to algae harvest framework ....... 1 41 Table A4. List of equations in water los s to algae harvest framework ............ 1 41 Table A 5 List of variables in phosphorous flow framework ............................ 1 42 Table A6. List of equations in phosphorous flow framework ........................... 1 4 3 Table A 7 List of variables in phosphorous mass balance framework ............ 1 44 Table A8. List of equations in phosphorous mass balance framework ........... 1 45

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v Table A9 List of variables in the nitrogen flow framework for organic N and ammonia ................................ ................................ ................. 1 4 6 Table A10. List of equations in the nitrogen flow framework for organic N and ammonia ................................ ................................ ................. 1 4 7 Table A 11 List of variables in the nitrogen flow framework for nitrat e and nitrogen gas ................................ ................................ ................... 1 48 Table A12. List of equations in the nitrogen flow framework for nitrate and nitrogen gas ................................ ................................ ................... 149 Table A 13 List of variables in nitrogen mass balance ................................ ...... 1 50 Table A14. List of equations in nitrogen mass balance ................................ .... 1 51 Table A 15 List of variables in soluble and nonsoluble carbon species model framework ................................ ................................ ............ 1 52 Table A16. List of equations in soluble and nonsoluble carbon species model framework ................................ ................................ ............ 1 54 Table A 17 List of variables in organic carbon and carbon dioxide species model framework. ................................ ................................ ........... 1 55 Table A18. List of equations in organic carbon and carbon dioxide species model framework ................................ ................................ ............ 1 5 6 Table A1 9 List of variables in carbon mass balance framework ...................... 1 57 Table A20. List of equations in carbon mass balance framework ..................... 1 58 Table A2 1. List of variables in calculating specific growth rate in the PPOR .... 1 59 Table A22. List of equations in calculating specific growth rate in the PPOR ................................ ................................ ............................. 1 60 Table A 2 3 List of variables for SRT framework in the PPOR .......................... 1 60 Table A24. List of equations for SRT framework in the PPOR ......................... 1 61 Table A 25 List of variables for algae growth in the PPOR ............................... 1 61 Table A26. List of equations for algae growth in the PPOR .............................. 1 62 Table A 27 List of variables in nitrogen utilization framework in the PP OR ...... 1 62

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vi Table A28. List of equations in nitrogen utilization framework in the PPOR ..... 1 6 3 Table A 29 List of variables in carbon utilization framework in the PPOR ........ 1 64 Table A30. List of equations in carbon utili zation framework in the PPOR ....... 164 Table A 31 List of variables in phosphorous utilization framework in the PPOR ................................ ................................ ............................ 1 65 Table A32. List of equations in phosphorous utilization framework in the PPOR ................................ ................................ ............................. 1 66 Table A 33 List of variables for substrate utilization rate framework in the PPOR ................................ ................................ ............................. 1 6 7 Table A34. List of equations for substrate utilization rate framework in the PPOR ................................ ................................ ............................. 167 Table A 35 List of variables for specific growth rate in the PNR ....................... 1 68 Table A36. List of equations for specific growth rate in the PNR ...................... 1 69 Table A 37 List of variables for SRT framework in the PNR ............................. 1 69 Table A38. List of equations for SRT framework in the PNR ............................ 1 70 Table A 39 List of variables for algae growth in the PNR ................................ 1 70 Table A40. List of equations for algae growth in the PNR ................................ 1 71 Table A4 1. List of var iables in nitrogen utilization framework in the PNR ......... 1 71 Table A42. List of equations for nitrogen utilization framework in the PNR ...... 1 72 Table A 43 List of variables in carbon utilization framework in the PNR ........... 1 7 3 Table A44. List of equations in carbon utilization framework in the PNR .......... 1 7 3 Table A 45 List of variables in phosphorous utilization framework in the PNR ................................ ................................ ............................... 1 7 4 Table A46. List of equations in phosphorous utilization framework in the PNR ................................ ................................ ............................... 1 75 Table A 47 List of variables for substrate utilization rate framework in the PNR ................................ ................................ ............................... 1 76

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vii Table A48. List of equations for substrate utilization rate framework in the PNR ................................ ................................ ............................... 17 6 Table A 49 List of variables for cost savings from reduced aeration ................. 1 77 Table A50. List of equations for cost s avi ngs from reduced aerat ion ............... 177 Table A 51 List of variables for cost savings from reduced chemical demand ................................ ................................ .......................... 1 78 Table A52. List of equations for cost savings from reduced chemical demand ................................ ................................ .......................... 178 Table A 53 List of variables for biogas processing framework .......................... 1 79 Table A54. List of equations for biogas processing framework ........................ 1 80 Table A 55 List of variables for biodiesel processing framework ...................... 1 81 Table A56. List of equations for biodiesel processing framework ..................... 18 3 Table A 57 List of variables for fert ilizer processing framework ........................ 1 8 4 Table A58. List of equations for fertilizer processing framework ...................... 18 5

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viii List of Figures Figure 1. Schematic of HFCAWTP. ................................ ................................ .. 4 Figure 2. Areas of potential synergy between algae growth and wastewater treatment. ................................ ................................ ..... 16 Fi gure 3 Basic components of a STELLA model. ................................ .......... 33 Figure 4. Schematic of the section of the treatment process at the HFCAWTP modeled in this study ................................ ................... 34 Figure 5 Conceptual f ramework of m odel c omponents ................................ .. 3 5 Figur e 6 Model interface for manipulating physical parameters of the treatment plant and influent flow characteristics ............................. 3 8 Figure 7 Conceptual flow of water through treatment plant and algae reactors. ................................ ................................ .......................... 39 Figure 8 A Model f ramework for w ater flow in STELLA model ......................... 40 Figure 8B. Conceptual water flow in STELLA model ................................ ........ 40 Figure 9 Model framework for water loss due to algae harvesting. ............... 4 1 Figure 10 Routing of electrons from an electron donor, such as BOD. ........... 42 Figure 11 A. Mass balance of carbon species ................................ ..................... 4 4 Figure 11B. Conceptual figure of carbon mass balance ................................ ..... 44 Figure 12A. Conceptual figure of carbon flow through the STELLA framework shown in Figure 12A. ................................ ................... 45 Figure 12 B Carbon flow in STELLA model ................................ ........................ 4 6 Figure 13 A Mass balance of nitrogen species in STELLA model ...................... 4 8

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ix Figure 13B. Conceptual figure of nitrogen mass balance. ................................ .. 48 Figure 1 4 A Nitrogen flow in STELLA model ................................ ...................... 4 9 Figure 14B. Conceptual figure of nitrogen flow through the STELLA framework shown in Figure 14A ................................ .................... 50 Figure 15 A Mass balance of phosphorous species in STELLA model .............. 51 Figure 15B. Conceptual figure of nitrogen mass balance ................................ ... 51 Figure 1 6 A Pho sphorous flow in STELLA model ................................ ............... 5 2 Figure 16B. Conceptual figure of phosphorous flow through the STELLA framework shown in Figure 16A ................................ .................... 52 Figure 1 7 Model interface for manipulating parameters related to algae growth kinetics and the physical characteristics of the algae basins ................................ ................................ ............................ 5 4 Figure 1 8 A Model framework for determination of specific growth rate in the PPOR from Monod kinetics ................................ ...................... 5 8 Figure 18B. Conceptual illustration of equation used to determine specific growth rate in the PPOR ................................ ................................ 58 Figure 1 9 A Model framework for algae production in the PPOR ....................... 60 Figure 19B. Conceptual figure of algae production in the PPOR ........................ 6 0 Figure 20 A Model framework for calculating the substrate utilization rate in the PPOR ................................ ................................ ................... 6 2 Figure 20B. Equations for substrate utilization rate framework in the PPOR shown in Figure 20A. ................................ ................................ ..... 6 2 Figure 21 A Model framework for ammonia nitrogen removal from the PPOR ................................ ................................ ............................. 6 6 Figure 21B. Conceptual illustration of ammonia utilization in the PPOR ............ 6 6 Figure 22 Model framework for movement of nitrogen in t he wastewater treatment plant ................................ ................................ ............... 67 Figure 2 3 Example of ammonia nitrogen being removed from wastewater framework after assimilation by algae ........................ 6 7

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x Figure 2 4 Model framework for calculating the volume of the PPOR as a function of HRT and flow diverted to algae basin, which are entered on the interface of the model. ................................ ........... 6 8 Figure 25. Model framework for calculating SRT ................................ .............. 6 9 Figure 26. Model interface for entering the cost per unit of secondary product produ c ed. ................................ ................................ ........... 70 Figure 27 Detail of model interface where user can define the route for secondary use of biomass ................................ .............................. 7 0 Figure 2 8 A Model framework for cost savings due to alga e assimilation and photosynthetic oxygenation ................................ ..................... 7 2 Figure 28B. Conceptual illustration for reduced aeration demand ...................... 7 3 Figure 29 A Model framework to calculate the benefits of reduced chemical additives ................................ ................................ .......... 7 4 Figure 29B. Conceptual illustration of savings due to reduced chemical demand ................................ ................................ .......................... 7 4 Figure 30 A. Model framework for biod iesel production calculations ................... 7 7 Figure 30B. Conceptual illustration of economic calculations in biodiesel processing train ................................ ................................ ............. 77 Fig ure 31 Model framework for calculating biogas production costs ............... 8 1 Figure 32 A Model fram ework for biogas calculations ................................ ........ 82 Figure 32B. Conceptual illustration of economic calculations in biogas processing train ................................ ................................ ............. 82 Figure 33 A Model framework for fer tilizer cost benefit analysis ......................... 8 6 Figure 33B. Conceptual illustration of economic calculations in fertilizer processing t rain ................................ ................................ ............. 87 Figure 3 4 Model framework for calculating fertilizer production costs ............. 8 7 Figure 35. Model parameter settings for influent wastewater characteristics sensitivity test ................................ .......................... 92

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xi Figure 36. Biomass production in the PPOR as a function of influent nutrient concentration. ................................ ................................ .... 93 Figure 37. Biomass production in the PPOR as a function of influent NH3 concentration ................................ ................................ .................. 9 4 Figure 38. Biomass production in the PPOR with increasing max. ................. 96 Figure 39. Biomass production as a function of harvest rate. ........................... 9 7 Figure 40. Specific growth rate as a function of harvest schedule. ................... 9 8 Figure 4 1 Calculated in the PPOR as a function of K ................................ .. 9 9 Figure 4 2 Calculated in the PNR as a function of K ................................ ...... 99 Figure 4 3 The effect of Y_NH3 on algae growth variables in th e PPOR. ...... 101 Figure 4 4 Cost savings from reduced aeration as a function of cost per unit oxygen. ................................ ................................ .................. 102 Figure 4 5 Cost savings from reduced chemical addition as a function of the cost of methanol. ................................ ................................ ..... 103 Figure 4 6 Cost of biodiesel production as a function of processing costs ..... 104 Figure 4 7 Cost of biodiesel production over varying biomass harvesting costs. ................................ ................................ ............................ 105 Figure 4 8 C ost of biodiesel production over varying biomass production costs ................................ ................................ ............................. 105 Figure 4 9 Cost of biodiesel production with added cost of secondary processing. ................................ ................................ ................... 106 Figure 50 Cost of biogas production as a function of processing costs. ........ 107 Figure 5 1 Cost of fertilizer production as a function of processing costs. ...... 108 Figure 5 2 Parameter se t tings for HFCAWTP case study .............................. 110 Figure 5 3 Biomass production at HFCAWTP in Case 1 ................................ 1 1 2 Figure 54 Biomass production at HFCAWTP in Case 2. ............................... 1 13 Figure 55 Biomass production at HFCAWTP in Case 3. ............................... 1 13

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xii Figure 56 Monod fractions in Cases 1 and 3. ................................ ................ 1 14 Figure 57 Biomass production as a function of specific growth rate at the HFCAWTP. ................................ ................................ ................... 11 5 Figure 58 Biomass production as a function of initial harvest. ....................... 1 16 Figure 59 Biomass production as a function of harvest amount, Case 1 conditions. ................................ ................................ ..................... 1 17 Figure 60 Biomass production as a function of harvest amount, Case 2 conditions. ................................ ................................ ..................... 117 Figure 61 Potential profits from biodiesel as a function of processing costs ................................ ................................ ............................. 120 Figure 62 Potential profits from biodiesel a s a function of market price ......... 121 Figure 63 Potential profit from biogas as a function of energy content .......... 122 Figure 64 Potential profit from fertilizer production as a function of market price ................................ ................................ .................. 1 2 3 Figure A 1 Detailed view of the water balance ................................ ............... 1 39 Figure A2. Detailed view of water loss to algae harvest ................................ 1 41 Figure A3. Phosphorous flow through treatment plant ................................ .... 1 42 Figure A4. Phosphorous mass bala nce framework in STELLA model ........... 1 4 4 Figure A5. Nitrogen flow framework for organic N and ammonia in the S TELLA model. ................................ ................................ ............ 1 4 5 Figure A6. Nitrogen flow framework for organic N and ammonia in STELLA model ................................ ................................ .............. 1 48 Figure A7. Nitrogen mass balance in STELLA model ................................ ..... 1 50 Figure A8. Flow of soluble and nonsoluble carbon species in STELLA model ................................ ................................ ............................ 1 5 2 Figure A9. Flow of organic carbon and carbon dioxide in STELLA model ...... 1 5 5 Figure A10. Carbon mass balance in STELLA model ................................ ...... 1 5 7

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xiii Figure A11. Calculated specific growth rate in the PPOR ................................ 1 59 Figure A12. SRT in the PPOR ................................ ................................ .......... 1 60 Figure A13. Algae growth framework in the PPOR in the STELLA model ........ 1 61 Figure A14. Nitrogen utilization in the PPOR ................................ .................... 1 62 Figure A15. Carbon utilization in the PPOR ................................ ..................... 1 6 3 F igure A16. Phosphorous utilization in the PPOR ................................ ............ 1 6 5 Figure A17. Substrate utilization in the PPOR in STELLA model ..................... 1 6 6 Figure A18. Specific growth rate in the PNR ................................ .................... 1 68 Figure A19. SRT framework in the PNR in the STELLA model ........................ 1 69 Figure A20. Algae growth framework in the PNR ................................ ............. 1 70 Figure A21. Nitrogen utilization framework for the PNR ................................ ... 1 71 Figure A22. Carbon utilization framework in the PNR ................................ ...... 1 72 Figure A23. Phosphorous utilization framework in the PNR ............................. 1 7 4 Figure A24. Substrate utilization rate framework in the PNR ............................ 1 7 5 Figure A25. Cost savings from reduced aeration framework in the STELLA model ................................ ................................ ............................ 1 7 7 Figure A26. Cost savings from reduced chemical demand framework ............. 1 78 Figure A27. Biogas processing framework in the STELLA model .................... 1 79 Figure A28. Biodiesel processing framework in the STELLA model ................. 1 81 Figure A29. Fertilizer processing framework in the STELLA model .................. 1 8 4 Figure C 1 Biomass production as a function of influent nutrient concentration in the PNR ................................ .............................. 20 4 Figure C 2 Biomass production in the PNR as a function of max ................. 20 5 Figure C3. Biomass production as a function of initial harvest rate, Case 2 ................................ ................................ .......................... 20 5

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xiv List of Acronyms BOD biochemical oxygen demand BNR biological nutrient removal BPR biological phosphorus removal COD chemical oxygen demand DO dissolved oxygen HFCAWTP Howard F. Curren Advanced W astewater Treatment P lant MGD million gallons per day MJ megajoules PAO phosphorous accumulating organisms PNR post nitrification reactor PP pentose phosphate pathway PPOR post pure oxygen reactor TCA tricarboxylic acid (citric acid) cycle TKN total K jeldhal nitrogen TN total nitrogen TSS total suspended solids VFA volatile fatty acids

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xv Abstract Based on a municipal wastewater treatment plant (WWTP) in Tampa, FL, a dynamic multiple systems model was developed on the STELLA software platform to explore algae biomass production in wastewater by incorporating two photobioreactors approach, the model examined the synergy through algal growth and substrate removal kinetics, as well as macroeconomic level analyses of algal biomass conversion to biodiesel, biogas, or fertilizer. A s ensitivity analys i s show ed that biomass production is highly dependent on Monod variables and harvesting regime and profitability was sensitive to processing costs, market prices of products, and energy environment. The model demonstrated that adequate nu growth. Biogas and fertilizer production were found to be profitable, but biodiesel was not, due to high processing costs under current technologies. Useful in determining the growth potential on a macro level t he model is a tool for identifying focus areas for bench and pilot scale testing.

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1 Chapter One : I ntroduction Domestic and industrial wastewater was aptly named for how it has historically been viewed: as a have become depleted and more difficult to extract, alternative sources of nutrients, water, and energy are being sought. Wastewater has been recognized as an accessible, abundant, and viable resource with g reat potential to be exploited as a renewable source of nutrients and energy. Modern agriculture and standard of living exerts an ever increasing demand for nutrients and energy, especially as the world population continues to grow. However, virgin nutrient sources such as phosphorous are finite, and others, such as ammonia, are produced at high energy costs. Fossil fuel based energy is also finite, and produces byproducts, such as greenhouse gases, that are detrimental to the environment. There is n o doubt that a more sustainable method of harvesting nutrients and energy is necessary to maintain a healthy global future. Algae cultivation in wastewater is one potential solution for nutrient and energy recovery. Although commercial algal culturing is not a new concept, it has gained more attention in the past decade and is recently gaining momentum. Algae have been shown to thrive in polluted water, removing nutrients and

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2 sequestering carbon as they grow. Microalgae, in particular, are a diverse group adaptable to many environments, and many species are well suited to thrive in wastewater conditions. Algal biomass grown in wastewater can be used as a renewable fertilizer or fermented to produce biogas. Some species also produce significant quantities o f lipids per dry cell weight, which can be turned into biofuel. Instead of losing nutrients through chemical precipitation or release to the atmosphere, as occurs in traditional wastewater treatment, incorporating algae into the process helps to close the nutrient loop and concentrate the energy source for subsequent use. This paper will begin by examining conventional wastewater treatment processes, and then explore the synergy of algae with those processes. Algal biology, metabolism, environmental condit ions affecting growth and lipid production will be discussed. Secondary products, including biodiesel, fertilizer, and biogas, potentially produced from algal biomass grown in wastewater will then be explored. With the aid of a model developed using S TELLA software, the theoretical yield of algae biomass based on nutrient availability and cycling th r ough the Howard F. Curren Advanced W astewater T reatment P lant (HFCAWTP) in Tampa, Florida will be examined. Two potential placements of an algae cultivation basin are explored, and the economic benefit of algal biomass production as biodiesel, biogas, and fertilizer will be examined. O ther potential cost savings resulting fro m incorporating algae into the treatment process such as reduced aeration and chemical demand, will be investigated

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3 Chapter Two : Background Background of Wastewater Treatment Plant Case Study The plant simulated in this model is the Howard F. Curren Advanced Wastewater Treatment Plant (HFCAWTP) in Tampa, Florida a three stage biological nutrient removal (BNR) plant. The first stage consists of a pure oxygen aerobic treatment basin for removal of influent BOD ; t he nitrification basin is the se cond stage, using air for aeration rather than pure oxygen. The third step is an anoxic denitrification filter, where an oxygen depleted environment allows denitrifiers to use nitrate as their electron acceptor. The plant does not have a dedicated phosphor us removal process, as the background phosphorus in receiving water is higher than the typical effluent concentration. The plant layout is shown in Figure 1.

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4 Figure 1. Schematic of HFCAWTP. The BNR plant consists of BOD removal, nitrification, denitrification, and post aeration/chlorination. Sedimentation basins follow each treatment basin, where wasted sludge is either recycled into the treatment process or routed to anaerobic digestion. As shown in Figure 1, t he plant includes sedimentation basins and an anaerobic digester with a digestion capacity of approximately 10 million gallons spread throughout seven tanks. T he solids handling and sidestream waste however, were not included in this model analysis. The wastewater flow through the pla nt is approximately 54.2 million gallons per day (MGD). The permit effluent requirements are less than 5 mg/L BOD, 5 mg/L total suspended solids (TSS), and 3 mg/L total nitrogen (TN). On average, the plant achieves over 99% removal of BOD and TSS, and over 92% removal of total nitrogen. The HFCAWT P was used as a case study for a number of reasons. First, although it is somewhat unique for utilizing a pure oxygen system for BOD removal, the overall set up of the plant is rather conventional, giving the mode l makes it a good candidate for algae production due to the abundance of sunlight and high temperatures Third, the plant is currently utilizing biogas produced from

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5 its a naerobic digester to offset energy costs, and therefore may be open to digesting algae biomass for further energy pro duction. Shortcomings of Conventional Wastewater Treatment Although nutrients are essential for proper ecosystem function, discharges of high concentrations of biologically available nutrients can be detrimental to the balance of aquatic ecosystems. An increase of nutrients can lead to eutrophication, depleting the oxygen availability within the receiving water (Barsanti and Gualtieri 2006 ; deBashan 2004; Olguin 2003). Because phosphorous is typically the limiting nutrient in freshwater ecosystems, wastewater discharges can potentially exceed the background phosphorous in these systems. Excess nitrogen can also not only disrupt the nutrie nt balance in aquatic ecosystems, but can interfere with chlorine disinfection regimes in tertiary wastewater treatment as well (Ahn 2006). Nitrogen and phosphorous are both important ingredients in many commercial products, including fertilizer and dete rgents. Nitrogen can be fixed from the atmosphere by certain bacteria or converted into ammonia by the energy intensive Haber Bosch process. However, this process requires 45 kJ/kg N fixed (Maurer et al., 2003) when compared to 5 kJ/kg N when nitrogen come s from organic sources, such as sludge (Fadare et al., 2010). Phosphorus, on the other hand, is not a renewable resource, but only enters the ecosystem through mining or the weathering of rocks. Phosphorus, an essential element in synthetic fertilizers, i s a limited resource, and worldwide production of phosphate is expected to run out in 50 135 years (Jasinki 2006 ;

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6 Dery et al. 2007). Because there is no adequate substitute for phosphorus, and ammonia production consumes considerable energy, recovering t hese nutrients from wastewater may not only be essential for sustaining modern agriculture, but important for reducing global energy use as well (deBashan 2004). Despite high energy inputs, conventional activated sludge processes do not allow for nutrient recovery, as nitrogen is lost as a gas and phosphorous typically precipitates in the sludge (Gonzalez 2008). Altho ugh employing BNR technology can save wastewater treatment plants the cost of chemical additives (deBashan 2004), the nutrient cycle remain s open. As discharge regulations become more stringent, treatment processes become more energy and operation ally intensive O ne means to recuperate added costs may be to harness the nutrient and energy supplied in wastewater through algae cultivation and r esell the biomass as a value added product. Although biomass production is one option for nutrient recovery in wastewater treatment, other techniques for nutrient recovery include struvite precipitation and nitrite recovery through pervaporation. Struvite recovery occurs by raising the pH to precipitate struvite ((NH 4 )MgPO 4 6H 2 O) from excess ammonia, phosphorous, and magnesium (Saidou et al., 2009) Pervaporation uses a membrane to separate constituents from water; it removes water using pressur e gradients to change volatile constituents to a vapor, thereby passing it through the membrane (Bhat and Aminabhavi, 2007). These nutrient recovery techniques, however, require energy input to create necessary environmental

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7 conditions. For a comprehensive review of nitrogen and phosphorous removal techniques, see Ahn (2006) and Parson and Smith (2008), respectively. Typical BNR plants can be energy intensive, require external inputs, and necessitate specialized maintenance that can be costly and time consu ming. Based on calculations provided by the Department of Energy and the Environmental Protection Agency (2000), for each kWh of energy used, 0.61 kg of carbon dioxide is produced. energy is used for drinking or wastewater services, roughly 45 million tons of greenhouse gases are added to the atmosphere from this sector ( US EPA 2000 ). Autotrophic algae sequester carbon dioxide during growth, helping to reduce the dependence on external energy and close the ene rgy loop. Further, algae biomass can be utilized for biofuel or biogas to offset this carbon footprint. T he H FCA WTP is able to mitigate energy use by utilizing biogas produced from the anaerobic digester sav ing the plant approximately $1,104,954 annually (City of Tampa 2010). Incorporating algal cultivation into the treatment process dependence on external energy. Other potential savings lie in the reduced oxygen demand for nit rification and reduced methanol addition for denitrification as a result of algal nutrient removal. These two cost reduction mechanisms will be discussed in more detail later in this paper. Basic Wastewater Treatment Although configurations of wastewater treatment plants can vary considerably, most municipal BNR plants focus on the removal of carbon,

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8 nitrogen, and occasionally phosphorous. Because the model employed in this study focused on a mass balance of these constituents, the typical fate of carbon, nitrogen, and phosphorous in standard treatment is briefly explained in this section. Carbon Removal Because wastewater constituents can be very diverse, carbon entering the plant is typically categorized with other electron donors as biochemical oxygen d emand (BOD) or chemical oxygen demand (COD). Carbon can be synthesized into biomass, removed via adsorption, or oxidized to carbon dioxide under aerobic conditions (Rittman and McCarty 2001). Influent organics can be coupled with denitrification to reduce both the oxygen demand in the influent and the carbon source needed for heterotrophic nitrogen removal. Typical treatment processes lose carbon as carbon dioxide, but incorporating autotrophic algal growth can help sequest e r it for future energy productio n Nitrogen Removal Conventional nitrogen removal typically occurs in two steps : nitrification and denitrification. Nitrification is the oxidation of ammonia to nitrate by autotrophic bacteria, using oxygen as an electron acceptor and carbon dioxide as t he carbon source (Rittman and McCarty 2001). Denitrification is typically the heterotrophic conversion of nitrate to nitrogen gas (through nitrite) under anoxic conditions, but can also be achieved by autotrophic bacteria utilizing hydrogen or sulfur as a n electron donor. Many carbon sources for denitrification have been used, including acetate, glucose, and methanol (Ahn 2006; Rittman and

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9 McCarty 2001). Found in peptides, enzymes, chlorophylls, ATP, ADP, RNA, DNA, among other components of the cell, nitrogen is a critical ingredient for cellular function (Barsanti and Gualtieri 2006), and will thereby be assimilated within growing and reproducing biomass (Rittman and McCarty 2001). Phosphorus Removal Most phosphorous in wastewater is dissolved, partitioned as 50% orthophosphate, 35% condensed phosphates, and 15% organic phosphates (Parson 2008) and can be removed both biologically and chemically. Because excess phosphorus under specific environmental conditions, the proc ess can be fragile and complex (Mulkerrins e t al. 2004 ; Lopez Vazquez et al. 2008 ; Rybicki 1997). Algae have exhibited similar luxury uptake capabilities as phosphorous accumulating organisms (PAO) under certain environmental conditions (Powell et al. 2008). Phosphorus can also be removed by phy sical means, such as adsorption or precipitation. Common chemicals used include alum or lime (Mulkerrins et al. 2004 ; Rybicki 1997), and pH regimes can influence precipitation with iron (Parsons 2008) or as struvite (Saidou et al. 2009). Algal treatmen t can be used in conjunction with chemicals to remove phosphorous from a system; algae interact with mineral complexes and both precipitate out together, enhancing removal (Hoffman 1998). Phosphorous is also removed from a system through assimilation in g rowing and reproducing biomass (Rittman and McCarty 2001), though in smaller amounts than nitrogen and carbon.

