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PAGE 1 Vibrofluidized Bed Drying Of Citrus Processing Residue For Byproduct Recovery by Eric A. Roe A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Chemical Engineering College of Engineering University of South Florida Major Professor: Richard A. Gilbert, Ph.D. William E. Lee, Ph.D William A. Miller, Ph.D. Carl J. Biver, Ph.D. Renee M. Goodrich, Ph.D. Date of Approval: November 14, 2003 Keywords: vibrating fluidized bed, fluidi zed bed, citrus byproducts, animal feed Copyright 2003, Eric A. Roe PAGE 2 Frustra fit per plura quod potest fieri per pauciora It is futile to do with more what can be done with fewer English philosopher and Franciscan monk William of Ockham ca.12851349 The ideal engineer is a composite He is not a scientist, he is not a mathematician, he is not a sociologist or a writer; but he may use the knowledge and techniques of any or all of these disciplines in solving engineering problems. N.W. Dougherty 1955 PAGE 3 ACKNOWLEDGMENTS I would like to express my sincere appreciation to my major professor and friend Dr. Richard Gilbert, for his enc ouragement, mentoring, support, and the opportunity to work on a project in whic h I am truly interested. His guidance, friendship, and sense of hum or have allowed me to complete this significant milestone. I would like to thank the members of my committee, Dr. Carl Biver, Dr. Renee Goodrich, Dr. William Lee, and Dr. Willia m Miller, for their input into the project and their time, especially at t he end of the project. I would like to sincerely thank Dr. Robert Braddock who c haired the dissertation defense. His level of interest and commitment to the project, and his valuable expertise in the citrus industry, helped to ensure that this research represents a valuable contribution. I would be remiss not to include special thanks to Dr. Scott Campbell who allowed me space in his labor atory during the early phases of this project. Thank you to my friends and family Having a great group of people like all of you in my life has made, and will cont inue to make, life that much richer. Finally, I want to thank my wife Be th! Without her support and love, I could not have completed this work and without her editing skills, this dissertation would have been a dozen or so runon sentences. PAGE 4 i TABLE OF CONTENTS LIST OF TABLES iv LIST OF FIGURES vi NOMENCLATURE ix ABSTRACT xii 1 INTRODUCTION 1 2 LITERATURE REVIEW 3 2.1 Fluidization 3 2.1.1 Fundamental Concepts 4 2.1.2 Pressure Drop 7 2.1.3 Geldart Classifications 9 2.1.4 Particle Size Distribution 10 2.1.5 Agglomeration 12 2.1.6 Design 16 2.1.7 Modeling 17 2.2 Drying 21 2.2.1 Drying Principles 22 2.2.2 Drying Equipment 27 2.2.3 Drying of Foods (Dehydration) 28 2.3 Fluidized Bed Drying 29 2.3.1 Advantages and Disadvantages 31 2.3.2 Vibrofluidized Bed Dryers 32 PAGE 5 ii 2.3.3 Modeling 35 2.4 The Citrus Industry 36 2.4.1 History 36 2.4.2 Economic Impact 38 2.4.3 Citrus Processing 42 2.4.4 Feed Mill Expectations 43 2.4.5 Feed Mill Operations 45 2.4.6 Feed Mill Regulatory Aspects 48 3 PROBLEM DEFINITION 50 4 RESEARCH PLAN 52 5 ECONOMIC EVALUATION 54 5.1 Introduction 54 5.2 Analysis 55 6 EXPERIMENTAL METHODS 60 6.1 Experimental Apparatus 60 6.1.1 Benchtop Vibroflu idized Bed Dryer 61 6.1.2 Data Acquisition 66 6.1.3 Instrument Calibration 68 6.2 Particle Size Distribution 72 6.3 Moisture Determination 73 6.4 Vibrofluidization Data 73 6.5 Drying Data 74 7 MODEL DEVELOPMENT 77 7.1 Introduction 77 7.2 ThreePhase VFBD Model 78 7.2.1 Bed Parameters 81 PAGE 6 iii 7.2.2 Constant Rate Period 83 7.2.3 Falling Rate Period 87 7.3 ThinLayer Drying Model 89 8 RESULTS AND DISCUSSION 91 8.1 Particle Size Distribution 91 8.2 Vibrofluidization 95 8.3 Vibrofluidized Bed Drying 98 8.4 Model Validation 106 8.4.1 Fluidization Parameters 106 8.4.2 ThreePhase VFBD Model 107 8.4.3 ThinLayer Drying Model 109 9 SUMMARY AND RECOMMENDATIONS 113 9.1 Summary 113 9.2 Recommendations 115 REFERENCE LIST 117 BIBLIOGRAPHY 123 APPENDICES 126 Appendix 1 Dryer Design & Construction 127 Appendix 2 ThreePhas e VFBD Model Code 130 Appendix 3 Particle Si ze Distribution Data 135 Appendix 4 Instrument Calibration Statistics 136 Appendix 5 ThinLayer Drying Parameter Determination 140 Appendix 6 Drying Model Regression Statistics 145 Appendix 7 Multimedia 148 ABOUT THE AUTHOR End Page PAGE 7 iv LIST OF TABLES Table 1 Characteristics of Selected Dryers 28 Table 2 Food Industry Applications for Selected Dryers 29 Table 3 Estimated Annual Economic Impact of the Citrus Industry on Floridas Economy, Avg. 199596 through 199900 41 Table 4 FBD Energy Requirements 56 Table 5 Thermocouple Calibrat ion Descriptive Statistics 71 Table 6 VFBD Minimum Vibrofluidization Results 98 Table 7 Drying Parameters 98 Table 8 Fluidization Parameters 107 Table 9 Regression Statistics for ThreePhase Model Validation 109 Table 10 Regression Data for Determination of Pages Equation Parameters 110 Table 11 Regression Statistics for ThinLayer Model Validation 112 Table 12 Sieving Data Tabulation 135 Table 13 Regression Statisti cs for A/D Calibration 136 Table 14 Regression Analysis of Va riance for the A/D Calibration 136 Table 15 Regression Statistics fo r Mass Flow Meter Calibration 137 Table 16 Regression Statistics for t he Differential Pressure Sensor Calibration 138 Table 17 Inlet Thermocouple Calib ration Descriptive Statistics 139 Table 18 Outlet Thermocouple Calibr ation Descriptive Statistics 139 Table 19 Regression Statistics fo r the ThreePhase Model at 144.7 C 145 PAGE 8 v Table 20 Regression Statistics fo r the ThreePhase Model at 117.7 C 145 Table 21 Regression Statistics fo r the ThreePhase Model at 137.7 C 145 Table 22 Regression Statistics fo r the ThreePhase Model at 152.4 C 146 Table 23 Regression Statistics fo r the ThreePhase Model at 104.1 C 146 Table 24 Regression Statistics for the ThinLayer Model at 144.7 C 146 Table 25 Regression Statistics for the ThinLayer Model at 117.7 C 146 Table 26 Regression Statistics for the ThinLayer Model at 137.7 C 147 Table 27 Regression Statistics for the ThinLayer Model at 152.4 C 147 Table 28 Regression Statistics for the ThinLayer Model at 104.1 C 147 PAGE 9 vi LIST OF FIGURES Figure 1 Fluidized Bed I ndustrial Applications 3 Figure 2 Fixed and Fluidi zed Bed Properties 5 Figure 3 Contacting Regimes 7 Figure 4 Ideal Pressure Drop Velocity Curve 9 Figure 5 Classification of Particles by Geldart 10 Figure 6 Agglomeration Effects 15 Figure 7 Transfers During Drying 23 Figure 8 Transport Proc esses During Drying 24 Figure 9 Typical Drying Curves 26 Figure 10 Classification of Dryers Based on Heat Transfer Mechanism 27 Figure 11 Standard Fluidized Bed Dryer 30 Figure 12 Dependence of Drying Rate on Vibrational Acceleration, A 2/g 34 Figure 13 Economic Structure of the Florida Citrus Industry 39 Figure 14 Orange Juice Trends 40 Figure 15 Grapefruit Juice Trends 41 Figure 16 Citrus Processing Operation 42 Figure 17 Processing Mass Balance 43 Figure 18 Feed Mill Operations 46 Figure 19 Three Types of Standard Citrus Dryers 47 Figure 20 Fluidized Bed Balance Program 58 Figure 21 Proposed FBD Feed Mill Payback Period 59 PAGE 10 vii Figure 22 Schematic of Lab Apparatus 61 Figure 23 Closeup Photograph of Laboratory Apparatus 63 Figure 24 Wide Shot of Laboratory Apparatus 64 Figure 25 Digital Video Acquisi tion of VFBD Experiment 65 Figure 26 LabVIEW Virtual Interface 67 Figure 27 LabVIEW Graphic Representation of Data Acquisition Program 68 Figure 28 Fluidized Bed Drying Schematic 79 Figure 29 Logarithmic Plot of Final P.S.D. 92 Figure 30 Bar Plot of Final P.S.D. 93 Figure 31 Final P.S.D. Cumulative Undersize Distribution by Mass 94 Figure 32 Fluidization Curve for VFBD Variant #1 96 Figure 33 Fluidization Curve for VFBD Variant #2 96 Figure 34 Fluidization Curve for VFBD Variant #3 97 Figure 35 Fluidization Curve for VFBD Variant #4 97 Figure 36 Experimental Drying Curves 99 Figure 37 Drying Trial 1 101 Figure 38 Drying Trial 2 102 Figure 39 Drying Trial 3 103 Figure 40 Drying Trial 4 104 Figure 41 Drying Trial 5 105 Figure 42 ThreePhase Model Predicted and Experimental Drying Curves 108 Figure 43 ThreePhase Drying Model Validation 109 Figure 44 ThinLayer Model Predicted and Experimental Drying Curves 111 Figure 45 ThinLayer Drying Model Validation 112 Figure 46 Schematic of Lab Apparatus 127 Figure 47 Photograph of 1st Generation FBD 128 PAGE 11 viii Figure 48 Photograph of Final VFBD 129 Figure 49 Flow Meter Calibration Plot 137 Figure 50 Differential Pressure Sensor Calibration Plot 138 Figure 51 Linear Regression for Drying Parameter Determination and Drying Curves, 144.7 C 140 Figure 52 Linear Regression for Drying Parameter Determination and Drying Curves, 117.7 C 141 Figure 53 Linear Regression for Dr ying Parameter Determination and Drying Curves, 137.7 C 142 Figure 54 Linear Regression for Drying Parameter Determination and Drying Curves, 152.4 C 143 Figure 55 Linear Regression for Drying Parameter Determination and Drying Curves, 104.1 C 144 PAGE 12 ix NOMENCLATURE A 2/g Vibrational acceleration ratio nondim A Amplitude of the Vibration mm C Moisture Content % cp Specific Heat of the Fl uid at Constant P cal/g c di Nominal Sieve Aperture Size of the ith Sieve mm dgw Geometric Mean Diameter of Particles by Mass mm dp Particle Diameter cm D Bed Diameter cm Deff Effective Diffusivity cm2/s Dab Binary Diffusivity for System AB cm2/s g Gravitational Acceleration cm/s2 G Mass Velocity of the Fluid (Air) g/cm2s ho Heat Transfer Coefficient W/cm2 c PAGE 13 x H Bed Height cm jD Chilton Coburn jfactor nondim kc Mass Transfer Coefficient cm/s kf Thermal Conductivity of Film at Mean Temperature W/cm c MR Moisture Ratio nondim M* Unaccomplished Moisture Change nondim M Moisture Content % n Number of Sieves +1 (pan) nondim Pi Percentage by Mass of Particles on ith sieve % Re Reynolds Number nondim Slog Geometric Std. Dev. of Lognormal Dist. by Mass nondim Sgw Geometric Std. Dev. of Particle Diameter by Mass mm Sc Schmidts Number nondim Sh Sherwoods Number nondim U Velocity cm/s ut Terminal Velocity of Particles cm/s PAGE 14 xi V Volumetric Flow Rate slpm VOM Minimum Superficial Veloci ty for Fluidization slpm Wi Mass on the ith Sieve g Y Humidity of the Air g water / g dry air PD Distributor Pressure Drop Pa PB Bed Pressure Drop Pa x Fraction of Bed Occupied by x phase nondim Porosity nondim s Spericity of Particle nondim Latent Heat of Vaporization cal/g Density of the Fluid (Air) g/cm3 p Density of the Particle g/cm3 c Tensile Strength of the Particle Pa Viscosity of the Fluid (Air) g/cm s Angular Frequency rad/s PAGE 15 xii Subscripts: b Bubble Phase d Dense Phase e Equilibrium conditions f Final conditions g Gas i Initial, Inlet m Mean Value mf Minimum Fluidization mvf Minimum Vibrofluidization o Outlet s Solid sat Saturation t Total v Vapor w Water PAGE 16 xiii VIBROFLUIDIZED BED DRYING OF CITRUS PROCESSING RESIDUE FOR BYPRODUCT RECOVERY Eric A. Roe ABSTRACT Approximately 44% of the citrus t hat is processed becomes processing residue. The residue consists of the nonjuice components of a citrus fruit, primarily peel and pulp, and is recovered by conversion to animal feed. The material is hygroscopic, agglomerating, has a wide particle size distribution, and must be carefully dried to avoid therma l damage to nutrients an d flavors. This dissertation evaluates the possibility of utilizing a vibrofluidized bed dryer for citrus processing residue. Results demonstr ate that it is po ssible to overcome the agglomeration difficulties associat ed with this material, offering an economically viable alternative processing methodology. To properly analyze this proposed system a benchtop vibrofluidized bed dryer was designed, constr ucted and instrumented. Vi brofluidizati on and batch drying trials were conducted and analyz ed. An economic evaluation of the proposed process was undertaken. Two ma thematical models of the drying process were developed and validated. PAGE 17 xiv Characteristics that describe the vi brofluidized bed drying of the residue were determined. The conditions that fac ilitated fluidization were: 1) A particle size distribution of the dried residue t hat was lognormal, had a geometric mean diameter, dgw, of 3.829 mm, and a geomet ric standard deviation, Sgw, of 2.49x1007 mm. 2) A vibrational acceleration, A 2/g, of 2.54. 3) A minimum vibrofluidization velocity, Umvf, of 4.2 cm/s. The cont rolling mechanism of the falling rate period was determined to be diffusion, with an effective diffusion coefficient, Deff, of 2.85x105 cm/s, and critical moisture content, Mc, of 30%. Economic evaluation of t he proposed method has a payback period of 4.34 years, and an estimated processing cost of $33 per ton of dried material. Models were developed based on bed hydrodynamics and threephase drying kinetics, and thinlayer drying. Both models accurately predicted the drying curves. The threephase kinetic drying model solved a series of simultaneous equations, and differential equations, based on moisture and enthalpy balances. This complex mo del successfully predicted the bed hydrodynamic properties and serves to fa cilitate scaleup, design, and bed configuration investigations. For t he thinlayer drying model, the drying constants, K & N, for P ages equation were determi ned as a function of bed temperature. This comput ationally simple, singlepar ameter model would serve process control algorithms. PAGE 18 1 1 INTRODUCTION Evidence of the presence of citrus in Florida dates back as early as 1579, in the region known as St. Augustine. It is believed that the ear liest plantings are attributed to the Spaniards, and by 1800, numerous groves had been planted near and around St. Augustine, Tampa Bay, and along the St. Johns River. In 1813, the United States annexed Florida, and the state experienced rapid expansion of citrus cultivation for comme rcial purposes. By the late 1800s, Florida was a wellestablished citrus pr oducing state, bearing record crop sizes and shipping citrus to northern cities. Present day figures reveal the 200203 Florida total orange crop forecast, released by the USDA Agricultural Statistics Board, was 200 million boxes5. The two divisions of the forecast are ear ly and midseason at 112 million boxes, and late type (Valencia) at 88 million boxes. In addition, the grapef ruit forecast was 39 million boxes3. Roughly 90 percent of the tota l orange crop is processed into juice and the remainder is shipped as fres h fruit. Citrus fruit is comprised of many parts; by weight, the juice only accounts for 50 60 percent. All other components must be disposed of; the peel (comprised of the flavedo and albedo), the segment membrane, juice vesicl es, seeds, and central core. It is to the processors advantage to convert this ma terial into valuable byproducts. The cost of converting the processing residue in to animal feed in a typical feed mill of PAGE 19 2 a citrus processing operation is approx imately $40.00 to $65.00/ton of dried pellets and the market price is approximately $40.00/ton 35,39. This is the primary driving force for finding an alternative proc ess that is more efficient and reduces production costs. It is my hypothesis that this residue can be dried in a fluidized bed dryer more efficiently, at a lower cost per ton, and with less damage. This hypothesis is explored systematically in this dissertat ion. Initially, a lit erature review is provided. This is follow ed by a definition of the pr oblem, a research plan, an economic evaluation, experiment ation, and process modeling. The model component of this dissertat ion begins with determination of the fluidized bed hydrodynamic parameters. Th is is followed by the development of two models for the fluidized bed drying of t he citrus particles: The first is based upon moisture and energy balances, while the second is based upon thinlayer drying. The dissertation concludes with an experimental evaluation of the models followed by results, conclusions and recommendations sections. PAGE 20 3 2 LITERATURE REVIEW 2.1 Fluidization In various operations, it is often nece ssary to contact granular material with a fluid (gas or liquid). The technique, that suspends or fluidizes the granular materials in a vertically rising fluid, is re ferred to as fluidizati on. It is a tool with many applications in the chemical, pet roleum and food processing operations. Figure 1 presents many of the current industrial applications arranged by dominating mechanisms. Solids drying Absorption Cooling Freezing Heat and/or Mass Transfer between gas & particles Plastics coating Granulation Mixing of solids Dust filtration Heat and/or Mass Transfer between particle & particle or particle & surface Heat treatment of textile fibers, wire, rubber, glass, and metal components Constant temp. baths Heat Transfer between bed & surface Physical Oil cracking, reforming Manufacture of: acrylonitile, polyethylene, chlorinated hydrocarbons Gas/gas reactions in which the solid acts as a catalyst or heat sink Coal combution & gasification Roasing of Ni & Zn sulfides Incineration of solid & liquid waste Decomposition of limestone Gas/solids reactions in which the solids are transformed Chemical Industrial Processes Figure 1 Fluidized Bed Industrial Applications29 PAGE 21 4 2.1.1 Fundamental Concepts Fluidization is the operation where a bed of particulate solids is made to behave like a liquid by the pass age of a fluid (gas or liquid) at a flow rate above a critical value 31. If a fluid is passed upward through a bed of particles at a low rate, the fluid merely percolates thr ough the void spaces between stationary particles; this is a fixed bed. With an in crease in flow rate, the particles move apart and a few move in restricted regions; this is an expanded bed. At even a higher flow rate, a point is reached where all the particles are just suspended by the upward flowing fluid. At this poi nt the frictional force between fluid and particles just counterbalances the weight of the particles, the vertical component of the compressive force due to adjacent particles disappears, and the pressure drop through any section of the bed nearly equals the weight of the fluid and particles in that section. A bed in this stat e is considered to be just fluidized or at minimum fluidization 42. At this point, the fluidiz ed bed begins to exhibit liquidlike behavior. At fluid velocities above the mini mum fluidization velocity the bed characteristics vary according to the flui d properties. In liqui dsolid systems, the bed expands in a smooth progressive manner. In gassolid systems, instabilities arise due to bubbling and channeling. Bec ause of these instabilities, the bed does not continue to expand and remains close to its volume at minimum fluidization. Both gas and liquid fluidi zed beds are considered to be densephase fluidized beds as long as the upper surface of the bed remains clearly defined 42. The liquidlike behavior of fluidized beds is illustrated in Figure 2. PAGE 22 5 Figure 2 Fixed and Fluidized Bed Properties PAGE 23 6 For example, a light object will float on t he surface and a heavy object will sink to the bottom of a fluidized bed. Solids will flow from a hole below the surface of the fluidized bed. The pressure difference between two points in a fluidized bed is approximately equal to the static head between thes e two points. When two fluidized beds are connected, their levels equalize. These properties allow for various c ontacting schemes to be devised. These are typically countercurrent, cr osscurrent, and solid circulation between multiple beds. In addition, the liquidlike behavior provides for rapid and easy transport, and intimate gas contact. These assets, and the flexibility for configuration, are commonly cited in t he recommendation of fluidized beds in industrial applications. Due to the effect of bed hydrodynam ics on heat and mass transfer to and from the particles within a fluidized bed, the quality, or type of, fluidization is also important to consider when designing a fl uidized bed process. There are several fluid/solids interaction regimes in fluidized bed processing. These are represented in Figure 3 (numbers correspond): 1) Fixed bed. 2) Fluidized bed at minimum fluidization. 