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10 Algae and Wastewater Treatment Algae ha ve been investigated for their potential use in wastewater treatment since the 1950s (Hoffman 1998) wit h a strong emphasis on suspended growth in shallow open ponds. Algae have gained attention in the wastewater industry for their potential for nutrient removal in domestic wastewaters (de Bashan and Bashan 2010 ; Powell et al. 2009), industrial wastewater (Bordel et al. 2009), and agricultural wastewater (Olguin 2003 ; Gonzalez et al. 1997 ; Gonzalez et al. 2008 ; Kamilya et al. 2006), as regulations push for better effluent quality (Powell et al. 2009). More recently, researchers have focused on a wider spectrum of algae technology in water treatment, such as immobilization in polymeric substances to enhance nutrient removal (De la Noue and Proulx 1988; de Bashan and Bashan 2010 ; Travieso et al. 1996), utilization of heterotrophic metabolism (Lee 2004 ; Miao and Wu 2004 ; Ogbonna and Tanaka 1996 ; Ogbonna et al. 2000 ; Yang et al. 2000), and potential uses of the algal biomass produced (Mulbry et al. 2008 ; Amin 2009 ; Chisti 2007 ; Tran et al. 2010). Algae are also being investigated as a means to bioaccumulate phosphorus (Powell et al. 2008). Theoretically, algae and activated sludge bacteria can cooperate in a symbiotic relationship; algae produce oxygen during photosynthesis that bacter ia, namely nitrifiers, utilize for growth, while consuming carbon dioxide produced by the bacteria (Bordel et al. 2009 ; Gonzalez et al. 2008). Utilizing and increase effl uent quality at wastewater treatment plants (Lee and Lee 2001 ;

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11 Bordel et al. 2009). Algae also have the potential to recover more nutrients in sludge than conventional systems using chemical precipitation (Hoffman 1998). Many algae species produce high volumes of lipids per cell weight (Xiong et al ., 2010), making them excellent candidates for biofuel production. In fact, microalgae have the highest oil yield among all other plants grown for biofuel, including palm, coconut, castor, and sunflower oils (Amin 2009). More importantly algae have demonst rated their toleranc e to the wastewater environment, giving them great potential to produce energy and capture nutrients without squandering arable land and scarce freshwater resources consumed during other biofuel production, such as corn based ethanol. Alga l Biology Although algae are not recognized as a taxonomically distinct group, they have much in common with each other and share many differences from other plants. Containing both prokaryotic and eukaryotic species, this diverse group of organisms i ncludes both micro and macro algae. Algae known as picoplankton can be as small as 0.2 2.0m, but microalgae in general range from a few micrometers to a few hundred micrometers (Barsanti and Gualtieri 2006). Algal biology encourages their potential fo r biomass cultivation; among the most photosynthetically efficient organisms, algae are non vascular and carry out simple cell division (Amin 2009). Most research regarding the combination of algae and wastewater treatment has focused on the growth of mic roalgae. Algae have many commercial uses, including aquaculture feed, sources of pigments, oils, stable isotope labeled biochemicals, new pharmaceuticals

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12 (Zaslavskaia et al. 2001), and biofuel (Xiong et al. 2010). Algae have been commercially grown for decades by the pharmaceutical and food industries, but their use for biofuel has been limited due to biological requirements. Growing algae on a large scale can necessitate large amounts of land, freshwater, and nutrients. However, coupling algae growth wi th wastewater treatment provides freshwater and nutrients essentially for free, while only requiring moderate space (Hoffman 1998) Algae can utilize ammonium, nitrate, or nitrite as a nitrogen source for growth and production of amino acids, proteins, or other cell constituents (Barsanti and Gualtieri 2006 ; Lee and Lee 2001). Although nitrate is typically the most available form of nitrogen, it appears that many species prefer ammonia for growth (Yang et al. 2000 ; Ogbonna et al. 2000). Algae have been shown to utilize a significant portion of ATP produced (45 82%) for cell maintenance (Yang et al. 2000). In general, the elemental make up of algae is about 50% carbon, 10% nitrogen, and 2% phosphorous (Rittman and McCarty 2001). Although the mechanism s of phosphate metabolism in algae cultivated in wastewater are not well studied (Lee and Lee 2001), some information is available for phosphorous partitioning within algae and wastewater. Orthophosphate is typically the limiting nutrient in freshwater ec osystems and is readily available for uptake by autotrophic organisms (Barsanti and Gualtieri 2006), but environmental conditions can influence the partitioning and uptake of phosphorous in algae (Powell et al. 2008). Similar to PAO, algae accumulate phosphorous in aerobic conditions and release it under anaerobic conditions, as

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13 it is consumed to produce energy (Rybicki 1997). Cells may store phosphates in cytoplasmic inclusions as polymers, polysaccharides, po hydroxybutyric acid (PHB), or fatty materials (Rittman and McCarty 2001). Aside polyphosphate under appropriate conditions (Powell et al. 2008). Most algae are photo autotrophic, using carbon dioxide as their carbon source, but some can survive heterotrophically, using acetate or another organic carbon source for cell metabolism (Rittman and McCarty 2001). Some species are mixotrophic, which allows them to utilize bot h metabolic strategies. Each metabolic strategy is exploited in different proportions (Barsanti and Gualtieri 2006) and little is known about the partitioning of metabolic types under varying conditions (Yang et al. 2000). Autotrophy Phototrophic metab olisms are energized through photosynthesis, where energy from the sun is used to reduce carbon dioxide to organic carbon (Barsanti and Gualtieri 2006). NADPH and ATP are formed using light energy in the first step of photosynthesis, followed by the redu ction of carbon dioxide in the dark reactions of the Calvin cycle. A high oxygen concentration can inhibit photosynthesis, causing the organisms to favor photorespiration (Yang et al. 2000). Autotrophy can be summarized by the generic reaction adapted fro m Barsanti and Gualtieri (2006): CO 2 + H 2 O + light (CH 2 O)n + O 2 (1)

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14 The subsequent carbon compounds produced are then later oxidized during respiration to release energy for the cell (Barsanti and Gualtieri 2006). Autotrophs can assimila te dissolved phosphates from their environment, incorporating them into their cell membranes, coenzymes, DNA, RNA, and ATP (Barsanti and Gualtieri 2006). According to Agren (2004), the ratio of carbon, nitrogen, and phosphorous changes within the cell dep growth rate. As growth rate increases, N:C ratio increases linearly, while P:C rati o increases quadratically. The e ffect of growth rate on the N:P ratio in autotrophs is not as apparent and can be affected by other environmental conditions other than nutrient supply. Approximately 40% of ATP produced by autotrophs is formed from mitochondrial oxidative phosphorylation (Yang et al. 2000). Yang et al. (2000) found that fixing carbon dioxide used about 77% of total ATP generated by algae, making the Calvin cycle the main energy sink for autotrophic algae. Heterotrophy There are three main pathways of organic carbon utilization in a heterotrophic metabolism : glycolysis, pentose phosphate (PP) pathway, and TCA (tricarboxylic acid or citric acid) cycle (Yang et al. 2000). Heterotrophs, like autotrophs, increase their cellular N:C and P:C ratios at high growth rates. Their N:P ratio decreases, however, because the cell produces more rRNA with growth, which requires an increased concent ration of phosphorous (Agren 2004).

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15 In a study by Yang et al. (2000) investigating algae growth via different metabolic pathways, heterotrophic cultivations yielded the most ATP, because carbon dioxide fixation was not necessary. Mixotrophic cultivations yielded the second highest amount, followed by autotrophic cultivations. Photosynthesis contributed about 63% of ATP production under mixotrophic conditions. Each type of cultivation required between 45 82% of total ATP yield for cell maintenance. Hetero trophic or mixotrophic growth does have some practical advantages over promoting solely autotrophic growth. Algae utilizing a heterotrophic metabolism can grow in light limited areas, such as cultures with high concentrations of biomass, where an organism utilizing an autotrophic metabolism would have difficulty (Ogbonna and Tanaka 1996), which may allow the reactor footprint to be reduced, as the depth of the culture is not limited by light penetration. Furthermore, light dependent biomass may grow in low er concentrations, making harvesting more difficult (Zaslavskaia et al. 2001). Eliminating the need to continuously mix reactors to intermittently expose the organisms to sunlight (Olguin 2003) could decrease energy costs. Mixotrophy Mixotrophy occurs when a culture utilizes both an autotrophic and a heterotrophic metabolism. Culture conditions require proper light intensity and duration, as well as an organic carbon source. In a study by Yang et al. (2000), microalgae cultivated under heterotrophic con ditions were able to generate the most ATP per supplied energy than those cultivated under mixotrophic or

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16 autotrophic conditions. However, cycling between autotrophic and heterotrophic conditions yielded the highest biomass production, as algae used the av ailable energy most efficiently in these conditions. Synergy of Wastewater Treatment and Algae Cultivation Algae ha ve the potential to help close the wastewater treatment loop on four fronts: sequestering carbon while utilizing an autotrophic met abolism assimilating nutrients in growth and reproduction harnessing energy for biofuel production, or reducing external inputs to the treatment process. This section summarizes a few of the most important conditions that affect algae growth, examined through con ditions typical in wastewater. Figure 2 highlights the areas of potential synergy between algae growth and wastewater treatment. Figure 2. Areas of potential synergy between algae growth and wastewater treatment.

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17 Environmental Conditions Affecting Growth Removal of nitrogen and phosphorous by algal assimilation varies depending on environmental conditions. As nutrient removal efficiency is directly related to algal productivity (Olguin 2003), it is important to understand the environmental conditi ons that inhibit or promote maximum biomass yield. Environmental conditions can affect different species to varying extents, but this survey will examine overall trends throughout the algal group. Light Light intensity and duration can affect the specific growth rate and nutrient removal capability of algae. Photosynthetic algae are typically cultured in the laboratory under light intensities in the range of 100 200 E sec 1 m 2 which is approximately equal to 5 10% of full daylight (Barsanti and Gualtieri 2006). Typical outdoor light intensity in equatorial areas is 2000 E sec 1 m 2 which can increase specific growth rate to a certain extent. However, algae reach a light saturation point when an increase in light intensity does not increase photosynthet ic activity. In fact, photoinhibition can occur if sunlight becomes too intense for the organisms, which subsequently reduces the algae growth rate (Chisti 2007). Although it can be more intense, nutrient removal has been shown to increase when algae are exposed to natural light instead of artificial (Travieso et al. 1995). In some cases, higher light intensity increases specific growth rate (Lee 2004), therefore more phosphate is consumed in metabolism and less is stored

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18 in the cells (Powell et al. 2008). Luxury phosphorous uptake is thereby more efficient at lower light intensities (~60E/m 2 s) (Powell et al., 2008). Higher light intensity can lead algae to store more carbohydrates in the cell, but carbohydrate storage could lead to night biomass l oss in cyclic light/dark cultiv ation (Ogbonna and Tanaka 1996); whe n light energy is not available, stored carbohydrates are used for metabolic processes. In fact, night biomass loss can be up to 35% of biomass produced under daylight conditions. Decreas ing the temperature at night can reduce night biomass loss, possibly due to decreased respiration (Ogbonna and Tanaka 1996). In two studies comparing the growth rate of Chlorella species under continuous light conditions and cyclic light/dark conditions, algae achieved a higher biomass production in a shorter time under continuous light conditions, due to biomass loss during the night in cyclic culture (Ogbonna and Tanaka 1996; Lee and Lee 2001). Furthermore, nutrient removal of C. sorokiniana was highe st under aerobic light conditions (Ogbonna and Tanaka 1996) and C. kessleri achieved a higher nitrate removal rate in continuous light cultivation compared to cyclic light/dark conditions (Lee and Lee 2001). However, cultivation under light/dark cycles y ielded slightly better phosphorus and organic carbon removal than continuous light conditions (Lee and Lee 2001). Temperature Temperature can have a significant effect on all biological wastewater treatment processes, including nitrification, denitrific ation, and algae biomass production. In fact, each 10C increase in temperature can cause specific growth

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19 rates to double in some species (Rittman and McCarty 2001). Also, temperature can affect cellular composition, including fatty acid composition, prot ein concentration, and nitrogen to carbon ratio, which would affect nutrient requirements and uptake of microalgae (Powell et al. 2008). For example, carbohydrate content of algae increased with lower temperatures, and protein content decreased (Ogbonna e t al. 1996). Most algal species are typically cultured in a temperature range of 16 27C (Barsanti and Gualtieri 2006), but can grow in the cooler temperatures typical of wastewater Temperature can affect phosphorus use by microalgae in a number of ways including the rate of metabolic processes, the ionic speciation of phosphate, and the physical properties of the water (Powell et al. 2009). For example, acid nonsoluble polyphosphate, which is typically us ed for storage of phosphorus, i s more pre valent in warmer water (25C) (Powell et al. 2008). Increased temperature also increased the percentage of phosphorous in the biomass of microalgae cultured in waste stabilization ponds (Powell et al. 2008). Temperature can also affect the biomass loss during the night by photosynthetic algae. In a study conducted by Ogbonna et al. (1996), night biomass loss decreased when night temperatures remained a constant 30C and day temperatures ranged from 25 37C. This temperature requirement, however, may be d ifficult to achieve under typical wastewater treatment conditions. pH Biological and chemical processes are both affected by pH, as nutrient speciation, and therefore availability, is strongly affected by this parameter. The

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20 acceptable pH range for most a lgal species is between 7 and 9, with an optimum range of 8.2 8.7 (Barsanti and Gualtieri 2006) which is slightly higher than typical wastewater pH. Although slight pH differences in wastewater have not been shown to completely inhibit algae growth nutr ient removal can be affected by high pH in wastewater. Ammonia removal by algae cultured in swine wastewater was inhibited by pH levels above 9 (Gonzalez et al. 2008). In a study conducted by de Bashan and Bashan (2010), phosphate removal by immobilized C pyrenoidosa was affected by pH in the range of 5 10, whereas nitrate removal was not affected. Autotrophic culture can affect solution pH, which in turn can affect non biological nutrient removal. As autotrophic algae remove carbon dioxide from solutio n, the increased pH can encourage the volatilization of ammonia (Olguin 2003). Elevated pH can also aid phosphorous precipitation with metal cations such as Ca 2+ Mg 2+ and Fe 2+ (Powell et al. 2008), or in algal mineral complexes (Hoffman 1998). The addition of carbon dioxide can help mitigate elevated pH in high density algal culture (Barsanti and Gualtieri, 2006). Nutrient Input Nutrient loading can affect the use and storage of nitrogen and phosphorous during algal growth and maintenanc e. For instance, concentrations of ammonia up to 400 mg/L did not inhibit growth in C. sorokiniana, but did affect the growth of S. platensis whereas high concentrations of other nutrients such as acetate, propionate, and phosphate, d id not adversely aff ect growth (Ogbonna et al., 2000) Similarly, manipulating nutrient concentrations in water can affect

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21 the biochemical composition of cells (Ogbonna and Tanaka 1996). For example, in a study conducted by Aslan et al. (2006), chlorophyll a production incre ased with increasing initial influent nutrient concentrations; increased chlorophyll production may limit light penetration and thereby limit growth. However, Mulbry et al. (2008) concluded that algal biomass production increased with increasing nitrogen a nd phosphorous loading. High ammonia concentrations have been shown to inhibit the growth of algae species in certain environments and affect removal rates. In one study comparing growth of three algae species in high nutrient conditions, ammonia removal r ates decreased as loading rate increased (Ogbonna et al. 2000). Ogbonna et al. (2000) noted that growth of C. sorokiniana or R. sphaeroides was not inhibited up to 400 mg N NH 4 +/L, but growth of S. platensis was completely inhibited when concentrations exceeded 200 mg N NH 4 +/L. Likewise, photosynthetic cultures of C. sorokiniana grown in aerobic conditions were inhibited by high ammonium concentrations (up to 1180 mg N NH 4 + per liter) in piggery wastewater wi th high pH (Gonzalez et al. 2008). Nitrate concentrations do not appear to affect algal growth to the extent that high ammonia concentrations can. Lee and Lee (2001) concluded that growth of C. kessleri was not inhibited by nitrate concentrations up to 1 49.9 mg/L, and Ogbonna et al. (2000) concluded that the growth of the three species mentioned in the above paragraph was not inhibited even up to concentrations of 700 mg/L.

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22 In a study by Ogbonna et al. (2000), ammonia appeared to be the preferred nitrogen source, as nitrate was only utilized when ammonia was no longer available. On the other hand, nitrogen limiting environments can trigger carbohydrate accumulation in cells, which could lead to biomass loss in cyclically cultivated (light/dark) Chlorella cells (Ogbonna and Tanaka 1996). High concentrations of phosphorous have been shown to be less inhibitive to algal growth than high nitrogen concentrations. In fact, algae h ave been successful at removing phosphorous from high strength wastewater. For example, C. vulgaris removed from 30 55% of phosphates, depending on incubation time, in dairy and pig farming wastewater with initial total phosphorous concentrations up to 111 mg/L (Gonzalez et al. 1997). Likewise, phosphate concentrations up to 100 mg/L did not significantly affect the growth or removal rate of three algal species studied by Ogbonna et al. (2000). B. braunii was also able to successfully remove nitrate and ph osphate from pretreated domestic a nd piggery wastewater (Metzger and Largeau 2005). C. vulgaris immobilized in polyurethane cubes and submerged in pretreated cattle manure, was able to remove between 48 64% of orthophosphate, with influent orthophosphate concentration of 34 mg/L (Travieso et al. 1995). In fact, a high initial phosphate 2009). Typical domestic wastewater influent characteristics fall within the range that alg ae can tolerate. Total nitrogen is typically around 50 mg/L, with about 30 mg/L as ammonia. Total phosphorus can range from 10 16 mg/L, with most

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23 phosphorous as orthophosphate (Henze et al. 2002). As demonstrated in the studies mentioned above, algae can also tolerate higher nutrient concentrations associated with agricultural waste Lipid Production Environmental conditions and availability of metabolic constituents can affect lipid production and quality within algae. Algae typically produce lipids when carbon is present in excess but another nutrient, such as nitrogen, is limited (Ratledge and Cohen 2008). Likewise, the fatty acid composition of lipids in cells cultivated under different metabolic environments varies depending on cultivation method (Ya ng et al. 2000). Heterotrophic lipid production is more efficient in nitrogen limited environments, but phototrophic cultivation requires more abundant nitrogen (Xiong et al ., 2010). Algae cultivated under heterotrophic conditions have been shown to produ ce more lipids than autotrophically cultivated cells (Tran et al. 2010), yielding 55.2% compared to 14.57% lipids respectively (Miao and Wu 2004), and the resulting bio oil is of higher quality. Heterotrophic cultivation may be more efficient for producing lipid s because these cells do not need chlorophyll. In a study by Xiong et al. (2010) where cultivation switched from phototrophic to heterotrophic conditions, the amount of chlorophyll within the algae cells decreased from 0.45 to 0.029 mg/g dry cell weight over a time period of 120 hours. When thylakoid membranes in chloroplasts disappeared within 48 hours after switching to heterotrophic conditions, large lipid droplets appeared within the cytoplasm. In another study

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24 by Miao and Wu (2004), no c hlorophyll was detected in heterotrophic cells after 120 hours of cultivation. Mixotrophic cultivation has also shown to be successful in producing lipids as cells can take advantage of multiple carbon sources. Lipid production in C. protothecoides reach ed up to 58.4% of dry cell weight under an optimized autotrophic fermentation cultivation model that used glucose as the carbon source in fermentation (Xiong et al. 2010). The increased lipid production was attributed to the continued fixing of carbon dio xide by Rubisco while cells simultaneously fermented sugar. In a strictly heterotrophic environment, the carbon dioxide released was a net loss of carbon. In the mixtotrophic cultivation, however, the cells were able to refix the carbon dioxide and route i t to lipid production, decreasing the net carbon release (Xiong et al. 2010). Autotrophic cultivation does have its advantages as well. Botryococcus braunii microalgae with up to 80% of dry mass as lipids, has been shown to increase doubling time and hy drocarbon production with the introduction of air enriched with carbon dioxide (Tran et al. 2010). Table 1 shows reported lipid yields of different algae species according to various studies. It is generally accepted that a lipid content of 40% by dry wei ght is needed for oil extraction and processing to be considered economically viable (Ratledge and Cohen 2008). The key to economical lipid production is to maximize biomass growth; however, many fast growing organisms contain less than 20% of their dry w eight as lipids, and species with high lipid contents (40 50% of dry weight) are generally slow growers (Xiong et al. 2010).

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25 Table 1. Varying lipid content per cell dry weight among algae species reported in different studies. Species Source H/A % Lipids /DW B. braunii Qin 2005, Metzger 2005 A 15 76 Chlorella sp Tran et al. 2010 A 25 32 I. galbana Ratledge and Cohen 2008 A 22 38 H. pluvialis Ratledge and Cohen 2008 A 30 40 Nannachloropsis sp Ratledge and Cohen 2008 A 31 68 Nitzschia sp Ratledge and Cohen 2008 A 45 P. incisa Ratledge and Cohen 2008 A 30 45 P. carterae Ratledge and Cohen 2008 A 33 C. protothecoides Miao and Wu 2004, Xiong et al. 2010 H 53 57.9 Note: As described above, lipid production can be somewhat unpredictable, depending on the environmental characteristics. Further research is needed in this area to determine optimal lipid production in wastewater conditions. However, because wastewater is typicall y not nutrient limiting, high lipid production may not be viable; to the knowledge of the author, this has not yet been demonstrated. Carbon Dioxide Retrieval Almost half of the dry weight of algae is carbon, which often originates as carbon dioxide. Due to the stoichiometric relationship of algae synthesis, algae has the potential to fix 183 tons of carbon dioxide per ton of biomass produced (Chisti 2008). Furthermore, by replacing a 100 MW coal thermal plant with liquid fuel from microalgae, 1.5 x 10^5 tons of carbon dioxide per year would be mitigated (Tran et al. 2010). Autotrophic algal growth can reduce the carbon footprint of a wastewater trea tment plant by sequestering carbon to offset energy needs of treatment.

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26 Oxygen and Chemical Demand Reduction Typical wastewater treatment plants run their aeration basins with a dissolved oxygen (DO) concentration between 4 10 mg/L (Bitton 1994). The pla nt modeled in this study maintains a DO concentration of 9.5 mg/L in the pure oxygen basin and 6 mg/L in the nitrification basin. When cultivated in photobioreactors, algae have demonstrated an oxygen production up to 10 g O 2 per m 3 per min (Chisti 2008), which could help alleviate aeration requirements in aerobic reactors, thereby reducing energy needs and costs. Likewise, the demand for methanol or other external carbon sources for denitrification is reduced as algae uptake nitrate. Reduced need for methanol reduces plant external input costs, storage requirements, and operating needs. Secondary Use of Algae Biomass Algae cultivation ha s recently attracted more attention because the biomass produced can be used for a number of secondary products, wit h benefits that help close the nutrient and energy cycle of conventional water treatment. If coupled with wastewater treatment, algae do not compete with food crops for arable land and nutrient supply is virtually unlimited. Some species maintain a high l ipid content, making them candidates for biofuel production. Algae biomass itself can also be processed into fertilizer or digested to produce biogas. Other products are possible, such as animal feed, but only biofuel, biogas, and fertilizer will be analyz ed in this model. Harvesting methods are an important area of current research and can create a bottleneck to algae cultivation. Physical means, such as microscreens,

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27 centrifugation, or flocculation can be used for harvesting algae (Molina Grima et al. 20 03), or chemical means, such as chitosan, alum, or ferric chloride can be used to flocculate the biomass (Amin 2009). Other innovative means utilizing natural processes such as evaporation are helping to bring costs down (Silberman 2010) while re ducing carbon dioxide concentration may also cause algae to autoflocculate (Amin 2009). An appropriate harvesting method is important, however, in maintaining low processing costs and s ustaining a concentrated biomass typically helps keep these costs down (Chis ti 2007). Biodiesel Biodiesel is manufactured by transesterification, which occurs when an alkoxy group is switched with an alcohol in an ester compound. Catalyzed by an acid or base, the oil combines with alcohol to form esters and glycerol (Amin 2009), and the solvent used to extract the oil from the biomass can be recovered and recycled (Chisti 2007). This process is already utilized to produce biodiesel from vegetable oil or animal fat. Many other extraction methods, such as using multiple so lvents, enzymes, osmotic shock, or carbon dioxide, have been developed, some allowing more than 95% retrieval of the oil present in the algae (Amin 2009). Algae can also be thermochemically converted to fuel through gasification, pyrolysis, and liquefacti on (Amin 2009). Bio oil produced using pyrolysis of algae cells yielded an oil product more suited for fuel and closer to the properties of fuel oil than oil from lignocellulosic materials, such as woody plants (Miao and Wu 2004). An energy consumption r atio that compares the amount of energy required for fast pyrolysis to the

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28 amount of energy produced in the process demonstrated that fast pyrolysis was a net energy producer for both heterotrophic and autotrophic cells (Miao and Wu 2004). Furthermore, fa st pyrolysis extracted approximately 58% of dry weight from microalgae, compared to 49% of dry weight of pine wood, cotton straw and stalk, and sunflower s (Tran et al. 2010). Biodiesel produced from algae have shown si milar properties to diesel fuel ( Amin 2009). Biodiesel is subject to standards in both the United States and European Union that restrict the amount of fatty acids that contain four or more double bonds, as these bonds can oxidize in storage. Although vegetable and algal oils tend to have hig her amounts of double bonded fatty acids, partial catalytic hydrogenation can help mitigate the amount (Chisti 2007). Biodiesel production can be expensive, but the costs can be recovered by selling the residual algae biomass for tertiary uses (Chisti 20 08). Biogas Biogas can be produced through anaerobic digestion of residual algal biomass, similar to how anaerobic digesters treating sludge are currently utilized at many wastewater treatment plants. The resulting biogas contains methane and carbon dioxi de, which can be bubbled back into the algae reactor as a carbon source or burned for energy. Depending on the type and quality of the biomass, biogas yield ranges from 0.15 to 0.65 m 3 per kg of dry biomass, containing an energy content of between 16,200 k J per m 3 to 30,600 kJ per m 3 (Chisti 2007).

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29 Furthermore, algae cells do not have the lignin and cellulose that other plant derived feedstock may have making them easier to break down ( Zamalloa et al., 2010). Also, the higher lipid content of certain species can yield more methane per gram of biomass during digestion than cells higher in proteins or carbohydrates (Zamalloa et al., 2010). However, although preliminary research shows that digestion of algae cells may take longer than conventional feedstock due to the degradability of the cell wall, further research is needed to optimize this process (Zamalloa et al., 2010). Fertilizer Algae biomass has comparable properties and thereby produces similar results as commercial fertilizers. Corn and cucumber seedlings grown in commercial potting mix augmented with either algal biomass or commercial fertilizer showed no significant difference in seedling mass, suggesting that algal biomass is an adequate substitute for commercial fertilizers (Mulbry et al. 2005). Utilizing algal biomass has a number of advantages over land applying conventional fertilizers. Applying dry biomass to fields prevents ammonia volatilization that occurs with land applied manure. Algal biomas s can also be applied without tilling, which allows for fertilization while crops are growing. The use of algae fertilizers also keeps heavy metals concentrations well below the limit mandated by the US EPA Part 503 biosolids rule (Mulbry et al. 2005 ; Mul bry et al. 2008). Further, a study conducted by Mulbry et al. (2006) suggests that nitrogen mineralization from algal biomass is more predictable than that of manure, making fertilizer application more reliable and reducing the threat of

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30 nutrient pollutio n. Algal biomass can be easily and safely stored between applications, and is less likely to contain pathogenic material than composted manure (Wilkie and Mulbry 2002). Summary of Background Algae growth in wastewater treatment has many facets, making it a complex and somewhat unpredictable process. However, the potential benefits for this marriage in closing the nutrient and energy loop in conventional wastewater treatment are substantial. Algal biology is compatible with conditions inherent in municipal and some industrial wastewaters, allowing for the chance to exploit this renewable resource. Although incorporating algae into wastewater treatment adds operational costs, the potential benefits may outweigh this added expense. While numerous studies have been conducted on algae growth within wastewater, as well as some calculations of the economics of processing and growing the biomass, little has been studied on combining the economics of the process with the biology. The model presented in this thesis w ill attempt to provide a macro scale view of the synergy between wastewater treatment and algae, and evaluate the potential costs and benefits viewed from biological and market constraints.

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31 Chapter Three : Model Framework General Model Background Models have long been used to gain a better understanding of wastewater treatment processes. Although these models have become quite sophisticated over time, they still have many limitations, which can restrict their widespread application (Gernaey and Sin 2008). However, models continue to be a useful tool in predicting influent and effluent characteristics and biological responses to environmental conditions. According to Gernaey et al. (2004), there are important steps in cr eating a valid model, including: defining the purpose of the model, selecting the proper model, collecting data, reconciling the data, and calibrating and unfalsifying the model. The purpose of the model will mainly steer the outcome of the subsequent step and simplifications to ensure it is applied properly within its boundaries. This chapter will discuss the purpose of the model the model framework and equations, and how the framework provides a connection between wastewater, algae, and macroeconomics.

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32 STELLA Software This model is built within the Systems Thinking Experimental Learning Laboratory with Animation (STELLA) software version 9.1.3 ( 1985 2009 ISEE systems ). STELLA uses a mult ilayer approach to model building, including an equation, model, map, and interface layer. Each layer allows the user to oversee a different aspect of the model, creating manageable mechanisms for keeping track of variables. Although STELLA software is ty pically used for environmental systems models, its user friendly interface allowed the end product to be highly interactive with inexperienced users. This was an important goal of the study; as many parameters within the model framework are subject to chan ge considerably (i.e. specific growth rates, influent characteristics ), it was imperative that it have the flexibility to adapt to individual circumstance s conditions, or case stud ies STELLA software was chosen to build the model due to the flexibility of the system components. Because STELLA does not have predefined processes and systems, a model could be constructed from scratch, adapting it to the unique goal of investigating a mass balance relationship in a macroeconomic framework. The interaction between system variables, including carbon, nitrogen, phosphorous, biomass, and economic outputs could all be simultaneously investigated in one software package. STELLA models have unique individual components that come together to illustrate relationships between inputs and va riables. The general components, shown in Figure 3, are described as follows :

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33 Figure 3. Basic components of a STELLA model. Stocks represent the accumulation portion of the model. Their value is equal to the in flows minus the out flows Stocks can be related to or affected by any other variable within the model. Flows link the relationship between two stocks, or represent a process in flow or outflow. Their main purpose is to keep materials flowing within the model, i.e. to deplete accumulation. Although flows can be uniflow or biflow, all flows within this model are uniflow. Flows can only be affected by or related to variables directl y connected to them. Converters serve a number of roles within the model framework. They can hold a constant value, receive external inputs, or perform algebraic calculations. As stated by STELLA, they they get their name. Converters can be related to or affect only those items directly connected to them Switches are converters that can trigger other specified converters to turn on or off. Multiple switches were installed in the model to turn on and off flow to the algae basin or select the desired secondary product process train

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34 Conceptual Approach The model was designed after the HFCAWTP, a BNR plant in Tampa, FL. Further discussion of the layout of the plant can be found in Chapter 2. Figure 4 sh ows the po rtion of the plant that is the focus of the model specifically the BOD removal basin, the nitrification basin, and the denitrification basin. Sedimentation tanks follow the first two stages of the treatment process, but their individual contributions were not considered in this model. Overall removal of BOD, ammonia, and nitrate as individual stages was considered, which did take into account settling of constituents within these basins. Figure 4 Schematic of the section of the treatment process at the HFCAWTP modeled in this study. Sedimentation basins were not considered individually, but removal rates due to settling were considered. The model can be conceptually separated into two groups: the wastewater treatment processes and the algae production processes. The two groups are linked by water and nutrient flow within the system. Mass balances were maintained within each nutrient group as described within each section Figure 5 shows the conceptual framework of the movement of constituents and processes included in the model. Three treatment basins were modeled, representing a pure oxygen BOD removal reactor, a nitrification reactor, an d a denitrification reactor. Clarifiers and anaerobic digesters were not included in the analysis.

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35 Figure 5 Conceptual f ramework of model c omponents Post clarifier flow between the reactors is diverted to the interstage algae basins: PPOR, the post pure oxygen reactor and the PNR, post nitrification reactor Potential biomass production can be evaluated under various conditions. Results are then analyzed economically in one of three process trains: biodiesel, biogas, or fertilizer. Two algae basins were incorporated into the conventional treatment process tr ain: a post pure oxygen reactor (PPOR) and a post nitrification reactor (PNR). An economic analysis was then conducted on turning the potential biomass produced into biodiesel, biogas, or fertilizer. Practical Approach The conceptual model was built with STELLA software to create a user friendly, flexible model. Although t he model is based on a case study of a BNR plant in Tampa, Florida, it can be easily adapted to represent other facilities. T he model framework, variab les, and inputs are described below Influent Flow of Nutrients: C, N, P Pure Oxygen Basin Denitrification Basin Algae Basin (PPOR) PP Algae Basin (PNR) Effluent Flow of Nutrients: C, N, P Flow of Nutrients: C, N, P Algae Biomass Produced Fertilizer Biogas Biodiesel Nitrification Basin

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36 Wastewater Framework The movement of nitrogen, phosphorous, and carbon species were tracked within the model. Within each nutrient group, subgroups were defined as described in Table 2. Nutrients were tracked to maintain a mass balance, following speciation changes within each subgroup as described below Table 2. List of nutrient groups tracked within the model and their associated species. Nutrient Group Model Nomenclature Model Group Species Included Phospho rous P1 soluble P phosphates P2 nonsoluble P phosphate complexes Nitrogen N1 o rganic N organic nitrogen N2 NH 3 ammonia N3 NO x nitrate/nitrite N4 nitrogen gas N 2 Carbon C1 S oluble dissolved organics C2 N onsoluble unavailable carbon C3 cellular carbon carbon assimilated C4 carbon dioxide CO 2 Data from the H F CAWTP was analyzed to determine average removal rates. Effluent concentrations were subtracted from the influent concentrations and the difference was divided by influent concentrations in order to determine the percent removal of each nutrient. Ammonia, nitrate/nitrite, and soluble carbon species were tracked in this manner as illustrated Removal Rate (%) = (S o S eff )/S o (2) where S o and S eff are the substrate influent and substrate effluent concentrations, respectively. Because the plant does not have a designated phosphorous

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37 removal process, the only soluble phosphorous removal mechanism considered was algae assimilation. Wastewater kine tics were determined based on plant data from the H F C AWTP Plant data was analyzed to determine average removal rates of carbon, nitrogen, and phosphorous within each basin. To maintain overall nutrient mass balance, the disappearance of one species trigge red the appearance of another. For example, during de nitrification, the removal of ammonia from the system indicated an increase of NO x Tempe rature and available substrate we re not directly included in the model for nitrification and denitrification rates but would be reflected in plant data. Appropriate removal rates for the season under investigation should be selected to ensure adequate representation of removal efficiency under desired conditions. Because nu trient removal rates are derived from plant data, decay of bacteria and subsequent release of nutrients is considered to be included in removal rate calculation s M ethanol (CH 3 OH) was chosen as the organic carbon source because the HFCAWTP is currently usi ng it for denitrification. Furthermore it is readily available to most treatment plants and the most widely used external carbon source. Due to its high bio degradability, it yields the highest denitrification rate of the most commonly used energy sources (Henze et al. 2002). Because the model is assuming that influent wastewater is of domestic origin, toxicity within the water is assumed to be negligible, and is therefore not included in the analysis (Henze et al. 2002). Likewise, it is assumed that onl y

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38 nitrogen, phosphorous, and carbon will limit algae growth, and other constituents, such as heavy metals, are not present in high enough concentrations to inhibit growth. Water Balance Water flow was tracked as shown in Figure s 7 8A 8B, and 9 to monito r mass balance. Figure 6 below shows the interface where flow and basin characteristics can be defined by the user Influent flow is entered on the interface of the model in gallons per day The model calculate s the flow to liters per day via a converter, ensuring all flows would be in liters per time throughout model calculations. Reactor volumes in liters, were also entered on the interface. Figure 6 Model interface for manipulating physical parameters of the treatment plant and influent flow characteristics.

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39 Water flow followed the conceptual path as shown in Figure 7 Flow to algae was diverted to the PPOR before the nitrification reactor and returned to the nitrification reactor. Similarly, flow was diverted after the nitrification reactor to the PNR and returned to the denitrification reactor. Figure 7 Conceptual flow of water through treatment plant and algae reactors. reactors. Water flow was tracked in the model by the framework shown in Figures 8A and 9 Water flow to the algae reactors was controlled by two switches that The user could also determine how much flow w ould be divert ed to the algae reactors. A percentage of flow was considered lost during the harvesting stage; this value could also be entered on the user interface (see Figure 17 ). This loss was removed from the wastewater treatment flow, but tracked in a separate train to ensure mass balance was maintained, as shown in Figure 9 This flexibility allows the user to account for water loss via harvesting and intracellular

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40 assimilation. The model currently does not explicitly model the harvesting process, but in future versions, the water will be returned to the headworks. Figure 8 A Model framework for w ater flow in STELLA model. See Tables A1 and A2 in Appendix A for full list of variables and equations Figure 8B. Conceptual water flow in STELLA model. This conceptual figure illustrates the movement of water in Figures 8A and 9.

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41 Figure 9 Model framework for water loss due to algae harvesting. See Tables A3 and A4 in Appendix A for full list of variables and equations. Nutrient availability by mass was calculated based on the flow and nutrient concentration within the water flow. All nutrients were considered available for Monod growth equations and those assimilated were subtracted from overall nutrient concentr ation on a stoichiometric basi s as described below Carbon Balance Carbon species were tracked in four parallel trains, one for each species: soluble carbon (C1), nonsoluble carbon (C2), cellular carbon (C3), and carbon dioxide (C4). Influent carbon i s entered on the interface as BOD ; this value was subsequently connected to the influent flow of the soluble carbon train (See Figure 6 for interface diagram) Carbon dioxide concentration is also entered in the interface; cellular and nonsoluble carbon are changed within the model framework only. Figure 12A shows the framework for the carbon species. Influent flow was multiplied by the influent concentrations, resulting in each species having the units of mass/time as shown in the generic equat ion below : C mg/L x Q L/day = W mg/day (3)

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42 where C is concentration of any constituent (i.e. nonsoluble carbon, cellular carbon, etc.), Q is the flow of water through the system, and W is the mass of the substrate (i.e. nonsoluble carbon, cellular carbon, etc.) per unit time The removal rate of BOD was calculated based on plant data, as described above. During a biological reaction, electrons flow from the electron donor to either synthesize biomass or reduce an electron acceptor, as shown in Figure 10 The fraction of electrons routed to synthesizing biomass is f s and the fraction of electrons routed to reducing an electron acceptor is f e The sum of f s and f e is equal to 1 (Rittman and McCarty, 2001). Figure 10 Routing of electrons from an electron donor, such as BOD. Electrons are routed to biomass synthesis ( f s ) and reducing an electron acceptor ( f e ). The partitioning of electrons is important when det ermining a complete reaction from redox half reactions. The electron acceptor half reaction is multiplied by the f e and the synthesis half reaction is multiplied by the f s The

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43 electron donor half reaction is added to the resulting electron acceptor and synthesis half reactions to obtain the overall reaction ( R ), as shown in E quation (4) R= f e *R a + f s *R c + R d (4) BOD is an electron donor; during its removal, some electrons are routed to algae synthesis ( f s ), whereas another fraction is used to reduce an electron acceptor ( f e ). An f s of 0.73 and f e of 0.27 was used to determine how the soluble carbon removed was partitioned into cellular carbon and carbon dioxide. The f s and f e values were multiplied by the removal rate as determined by p lant data to determine final end product mass Figure 12A shows where soluble carbon (C1) was converted to cellular carbon (C3) and carbon dioxide (C4) in the pure oxygen and nitrification basins. Carbon dioxide was removed from the system based on the st oichiometry of algae growth. This will be further defined in the Algae Processes section of this chapter. Mass balance was tracked as shown in Figure 11A Influent carbon species were added together to track the total mass of influent carbon. The mass of c arbon species leaving the denitrification basin (i.e. soluble, nonsoluble cellular, and carbon dioxide) were added to the mass of carbon assimilated in algae in order to maintain mass balance through the system

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44 Figure 11 A Mass balance of carbon sp ecies. Total influent carbon was compared to total effluent carbon species using the framework above. TC MB In and TC MB Out were plotted on graphs and numerically monitored to maintain mass balance throughout different simulations. See Tables A19 and A20 in Appendix A for full list of variables and equations. Figure 11B. Conceptual figure of carbon mass balance. This figure illustrates how the mass balance was tracked using the STELLA framework in Figure 11 A

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45 Figure 12 A Conceptual figure of carbon flow through the STELLA framework shown in Figure 12 B

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46 Figure 12 B Carbon flow in STELLA model. Carbon species tracked were as follows: soluble carbon (C1), nonsoluble carbon (C2), cellular carbon (C3), carbon dioxide (C4) See Tables A15, A16, A17, and A18 in Appendix A for full list of variables and equations.

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47 Nitrogen Balance Nitrogen species were tracked in four parallel trains: organic nitrogen (N1), ammonia (N2), nitrate/nitrite (N3), and nitrogen gas (N4). Influent nitrogen was dependent on concentrations entered on the interface for TKN and ammonia (See Figure 6 for interface diagram) Influent nitrate/nitrite and nitrogen ga s were entered directly into the model through a converter. The framework of the nitrogen species is shown in Figure 14A Influent concentrations were multiplied by the influent flow to put each species in units of mass per time as described above with E qu ation (3 ) Nitrogen removal was determined from plant data as described above. Nitrogen removal occurred in the pure oxygen basin and the nitrification basin, where ammonia was converted to nitrate/nitrite. Nitrate/nitrite was then converted to nitrogen ga s in the denitrification basin. The movement of each species through the system is shown in Figure 1 4A as flows connecting stocks in parallel trains. Ammonia and nitrite/nitrate were removed in the nitrification basin and denitrification basin due to alg ae assimilation, as described in the Algae Processes section of this chapter. Nitrite was considered an intermediary species; therefore all nitrate/nitrite in the nitrogen reservoir was available for algae growth. Nitrogen mass balance was monitored as sh own in Figure 1 3A .The mass of all influent nitrogen species were summed and compared against the total mass of effluent nitrogen to verify the mass balance. Effluent mass included each

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48 species flow from the denitrification basin as well as the nitrogen ass imilated during algae growth. Figure 1 3 A Mass balance of nitrogen species in STELLA model. Total influent nitrogen was compared to total effluent nitrogen species using the framework above. TN MB In and TN MB Out were plotted on graphs and numerically monitored to maintain mass balance througho ut different simulations. See Tables A13 and A14 in Appendix A for full list of variables and equations. Figure 13B. Conceptual figure of nitrogen mass balance. This figure illustrates how the mass balance was tracked using the STELLA framework in Figure 13A.

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49 Figure 1 4 A Nitrogen flow in STELLA model. Species tracked included organic nitrogen (N1) ammonia (N2), nitrate/nitrite (N3), nitrogen gas (N4). See Tables A9, A10, A11, and A12 in Appendix A for full list of variables and equations.

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50 Figure 14B. Conceptual figure of nitrogen flow through the STELLA framework shown in Figure 14A. Phosphorous Balance Phosphorus was tracked in two parallel trains; species included soluble (P1) and nonsoluble (P2) phosphorus. Influent phosphorous was dependent on the value entered on the interface of the model (See Figure 6 for diagram of interface) Nonsoluble phosphorous was calculated as the difference between the influent total phosphorus and influent soluble phosphorus. The framework of the phosphorous sector of the model is shown in Figure 1 6A As mentioned previously, a p hosphorous removal rate was not c alculated since the H F CAWTP does not have a designated phosphorous removal process ; The only phosphorous rem ov al mechanism in the model was algae assimilation Phosphorous mass balance was tracked in the same way as nitrogen and carbon was verified Total influent mass of phosphorous was summed in one stock, and total effluent mass of phosphorous was summed in a parallel stock ; effluent phosphorous included mass of phosphorous leaving the denitrification

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51 reactor as well as that assimilated by algae. The utilized stock and flow framework is shown in Figure 1 5A Figure 1 5 A Mass balance of phosphorous species in STELLA model. Total influent phosphorous was compared to total effluent phosphorous species using the framework above. TP MB In and TP MB Out were plotted on graphs and numerically monitored to maintain mass balance throughout different simulations. See Tables A7 and A8 in Appendix A for full list of variables and equations. Figure 15B. Conceptual figure of nitrogen mass balance. This figure illustrates how the mass balance was tracked using the STELLA framework in Figure 15A.

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52 Figure 1 6 A Phosphorus flow in STELLA model. Species include soluble (P1) and nonsoluble (P2). See Tables A5 and A6 in Appendix A for full list of variab les and equations. Figure 16B. Conceptual figure of phosphorous flow through the STELLA framework shown in Figure 16A.

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53 Algae Growth Framework As shown in Figure 5 two algae basins were incorporated into the H F CAWTP facility: a post pure oxygen reactor (PPOR) and a post nitrification reactor (PNR). Nutrients were diverted from the conventional treatment plant process based on the amount of flow sent to the basins which can be determined on the user interface A s influent to the algae basins was considered to be post clarifier effluent in both cases, it is assumed that only dissolved species of nutrients are available. Algae are assumed to remain in the algae basin and do not contribute to nutrient input to the w astewater treatment process i.e. it is assumed a solids separation step, such as a clarifier, will be used to retain algae within the PPOR and PNR Likewise, algae are not entering the algae basin from the wastewater process. Algae are removed from the sy stem through harvesting and added to the process through growth. Figure 1 7 shows the model interface for entering variables related to algae growth. The values entered on the interface give the model important flexibility for adapting to site specific conditions. Certain variables, such as specific growth rate, can also represent environmental conditions not explicitly considered by the model. Algae b asins could be turned on or off at the model interface by two by zero, essentially sh utting down their growth. Buttons for turning on/off the

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54 Figure 1 7 Model interface for manipulating parameters related to algae growth kinetics and the physical characteristics of the algae basins.

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55 algae basin, as well as selecting the desired process for biomass secondary product (i.e. biodiesel, biogas, fertilizer), are shown in Figure 1 7 Maximum and Calculated Specific Growth Rate Because all variables, such as light intensity and temperature, are not included in the model explicitly, it is assumed such growth constraints are represented within the maximum specific growth rate selected. For example, if the maximum specific growth ra te of a species has been determined under certain light conditions, the growth rate can be plugged into the model at the interface to see the projected growth of that species under the set conditions Similarly, reactor configuration, temperature, and pH c an be represented within the maximum specific growth rate selected Although it has been discussed within Chapter Two that algae can grow autotrophically heterotrophically, and mixotrophically, this model will only consider autotrophic growth. Algae growt h equations are written with carbon dioxide as a potential limiting nutrient, assuming organic carbon will not be utilized. This is an important limitation for the model and an area for future improvement, since heterotrophic growth can be quite significan t. Algae growth was determined by Monod kinetics, based on the limiting nutrient of phosphorous, carbon dioxide, or nitrogen Algae growth in the PPOR was considered to be exclusively due to growth via ammonia assimilation, whereas algae growth in the PNR only considered nitrate as a nitrogen source. However, maximum specific growth rates for either nitrogen source could be set separately within the interface. This allows for flexibility within the model, in that

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56 one species can the oretically and conceptually be placed in one basin and allow for another species with a different growth rate to be placed in the other. The assumption that algae species will preferentially use one nitrogen source over another has been documented in the l aboratory (Aslan et al., 2006; Tam and Wong, 1996; Olguin, 2003). The model relied on Monod kinetics to determine algae production, kinetics which express es rate and the availability of a rate limitin g substrate. The half saturation constant, K is the available substrate needed in order for the organism to achieve half its maximum specific growth rate. Ideally, the Monod fraction, shown in Equation (5) would be as close to 1 as possible in order to ma intain the calculated specific growth rate as close to the maximum specific growth rate as possible. This is achieved through a high substrate concentration or a relatively low half saturation concentration. The calculated specific growth rate is defined a s (5) where calc is the calculated specific growth rate, X is the concentration of active biomass, dX/dt is the rate of change of biomass concentration, S is the concentration of available biomass, K is the half saturation constant, and max is the maximum specific growth rate (Rittman and McCarty, 2001) The specific growth rate was calculated based on the Monod relationship shown in Equation (5) but modified to accommodate the use of multiple subst rates as discussed in Rittman and McCarty (2001) :

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57 ( 6 ) where max is the maximum specific growth rate, entered at the user inter face for either the PPOR or PNR; b is the algae decay rate, also entered on the interface. The equation is written to take the minimum Monod fraction, in order to calculate the max based on the most limiting condition. The half saturation constants are represented by K N K C and K P for ni trogen, carbon, and phosphorous, respectively. A separate value for the half saturation constants for either nitrogen source, as well as carbon and phosphorous, can be entered on th e interface (see F igure 1 7 ). The respective available substrate concentrati on of nitrogen, carbon, and phosphorous ( S N S C and S P ) are drawn from the remaining substrate concentration in the algae basin after algae growth, as described later in th is Chapter The specific growth rate was determined at each iteration as described in the following equation (7 ) where u t+1 is the calculated specific growth rate based on the available substrate at that iteration, S t+1 and K is the half saturation constant corresponding to each substrate. Each subs trate was included as shown in E quation ( 6 ). Figure 1 8A shows the model framework for determining the specific growth rate for algae utilizing ammonia in the PPOR An identical framework was also developed for growth in the PNR using flows and concentrations leaving the nitrification basin of the treatment plant.

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58 Figure 18 A Model framework for determination of specific growth rate in the PPOR from Monod kinetics. An identical framework was used for the PNR. See Tables A21 and A22 in Appendix A for full list of variables and equations. Figure 18B. Conceptual illustration of equation used to determine specific growth rate in the PPOR. The available substrate is divided by the volume of the algae reactor in order to convert to c oncentration. The volume is determined by the HRT and flow rate to the algae basin.

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59 Algae Growth Algae growth was determined based on the specific growth rate determined via Monod kinetics as described above. T he equation used to determine new algae generated was ( 8 ) where R gen is rate of generation of algae, X t is the initial mass of algae present and calc is the calculated specific growth rate determined as descri bed in E quation ( 6 ). A lgae accumulation i s calculated based on the amount of algae generated minus the amount of algae harvested per day. Algae are pulse harvested based on a percentage of algae accumulated in the basin i.e. the user can set how much algae to re move, how often, at what time interval over the duration of the simulation on the user interface The net production in the basin was calculated as (9 ) where R net is net rate of algae generation in mass per day, R gen is rate of algae generation, R rem is rate of algae harvest, and k harve s t is the rate of algae harvested per day, set at specific time intervals on the user interface The amount of algae harvested represented in the last term, i s the algae sent to processing in the byproduct section of the model. The framework for determining algae biomass production in the PPOR is shown in Figure 1 9A An identical framework was built to determine biomass

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60 production in the PNR. The stock represents the algae accumu lating in the algae basin. The flow entering is determined as described in E quation (7 ) Figure 1 9 A Model framework for algae production in the PPOR. An identical framework was built for algae growth in the PNR. See Tables A25 and A26 in Appendix A for full list of variables and equations. Figure 19B. Conceptual figure of algae production in the PPOR

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61 Determinin g Substrate Utilization Rate and Yield Coefficient Monod kinetics relate s the specific growth rate ( ), substrate utilization rate ( q ), and yield coefficient ( Y ) by the equation (10 ) where q t is the substrate utilization rate, defined as substrate consumed per biomass produced per unit time; t is the calculated specific growth rate with units of biomass produced per biomass present per time; and Y is the yield coefficient, defined as the amount of biomass produced per substrate consumed. A new q t was calculated at each iteration based on the re al time specific growth rate de termined by available substrate, and a separate q t was calculated for each substrate (i.e. ammonia, nitrate, carbon dioxide, phosphorous). Figure 20A shows the model framework for calculating q t for each substrate utilized in the PPOR The nitrogen source utilized in the PPOR is ammonia An i dentical framewo rk was developed for the PNR, w h ere nitrate is utilized as the nitrogen source

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62 Figure 20 A Model framework for calculating the substrate utilization rate in the PPO R. The q t is determined by the available substrate, calculated specific growth rate, and stoichiometric relationship of each constituent to growth. See Tables A33 and A34 in Appendix A for full list of variables and equations. Figure 20B. Equations for substrate utilization rate framework in the PPOR shown in Figure 20A. The yield coefficient was calculated based on the stoichiometric relationship between each elemental constituent an d subsequent algae growth. The following equations were used to determine the yield coefficient using ammonia (10) and nitrate (11) as a nitrogen source to generate algae with the empirical formula of C 100 O 48 H 183 N 11 P The eq uations were derived from Rittman and McCarty (2001) and t he formula was borrowed from Grobbelaar (200 4 ) This molecular formula was chosen instead of the classic Redfield Ratio of C:N:P of 106:16:1 (Re d field, 1934) because the Redfield Ratio describes marine algae

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63 in the natural environment, whereas the other formula is s pecific for microalgae cultured in an engineered environment. The Redfield Ratio may be a consequence of the biogeochemical environment within marine ecosystems, which would be quite different than wastewater cond itions. Other studies have shown rate (Agren, 2004) and environmental conditions (Zamalloa et al. 2010) Although the Grobbelaar (2004) formula was chosen f or model calculations, t he stoi chiometric ratios and yield coefficients can be changed within the model if the user decides it is necessary. 100 CO 2 + 73.5 H 2 O + 11 NH 3 + 1 H 3 PO 4 = 1 C 100 O 48 H 183 N 11 P + 114.75 O 2 (11 ) 100 CO 2 + 90 H 2 O + 11 N O 3 + 1 H 3 PO 4 = 1 C 100 O 48 H 183 N 11 P + 139.5 O 2 (12 ) Specifically, Y for each substrate was calculated using the following equations (13 ) where A denotes algae biomass and N denotes ammonia as nitrogen. Similar calculations were conducted for each growth constituent (1 4 ) where A denotes algae biomass and C denotes carbon dioxide as carbon;

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64 (15 ) where A denotes algae biomass and P denotes H 3 PO 4 as phosphorous. Table 3 Calculated yield coefficients for determination of q t PPOR PNR N Source as N 15.26 15.26 CO 2 C 1.96 1.96 P 78.37 78.37 Note: a low Y demonstrates that more of this substrate is required to produce one unit of biomass. The stoichiometric relationships were built into the model using converters which are shown in Figure 20A as Y_N1, Y_C4, and Y_P1 If the yield coefficient changes, for example, with a different molecular formula, this variable can be changed on the model interface Determining Substrate Removal via Biomass Assimilation Substrate removal i s calculated for carbon dioxide and phosphorous in both al gae reactors. Ammonia i s rem oved in the PPOR, and nitrate i s removed in the PNR. Substrate removed i s based on the q t and is subsequently related to the specific growth rate at a given point in time. The rate of substrate removal was defined as (1 6 )

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65 where q t is the substrate utilization rate in mass per unit biomass per time, and X t is the mass of active biomass. To determine the substrate remaining after assimilation, the substrate utilized was subtracted from the influent substrate (17 ) where S t+1 is the concentration of substrate at the next time step (t+ t) and S t is the available substrate Available substrate was calculated in the stock by multiplying the influent mass flow by the HRT, to obtain a given available reservoir mass of nutrient. The substrate utilized was subtracted from the reservoir mass. Removal was calculated separately for each substrate involved in algae growth and subsequently subtracted from both the algae a nd wastewater system. Figure 21A shows the framework for ammonia nitrogen removal in the PPOR. Removal of each substrate was driven by a switch built into each framework; the PPOR utilized the O2 switch, whereas the PNR utilized the Nit Switch.

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66 Figu re 21 A Model framework for ammonia nitrogen removal from the PPOR. Similar substrate removal calculations were made for each constituent involved in algae growth. Likewise, an identical framework was developed for the PNR. See Tables A27 and A28 in Append ix A for full list of variables and equations. Figure 21B. Conceptual illustration of ammonia utilization in the PPOR. Figure s 22 and 2 3 show an example of how the ammonia is removed from the wastewater treatment plant once it is as similated by the a lgae. Figure 22 shows the overall nitroge n framework; t he area highlighted in the box is shown in Figure 2 3 with an arrow pointing to the specific region where ammonia nitrogen is drained from the plant. The substrate is removed from the plant to maintain mass balance.

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67 Figure 22 Model framework for movement of nitrogen in the wastewater treatment plant. The highlighted box is shown in more detail in Figure 2 3 Figure 2 3 Example of ammonia nitrogen being removed from wastewater framework after assimilation by algae. N2_to_A is the flow of ammonia to algae via assimilation.

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68 Hydraulic Retention Time in Algae Basins Hydraulic retention time in each algae basin was determined based on the value entered on the interface page of the model (see Figure 1 7 ) Basin volume was calculated based on the flow rate diverted to the algae multiplied by the HRT, as shown in the generic equation below: V A = Q A HRT (1 8 ) where V A is the volume of the algae reactor and Q A is the flow rate diverted to the respective basin. The model f ramework for HRT in the PPOR is shown in 24 Figure 2 4 Model framework for calculating the volume of the PPOR as a function of HRT and f low diverted to algae basin, which are entered on the interface of the model. Solids Retention Time The retention time of algae in the PPOR and PNR was determined by the following equation (19 ) where X a is the mass of active algae in the reactor and X h is the mass of algae harvested per time. The mass of algae is the accumulation in the reactor, and the amount and rate of removal is set on the interface as the harvest percentage and frequency. Figure 2 5 shows the model framework of calculating SRT.

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69 Figure 2 5 Model framework for calculating SRT. See Tables A23 and A24 in Appendix A for full list of variables and equations. Algae Production Costs & Benefits Calculations Once the mass of algae produced was determined based on Monod kinetics and stoichiometric relatio nships as described above, an analysis was conducted to determine the potential macro economic benefits of incorporating algae into conventional treatment. Certain costs and benefits, such as biomass production costs, harvesting costs, and reduced aeration and chemical additives, were the same for all secondary use processes. However, the process costs as well as benefits for biodiesel, biogas, and fertilizer were calculated separately. All secondary product calculations, variables, and processes are define d below. Because literature is limited on full scale algae production and processing, the most appropriate values available were chosen when specific calculations were not available. A s research and development of algal production progresses, it is expected that production and processing costs will decrease. Changing market prices and product benefits can be easily reflected through the model interface. Figure 2 6 shows the model interface where cost per unit product can be defined by the user as i t is expected that prices will vary depending on market cond itions and geographic location.

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70 Figure 2 6 Model interface for entering the cost per unit of secondary product produced. T he user can decide wh ich process to route harvested a lgae biomass to on the interface Options included biodiesel, biogas or fertilizer. If biodiesel i s chosen, the user could decide to further process leftover biomass into biogas or fertilizer or no further processing. These choices a re made by the buttons shown in Figure 27 Figure 2 7 Detail of m odel interface where user can define the route for secondary use of biomass.