3) Smooth fluidiza tion. 4) Bubbling fluidization. 5) Slugging (axial slugs). 6) Slugging (flat slugs). 7) Turbulent fluidization. 8) Lean phase fluidization with pneumatic transport. PAGE 24 7 Figure 3 Contacting Regimes 2.1.2 Pressure Drop The force balance across a fluidized bed dictates that the pressure loss across the bed of particles is equal to the weight of the bed particles per unit area of the bed. Hence: weight of particlesupthrust on particles P cross sectional area of bed (1) A typical way to evaluate a beds fluidization state is to track the pressure drop as a function of fluid velocity. An idealized representation of the pressure drop velocity relationship is presented in Figure 4 22. A wellfluidized bed has a constant pressure drop when the fluid velocity is increased above the minimum fluidization velocity. However, identifyi ng the minimum fluidization velocity may be difficult. Kunni & Levenspiel 42 describe the relationship between velocity and PAGE 25 8 pressure drop: As the fluid flow incr eases in a fixed bed, the pressure drop increases proportionally. As the fluid velocity increases further, a maximum pressure drop is observed. In the straightline region of increasing velocity, below this maximum, the bed is consider ed to be a fixed bed. This region is described in general by the Ergun equation: 2 2 f 323 svsv(1)U P(1)U 1501.75 Hxx (2) As the fluid velocity increases above this maximum, the bed achieves fluidization. At this point, the bed expands and the pressu re drop remains fairly constant with increasing fluid velocity. The fluidiz ed bed region is described by the following equation: pfHA1g P A (3) where H is the bed height, is the is the bed voidage, p is the particle density, f is the fluid density, and A is the bed cross sectional area. When the pressure drop fluctuates with increasing fluid velocity, a slugging bed is created. A slugging bed is undesirable because the dryi ng fluid does not uniformly contact the material to be dried 48. PAGE 26 9 Fluid VelocityPressure Drop Fixed Bed RegionFluidized Bed Region Increasing velocity Decreasing velocity Min.fluidization velocity ^ > Figure 4 Ideal Pressure Drop Velocity Curve 2.1.3 Geldart Classifications In much of the literature, invest igations into how particle properties influence fluidization behavior have been undertaken. Geldart27,28 developed a way to classify particles and their flui dization behavior. This nomenclature is used throughout fluidization literature. Klinzing40 summarizes these classifications as follows: Group B particles contain materials such as sand and glass beads. They have a medium parti cle density and a size range of 75 to 600 microns. These particles fluidize easily, forming bubbles at, or slightly above, the minimum fluidization velo city. Group C particles are cohesive with strong interparticle forces. Generally, they have a diameter of less than 50 microns. They tend to form plugs or channels duri ng fluidization. Group A particles are generally intermediate in size between gr oups B and C. They typically show an extended region nonbubbling above the minimu m fluidization velocity. These PAGE 27 10 materials are rather ideal for processing in a fluidization mode. Group D particles are large and dense. They form permeabl e beds with high minimum fluidization velocities, and tend to spout and channel rather than fluidize. These classifications are represented graphically in the following figure, adapted from the Miyauchi et al. 47. The region A1 in the figure repres ents properties desired for wellbehaved FCC catalyst. 0.01 0.1 1 10 10100100010000 Particle Size, dp, micronsParticle Density, Dp, g/cm^3 Figure 5 Classification of Particles by Geldart 2.1.4 Particle Size Distribution A fluidizable particle is granular, and may be monodisperse (all particles of the same size) or polydisperse (a mixture of particle sizes)70. The determination of the particle properties is essential for fully understanding the fluidization process. The particle sizes of a polydis perse material are typically determined by sieving. Sieving has been used since early Egyptian times for the preparation of C A B A 1 D PAGE 28 11 foods. It is a particularly useful tec hnique since particles are classified on the basis of size alone, independent of thei r other properties (density, surface properties, etc.)7. Typically, particle size data is presented in histograms, density distributions, and cumulative distributions. The size of particles is reported in terms of geometric mean diameter, dgw, and geometric standard deviation by mass, Sgw. The American Society of Agricultural Engineering 8 cites the following calculation formulas, for these descrip tors, based upon derivations by Pfost and Headley and Soknhansanj and Yang: 1 gwlog dlogii iWd W (4) 1 11 loglog1 loglog 2 gwgwSdSS (5) where, 1/2 2 logloglogiigw iWdd S W (6) For nonspherical particles, sieving can overestimate the particle diameter, dp, defined as the diameter of a sphere t he same volume as the particle. To account for this, most fluidization work uses a product of particle sphericity and particle diameter, s and dp, for a complete sizeshape de scription of a particle. Particle sphericity is defined as the surf ace area of a reference sphere having the same volume as the particle divided by the surface area of the particle. Sphericity equals one for sphere, and is between zero and one for other shapes7. PAGE 29 12 2.1.5 Agglomeration Agglomeration is the amassing of particles during processing. It can present both a processing probl em or an aid when attempting fluidization. In the former, sticky particles can agglomerate causing a significant increase in the minimum fluidization velocity of a forming bed, or deflu idization of a stable bed. In the latter case, binders can be added to the fluidized bed in order to agglomerate fine materials and facilita te fluidization. The tendency to agglomerate depends on the stickiness of t he particles (which can be a function of temperature), the available surfac e area, and the particl e momentum. In general the agglomerating tendency, Agp, is: pab Ag c (7) At present time, there is not a quantitat ive relationship between these variables, and experiments are required to deter mine conditions for stable operation29. Passos and Muhumdar 52 present an investigation into the cohesive forces that develop in the drying of wet particles. Specifically, they discuss the drying of pasty materials. This system becomes complex due to the development of cohesive forces resulting from liquid br idges between particles. These forces affect gas and solids flow leading to unc ontrollable agglomerati on, defluidization and poor gassolids contacting. To determine the effects of a viscous fluid on the fluidization of particles, they coated gl ass beads and plastic pellets with varying levels of glycerol, and observed the result s. They performed their experiments in both a fluidized bed and a s pouted bed. The experimental results are presented as both the pressure drop as a functi on of the air velocity, and the bed voidage PAGE 30 13 associated with different coating levels. This data demonstrates the difficulties associated with fluidizing sticky particles At a lower liquid content, the bed of wet particles expands which hinders in cipient fluidization; the minimum fluidization velocity is increased. At hi gh liquid contents, the bed of wet particles contract and particles agglomer ate even at high gas flows. In a similar fashion, McLaughlin and Rhodes 46 investigated agglomeration by studying the effects of the addition of nonvolatile liquids with different viscosities and surface tension values to a gassolid fluidized bed. Experimentally, the authors used Gel dart group B particles at ambient temperature to avoid the effects of te mperature on the parti cles and the liquids tested. These particles have low interpar ticle forces and typically bubbling of the fluidizing gas occurs at the minimum fl uidization velocity. The authors also monitored bed behavior in order to classi fy the particle as either exhibiting Geldart group B, A, or C c haracteristics. Group B par ticles are described above, while group A particles can achiev e nonbubbling fluidization, and group C particles exhibit cohesive powder characte ristics with bed defluidization occurring as cracks and channels form in the bed. Additionally, McLaughlin and Rhodes modeled their process and developed a total interparticle force term, FIP, that is a combination of the viscous force and the surface tension effects. They use this interparticle force, in a ratio with the drag force on the particle, to pl ot versus liquid addition and the particles group classification. This data is t hen evaluated to develop a criterion for bed PAGE 31 14 transition characterization from group B to A to C particles, effectively predicting the onset of bed defluidization. Figure 6 summarizes some of these results. From the two plots provi ded, one can see that the tr ansition from B to A, and A to C group classifications corresponds to ratios of interparticle force to fluid drag force of 0.06 and 1.07 respectively for the top figure, and 0.02 and 0.7 for the lower figure. The authors then state that the transiti ons from B to A occur at ratios between 0.02 and 0.06, and A to C occur between ratios of 0.7 and 1.07, and that the Geldart group transitions occu r at fixed values in these ranges. Looking at the simplified force ratio plot in the lower portion of Figure 6, it may be of more use to fit equations to the dat a curves. This will allow the behavior transition information to be easily related to the ratio of free liquid to solids. PAGE 32 15 where Geldart group B, group C, group A, group A/C Figure 6 Agglomeration Effects PAGE 33 16 2.1.6 Design Critical information needed for the des ign of a fluidized bed for physical operations, such as heat and ma ss transfer and drying, includes42: 1) The drying rate of the material. 2) The tendency of the solids to agglomerate, break or erode. 3) The tendency of the solids to coat the wall surfaces of the bed. 4) The effective particle diameter or particle si ze distribution. 5) The effective bubble diameter expected in the bed. 6) Properties of the exit gas stream relating to possible combustion. Items 1 to 4 are usually determi ned in the laboratory utilizing benchtop experiments. Item 5 is most often approx imated using an empirical relation, such as the one presented in t he model development section. Item 6 must be considered due to the probable ex istence of fine solids in the exit gas stream. Where fines flow in a system, static charges may build and discharge causing a dust explosion. After considering the above items, design of the fluidized bed can begin. The primary factors influenc ing the quality of fluidiza tion are the distributor plate and the bed geometry. Whitehead 72 indicates that the understanding of the effects resulting from the beddistributor interacti ons is essential for design and operation. For good quality fluidiza tion, the gas needs to be uniformly distributed across the entire bed cross secti on. The distributor must accomplish this and support the weight of the bed dur ing startup and shutdown, minimize the aeration of the bed materi al, not plug or foul during long periods of operation, PAGE 34 17 and prevent fine particles from falling into the plenum beneath the distributor 61, 48. Sufficient pressure drop across the di stributor is required to achieve equal distribution of the gas fl ow over the entire distributor. Agarwal et. al. 6 believe, along with others, that the cr itical distributor design crit eria is the ratio of the pressure drop across the distributor to the pressure drop across the bed. They recommend that the ratio of pressure drops should be 0.1 to 0.3, with agglomerating and hard to fluidize material s at the higher end of the range. This agrees with the ranges presented in Whitehead72, which surveys the finding of several other investigators. Rather than use the lowend ratio, 0.3, for agglomerating materials, Qureshi et al. 57 suggest a minimal value of 0.01 and offer an equation for determining an ideal ratio of pressures. This equation relates the bed diameter and height to the ra tio of the distributor pressure drop, PD, to the bed pressure drop, PB, by the following equation: D BP D =0.01+0.21exp P2H (8) where D is the bed diameter and H is t he bed height. A direct relation exists between the bed pressure drop and the bed hei ght. To predict the bed pressure drop, PB, Kuni and Levenspiel32 proposed the following relation: bmfpfPH1g (9) 2.1.7 Modeling Essential velocity information, requir ed for modeling fluidization, includes the terminal velocity, the minimum flui dization velocity, the bubble velocity and PAGE 35 18 the superficial velocity for the fluidized bed. For fluidization situations that include large and irregular particles, su ch as orange peel particles, these operation parameters are best determined by experimentation, but can be approximated with the following set of equations: The terminal velocity, ut, is given by Newtons law as ut = [gdp 2( p)]/18 (10) The minimum fluidization velocity, VOM, can be obtained from VOM = [ sdpg( p) 3/1.75 ]1/2. (11) However, it is often more convenient to use the terminal to minimum fluidization velocity ratio given as ut /Vmf = 1.75 [gdp ( p) / ]1/2[1.75 /( gdp ( p) 3)]1/2 (12) where ut = 2.32 Vmf / 1.5. (13) Determination of the remaining two velocity values depends on the operational conditions. If bubbling fluidiza tion is assumed, then the expansion of the bed comes mainly from the space o ccupied by the gas bubbles. Under these conditions, the following approximations may be made to determine the bubble velocity, ub, and the superficial velocity, U, ub 0.7 (g db)1/2 (14) U = b ub + (1b)Vmf (15) given the fraction of the bed occupied by bubbles, b. If a force balance approach is ta ken in determining the minimum fluidization velocity, the agglomerating char acteristics of the material must be incorporated into the fluidization force balance. To address agglomeration in a PAGE 36 19 force balance, Passos & Mujumdar52 account for the interparticle forces generated by the addition of the liquid bi nder. The authors apply a momentum balance to the bed structure and estimate the average tensile strength by developing a stress term, c, associated with the interparticle cohesion, which is a function of the pressure drop across the bed, P, and the bed height at minimum fluidization, Hmf, l cMAX mfP'L K 2H (16) where wlmfl MAXwl wl[1exp(2tanDH/L)] K=*(1+sin)(1+D) 2tanD (17) This stress term is a function of the pa rticle properties, the interaction between the particle and the bed wall, the fl uid flow, bed geometry, and the bed dimensions. It is then used to calculate an interparticle force, FH, 2 p Hc8(d/) F 9(1)N (18) which can be used in the particle force balance necessary for a fluidization model, where N represents the average number of contact points between a particle and its neighbors, is the sphericity of the particle, dp is the particle diameter, and is the bed void fraction. The authors compared their interparticle force equation with a published one for capillary binding force, Fc. They found that the FH equation produces a force valu e of the same magnitude as Fc with fewer parameters. PAGE 37 20 Passos and Mujumdars interparticle force equation could help in the development of a model for the fluidizati on of the citrus particles, based upon force balances. The basic model would be developed by applying force balances on the particle, related to the fluid flow a nd gravitational effects. The inclusion of this interparticle force will add a factor to the model not previously considered, and will most likely assist in determining an accurate minimum fluidization velocity. As mentioned in the section 2.1.5, McLaughlin and Rhodes46 address agglomeration by using a total interparticle force term, FIP, which is a combination of the viscous force and the surface tension force, IPVSFFF (19) The viscous force term, FV, accounts for liquid bridging between the particles, and is developed by using the particle di ameter, the liquid viscosity, the contact angle between particles and the characteristic frequency for particle oscillation, 22 VF(3/8)dsin (20) The surface tension term, Fs, was estimated by 2 SFdsin (21) where the is the liquid surface tension, d is the particle diameter, and is the particle contact angle. The total inter particle force is the sum of these two components and is represented as 222 IPF(3/8)dsindsin (22) PAGE 38 21 The determination of the characte ristic frequency and the contact angle are critical for this interparticle force approximation to be of use. In McLaughlin and Rhodes case, the contact angle was measured by using scanning electron microscopy on a sample of particles fr om the bed. The characteristic frequency of particle oscillation was not measured, but was approximated by measuring the oscillation frequency of bed pressure dr op. The assumption is that the microscopic motions that make up the particle oscillation frequency can be approximated by the bulk particle moti on effect on the bed pressure drop. For large particulate fluidization, the determination of the interparticle force terms of the force components (Fv & Fs), the approximati ons are too limited to be of value in the fluidization model. The contact angle measurement is taken at one point in time when t he particles are at rest, and not being fluidized. The contact angle will change according to bed behavior, thus changing the interparticle force term. In addition, t he approximation of the microscopic particle characteristic oscillation frequency, by the bed pressure drop frequency, for powders is weak. For large particles, van der Walls forces will most likely contribute strongly to the oscillation fr equency, but will not be expressed in the pressure drop at the macroscopic scale of the bed. 2.2 Drying Drying consists of a unit operation in which a liquid, typically water, is removed from a material in equipment term ed dryers, it is traditionally defined as the unit operation that converts a liquid, so lid, or semisolid feed material into a PAGE 39 22 solid product of significantly lower moisture content 11. The use of heat to remove liquid distinguishes drying from mechanical drying methods such as centrifugation, decantation, pressing, or sedimentation 44. Drying is a process of simultaneous heat and mass transfer. Heat is supplied to the material to facilitate the evaporation of moisture; subsequently, the moisture is removed from the material into the drying medium In dried citrus pulp production, the Florida citrus industry feed mill current ly uses pressing and evaporation of the press liquid, followed by airdrying. 2.2.1 Drying Principles For the majority of industrial dryi ng processes, preheated air is used as the drying agent. This airw ater vapor mixture transmits heat to the material surface via convection, and then by conduction to the interior of the material. In the opposite direction, moisture is simult aneously removed from the material. As a liquid, it moves from the inside of the material to the surface, and then evaporates by convection to the drying medium 65. This process is represented in Figure 7. PAGE 40 23 Figure 7 Transfers During Drying The ability of air to remove moisture from a material depends upon the temperature and the am ount of water vapor already c ontained in the air stream. The content of water vapor contained in the air stream is expressed as either absolute humidity (the mass of water vapor per unit mass of dry air), or relative humidity (the ratio of the parti al pressure of water vapor in the air, to the partial pressure of saturated water vapor at the same temperatur e, multiplied by onehundred) 25. The temperature of air can be det ermined using either a drybulb or wetbulb thermometer. Drybulb tem perature is measured using a standard thermometer. A thermometer whose bulb is covered with a wet cloth measures wetbulb temperature. Heat is removed from the thermometer bulb as the water PAGE 41 24 in the cloth evaporates. The difference between these two tem peratures is used to calculate the relative humidity of the air. Typically, the formulation of a drying m odel is complex, as three types of transport exist for the liquid and v apor, presented in Figure 8 (numbers correspond): 1) Transport of liquid within t he solid. 