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71 The following sections define the calculations behind the cost/benefit analysis of the biomass processing step First, the co sts and benefits common to all uses are defined, followed by specific sections for each process Benefits of Reduced Aeration Cost savings from reduced aeration was considered on two fronts. First, as algae assimilated ammonia, this particular pool of amm onia no longer needed to be nitrified. Second, as the algae are growing, they produce oxygen, as described in E quation (10 ) The model considered that as algae would assimilate ammonia nitrogen, it would no longer be necessary to nitrify that particular pool of nitrogen, thereby creating a cost savings for the plant in terms of aeration energy. According to Maurer et al. (2003), the electricity demand for nitrification is 17 MJ per kg of nitrogen removed. Using the conversion of 1kWh per 3.6 MJ and an energy cost of $0.12 per kWh, a cost of $0. 5667 per kg ammonia was determined; this value was used to convert the reduced demand i nto monetary savings. Although the stoichiometric relationship between oxygen and nitrogen described below would not change, the value of the cost per kg ammonia nitrified is dependent on both the aeration technology and electricity costs. For example, Zam alloa et al. (2010) Because this value can fluctuate, the user can determine the value on the interface of the model. The ramifications of this value are studied more closely in the sensit ivity analysis in Chapter Four.

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72 Furthermore, algae produce oxygen as a byproduct of growth, as shown in Equation (10). Combining the stoichiometric relationships in Equation (10) with those in E quation (19) ( Henze et al. 2009) results in Equation (20) 1 NH 4 + + 1.86 O 2 + 1.98 HCO 3 = 0.02 C 5 H 7 O 2 N + 0.98 NO 3 + 1.88 H 2 CO 3 + 1.04 H 2 O (20 ) The equation used to calculated costs saving from oxygenic growth was (21 ) where kgA is the amount of algae biomass produced. The cost savings calculated through reduced aeration was added to the cost savings resulting from oxygen produced from algal photosynthesis. Figure 28A shows the model framework for calculating the cost sav ings from reduced aeration demand Figure 2 8 A Model framework for cost savings due to algae assimilation and photosynthetic oxygenation. See Tables A49 and A50 in Appendix A for full list of variables and equations.

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73 Figure 28B. Conceptual illustration for reduced aeration demand. It should be noted that denitrification inhibition due to the presence of oxygen wa s not considered in this model and oxygen produced during growth in the PNR was not tracked. Reduced Chemical Additives Denitrification at the HCAWTP occurs through the addition of m ethanol (CH 3 OH) as an external carbon source. Based on algae assimilation of nitrate, the reduced amount of chemical additives for denitrification was determined The chemical demand used was 3.4 kg methanol required per kg of nitrate denitrified (Maurer et al. 2003). Reduced nitrate concentration due to algal assimilation was equated to savings in methanol addition. The cost of methanol can be easily changed on th e user interface if the market fluctuates. The equation to determine cost savings is as follows (2 2 ) Figure 2 9A shows the model framework for cost savings due to chemical use reduction. Equation ( 2 1 ) is calculated in the first flow of the diagram. This equation is used to represent cost savings in all secondary process outputs.

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74 Figure 2 9 A Model framework to calculate the benefits of reduced chemical additives. See Tables A51 and A52 in Appendix A for full list of varia bles and equations. Figure 29B. Conceptual illustration of savings due to reduced chemical demand. Biomass Production Costs Biomass production costs were determined from literature and ranged from $32/kg (Molina Grima et al. 2003) to $3/kg (Chisti 2008). A sensitivity analysis was conducted (see Chapter Five) to determine the best estimate, and the value was assumed to be the same for all products. Because neither study account ed for the use of wastewater as a source of nutrients costs were adapte d from published calculations, subtracting those costs, such as media storage and

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75 production, which would be unnecessary with wastewater incorporated into the process. This assumption was also based on a preliminary life cycle assessment conducted by Aresta et al. (2005) that concluded that producing algae on wastewater effluent could produce a net ener gy gain. Biomass production costs were entered into the model using a converter. If production costs fluctuate in the future, as research and development improve process efficiency, this converter can be easily adapted to reflect such changes. Biomass Harvesting Costs Biomass harvesting costs were broad within the literature, ranging from $0.12 per kilogram of algae harvested (Molina Grima et al. 2003) to just $0.002 per kilogram (Silberman 2010). Molina Grima et al. (2003) conducted an extensive stu dy encompassing many different harvesting methods, but the article may be slightly outdated, as more efficient technologies have developed over the past few years Harvest costs were investigated and further discussed in the sensitivity analysis in Chapter Five. Similar to biomass production costs, harvesting costs were added to the model using a converter. If costs change depending on technology or conditions at a particular plant, the converter can be adapted to reflect those conditions. Secondary Produ ct Calculations The model is built to conduct a macroeconomic analysis was conducted to assess on processing the harvested algae biomass into biodiesel, bioga s, or f ertilizer. If biodiesel i s the desired end product the model i s constructed to allow for additional cost benefit analysis of using the leftover biomass for biogas or

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76 fertilizer. Each process was evaluated separately, based on best available cost estimates from literature and market prices. Choice of which process to use could be made by depressing buttons on the interface (see Figure 2 7 ). Biodiesel Calculations Calculations for biodiesel processing were adapted from Molina Grima et al. (2003). Production costs of crude esterified oil were used based on a list of expenses completed by the authors. The estimation includes raw materials costs, utilities, and fixed capital costs per year. Landfill costs were eliminated from the original calculations because the model assumes the leftover biomass will be used fo r furth er processing. The value adapted from the paper was $ 71 per kilogram of algae processed. This cost was then added to the cost of biomass production and har vesting costs Figure 30A shows the cost framework for biodiesel production in the model

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77 Figure 3 0 A Model framework for biodiesel production calculations. Individual costs and benefits are summed; costs are then subtracted from benefits to determine overall profit. See Tables A55 and A56 in Appendix A for full list of variables and equations. Figure 30B. Conceptual illustration of economic calculations in biodiesel processing train.

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78 Biodiesel calculations can be broken down into cost and benefits. Costs involved in biodiesel production include the cost of biomass production, harvesting costs, and the cost of biodiesel production itself. Other costs factored in were the costs of fertilizer or biogas production associated with further processing of leftover biomass. The equation used to calculate costs was as follows (2 3 ) where kgA is the mass of algae produced in kg, $BDprod is the cost of biodiesel production per mass of algae processed, $Aprod is the cost of algae production per unit algae, and $Aharv is the cost of harvesting per unit algae. This calculation occurs in the top portion of the schematic shown in Figure 30A The the equation by 1 or 0. Depending on which process the user chooses for further processing of leftover biomass (or the choice of no further processing), additional costs are added to the above equation (2 4 ) where %Oil is the percent of algae biomass composed of extractable oil, kgA is the mass of algae processed, and $process is the cost of either process (biogas or fertilizer) per unit algae processed. The percent of oil in the algae can be entered on the user interface. The leftover biomass was considered that

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79 percentage which was not lipids, i.e. one minus the lipid percentage. If the user chooses not to further process the leftover biomass, no additional costs are added to E quation (2 2 ). The monetary benefits of biodiesel processing a re also calculated in a series of steps. First, the potential profit for selling biodiesel i s calculated based on the amount of oil produced per biomass and the market price of biodiesel. Both these variab les are subject to change and a re therefore written into th e interface of the model. Costs savings realized due to reduced aeration demand and chemical additives a re also added to the potential benefits. Figure s 30A and 30B show the model framework for the cost/ benefit analysis of biodiesel; benefits are calculate d in the lower flow The equation used to calculate economic benef its of biodiesel production was (2 5 ) where $MeOH is the money saved from chemical additive reduction, $O2 is the money saved from reduced aeration demand, kgOil/kgA is the percent of oil per unit algae, LOil/kgOil is the volume of oil per mass of oil, defined as the density of biodiesel of 0.88 kg/L ( Alptekin and Canakci 20 08 ), $BD is the market value of biodiesel, based on market prices, which can be entere d on the model interface; the value of $3.10 was used in model simulations for this study Depending on the user selected use of leftover biomass, additional monetary benefits were added such as

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80 (2 6 ) where $market is the market value of biogas or fertilizer per unit algae. If the user selects to not further process biomass, no additional benefits are added. Overall profit from biodiesel was calculated by subtracting the overall costs from the overall benefits BD_Benefits BD_Costs = BD_Profit (27 ) Profit was reported in USD per day in the outgoing flow of the final stock. Biogas C alculations Costs associated with anaerobic digestion of algae biomass to produce biogas were adapted from Gebrezgabher et al. (2010) a study that analyzed the costs of producing biogas from va rying substrates, including labor costs Calculations related to biogas production from energy maize and food waste were used for this model, as they were the closest in composition to algal biomass and had the highest, and therefore most conservative, values. Values used for biogas production costs and labor costs were $0.048 and $0.054 per kilogram of biomass processed, respectively. The model framework for this calcula tion is shown in Figure 31 Labor costs and biogas production costs were added together to obtain process costs.

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81 Figure 31 Model framework for calculating biogas production costs. Labor and processing costs were adapted from Gebrezgabher et al. (2010) and were set at $0.054/kg algae and $0.048/kg algae, respectively. Costs were calculated by adding all costs associated with biogas production (2 8 ) where kgA is the mass of algae processed, $BGprod is the cost of biogas prod uction per unit algae, $Aprod is the production cost of culturing algae per unit algae and $Aharv is the harvesting costs per unit algae.

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82 Figure 32 A Model framework for biogas calculations. Costs were subtracted from benefits to calculate overall net profit. See Tables A53 and A54 in Appendix A for full list of variables and equations. Figure 32B. Conceptual illustration of economic calculations in biogas processing train.

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83 Benefits were calculated by adding the monetary benefit of selling biogas t o the amount of money saved via reduced aeration and chemical additive s Biogas yield was based on converting the amount of algae produced to a mass of COD, then subsequently converting the mass of COD to the volume of methane theoretically possible per mass of COD (Rittman and McCarty 2001). Algae was converted to mass of COD by the follo wing steps : First, the oxygen equivalent of algae cells was determined based on the following equation C 100 O 48 H 183 N 11 P + 227/2 O 2 = 100 CO 2 + 11 NH 3 + 75 H 2 O (2 9 ) Next, the COD of the cells was determined by the following equation (30 ) where molA and kgA is the moles of algae and mass of algae, respectively T he value of 1.545 kg COD/kg algae was used. Methane production was estimated as the grams of methane produced per gram COD, as shown in the following steps (Rittman and McCarty, 2001) A stoichiometric relationship between digested algae and methane produced was determined using the overall equation previously discussed in E quation (4) R= f e R a + f s R c + R d ( 4 ) where R a is the electron acceptor half reaction, R c is the cell synthesis equation, and R d is the electron donor half reaction. The yield of the digesting organisms is assumed to be 0.07 gVSS/gCOD; therefore, f s is equal to 0.1 and f e is equal to 0.9. The R d was developed based on the custom organic half reaction equation

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84 per Rittman and McCarty (2001) and the molecular formula for algae used throughout this report. The overall R equation was calculated as follows Rd = 0.0022 C 100 O 48 H 183 N 11 P + 0.3590H 2 O = 0 .1960CO 2 + 0.0242NH 4 + + 0.0242HCO 3 + H + + e f e *R a = 0.1125 CO 2 + 0.9 H + + 0.9 e = 0.1125 C H 4 + 0.2250 H 2 O f s *R c = 0.02 00 CO 2 + 0.005 HCO 3 + 0.005 NH 4 + + 0.1 H + + 0.1 e = 0.005 C 5 H 7 O 2 N + 0.04 50 H 2 O R = 0.0022 C 100 O 48 H 183 N 11 P + 0. 0890 H 2 O = 0.0 635 CO 2 + 0.0192 NH 4 + + 0.0 192 HCO 3 + 0.1125 C H 4 + 0.005 C 5 H 7 O 2 N ( 3 1 ) Using the molar relationships determined from R, the amount of biogas (as methane) was calculated ( 3 2 ) where volume of methane is considered at standard temperature (0C, 273K) and pressure (1 atm). To convert to a temperature of 20C (293K), the following equation was used ; (33 ) where V 1 is the vol ume of methane calculated from E quation ( 32 ) above, T 1 is at STP, and T 2 is considered 20C. The value of 523 L methane per kg algae was used in the model. The market price for biogas was determined based on Emcon Associates (1980). Assuming a 55% methane content in biogas produced, the conversion of 20490 kJ/m3 biogas was determined. The commodity price of $4.08/MmBTU

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85 was used ( www.bloomberg.com/energy acce ssed 9/28/2010). To convert the energy content to monetary value the following equation was used (34) Benefits from producing algae were calculated by adding the savings from reduced chemical demand and aeration requirements to the estimated profit from selling the biogas produced. Conversions per unit algae were calculated as described above. ( 3 5 ) where $MeOH is the savings due to reduced chemical additives, $O 2 is the savings due to reduced aera tion needs LCH 4 /kgCOD is liters of methane produced per mass of COD digested, kgCOD/kgA is the mass of COD available per mass of algae biomass and $/LCH4 is the market price of biogas The value per BTU of biogas c an be changed on the model interface. Utilizing the leftover digester centrate or biomass as fertilizer was not included as a benefit in this model. To gain overall net profit, costs are sub tracted from benefits such that BG_Benefits BG_Costs = BG_Profit (3 6 ) where BG is an abbreviation for biogas. Profits were reported in USD per day.

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86 Fertilizer Calculations Fer tilizer cost benefit analysis i s conducted similarly to biodiesel and biogas. Costs were subtracted from benefits to calculate overall net profit. Figure 3 3A shows the model framework for fertilizer processing Fertilizer processing via the button Figure 33 A Model framework for fertilizer cost benefit analysis. See Tables A57 and A58 in Appendix A for full list of variables and equations.

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87 Figure 33B. Conceptual illustration of economic calculations in fertilizer processing train. The cost of fertilizer processing w as adapted from Fadare et al. (2010). Costs adapted for the model were for pelletized fertilizer production, which was chosen to be conservative and because it was similar to the case of HFCAWTP. Figure 3 4 shows the model framework for calculating fertilizer production costs. Figure 34 Model framework for calculating fertilizer production costs. The cost of fertilizer production was calculated with the equation (3 7 ) where kgA is the mass of algae processed. The values of 0.277 kWh/MJ and $0.12 USD/kWh w ere used as conversion factors in the equation. The total energy (MJ) required per kilogram of biomass processed was adapted from Fadare et al. (2010) The inclusion of superfluous steps in the

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88 process, such as sorting, a s well as the higher energy prices was considered to balance the lower labor costs reflected in the study. A value of 0.33 MJ per kg of algae processed was used for this model. Calculations for total fertilizer costs included harvesting and biomass production costs as well as processing costs (3 8 ) where kgA is the mass of algae biomass processed, $Fprod is the cost of fertilizer processing per unit algae, $Aprod is the cost of algae production per unit algae, and $harv is the cost of harvesting per unit algae. Benefits were calculated by adding c ost savings due to reduced chemical additives and aeration demand to profit generated from sale of fertilizer. As not all of the biomass would be directly converted to fertilizer, a conversion factor of 0.5 was used; i.e. h alf of the biomass was considere d to be converted to fertilizer The cost of fertilizer was taken from market prices of comparable products and could b e changed on the interface of the model. Benefits were calculated based on the following equation (3 9 ) where $MeOH is the cost savings from reduced chemicals required, $O2 is the cost savings from reduced aeration, kgA is the algae biomass processed, kgFert/kgA is the conversion factor for fertilizer produced per unit algae, and $Fert/kgFert is the monetary value per unit algae.

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89 Overall profit from fertilizer production wa s determined by subtracting the total costs from the total benefits as shown in the equation below F_Benefits F_Costs = F_Profit (40 ) and was reported in USD/day.

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90 Chapter Four : Sensitivity Analysis The model was run through a series of sensitivity tests, testing both biological and economic parameters, to determine how and to what extent change s in certain variables affected biomass production and economic viability The most sensitive ranges for variables were also determined when appl icable. Results of the sensitivity analysis are presented in this section. As discussed in the previous section, the model was built to have two algae reactors, the post pure oxygen reactor (PPOR) and the post nitrification reactor (PNR). In the sensitivit y analysis, the effects of the changing parameters were evaluated in terms of algae biomass production unless otherwise noted. Wastewater Variables Because biomass production is intimately connected to wastewater characteristics, the wastewater framework was first tested to determine which variables were most sensitive. Mass balance of water flow and nutrients was maintained throughout all tests, which was verified through the mechanisms described in Chapter Three. Wastewater Influent Characteristics Infl uent wastewater characteristics to a typical domestic wastewater plant can fluctuate daily and/or seasonally. Since algae biomass production is greatly

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91 influenced by available substrates, the model was tested against varying influent loads to investigate the affect on biomass production. The model was run under typical plant loading, high loading, and under limiting conditions of influent nitrogen, phosphorous, and carbon dioxide. Figure 35 shows the setting for Trial 1; all settings except for influent water characteristics, remained constant throughout subsequent trials. Table 4 shows the concentrations selected for influent ammonia, soluble phosphorous, and carbon dioxide under the various trials Note that the model converts influent ammonia to nitra te at a specific removal rate, so influent nitrate concentration was not varied. Table 4 Concentration ranges of influent ammonia, soluble phosphorous, and carbon dioxide selected for wastewater characteristics sensitivity analysis. Nutrient Low Typica l High N H 3 N 5 35 70 Soluble P 2 4.3 20 CO 2 C 10 32 64 Note: Concentrations are in mg/L. Table 5 Trial matrix for varying influent wastewater characteristics. Nutrient Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 NH 3 N Typ High Low Typ Typ Soluble P Typ High Typ Low Typ CO 2 C Typ High Typ Typ Low

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92 Figure 35 Model parameter settings for influent wastewater characteristics sensitivity test. All other variables were kept constant during this sensitivity analysis thereby specifically testing the effect of influen t wastewater characteristics on algae biomass product ion. Figure 36 shows a comparison of the biomass generated under each trial test. Biomass production increased with higher loading (Trial 2) ; algae in n itrogen and phosphorous limiting trials (Trials 3&4) were washed out, as growth could not keep up with harvest. Biomass production was stable with limited carbon dioxide (Trial 5) although at lower levels than typical or high loading conditions. Lines are jagged due to harvesting. Results for the PNR can be found in Appendix C.

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93 Figure 36 Biomass production in the PPOR as a function of influent nutrient concentration Trial 2 is on the secondary y axis ; all other Trials are on the primary y axis For explanation of Trial details, see Table s 4 and 5 Line oscillations are due to harvest events. Nutrient limitation can be a consequence of varying influent concentrations. Figure 37 show the results of influent ammonia concentration on biomass production in the PPOR when harvest rate w as set to 50% harvest every 3 days Influent concentration was varied from 5 80 mg/L. Biomass growth is limited at influent concentrations of 5 mg NH3 N/L, but grows at a much higher capacity as influent concentration increases. In fact, biomass production is the same at concentrations above 40mg/L, indicating another nutrient becomes limi ting at this point.

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94 Figure 37 Biomass production in the PPOR as a function of influent NH3 concentration. Trials with 40mg/L and above follow the same upward trend. Line oscillations are due to harvest events. Other Wastewater Parameters Other physical wastewater parameters, such as HRT, flow diverted to the algae basins, and plant removal rates did not affect overall biomass production. This is because algae SRT remained constant through trials for other physical parameters. For example, althou gh HRT or flow is increased, the volume of the algae basin is subsequently increased due to the model framework discussed in Chapter 3. This normalizes the available concentration to volume, equalizing the influent concentration. As harvest rate remained c onstant, an increase in available substrate would not affect algae growth, as they are limited by the amount of time they have to assimilate the substrate.

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95 Algae Growth Variables As discussed in Chapter Two, algal species are very diverse, ranging in ph ysiology, specific growth rates, metabolic preferences, etc. Therefore, a sensitivity test was conducted on variables that may directly affect the growth of algae. Specific Growth Rate and Harvest Waste Rate Because the model can not take into account ever y environmental condition that could a ffect algae growth, the choice of specific growth rate for simulations is important. Specific growth rate was randomly varied from 0.1 to 2.5 per day. Figure 38 shows how biomass production in the PPOR increases with increasing max, until substrate availability limits growth. The harvest rate was set to remove 50% of the biomass every 3 days, which was too high for specific growth rates below 0.9/day. For results in the PNR see Appendix C.

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96 Figure 38 Biomass production in the PPOR with increasing max. max of 1.17 and 2.5 per day are set to the secondary axis. Line oscillations are due to harvest events. Biomass harvest rate works very closely with specific growth rate; if the harvest rate is too high, all algae will be washed out and no growth will occur. Harvest amount was varied from 10 50% of accumulated algae with harvest frequency set constant at every 3 days, and max of 1 /day. Figure 39 shows the biomass production in the PPOR under these conditions. With a max of 1 /day, algae is washed out when harvest rate is 50% as growth is physiologically limited

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97 Figure 39. Biomass production as a function of harvest rate. Each line represents a harvest rate in percent of biomass in the basin per day. Algae is washed out of the system wh en harvest rate becomes too high under conditions tested The harvest rate also affected the calculated specific growth rate, as shown in Figure 40. The model was run maintaining all variables th e same between the PPOR and PNR, including specific growth rate of 1/day, flow of 1 MGD, and a decay constant of 0.2 /day. Harvest was set in the PPOR to zero, whereas the harvest in the PNR was 50% every 10 days, beginning on day 10. As shown in Figure 40 specific growth rate in both reactors starts high, but as algae grow and assimilate substrate, calculated specific growth rate decreases. However, in the PPOR, where no algae was harvested, the specific growth rate decreased faster, as more algae were as similating more substrate.

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98 Figure 40. Specific growth rate as a function of harvest schedule. Harvest in the PNR was set to 50% every 10 days, beginning on day 10; harvest was zero in the PPOR. Half Saturation Constants Because the model relies heavily on Monod kinetics, biomass production can be influenced by the selection of the half saturation constant ( K ) for ammonia, nitrate, carbon dioxide, and soluble phosphorous. Therefore, the K for each parameter was tested over a range of 1e 7 to 1e 3 mg/L. Results are shown in Figures 4 1 and 4 2 In the PPOR, varying the half saturation constant of NOx species did not affect the calculated , as algae in this basin are only considered to be growing on ammonia. Likewise, K_N H3 did not affect the in the PNR. However, varying the K for other nutrients did affect calculated In general, a s K values increased, decrease d This would be expected; as the K value increases, more substrate is needed in order to keep the fraction close to 1, thereby maintaining calculated close to max.

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99 Figure 4 1 Calculated in the PPOR as a function of K Each line represents a different simulation where the K for each nutrient was independently varied while other K values were kept constant. Figure 4 2 Calculated in the PNR as a function of K Each line represents a different simulation where the K for each nutrient was varied while other K values were k ept constant.

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100 Yield Coefficient Biomass yield ( Y ), or biomass produced per unit substrate consumed, also may affect biomass production when calculated by Monod kinetics. Also, as discussed in Chapter Three, the molecular formula for algae can vary depending on species, growth conditions, or habitat. Therefore, the sensitivity of this varia ble was tested to identify the e ffect a different molecular formula may have on overall substrate removal. In general, a s Y increases, more biomass is produced per unit substrate. Empirically, a higher Y means that less substrate is necessary to produce one unit of algae; conversely, more substrate needed per unit algae w ill decrease yield. In terms of substrate assimilation, a higher yield corresponds to a lower substrate utilization rate ( q ); therefore, although biomass production may be constant less substrate is removed per unit algae produced. Figure 4 3 shows this trend when Y_NH3 is varied from 5 25 kg biomass produced/ kg substrate consumed.

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101 Figure 4 3 The effect of Y_NH3 on algae growth variables in the PPOR. Biomass produced is plotted on the primary vertical axis, and q_NH3 is plotted on the secondary axis. Varying Y will not affect algae growth, but may affect the substrate assimilated during algae growt h. Therefore, molecular formula and accurate representation via Y is important to predict accurate substrate removal via algae production. Economic Variables All sensitivity tests conducted for the economic variables used specific growth rates of 1/day, harvest rates of 5 0% every 3 days and a flow rate of 1 MGD. Plant influent nutrient characteristics were 35 mg N/L, 191 mg/L BOD, 4.3 mg P sol /L, and 32 mg CO2 C/L. Cost Savings from Reduced Aeration Energy requirements for nitrification and BOD removal can be a substantial cost sink for a wastewater treatment plant. The model considers

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102 reduced aeration requirements due to reduced nitrification demand as well as oxygen produced through oxygenic photosy nthesis. This section investigates the effect of the price per unit of oxygen on overall cost savings. Figure 4 4 shows the increase in cost savings realized with increasing cost per unit oxygen. This section is very sensitive to this variable; a quantity o f $0. 23 per unit oxygen was used for further calculations as explained in Chapter 3 Figure 4 4 Cost savings from reduced aeration as a function of cost per unit oxygen. Cost Savings from Reduced Chemical Addition Chemical addition can also be a significant portion of a wastewater HFCAWTP, for example, uses about 2 million gallons of methanol per year, which costs between $1.5 and $7 million USD per year, depending on fluctuating market pri ces for methanol (ranging between $0.75 and $3.50) (personal communications, Tim Ware, September 2010). This section tests the sensitivity of the cost of methanol on overall cost savings benefits from

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103 reduced chemical addition. As shown in Figure 4 5 the co st of methanol does make a significant difference in the cost savings realized from reduced chemical demand. Figure 4 5 Cost savings from reduced chemical addition as a function of the cost of methanol. Biodiesel Biodiesel production has many variables which could affect the overall profit. Variables tested in this section include the market price of biodiesel and the production costs. This section also investigates whether biogas or fertilizer costs affect the overall profit realized. Biodie sel processing costs were varied to see the effect on overall biodiesel costs. The results of the sensiti vity test are shown in Figure 4 6 ; as biodiesel processing costs increased, biodiesel production costs increase as well.

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104 Figure 4 6 Cost of biodiesel production as a function of processing costs. Next, harvesting costs and biomass production costs were varied to investigate the sensitivity of overall costs Harvesting costs were varied from $0.002 to $0.12 per kilogram harvested, as these we re the cost ranges found in literature. As shown in Figure 4 7 the cost of biomass harvesting does not significantly affect over biodiesel production costs.

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105 Fig ure 4 7 Cost of biodiesel production over varying biomass harvesting costs. The cost of biomass production was varied from $3 to $32 based on values found in literature. As shown in Figure 4 8 varying biomass production costs did not significantly affect overall biodiesel production costs. Figure 4 8 Cost of biodiesel production over varying biomass production costs.

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106 Because the model gives the option to further process leftover biomass after biodiesel processing, the additional costs from secondary processing were investigated. As shown in Figure 4 9 the additional pr oduction costs of secondary processing do not significantly affect the overall cost of biodiesel production. Figure 4 9 Cost of biodiesel production with added cost of secondary processing. Biogas Variables affecting the overall production costs of bi ogas were similarly investigated. Biogas production costs were varied from $0.10 to $5.00 per kilogram processed. Increasing the biogas processing costs did affect the overall production costs, as shown in Figure 50

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107 Figure 50 Cost of biogas production as a function of processing costs. Fertilizer Fertilizer costs were analyzed similar to biodiesel and biogas. Processing costs were varied in order to see the effect on overall production costs by varying the energy required for processing As shown in Figure 5 1 processing costs do not significantly affect overall production costs of fertilizer.

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108 Figure 5 1 Cost of fertilizer production as a function of processing costs.

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109 Chapter F i ve : Results After verifying the model response to change s in variables as shown in Chapter Four, a case study was conducted on the HFCAWTP. Model parameters were set to mimic the conditions at the treatment plant based on average influent characteristics in 2009. All parameters were set as shown in Figure 5 2 except those parameteres listed in Table 6 which were varied to represent different cases. Case 1 used specific growth rates published for Chlorella sp for growth on ammonia of 0.214 /day (Tam and Wong 1996) and nitrate of 0.238 /day (Ong et al. 2010). T he growth rate in Case 2 wa s increased to 1 /day for each nitrogen source to see the effects of a faster growing species on biomass production and eco nomics. Algae death rates have been reported to range between 0.01 0.5 per day, depending on environmental conditions (Ambrose et al., 2006). For these simulations, a decay rate of 0 .02 / day was chosen. Case 3 mimics the conditions of Case 1, but with an i ncreased flow rate and HRT.

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110 Figure 5 2 Parameter settings for HFCAWTP case study. Potential Biomass Production at HFCAWTP Three case studies were run under conditions based on the HFCAWTP in Tampa, FL, described in Chapter 3. Parameters for each case are outlined in Table 6.