2) Evaporat ion of liquid from the surface of the solid. 3) Transport of vapor away from the solid. One, or a combination of the following mechanisms, controls the transport of liquid within the solid: Capillary flow, liquid diffusion, vapor diffusion, and/or viscous flow. The evaporation process is influenced by the particle surface area and local pressure environment. The transport of vapor away from the solid is affected by the gas flow and its path of travel. Determining the dominant mechanisms is critical for model development. 1 2 3 Figure 8 Transport Processes During Drying PAGE 42 25 Drying data is typically presented as a pair of standard drying curves. The first curve plots moisture content vers us drying time; the second curve plots drying rate versus moisture content. The data for determining representative curves is usually obtained under laborat ory conditions by measuring the mass and temperature change of a mate rial sample with time 65. The explanation of the shape of the drying curve is closel y related to the mass and heat transfer operations within the system. Typical representations of these c onvective drying curves are presented in Figure 9. Using these curves, the dr ying process can be described as a series of steps in which the drying rate plays a key role 12. The period from point A to B represents the warm up period for t he product. Point B represents the equilibrium temperature of t he product surface. After this warm up period, the curve takes on a linear characteristic; this period from point B to C is known as the constant rate period. During this per iod, the free water on the surface of the product is removed. This period is char acterized by a constant drying rate, and lasts only as long as the water is supplied to surface as fast as it is evaporated away. The period from point C to D is k nown as the falling rate period. Here the drying rate starts to decrease, as the rate of drying is gov erned by the transport of water from the interior to the surfac e of the product. Fina lly, the period from D to E represents the second falling rate per iod, where the surface is completely dry and the plane of evaporation recedes from the surface 12. Point C is often referred to as the critical moisture content, Mc, and point E is often referred to as the equilibrium moisture content, Me. PAGE 43 26 Figure 9 Typical Drying Curves PAGE 44 27 2.2.2 Drying Equipment Dryers are often classified accordi ng to the method by which heat is transferred to the wet solid. The heat required for drying may be supplied by convection (direct), conduction (indirect), and/or radiation. Both direct and indirect dryers are used industrially. Dire ct dryers use hot gas, typically air, to contact the material. The vaporized li quid is transported aw ay in the heating medium. In indirect dryers, heat is conduc ted into the material by the hot metal walls of the dryer, and through particle contact 12. The vaporized liquid is removed independently from t he heating medium. Perry 55 presents a classification system for industrial drye rs based on the method of heat transfer, which is adapted in Figure 10. Continuous Tray Continuous Sheeting Pneumatic Conveying Rotary Spray ThroughCirculation Tunnel Fluidized Bed Continuous ThroughCirculation Tray & Compartment Fluidized Bed Batch Direct Dryers (Convection Dryers) Radiant Heat Dryers (Infrared Heating) Cylinder Drum Screwconveyor Rotary Vibrating Tray Continuous Agitated Pan Freeze Vacuum Rotary Vacuum Tray Batch Indirect Dryers (Conduction Dryers) Industrial Dryers(Producing a dry solid product from a wet feed) Figure 10 Classification of Dryers Based on Heat Transfer Mechanism Engineering characteristics for the most common types of dryers are summarized in Table 1 69. PAGE 45 28 Table 1 Characteristics of Selected Dryers Dryer Type Evaporation Capacity (kgw/m2h) (kgw/m3h)* Energy Consumption (kJ/kgw) Thermal Efficiency (%) Residence Time (s,min,h) Tray or Cabinet 0. 11 30004500 5080 224 h Tunnel & Conveyor 518 40006000 3560 10180 m Rotary 30120* 35006000 4070 1060 m Fluidized Bed 3090 31006000 4080 530 m Pneumatic 10100* 35005000 5075 215 s Spray 130* 40005000 5060 5120 s Drum 430 30003500 7085 1030 s Vacuum & Freeze 17 >7500 124 h Mujumdar and Menon 50 provide detailed classification schemes for industrial dryers with criteria necessa ry for appropriate selection. At the minimum, the following quantitative informati on is required to arrive at a suitable dryer selection41: 1) Dryer throughput and mode of production (batch/continuous). 2) Pr operties and variability of the wet feed and desired final product specifications. 3) Upstream and downstream processi ng operations. 4) Drying kinetics. 5) Qualit y parameters. 6) Safety aspects, such as fire and explosion hazards. 7) Value of t he product. 8) Flexibility in capacity requirements. 9) Type and cost of fuel and electricity. 2.2.3 Drying of Foods (Dehydration) The drying of foods is o ften referred to as dehydration. This differentiation is due to the fact that dehydration usually implies the removal of water, accompanied by a chemical change, whic h typically occurs in food drying 44. There are many reasons to dry foods and foremost among these is preservation. Dried foods can be stored for long periods of time due to their low water activity. The microorganisms that cause spo ilage and decay are unable to grow and PAGE 46 29 multiply in the absence of sufficient wate r, and many of the enzymes that cause undesirable reactions to occur in f oods cannot function without water 24. In addition to the increased stability of t he food, drying causes a significant reduction in the weight and volume of the material. This contributes to reduced costs of packaging, handling, stor ing and distributing the foodstuffs 69. Dryer selection is based upon the raw material properties, specifications for the final product, and dryer characterist ics. Food product applications for the most common types of dryers are presented in Table 2 69. Table 2 Food Industry Applications for Selected Dryers Dryer Type Product Application Tray or Cabinet Fruits, veget ables, meats, confectioneries Tunnel Fruits, vegetables Belt Conveyor Grains, fruits, vegetables, cereals, nuts Rotary Seeds, grains, starch, sugar crystals Pneumatic or Flash Starch, pulps, crops, granules, powders Fluidized Bed Vegetables, granules, grains, peas Spray Milk, cream, coffee, tea, juices, eggs, extracts, syrups Drum Milk, soups, flakes, baby cereals, juices, purees Foam Mat Fruit juices and purees Puffing Fruits, vegetables Freeze Flakes, juices, meat, shri mp, coffee, vegetables, extracts. 2.3 Fluidized Bed Drying Dryers, in which the drying gas fluidi zes the solids, are known as fluidized bed, or fluidbed, drye rs (FBD). Figure 11 represents a typical continuous fluidized bed dryer 54. The process has been used industrially since 1948, and today is one of the most co mmon types of dryers used in industry to produce dry particulate products such as polymers, fertilizers, pharmaceuticals, sand, PAGE 47 30 crushed minerals, and crystalline material s. The primary reasons for its popularity are due to its simple c onstruction and low maintenance costs 10. Figure 11 Standard Fluidized Bed Dryer The two main categories of fluidiz ed bed dryers are batch and continuous. Batch FBDs are normally used when the production scale is small, and diverse products need to be run on the same production line 59. They have superceded tray dryers as the most ec onomic method of drying powders 10. Continuous, or wellmixed, FBDs facilitate drying of larger production volumes than batch dryers. They are considered wellmi xed because the particle residence time approaches the perfect mixing law. Becaus e of this near perfect mixing, the bed PAGE 48 31 has a uniform composition and temperature equal to the temperature of the outlet product and exhaust gas streams 10. Hence, the wet feed falls into a bed of almost dry particles, fac ilitating the processing of wetter feedstocks than possible in a batch FBD. The main drawback a ssociated with a continuous FBD is that the wide particle residence time distribut ion leads to a wide range of moisture content in the final product 59. 2.3.1 Advantages and Disadvantages Fluidized bed drying of granular flui dizable material gives several advantages over alternative processes 29,31,54: 1) Temperature is uniform throughout the bed so that ev en product dryness is obtained. 2) There is little chance that sensitive materials will suffe r local overheating. 3) The excellent heat transfer coefficient from heating surfaces produces lowcost, minimum surface requirements. 4) The handling of particles is quite gentle compared to other types of dryers. 5) The lack of moving parts keeps reliability high with low maintenance costs. 6) A continuous process coupled with high throughput is possible. 7) The dryer is mounted vertic ally and saves space; this is especially important at plants where s pace is limited or land costs are high. 8) No skilled operator is required to operate the dryer. The main disadvantage associated with fluidized bed dryers is that many materials are difficult to fluidize. Some potential feedstocks are too wet to fluidize, due to excessive surface moistu re causing agglomeration complications. Another limitation is enc ountered when the feedstock has a very wide particle size distribution. In this case, the ai r velocity required to fluidize the large PAGE 49 32 particles can cause elutriation (undesir ed pneumatic transport out of the bed) of small particles 59. Some other disadvantages associated with fluidized bed dryers are 23: 1) Depending upon the particles, ther e may be erosion to the pipes and fluidization chamber due to particle abras ion. Should this be the case, more expensive, erosion resistant, materi als would be required for equipment fabrication. 2) Elut riation of fines are inevitable. 3) The hydrodynamic features of the bed are complex, and hence mode ling and scaleup are difficult. 4) Defluidization may occur if particle agglomeration arises during the drying process. 2.3.2 Vibrofluidized Bed Dryers A vibrofluidized bed, or vibrating flui d bed dryer (VFBD), is typically a plug flow bed with a vibrating distributor plat e, or a vibrating fl uid bed conveyor. It offers several advantages over a standard FBD because any agglomerates arising in the feed will be kept moving by the vibrations of the distributor until they have dried sufficiently to breakup. Sec ondly, feeds with a wide particle size distribution can be processed successfully in this type of bed. The air velocity can be set low enough to avoid excessive el utriation of the smaller particles, while the largest particles are kept movi ng by the vibration. Finally, these beds are frequently used with feeds of entirel y large particles, and with a minimum fluidization velocity greater than 1 m/s. Often beds of these types of particles must be operated with excessive air veloci ties, which are great er than required to satisfy mass and heat transfer considerations The use of the VFBD allows the PAGE 50 33 air velocity to be kept in the vicinity of the minimum, with consequent savings in capital and operational costs 29. The nondimensional ratio, vibration acceleration, A 2/g, where A is the amplitude of vibration, is the angular frequency, and g is acceleration due to gravity, is a key property for describi ng vibrated and vibrofluidized beds. This property serves as a representation of the mechanical input to the system, and most VFB properties are linked to it. For A 2/g < 1, particles do not jump, they just slide against each other, reducing in terparticle friction and bed voidage. In this range of A 2/g, vibration is used for the compaction of powders. Upon increased vibration acceleration, a point is reached where the normal vertical force reaches zero and the bed loses cont act with the supporting plane, but does not change its location. Fo r greater values of A 2/g, the bed separates from the plane at greater angles and the flight time is increased. Many authors report an optimum range of vibration acceleration in which the bed structure is most suitable for drying and the drying rate is greatest. According to Mushtayev et al., Cheveilenko et al., and Osisnskii et al., the best results are obtained for A 2/g = 23. It is recomm ended that, at the minimum, A 2/g should be near 1, while at the maximum, A 2/g should be near 6. At a constant air velocity, the influence of A 2/g on the drying rate can be represented as in Figure 12 51. PAGE 51 34 Vibration AccelerationDrying Rat e 1 Figure 12 Dependence of Drying Rate on Vibrational Acceleration, A 2/g As in a nonvibrated fluidized bed, pr essure drop across the vibrofluidized bed, Pvb, is a direct function of bed height. It is generally reported that pressure drop is reduced by vibration. The reduc tion is mainly ascribed to the increased bed voidage of a vibrofluidized bed, in co mparison with a fluidized bed. This observation is seldom seen at low vibrational acceleration (A 2/g < 1). Gupta and Mujumdar proposed the following corre lation between fluidized bed pressure drop and vibrofluidized bed pressure drop as a function of the particle size, dp, bed height, H, the vibrational acceleration, A 2/g, and the particle sphericity, : 0.946 0.606 2 p 1.637 vbbd A PP10.0935.0 Hg (23) PAGE 52 35 In this correlation, the vibrated fluidi zed bed pressure drop relates to the upper plateau of the vibrofluidization curv e. The equation reportedly holds for frequencies higher than a threshold frequency of 4 to 6.4 hertz. 2.3.3 Modeling Modeling a vibrofluidized bed dryer is a challenge that requires the combination of all the co mponents presented thus far: 1) The fluidization equations developed earlier must be coupl ed with vibrational acceleration correlations. 2) Drying equations bas ed on moisture and enthalpy balances, which correspond to the same parameter s, must be derived. 3) Additional parameters must be determined, as needed, to satisfy the relations previously set forth. Principally these are t he heat and mass transfer coefficients between the particles and the fluidizing medium. The mass transfer coefficient, kc, that represents the mass transfer from the surface of a solid particle falli ng through a gas, may be determined from considering a single sphere and using t he Chilton and Colburn jfactor analogy, jD = (kc/Um)Sc2/3 (24) in combination with the Dwivedi and Upahyad correlation for fluidized beds 23, jD = 0.765/Re0.82 + 0.365/Re0.386 (25) which is valid over the range 0.01 Re 15,000, where the Reynolds number is expressed in terms of the superfici al velocity, U, the gas density, the particle diameter, dp, and the gas viscosity, 33 Re = Udp/ (26) PAGE 53 36 The heat transfer coefficient, ho, within a fluidized bed dryer can be estimated using heat transfer between a fl owing fluid and the surface of a single sphere. The following equation is recommended: ho= [2.0 + 0.60(dpG/ )0.50(cp /kf)1/3]( kf/dp) (27) with G = ut (28) where ut is the terminal velocity of the particles 45. 2.4 The Citrus Industry The optimal application of the conc epts associated with fluidization, drying, and fluidized bed drying to any industrial process requires an understanding of that industry. This section serves to provide that link to the citrus industry. The familiarization begi ns with a brief overview of history industry. 2.4.1 History The original home of citrus fruits is the southeastern and eastern regions of Asia, China, Cochin Ch ina and the Malayan Archipelago 67. The introduction of citrus to Europe dates back to t he third century B.C ., when Alexander the Great conquered Western Asia. Explorer s, soldiers, and crusaders all played a part in spreading citrus fruits throughout the Mediterranean world. Citrus had its beginnings in Flor ida about 1579 near St. Augustine. Wherever Spanish settlements arose, citrus plantings were not too far behind. In Florida, citrus was further spread by traveling Indians. By 1800, there were numerous groves planted by the Spani ards and other settlers, around St. PAGE 54 37 Augustine, Tampa Bay, and along the St. J ohns River. Shortly after the United States annexed Florida, settlers r apidly expanded the groves, and growers began shipping fruit commercially by boat to northern cities. The close of the Civil War marked the beginning of rapi d development of commercial Florida Citrus. In 1886, the crop reached a vo lume of over one million 90pound boxes for the first time 1. The next major development in the citr us industry was frozen concentrate orange juice. Born in wartime, this in vention transformed Florida from a state known for its fresh fruit, to the secondla rgest seller of orange juice in the world. Louis Gardner MacDowell, Cedric Donal d Atkins, and Edwin L. Moore were brought together in 1942 when the federal government a sked the Florida Citrus Commission to develop a new orange juice product it could transport to troops starving for vitamin C on the battlefields of Europe. Operating from a tiny U.S. governmentowned building in Winter Haven, the trio worked for three years to develop the product and ways to produce i t. The result of their dedicated research was a process that involved ev aporating the water from the juice at 80 degrees Fahrenheit, then returning a small, flavorful dose of fresh juice. The team then chilled the soluti on, canned it and froze it. By the time a U.S. patent was awarded on Nov. 9, 1948, the war wa s over and the process was being used successfully in commercial operations in Florida 73. Production of citrus in Florida today approximately equals the total production of all other major fruits in the United States. For the 199697 season, PAGE 55 38 the production of commercial citrus in Florida was approximately 295 million boxes. This figure is inclusive of oranges, grapefruit, tangelos, and limes 2. The huge growth of the citrus industr y in Florida cannot be attributed to any single factor. However, a major factor is the increase in technology that has enabled the processing, storage and shippi ng of fruit and juice to an everincreasing market. In addition, the devel opment of disease resistant varieties that flourish in the Florida climate, soil conditioned with ever improving agricultural practices, the increasi ng level of nutritional awareness among consumers, and its distinctive flavor has ensured that demand for citrus and citrus juices is always high. 2.4.2 Economic Impact Citrus fruits, including oranges, grapef ruit, tangelos, tangerines, limes and specialty fruits, are Floridas largest ec onomic agricultural commodity. Florida is the worlds leading producer of grapefruit, and only second to Brazil in the production of oranges. The state produces over 80% of the United States supply of citrus products. For the 19992000 season, the major economic factors associated with the citrus industry were estimated at $9.13 billion in industry output, $4.18 billion in value added, and 89,700 jobs34. The economic structure of the Florida citrus industry is illustrated in Figure 13. According to the Florida Department of Citrus, the estimated average FOB value of the Florida citrus crop for the 199596 thru 19992000 seasons was 3,989.5 million dollars. This is inclus ive of both fresh and processed oranges, and grapefruit. This value only represent s a good estimate due to the fact that PAGE 56 39 most Florida citrus compani es are privately held or divisions within large multinational corporations. Figure 13 Economic Structure of the Florida Citrus Industry Estimates for the size of the crop are based on sampling and public information. The Florida Agricultural Statistics Service forecast, for the 200203 season, estimates the Florida crop (a ll oranges) at 197.0 million boxes (199798 actual: 244.0 million boxes). This drop of 14.3% in the crop size will drive prices up within the industry. A strong indicator of this is the orange juice (OJ) retail price. A.C. Neilsen reports that at $4.44 a gallon, re tail prices are 18% higher than five years ago. Retail sales for both orange and grapefruit juice are relatively stable. Figures 14 & 15 present the juice sales volume and value data graphically 2,4. Recently there has been concer n expressed about the future of PAGE 57 40 the Florida citrus industry based upon the recent reduced per capita consumption of orange juice, lower per box orange pr ices, and increased imports into North America from Brazil 17. In the same article, Tom Sp reen, a University of Florida agricultural economist, is quoted as sayi ng Projected growth rates in both production and consumption over the next ten years are expected to be lower than those realized over the last ten years. However, considering the longterm trends in a society where demand for ci trus products has been steady or on the rise, the outlook for Florida Citrus gr owers and processors is still good, but may not be as positive as it was three years ago. Orange Juice Retail Sales, U.S. 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000197 677 197 778 197 879 197 980 198 081 198 182 198 283 198 384 198 485 198 586 198 687 198 788 198 889 198 990 199 091 199 192 199 293 199 394 199 495 199 596 199 697 199 798 199 899 199 900 200 001 200 102Oct. Sept. SeasonSeries Specific Units, see legend Volume (millions SSE gals.) Value (mil. $) Figure 14 Orange Juice Trends PAGE 58 41 Grapefruit Juice Retail Sales, U.S. 0 50 100 150 200 250 300 350 400 450 5001976 7 7 1 97778 1978 7 9 1979 8 0 1 98081 1981 8 2 1982 8 3 1 98384 1984 8 5 1 98586 1 98687 1987 8 8 1 98889 1 98990 1990 9 1 1 99192 1 99293 1993 9 4 1 99495 1 99596 1996 9 7 1 99798 1998 9 9 1999 0 0 2 00001 2001 0 2Oct. Sept. SeasonSeries Specific Units, see legend Volume (millions SSE gals.) Value (mil. $) Figure 15 Grapefruit Juice Trends In addition to direct sales for the pr ocessed citrus industry the Florida Department of Commerce, Bureau of Economic Analysis and the Florida Department of Citrus compiled the fo llowing data (Table 3) evaluating the economic impact that the entire citrus industry has on Floridas economy. Table 3 Estimated Annual Economic Impact of the Citrus Industry on Floridas Economy, Avg. 199596 thru 199900 Earnings Output/Sales Employment Item Millions $ Equiv. Full Time Jobs Fresh 337.0 1,064.2 16,705 Processed 1,923.4 6,821.5 57,201 TOTAL 2,260.4 7,885.7 73,905 PAGE 59 42 2.4.3 Citrus Processing In Florida, the majority of the ci trus crop goes to processed products rather than for fresh fruit consumption. The typical Florida citrus processing system can be best summarized as a collect ion of several processing units that comprise the operation. These units are Fruit Receiving, Fruit Processing, Juice Handling, and ByProduct Recovery (Figure 16). State Test Sampler (Load sampled and tested by Fl. D.O.Ag.) Oil / water emulsion to oil recovery Oil Extraction Sludge to Feedmill Long term Storage Packaging Evaporators Juice Chillers Chill to 35F Storage Tanks Coldwall Run Tanks Juice HandlingJuice Stream Centrifuge (seasonal) To reduce oil and juice viscosity Juice Pulp to Storage Pulp Wash Pulp, rag & seeds to Feedmill Pulp Wash System Pulp, rag, & seeds to Pulpwash system Pulp Recovery System Pulp, Rag and Seeds Juice, pulp, rag & seeds to Juice Finishers Peel to Feedmill Juice Extraction Fruit Sizing Culls to Feedmill Fruit Cleaning and Final Grading Fruit Processing Fruit Bins (Fruit held until needed by processing) Culls to Feedmill Fruit Unloading (Washing, detrashing, initial grading) Scale House (Loads Weighed) Fruit from groves to trailer staging Fruit Receiving Figure 16 Citrus Processing Operation In general, Fruit Receiving is responsib le for the fruit from the time it arrives at the processing plant in bulk tra ilers, or field boxes, until it is stored in PAGE 60 43 the fruit bins with a completed State Ins pection tag in place. Fruit Processing draws the fruit from the storage bins and is responsible for final grading and extraction. In Florida, there are two pr imary types of extrac tors used, the Brown system (Brown Citrus Systems, Winter Haven, FL) and t he FMC system (FMC Citrus Division, Lakeland, FL). Though t hese two systems are different in their approach to juice extraction, their results are the same. Juice Handling is responsible for taking the freshly extract ed juice, processing it and transporting it to storage. ByProduct Recovery not onl y deals with the recovery of valuable byproducts, but the conversion of processi ng residues into a sellable product, which can pose a serious disposal problem. The unit operations contained within, and the interconnectivity of these processi ng units, is presented in the flowchart (Figure 16). Since byproduct recovery is integrated into the processing operations it is not presented as a separ ate sequence, but is represented as the grey boxes in the flowchart. 2.4.4 Feed Mill Expectations In the state of Florida, ever y 1000 boxes (90,000 pounds) of oranges processed generates 40,000 pounds of peel, pulp and seeds (Figure 17). 18.2 Metric Tons Peel, Pulp, & Seeds *If evaporated: 3,130 L of 65 degree brix Concentrate 3.2 Kg Orange Essence Oil 45.5 Kg Orange Aroma 22.7 Metric Tons 11.8 degree brix Juice (21,711 L) 113.6 Kg Cold Pressed Oil 1,000 Boxes of Valencia Oranges (40.9 Metric Tons) Figure 17 Processing Mass Balance 66 PAGE 61 44 This juiceprocessing residue became a se rious disposal problem as greater and greater quantities of ci trus were processed 38. In order to dispose of this residue and turn it into a sellable product, the i ndustry converts this residue into a byproduct used as livestock feed. The curr ent process employed utilizes presses, rotating dryers, and a waste heat evaporator that dries the feedstock from 80% to 10% moisture, creating dried citrus pulp (DCP). The majority of processors further process the dried peel and pulp by pelletizing the material to create citrus pulp pellets (CPP). The average seasonal production of dried pulp and pellets, from Florida citrus processors for the 200102 and 200203 seasons, was 937,368 tons 13. DCP and CPP are primarily utiliz ed as livestock feed for cattle and sheep. It is second only to corn as a source of concentra ted feed nutrients. It is a good source of calcium with a bulk ca rbohydrate concentrate that is fairly high in energy, but low in phosphorous and carotene 60. Today, roughly 90% of the DCP and CPP produced in the state of Florida is exported to Europe via the Netherlands 39. In 2001, a monitoring progr am was established for elevated levels of dioxin in DCP and CPP. The source for dioxin in the product has been traced to the addition of the wrong type of lim e in the existing feed mill process. Two main factors to consider in t he drying of peel residue are the drying temperature and the final moisture cont ent. Temperature is of importance because as it increases, it has a detriment al effect on the nutritional value of the final dried feed. If the te mperature is too high, excessive dark coloration occurs and the feed becomes less palatable. T he current industry standard for drying is an exit gas tem perature of 150C with a product temperature of between 75 PAGE 62 45 80C 16. The final moisture content should be in the range of 10 to 12%. High moisture content feed will have a tenden cy to mold in storage, and possibly generate sufficient heat for spontaneous combustion. 2.4.5 Feed Mill Operations A feed mill is comprised of many more components than the dryer. Typically, the operation is comprised of the following unit operations: 1) Peel Storage. 2) Lime addition and reaction. 3) Hammer mill. 4) Pressing & molasses concentration. 5) Drying. 6) Pelletizing. 7) Finished product storage. A simplified process diagram of these uni t operations is presented in Figure 18. This flow diagram primarily addresses the flow of materials from one unit operation to another. Not included in this diagram are several control schemes that must be incorporated into the proces s. These include a pH control loop for the lime addition, the furnac e temperature, the dryer temperature (furnace exit and recirculated air control), and various pull out belts, screw conveyors, and blower motor systems. In Figure 18, the molasses produced by the evaporator is recycled into the feed stream. This is not always the case and molasses may be recovered from the process as a standalone byproduct, typically sold as a alcohol fermentation substrate 16. As a result of t he molasses concentration process, oil not removed in the proc essing operation can be recovered as dlimonene, also a standalone byproduct. PAGE 63 46 Figure 18 Feed Mill Operations In the unit operations diagramed in Fi gure 18, there are several equipment options for many of the st eps. A shredder could replace the hammer mill used to reduce the particle size of the peel. The press utilized can be one of various types available. Kesterson 38 discusses four types, typical in Florida feed mills: 1) Davenport press. 2) Louisville continuous press. 3) Vincent continuous press. 4) Zenith pulp press. Of these, only t he Vincent and Zenith presses are currently in use. All operate on the same princi ple and mechanically reduce the material liquid content from ~80 to 70% water c ontent. This expressed press liquor is sent to a waste heat evaporat or that utilizes the exiti ng air from the dryer to concentrate it into approximately 40Brix molasses. This operation helps to shift some of the energy load from the dryer. The three types of dryers used by the citrus industry as presented by Kesterson 38 are direct fired rotary, triple pass parallel heat flow, and the rotary st eam tube rotary. These are shown PAGE 64 47 schematically in Figure 19. Currently, the majority of feed mills utilize the rotary direct fired dryer, very few use the triple pass parallel heat flow, and no steam tube rotary dryers are in use 14. Disadvantages to these type of dryers include excessive kiln temperatures, burning of fines, lower yield, and fire hazard from burning particles 32. However, these have so mewhat been eliminated by lowering the temperature of the dryer or employing better process control. Figure 19 Three Types of Standard Citrus Dryers 30 Typically the dryer reduces the moistu re content from approximately 70 to 18%. The material is not dried to its final target moisture content of 12%, PAGE 65 48 because the pellet mills require a slightly higher moisture content to form stable pellets, and the pelletizing and cooling operation further reduce the moisture to approximately 10 12%. Based on conversations with industry re searchers initiated in December 2000 35,39, the cost of converting the peel re sidue into animal feed, in the abovedescribed operation, is either a breakeven or a loss situation. In the worst case, the manufacturing cost is approximately $65.00/ton of dried pellets, while the market price is $40.00/ton. This econom ic inefficiency was the primary driving force for finding an alternative process that is more efficient and reduces production costs. 2.4.6 Feed Mill Regulatory Aspects The most significant regulations that affect the feed mill processes are environmental. The governing constraint is the Title V regulation adopted by the U.S. Environmental Protecti on Agency (EPA) in July 1992. This rule requires all major sources of regulated air pollut ants to apply for, and obtain, a Title V operating permit. The citrus industry has determined that existing feed mills meet the criteria for major source s due to the volatile organic compounds (VOCs) that exit with the dryer air. The primary VOC exit ing feed mills is dlimonene, a volatile terpene hydrocarbon 30. The source of this VOC is typically due to inefficient recovery of peel o il in the processing operation and dlimonene in the molasses process 16. In addition to VOCs, Title V dictates that pollutants must also be monitored and controlled in the feed mill oper ations. These PAGE 66 49 pollutants include particulate matter, sulf ur dioxide, and emissions which include carbon monoxide and nitrogen due to fuel combustion 19. In addition to the Title V program, another air regulator y program that affects citrus feed mills is the preventi on of significant deterioration (PSD) new source review requirements. PSD new source review applies to major sources and major modifications. Under this regulat ion, the implementat ion of a fluidized bed design would be considered a major modification and would be subject to PSD review. PAGE 67 50 3 PROBLEM DEFINITION Present techniques employed for the di sposal of citrus processing residue are economically inefficient: They have oper ational costs higher than, or close to, the saleable value of the product. This research focuses on developing a viable alternative feed mill proces s. A vibrofluidized bed drying (VFBD) system would replace the presses, evaporator, and rotary kiln dryer currently being utilized. In this process, substantial savings should be realized in energy, operation and maintenance costs. The loss of t he additional byproducts, molasses and dlimonene, produced in the existing process, will offset some of these savings. Before a pilot scale VFBD can be designed and demonstrated, drying and fluidization parameters will need to be determined. In earlier work, Roe 63 determined the following dr ying parameters in a nonfluidized state; the mechanisms of both drying rate periods, and the drying rate, critical moisture content, and diffusion coefficient of the residue. However, the fluidization parameters still need to be determined and t he drying parameters verified in the fluidized state. These values will be obtained with a benchtop unit developed for this research and described in secti on 6.1.1. The additional fluidization parameters are a particle size distribution that will allow fluidization to occur, the minimum fluidization velocity for this parti cle size distribution, and the exploration of vibrational energy input. PAGE 68 51 A mathematical understanding of the drying process will be necessary to develop a process that is energy effi cient, scaleable, and meets the quality requirements of the product. The m odel, or models, will need to be rigorous enough to predict the bed hydrodynamic properties, as well as the drying process. Additionally, the models will need to be verified by comparison with experimental data. PAGE 69 52 4 RESEARCH PLAN The research for this dissertation focuses on the feasibility, development, modeling, and model verification of a new and state of the art system for the drying of citrus processing residue in a vi brofluidized bed dryer. This research progresses through three phases. Phas e 1 involves preliminary economic evaluation and modeling. In Phase 2, a benchtop unit is designed, built, and instrumented, with experim ents conducted to verify the drying parameters and determine the fluidization design parameter s. In Phase 3, the experimentally determined parameters are used to refine the model, and the model is verified. The starting point for Phase 1 is the fluidized bed dryer model developed in earlier work by Roe 63. This threephase dr ying model will be expanded to account for vibratory energy input requir ed to overcome agglomeration issues. The economic evaluation will be init iated based upon energy balances and parameter predictions from the model. In Phase 2, instrumentation is developed, installed, and calibrated, and experiments run with the bench top vibrofluidized bed to determine vibrofluidization and drying parameters. The model predi cted fluidization velocity from Phase 1 is used to initiate this exper imental phase. Here a particle size that fluidizes, the proper vibr ational acceleration, mini mum vibratory fluidization PAGE 70 53 velocity, the controlling mechanisms in the constant and falling rate periods, and the effective diffusion coefficient of t he material are determined experimentally. Finally, in Phase 3, the models ar e refined and verified, and the economic evaluation is finalized based on the su ccessful operating conditions. The fluidization and drying data fr om Phase 2 is used to refine the kinetic threephase model and predict the param eters of a second drying model based on thinlayer drying. Upon completion of model re finement and parameter prediction portion of Phase 3, both models are used to predict the drying rate in both the constant rate and falling rate periods. Dryi ng curves are generated and verified by comparing experimental results with the predicted values. The economic analysis will also be updated based on the re sults from Phase 2, and used to predict both the payback period associated wit h the installation of a vibrofluidized bed drying system in a medium sized ci trus processing plant and the cost associated with producing the final product. PAGE 71 54 5 ECONOMIC EVALUATION 5.1 Introduction The current feed drying system incurs a high cost to the processor. The first requirement for the proposed syst em is a demonstration of improved economic performance. A good first pas s economic comparison is an energy analysis of the two processes. Th is comparison will be based on the energy required to remove a standard unit of water from the material using rotary drying (the industry standard), and using fluidiz ed bed air drying (the proposed system). Flink 26 presents a system of equations and assu mptions for this method. Energy consumption data on a pilot scale ro tary system has been acquired, and will be compared to similar data collected on the laboratory bench top fluidized bed apparatus. Since the feed mill contains many more unit operations than just the dryer, an economic analysis method that includes the entire proce ss, and considers more than just energy consumption, will be conducted on t he proposed system. Candidate methods that c ould be utilized to evaluate fixed and operating costs include: 1) Discounted CashFlow Rate of Return (DCFRR) includes all of the cash flows over an entire project life and adj usts them to one fix ed point in time. 2) BenefitCost Analysis a courser method comparing the capital costs, operating costs, savings, and factors fo r benefits, such as reduced damage to PAGE 72 55 the surroundings and increased safety. 3) Payout time with and without interest a quick cost comparison me thod that determines the ti me required to reduce an investment to zero. 4) Return on Or iginal Investment (DuPonts method) calculates the percentage relationship of the average annual profit to the original investment without factoring in the time value of money. 