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111 Table 6 Simulation parameters for case studies at HFCAWTP. Case 1 Case 2 Case 3 PPOR max (NH3) (/day) 0.214 1 0.214 b (/day) 0.02 0.02 0.02 HRT (days) 1 1 5 Flow (MGD) 1 1 15 Harvest Amount 25% 25% 25% Initial Harvest 20 20 20 Harvest Frequency 1 4 1 4 1 4 PNR max (NO3) (/day) 0.238 1 0.238 b (/day) 0.02 0.02 0.02 HRT (days) 1 1 5 Flow (MGD) 1 1 15 Harvest Amount 25% 25% 25% Initial Harvest 20 20 20 Harvest Frequency 1 4 1 4 1 4 In Cases 1 and 3, biomass production appears to be limited by specific growth rate, as shown by the longer lag phase in these Cases versus Case 2 which had a higher specific growth rate. Figure 5 3 54 and 5 5 show results from each case. The Monod fractions, i.e. corresponding results from the generic equation (40 ) where S is available substrate and K is the corresponding half saturation constant, are also shown in the Figures. The Monod fraction with the lowest

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112 value is the limiting nutrient in each case. As shown, the Monod fraction do es not change in Cases 1 and 3, with low specific growth rate. However, in Case 2, when algae is growing at a much faster rate, the Monod fracti on for carbon dioxide drops off dramatically during the exponential growth phase, essentially limiting growth in this Case. Figure 5 3 Biomass production at HFCAWTP in Case 1. Note Monod fractions do not change over time, and phosphorous is the limiting nutrient in both basins. Line oscillations are due to harvest events.

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113 Figure 5 4 Biomass production at HFCAWTP in Case 2. Note the drop in the Monod fraction for carbon dioxi de as the algae reach exponential growth phase. Figure 5 5 Biomass production at HFCAWTP in Case 3. Note the Monod fractions do not change over time; phosphorous remains the limiting nutrient in this case.

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114 In all cases, the biomass production was the same regardless whether both reactors were functioning or if only one was functioning at a given time. In Cases 1 and 3, phosphorous was the limiting nutrient, as evidenced by the Monod fractions shown in Figure s 5 3 and 5 5 Although phosphorus begins as the limiting nutrient in Case 3, as shown in Figure 5 5 carbon dioxide becomes limiting as algae reach the exponential growth phase. Figure 5 6 compares the Monod fractions in Cases 1 and 3 at start up. Note that the fractions are higher in Case 3, when HRT and flow to the algae basins are increased, thereby increasing available substrate. Phosphorous is the limiting nutrient in both cases at start up, as shown in the Figure by the smallest columns. Monod fraction s also were not significantly different between the PPOR and the PNR, showing the same limiting factors in both reactors. Figure 5 6 Monod fractions in Cases 1 and 3. Note that the legend reading from left to right, top to bottom, is the same order asbars reading from left to right.

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115 As biomass production is dependent on the specific growth rate of the algae species chosen, a sensitivity test was conducted on the case study. All parameters were kept constant as noted above for Case 1, and harvest rat e was set to 25% every 14 days, with initial withdrawal at day 16. Figure 5 7 shows the total biomass harvested possible at Day 100 (6 th harvesting cycle) as a function of specific growth rates with both the PPOR and PNR in operation. As shown in the Figure specific growth rate has a large impact when it is less than approximately 2 /day, but at higher rates other factors, such as substrate availability, limit growth. Figure 5 7 Biomass production as a function of specific growth rate at the HFCAWTP. Note conditions are those of Case 1 from Table 6 with harvest rate of 25% every 14 days, with initial harvest at 16 days. Values shown are harvest values from day 100. Biomass production can also be influenced by the timing of the algae harvest. Figure 5 8 shows the effect of varying the initial harvest over 20, 50, and 100 days under Case 1 conditions. If harvest is delayed for 100 days, the algae

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116 reach steady state faster, as they are allowed to gain a better foothold before being washed out. Similar results were found for Case 2; Figure C3 in Appendix C illustrates this data. Figure 5 8 Biomass production as a function of initial harvest. This data is from Case 1 conditions. Harvest amount will also affect biomass production, as harvesting too much can cause the population to be washed out. This is shown in Figure 5 9 where harvesting amount was varied from 10 to 50% removed every 14 days. Under Case 1, algae growth was severly stunted in both reactors when the harvest rate was 50%, and in the PPOR when the harvest rate was 25%. Figure 60 shows the results under Case 2 conditions ( 1/day); production increased with decreasing removal rates. Steady state was obtained in all scenarios, but biomass production was higher when less algae was harvested.

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117 Figure 5 9 Biomass production as a function of harvest amount, Case 1 conditions. F igure 60 Biomass production as a function of harvest amount, Case 2 conditions. Economic Viability The economic viability for growing algae at the HFCAWTP was evaluated under a best, average, and worst case scenario as outlined in Table 7 Variables that would affect costs or benefits of algae production were varied over ranges

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118 either found in literature or from historical price ranges. The best case scenario is meant to represent a time when resources may be scarce and energy price s are high, reflected in the high market price of products, aeration, and methanol. The worst case represents a time when resources may be abundant, and energy is relatively cheap, making algae production less economically attractive. The average case repr esents a market atmosphere in between these two extremes. This analysis is important due to the high variability in the energy and commodities market. For example, the cost of methanol has varied between $0.75 and $3.50 per gallon over the past few years, which greatly affects the budget of a wastewater treatment plant. Similarly, as stated in Chapter Four, the cost of aeration for nitrification can vary depending on electricity costs and oxygen transfer efficiency. The cost per kg of N removed has been rep orted (approximately $4.86) (Zamalloa et al., 2010). Table 8 shows the potential profits under each scenario per kg of algae produced. As shown, under the conditions presented, biodi esel production is not profitable, even under the best case scenario. However, biogas and fertilizer production are both profitable under best case scenario. Biogas production is also profitable under average conditions, and very close to profitable under even worst case scenario.

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119 Table 7 Parameter settings for economic viability analysis. Reduced Aeration Reduced Chemical Additives Harvesting Costs Biomass Production Costs Biodiesel Biogas Fertilizer $/kg N nitrifi ed $/L MeOH $/kg $/kg % Oil $/L Market Price BD Process $/L Market Price BG Process % Biomass Conver ted to Product $/kg Market Price Fert ilizer Processing Best Case $3.50 $3.50 $0.00 6 $3.00 80% $3.15 $10.00 $0.01 $0.10 80% $3.00 $0.10 Average Case $1.00 $1.75 $0.12 $3.00 40% $2.00 $20.00 $0.01 $1.00 70% $2.00 $0.17 Worst Case $0.50 $0.75 $0.12 $3.00 30% $1.00 $70.00 $0.0 0 0 1 $1.00 50% $1.00 $0.25

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120 Table 8. Potential profits under best, average, and worst case scenario conditions per kg of algae produced. Biodiesel Biogas Fertilizer Best Case $8.29 $6.92 $1.80 Average Case $21.49 $4.33 $0.97 Worst Case $72.43 $ 3 62 $2.44 Next, an analysis was conducted to determine how market prices of the final product and processing costs would affect potential profits. Figure 6 1 shows the effect of varying the processing costs of biodiesel on the potential profit ; processing costs would have to fall below $1.60 to turn a profit, with all other best case scenario conditions held constant. Figure 6 1 Potential profits f r om biodiesel as a function of processing costs. Figure 6 2 shows the potential profits of biodiesel as a function of market price of biodiesel per liter. As shown, under the best case scenario conditions, the market price of biodiesel would have to reach $15.00 per liter before the

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121 processing became profitable. It should be noted, however, that this value is dependent on many variables and would fluctuate under different conditions. Figure 6 2 Potential profits from biodiesel as a function of market price. Biogas production was shown to be profitable under best and average case scenarios. However, under the worst case scenario, it is not profitable, even if production costs were zero. This is due to the low benefit of reduced aera tion and methanol costs of the worst case scenario. The market price of biogas ca n change considerably depending on the BTU content ; therefore, an analysis was conducted on the best case scenario to determine the minimum energy content required to maintain profitability. the conversion of $4.08/MmBTU was used ( www.bloomberg.com/energy accessed 2010). As shown in Figure 6 3 biogas content would need to remain above 250 BTU/L, if the price per BTU remained as stated.

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122 Figure 6 3 Potential profit from biogas as a function of energy content BTU content was calculated based on a price conversion of $4.06/MmBTU. Although fertilizer production was not profitable under the average and worst case conditions outlined in Table 7, Figure 6 4 shows how the market pric e of fertilizer would influence this outcome. As shown, fertilizer production could be profitable if the market price exceed $3.50 in the average case and $6.00 in the worst case. Again, it should be noted that these numbers are a reflection of all variabl es in Table 7 and would change if other parameters were varied.

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123 Figure 6 4 Potential profit from fertilizer production as a function of market price. The economic analysis determined that algae production can be profitable at the HFCAWTP, depending on the market conditions and cost of energy. Projections are highly dependent on a number of parameters, including the cost and efficiency of aeration, the c ost of methanol, the market price of products, and processing costs. This is an area to focus on for further calibration of the model, as pilot studies and full scale operations make more data available for these values.

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124 Chapter Six : Conclusions and Future Research Conclusions The synergy of wastewater treatment and algae biomass production has great potential to close the nutrient and energy loop of the wastewater treatment proce ss. This model has demonstrated that on a mass balance scale it is f easible to incorporate a n algae reactor at a wastewater treatment facility. Adequate nutrients and carbon dioxide are available for growth, although carbon dioxide and phosphorous can become limiting, as shown with the HFCAWTP case study. The model has al so identified potential important areas of sensitivity within the algae and wastewater marriage before accurate predictions of biomass production can be obtained. Among the most sensitive biological parameters include half saturation constants, specific gr owth rate, and the frequency and amount of biomass harvested Assimilation of nutrients is dependent on the yield coefficient, which can also vary depending on the algal species cultivated. Although many biological parameters are either sensitive or case specific, the model is a tool for recognizing research areas for pilot scale testing. Monod kinetics coefficients, for example, are very important for accurate predictions. T he model is also a tool for assessing the applicability of algae production at di fferent treatment plants with specific waste streams The model was built with a high

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125 degree of flexibility in order to be adaptable to a wide range of sites and conditions. Economic parameters, such as processing costs, can greatly affect model output. As wastewater characteristics, climate, equipment efficiencies, and market prices can fluctuate geographically, bench or pilot scale studies would be important for verifying and/or obtaining accurate values for these sensitive variables. The next version of the model will address economics in more detail, which should aid in more accurate predictions. P rocessing costs and biomass production costs are expected to decrease with further research and development of more efficient technologies. This is alrea dy evidenced in the reduction of algae harvesting costs over the past few years. Therefore, it is expected that the synergy between algae and wastewater will become more cost efficient in the future. The model has set up a framework for evaluating the link age between the biological and economic sides of algae biomass production for future research. Although the model has some limitations, it is an important first step in understanding the potential partnership between wastewater treatment and algae producti on as a means to close the nutrient and energy cycles. As energy and nutrient demands continue to rise with increasing population, it is imperative to harness and recycle these resources. Wastewater is a potential source of nutrients, freshwater, and energ y; algal biology makes them great candidates for efficiently converting these wastes into resources. As demonstrated in the mass balance of the case study, adequate carbon dioxide can exist within an already

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126 operating treatment facility, eliminating the ne ed for supplemental carbon dioxide addition. This carbon dioxide, typically released by the plant, can be harnessed and rerouted to other forms of energy. Incorporating algae into a conventional wastewater treatment plant has the potential to harness prev iously wasted resources for use as a secondary product. The mass balance approach has demonstrated the viability of the process, identified weaknesses for further research, and created a framework to evaluate future case studies. As research and technology become more efficient, and algal growth kinetics under varying environmental conditions are better understood, the model can be adapted and calibrated to reflect these changes. Future Research This model is a first step in examining the potential for alg ae growth from a mass balance perspective. As the synergy between algae and wastewater is still novel, data from full scale processes is not yet available. Future research should include studying algae kinetics in actual wastewater, to better understand th e relationship between K, Y, and substrate utilization. Many algae species can utilize both ammonia and nitrate as a nitrogen source, though they may prefer one over the other. Further work on the model should include the ability of algae to use both nit rogen sources in each reactor. Although, as a group, algae can grow utilizing numerous metabolic strategies, this model only considers autotrophic growth. It would be an important next step to examine the contribution of heterotrophic and mixotrophic alga l growth within the mass balance, on a competitive or non competitive basis.

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127 Literature has shown that heterotrophic and mixotrophic metabolisms can be more efficient than an autotrophic metabolism, leading to higher growth rates. Heterotrophic growth also could help reduce COD load and contribute to nutrient harnessing. Furthermore, depending on the reactor configuration and mixing, algae may become light limited, making heterotrophic growth more important. Light limitation is another important environmental condition that could affect algae growth. Future versions of the model should include light limitation, as too little or too much light can alter growth kinetics. Currently, light limitation is assumed to be built into the maximum specific gr owth rate selected for simulations. Similarly, trace elements, such as selenium, can limit or promote algae growth under varying concentrations. Likewise, endocrine disrupting compounds may also affect algae growth. Investigating the effect of trace elemen ts would be an important area to focus future research. On the economic side, a more detailed breakdown of cost/benefit inputs would aid in identifying key areas for cost reduction, making the entire process more economically viable. Currently costs, in ge neral, are bundled into one overall processing cost; however, this may not be entirely accurate. For instance, due to economies of scale, typically as production increases, costs per unit decrease. This is not easily reflected in the current model, but wou ld be an area for future research in subsequent versions. Similarly, biomass production and harvesting processes could be broken out into more detail. Future versions of the model could include an algae

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128 dewatering step, which would allow for increased flex ibility with water and nutrient losses with harvesting, as well as testing different technologies. Like many conventional treatment plants, t he HFCAWTP returns the anaerobic digester sidestream waste to the headworks o f the plant. This waste stream c ould be suitable for algae growth due to its high nutrient content. Future work on the model should include an algae basin after the digester to analyze possible nutrient reductions before the sidestream is returned to the treatment plant headworks. The cu rrent model uses removal rates from plant data, but a future version of the model could include wastewater kinetics similar to the algae kinetics. This would allow for more flexibility in the wastewater framework, creating a means to investigate calculated removal efficiencies. Outputs from the wastewater framework could be calibrated from plant data under varying conditions. Future research would also include lab and pilot scale studies. For example, calibrating the model to actual plant conditions would b e very important. Likewise, determining Monod kinetics on actual wastewater streams would help produce more accurate predictions of algae growth, as the Monod kinetics were determined to be among the most sensitive. Another question to investigate would be whether or not denitrifiers can use soluble microbial products (SMP) generated in the PNR by algae as a carbon source. Although there are some limitations and inherent assumptions built into the model, it is an important first step in understanding the ma ss balance relationship between algae and wastewater treatment. The model was built with

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129 as much flexibility as possible, allowing for expansion and adaptation to accommodate future research goals.

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138 Appendices

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139 Appendix A : List of Variables Water Flow Figure A 1 Detailed view of the water balance. Table A 1 List of v ariables in the water balance framework. Notation in Model Description Units or Value Q_o Influent flow to plant L/day Q_O2 Flow from cBOD reactor L/day Q_nit Flow from nitrification reactor L/day Q_e Effluent flow from plant L/day Q_PPOR Flow to PPOR L/day Qr_PPOR Flow returned to plant from PPOR L/day Q_PNR Flow to PNR L/day Qr_PNR Flow returned to plant from PNR L/day O2_Q Stock for water in cBOD reactor L Nit_Q Stock for water in nitrification reactor L Denit_Q Stock for water in denitrification reactor L Flow Flow entered on interface GPD L_conv Converter for gallons to liters L/gall Calc_Flow Converter to put flow into liters L/day Percent Flow to PPOR Converter entered on interface; amount of water diverted to PPOR %

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140 Appendix A (Continued) Table A 1 (cont.) Notation in Model Description Units or Value PPOR Switch for turning on/off water flow to PPOR unitless Q_Harv_PPOR Flow of water leaving system with algae harvest in PPOR L/day Percent Flow to PNR Converter entered on interface; amount of water diverted to PNR % PNR Switch for turning on/off water flow to PPOR unitless Q_Harv_PNR Flow of water leaving system with algae harvest in PNR L/day Table A2 List of equations in the water balance framework. Notation Equation Init ial Value Component Q_o = Calc_Flow n/a F low O2_Q(t) = O2_Q(t dt) + (Q_o Q_O2 Q_PPOR) dt 0 S tock Q_O2 = Q_o Q_PPOR n/a F low Q_PPOR = (Q_o*Percent_Flow__to_PPOR)*PPOR n/a F low Nit_Q(t) = Nit_Q(t dt) + (Q_O2 + Qr_PPOR Q_nit Q_PNR) dt 0 S tock Qr_PPOR = Q_PPOR Q_Harv_PPOR n/a F low Q_PNR = PNR*(Q_O2*Percent_Flow__to_PNR) n/a F low Q_nit = Q_O2+Qr_PPOR Q_PNR n/a F low Denit Q(t) = Denit_Q(t dt) + (Q_nit + Qr_PNR Q_e) dt 0 S tock Q_e = Q_nit+Qr_PNR n/a F low Qr_PNR = Q_PNR Q_Harv_PNR n/a F low

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141 Appendix A (Continued) Figure A 2 Detailed view of water loss to algae harvest. Table A 3. List of variables within water loss to algae harvest framework. Notation in Model Description Units or Value Q_Harv_PPOR Flow of water leaving system with algae harvest in PPOR L/day Qr_PPOR Flow returned to plant from PPOR L/day Q%_Lost_w_Harvest_PPOR The percentage of the water flow to the PPOR that's removed during harvesting unitless Q_Harv_PNR Flow of water leaving system with algae harvest in PNR L/day Q_PNR Flow to PNR L/day Q%_Lost_w_Harvest_PNR The percentage of the water flow to the PNR that's removed during harvesting L/day Q_loss Total water lost to algae harvesting L/day Q_Loss_to_Algae stock to track water volume lost to algae harvest L Table A4. List of equations in water loss to algae harvest framework. Notation Equation Init ial Value Component Q_Harv_PPOR = Q%_Lost_w__Harvest_PPOR*Q_PPOR n/a flow Q_Loss_to_Algae = Q_Loss_to_Algae(t dt) + (Q_Harv_PPOR + Q_Harv_PNR Q_loss) dt 0 stock Q_Harv_PNR = Q_PNR*Q%_Lost_w__Harvest_PNR n/a flow Q_loss = Q_Harv_PNR+Q_Harv_PPOR n/a flow

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142 Appendix A (Continued) Phosphorous Flow through Treatment Plant Figure A3 Phosphorous flow through treatment plant. Table A 5 List of variables in phosphorous flow framework Notation in Model Description Units or Value Inf_P1 Flow of influent soluble P kg/day P1_Inf Stock of soluble P k g P1_o Flow of soluble P in influent kg/day O2_P1 Stock of soluble P k g P1_O2 Flow of soluble P out of cBOD reactor kg/day Nit_P1 Stock of soluble P k g P1_n Flow of soluble P out of nitrification reactor kg/day Denit_P1 Stock of soluble P k g P1_dn Flow of soluble P out of denitrification reactor kg/day Inf_P2 Flow of influent nonsoluble P kg/day P2_Inf Stock of nonsoluble P k g P2_o Flow of nonsoluble P in influent kg/day O2_P2 Stock of nonsoluble P k g P2_O2 Flow of nonsoluble P out of cBOD reactor kg/day Nit_P2 Stock of nonsoluble P k g P2_n Flow of nonsoluble P out of nitrification reactor kg/day Denit_P2 Stock of nonsoluble P k g P2_dn Flow of nonsoluble P out of denitrification reactor kg/day

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143 Appendix A (Continued) Table A 5 (cont.) Notation in Model Description Units or Value TP_Eff Stock of total phosphorous k g TP_Eff_t Flow of effluent total phosphorous kg/day Inf_Sol_P Influent soluble P mg/L Inf_TP Influent TP mg/L Calc_Flow Water flow into wastewater plant L/day mg_kg mg to kg converter 1000mg/kg P1_to_A Soluble P routed to algae, PPOR kg/day P1_to_A_2 Soluble P routed to algae, PNR kg/day P1_assim Soluble P assimilated in PPOR kg/day P1_assim_PNR Soluble P assimilated in PNR kg/day Table A6. List of equations in the phosphorous flow framework. Notation Equation Init ial Value Component Inf_P1 = Calc_Flow*Inf_Sol_P/mg_to_kg n/a flow P1_Inf(t) = P1_Inf(t dt) + (Inf_P1 P1_o) dt 0 stock P1_o = Inf_P1 n/a flow O2_P1(t) = O2_P1(t dt) + (P1_o P1_O2) dt 0 stock P1_O2 = P1_o n/a flow Nit_P1(t) = Nit_P1(t dt) + (P1_O2 P1_n P1_to_A) dt 0 stock P1 to A = P1_assim n/a flow P1_n = P1_O2 P1_to_A n/a flow Denit_P1(t) = Denit_P1(t dt) + (P1_n P1_dn P1_to_A2) dt 0 stock P1_dn = P1_n P1_to_A2 n/a flow P1_to_A2 = P1_assim_PNR n/a flow TP_Eff(t) = TP_Eff(t dt) + (P2_dn + P1_dn TP_Eff_t) dt 0 stock TP_Eff_t = P1_dn+P2_dn n/a flow Inf_P2 = Calc_Flow*Inf_Insol_P/mg_to_kg n/a flow P2_Inf(t) = P2_Inf(t dt) + (Inf_P2 P2_o) dt 0 stock

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144 Appendix A (Continued) Table A6. (cont.) Notation Equation Initial Value Component P2_o = Inf_P2 n/a flow O2_P2(t) = O2_P2(t dt) + (P2_o P2_O2) dt 0 stock P2_O2= P2_o n/a flow Nit_P2(t) = Nit_P2(t dt) + (P2_O2 P2_n) dt 0 stock P2_n = P2_O2 n/a flow Denit_P2(t) = Denit_P2(t dt) + (P2_n P2_dn) dt 0 stock P2_dn = P2_n n/a flow Phosphorous Mass Balance Figure A4 Phosphorous mass balance framework in STELLA model. Table A 7 List of variables in phosphorous mass balance framework. Notation in Model Description Units or Value TP_In Flow of total P entering the system kg/day Inf_P1 Flow of influent soluble P kg/day Inf_P2 Flow of influent nonsoluble P kg/day P_MB Stock of total P entering the system kg

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145 Appendix A (Continued) Table A 7 (cont.) Notation in Model Description Units or Value TP_MB_In Flow of total P entering the system kg/day P2_dn Flow of effluent nonsoluble P kg/day P1_dn Flow of effluent soluble P kg/day TP_Out Flow of total P leaving the system kg/day TP_MB_Out Flow of total P leaving the system kg/day P1_to_A Flow of soluble P assimilated in PPOR kg/day P1_to_A2 Flow of soluble P assimilated in PNR kg/day P_MB_Out Stock of total P leaving the system kg Table A8. List of equations in phosphorous mass balance framework. Notation Equation Init ial Value Component TP_In = Inf_P1+Inf_P2 n/a flow P_MB = P_MB(t dt) + (TP_In TP_MB_In) dt 0 stock TP_MB_In = TP_In n/a flow TP_Out = P1_dn+P1_to_A+P1_to_A2+P2_dn n/a flow P_MB_Out = P_MB_out(t dt) + (TP_Out TP_MB_Out) dt 0 stock TP_MB_Out = TP_Out n/a flow Nitrogen Flow through Treatment Plant Organic N and Ammonia Figure A 5 Nitrogen flow framework for organic N and ammonia in the STELLA model.

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146 Appendix A (Continued) Table A 9 List of variables in the nitrogen flow framework for organic N and ammonia. Notation in Model Description Units or Value Inf_N1_flow Flow of influent organic N kg/day N1_Inf Stock of influent organic N kg N1_o Flow of influent organic N kg/day O2_N1 Stock of organic N in cBOD reactor kg N1_O2 Flow of organic N from cBOD reactor kg/day Nit_N1 Stock of organic N in nitrification reactor kg Denit_N1 Stock of organic N in denitrification reactor k g N1_dn Flow of organic N from denitrification reactor kg/day mg_to_kg Conversion from mg to kg 1000mg/kg Calc_Flow Influent water flow L/day Inf_N2_flow Flow of influent ammonia kg/day N2_Inf Stock of influent ammonia k g N2_o Flow of influent ammonia kg/day O2_N2 Stock of ammonia in cBOD reactor k g N2_O2 Flow of ammonia from cBOD reactor kg/day Nit_N2 Stock of ammonia in nitrification reactor k g N2_n Flow of ammonia from nitrification reactor kg/day Denit_N2 Stock of ammonia in denitrification reactor k g N2_dn Flow of ammonia from den i trification reactor kg/day TN_Eff Stock of effluent total nitrogen k g TN_Eff_t Flow of effluent TN kg/day Inf_NH3 Influent ammonia concentration mg/L Inf_TKN Influent TKN concentration mg/L Inf_N1 Influent organic N concentration mg/L O2_N2_to_N3 Flow of ammonia to nitrate in cBOD reactor kg/day O2_kN2_to_N3 Rate of conversion of ammonia to nitrate /day Nit_kN2_to_N3 Rate of conversion of ammonia to nitrate /day Nit_N2_to_N3 Flow of ammonia to nitrate in nitrification kg/day N2_to_A Flow of ammonia assimilated into algae kg/day N2_assim Flow of ammonia assimilated into algae kg/day

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147 A ppendix A (Continued) Table A10. List of equations in the nitrogen flow framework for organic N and ammonia. Notation Equation Init ial Value Component Inf_N1_flow = Calc_Flow*Inf_N1/mg_to_kg n/a flow N1_Inf(t) = N1_Inf(t dt) + (Inf_N1_flow N1_o) dt 0 stock N1_o = Inf_N1_flow n/a flow O2_N1(t) = O2_N1(t dt) + (N1_o N1_O2) dt 0 stock N1_O2 = N1_o n/a flow Nit_N1(t) = Nit_N1(t dt) + (N1_O2 N1_n) dt 0 stock N1_n = N1_O2 n/a flow Denit_N1(t) = Denit_N1(t dt) + (N1_n N1_dn) dt 0 stock N1_dn = N1_n n/a flow Inf_N2_flow = Calc_Flow*Inf_NH3/mg_to_kg n/a flow N2_Inf(t) = N2_Inf(t dt) + (Inf_N2_flow N2_o) dt 0 stock N2_o = Inf_N2_flow n/a flow O2_N2(t) = O2_N2(t dt) + (N2_o N2_O2 O2_N2_to_N3) dt 0 stock O2_N2_to_N3 = N2_o*Nit_Rate_in_cBOD n/a flow N2_O2 = N2_o O2_N2_to_N3 n/a flow Nit_N2(t) = Nit_N2(t dt) + (N2_O2 N2_n N2_to_A Nit_N2_to_N3) dt 0 stock Nit_N2_to_N3 = N2_O2*Nit_Rate_in_Nit_Reactor n/a flow N2_to_A = N2_assim n/a flow N2_n = N2_O2 N2_to_A Nit_N2_to_N3 n/a flow Denit_N2(t) = Denit_N2(t dt) + (N2_n N2_dn) dt 0 stock N2_dn = N2_n n/a flow TN_Eff(t) = TN_Eff(t dt) + (N1_dn + N2_dn + N3_dn + N4_dn TN_Eff_t) dt 0 stock TN_Eff_t = N1_dn+N2_dn+N3_dn+N4_dn n/a flow

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148 Appendix A (Continued) Nitrogen Flow through Treatment Plant NOx and Nitrogen Gas Figure A 6 Nitrogen flow framework for organic N and ammonia in the STELLA model. Table A 11 List of variables in the nitrogen flow framework for nitrate and nitrogen gas. Notation in Model Description Units or Value Inf_NOx Influent concentration of NOx mg/L Calc_Flow Water flow through plant L/day mg_to_kg Conversion of mg to kg 1000mg/kg Inf_N3_flow Flow of influent NOx kg/day N3_Inf Stock of influent NOx kg N3_o Flow of influent NOx kg/day O2_N3 Stock of NOx in cBOD reactor kg N3_O2 Flow of NOx from cBOD reactor kg/day Nit_N3 Stock of NOx in nitrification reactor kg N3_n Flow of NOx from nitrification reactor kg/day Denit_N3 Stock of NOx in denitrification reactor kg N3_dn Flow of NOx from denitrification reactor kg/day Inf_N2 Influent concentration of N2 (gas) mg/L Inf_N4_flow Flow of influent N2 kg/day