5) Net Present Value (NPV) compares the projec ts on the basis of present value allowing for the time value of money, since all cash flow s are related to a base time before comparisons are made. 5.2 Analysis Economic analysis was conducted usi ng BenefitCost Analysis coupled with payback period (Payout time). The parameters used for the analysis were the BenefitCost profile and data collected from the bench top vibrofluidized bed, which was then scaled up for a medium sized citrus processing plant. Key to this twoprong approach is the costsavings and benefitdisbenefit profile development. Costsavings cons ist of the capital outlay (equipment, design, fees, construction, engineeri ng, working capital), annual expenses (operating costs, maintenance, depreciati on), capital savings (salvage value) and annual saving (feed sales). Benefitd isbenefits are comprised of benefits (reduced operating cost, increased safe ty, Title V issues) and disbenefits (increase in production time, loss of production, increased hazards). As an example of profile development, consider a medium sized plant that processes 80,000 boxes of fr uit/day. A processing plant with that capacity would PAGE 73 56 generate 1.44 x 106 Kg of peel, pulp and seeds at 80% moisture to be dried per day. Based on the following experimental results from benchtop vibrofluidized bed trials, drying time of 30 minutes with an average drying temperature of 150 C, fluidization velocity of 1 m/s in a 7.6 cm diameter bed, heat transfer coefficient of 0.2 W/cm2 oC, and mass transfer coefficient of 7.1 cm/sec, the bed would need to accommodate approximately 40m3 of product at one time. Assumptions were made for capital cost ing purposes which include bed diameter of 3m, air velocity of 2 times the mi nimum fluidization velocity, bed height of 5.66m, fluidized bed tower height of 18m, material of construction will be 304SS, energy costs $0.06 kWhr, and additional equi pment (in addition to the fluidized bed dryer) consisting of furnace, blower, ducting, cyclone, and controls. Table 4 FBD Energy Requirements Plant Capacity (4,000 boxes/hr) 163,296 kg/hr Unloading time 20 hrs/day Incoming fruit (80,000 boxes/day) 3,265,920 kg/day Peel, rag & seeds (80% moisture) 1,437,005 kg/day Operating Days (Nov. June) 250 days/year Drying Temperature (air exhaust) 150 oC Drying Time 30 min. Fluidization Velocity 1.03 m/s Water removal req's 1,120,864 kg/day Dry product out (10% moisture) 316,141 kg/day Enthalpy of the drying air 324.68 KJ/kg air Enthalpy of the drying out 310.96 KJ/kg air Enthalpy of the solid in 83.85 KJ/kg product Enthalpy of the solid out 37.04 KJ/kg product Humid Heat of the Air 1.01 KJ/kg air K Energy Req's for water removal (from balances, see Figure 20) 212,125,701 KJ/day Energy Req's for fluidization 198,548,652 KJ/day Energy for year 1.03 x1011 KJ/yr $/yr for dryer 1,804,914 $/yr $/ton of dried product (Dryer only) 21 PAGE 74 57 Cost estimates for energy we re based on scaled up equipment and enthalpy balances on the dryer. Tabl e 4 presents summarized assumptions and energy calculations. The energy requirem ents for water removal were calculated using the enthalpy balance program developed for this dissertation and presented in Figure 20. This program allows the user to specify the feed flow rate, moisture content and temperature, t he drying air flow rate and temperature, the exiting product moisture content and temperature, and finally the exit air temperature. For ease in calculation, the heat capacities of the bed constituents and enthalpy of evaporation were taken as constants instead of as functions of temperature. These values change only about 10 % over the temperature ranges in this scenario, which was determined to be acceptable. In addition, the balance was conducted such that exit air stream is not necessarily saturated. For example, at the conditions specified in Figure 20, based on physical observations in the laboratory, the predicted exit air is not saturat ed. This results in a process that is less efficient than it could be. This inefficiency only serves to overestimate the energy consumption, and subsequently the costs, making the economic analysis more conservative. For the proposed fluidized bed f eed mill, these assumptions and calculations result in a realistic payback period of 4.34 years, reducing the initial investment to zero. The annual expenses used to calculate this payback period are presented tabularly and graphically in the tenyear economic analysis presented in Figure 21. T he payback period does not reflect the loss of income associated with the sale of molasse s and dlimonene as separate byproducts. PAGE 75 58 Figure 20 Fluidized Bed Balance Program PAGE 76 59 Figure 21 Proposed FBD Feed Mill Payback Period As an additional economic consideration, the cost per ton of dried feed was calculated from this cost estimate. This is a fairly common industry unit for feed cost. Based upon this scale up and estimates of the support equipment, the estimated product cost for the proposed fl uidized bed drying system is $33/ton. The current price for feed is $40/ton, while the present co st associated with producing it, in existing feed mills, can be as much as $65/ton. PAGE 77 60 6 EXPERIMENTAL METHODS 6.1 Experimental Apparatus Large portions of the personal energies associated with this study were directed at developing a fully instrument ed, effective benchtop vibrofluidized bed dryer. The starting point for development was a fluidized bed previously used for studies related to the defluidization of viscous materials 48, and preliminary investigations into fluidi zed bed drying of citrus pulp 63. The fluidized bed was modified for the input of vibrational energy through attachment to a variable speed motor and cam, setup with a connec ting rod that facilitates stroke adjustment, suspension on rubber struts, flex ible attach points for instrumentation and air supply, and reinforcem ent of the distributor pl ate and calming section of the bed. Two portable air compressors, coupled in parallel, provided the drying and fluidizing air supply. Because the pressure drop through the heat exchanger was too great, the heat exchange coils within the oven were reworked using larger diameter tubing. An isolated chamber for the mass flow meter was constructed upstream of the heat exchanger, to isolate the meter from vibration. It was designed so that the incoming air would not impinge on the sensor, thus, preventing a faulty reading. PAGE 78 61 6.1.1 Benchtop Vibrofluidized Bed Dryer The experimental apparatus used for this project is shown schematically in Figure 22 and photographically in Figures 23, 24, and 25. Figure 22 Schematic of Lab Apparatus The main body of the fluidization apparat us contains two sections. The upper section is the freeboard, while the lower c hamber is the actual fluidized bed. The dryer had a diameter of 7. 6 centimeters and a height of 30.0 centimeters. The material to be fluidized is placed on a 70 mesh screen which is supported by a 10 mesh distributor plate. A calming secti on was installed under t he distributor plate so that the fluidizing gas would be distri buted uniformly to the bed. The entrance PAGE 79 62 of the calming section was f illed with lead spheres to assist in air distribution prior to the distributor plate. Figure 23 provides a good view of the fluidization chamber and the vibrational system. The key element s to observe here are the flexible connections for the instrumentation and the air supply, and the design of the vibratory system. The vibratory system consists of the black rubber suspension system, corner bracing on the bed fram e, variable speed motor and adjustable stroke linkage. In the wide shot presented in Figur e 24, the instrument system can be seen. The data acquisition system, as we ll as any transducers that could be, were isolated from vibration by location off of the table with the VFBD, and in the cabinet to the right. The oven, with t he heat exchanger for the drying air, is located under the table. The white tube in the lower right is a portion of the chamber constructed for the mass air fl ow meter, and located upstream of the oven. The video monitor, in the upper right corner of the picture, was connected to a second video camera located to t he right of the VFBD and allowed for remote closeup monitoring of the VFBD during experimental trials. The view provided in Figure 25 pr ovides a good representation of the digital video acquisition setup. The ca mera was a Sony digital video camera collecting video at 30 frames per second. Additionally, notice two changes to the system since Figure 23: 1) The drying air supply to the VFBD is now a braided stainless steel line, to accommodate the motion and high air temperature. 2) The relative humidity sensor has been added and is located at the top of the VFBD. PAGE 80 63 Figure 23 Closeup Photogr aph of Laboratory Apparatus PAGE 81 64 Figure 24 Wide Shot of Laboratory Apparatus PAGE 82 65 Figure 25 Digital Video Acquisition of VFBD Experiment PAGE 83 66 The fluidizing gas used was compressed air. The 90 psi air supply was provided by portable air compressors jo ined in parallel. The air was passed through a deoiling and drying filter, and then to a regulator to control the quantity delivered to the system. Prior to feedi ng into the apparatus, the air was passed through a heat exchanger. The heat exchanger was a coil of inch tubing contained within a high tem perature electric oven. The oven cycle time and element voltage could be adjusted to c ontrol the exit air temperature. 6.1.2 Data Acquisition The Vibrofluidized Bed Dryer (VFB D) was fully instru mented utilizing the following: 1) Transducers monitoring t he variables of interest. 2) Signal conditioning accessories filtering and opt imizing the transducer signals for the input range of the data acquisition card. 3) Data acquisition collection box the outputs of the signal conditioners ar e wired and routed to a ribbon cable connected to the data acquisition card. 4) Data acquisition card an A/D card used to interface the measurement data and the computer. 5) LabVIEW Software used to control the data acquisition and display. Air temperature was moni tored at the inlet and outlet of the FBD, using type T thermocouples. The differential pr essure of the air stream, across the FBD, was measured using a Validyne DP 15TL differential pressure transducer with a CD12 transducer indicator, and an Omega PX138 pressure sensor. The air flow was measured at t he top of the fluidization chamber with a Kurtz series 410 insertion mass flow element, and a se ries 155 ADAM mass flow computer. A Dwyer pitot tube and manomet er were also placed at the top of the chamber. PAGE 84 67 From this, a secondary noninterfaced ai rflow measurement was calculated by using the Air Velocity Calculator supplied wit h the pitot tube. The exit air relative humidly was measured using an Omega PX138 relative humidity sensor. Data acquisition was accomplished by using a National Instruments DAQCard700 PCMCIA card. This card allowed for 8 differential analog input channels, and has a 100 kS/s sample sampling rate, and 12 bit resolution. The card was connected to a Dell Inspiron 7000 laptop computer running LabVIEW 6i software on a Windows 98 operating system. A LabVIEW virtual interface was writt en that allowed for the simultaneous collection of the temperature, pressure, re lative humidity, and air mass flow data. These data streams were collected simultaneously while being displayed graphically on the computer, and being written to Excel files for later analysis. The LabVIEW virtual interface and visual programming are presented in Figures 26 and 27 respectively. Figure 26 LabVIEW Virtual Interface PAGE 85 68 Figure 27 LabVIEW Graphic Representat ion of Data Acquisition Program 6.1.3 Instrument Calibration Prior to experimentati on, the data acquisition system was checked for reliability. This entailed calibrati ng not only the trans ducers used in data collection, but also the data acquisition s ystem itself. Calibrations conducted in this investigation included the following: 1) Data acquisition syste m. 2) Mass air PAGE 86 69 flow meter. 3) Thermocouples. 4) Diffe rential pressure sensors. 5) Relative humidity sensor. The data acquisition system out lined above, N.I. DAQCard700 and Dell Inspiron 7000 laptop computer running LabVIEW 6i on a Windows 98 operating system, was checked by sending know n signals to the analog input channels and monitoring the recorded signals. The si gnal provided to the card was delivered by a Sun Equip. Co. D.C. power suppl y model PS303. This allowed for a stable voltage to be supplied to each channel of the card, at voltages in ranges similar to those from the instrumentati on transducers. Additionally, an accurate multimeter, Fluke model 23, read the voltage going to the card to verify the signal voltage. A plot of the voltage supplied to the card and the average of the 51 recorded voltages, yielded a straight line with a slope of 1.000.00. Regression statistics for the calibration can found in Appendix 4. In order to ensure that the signal acquired by the data acquisition system was not aliased, trials were conducted to determine the Nyqui st frequency of the system. A signal generator was connected to the five differential inputs on the DAQCard. A signal of a known amp litude and frequency was delivered to these inputs simultaneously. The sampling fr equency of the system was varied and the resulting data was analyzed via Fourier trans form to determine at what point the digital signal no longer represented t he analog input. For this system the maximum signal frequency that could be reli ably measured to avoid aliasing, the Nyquist frequency, was 50 hertz. The sampling frequency used for data collection in this research was below this maximum at 10 hertz and showed an PAGE 87 70 error of less than 1% from the Four ier transform analysis on simultaneous data acquisition on all input channels. The Kurtz mass airflow sensor wa s calibrated using two different references simultaneously. A rotamete r placed in line after the pressure regulator, and a pitot tube placed in the exit of the fluidization chamber, were the two references. The pitot tube was connected to a differential pressure transducer, whose output was referenced to a lookup table to provide the air velocity. To ensure that the calibration was accurate for the temperatures to be used in the dryer, the calibration was conducted at 100C. The airflow was varied, via the pressure regulator, in in tervals of 5 SCFM on the rotameter scale from 0 to 40 SLPM, and then to 8 FPM as indicated by the pitot tube. For each reference reading, the transduc er output from the Kurtz flow meter was recorded. After the Kurtz flow meter was calibrated us ing its internal pr ocedures, statistical analysis of the data show ed strong agreement between t he three devices. The value of the correlation coefficient, R2, for the 3 trials was 0.994. A plot of the calibration data and the regression st atistics can be found in Appendix 4. The thermocouples, and their asso ciated signal conditioners, were calibrated using a replicated twopoint calibration. For each thermocouple, temperature readings, at ambient (21.11C) and at waters boiling point (100.0C), were collected with the data acquisi tion system. Three replicates of each reading were conducted with each thermo couple. Statistical analysis of the combined data sets, presented in Table 5, revealed that the thermocouples were PAGE 88 71 reporting within acceptable limit s. Descriptive statistics for the individual sets, and the combined set, can be found in Appendix 4. Table 5 Thermocouple Calibration Descriptive Statistics Mean Std. Error Std. Deviation Sample Variance Inlet Ambient 21.357 0.392 3.034 9.206 Inlet Boiling 100.379 0.287 2.223 4.942 Outlet Ambient 21.812 0.282 2.181 4.759 Outlet Boiling 100.785 0.306 2.368 5.605 The Omega model PX138 differential pr essure sensor was calibrated by using a Barnart Vacuum Pressure station. This device allowed for the application of a vacuum, or positive pressure, to the ports of the sensor. For calibration, the input provided to the sensor was varied fr om psi to 3 psi in 1 psi steps. The pressure reading from the data acquisiti on system was com pared to the applied input. This procedure was repeated for bot h ports on the sensor. The value of the correlation coefficient, R2, for the 3 trials was 0. 9997. When plotted the data produced a linear graph with a slope of 1.003 and an intercept of 0.005. A plot of the calibration data and the regression st atistics can be found in Appendix 4. The manufacturers of the relative humidity sensor indicated that no calibration was required. In order to c onfirm the accuracy of the sensor it was tested by exposure to known humidit y environments. When exposed to dry heated air from the system the output si gnal indicated the proper humidity. PAGE 89 72 When exposed to a saturated environm ent, a sealed headspace over distilled water, the output signal indicated t he appropriate 100% relative humidity. 6.2 Particle Size Distribution A particle size distribution that fac ilitates fluidizati on, and the repeatable procedure to create that distribution, needed to be determined. This was accomplished by the creation and characteriza tion of a particle size distribution of feed material from peel cups and pomac e from Brown extracted Valencia oranges. Initially, the peel material was ac quired from the peel bins at a citrus processor. For the majority of the flui dization and drying trials the material was acquired from the Brown Citru s Systems pilot plant in Winter Haven, Florida. The optimization of a particl e size distribution that fa cilitates fluidization is a practical exercise because industrial particle size preparation equipment is effective and economical. For particle size preparation in the laboratory, the peel s were quartered and placed into a Zyliss food chopper with the correct ratio of finisher pomace. A quantified number of plunges were made with the chopper to prepare the feed lot. This feed material was then tested in the VFB drying apparatus for quality of fluidization and its particle size distri bution characteriz ed using ASAE Standard: ANSI/ASAE S.319.3 Jul 97, Method of De termining and Expressing Fineness of Feed Materials by Sieving 8. PAGE 90 73 6.3 Moisture Determination Moisture must be monitored over dr ying time in order to create drying curves that facilitate the det ermination of the periods of drying, critical moisture content, and the controlling mechanism of the falling rate period. The standard methodology utilized to determine the mo isture content was ASAE S358.2 Dec 99, Moisture Meas urement Forages 9. During the drying process, the wet material being dried was removed from the fluidization chamber, placed in a tared glass petri dish, and weighed at periodi c time intervals. After the material in the bed was dry, the sample was placed in the dish, placed in the drying oven, and allowed to dry for 24 hours. The oven was set at 87.8 oC. The oven also contained a desiccator to control the relati ve humidity inside the oven. At the end of this drying period, the sample was reweighed to determine the mass of dry material. The percent moisture, dry basis, was determined as dbMass of wet material Mass of dry material % Moisture = Mass of dry material = M. (29) Additionally, the percent moisture, wet basis, was determined by wbMass of wet material Mass of dry material % Moisture = Mass of wet material (30) 6.4 Vibrofluidization Data Trials were conducted to determine the minimum vibrofluidization velocity, Vmvf, of the peel material. The vibratory mechanism was modified to allow for 4 different stroke values, and set angul ar frequency value, measured using a phototachometer. These configurations created vibrational acceleration, A2/g, PAGE 91 74 values of 1.0188, 1.5282, 2.5471, and 3.0565. Each of these variations was tested to determine quality of fluidization. The procedure for data collection was methodical. The dryer was charged with a measured mass of wet material. The data acquisition system was started to collect mass flow and bed pressure drop data. The initial bed height was measured. The air supply was gradually increased to 50 PSI. The quality of fluidization was observed and noted. The vibration was start ed. The dynamic bed height was measured. The quality of fluidization was observed and noted. The air supply was slowly reduced to zero. This data was analyzed by plotting the pressure drop across the bed versus the air flow rate, to determine the minimum vibrofluidization veloci ty and quality of fluidization. 6.5 Drying Data During the drying trials, realt ime bed data was collected from the instrumentation described in section 6.1. 2. Additionally, the bed was sampled, during the drying trials, to collect data on the solids moisture content. These samples were processed, as outlined in section 6.3, and the resulting moisture content versus time data was plotted and analyzed. These drying curves reveal the different periods of drying and the cr itical moisture content. To further facilitate the analysis of the drying data and model predictions, the moisture ratio, MR, was determined for each solids sample from the dryer, where e oeMM MR MM (31) PAGE 92 75 To verify the dominant moisture transport mechanism, the unaccomplished moisture change was plotted versus time. Unaccomplished moisture change, M*, is defined as the rati o of free moisture in the solid at a specific time, M, to the total free moisture present at the start of the falling rate period, Mc. The slope of this semilogrit hmic plot established whether a relationship exists in the falling rate period. If the result of the plot of M* versus time is a straight line, the controlling me chanism in the falling rate period is based on either diffusion, or capillary flow. Assuming that the total drying time is a direct summation of the falling rate drying period and the constant drying rate period, the slope of the falling rate curve is related to the constant drying ra te, and the time in t he falling rate period, tf, can be calculated from the energy trans fer in the falling rate period and the inverse of the unaccomplished moisture change, by pce ce f tsed(MM) MM tln h(TT)MM (32) If the slope from this equati on agrees with the experiment al data, the moisture movement is by capillary flow. If the slopes do not agree, t he movement is by diffusion 55. The diffusion coefficient is an import ant parameter to k now when a Fickian model is used in the falling rate per iod. Since its physical meaning is questionable, especially in the drying of biological materials where moisture movement is complex, it is often refe rred to as the effective diffusivity, Deff 62. The most practical method to determine the effective diffusivity is based on the solution of Ficks second law. The so lution for Ficks diffusion equation with one PAGE 93 76 dimensional moisture transfer and constant diffusivity for a sphere is given by Crank21 as 22 e eff 222 n1 ceMM 61n M*expDt MMnr (33) where M* represents the unaccomplished moisture change. The expansion of equation (32) for the three series is FiFiFi9.8N39.5N88.8NM*0.608e0.152e0.06 (34) where NFi is the Fick number equal to Defft/L2 and L is the characteristic dimension of the geometry. Crank further reduces this equation to ln(M*)Constantst (35) where s is the slope equal to the dehydration constant, c Defft/L2, and c is the constant in the first series, c = 9.8. This equation has the familiar linear form, and the effective diffusivity can be calc ulated from the sl ope of the natural logarithm of the unaccomplished moisture change plotted versus time, as shown by the following equation: 2 effs(L) D c (36) PAGE 94 77 7 MODEL DEVELOPMENT 7.1 Introduction The secret for success for fluidi zed bed drying is bubble action. The bubbling action, within a fluidized bed, prom otes mixing and leads to uniformity in the bed temperature, which yi elds high rates of internal heat and mass transfer. The modeling of drying in such a bed require s that the parameter s at the point of minimum fluidization be determined, the drying mechanisms in the constant and falling rates are understood, and relations for the appropriate constants are determined. Drying kinetic models are typically based on the premise that the bed drying activity can be modeled using tr ansport properties between phases within the dryer. Typically the dryer is r epresented as three phas es; a solids phase, an interstitial gas phase, and a bubble phase, with heat and mass transfer occurring between the phases. A model based on this approach is presented in section 7.2. Due to the excellent particle/gas mixi ng in a fluidized, or vibrofluidized bed, it has been suggested that drying can be modeled on thinlayer drying. The underlying assumption is that there is su fficient particle surface area exposed to the drying air, such that the system approximates thinl ayer drying. In this approach, the drying const ants, K and N, are used in stead of the transport PAGE 95 78 properties. This approach has oft en been used for food, and especially for grains. A model based on this methodol ogy is presented in section 7.3. 7.2 ThreePhase FBD Model Combining the modeling concepts pres ented thus far, the Threephase drying process model requires the followi ng five step operational sequence: 1) Enter the experimentally det ermined operating conditions. 2) Choose a minimum fluidization correlation. 3) Simultaneously solve the equations for bed dynamics. 4) Use the fourth order RungeKutta method to evaluate the drying rate differential equations. 5) Plot the resu lts of moisture content versus time. The necessary constant and falling rate models developed herein are based upon the original work of Srinivasa Kannan et al.36, and modified to account for the agglomerating characterist ics of the feed mate rial and the use of a vibrofluidized bed. The complexity i nherent in this agglomerating fluidized system require the introduction of t he following assumptions during the development of the model: 1) The system is operat ing in batch mode. 2) Particles are homogeneous in character, mostly spherical in shape, and do not shrink during drying. 3) All particles within the bed are t he same temperature and have the same moisture content, at any point in the drying process. 4) The exiting drying fluid is in equilibrium with the particles. 5) Bubble size is uniform and does not depend upon location within the bed. 6) Intraparticle moisture movement can be characterized using Ficks law, and effective diffusivity. PAGE 96 79 Figure 28 schematically represents the twophase batch fluidized bed dryer used in this research. In the figur e, C represents the moisture content of the solids, T is the temperat ure of that stream, Y is the humidity of the stream, and m is the stream mass flow. The dense phase consists of the solids phase and the interstitial gas phase. The bubble phase is the hot inlet air stream that fluidizes the solids, and serves as the drying medium. mt, To, Yo Ci, Ti md, Td, Yd mb, Tb, Yb Dense Phase hb Bubble Phase (solids & instersitial gas phases) Td, Yd, ky, mf kb Tb, Yb, b mb md Co, To mt, Ci, Ti, Yi Figure 28 Fluidized Bed Drying Schematic PAGE 97 80 The moisture and enthalpy balance equati ons, for this system, are used to develop the drying model, and are presented below. For convenience, the equations in each section of the M odel Development c hapter are labeled specifically for that section. The equati ons in this section follow the B# format. The dense phase solids moisture balance is presented first as amount of solids in the bed multiplied by rate of removal of moisture in the bed per bed volume, dC/dt, set equal to the bed average change in moisture content per change in time, W ,: smfbdC 11W dt (B1) where mf and b are the void fractions at minimum fluidization conditions and the bubble phase portion, respectively. The dense phase interstitial gas phase moisture balance reflects the change in humidity, Y, of the inters titial gas phase due to contributions from the solids and bubble phases, and is also related to the bed average change in moisture content per change in time: gbgb gmfbgddidb bdY6k 1mYYYYW dtd (B2) The dense phase solids enthalpy balance is the rise in sensible heat of the solids set equal to the heat input into the syst em, Q, minus the loss of heat through evaporative cooling, W represented as: s smfp,sp,wdT 1ccCQW dt (B3) PAGE 98 81 The dense phase interstitial gas phase ent halpy balance represents the enthalpy transfer from the drying medium, bubble phase, and the particles, solids phase, to the interstitial gas: g bb smfbgvigdgviidbd bp,p,p,p,dT 6h 1ccYmccYTTTTQ dtd (B4) Following similar derivations for t he bubble phase, the following balances result: The bubble phase solids moisture balance bgb b gbgbbidb b6k dY mYYYY dtd (B5) Bubble phase interstitial gas phase enthalpy balance bbb sbp,gp,vigbp,gp,viibbd bdT6h ccYmccYTTTT dtd (B6) The transport of mass and heat between t hese phases establishes the drying rates in both the constant and falling ra te periods. The next two subsections present a derivation of these two drying rates. 7.2.1 Bed Parameters The bed dynamics model starts by determining the minimum fluidization parameters based upon the empirical conditions As cited by Pakowski in his chapter on vibrated bed dryers 51, Jinescu developed the expression chosen for evaluating the minimum vibrofluidization velocity, Umvf, specifically for vibrofluidized beds of agglomerating materials as 2 mvfmf1kA UU1 2jg (F1) PAGE 99 82 where j is the sum of lift and fall time di vided by the vibration period, and k is the coefficient of collision elasticity, 0< k<1. The equation is adjusted for the minimum fluidization velocity, Umf, based on the assumption that at incipient vibrofluidization, the time that bed lifts up during the flight period is equal to the time of fall51. The minimum fluidization velocity was determined using the correlation for large particles proposed by Kunii and Levenspiel 42 as 3 pg0 2 mfsp .5 gUdg 1.75 (F2) for Rep,mf >1000, where s is the particle sphericity, dp is the mean particle diameter, p and g are the densities of the par ticle and the fluidizing gas, and 0 is the static bed voidage. For comparison purposes, the equati on for the minimum fluidization velocity for coarse particles equation, given by Chitester, et al.20, of Umf = [ g / gdp]((28.7)2 + 0.0494 Ar)0.5 28.7 (F3) was also used, where Ar = dp 3g( s g)g / g 2. (F4) Equation F3 can be used in place of equation F2 to fulfill the Umf requirement in equation F1. Equations F2 and F3 are onl y two, of dozens, of semiempirical relations for the minimum fluidization velocity available in literature. For the bubble phase parameters, Ub and db, equations by Werther and Mori and Wen cited by Kannan 36 were used. The Bubble rise velocity equation, given by Werther as Ub = 1.6(Dt)0.4 (gdb)0.5 + (U Umf). (F5) PAGE 100 83 Bubble diameter equation, given by Mori and Wen as db = 0.64[AT(U Umf)]2/5. (F6) Additionally, relationships for the bed voidage, and the bed voidage at minimum fluidization conditions, mf, are required. For t he purpose of estimating the bed voidage or porosity, the correlati on of Dakshinamurthy et al., cited by Gupta 31, was chosen. Their correlation is based on large volume of data obtained for various particles. The correlation is b 0.08 gl l gl tU U () U (F7) where = 2.12 and b = 0.41. Additionally, the minimum fluidization bed voidage was determined using the correlation for large particles proposed by Kunii and Levenspiel 42 as mf 3 = Umf 2 1.75 g / dpg s( sg). (F8) 7.2.2 Constant Rate Period The starting point for the determinati on of the constant rate period drying rate is the moisture and enthalpy balances, for the solids and the interstitial gas in the dense phase. The moisture balanc e for the solids in the fluidized bed yields an expression for the rate of mois ture removal per volume of the bed, W, as W = s(1f)dC/dt. (CR1a) If v is the bubble void fraction and b is the volume fraction of the bubbles in the bed, then the average bed voidage, f, is given by f = bfv + (1+ b) e (CR1b) PAGE 101 84 when there are no solids in the bubbles, v = 1. An emulsi on phase exists at minimum fluidization. The void fraction of the emulsion phase, e, equals the void fraction at minimum fluidization, mf, and (1 f) = (1 b)(1 mf). (CR1c) The substitution of equation CR1c into CR1a gives the required moisture balance for the solids in the dense phase as a function of the change in the moisture content of the solids, C, W = s(1 mf)(1 b) dC/dt. (CR2) This expression also indicates that W is proportional to the solids fraction in the bed. The moisture balance for the inters titial gas in the dense phase is a threeterm expression given by W = gmf(1 b) dYg/dt + gmd(Yd Yi) + 6Kbgb(Yd Yb)/ db. (CR3) Equating expressions CR2 and CR3, and rearranging, gives a relationship between the change in humidity of the air, Yg, and C as a function of time gmf(1 b) dYg/dt + gmd(Yd Yi) = s(1 mf)(1 b) dC/dt + 6Kbgb(Yd Yb)/ db. (CR4) The enthalpy balance for the solids in the dense phase is given by s(1 mf)(1 b)(cp,s + cp,w C) dTs/dt = Q W. (CR5) In this equation, s(1 mf)(1 b) represents the solids fr action in the bed. The complete term on the left hand side of t he equation represents the rise in the sensible heat of the solids. The first term on the right side of the equation, Q, PAGE 102 85 represents the heat input, while the second term, W, is the heat loss through evaporation of moisture from the solids. The enthalpy balance for the interstitial gas in the dense phase is given by gmf(1 b)(cp,g + Yicp,v) dTg/dt = gmd(cp,g + Yicp,v)(Ti Td) + 6hbb(Tb Td)/ db + Q. (CR6) In this equation, the first and second terms on the right hand side of equation represent the enthalpy transfer from t he drying medium to the dense phase, and from the bubble phase to the dense phase. Combining the enthalpy balance equations, CR5 and CR6, and substituting in W from CR3, we achieve the overall balance equation s(1 mf)(1 b)(cp,s + cp,w C) dTs/dt = gmd(cp,g + Yicp,v)(Ti Td) gmf(1 b)(cp,g + Yicp,v) dTg/dt + 6hbb(Tb Td)/ db [ gmf(1 b) dYg/dt + gmd(Yd Yi) + 6Kbgb(Yd Yb)/ db]. (CR7) If the terms involving the rate of change of humidity with respect to time, dYg/dt, and the change in the temperatur e of the gas with time, dTg/dt, are assumed small compared to the corresponding c onvective terms, equations CR3, CR4, and CR7 reduce to W = gmd(Yd Yi) + 6Kbgb(Yd Yb)/ db (CR8) gmd(Yd Yi) = s(1 mf)(1 b) dC/dt + 6Kbgb(Yd Yb)/ db (CR9) s(1 mf)(1 b)(cp,s + cp,w C) dTs/dt = gmd(cp,g + Yicp,v)(Ti Td) + 6hbb(Tb Td)/ db [ gmd(Yd Yi) + 6Kbgb(Yd Yb)/ db]. (CR10) Because the bed temperature is constant in the constant ra te period, the lefthand side of equation CR10 should be set to zero. This leaves PAGE 103 86 gmd(cp,g + Yicp,v)(Ti Td) + 6hbb(Tb Td)/ db [ gmd(Yd Yi) + 6Kbgb(Yd Yb)/ db] = 0 (CR11) from which the densephas e gas temperature, Td, and humidity, Yd can be determined. Following similar derivations for t he bubble phase, neglecting the rate of change of the humidity and temperatur e when compared to the corresponding convective terms, the moisture balance becomes gmb(Yb Yi) = 6Kbgb(Yd Yb) / db (CR12) or Yb = (6KbbYd + dbmbYi) / (dbmb+ 6Kbb). (CR13) The enthalpy balance becomes gmb(cp,g + Yicp,v)(Ti Tb) = 6hbb(Tb Td) (CR14) or Tb = [ gmbTi db(cp,g + Yicp,v) + 6hbbTd] [6hbb + gmbdb(cp,g + Yicp,v)]. (CR15) Since the resistance for mass transfer lies in the film surrounding the solid, W = (1 b) gaKy(Ysat Yd), (CR16) substituting equation CR16 into CR8 gives gmd(Yd Yi) + 6Kbgb(Yd Yb)/ db = (1 b) gaKy(Ysat Yd). (CR17) The drying rate during the const ant rate period is obtained by simultaneously solving equations CR9, CR11, CR13, CR15 and CR17. The differential equations, CR9 & CR10, are solved using fourth order RungeKutta algorithm to evaluate dC/dt at t+ t. PAGE 104 87 A number of semiempirical equations are used to obtain required values for Umf, Ub, db, mf, Kb, Ky, hb, and Ysat. Beyond the relations provided in section 7.2, the follow equations for mass and heat transfer coefficients, cited by Kannan36, were used: Mass transfer coeffi cient from the dense phase to the bubble phase equation, given by Sit and Grace as Kb = Umf/3 + [(4DmmfUb)/( db)]0.5. (CR18) Mass transfer coefficient from the particl e surface to the bulk gas equation, given by Ranz as Ky = (Dm / dp s) [2 + 1.8 Remf 0.5Sc0.33] (CR19) where, Remf = gUmfdp / g and Sc = g/( gDAB). (CR20) Heat transfer coefficient from the bubble phase to the dense phase prediction equation hb = Umfg /3 + [(4 gKbmfUb)/( db)]0.5. (CR21) Finally, the saturation humidity equation from Treybal 68 Ysat = .621 Pwatersat / (1.0133x105 Pwatersat) (CR22) where, ln (Pwatersat) = (5800.2206/T) + 1.3915 0.0486 T + 0.4176 x 104 T2 0.1445x107 T3 + 6.546 ln(T). (CR23) 7.2.3 Falling Rate Period The falling rate period begins at the critical moisture content, Mc, where the constant rate period ends. Here, the dr ying rate is controlled by the moisture transport out of the solid. Having determi ned, in Phase 2 of the research, that PAGE 105 88 the controlling mechanism for the falling ra te period is diffusion, the moisture movement can be defined by Ficks diffusion equation C/ t = Deff ( 2C/ r2). (FR1) The diffusion equation, for the falling rate period for a sphere, can be derived by assuming that the surface is at equilib rium with the moisture, and that the moisture distribution is uniform. For these conditions, the following equation is obtained 12 (C Cs)/(Co Cs)= (6/ 2) [1/n2 exp(n2Defft / r2)] (FR2) where C is the moisture content at time, t, Co is the initial moisture content, and Cs is the surface moisture content. This equation simplifies to a limiting form of the diffusion equation, represented as (C Cs)/(Co Cs)= (6/ 2) exp(Defft / r2). (FR3) Equation FR3 may be differentiated to give the drying rate as dC/dt = ( 2 Deff / 6r2) (C Cs). (FR4) Simultaneous solution of this rate equation, along with the equations presented in the constant rate period, predicts the drying rate, temperature and humidity in the phases, and the moisture rati o, during the falling rate period. For purposes of numerical solution, the m odel employs a classical fourthorder RungeKutta algorithm to solve the series of firstorder differential equations. PAGE 106 89 7.3 ThinLayer Drying Model Due to the thorough mixing achieved with fluidization and vibrofluidization, the drying process has been treated as thinlayer drying by other researchers, Ramesh and Rao58, Shilton and Niranjan64, Prasad et al.56. The thinlayer model describes drying in a unified way, regardless of the controlling mechanism using two drying c onstants, K and N. This approach has proved to be a suitable model for the purposes of proc ess design, optimization, and replacement of models w here a large number of iter ative calculations are required37. The starting point for a generally a ccepted model for thinlayer drying is Pages equation (1949) given as edM K(MM) dt (TL1) where M is the moisture content at time t, and Me is the equilibrium moisture content. The solution of equation TL1 results in e oeMM MRexp(Kt) MM (TL2) where MR is the moisture ratio at time t, and M0 is the initial moisture content. The limitations of this equat ion in predicting the drying curves necessitated the introduction of a second drying parameter, N 49: N e oeMM MRexp(Kt) MM (TL3) PAGE 107 90 As suggested by Brooker et al.18, and Weller and Bunn 71, for practical reasons, the equilibrium moisture content, Me, of the dried product can be taken as the final moisture content, Mf, of the product. Hence, Pages equation becomes N f ofMM MRexp(Kt) MM (TL4) The analysis of the exper imental drying data will yield equations for the Page equation parameters, K and N, in terms of a drye r property. Substitution of these equations into equation TL4, and t hen solving equation TL4 over time, will predict the drying time at t he vibrofluidization velocity assuming that the initial and final moisture content, and a dryer operating parameter used to define K and N, are known. PAGE 108 91 8 RESULTS AND DISCUSSION 8.1 Particle Size Distribution To determine the fluidizable particle size, the raw material was manually chopped into a size distribution that flui dized in the apparatus. With each particle size distribution tested the airflow rate was started at the va lue predicted by the model and increased manually until stable fl uidization conditions were achieved, or the maximum available air velocity wa s met. The dried material from these trials was then characterized by ANSI/ASAE S.319.3 Ju l 97, Method of Determining and Expressing Fineness of Feed Materials by Sieving, which is the standard method to determine the par ticle size distribution. A particle size distribution that resembled normal, or lognormal, distribution was desired, with bimodal distributions avoided. These tests were used to develop a consistent feed material for the vibrofluidized bed dryer. The resulting material had a lognormal particle size distribution with a particle size between 1 and 7 mm with a tail of particl es smaller than 1 mm, a geometric mean diameter, dgw, or median size of particles by mass, of 3.829 mm, with a geometric standard deviation of lognorma l distribution by mass, Slog, of 1.23E08, and a geometric standard deviation of par ticle diameter by mass, Sgw, of 2.49E07 mm. This particle size distribution is sim ilar to the one report ed by Braddock and Miller 15 for press cake and dried pulp. The ma in difference is that their reported PAGE 109 92 particle size distribution was bim odal with a peak near 1.5 mm and another fraction distributed in the 2.2 to 6 mm range. To facilitate fluidization and consistent product dryness, t he particle size distribution achieved in this research is more uniform than standard press cake and dried pulp. The data sheet for tabulat ion of the sieving data, and calculation of the lognormal particle size distribution param eters, is present ed in Appendix 3. Graphical representations of the particle size distribut ion (P.S.D.) used in the drying experiments are presented in Fi gures 29, 30, and 31 as an exponential plot, linear bar chart, and the cumulative undersize distribution plot, respectively. 