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149 Appendix A (Continued) Table A 11 (cont.) Notation in Model Description Units or Value N4_Inf Stock of influent N2 kg N4_o Flow of influent N2 kg/day O2_N4 Stock of N2 in cBOD reactor kg N4_O2 Flow of N2 from cBOD reactor kg/day Nit_N4 Stock of N2 in nitrification reactor kg N4_n Flow of N2 from nitrification reactor kg/day Denit_N4 Stock of N2 in denitrification reactor kg N4_dn Flow of N2 from denitrification reactor kg/day DN_kN3_to_N4 Rate of conversion of NOx to N2 /day DN_N3_to_N4 Flow of NOx to N2 kg/day N3_toA2 Flow of NOx to algae kg/day N3_assim_PNR Flow of NOx assimilated by algae in PNR kg/day Table A12. List of equations in the nitrogen flow framework for nitrate and nitrogen gas. Notation Equation Init ial Value Component Inf_N3_flow = Calc_Flow*Inf_NOx/mg_to_kg n/a flow N3_Inf(t) = N3_Inf(t dt) + (Inf_N3_flow N3_o) dt 0 stock N3_o = Inf_N3_flow n/a flow O2_N3(t) = O2_N3(t dt) + (N3_o + O2_N2_to_N3 N3_O2) dt 0 stock N3_O2 = O2_N2_to_N3+N3_o n/a flow Nit_N3(t) = Nit_N3(t dt) + (N3_O2 + Nit_N2_to_N3 N3_n) dt 0 stock N3_n = N3_O2+Nit_N2_to_N3 n/a flow Denit_N3(t) = Denit_N3(t dt) + (N3_n N3_dn N3_to_A2 DN_N3_to_N4) dt 0 stock N3_dn = N3_n DN_N3_to_N4 N3_to_A2 n/a flow DN_N3_to_N4 = N3_n*Denit_Rate n/a flow N3_to_A2 = N3_assim__PNR n/a flow Inf_N4_flow = Calc_Flow*Inf_N2/mg_to_kg n/a flow N4_Inf(t) = N4_Inf(t dt) + (Inf_N4_flow N4_o) dt 0 stock N4_o = Inf_N4_flow n/a flow

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150 Appendix A (Continued) Table A12. (cont.). Notation Equation Init ial Value Component O2_N4(t) = O2_N4(t dt) + (N4_o N4_O2) dt 0 stock N4_O2 = N4_o n/a flow Nit_N4(t) = Nit_N4(t dt) + (N4_O2 N4_n) dt 0 stock N4_n = N4_O2 n/a flow Denit_N4(t) = Denit_N4(t dt) + (N4_n + DN_N3_to_N4 N4_dn) dt 0 stock N4_dn = N4_n+DN_N3_to_N4 n/a flow Nitrogen Mass Balance Figure A7 N itrogen mass balance in STELLA m odel Table A 13 List of variables in nitrogen mass balance. Notation in Model Description Units or Value TN_MB_In_1 Flow of total N species entering system kg/day TN_MB_In_Stock Stock of total N species entering system k g TN_MB_In Flow of total N species entering system kg/day Inf_N1_flow Flow of organic N entering system kg/day Inf_N2_flow Flow of ammonia entering system kg/day Inf_N3_flow Flow of NOx entering system kg/day

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151 Appendix A (Continued) Table A13 (cont.) Notation in Model Description Units or Value Inf_N4_flow Flow of influent N2 kg/day N4_Inf Stock of influent N2 kg N4_o Flow of influent N2 kg/day O2_N4 Stock of N2 in cBOD reactor kg N4_O2 Flow of N2 from cBOD reactor kg/day Nit_N4 Stock of N2 in nitrification reactor kg N4_n Flow of N2 from nitrification reactor kg/day Denit_N4 Stock of N2 in denitrification reactor kg N4_dn Flow of N2 from denitrification reactor kg/day DN_kN3_to_N4 Rate of conversion of NOx to N2 /day DN_N3_to_N4 Flow of NOx to N2 kg/day N3_toA2 Flow of NOx to algae kg/day N3_assim_PNR Flow of NOx assimilated by algae in PNR kg/day Table A14 List of equations in nitrogen mass balance. Notation Equation Initial Value Component TN_MB_In_1 = Inf_N1_flow+Inf_N2_flow+Inf_N3_fl ow+Inf_N4_flow n/a flow TN_MB_In_Stock = TN_MB_In_Stock(t dt) + (TN_MB_In_1 TN_MB_In) dt 0 stock TN_MB_In = TN_MB_In_1 n/a flow TN_MB_Out_1 = N1_dn+N2_dn+N2_to_A+N3_dn+N 3_to_A2+N4_dn n/a flow TN_MB_Out_Stock = TN_MB__Out_Stock(t dt) + (TN_MB_Out_1 TN_MB_Out) dt 0 stock TN_MB_Out = TN_MB_Out_1 n/a flow

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152 Appendix A (Continued) Carbon Flow through Treatment Plant Soluble and Nonsoluble Carbon Figure A8 Flow of soluble and nonsoluble carbon species in STELLA model. Table A 15 List of variables in soluble and nonsoluble carbon species model framework. Notation in Model Description Units or Value Inf_BOD Influent concentration of BOD, i.e. soluble C mg/L Inf_Sol_C Influent concentration of BOD, i.e. soluble C mg/L Calc_Flow Flow of water through system L/day mg_to_kg Conversion of mg to kg 1000mg/kg Inf_C1 Flow of influent soluble C kg/day C1_Inf Stock of influent soluble C kg C1_o Flow of influent soluble C kg/day O2_C1 Stock of soluble C in cBOD reactor kg C1_O2 Flow of soluble C from cBOD reactor kg/day Nit_C1 Stock of soluble C in nitrification reactor kg C1_n Flow of soluble C from nitrification reactor kg/day Denit_C1 Stock of soluble C in denitrification reactor kg C1_dn Flow of soluble C from denitri fi cation reactor; effluent kg/day Inf_Insol_C Influent concentration of nonsoluble C mg/L

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153 Appendix A (Continued) Table A15 (cont.) Notation in Model Description Units or Value Inf_C2 Flow of influent insoluble C kg/day C2_Inf Stock of influent insoluble C kg C2_o Flow of influent insoluble C kg/day O2_C2 Stock of insoluble C in cBOD reactor kg C2_O2 Flow of insoluble C from cBOD reactor kg/day Nit_C2 Stock of insoluble C in nitrification reactor kg C2_n Flow of insoluble C from nitrification reactor kg/day Denit_C2 Stock of insoluble C in denitrification reactor kg C2_dn Flow of insoluble C from denitrification reactor kg/day C_Eff Stock of effluent total carbon from the system kg C_Eff_t Flow of effluent total carbon from the system kg/day O2_kC1_to_C4 Rate of conversion of soluble carbon to carbon dioxide in cBOD reactor /day O2_C1_to_C4 Flow of soluble carbon to carbon dioxide from cBOD reactor kg/day O2_kC1_to_C3 Rate of conversion of soluble carbon to organic carbon in cBOD reactor /day O2_C1_to_C3 Flow of soluble carbon to organic carbon from cBOD reactor kg/day Nit_kC1_to_C4 Rate of conversion of soluble carbon to carbon dioxide in nitrification reactor /day Nit_C1_to_C4 Flow of soluble carbon to carbon dioxide from nitrification reactor kg/day Nit_kC1_to_C3 Rate of conversion of soluble carbon to organic carbon in nitrification reactor /day Nit_C1_toC3 Flow of soluble carbon to organic carbon from nitrification reactor kg/day O2_kC1_to_C4 Rate of conversion of soluble carbon to carbon dioxide in cBOD reactor /day O2_C1_to_C4 Flow of soluble carbon to carbon dioxide from cBOD reactor kg/day O2_kC1_to_C3 Rate of conversion of soluble carbon to organic carbon in cBOD reactor /day O2_C1_to_C3 Flow of soluble carbon to organic carbon from cBOD reactor kg/day Nit_kC1_to_C4 Rate of conversion of soluble carbon to carbon dioxide in nitrification reactor /day Nit_C1_to_C4 Flow of soluble carbon to carbon dioxide from nitrification reactor kg/day

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154 Appendix A (Continued) Table A15 (cont.) Notation in Model Description Units or Value Nit_kC1_to_C3 Rate of conversion of soluble carbon to organic carbon in nitrification reactor /day Nit_C1_to C3 Flow of soluble carbon to organic carbon from nitrification reactor kg/day Table A16 List of equations in soluble and nonsoluble carbon species model framework Notation Equation Init ial Value Component Inf_C1 = Calc_Flow*Inf_Sol_C/mg_to_kg n/a flow C1_Inf(t) = C1_Inf(t dt) + (Inf_C1 C1_o) dt 0 stock C1_o = Inf_C1 n/a flow O2_C1(t) = O2_C1(t dt) + (C1_o C1_O2 O2_C1__to_C3 O2_C1_to_C4) dt 0 stock O2_C1_to_C4 = C1_o*O2_kC1_to_C4 n/a flow O2_C1_to_C3 = C1_o*O2_kC1_to_C3 n/a flow C1_O2 = C1_o O2_C1_to_C4 O2_C1__to_C3 n/a flow Nit_C1(t) = Nit_C1(t dt) + (C1_O2 C1_n Nit_C1_to_C3 Nit_C1_to_C4) dt 0 stock Nit_C1_to_C4 = C1_O2*Nit_kC1__to_C4 n/a flow Nit_C1_to_C3 = Nit_kC1_to_C3*C1_O2 n/a flow C1_n = C1_O2 Nit_C1_to_C3 Nit_C1_to_C4 n/a flow Denit_C1(t) = Denit_C1(t dt) + (C1_n C1_dn) dt 0 stock C1_dn = C1_n n/a flow Inf_C2 = Calc_Flow*Inf_Insol_C/mg_to_kg n/a flow C2_Inf(t) = C2_Inf(t dt) + (Inf_C2 C2_o) dt 0 stock C2_o = Inf_C2 n/a flow O2_C2(t) = O2_C2(t dt) + (C2_o C2_O2) dt 0 stock C2_O2 = C2_o n/a flow Nit_C2(t) = Nit_C2(t dt) + (C2_O2 C2_n) dt 0 stock C2_n = C2_O2 n/a flow Denit_C2(t) = Denit_C2(t dt) + (C2_n C2_dn) dt 0 stock C2_dn = C2_n n/a flow C_Eff(t) = C_Eff(t dt) + (C1_dn + C3_dn + C4_dn + C2_dn C_Eff_t) dt 0 stock C_Eff_t = C1_dn+C2_dn+C3_dn+C4_dn n/a flow

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155 Appendix A (Continued) Carbon Flow through Treatment Plant Organic Carbon and Carbon Dioxide Figure A9 Flow of organic carbon and carbon dioxide in STELLA model. Table A 17 List of variables in organic carbon and carbon dioxide species model framework. Notation in Model Description Units or Value Inf_Cellular_C Concentration of influent cellular C mg/L Inf_C3 Flow of influent cellular C kg/day C3_Inf Stock of influent cellular C kg C3_o Flow of influent cellular C kg/day O2_C3 Stock of cellular C in cBOD reactor kg C3_O2 Flow of cellular C from cBOD reactor kg/day Nit_C3 Stock of cellular C in nitrificat i on reactor kg C3_n Flow of cellular C from nitrification reactor kg/day Denit_C3 Stock of cellular C in denitrificat i on reactor kg C3_dn Flow of cellular C from denitrification reactor kg/day Calc_Flow Flow of water through system L/day mg_to_kg Conversion of mg to kg 1000mg/kg Inf_CO2 Concentration of influent CO2 mg/L Inf_C4 Flow of influent CO2 kg/day C4_Inf Stock of influent CO2 k g

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156 Appendix A (Continued) Table A17 (cont.) Notation in Model Description Units or Value C4_o Flow of influent CO2 kg/day O2_C4 Stock of CO2 in cBOD reactor k g C4_O2 Flow of CO2 from cBOD reactor kg/day Nit_C4 Stock of CO2 in nitrification reactor k g C4_n Flow of CO2 from nitrification reactor kg/day Denit_C4 Stock of CO2 in denitrification reactor kg C4_dn Flow of CO2 from denitrification reactor kg/day C4_to_A Flow of CO2 assimilated in algae in PPOR kg/day C4_assim Flow of CO2 assimilated in algae in PPOR kg/day C4_to_A2 Flow of CO2 assimilated in algae in PNR kg/day C4_assim_PNR Flow of CO2 assimilated in algae in PNR kg/day Table A18 List of equations in organic carbon and carbon dioxide species model framework. Notation Equation Initial Value Component Inf_C3 = Calc_Flow*Inf_Cellular_C/mg_to_kg n/a flow C3_inf(t) = C3_Inf(t dt) + (Inf_C3 C3_o) dt 0 stock C3_0 = Inf_C3 n/a flow O2_C3(t) = O2_C3(t dt) + (C3_o + O2_C1__to_C3 C3_O2) dt 0 stock C3_O2 = C3_o+O2_C1__to_C3 n/a flow Nit_C3(t) = Nit_C3(t dt) + (C3_O2 + Nit_C1_to_C3 C3_n) dt 0 stock C3_n = C3_O2+Nit_C1_to_C3 n/a flow Denit_C3(t) = Denit_C3(t dt) + (C3_n C3_dn) dt 0 stock C3_dn = C3_n n/a flow Inf_C4 = Calc_Flow*Inf_CO2/mg_to_kg n/a flow C4_Inf(t) = C4_Inf(t dt) + (Inf_C4 C4_o) dt 0 stock C4_o = Inf_C4 n/a flow O2_C4(t) = O2_C4(t dt) + (C4_o + O2_C1_to_C4 C4_O2) dt 0 stock C4_O2 = C4_o+O2_C1_to_C4 n/a flow Nit_C4(t) = Nit_C4(t dt) + (C4_O2 + Nit_C1_to_C4 C4_n C4_to_A) dt 0 stock

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157 Appendix A (Continued) Table A18 (cont.) Notation Equation Initial Value Component C4_to_A = C4_assim n/a flow C4_n = C4_O2+Nit_C1_to_C4 C4_to_A n/a flow Denit_C4(t) = Denit_C4(t dt) + (C4_n C4_dn C4_to_A2) dt 0 stock C4_to_A2 = C4_assim_PNR n/a flow C4_dn = C4_n C4_to_A2 n/a flow Carbon Mass Balance Figure A10 Carbon mass balance in STELLA m odel Table A19 List of variables in carbon mass balance framework Notation in Model Description Units or Value Inf_C1 Flow of influent soluble carbon kg/day Inf_C2 Flow of influent nonsoluble carbon kg/day Inf_C3 Flow of influent cellular carbon kg/day Inf_C4 Flow of influent CO2 kg/day TC_MB_o Flow of influent total carbon species kg/day TC_Mbo Stock of total influent carbon species kg TC_MB_In Flow of influent total carbon species kg/day

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158 Appendix A (Continued) Table A19 (cont.) Notation in Model Description Units or Value C1_dn Flow of effluent soluble carbon kg/day C2_dn Flow of effluent insoluble carbon kg/day C3_dn Flow of effluent cellular carbon kg/day C4_dn Flow of effluent CO2 kg/day C4_to_A Flow of CO2 assimilated to algae in PPOR kg/day C4_to_A2 Flow of CO2 assimilated to algae in PNR kg/day TC_MB_e Flow of total effluent carbon species kg/day TN_Mbe Stock of total effluent carbon species k g TC_MB_Out Flow of total effluent carbon species kg/day Table A20 List of equations in carbon mass balance framework Notation Equation Initial Value Component TC_MB_o = Inf_C1+Inf_C2+Inf_C3+Inf_C4 n/a flow TC_Mbo(t) = TC_MBo(t dt) + (TC_MB_o TC_MB_In) dt 0 stock TC_MB_In = TC_MB_o n/a flow TC_MB_e = C1_dn+C2_dn+C3_dn+C4_dn+C4_to_A+ C4_to_A2 n/a flow TN_Mbe(t) = TN_MBe(t dt) + (TC_MB_e TC_MB_Out) dt 0 stock TC_MB_Out = TC_MB_e n/a flow

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159 Appendix A (Continued) Specific Growth Rate in the PPOR Figure A11 Calculated specific growth rate in the PPOR. Table A2 1 List of variables in calculating specific growth rate in the PPOR Notation in Model Description Units or Value Q_o Flow of water from BOD reactor L/day Percent_Flow_to_PPOR Percent of water from BOD reactor diverted to PPOR unitless HRT_PPOR HRT of the PPOR days Vol_O2_Basin volume of the PPOR L PPOR Switch to divert water to PPOR unitless umax NH3 max for growth on NH3 /day K_NH3 half saturation constant for ammonia kg/L K_CO2 half saturation constant for carbon dioxide kg/L K_Psol half saturation constant for soluble phosphorous kg/L PPOR_b decay rate of algae in PPOR /day u_calc_PPOR calculated in PPOR for growth on ammonia /day u_calc_PPOR_2 stock for calculated /day N2_Accum_PPOR nitrogen accumulated in the PPOR kg C4_Accum_PPOR carbon accumulated in the PPOR kg P1_Accum_PPOR phosphorous accumulated in the PPOR kg

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160 Appendix A (Continued) Table A22 List of equations in calculating specific growth rate in the PPOR Notation Equation Initial Value Component Vol_O2_A_Basin = HRT_PPOR*(Percent_Flow__to_PP OR*Q_o) n/a converter u_calc_PPOR = ((umax__NH3*(MIN(((N2_Accum_P POR)/((K_NH3*Vol_O2__A_Basin)+ (N2_Accum_PPOR))),((P1_Accum_ PPOR)/((K_Psol*Vol_O2__A_Basin) +(P1_Accum_PPOR))),((C4_Accum _PPOR)/((C4_Accum_PPOR)+(K_C O2*Vol_O2__A_Basin)))))) PPOR_b)*PPOR n/a flow u_calc_PPOR_2(t) = u_calc_PPOR_2(t dt) + (u_calc_PPOR) dt 0 stock N2_Accum_PPOR(t) = N2_to_Algae*HRT_PPOR 0 stock C4_Accum_PPOR(t) = C4_to_Algae*HRT_PPOR 0 stock P1_Accum_PPOR(t) = P1_to_Algae*HRT_PPOR 0 stock SRT in PPOR Figure A12 SRT in the PPOR. Table A23 List of variables for SRT framework in the PPOR Notation in Model Description Units or Value X_accumulated_PPOR mass of algae in PPOR kg PPOR_Amount mass of algae removed from PPOR kg PPOR_Freq frequency of algae removal from PPOR days SRT_PPOR time algae remains in the PPOR days

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161 Appendix A (Continued) Table A24 List of equations for SRT framework in the PPOR Notation Equation Initial Value Component X_accumulated_PPOR = X_accumulated_PNR(t dt) + (X_generated_PNR Harvest_Rate_PNR) dt 10 stock SRT_PPOR = X_accumulated_PPOR/(PPOR_A mount/PPOR_Freq) n/a converter Algae Growth in PPOR Figure A13 Algae growth framework in the PPOR in the STELLA m odel Table A25. List of variables for a lgae growth in the PPOR Notation in Model Description Units or Value u_calc_PPOR calculated specific growth rate in PPOR /day X_generated_PPOR algae growth kg/day X_accumulated PPOR mass of algae in PPOR kg PPOR_Amount mass of algae removed from PPOR kg PPOR_%_Removed percent of accumulated algae in PPOR to be removed unitless PPOR Harvest Freq frequency of algae harvesting days PPOR Freq frequency of algae harvesting days PPOR Init Rem initial harvest time days

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162 Appendix A (Continued) Table A25. (cont.) Notation in Model Description Units or Value PPOR Init initial harvest time days Harvest PPOR flow of algae being harvested kg/day Table A26. List of equations for a lgae growth in the PPOR. Notation Equation Initial Value Component X_generated_PPOR = X_accumulated_PPOR*u_calc_P POR n/a flow X_accumulated_PPOR(t) = X_accumulated_PNR(t dt) + (X_generated_PNR Harvest_Rate_PNR) dt 10 stock Harvest_PPOR = Pulse((PPOR_Amount),PPOR_In it,PPOR_Freq) n/a flow Nitrogen Utilization in the PPOR Figure A14 Nitrogen utilization in the PPOR. Table A 27 List of variables in nitrogen utilization framework in the PPOR Notation in Model Description Units or Value Percent Flow to PPOR percent of flow diverted from water flow to plant unitless PPOR switch to turn on PPOR unitless N2 to Algae flow of nitrogen to PPOR kg/day N2 O2 flow of nitrogen from BOD reactor kg/day N2 Accum PPOR nitrogen available in the PPOR kg N2 from PPOR flow of nitrogen leaving the PPOR kg/day

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163 Appendix A (Continued) Table A27 (cont.). Notation in Model Description Units or Value N2 assim flow of nitrogen assimilated in algae kg/day q N2 nitrogen substrate utilization rate kg/kg day X generated PPOR algae growth in PPOR kg N2 accum in algae amount of nitrogen accumulated in algae kg Table A28 List of equations in nitrogen utilization framework in the PPOR Notation Equation Initial Value Component N2_to_Algae = N2_O2*Percent_Flow__to_PPOR*PP OR n/a flow N2_Accum_PPO R(t) = N2_Accum_PPOR(t dt) + (N2_to_Algae N2_from_PPOR N2_assim) dt N2_to_Al gae*HRT_ PPOR stock N2_assim = X_generated_PPOR*q_N2 n/a flow N2_accum_in_alg ae(t) = N2_accum_in_algae(t dt) + (N2_assim) dt N2_assim stock N2_from_PPOR = N2_to_Algae N2_assim n/a flow Carbon Utilization in the PPOR Figure A15 Carbon utilization in the PPOR.

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164 Appendix A (Continued) Table A29 List of variables in carbon utilization framework in the PPOR Notation in Model Description Units or Value Percent Flow to PPOR percent of flow diverted from water flow to plant unitless C4 O2 flow of carbon from BOD reactor kg/day PPOR switch to turn on PPOR unitless C4 to Algae flow of carbon to PPOR kg/day C4 Accum PPOR mass of carbon available in PPOR kg C4 from PPOR flow of carbon leaving PPOR kg/day C4 assim amount of carbon assimilated in algae kg/day q C4 carbon substrate utilization rate kg/kg day X generated PPOR algae growth in PPOR kg/day C4 accum in algae carbon accumulated in algae k g Table A30 List of equations in carbon utilization framework in the PPOR Notation Equation Initial Value Component C4_to_Algae = C4_O2*Percent_Flow__to_PPOR* PPOR n/a flow C4_Accum_PPOR(t) = C4_Accum_PPOR(t dt) + (C4_to_Algae C4_from_PPOR C4_assim) dt C4_to_Alg ae*HRT_ PPOR stock C4_assim = X_generated_PPOR*q_C4 n/a flow C4_accum_in_algae(t ) = C4_accum_in_algae(t dt) + (C4_assim) dt 0 stock C4_from_PPOR = C4_to_Algae C4_assim n/a flow

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165 Appendix A (Continued) Phosphorous Utilization in PPOR Figure A16 Phosphorous utilization in the PPOR. Table A 3 1 List of variables in phosphorous utilization framework in the PPOR. Notation in Model Description Units or Value Percent Flow to PPOR percent of flow diverted from water flow to plant unitless PPOR switch to turn on PPOR unitless P1 to Algae flow of phosphorous to PPOR kg/day P1 O2 flow of phosphorous from BOD reactor kg/day P1 Accum PPOR phosphorous available in the PPOR kg P1 from PPOR flow of phosphorous leaving the PPOR kg/day P1 assim flow of phosphorous assimilated in algae kg/day q P1 phosphorous substrate utilization rate kg/kg day X generated PPOR algae growth in PPOR kg P1 accum in algae amount of phosphorous accumulated in algae kg

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166 Appendix A (Continued) Table A32 List of equations in phosphorous utilization framework in the PPOR. Notation Equation Initial Value Component P1_to_Algae = P1_O2*Percent_Flow__to_PPOR*PP OR n/a flow P1_Accum_PPOR (t) = P1_Accum_PPOR(t dt) + (P1_to_Algae P1_from_PPOR P1_assim) dt P1_to_A lgae*HR T_PPO R stock P1_assim = X_generated_PPOR*q_P1 n/a flow P1_accum_in_alga e(t) = P1_accum_in_algae(t dt) + (P1_assim) dt 0 stock P1_from_PPOR = P1_to_Algae P1_assim n/a flow Substrate Utilization Rate in PPOR Figure A17 Substrate utilization rate in the PPOR in STELLA m odel

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167 Appendix A (Continued) Table A 33 List of variables for substrate utilization rate framework in the PPOR. Notation in Model Description Units or Value Y_NH3 PPOR half saturation constant for ammonia unitless q_N2 nitrogen substrate utilization rate unitless q_N2_stock accumulation of q kg/day u_calc_PPOR calculated specific growth rate in PPOR kg/day Y_CO2 PPOR half saturation constant for carbon k g q_C4 carbon substrate utilization rate kg/day q_C4_stock accumulation of q kg/day Y_Psol PPOR half saturation constant for phos p horous kg/kg day q_P1 phosphorous substrate utilization rate kg q_P1_stock accumulation of q kg Table A34 List of equations for substrate utilization rate framework in the PPOR. Notation Equation Initial Value Component q_N2 = u_calc_PPOR/Y_NH3_PPOR n/a flow q_N2_stock(t) = q_N2_stock(t dt) + (q_N2) dt 0 stock q_C4 = u_calc_PPOR/Y_CO2_PPOR n/a flow q_C4_stock(t) = q_C4_stock(t dt) + (q_C4) dt 0 stock q_P1 = u_calc_PPOR/Y_Psol_PPOR n/a flow q_P1_stock(t) = q_P1_stock(t dt) + (q_P1) dt 0 stock

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168 Appendix A (Continued) Specific Growth Rate in PNR Figure A18 Specific growth rate in the PNR. Table A 35 List of variables for specific growth rate in the PNR Notation in Model Description Units or Value Q_O2 Flow of water from nitrification reactor L/day Percent_Flow_to_PNR Percent of water from nitrification reactor diverted to PNR unitless HRT_PNR HRT of the PNR days Vol_Nit_Basin volume of the PNR L PNR Switch to divert water to PNR unitless umax NO3 max for growth on NO3 /day K_Nox half saturation constant for nitrate kg/L K_CO2 half saturation constant for carbon dioxide kg/L K_Psol half saturation constant for soluble phosphorous kg/L PNR_b decay rate of algae in PNR /day u_calc_PNR calculated in PNR for growth on nitrate /day u_calc_PNR_2 stock for calculated /day N3_Accum_PNR nitrogen accumulated in the PNR kg C4_Accum_PNR carbon accumulated in the PNR kg P1_Accum_PNR phosphorous accumulated in the PNR kg

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169 Appendix A (Continued) Table A36 List of equations for specific growth rate in the PNR Notation Equation Initial Value Component Vol_Nit_A_Basin = HRT_PNR*(Q_O2*Percent_Flow_ _to_PNR) n/a converter u_calc_PNR = ((umax_NO3*(MIN(((N3_Accum_P NR/Vol_Nit_A__Basin)/((K_NOx)+ (N3_Accum_PNR/Vol_Nit_A__Ba sin))),((P1_Accum_PNR/Vol_Nit_ A__Basin)/((K_Psol)+(P1_Accum_ PNR/Vol_Nit_A__Basin))),((C4_Ac cum_PNR/Vol_Nit_A__Basin)/((K_ CO2)+(C4_Accum_PNR/Vol_Nit_ A__Basin)))))) PNR_b)*P NR n/a flow u_calc_PNR_2(t) = u_calc_PNR_2(t dt) + (u_calc_PNR) dt 0 stock N3_Accum_PNR(t) = N3_accum_in_PNR(t dt) + (N3_assim__PNR) dt N3_to_PNR *HRT_PNR stock C4_Accum_PNR(t) = C4_accum_in_PNR(t dt) + (C4_assim_PNR) dt C4_to_PNR *HRT_PNR stock P1_Accum_PNR(t) = P1_accum_in_PNR(t dt) + (P1_assim_PNR) dt P1_to_PNR *HRT_PNR stock SRT in PNR Figure A19 SRT framework in the PNR in the STELLA m odel Table A 37 List of variables for SRT framework in the PNR Notation in Model Description Units or Value X_accumulated_PNR mass of algae in PNR kg Amount mass of algae removed from PNR kg Frequency_PNR frequency of algae removal from PNR days SRT_PNR time algae remains in the PNR days

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170 Appendix A (Continued) Table A38. List of equations for SRT framework in the PNR Notation Equation Initial Value Component X_accumulated_ PNR(t) = X_accumulated_PNR(t dt) + (X_generated_PNR Harvest_Rate_PNR) dt 10 stock SRT_PNR = X_accumulated_PNR/(Amount/Frequency__ PNR) n/a converter Algae Growth in PNR Figure A20 Algae growth framework in the PNR Table A 39 List of variables for a lgae growth in the PNR. Notation in Model Description Units or Value u_calc_PNR calculated specific growth rate in PNR /day X_generated_PNR algae growth kg/day X_accumulated PNR mass of algae in PNR kg Amount mass of algae removed from PNR kg PPOR_%_Rem percent of accumulated algae in PNR to be removed unitless PNR Harvest Freq frequency of algae harvesting days Frequency PNR frequency of algae harvesting days PNR Init Rem initial harvest time days Init PNR initial harvest time days Harvest Rate PPOR flow of algae being harvested kg/day

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171 Appendix A (Continued) Table A40 List of equations for a lgae growth in the PNR. Notation Equation Initial Value Component X_generated_PNR = X_accumulated_PNR*u_calc_PNR n/a flow X_accumulated_PN R(t) = X_accumulated_PNR(t dt) + (X_generated_PNR Harvest_Rate_PNR) dt 10 stock Harvest_PNR = Pulse((Amount),Init_PNR,Frequency__P NR) n/a flow Nitrogen Utilization in PNR Figure A21 Nitrogen utilization framework for the P NR. Table A4 1 List of variables in nitrogen utilization framework in the P N R. Notation in Model Description Units or Value Percent Flow to PNR percent of flow diverted from water flow to plant unitless PNR switch to turn on PNR unitless N3 to PNR flow of nitrogen to PNR kg/day N3 n flow of nitrogen from nitrification reactor kg/day N3 Accum PNR nitrogen available in the PNR kg

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172 Appendix A (Continued) Table A4 1 (cont) Notation in Model Description Units or Value N3 from PNR flow of nitrogen leaving the PNR kg/day N3 assim flow of nitrogen assimilated in algae kg/day q N3 PNR nitrogen substrate utilization rate kg/kg day X generated PNR algae growth in PNR kg N3 accum in algae amount of nitrogen accumulated in algae kg Table A42 List of equations in nitrogen utilization framework in the P N R. Notation Equation Initial Value Component N3_to_PNR = N3_n*PNR*Percent_Flow__to_PNR n/a F low N3_Accum_PN R(t) = N3_Accum_PNR(t dt) + (N3_to_PNR N3_from_PNR N3_assim__PNR) dt N3_to_PN R*HRT_P NR S tock N3_assim_PNR = X_generated_PNR*q_N3_PNR n/a F low N3_accum_in_ PNR(t) = N3_accum_in_PNR(t dt) + (N3_assim__PNR) dt N3_assim __PNR S tock N3_from_PPO R = N3_to_PNR N3_assim__PNR n/a F low Carbon Utilization in the PNR Figure A22 Carbon utilization framework in the PNR.