0.01 0.10 1.00 10.00 100.00 0.100 1.000 10.000 Sieve Opening (mm)Percent Within Size (%) a b c avg Figure 29 Logarithmic Plot of Final P.S.D. PAGE 110 93 Figure 30 Bar Plot of Final P.S.D. PAGE 111 94 Figure 31 Final P.S.D. Cumulative Undersize Distribution by Mass PAGE 112 95 8.2 Vibrofluidization Using processing residue with t he particle size distribution described in section 8.1, the vibrofluid ization velocity was determined as outlined in section 6.4. Tests were conducted at four different vibrat ional acceleration, A 2/g, values of 1.0188, 1.5282, 2.5471, and 3.0565, and are represented below in Figures 32 35, respectively. Ob serve that the hyst eresis between the increasing and decreasing velocity curv es reduces, and the stability of the pressure drop above the minimum fluidi zation velocity increases, as the vibrational acceleration values approach the optimal conditions. This type of response to vibrational acceleration is typical. It follows the convention presented by Pakowski 51, based upon analysis of VFBD lit erature, that there is an optimal range of vi brational acceleration where the bed structure is most suitable for drying, where 2 A 2/g 3. The optimal A 2/g value was determined to be 2.5471 in the 3rd test configuration. Us ing the results from this configuration, the optimal minimu m vibrofluidization velocity, Umfv, and the bed pressure drop, P, were determined to be 10.9 cm/sec and 3900 Pa, respectively. These results, and the val ues from all 4 tria ls, are presented in Table 6. PAGE 113 96 Fluidization Curve 1 (Mass in bed = 235g, Vibrational Acceleration = 1.019)0.0 0.1 1.0 10.0 100.0 1000.0 10000.01.0010.00100.001000.00Volumetric Air Flow Rate (SLPM)Pressure Drop across Bed (Pa) Increasing Flow Rate Decreasing Flow Rate Figure 32 Fluidization Curve for VFBD Variant #1 Fluidization Curve 2 (Mass in bed = 234g, Vibrational Acceleration = 1.528)0.0 0.1 1.0 10.0 100.0 1000.0 10000.01.0010.00100.001000.00Volumetric Flow Rate (SLPM)Pressure Drop across Bed (Pa) Increasing Flow Rate Decreasing Flow Rate Figure 33 Fluidization Curve for VFBD Variant #2 PAGE 114 97 Fluidization Curve 3 (Mass in bed = 233g, Vibrational Acceleration = 2.547)0.0 0.1 1.0 10.0 100.0 1000.0 10000.01.0010.00100.001000.00Volumetric Flow Rate (SLPM)Pressure Drop across Bed (Pa) Increasing Flow Rate Decreasing Flow Rate Figure 34 Fluidization Curve for VFBD Variant #3 Fluidization Curve 4 (Mass in bed = 232g, Vibrational Acceleration = 3.056)0.0 0.1 1.0 10.0 100.0 1000.0 10000.01.0010.00100.001000.00Volumetric Flow Rate (SLPM)Pressure Drop across Bed (Pa) Increasing Flow Rate Decreasing Flow Rate Figure 35 Fluidization Curve for VFBD Variant #4 PAGE 115 98 Table 6 VFBD Minimum Vibrofluidization Results Trial # Weight of Bed (g) Vibrational Acceleration A 2/g Minimum Fluidization Velocity (SLPM) Minimum Fluidization Velocity (cm/s) Pressure Drop across Bed (Pa) 1 234.77 1.019 256 23.7 2200 2 233.56 1.528 171 15.9 2700 3 233.27 2.547 118 10.9 3900 4 232.06 3.056 149 13.8 2900 8.3 Vibrofluidized Bed Drying In earlier work 63, the drying parameters of t he residue were determined in a nonfluidized state. These include the dr ying rate of the re sidue, the critical moisture content of the residue, Mc, the mechanisms of bot h drying rate periods, and the effective diffusion coefficient, Deff. These parameters are compared to the values determined in the vibrofluidized bed dryer in Table 7. The values for the critical moisture c ontent are in agreement with the results presented by Braddock and Miller 15 for the drying of press ca ke. At three different temperatures, they report a constant ra te period from 73% to 25% moisture content, and a falling rate below that, indi cating a critical moisture content of 25%. Table 7 Drying Parameters Bed Type Mc (%) C.R. drying mechanism F.R. drying mechanism Deff (cm/s) FBD 25 Surface Evap.Diffusion 8.28E5 VFBD 30 Surface Evap.Diffusion 2.85E05 PAGE 116 99 The drying curves for each of thes e trials are presented in Figure 36. These curves are also evident in Figur es 42 and 44, since the model verification was anchored to the product dryness and drying time. Experimental Drying Curves (15)VFBD Citrus Pulp & Peel0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 051015202530Time (min.)Moisture Ratio M.R. 1 M.R. 2 M.R. 3 M.R. 4 M.R. 5 1) 144.65 C 2) 117.65 C 3) 137.73 C 4) 152.40 C 5) 104.13 C Figure 36 Experimental Drying Curves Figure 36 shows expected behavior for the dr ying trials as a function of average bed temperature. For all 5 temperatur es, the three periods of drying can be observed. Initially, prior to a time of 5 minutes, the drying rate is slow during the warm up period. After that initial peri od, the drying enters the constant rate period. This can be observed in all the se ries by the straight line region from 5 PAGE 117 100 minutes to 13 15 minutes, or from the moisture ratio of 95 80 down to 36 24. This point of transition, from the constant rate per iod to the falling rate period at a moisture ratio of 30%, is the critical moisture content. Below this point, all the series can be seen to exhibit falling rate characteristics as the moisture ratio approached the equilibrium moisture content a symptotically. Additionally, it can be observed that the trial c onducted at the lowest temper ature, trial 5 (the purple diamond), has the slowest drying rate, as evidenced by the higher moisture ratio at each time step compared to the other tria ls. In the constant rate period, this convention also follows with the other te mperature groupings. In the falling rate period, the drying rates are roughly equiva lent, since the controlling mechanism is now the diffusion of moisture from the interior of the particle to the surface. The data collected from the instrument ation during the drying trials are presented in Figures 37 41. These ar e provided to give the reader a more complete picture of the drying process. In these figures it can be observed: 1) The pressure drop across the bed increas ed until fluidization occurred, and then remained stable throughout the run, indi cating good quality fluidization without bed destabilization. 2) The exit gas tem perature was offset from the inlet gas temperature during the constant rate period, and began to appr oach it during the falling rate period when there was less evaporative cooling from the particle surfaces. 3) The exit gas humidity initially rose to the point of saturation, and then reduced as the moisture content in the bed decreased. 4) The pressure drop across the bed diminished, due to reduced bed mass from both water removal due to drying, and sample removal for moisture analysis. PAGE 118 101 Figure 37 Drying Trial 1 PAGE 119 102 Figure 38 Drying Trial 2 PAGE 120 103 Figure 39 Drying Trial 3 PAGE 121 104 Figure 40 Drying Trial 4 PAGE 122 105 Figure 41 Drying Trial 5 PAGE 123 106 8.4 Model Validation The mathematical models of the drying process were verified by comparing experimentally measured flui dization parameters and drying curves with the model predictions. The thr eephase vibrofluidized bed model predicted the bed hydrodynamic, or fluidization, param eters in the proce ss of calculating the drying curves. The co mparison of these parameter s is presented in section 8.4.1 with the experimenta lly determined optimal vibrational acceleration. The validation of the model predicted drying cu rves, for the threephase and thinlayer drying models, are presented in secti ons 8.4.2 and 8.4.3, respectively. 8.4.1 Fluidization Parameters As indicated in section 2.3, FBD s are categorized as either batch or continuous type processes. The necessary particle size for fluidization, and the minimum fluidization velocity, in a batch dryer, were determined by experimentation. This test al so determined if the material is fluidizable. After the particle size distribution, vibrational acceleration and fluidization was achieved, the minimum fluidization velocity was compared to the model predicted value. To determine the fluidization velocity the predicted fluidization velocity from the steady state phase 1 model was used as a starting point. The airflow rate was started here, and then adjusted to reach good fluidization conditions. Since air velocity alone was not sufficient to achieve stable fluidization, the vibratory mechanism was added into the des ign matrix. Tests were conducted at four different vibrational acceleration, A 2/g, values of 1. 0188, 1.5282, 2.5471, and 3.0565. The optimal A 2/g value was determined to be 2.5471. The PAGE 124 107 experimental and predicted fluidization par ameters are based on this level of vibrational input. In Tabl e 8, the fluidization paramet ers predicted by the model are tabulated with the exper imentally determined values. Table 8 Fluidization Parameters Umf (cm/s) Umvf (cm/s) Vmvf (SLPM) Pmvf (Pa) (non.dim.) Experimental 10.9 118 3900 .52 Predicted 51.68 11.72 126 3561 .61 The predicted minimum fl uidization velocity, Umf, of 51.68 cm/s was beyond the capability of the system. If the system had the ability to supply air at that flow rate, only the largest, densest par ticles would remain in the bed. When examining the remainder of t he results, consider that these values all reflect a batch vibrofluidized bed dryer. If the system under consideration were continuous, these parameters would not change. The residence time distribution in a continuous VFBD would mainly a ffect the drying rate and final product moisture content. 8.4.2 ThreePhase VFBD Model A plot of the exper imental and predicted drying curves, for the experimental bed temperatures, is plo tted in Figure 42. The data points represent moisture ratio values sampl ed during the drying trials. The curves represent the moisture ratio predicted by the model. PAGE 125 108 Drying Curves (ThreePhase Model)VFBD Citrus Pulp & Peel0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 051015202530Time (min.)Moisture Ratio M.R. 1 M.R. 2 M.R. 3 M.R. 4 M.R. 5 M.R. Predicted 1 M.R. Predicted 2 M.R. Predicted 3 M.R. Predicted 4 M.R. Predicted 5 1) 144.65 C 2) 117.65 C 3) 137.73 C 4) 152.40 C 5) 104.13 C Figure 42 ThreePhase Model Predicted and Experimental Drying Curves Performing a regression analysis, on the combined data sets, tested the statistical validity of the threephase drying model. The combined data set is plotted in Figure 43. If the model perfe ctly predicted the ex perimental data, all the data points would fall dire ctly on the 1:1 ratio line. The regression statistics for the combined data set is presented in Table 9, and the individual data sets are presented in Appendix 6. PAGE 126 109 Moisture Ratio Predicted Using the ThreePhase Model0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.00.20.40.60.81.0MR ExperimentalMR Predicted Figure 43 ThreePhase Drying Model Validation Table 9 Regression Statistics for ThreePhase Model Validation Number of Observations Correlation Coefficient (R2) Standard Error Upper 95% Confidence Limit Lower 95% Confidence Limit 37 0.9940 0.0295 1.0302 0.9769 Sum of Square Regression Sum of Square Residual Mean Square of Regression Mean Square of Residual FRatio 5.099 3.054E2 5.099 8.720E4 5.844E3 8.4.3 ThinLayer Drying Model As formulated in the m odel development section, Pages equation for thinlayer drying was used to predict the dr ying curves for the vibrofluidized bed drying of citrus peel and pulp. The param eters of Pages equati on, N & K, were determined by rearranging Pages equation (TL4) into the form Y=mx + C; the equation PAGE 127 110 ln(ln(MR))Nln(t)ln(K) (TL5) of a straight line. The graph of ln(ln( MR)) on the Y axis and ln(t) on the xaxis, will yield the slope as N, and the yinterc ept as ln(K). These values were calculated for each temperat ure of the drying trials and are shown in Table 10 (see Figures 51 55 in Appendix 5 for more information). Table 10 Regression Data for Determi nation of Pages Equation Parameters Trial # Avg. Bed Temperature, C N ln (K) R2 1 144.65 2.0568 5.0396 0.9958 2 117.65 2.3600 6.0145 0.9974 3 137.73 1.9776 4.2440 0.9890 4 152.40 1.9289 4.5793 0.9855 5 104.13 2.9921 7.7075 0.9940 Performing regression analysis and mi nimizing the standard error of deviation, the moisture ratio, time, and temperature were analyzed to determine the Page equation paramet ers as a function of the dr ying temperature. The bestfit polynomial for the data was deter mined by curvilinear regression as K = 1.565E7T3 5.724E5T2 + 7.068E3T 0.2917 with an R2 = 1.0 (TL6) N = 2.531E5T3 + 0.01016T2 1.364T + 63.436 with an R2 = 0.9969. (TL7) A similar third order polynomial wa s obtained by Ramesh and Srinivasa Rao58, for the vibrofluidized bed drying of ri ce. Similar second order polynomials were obtained by Pathak et al.53, and Prasad et al.56, for the thinlayer drying of rapeseed, and the fluidized bed drying of rough rice, respectively. A plot of the PAGE 128 111 experimental and predicted drying cu rves, for the experimental bed temperatures, is plotted in Figure 44. Drying Curves (ThinLayer Model)VFBD Citrus Pulp & Peel0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 051015202530Time (min.)Moisture Ratio M.R. 1 M.R. 2 M.R. 3 M.R. 4 M.R. 5 M.R. Predicted 1 M.R. Predicted 2 M.R. Predicted 3 M.R. Predicted 4 M.R. Predicted 5 1) 144.65 C 2) 117.65 C 3) 137.73 C 4) 152.40 C 5) 104.13 C Figure 44 ThinLayer Predicted and Experimental Drying Curves Performing a regression analysis, on the combined data sets, tested the statistical validity of the thinlayer dryi ng model. The combined data set is plotted in Figure 45. If the model perfectly predicted the exper imental data, all the data points would fall directly on the 1:1 ratio line. The regression statistics for the PAGE 129 112 data set are presented in Table 11, and t he individual data sets are presented in Appendix 6. Moisture RatioPredicted Using the Thin LayerModel0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.00.10.20.30.40.50.60.70.80.91.0MR ExperimentalMR Predicted Figure 45 ThinLayer Drying Model Validation Table 11 Regression Statistics for ThinLayer Model Validation Number of Observations Correlation Coefficient (R2) Standard Error Upper 95% Confidence Limit Lower 95% Confidence Limit 37 0.9936 0.0305 1.0225 0.9675 Sum of Square Regression Sum of Square Residual Mean Square of Regression Mean Square of Residual FRatio 5.013 3.25E2 5.013 9.27E4 5.406E3 PAGE 130 113 9 SUMMARY AND RECOMMENDATIONS 9.1 Summary To study and evaluate the fluidiz ed bed drying of citrus processing residue, a benchtop vibrofluidized bed dr ying system was successfully designed executed, and modeled. The residue cons ists of the nonjuice components of a citrus fruit; primarily peel and pulp. The material is hygroscopic, agglomerating, has a wide particle size distribution, and must be dried in a controlled environment to avoid thermal damage to nut rients and flavors. The driving force for this research was the economic c onstraints of the existing process. Sieving was used to characterize the par ticle size distribution of the dried citrus residue that facilitated fluidization. The resulting material had a lognormal particle size distribution, a particle size between 1 and 7 mm with a tail of particles smaller than 1 mm, a geometri c mean diameter, or median size of particles by mass, dgw, of 3.829 mm, a geometric st andard deviation of lognormal distribution by mass, Slog, of 1.23E08, and a geomet ric standard deviation of particle diameter by mass, Sgw, of 2.49E07 mm. Using the feed material described by the sieving analysis, vibrofluidization trials were undertaken. The test matrix a llowed for varying air flow rates at four different vibrational acceleration levels. The configuration that best facilitated fluidization was a vibrational acceleration, A 2/g, of 2.54, a minimum PAGE 131 114 vibrofluidization velocity, Umvf, of 4.2 cm/s, and a bed pressure drop, P, of 3900 Pa. All of these values were consis tent with values predicted in the bed dynamics portion of the threephase fluidized bed dryer model. The drying parameters of the residue we re determined in the vibrofluidized bed batch drying trials. These include: 1) The critical moisture content of the residue, MCc, of 30%. 2) The mechanisms of both drying rate periods, surface evaporation in the constant rate period, and diffusion in the falling rate period. 3) The effective diffusion coefficient, Deff, of the processing residue of 2.85x105 cm/s. Two models (three phase and thinlayer) were developed to predict vibrofluidized bed drying. Both were va lidated by comparing predictions versus experimental trials. The first, the threephase model, solved a series of simultaneous equations to predict bed hy drodynamics, and then used a fourthorder RungeKutta algorithm to solv e the moisture and enthalpy balance differential equations. The model succe ssfully predicted the bed hydrodynamic properties and the drying curves. In t he second model, the thinlayer drying model, based on Pages equation, the drying constants, K & N, were determined as a function of bed temper ature to be K = 1.565E7T3 5.724E5T2 + 7.068E3T 0.2917, and N = 2.531E5T3 + 0.01016T2 1.364T + 63.436. These equations, coupled with Pages equation, su ccessfully predict the drying curves and are consistent with other fluidi zed bed drying models for hygroscopic materials. PAGE 132 115 Based upon results of these trials, economic evaluation of the proposed process shows it to be advantageous w hen compared to the existing process that breaks even, or generates a loss. The proposed vibr ofluidized bed drying method has an acceptable payback peri od of 4.34 years, and an estimated processing cost per ton of dried materi al of $33, which appears to make it a profitable enterprise. In conclusion, this dissertation has dem onstrated that this research, into a vibrofluidized bed drying oper ation represents stateof theart advancement in the citrus feed mill process. In addition, there are seve ral valuable byproducts of this research: 1) A spreadsheet based balance program to predict energy usage in a fluidized bed dryer when the user input s the feed flow rate, moisture content and temperature, the air feed moisture content and temper ature, the product moisture content and temperature, and the exhaust gas tem perature. 2) A rigorous kinetic vibrofluidized bed dryi ng model based on moisture and enthalpy balances and bed hydrodynamics, which pr edicts the fluidization parameters and drying curves. This complex model serves to facilitate scaleup and bed configuration investigations. 3) A simple single parameter model for the drying of citrus processing residue based on thin layer drying. This model is computationally simple and would se rve process control algorithms. 