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173 Appendix A (Continued) Table A 43 List of variables in carbon utilization framework in the PNR Notation in Model Description Units or Value Percent Flow to PNR percent of flow diverted from water flow to plant U nitless C4 n flow of carbon from nitrification reactor kg/day PNR switch to turn on PNR U nitless C4 to PNR flow of carbon to PNR kg/day C4 Accum PNR mass of carbon available in PNR K g C4 from PNR flow of carbon leaving PNR kg/day C4 assim PNR amount of carbon assimilated in algae kg/day q C4 PNR carbon substrate utilization rate kg/kg day X generated PNR algae growth in PNR kg/day C4 accum in PNR carbon accumulated in algae K g Table A44. List of equations in carbon utilization framework in the PNR Notation Equation Initial Value Component C4_to_PNR = C4_n*PNR*Percent_Flow__to_PNR n/a F low C4_Accum_PN R(t) = C4_Accum_PNR(t dt) + (C4_to_PNR C4_from_PNR C4_assim_PNR) dt C4_to_P NR*HRT _PNR S tock C4_assim_PNR = X_generated_PNR*q_C4_PNR n/a F low C4_accum_in_ PNR(t) = C4_accum_in_PNR(t dt) + (C4_assim_PNR) dt 0 S tock C4_from_PNR = C4_to_PNR C4_assim_PNR n/a F low

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174 Appendix A (Continued) Phosphorous Utilization in the PNR Figure A23 Phosphorous utilization framework in the P N R Table A 45 List of variables in phosphorous utilization framework in the P N R. Notation in Model Description Units or Value Percent Flow to PNR percent of flow diverted from water flow to plant unitless PNR switch to turn on PNR unitless P1 to PNR flow of phosphorous to PNR kg/day P1 n flow of phosphorous from nitrification reactor kg/day P1 Accum PNR phosphorous available in the PNR kg P1 from PNR flow of phosphorous leaving the PNR kg/day P1 assim PNR flow of phosphorous assimilated in algae kg/day q P1 PNR phosphorous substrate utilization rate kg/kg day X generated PNR algae growth in PNR kg P1 accum in PNR amount of phosphorous accumulated in algae kg

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175 Appendix A (Continued) Table A46. List of equations in phosphorous utilization framework in the P N R. Notation Equation Initial Value Component P1_to_PNR = PNR*P1_n*Percent_Flow__to_PNR n/a flow P1_Accum_PN R(t) = P1_Accum_PNR(t dt) + (P1_to_PNR P1_from_PNR P1_assim_PNR) dt P1_to_PNR* HRT_PNR stock P1_assim_PNR = X_generated_PNR*q_P1_PNR n/a flow P1_accum_in_ PNR(t) = P1_accum_in_PNR(t dt) + (P1_assim_PNR) dt 0 stock P1_from_PNR = P1_to_PNR P1_assim_PNR n/a flow Substrate Utilization Rate in the PNR Figure A24 Substrate utilization rate framework in the PNR.

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176 Appendix A (Continued) Table A 47 List of variables for substrate utilization rate framework in the PNR Notation in Model Description Units or Value Y_NOx PNR half saturation constant for nitrate unitless q_N3_PNR nitrogen substrate utilization rate unitless q_N3_stock accumulation of q kg/day u_calc_PNR calculated specific growth rate in PNR kg/day Y_CO2 PNR half saturation constant for carbon kg q_C4_PNR carbon substrate utilization rate kg/day q_C4_stock_2 accumulation of q kg/day Y_Psol PNR half saturation constant for phosphorous kg/kg day q_P1_PNR phosphorous substrate utilization rate kg q_P1_stock_2 accumulation of q kg Table A48 List of equations for substrate utilization rate framework in the PNR Notation Equation Initial Value Component q_N3_PNR = u_calc_PNR/Y_NOx_PNR n/a flow q_N3_stock(t) = q_N3_stock(t dt) + (q_N3_PNR) dt 0 stock q_C4_PNR = u_calc_PNR/Y_CO2_PNR n/a flow q_C4_stock_2(t) = q_C4_stock_2(t dt) + (q_C4_PNR) dt 0 stock q_P1_PNR = u_calc_PNR/Y_Psol_PNR n/a flow q_P1_stock_2(t) = q_P1_stock_2(t dt) + (q_P1_PNR) dt 0 stock

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177 Appendix A (Continued) Cost Savings from Reduced Aeration Figure A25 Cost savings from reduced aeration framework in the STELLA m odel Table A 49 List of variables for cost savings from reduced aeration. Notation in Model Description Units or Value Cost Aeration per kg NH3 estimated cost to nitrify kg NH3 $/kg $kgNH3 estimated cost to nitrify kg NH3 $/kg Harvest PPOR algae harvested from PPOR kg/day N2 assim nitrogen assimilated by algae in PPOR kg/day O2 in oxygen savings calculated $/day molO2 per molA stoichiometric ratio of oxygen to algae during growth unitless kgN per kgA stoichiometric ratio of oxygen to algae during growth unitless molO2 per NH3 stoichiometric ratio of oxygen to nitrogen unitless O2 Saved2 stock of oxygen saved $ O2 Benefits oxygen savings calculated $/day Table A50. List of equations for cost savings from reduced aeration. Notation Equation Initial Value Component O2_in = (molO2_per_molA*(1/mol_O2_per_NH3)*kgN _per_kgA*$kgNH3*Harvest_PPOR)+(N2_assi m*$kgNH3) n/a flow O2_saved2(t) = O2_Saved2(t dt) + (O2_in O2_Benefits) dt 0 stock O2_Benefits = O2_in n/a flow

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178 Appendix A (Continued) Cost Savings from Reduced Chemical Demand Figure A26 Cost savings from reduced chemical demand framework. Table A51 List of variables for cost savings from reduced chemical demand. Notation in Model Description Units or Value Cost per L MeOH cost of methanol per liter $/L MeOH NO3 mass stoichiometric ratio of methanol to nitrate (mass) unitless N3 assim PNR nitrate assimilated in the PNR kg/day MeOH L to kg amount of methanol (volume) per mass L/kg MeOH per NO3 stoichiometric ratio of methanol to nitrate (moles) unitless MeOH In flow of cost savings from reduced methanol $/day MeOH Saved stock of cost savings from reduced methanol $ MeOH Benefits flow of cost savings from reduced methanol $/day Table A52 List of equations for cost savings from reduced chemical demand. Notation Equation Initial Value Component MeOH_In = (MeOH_NO3__mass*(N3_assim__PNR)* Cost_per_L_MeOH)/MeOH_L__to_kg n/a flow MeOH_Saved (t) = MeOH_Saved(t dt) + (MeOH_In MeOH__Benefits) dt 0 stock MeOH_Benefits = MeOH_In n/a flow

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179 Appendix A (Continued) Biogas Calculations Figure A27 Biogas processing framework in the STELLA m odel Tab le A 53 List of variables for biogas processing framework Notation in Model Description Units or Value Harvesting Costs cost of harvesting biomass $/kg Cost of Biomass Production cost of biomass production $/kg BG Process biogas total processing costs $/kg Labor Costs cost of labor in processing costs $/kg BG Est Costs cost of biogas production $/kg A to BG Costs total costs of biogas production $/kg Biogas Costs stock of total costs $

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180 Appendix A (Continued) Tab le A53 (cont.) Notation in Model Description Units or Value BG Costs total costs of biogas production $/kg Biogas switch to turn on biogas processing unitless Harvest PPOR flow of algae from PPOR kg/day Harvest Rate PNR flow of algae from PNR kg/day Profit BG stock of total costs minus total benefits $ BG Profit flow of overall profit $/day MeOH Benefits cost savings from reduced chemical additives $/day O2 Benefits cost savings from reduced aeration $/day CH4gCOD methane production per unit COD L/kg gCOD_galgae mass of COD per mass of algae kg/kg Biogas $ per L sale price of biogas per L $/L A to BG Benefits total benefits of biogas production $/day Biogas Benefits stock of total benefits of biogas production $ BG Benefits total benefits of biogas production $/day Tab le A54 List of equations for biogas processing framework Notation Equation Initial Value Component BG_Process = BG_Est_Costs+Labor_Costs n/a converter A_to_BG_ Costs = Biogas*(((Harvest_PPOR+Harvest_Rate_PNR)* BG_Process)+((Harvest_PPOR+Harvest_Rate_ PNR)*Cost_of_Biomass_Production)+(Harvestin g_Costs*(Harvest_PPOR+Harvest_Rate_PNR))) n/a flow Biogas Costs(t) = Biogas_Costs(t dt) + (A_to_BG_Costs BG_Costs) dt 0 stock BG_Costs = A_to_BG_Costs n/a flow A_to_BG_ Benefits = Biogas*(MeOH__Benefits+O2_Benefits+((Harves t_PPOR+Harvest_Rate_PNR)*CH4gCOD*gCOD __galgae*Biogas_$__per_L)) n/a flow Biogas_ Benefits(t) = Biogas_Benefits(t dt) + (A_to_BG_Benefits BG_Benefits) dt 0 stock BG_Benefits = A_to_BG_Benefits n/a flow Profit_BG(t) = Profit_BG(t dt) + (BG_Costs + BG_Benefits BG_Profit) dt 0 stock BG_Profit = BG_Benefits BG_Costs n/a flow

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181 Appendix A (Continued) Biodiesel Calculations Figure A28 Biodiesel processing framework in the STELLA m odel Table A 55 List of variables for biodiesel processing framework Notation in Model Description Units or Value Harvesting Costs cost of harvesting biomass $/kg Cost of Biomass Production cost of biomass production $/kg Secondary Fertilizer switch to turn on further processing to fertilizer unitless Secondary Biogas switch to turn on further processing to biogas unitless Cost BD Production cost of biodiesel production $/kg

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182 Appendix A (Continued) Table A55 (cont.) Notation in Model Description Units or Value Oil Percent Per Biomass percent of biomass that is oil unitless Cost Fert Prod cost of fertilizer production $/kg BG Process cost of biogas production $/kg A to BD Costs flow of biodiesel costs $/day Biodiesel Costs stock of biodiesel costs $ BD Costs flow of biodiesel costs $/day Harvest PPOR flow of algae harvested from PPOR kg/day Harvest Rate PNR flow of algae harvested from PNR kg/day Biodiesel switch to turn on biodiesel processing unitless No Further Process switch to turn off any further processing of biomass unitless Biodiesel $ per L cost of biodiesel per volume of biodiesel $/L Fertilizer $ per kg cost of fertilizer per kg produced $/kg CH4gCOD methane production per unit COD L/kg Biogas $ per L sale price of biogas per L $/L gCODgalgae mass of COD per mass of algae kg/kg MeOH Benefits cost savings from reduced chemical additives $/day O2 Benefits cost savings from reduced aeration $/day Oil Lkg density of biodiesel L/kg A to BD Benefits flow of biodiesel benefits $/day Biodiesel Benefits stock of biodiesel benefits $ BD Benefits flow of biodiesel benefits $/day Profit BD stock of biodiesel profit $ BD Profit flow of biodiesel profit $/day

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183 Appendix A (Continued) Table A56 List of equations for biodiesel processing framework Notation Equation Initial Value Component A_to_BD_ Costs = Biodiesel*(((Harvest_PPOR+Harvest_Rate_PNR)*C ost_BD_Prod)+((Harvest_PPOR+Harvest_Rate_PN R)*Cost_of_Biomass_Production)+(Harvesting_Cost s*(Harvest_PPOR+Harvest_Rate_PNR))) + (Secondary_Fertilizer*((1 Oil_Percent_Per_Biomass)*(Harvest_PPOR+Harves t_Rate_PNR)) *Cost_Fert_Prod) + (Secondary_Biogas*((1 Oil_Percent_Per_Biomass)*(Harvest_PPOR+Harves t_Rate_PNR))*BG_Process) n/a flow Biodiesel Costs(t) = Biodiesel_Costs(t dt) + (A_to_BD_Costs BD_Costs) dt 0 stock BD_Costs = A_to_BD_Costs n/a flow A_to_BD_ Benefits = Biodiesel*(MeOH__Benefits+O2_Benefits+ ((Harvest_PPOR+Harvest_Rate_PNR)*Oil_Percent_ Per_Biomass*Oil_Lkg*Biodiesel_$_per_L)) + (Secondary_Biogas*((1 Oil_Percent_Per_Biomass)*(Harvest_PPOR+Harves t_Rate_PNR)*CH4gCOD*gCOD__galgae*Biogas_$_ _p er_L)) + (Secondary_Fertilizer*((1 Oil_Percent_Per_Biomass)*(Harvest_PPOR+Harves t_Rate_PNR)*Fertilizer_$_per_kg)) n/a flow Biodiesel_ Benefits(t) = Biodiesel_Benefits(t dt) + (A_to_BD_Benefits BD_Benefits) dt 0 stock BD_ Benefits = A_to_BD_Benefits n/a flow Profit_BD (t) = Profit_BD(t dt) + (BD_Costs + BD_Benefits BD_Profit) dt 0 stock BD_Profit = BD_Benefits BD_Costs n/a flow

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184 Appendix A (Continued) Fertilizer Calculations Figure A29 Fertilizer processing framework in the STELLA m odel Table A 57 List of variables for fertilizer processing framework Notation in Model Description Units or Value Harvesting Costs cost of harvesting biomass $/kg Cost of Biomass Production cost of biomass production $/kg Cost Fert Prod cost of fertilizer production $/kg A to Fert Costs flow of costs of fertilizer production $/day Fert Costs stock of fertilizer costs $ MJ per kg energy required for fertilizer production MJ/kg kWh per MJ conversion of kWh to MJ kWh/MJ $ per kWh cost of kWh $/kWh F Costs flow of costs of fertilizer production $/day

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185 Appendix A (Continued) Table A 57 (cont.) Notation in Model Description Units or Value Fertilizer switch to turn on fertilizer processing unitless Harvest PPOR flow of algae from PPOR kg/day Harvest Rate PNR flow of algae from PNR kg/day Fert Profit stock of fertilizer profit $ F Profit flow of fertilizer profits $/day O2 Benefits flow of benefits from reduced aeration $/day MeOH Benefits flow of benefits from reduced chemical additives $/day Fert per Biomass fraction of biomass converted to fertilizer unitless Fertilizer $ per kg market price of fertilizer $/kg A to Fert Benefits flow of fertilizer benefits $/day Fert Benefits stock of fertilizer benefits $ F Benefits flow of fertilizer benefits $/day Table A58 List of equations for fertilizer processing framework Notation Equation Initial Value Component Cost_Fert _Prod = MJ_per_kg*kWh_per_MJ*$_per_kWh n/a converter A_to_Fert _Costs = Fertilizer*(((Harvest_PPOR+Harvest_Rate_PNR)*Co st_Fert_Prod)+((Harvest_PPOR+Harvest_Rate_PN R)*Cost_of_Biomass_Production)+(Harvesting_Cost s*(Harvest_PPOR+Harvest_Rate_PNR))) n/a flow Fert Costs(t) = Fert_Costs(t dt) + (A_to_Fert_Costs F_Costs) dt 0 stock F_Costs = A_to_Fert_Costs n/a flow A_to_Fert _Benefits = Fertilizer*(MeOH__Benefits+O2_Benefits+((Harvest_ PPOR+Harvest_Rate_PNR)*Fert_per__Biomass*Fer tilizer_$_per_kg)) n/a flow Fert_Bene fits(t) = Fert_Benefits(t dt) + (A_to_Fert_Benefits F_Benefits) dt 0 stock F_Benefits = A_to_Fert_Benefits n/a flow Fert_Profit (t) = Fert_Profit(t dt) + (F_Costs + F_Benefits F_Profit) dt 0 stock F_Profit = F_Benefits F_Costs n/a flow

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186 Appendix B : List of Equations Biodiesel_Benefits(t) = Biodiesel_Benefits(t dt) + (A_to_BD_Benefits BD_Benefits) dt INIT Biodiesel_Benefits = 0 INFLOWS: A_to_BD_Benefits = Biodiesel*(MeOH__Benefits+O2_Benefits+ (((Harvest_PPOR/(DT_1*PPOR_Freq))+(Harvest_Rate_PNR/(DT_1*Frequency_ _PNR)))*Oil_Percent_Per_Bi omass*Oil_Lkg*Biodiesel_$_per_L)) + (Secondary_Biogas*((1 Oil_Percent_Per_Biomass)*((Harvest_PPOR/(DT_1*PPOR_Freq))+(Harvest_Rat e_PNR/(DT_1*Frequency__PNR)))*CH4gCOD*gCOD__galgae*Biogas_$__per_ L)) + (Secondary_Fertilizer*((1 Oil_Percent_Per_Biomass)*((Harv est_PPOR/(DT_1*PPOR_Freq))+(Harvest_Rat e_PNR/(DT_1*Frequency__PNR)))*Fertilizer_$_per_kg)) OUTFLOWS: BD_Benefits = A_to_BD_Benefits Biodiesel_Costs(t) = Biodiesel_Costs(t dt) + (A_to_BD_Costs BD_Costs) dt INIT Biodiesel_Costs = 0 INFLOWS: A_to_BD_Cos ts = Biodiesel*((((Harvest_PPOR/(DT_1*PPOR_Freq))+(Harvest_Rate_PNR/(DT_1*F requency__PNR)))*Cost_BD_Prod)+(((Harvest_PPOR/(DT_1*PPOR_Freq))+(Ha rvest_Rate_PNR/(DT_1*Frequency__PNR)))*Cost_of_Biomass_Production)+(Ha rvesting_Costs*((Harvest_PPOR/(DT_1*PPOR_Fr eq))+(Harvest_Rate_PNR/(DT _1*Frequency__PNR))))) + (Secondary_Fertilizer*((1 Oil_Percent_Per_Biomass)*((Harvest_PPOR/(DT_1*PPOR_Freq))+(Harvest_Rat e_PNR/(DT_1*Frequency__PNR))))*Cost_Fert_Prod) + (Secondary_Biogas*((1 Oil_Percent_Per_Biomass)*((Harvest_PPO R/(DT_1*PPOR_Freq))+(Harvest_Rat e_PNR/(DT_1*Frequency__PNR))))*BG_Process) OUTFLOWS: BD_Costs = A_to_BD_Costs Biogas_Benefits(t) = Biogas_Benefits(t dt) + (A_to_BG_Benefits BG_Benefits) dt INIT Biogas_Benefits = 0 INFLOWS: A_to_BG_Benefits = Biogas*( MeOH__Benefits+O2_Benefits+(((Harvest_PPOR/(DT_1*PPOR_Freq)) +(Harvest_Rate_PNR/(DT_1*Frequency__PNR)))*CH4gCOD*gCOD__galgae*Bi ogas_$__per_L)) OUTFLOWS: BG_Benefits = A_to_BG_Benefits Biogas_Costs(t) = Biogas_Costs(t dt) + (A_to_BG_Costs BG_Costs) dt

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187 Appendix B (Continued) INIT Biogas_Costs = 0 INFLOWS: A_to_BG_Costs = Biogas*((((Harvest_PPOR/(DT_1*PPOR_Freq))+(Harvest_Rate_PNR/(DT_1*Fre quency__PNR)))*BG_Process)+(((Harvest_PPOR/(DT_1*PPOR_Freq))+(Harves t_Rate_PNR/(DT_1*Frequency__PNR)))*Cost_of_Biom ass_Production)+(Harves ting_Costs*((Harvest_PPOR/(DT_1*PPOR_Freq))+(Harvest_Rate_PNR/(DT_1*F requency__PNR))))) OUTFLOWS: BG_Costs = A_to_BG_Costs C1_Conc(t) = C1_Conc(t dt) + (C1_Eff C1__Discharge_Conc) dt INIT C1_Conc = 0 INFLOWS: C1_Eff = C1_dn OUTFLOWS: C1__Discharge_Conc = C1_Eff*mg_to_kg/Calc_Flow C1_Inf(t) = C1_Inf(t dt) + (Inf_C1 C1_o) dt INIT C1_Inf = 0 INFLOWS: Inf_C1 = Calc_Flow*Inf_Sol_C/mg_to_kg OUTFLOWS: C1_o = Inf_C1 C2_Inf(t) = C2_Inf(t dt) + (Inf_C2 C2_o) dt INIT C2_Inf = 0 INFLOWS: Inf_C2 = Calc_Flow*Inf_Insol_C/mg_to_kg OUTFLOWS: C2_o = Inf_C2 C3_Inf(t) = C3_Inf(t dt) + (Inf_C3 C3_o) dt INIT C3_Inf = 0 INFLOWS: Inf_C3 = Calc_Flow*Inf_Cellular_C/mg_to_kg OUTFLOWS: C3_o = Inf_C3 C4_accum_in_algae(t) = C4_accum_in_al gae(t dt) + (C4_assim) dt INIT C4_accum_in_algae = 0 INFLOWS: C4_assim = X_generated_PPOR*q_C4 C4_accum_in_PNR(t) = C4_accum_in_PNR(t dt) + (C4_assim_PNR) dt INIT C4_accum_in_PNR = 0 INFLOWS: C4_assim_PNR = X_generated_PNR*q_C4_PNR

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188 Appendix B (Continued) C4_Accum_PNR(t) = C4_Accum_PNR(t dt) + (C4_to_PNR C4_from_PNR C4_assim_PNR) dt INIT C4_Accum_PNR = C4_to_PNR*HRT_PNR INFLOWS: C4_to_PNR = C4_n*PNR*Percent_Flow__to_PNR OUTFLOWS: C4_from_PNR = C4_to_PNR C4_assim_PNR C4_assim_PNR = X_gen erated_PNR*q_C4_PNR C4_Accum_PPOR(t) = C4_Accum_PPOR(t dt) + (C4_to_Algae C4_from_PPOR C4_assim) dt INIT C4_Accum_PPOR = C4_to_Algae*HRT_PPOR INFLOWS: C4_to_Algae = C4_O2*Percent_Flow__to_PPOR*PPOR OUTFLOWS: C4_from_PPOR = C4_to_Algae C4_assim C4_a ssim = X_generated_PPOR*q_C4 C4_Inf(t) = C4_Inf(t dt) + (Inf_C4 C4_o) dt INIT C4_Inf = 0 INFLOWS: Inf_C4 = Calc_Flow*Inf_CO2/mg_to_kg OUTFLOWS: C4_o = Inf_C4 C_Eff(t) = C_Eff(t dt) + (C1_dn + C3_dn + C4_dn + C2_dn C_Eff_t) dt INIT C_Eff = 0 INFLOWS: C1_dn = C1_n C3_dn = C3_n C4_dn = C4_n C4_to_A2 C2_dn = C2_n OUTFLOWS: C_Eff_t = C1_dn+C2_dn+C3_dn+C4_dn Denit_C1(t) = Denit_C1(t dt) + (C1_n C1_dn) dt INIT Denit_C1 = 0 INFLOWS: C1_n = C1_O2 Nit_C1_to_C3 Nit_C1_to_C4 OUTFLOWS: C1_dn = C1_n Denit_C2(t) = Denit_C2(t dt) + (C2_n C2_dn) dt INIT Denit_C2 = 0 INFLOWS: C2_n = C2_O2 OUTFLOWS: C2_dn = C2_n

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189 Appendix B (Continued) Denit_C3(t) = Denit_C3(t dt) + (C3_n C3_dn) dt INIT Denit_C3 = 0 INFLOWS: C3_n = C3_O2+Nit_C1_to_C3 OUTFLOWS: C3_dn = C3_n Denit_C4(t) = Denit_C4(t dt) + (C4_n C4_dn C4_to_A2) dt INIT Denit_C4 = 0 INFLOWS: C4_n = C4_O2+Nit_C1_to_C4 C4_to_A OUTFLOWS: C4_dn = C4_n C4_to_A2 C4_to_A2 = C4_assim_PNR Denit_N1(t) = Denit_N1(t dt) + (N1_n N1_dn) dt INIT Den it_N1 = 0 INFLOWS: N1_n = N1_O2 OUTFLOWS: N1_dn = N1_n Denit_N2(t) = Denit_N2(t dt) + (N2_n N2_dn) dt INIT Denit_N2 = 0 INFLOWS: N2_n = N2_O2 N2_to_A Nit_N2_to_N3 OUTFLOWS: N2_dn = N2_n Denit_N3(t) = Denit_N3(t dt) + (N3_n N3_dn N3_to_A2 DN _N3_to_N4) dt INIT Denit_N3 = 0 INFLOWS: N3_n = N3_O2+Nit_N2_to_N3 OUTFLOWS: N3_dn = N3_n DN_N3_to_N4 N3_to_A2 N3_to_A2 = N3_assim__PNR DN_N3_to_N4 = N3_n*Denit_Rate Denit_N4(t) = Denit_N4(t dt) + (N4_n + DN_N3_to_N4 N4_dn) dt INIT Denit_N4 = 0 INFLOWS: N4_n = N4_O2 DN_N3_to_N4 = N3_n*Denit_Rate OUTFLOWS: N4_dn = N4_n+DN_N3_to_N4 Denit_P1(t) = Denit_P1(t dt) + (P1_n P1_dn P1_to_A2) dt INIT Denit_P1 = 0 INFLOWS:

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190 Appendix B (Continued) P1_n = P1_O2 P1_to_A OUTFLOWS: P1_dn = P1_n P1_to_A2 P1_to_A2 = P1_assim_PNR Denit_P2(t) = Denit_P2(t dt) + (P2_n P2_dn) dt INIT Denit_P2 = 0 INFLOWS: P2_n = P2_O2 OUTFLOWS: P2_dn = P2_n Denit_Q(t) = Denit_Q(t dt) + (Q_nit + Qr_PNR Q_e) dt INIT Denit_Q = 0 INFLOWS: Q_nit = Qr_PNR+Q_O2 Qr_PNR = Q_PNR Q_Harv_PNR OUTFLOWS: Q_e = Q_nit+Qr_PNR Fert_Benefits(t) = Fert_Benefits(t dt) + (A_to_Fert_Benefits F_Benefits) dt INIT Fert_Benefits = A_to_Fert_Benefits INFLOWS: A_to_Fert_Benefits = Fertilizer*(MeOH__Benefits+O2_Benefits+((((Harvest_PPOR/(D T_1*PPOR_Freq ))+(Harvest_Rate_PNR/(DT_1*Frequency__PNR))))*Fert_per__Biomass*Fertiliz er_$_per_kg)) OUTFLOWS: F_Benefits = A_to_Fert_Benefits Fert_Costs(t) = Fert_Costs(t dt) + (A_to_Fert_Costs F_Costs) dt INIT Fert_Costs = 0 INFLOWS: A_to_Fert_Costs = Fertilizer*(((((Harvest_PPOR/(DT_1*PPOR_Freq))+(Harvest_Rate_PNR/(DT_1* Frequency__PNR))))*Cost_Fert_Prod)+((((Harvest_PPOR/(DT_1*PPOR_Freq))+ (Harvest_Rate_PNR/(DT_1*Frequency__PNR))))*Cost_of_Biomass_Production) +(Harvesting_Costs*(((Harvest_PPOR/(DT_1*PP OR_Freq))+(Harvest_Rate_PN R/(DT_1*Frequency__PNR)))))) OUTFLOWS: F_Costs = A_to_Fert_Costs Fert_Profit(t) = Fert_Profit(t dt) + (F_Costs + F_Benefits F_Profit) dt INIT Fert_Profit = 0 INFLOWS: F_Costs = A_to_Fert_Costs F_Benefits = A_to_Fert_Benefits OUTFLOWS:

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191 Appendix B (Continued) F_Profit = F_Benefits F_Costs MeOH_Saved(t) = MeOH_Saved(t dt) + (MeOH_In MeOH__Benefits) dt INIT MeOH_Saved = 0 INFLOWS: MeOH_In = (MeOH_NO3__mass*(N3_assim__PNR)*Cost_per_L_MeOH)/MeOH_L__to_kg OUTFLOWS: MeOH__Benefits = MeOH_In N1_Inf(t) = N1_Inf(t dt) + (Inf_N1_flow N1_o) dt INIT N1_Inf = 0 INFLOWS: Inf_N1_flow = Calc_Flow*Inf_N1/mg_to_kg OUTFLOWS: N1_o = Inf_N1_flow N2_accum_in_algae(t) = N2_accum_in_algae(t dt) + (N2_assim) dt INIT N2_accum_i n_algae = N2_assim INFLOWS: N2_assim = X_generated_PPOR*q_N2 N2_Accum_PPOR(t) = N2_Accum_PPOR(t dt) + (N2_to_Algae N2_from_PPOR N2_assim) dt INIT N2_Accum_PPOR = N2_to_Algae*HRT_PPOR INFLOWS: N2_to_Algae = N2_O2*Percent_Flow__to_PPOR*PPOR OUTFLOWS: N2_from_PPOR = N2_to_Algae N2_assim N2_assim = X_generated_PPOR*q_N2 N2_Conc(t) = N2_Conc(t dt) + (N2_Eff N2_Discharge_Conc) dt INIT N2_Conc = 0 INFLOWS: N2_Eff = N2_dn OUTFLOWS: N2_Discharge_Conc = N2_Eff*mg_to_kg/Calc_Flow N2_Inf(t) = N2_Inf(t dt) + (Inf_N2_flow N2_o) dt INIT N2_Inf = 0 INFLOWS: Inf_N2_flow = Calc_Flow*Inf_NH3/mg_to_kg OUTFLOWS: N2_o = Inf_N2_flow N3_accum_in_PNR(t) = N3_accum_in_PNR(t dt) + (N3_assim__PNR) dt INIT N3_accum_in_PNR = N3_assim__PNR INFLOWS: N3_assim__PNR = X_generated_PNR*q_N3_PNR

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192 Appendix B (Continued) N3_Accum_PNR(t) = N3_Accum_PNR(t dt) + (N3_to_PNR N3_from_PNR N3_assim__PNR) dt INIT N3_Accum_PNR = N3_to_PNR*HRT_PNR INFLOWS: N3_to_PNR = N3_n*PNR*Percent_Flow__to_PNR OUTFLOWS: N3_from_PNR = N3_ to_PNR N3_assim__PNR N3_assim__PNR = X_generated_PNR*q_N3_PNR N3_Inf(t) = N3_Inf(t dt) + (Inf_N3_flow N3_o) dt INIT N3_Inf = 0 INFLOWS: Inf_N3_flow = Calc_Flow*Inf_NOx/mg_to_kg OUTFLOWS: N3_o = Inf_N3_flow N4_Inf(t) = N4_Inf(t dt) + (Inf_N4_flow N4_o) dt INIT N4_Inf = 0 INFLOWS: Inf_N4_flow = Calc_Flow*Inf_N2/mg_to_kg OUTFLOWS: N4_o = Inf_N4_flow Nit_C1(t) = Nit_C1(t dt) + (C1_O2 C1_n Nit_C1_to_C3 Nit_C1_to_C4) dt INIT Nit_C1 = 0 INFLOWS: C1_O2 = C1_o O2_C1_to_C4 O2_C1__to_C3 OUTFLOWS: C1_n = C1_O2 Nit_C1_to_C3 Nit_C1_to_C4 Nit_C1_to_C3 = Nit_kC1_to_C3*C1_O2 Nit_C1_to_C4 = C1_O2*Nit_kC1__to_C4 Nit_C2(t) = Nit_C2(t dt) + (C2_O2 C2_n) dt INIT Nit_C2 = 0 INFLOWS: C2_O2 = C2_o OUTFLOWS: C2_n = C2_O2 Nit_C3(t) = Nit_C3(t dt) + (C3_O2 + Nit_C1_to_C3 C3_n) dt INIT Nit_C3 = 0 INFLOWS: C3_O2 = C3_o+O2_C1__to_C3 Nit_C1_to_C3 = Nit_kC1_to_C3*C1_O2 OUTFLOWS: C3_n = C3_O2+Nit_C1_to_C3 Nit_C4(t) = Nit_C4(t dt) + (C4_O2 + Nit_C1_to_C4 C4_n C4_to_A) dt INIT Nit_C4 = 0

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193 Appendix B (Continued) INFLOWS: C4_O2 = C4_o+O2_C1_to_C4 Nit_C1_to_C4 = C1_O2*Nit_kC1__to_C4 OUTFLOWS: C4_n = C4_O2+Nit_C1_to_C4 C4_to_A C4_to_A = C4_assim Nit_N1(t) = Nit_N1(t dt) + (N1_O2 N1_n) dt INIT Nit_N1 = 0 INFLOWS: N1_O2 = N1_o OUTFLOWS: N1_n = N1_O2 Nit_N2(t) = Nit_N2(t dt) + (N2_O2 N2_n N2_to_A Nit_N2_to_N3) dt INIT Nit_N2 = 0 INFLOWS: N2_O2 = N2_o O2_N2_to_N3 OUTFLOWS: N2_n = N2_O2 N2_to_A Nit_N2_to_N3 N2_to_A = N2_assim Nit_N2_to_N3 = N2_O2*Nit_Rate_in_Nit_Reactor Nit_N3(t) = Nit_N3(t dt) + (N3_O2 + Nit_N2_to_N3 N3_n) dt INIT Nit_N3 = 0 INFLOWS: N3_O2 = O2_N2_to_N3+N3_o Nit_N2_to_N3 = N2_O2*Nit_Rate_in_Nit_Reactor OUTFLOWS: N3_n = N3_O2+Nit_N2_to_N3 Nit_N4(t) = Nit_N4(t dt) + (N4_O2 N4_n) dt INIT Nit_N4 = 0 INFLOWS: N4_O2 = N 4_o OUTFLOWS: N4_n = N4_O2 Nit_P1(t) = Nit_P1(t dt) + (P1_O2 P1_n P1_to_A) dt INIT Nit_P1 = 0 INFLOWS: P1_O2 = P1_o OUTFLOWS: P1_n = P1_O2 P1_to_A P1_to_A = P1_assim Nit_P2(t) = Nit_P2(t dt) + (P2_O2 P2_n) dt INIT Nit_P2 = 0 INFLOWS:

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194 Appendi x B (Continued) P2_O2 = P2_o OUTFLOWS: P2_n = P2_O2 Nit_Q(t) = Nit_Q(t dt) + (Q_O2 + Qr_PPOR Q_nit Q_PNR) dt INIT Nit_Q = 0 INFLOWS: Q_O2 = Q_o Q_PPOR Qr_PPOR = Q_PPOR Q_Harv_PPOR OUTFLOWS: Q_nit = Qr_PNR+Q_O2 Q_PNR = PNR*((Q_O2*Percent_Flow__to_PNR)+Qr_PPOR) O2_C1(t) = O2_C1(t dt) + (C1_o C1_O2 O2_C1__to_C3 O2_C1_to_C4) dt INIT O2_C1 = 0 INFLOWS: C1_o = Inf_C1 OUTFLOWS: C1_O2 = C1_o O2_C1_to_C4 O2_C1__to_C3 O2_C1__to_C3 = C1_o*O2_kC1_to_C3 O2_C1_to_C4 = C1_o* O2_kC1_to_C4 O2_C2(t) = O2_C2(t dt) + (C2_o C2_O2) dt INIT O2_C2 = 0 INFLOWS: C2_o = Inf_C2 OUTFLOWS: C2_O2 = C2_o O2_C3(t) = O2_C3(t dt) + (C3_o + O2_C1__to_C3 C3_O2) dt INIT O2_C3 = 0 INFLOWS: C3_o = Inf_C3 O2_C1__to_C3 = C1_o*O2_kC1_to_C3 OUTFLOWS: C3_O2 = C3_o+O2_C1__to_C3 O2_C4(t) = O2_C4(t dt) + (C4_o + O2_C1_to_C4 C4_O2) dt INIT O2_C4 = 0 INFLOWS: C4_o = Inf_C4 O2_C1_to_C4 = C1_o*O2_kC1_to_C4 OUTFLOWS: C4_O2 = C4_o+O2_C1_to_C4 O2_N1(t) = O2_N1(t dt) + (N1_o N1_O2) dt INIT O2 _N1 = 0 INFLOWS:

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195 Appendix B (Continued) N1_o = Inf_N1_flow OUTFLOWS: N1_O2 = N1_o O2_N2(t) = O2_N2(t dt) + (N2_o N2_O2 O2_N2_to_N3) dt INIT O2_N2 = 0 INFLOWS: N2_o = Inf_N2_flow OUTFLOWS: N2_O2 = N2_o O2_N2_to_N3 O2_N2_to_N3 = N2_o*Nit_Rate_in_cBOD O2_N3(t) = O2_N3(t dt) + (N3_o + O2_N2_to_N3 N3_O2) dt INIT O2_N3 = 0 INFLOWS: N3_o = Inf_N3_flow O2_N2_to_N3 = N2_o*Nit_Rate_in_cBOD OUTFLOWS: N3_O2 = O2_N2_to_N3+N3_o O2_N4(t) = O2_N4(t dt) + (N4_o N4_O2) dt INIT O2_N4 = 0 INFLOWS: N4_o = Inf_N4_flow OUTFLOWS: N4_O2 = N4_o O2_P1(t) = O2_P1(t dt) + (P1_o P1_O2) dt INIT O2_P1 = 0 INFLOWS: P1_o = Inf_P1 OUTFLOWS: P1_O2 = P1_o O2_P2(t) = O2_P2(t dt) + (P2_o P2_O2) dt INIT O2_P2 = 0 INFLOWS: P2_o = Inf_P2 OUTFLOWS: P2_O2 = P2_o O2_Q(t) = O2_Q(t dt) + (Q_o Q_O2 Q_PPOR) dt INIT O2_Q = 0 INFLOWS: Q_o = Calc_Flow OUTFLOWS: Q_O2 = Q_o Q_PPOR Q_PPOR = (Q_o*Percent_Flow__to_PPOR)*PPOR O2_Saved2(t) = O2_Saved2(t dt) + (O2_in O2_Benefits) dt

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196 Appendix B (Continued) INIT O2_Saved2 = 0 INFLOWS: O2_in = (molO2_per_molA*(1/mol_O2_per_NH3)*kgN_per_kgA*$kgNH3*(Harvest_PPO R/(DT_1*PPOR_Freq)))+(N2_assim*$kgNH3) OUTFLOWS: O2_Benefits = O2_in P1_accum_in_algae(t) = P1_accum_in_algae(t dt) + (P1_assim) dt INIT P1_accum_in_algae = 0 INFLOWS: P1_assim = X_generated_PPOR*q_P1 P1_accum_in_PNR(t) = P1_accum_in_PNR(t dt) + (P1_assim_PNR) dt INIT P1_accum_in_PNR = 0 INFLOWS: P1_assim_PNR = X_generated_PNR*q_P1_PNR P1_Accum_PNR(t) = P1_Accum_PNR(t dt) + (P1_to_PNR P1_from_PNR P1_assim_PNR) dt INIT P1_Accum_PNR = P1_to_PNR*HRT_PNR INFLOWS: P1_to_PNR = PNR*P1_n*Percent_Flow__to_PNR OUTFLOWS: P1_from_PNR = P1_to_PNR P1_assim_PNR P1_assim_PNR = X_generated_PNR*q_P1_PNR P1_Accum_PPOR(t) = P1_Accum_PPOR(t dt) + (P1_to_Algae P1_from_PPOR P1_assim) dt INIT P1_Accum_PPOR = P1_to_Algae*HRT_PPOR INFLOWS: P1_to_Algae = P1_O2*Percent_Flow__to_PPOR*PPOR OUTFLOWS: P1_from_PPOR = P1_to_Algae P1_assim P1_assim = X_generated_PPOR*q_P1 P1_Inf(t) = P1_Inf(t dt) + (Inf_ P1 P1_o) dt INIT P1_Inf = 0 INFLOWS: Inf_P1 = Calc_Flow*Inf_Sol_P/mg_to_kg OUTFLOWS: P1_o = Inf_P1 P2_Inf(t) = P2_Inf(t dt) + (Inf_P2 P2_o) dt INIT P2_Inf = 0 INFLOWS: Inf_P2 = Calc_Flow*Inf_Insol_P/mg_to_kg OUTFLOWS: P2_o = Inf_P2

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197 Appendix B (C ontinued) Profit_BD(t) = Profit_BD(t dt) + (BD_Costs + BD_Benefits BD_Profit) dt INIT Profit_BD = 0 INFLOWS: BD_Costs = A_to_BD_Costs BD_Benefits = A_to_BD_Benefits OUTFLOWS: BD_Profit = BD_Benefits BD_Costs Profit_BG(t) = Profit_BG(t dt) + (BG_Costs + BG_Benefits BG_Profit) dt INIT Profit_BG = 0 INFLOWS: BG_Costs = A_to_BG_Costs BG_Benefits = A_to_BG_Benefits OUTFLOWS: BG_Profit = BG_Benefits BG_Costs P_MB(t) = P_MB(t dt) + (TP_In TP_MB_In) dt INIT P_MB = 0 INFLOWS: TP_In = Inf_P1+ Inf_P2 OUTFLOWS: TP_MB_In = TP_In P_MB_out(t) = P_MB_out(t dt) + (TP_Out TP_MB_Out) dt INIT P_MB_out = 0 INFLOWS: TP_Out = P1_dn+P1_to_A+P1_to_A2+P2_dn OUTFLOWS: TP_MB_Out = TP_Out q_C4_stock(t) = q_C4_stock(t dt) + (q_C4) dt INIT q_C4_stock = 0 INFLOWS: q_C4 = u_calc_PPOR/Y_CO2_PPOR q_C4_stock_2(t) = q_C4_stock_2(t dt) + (q_C4_PNR) dt INIT q_C4_stock_2 = 0 INFLOWS: q_C4_PNR = u_calc_PNR/Y_CO2_PNR Q_Loss_to_Algae(t) = Q_Loss_to_Algae(t dt) + (Q_Harv_PPOR + Q_Harv_PNR Q_loss) dt INIT Q_Loss_to_Algae = 0 INFLOWS: Q_Harv_PPOR = Q%_Lost_w__Harvest_PPOR*Q_PPOR Q_Harv_PNR = Q_PNR*Q%_Lost_w__Harvest_PNR OUTFLOWS: Q_loss = Q_Harv_PNR+Q_Harv_PPOR q_N2_stock(t) = q_N2_stock(t dt) + (q_N2) dt

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198 Appendix B (Continued) INIT q_N2_stock = 0 INFL OWS: q_N2 = u_calc_PPOR/Y_NH3_PPOR q_N3_stock(t) = q_N3_stock(t dt) + (q_N3_PNR) dt INIT q_N3_stock = 0 INFLOWS: q_N3_PNR = u_calc_PNR/Y_NOx_PNR q_P1_stock(t) = q_P1_stock(t dt) + (q_P1) dt INIT q_P1_stock = 0 INFLOWS: q_P1 = u_calc_PPOR/Y_Psol_PPO R q_P1_stock_2(t) = q_P1_stock_2(t dt) + (q_P1_PNR) dt INIT q_P1_stock_2 = 0 INFLOWS: q_P1_PNR = u_calc_PNR/Y_Psol_PNR TC_MBo(t) = TC_MBo(t dt) + (TC_MB_o TC_MB_In) dt INIT TC_MBo = 0 INFLOWS: TC_MB_o = Inf_C1+Inf_C2+Inf_C3+Inf_C4 OUTFLOWS: TC_MB_In = TC_MB_o TN_Conc(t) = TN_Conc(t dt) + (TN_Eff_t TN_Discharge_Conc) dt INIT TN_Conc = 0 INFLOWS: TN_Eff_t = N1_dn+N2_dn+N3_dn+N4_dn OUTFLOWS: TN_Discharge_Conc = TN_Eff_t*mg_to_kg/Calc_Flow TN_Eff(t) = TN_Eff(t dt) + (N1_dn + N2_dn + N3_dn + N4_dn TN_Eff_t) dt INIT TN_Eff = 0 INFLOWS: N1_dn = N1_n N2_dn = N2_n N3_dn = N3_n DN_N3_to_N4 N3_to_A2 N4_dn = N4_n+DN_N3_to_N4 OUTFLOWS: TN_Eff_t = N1_dn+N2_dn+N3_dn+N4_dn TN_MBe(t) = TN_MBe(t dt) + (TC_MB_e TC_MB_Out) dt INIT TN_MBe = 0 I NFLOWS: TC_MB_e = C1_dn+C2_dn+C3_dn+C4_dn+C4_to_A+C4_to_A2 OUTFLOWS: TC_MB_Out = TC_MB_e TN_MB_In_Stock(t) = TN_MB_In_Stock(t dt) + (TN_MB_In_1 TN_MB_In) dt

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199 Appendix B (Continued) INIT TN_MB_In_Stock = 0 INFLOWS: TN_MB_In_1 = Inf_N1_flow+Inf_N2_flow+Inf_N3_flow+Inf_N4_flow OUTFLOWS: TN_MB_In = TN_MB_In_1 TN_MB__Out_Stock(t) = TN_MB__Out_Stock(t dt) + (TN_MB_Out_1 TN_MB_Out) dt INIT TN_MB__Out_Stock = 0 INFLOWS: TN_MB_Out_1 = N1_dn+N2_dn+N2_to_A+N3_dn+N3_to_A2+N4_dn OUTFLO WS: TN_MB_Out = TN_MB_Out_1 TP_Conc(t) = TP_Conc(t dt) + (TP_Eff_t TP_Discharge_Conc) dt INIT TP_Conc = 0 INFLOWS: TP_Eff_t = P1_dn+P2_dn OUTFLOWS: TP_Discharge_Conc = TP_Eff_t*mg_to_kg/Calc_Flow TP_Eff(t) = TP_Eff(t dt) + (P2_dn + P1_dn TP_Eff_t ) dt INIT TP_Eff = 0 INFLOWS: P2_dn = P2_n P1_dn = P1_n P1_to_A2 OUTFLOWS: TP_Eff_t = P1_dn+P2_dn u_calc_PNR_2(t) = u_calc_PNR_2(t dt) + (u_calc_PNR) dt INIT u_calc_PNR_2 = 0 INFLOWS: u_calc_PNR = ((umax_NO3*(MIN(((N3_Accum_PNR/Vol_PNR_1)/((K_NOx)+(N3_Accum_PNR/ Vol_PNR_1))),((P1_Accum_PNR/Vol_PNR_1)/((K_Psol)+(P1_Accum_PNR/Vol_ PNR_1))),((C4_Accum_PNR/Vol_PNR_1)/((K_CO2)+(C4_Accum_PNR/Vol_PNR _1)))))) PNR_b)*PNR u_calc_PPOR_2(t) = u_calc_PPOR_2(t dt ) + (u_calc_PPOR) dt INIT u_calc_PPOR_2 = 0 INFLOWS: u_calc_PPOR = ((umax__NH3*(MIN(((N2_Accum_PPOR)/((K_NH3*Vol_PPOR_1)+(N2_Accum_ PPOR))),((P1_Accum_PPOR)/((K_Psol*Vol_PPOR_1)+(P1_Accum_PPOR))),((C 4_Accum_PPOR)/((C4_Accum_PPOR)+(K_CO2*Vol_PPOR_1)))))) P POR_b)*PPOR X_accumulated_PNR(t) = X_accumulated_PNR(t dt) + (X_generated_PNR Harvest_Rate_PNR) dt

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200 Appendix B (Continued) INIT X_accumulated_PNR = 10 INFLOWS: X_generated_PNR = X_accumulated_PNR*u_calc_PNR OUTFLOWS: Harvest_Rate_PNR = Pulse((Amount ),Init_PNR,Frequency__PNR) X_accumulated_PPOR(t) = X_accumulated_PPOR(t dt) + (X_generated_PPOR Harvest_PPOR) dt INIT X_accumulated_PPOR = 10 INFLOWS: X_generated_PPOR = X_accumulated_PPOR*u_calc_PPOR OUTFLOWS: Harvest_PPOR = Pulse((PPOR_Amount),PPOR _Init,PPOR_Freq) $kgNH3 = Cost_Aeration__per_kg_NH3 $_per_kWh = .12 $_per__quantity_O2 = 10 Amount = X_accumulated_PNR*PNR_%_Rem BG_Est_Costs = .048 BG_Process = .1 Biodiesel = 1 Biodiesel_$_per_L = 3.15 Biogas = 1 Biogas_$__per_L = 7.92*10^ 5 BOD_Rem_BOD_Reactor = .79 BOD_Rem_Nit_Reactor = .85 Calc_Flow = Flow_GPD*L_conv CH4gCOD = 487 Cost_Aeration__per_kg_NH3 = .2369 Cost_BD_Prod = 71 Cost_Fert_Prod = MJ_per_kg*kWh_per_MJ*$_per_kWh Cost_of_Biomass_Production = 3 Cost_per_L_MeOH = 3.5 Denit_Rat e = .48 DT_1 = 100 Fertilizer = 1 Fertilizer_$_per_kg = 3 Fert_per__Biomass = .5 Flow_GPD = 96000000 Frequency__PNR = PNR_Harvest__Freq gCOD__galgae = 1.545 Harvesting_Costs = .12 HRT_DN__Basin = Vol_Denit__Basin/Calc_Flow HRT_Nit__Basin = Vol_Nit_Basin/Calc_Flow HRT_O2__Basin = Vol_O2_Basin/Calc_Flow

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201 Appendix B (Continued) HRT_PNR = 1 HRT_PPOR = 1 Inf_BOD = 10 Inf_Cellular_C = 0 Inf_CO2 = 32 Inf_Insol_C = 1 Inf_Insol_P = Inf_TP Inf_Sol_P Inf_N1 = Inf_TKN Inf_NH3 Inf_N2 = 0 Inf_NH3 = 1 Inf _NOx = 0 Inf_Sol_C = Inf_BOD*1 Inf_Sol_P = 1 Inf_TKN = 5 Inf_TP = 1 Init_PNR = PNR_Init_Rem kgN_per_kgA = .006 kWh_per_MJ = 1/3.6 kWh_per__m3 = 1 K_CO2 = .0001*10^ 3 K_NH3 = 3.15e 5 K_NOx = 1.2*10^ 9 K_Psol = .0000001*10^ 3 Labor_Costs = .054 L_conv = 3.785 MeOH_L__to_kg = .8 MeOH_NO3__mass = 3.4 MeOH__per_NO3 = .167/.100 mg_to_kg = 1000000 MJ_per_kg = 5 molO2_per_molA = 114.75 mol_O2_per_NH3 = 1.86 Mon_C4_PNR = C4_Accum_PNR/(C4_Accum_PNR+(K_CO2*(Percent_Flow__to_PNR*(Q_o Q_o*Q%_Lost_w__Harvest_PPOR)))) Mon_C4_PPOR = C4_Accum_PPOR/(C4_Accum_PPOR+(K_CO2*Percent_Flow__to_PPOR*Q_o) ) Mon_N2_PPOR = N2_Accum_PPOR/(N2_Accum_PPOR+(K_NH3*Percent_Flow__to_PPOR*Q_o) )

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202 Appendix B (Continued) Mon_N3_PNR = N3_Accum_PNR/(N3_Accum_PNR+(K_NOx*(Percent_Flow__to_PNR*(Q_ o Q_o*Q%_Lost_w__Harvest_PPOR)))) Mon_P1_PNR = P1_Accum_PNR/(P1_Accum_PNR+(K_Psol*(Percent_Flow__to_PNR*(Q_o Q_o*Q%_Lost_w__Harvest_PPOR)))) Mon_P1_PPOR = P1_Accum_PPOR/(P1_Accum_PPOR+(K_Psol*Percent_Flow__to_PPOR*Q_o)) MW_N = 14 MW_O2 = 32 Nit_kC1_to_C3 = .73*BOD_Rem_Nit_Reactor Nit_kC1__to_C4 = .27*BOD_Rem_Nit_Reactor Nit_Rate_in_cBOD = .22 Nit_Rate_in_Nit_Reactor = .49 No_Further_Process = 1 O2_kC1_to_C3 = BOD_Rem_BOD_Reactor*.73 O2_kC1_to_C4 = .27*BOD_Rem_BOD_Reactor O2_N_stoich = MW_O2/MW_N Oil_Lkg = .88 Oil_Percent_Per_Biomass = .4 Percent_Flow__to_PNR = .5 Percent_Flow__to_PPOR = .5 PNR = 1 PNR_%_Rem = .1 PNR_b = .1 PNR_Harvest__Freq = 3 PNR_Init_Rem = 2 PPOR = 1 PPOR_%__Removed = .5 PPOR_Amount = X_accumulated_PPOR*PPOR_%__Removed PPOR_b = .1 PPOR_F req = PPOR_Harvest_Freq PPOR_Harvest_Freq = 5 PPOR_Init = PPOR_Init_Rem PPOR_Init_Rem = 3 Q%_Lost_w__Harvest_PNR = .10 Q%_Lost_w__Harvest_PPOR = .10 Secondary_Biogas = 1 Secondary_Fertilizer = 1 SRT_PNR = X_accumulated_PNR/(Amount/Frequency__PNR) SRT_PPOR = X_accumulated_PPOR/(PPOR_Amount/PPOR_Freq) umax_NO3 = 1.512 umax__NH3 = 1.512

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203 Appendix B (Continued) Vol_Denit__Basin = 5000000*3.785 Vol_Nit_Basin = 5000000*3.785 Vol_O2_Basin = 5000000*3.785 Vol_PNR = Vol_PNR_1*.264 Vol_PNR_1 = HRT_PNR*((Percent_Flow__to_PNR*(Q_o Q_o*Q%_Lost_w__Harvest_PPOR))) Vol_PPOR = Vol_PPOR_1*.264 Vol_PPOR_1 = HRT_PPOR*(Percent_Flow__to_PPOR*Q_o) Y_CO2_PNR = 1.96 Y_CO2_PPOR = 1.96 Y_NH3_PPOR = 15.26 Y_NOx_PNR = 15.26 Y_Psol_PNR = 78.37 Y_Psol_PPOR = 78.37

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204 Appendix C : Extra Figures Influent Wastewater Characteristics Figure C1 Biomass production as a function of influent nutrient concentration in the PNR.

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205 Appendix C (Continued) Specific Growth Rate and Harvest Rate Figure C2 Biomass production in the PNR as a function of umax. Figure C3 Biomass production as a function of initial harvest rate Case 2.

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A bout the Author Ivy Cormier was born in Massachusetts and earned her Bachelor of Science in Environmental Science from the University of San Francisco. Throughout her academic career, Ivy has studied in Washington, D.C., Mexico, Australia, Brazil, and the Netherlands. Her research experience includes a study to optimize the growth of select algae species on high strength waste streams at the UNESCO IHE Institute for Water Education. She has worked as a Pilot Technician for a biological wastewater treatment company, studyin g the effectiveness of a novel process with municipal and industrial wastewater streams. Ivy was most recently the Operating Permit Coordinator in the On Site Sewage Treatment and Disposal System Program at the Hillsborough Health Department.


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A stella model for integrated algal biofuel production and wastewater treatment
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by Ivy Cormier.
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[Tampa, Fla] :
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2010.
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Thesis (MSES)--University of South Florida, 2010.
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ABSTRACT: Based on a municipal wastewater treatment plant (WWTP) in Tampa, FL, a dynamic multiple-systems model was developed on the STELLA software platform to explore algae biomass production in wastewater by incorporating two photobioreactors into the WWTP's treatment train. Using a mass balance approach, the model examined the synergy through algal growth and substrate removal kinetics, as well as macroeconomic-level analyses of algal biomass conversion to biodiesel, biogas, or fertilizer. A sensitivity analysis showed that biomass production is highly dependent on Monod variables and harvesting regime, and profitability was sensitive to processing costs, market prices of products, and energy environment. The model demonstrated that adequate nutrients and carbon dioxide are available in the plant's influent to sustain algal growth. Biogas and fertilizer production were found to be profitable, but biodiesel was not, due to high processing costs under current technologies. Useful in determining the growth potential on a macro-level, the model is a tool for identifying focus areas for bench and pilot scale testing.
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Advisor: Daniel Yeh, Ph.D.
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Mass balance
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Algae economics
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Monod kinetics
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