9.2 Recommendations The results of this dissertation lead to several avenues for future research. Though it is suggested in liter ature by Liedy and Hilligardt 43, that scale up from PAGE 133 116 batchwise laboratory fluidized bed drye rs to production continuous operation dryers is possible, it woul d be quite a leap of faith to scale up directly from the benchtop to the plant floor. Instead, the concept of vibrofluidized bed drying of citrus processing residue should be further studied using a medium scale pilot plant dryer. Hence, trials could be run in concert with pilot scale rotary kiln drying process to determine if t he economic advantages presented in this dissertation are great enough to warrant replacement of aging citrus feed mill components. As evidenced in the drying trial figures, the control of the inlet temperature was difficult in the benchtop unit. T hough the system was allowed to reach steady state prior to the introduction of material into the bed, the drying temperature rose above the se t point in every trial. Instrumenting a control loop into the apparatus should be explored. This better control would facilitate determination of the relationship betw een drying temperature and drying rates. The relationship between the VFBD processing alternative and the emission of volatile organic compounds (VOCs) should be further studied. Although citrus processors attempt to reco ver most of the essential oils in the peel, the residual will be driven off in the drying process. The current process allows for at least some recovery of t he oil left in the processing residue via the molasses process, recovering dlimonene. Citrus processing plants are increasingly coming under the scrutiny of the EPA in relation to Title V issues. Establishing the emission rates for this process will be essential for getting the vibrofluidized bed drying process permitted for use in citrus feed mills operating in Florida. PAGE 134 117 REFERENCE LIST 1. Bulletin #177; The Story of Florida Citrus, State of Florida Department of Agriculture: FL, 1962. 2. 1999 Citrus Reference Book April 1999. Web Page, http://www.fred.ifas.ufl.edu/citrus/t od.html, accessed Jan. 15, 2000. 3. Mar. 2002. Citrus Crop Forecast. Web Page, www.nass.usda.gov/fl/citrus/cit/ 200102/cit0302.html, accessed Mar. 11, 2002. 4. 2003 Citrus Reference Book 2003. Web Page, http://www.fred.ifas.ufl.edu/citrus /pubs/ref/index2.htm, accessed Oct. 3, 1909. 5. May 2003. Citrus Estimate Revised. Web Page, www.bizjournals.com/tampabay/sto ries/2003/05/12/daily3.html, accessed May 13, 2003. 6. Agarwal, J.C.; Davis, W.L.; King, D.T. Chemical Engineering Progress 1962, 58 (85). 7. Allen T. Forth ed.; Powder Technology Series; Chapman and Hall: London, 1990. 8. ASAE Standards 2000 ASAE S319.3 JUL97 Method of Determining and Expressing Fineness of Feed Materials by Sieving; ASAE The Society for engineering in agricultu ral, food, and biological systems: St. Joseph, MI, 2000. 9. ASAE Standards 2000 ASAE S358.2 DEC99 Moisture Measurement Forages ; ASAE The Society for engineering in agricultural, food, and biological systems: St. Joseph, MI, 2000. 10. Bahu, R.E. Chapter 4 Fluidized Bed Dryers. in Industrial Drying of Foods, First ed.; Baker, C. G. J., Editor; Blackie Academic & Professional: London, UK, 2000; p 6589. PAGE 135 118 11. Baker, C.G.J. Industrial Drying of Foods; First ed. Blackie Academic and Professional: London, UK, 1997. 12. BarbosaCanovas, G.V.; VegaMercado, H. Dehydration of Foods; First ed. Food Engineering Series Chapman & Hall: New York, NY, 1996. 13. ByProducts Committee FCPA. Mar. 1908. ByProducts SemiMonthly Report Carry Over, Pack, Movement, and Goods on Hand. Web Page, http://www.fcplanet.org, accessed Mar. 18, 1909. 14. Braddock, R.J., Discussion With Author. Tampa, FL, October 30, 2003. 15. Braddock, R.J.; Miller W.M. Some Mo isture Properties of Dried Citrus Peel in Proceedings of the Florida St ate Horticultural Society; 1978; p 106109. 16. Braddock, R.J. Handbook of Citrus ByProducts and Processing Technology; First ed. John Wiley & Sons: New York, 1999. 17. Braga, M. Low prices; high tensions. in HeraldTribune October 20, 2003, Business Section, p 1011, 18. 18. Brooker, D.B.; Bakker Arkema, F.W .; Hall, C. W. Theory and simulation of cereal grain drying. in Drying Cereal GrainAVI Publishing Co.: Westport, CN, 1974; pp 185221. 19. Buff, D. A. VOC Emissions from Citrus Processing Plants in Transactions of the 1997 Citrus Engineering Conference; ASME: 1997; p p.65. 20. Chitester, D.C.; et al. Chemical Engineering Science 1984, 39, p253. 21. Crank, J. The Mathematics of Diffusion; Second ed. Oxford University Press: Oxford, UK, 1995. 22. Davidson, J.F.; Harrison, D. Fluidization; Academic Press: London, 1971. 23. Dwivedi; Upahyah A Finite Element Model for Coupled Equations in ASAE Journal 1989, Paper No. 986578. 24. Earle, R.L. Unit Operations in Food Processing; Second ed. Pergamon Press: New York, 1983. 25. Fellows, P.J. Food Processing Technology Principles and Practice; Woodhead Publishing Limited: Cambridge, UK, 1998. 26. Flink, J.M. Energy Analysis in Dehydration Processes in Food Technology 1977, 31 (3), p7784. PAGE 136 119 27. Geldart, D. Powder Technology 1973, 7, p285. 28. Geldart, D. Powder Technology 1978, 19, p133. 29. Geldart, D. Gas Fluidization Technology; John Wiley & Sons Ltd.: Chichester, UK, 1986. 30. Gentry, T.S.; Braddock, R.J.; M iller, W.M.; Sims, C.A.; Gregory J.F. Volatile Organic Compounds From Citrus Feed Mill Emissions in Journal of Food Process Engineering 2001, 24, p115. 31. Gupta, C.K.; Sathyamorthy, D. Fluid Bed Technology in Materials Processing; CRC Press: Boca Raton, FL, 1999. 32. Heid, J.L. Drying Citrus Canner y Wastes and Disposing of Effluents in Food Ind. 1945, 17. 33. Hines, A.L.; Maddox, R. N. Mass Transfer Fundamentals and Applications; PrenticeHall International Series in the Physical and Chemical Engineering Sciences PTR PrenticeHall, Inc.: Englewood Cliffs, NJ, 1985. 34. Hodges, A.; Phillippakos, E.; Mulkey D.; Spreen, T.; Muraro, R. Economic Information Report 012; Economic Impact Of Florida's Citrus Industy, 19992000 University of Florida: Gainesville, FL, 2001. 35. Industry Researcher, Discussion Wi th Corporate Researcher, Orlando, FL, December 2000. 36. Kannan, C.S.; Subba Rao, S.; Varma, Y.B.G. Kinetic Model for Drying of Solids in Batch Fluidized Beds in Industrial & Engineering Chemistry Research 1994, 33(2), p363370. 37. Karathanos, V.T.; Belessiotis, V.G. Application of a ThinLayer Equation to Drying Data of Fresh and Semidried Fruits in Journal of Agricultural Engineering Research 1999, (74), p355361. 38. Kesterson, J.W.; Braddock, R.J. ByProducts and Specialty Products of Florida Citrus; Univ. of Florida IFAS: Gainesville, FL, 1976. 39. King, D. "Feed Mill Q.A. Pr ograms and the European Market"; at 2003 Citrus Processing Short Course Clearwater Beach, FL. 40. Klinzing, G.E. Fluidization Solids Handling: Storage, Flow & Conveying of Bulk Solids; Univ. of Florida: Gainesville, FL, 1998; Chapter 2. 41. Kudra, T.; Mujumdar, A.S. Advanced Drying Technologies; Marcel Dekker: New York, 2002. PAGE 137 120 42. Kunii, D.; Levenspiel, O. Fluidization Engineering; Second ed. ButterworthHeinemann Series in Chemical Engineering, ButterworthHeinemann: Stoneham, MA, 1991. 43. Liedy, W.; Hilligardt, K.A Contribut ion to the ScaleUp of Fluidised Bed Driers and Conversion from Batchw ise to Continuous Operation in Chem. Eng. Process. 1991, 30, p5158. 44. Marshall, W.R. Jr. 2000. Drying. Web Page, http://www.acessscience.com, accessed Aug. 1, 1927. 45. McCabe, W.l.; Smith, J.C.; Harriott, P. Unit Operations of Chemical Engineering; Fifth ed. McGrawHill, Inc.: New York, NY, 1993. 46. McLaughlin, L.J.; Rhodes, M.J. Predict ion of Fluidized Bed Behavior in the Presence of Liquid Bridges in Powder Technology 2001, 114, p213223. 47. Miyauchi, T.; Furusaki, S.; Mo rooka, S.; Ikeda, Y. Transport Phenomena and Reaction in Fluidized Catalyst Beds. in Advances in Chemical Engineering; Drew, T. B., Editor; Academic Press: New York, NY, 1981; Vol. 11, p276448. 48. Mohammadi, K.P. Ph.D. Doctorial Dissertation, Defluidization Behavior of Viscous Materials, University of South Florida, Tampa, FL, 1991. 49. Morey, R.V.; Li, H. Thinl ayer Equation Effects on Deepbed Drying Prediction in Transactions of the ASAE 1984, 27(6), p192428. 50. Mujumdar, A.S.; Menon, M.L. Drying of Solids: Principles, Classification, and Selection of Dryers. In Handbook of Industrial Drying, Second Edition ed.; Mujumdat, A. S., Ed .; Marcel Dekker: New York, 1995; p139. 51. Pakowski, Z. ; Mujumdar, A.S.; Strumillo, C. Theory and Application of Vibrated Beds and Vibrated Fluid Beds for Drying Processes. In Advances in Drying ; Mujumdar, A. S., Editor; Hemisphere Publishing Corp.: Washington, 1984; Vol. 3, p245306. 52. Passos, M.L.; Mujumdar, A.S. Effect of Cohesive Forces on Fluidized and Spouted Beds of Wet Particles in Powder Technology 2000, 110, p222238. 53. Pathak, P.K.; Agarwal, W.C.; Si ngh, B.P.N. Thinlayer Drying Model for Rapeseed in Transactions of the ASAE 1991, 34(6), p25058. 54. Pell, M. Handbook of Powder Technology Gas Fluidization; Elsevier: 1990. PAGE 138 121 55. Porter, H.F.; Schurr; Wells; Se mrau. Section 20 Solids Drying and GasSolid Systems. In Perry's Chemical Engineers' Handbook, Sixth ed.; Perry, R. H.; Green, D., Ed itor; McGrawHill, Inc.: 1984. 56. Prasad, B.V.S.; Chandra, P.K.; Ba l, S. Drying Parboiled Rough Rice in Stationary, Semifluidized and Fluidized Conditions. in Transactions of the ASAE 1994, 37(2), p589.94. 57. Qureshi, A.E.; Creasy, D.E. Powder Technology 1979, 22(113). 58. Ramesh, M.N.; Srinivasa Rao, P. N. Drying Studies of Cooked Rice in a Vibrofluidised Bed Drier in Journal of Food Engineering 1996, 27, p389396. 59. Reay, D. Fluid Bed Drying. in Gas Fluidization Technology; Geldart, D., Editor; WileyInterscience: New York, 1986. 60. Redd, J.B.; Shaw, P.E.; Hendrix, C.M. Jr.; Hendrix, D.L. Quality Control Manual for Citrus Processing Plants Volume 3; Agscience: Auberndale, FL, 1996. 61. Reddy Karri, S.B.; Knowlton, T. M. Gas Distributor and Plenum Design in Fluidized Beds. in Fluidization Solids Handling And Processing; Yang, W.C., Editor; Noyes Publications: Westwood, NJ, 1999. 62. Roberts, J.S. Ph.D. Dissert ation, Understanding the Heat and Mass Transfer of Hygroscopic Porous Material, Rutgers University, New Brunswick, NJ, 1999. 63. Roe, E.A. Masters Thesis, Prelim inary Investigation Into Fluidized Bed Drying of Citrus Processing Residue University of South Florida, Tampa, FL, 1998. 64. Shilton, N.C.; Niranjan, K. Fluidization and its application to food processing in Food. Struct. 1993, 12, p199215. 65. Strumillo, C.; Kudra, T. Drying: Principles, Applications and Design; Topics in Chemical Engineering Gordon and Breach Science Publishers: New York, NY, 1986. 66. Tastemaker, Inc., Citrus Products Presentation to Tropicana Products, Inc. 1994. 67. Ting, S.V. Chapter 3 Citrus Fruits. In Biochemistry of Fruits and Their Products 1971. 68. Treybal, R.E. MassTransfer Operations; McGraw Hill: New York, 1980. PAGE 139 122 69. Valentas, K.J.; Rotstein, E.; Singh, R. P. Handbook of Food Engineering Practice; CRC Press: Boca Raton, FL, 1997. 70. Vanecek, V.; Markvart, M.; Drbohlav R. Fluidized Bed Drying; Chemical and Process Engineering Series Leonard Hill Books: London, UK, 1966. 71. Weller, C.L.; Bunn, J.M. Drying Ra te Constants for Yellow Dent Corn as Affected by Fatty Acid Ester Treatments in Transactions of the ASAE 1993, 36(6), p181519. 72. Whitehead, A.B. Distributor C haracteristics and Bed Properties in Fluidization, Second ed.; Davidson; Clift; Harrison, Editors; Academic Press: London, UK, 1985. 73. Youngblood, E.G. Most Important Fl oridians of the 20th Century C.D. Atkins, Louis MacDowell, & Edwin Moore in The Lakeland Ledger January 25, 1999. PAGE 140 123 BIBLIOGRAPHY The Sunshine Feed [VHS], State of Florida, 1976. ASAE Standards 2000 ASAE S248.3 DEC95 Construction and Rating of Equipment for Drying Farm Crops ; ASAE The Society for engineering in agricultural, food, and biological systems: St. Joseph, MI, 2000. ASAE Standards 2000 ASAE S269.4 DEC96 Cubes, Pellets, and Crumbles Definions and Methods for Determining Density, Durability, and Moisture Content; ASAE The Society for engineering in agricultural, food, and biological systems: St. Joseph, MI, 2000. Bird, R.B.; Stewart, W.E.; Lightfoot, E.N. Transport Phenomena; John Wiley & Sons, Inc.: New York, NY, 1960. Braddock, R.J. ByProducts of Citrus Fruit. Food Technology, 1995; 49 (9), p74, 7677. Braddock, R.J.; Cadwallader, K.R. Citrus ByProducts Manufacture for Food Use. Food Technology, 1992; 46 (2), p105110. Braddock, R.J.; Kesterson, J.W.; Miller, W.M. Efficient Processing of Orange Juice Extractor Residues into Byproducts in Proceedings of the International Society of Citriculture; 1977; p737738. Bunk, S.A.; DAcierno, J.P. Selecting a Winner in Fluidization. McGrawHill Companies, Inc.: New York, NY, 1999; 106(5), p8693. Chandran, A.N.; Subba Rao, S.; Varma, Y. B.G. Fluidized Bed Drying of Solids in AIChE Journal 1990, 36(1), p2938. Chen, H. Ph.D. Doctoral Dissertation, Simulation of TwoStage Drying of InShell Pistachio Nuts, University of California Davis, 1990. Cheremisinoff, N.P. Applied Fluid Flow Measurements; Marcel Dekker, Inc.: New York, NY, 1979. Christansen, O.B.; Sutera Sardo, M. Fi nd the Optimum Flash Dryer to Remove Surface Moisture. AIChE: New York, NY, 2001; 97(8), p 5458. PAGE 141 124 Cussler, E.L. Diffusion Mass Transfer in Fluid Systems; Second ed. Cambridge University Press: Cambridge, UK, 1997. Davidson, J.F.; Clift, R.; Harrison, D. Fluidization 2nd Edition; Academic Press: London, 1985. de Nevers, N. Fluid Mechanics for Chemical Engineers; McGrawHill, Inc.: New York, NY, 1991. DiMattia, D.G.; Amyote, P.R.; Hamdu llahpur, F. Fluidized Bed Drying of Large Particles in Transactions of the ASAE 1996, 39(5), p17451750. Eckert, E.R.G.; Drake, R.M. Jr. Heat and Mass Transfer; Second ed. McGraw Hill Series in Mechanical Engineering McGraw Hill Book Company, Inc.: New York, NY, 1959. Fan, L.S. GasLiquidSolid Fluidization Engineering; Butterworth Series in Chemical Engineering Butterworth Publishers: Stoneham, MA, 1989. Geankoplis, C.J. Transport Processes and Unit Operations; Third ed. PTR Pretice Hall: New Jersey, 1993. Humphreys, K.K. Jelen's Cost and Optimization Engineering; Third ed. McGrawHill, Inc.: NewYork, NY, 1991. Ilegbusi, O.J.; Iguchi, M.; Wahnsiedler, W. Mathematical and Physical Modeling of Materials Processing Operations; Chapman & Hall / CRC: Boca Raton, FL, 2000. Irudayaraj, J. Food Processing Operations Modeling: Design and Analysis; Food Science and Technology Marcel Dekker, Inc.: New York, NY, 2001. Kesterson, J.W.; Crandall, P.G.; Braddock, R.J. The Heat of Combustion of Dried Citrus Pulp in Journal of Food Process Engineering 1979, 3 p15. Kiranoudis, C.T.; Maroulis, Z.B.; Marinos Kouris, D. Modeling and Optimization of Fluidized Bed and Rotary Dryers in Drying Technology 1997, 15 (3&4), p735763. Liptak, B. Optimizing Dryer Performanc e Through Better Control. McGrawHill Companies, Inc.: New York, NY, 1998; 105(2), p110114. Liptak, B. Optimizing Dryer Performanc e Through Better Control Part 2. McGrawHill Companies, Inc.: New York, NY, 1998; 105(3), p96104. Miller, W.M.; Braddock, R.J. Micr owave Drying of Citrus Peel Proceedings of the Florida State Horticultural Society; 1982; p204207. PAGE 142 125 Milota, M.R. Ph.D. Doctoral Dissertat ion, Engineering Study on the Drying of Wood Particles in a Fluidized B ed, Oregon State University, 1984. Mohsenin, N.N. Thermal Properties of Foods and Agricultural Materials; Gordon and Breach, Science Publishers, Inc.: New York, NY, 1980. Rafson, H.J. Odor and VOC Control Handbook; McGrawHill: New York, NY, 1998. Reid, R.C.; Prausnitz J.M ; Poling, B.E. The Properties of Gases & Liquids; Fourth ed. McGrawHill, Inc.: New York, NY, 1987. Rice, R.G.; Do, D.D. Applied Mathematics and Modeling for Chemical Engineers; John Wiley & Sons, Inc.: New York, NY, 1995. Shaw, F.V. Fresh Options in Drying. McGrawHill Companies, Inc.: New York, NY, 1994; 101 (7), p7684. Singh, R.P. Computer Applications in Food Technology; first ed. Food Science and Technology Academic Press, Inc.: San Diego, CA, 1996. Ting, S.V.; Rouseff, R.L. Citrus Fruits and Their Products: Analysis and Technology; Marcell Dekker: New York, N.Y., 1986. Turner, I.; Mujumdar, A.S. Mathematical Modeling and Numerical Techniques in Drying Technology; Marcel Dekker, Inc.: New York, NY, 1997. Van Arsdel, W.B.; Copley M.J. ; Morgan, A.I. Jr. Food Dehydration Volume 1; Second ed. The AVI Publishing Company, Inc.: Westport, CT, 1973. Van Arsdel, W.B.; Copley M.J. ; Morgan, A.I. Jr. Food Dehydration Volume 2; Second ed. The AVI Publishing Company, Inc.: Westport, CT, 1973. van Ballegooijen, W.G.E.; van Loon, A. M.; van der Zanden, A.J.J. Modeling DiffusionLimited Drying Behavior in a Batch Fluidized Bed Dryer in Drying Technology 1997, 15 (3&4), p837855. van't Land, C.M. Industrial Drying Equipment: Selection and Application; Chemical Industries 45; Marcel Dekker, Inc.: New York, NY, 1991. Vergnaud, J.M. Drying of Polymeric and Solid Materials; SpringerVerlag: London, UK, 1992. Walas, S.M. Chemical Process Equipment Selection and Design; ButterworthHeinemann Series in Chemical Engineering ButterworthHeinemann: Stoneham, MA, 1990. PAGE 143 126 APPENDICES PAGE 144 127 APPENDIX 1 DRYER DESIGN & CONSTRUCTION Figure 46 Schematic of Lab Apparatus PAGE 145 128 Appendix 1 (Continued) Figure 47 Photograph of 1st Generation FBD PAGE 146 129 Appendix 1 (Continued) Figure 48 Photograph of Final VFBD PAGE 147 130 APPENDIX 2 THREEPHASE VFBD MODEL CODE Rules ;Bed Hydrodynamic Properties Umf=((s*dp*g*(rhoprho)* 0^3)/(1.75*rho))^.5 Vmf=Umf*.384 uT=(2.32*Umf)/( 0^1.5) Vt=uT*.384 ub=0.7*((g*db)^.5) Vb=ub*.384 U= b*ub+(1b)*Umf vib=(A* ^2)/(g/100) g=(1.1555E14*T^3)+(9.5728E11* T^2)+(3.7604E08*T)3.4484E06 Umvf=5.238*((rhop/rho)^.63)*((1/ g)^.33)*((dp/100)^.88)*(1c*(vib)) Vmvf=Umvf*.384 Umvf1=Umf*(1((1+k)/(6.28*j))*(vib)) Vmvf1=Umvf1*.384 (HdH)/Hd=( 0)/(1) ( 10)/(11)=1exp(0.54*(10/Vmvf11)*(vib)^(.75*Vmvf1/10)) P=H*(1)*(rhoprho)*(g) Pv=P*(10.0935*(dp/Hd)^0. 946*(vib)^0.606*s^1.637) db=0.474*(((UUmvf1)/(1.6*Dt^.4*g^. 5))^.4)*(Hd+3.94*Adp^.5)^.8 ;db=0.64*(Ab*(UUmvf1)^.4) Re=U*dp/g Sc=g/(rhoDab/1000) BV=Ab*Hd/28316.736 (1)=(1b)*(10.4) aif=6*(1)/(s*dp) ;Balance & Humidity Equations mb=Vb/BV mt=V/BV md=mtmb Vd=md*BV ln(Pwsat) = (5800.2206/Ti) + 1.3915 0.0486*Ti + 0.4176E4*Ti^2 0.1445E7*Ti^3 + 6.546*ln(Ti) Ysat = .621*Pwsat / ((1.0133E5) Pwsat) Yb = (6*Kb* b*Yd + db*mb*Yi) / (db*mb+ 6*Kb* b) Yd*md + Yb*mb = Ysat*mt Td*md + Tb*mb = To*mt Tb = (rho*mb*Ti*db*( g + Yi* v) + 6*hb* b*Td) / (6*hb* b + rho*mb*db*( g + Yi* v)) rho*ub*(YdYi)(6*Kb*rho* b/db)*(YbYd)=(1b)*(rho*aif*Ky*(YsatYd)) ;Heat & Mass Transfer Kb=(Umvf1/3)+(4*Dm**ub/(*db))^.5 PAGE 148 131 Appendix 2 (Continued) Ky=(Dm/ *dp* )*(2+(1.8*Remvf^.5*Sc^.33)) hb=(Umvf1*rho* g/3)+(4* g*rho*Kg* *ub/( *db)) ; *** Solving ODEs by Fourth Order RungeKutta method *** call RK4('TWO,'y,'t,2) ; standard RK Procedure: RK4 ;Classical 4thOrder RungeKutta method ;Input Variables: EQ,y,x,ne ; Notation: EQ name of the func tion with the 1storder equations ; y master list with names of lists representing ; the unknown functions ; x independent variable (list) ; ne number of the 1storder equations ; K master list with names of lists of RK coefficients ; 'K#1 through 'K#4 ; @yi,@ye auxiliary lists ; Description: This procedure function is an implementation of the classical ; 4thorder RungeKutta method for numeric al integration of sets of ordinary ; differential equations repres ented by 1storder equations ; Usage notes: ; 1. The list x and the initial conditi ons in the 1st elements of lists ; y1, y2, ... must be set prior to calling RK4. ; 2. The set of 1storder differ ential equations must be defined in a ; function the name of which is passed as the value of EQ The form ; of equations must be as follows: ; y`[i] = fi(x, y[1], y[2], ..., y[n]) ; The names y`, y, x or any other names are local to that function and ; may be freely chosen; they map into the list names Kj and @ye, and ; into the current value of independent variable xi in this function. ; 3. Parameter variables may be used for transmitting the values of equation ; constants (if there are any) direct ly from the Variable Sheet to the ; Function Subsheet specifying the 1storder equations. ; 4. Procedure RK4 can handle any number of 1storder linear and nonlinear ; ordinary differential equations. The master list y (i.e. the list ; with the name passed onto y as symbolic value when calling RK4) ; must contain as its elements appr opriate names of subordinate lists. for j=1 to 4 'K[j][1]:= j ; seeding a matr ix of RK coefficients PAGE 149 132 Appendix 2 (Continued) next j for e=1 to ne call blank(y[e],2,length(y[e])) ; error indicates missing next e ; element in master list y xi:= x[1] for i=2 to length(x) call statmsg('Solving,'at,x,x[i]) for e=1 to ne '@yi[e]:= y[e][i1] ; erro r at i=2 indicates missing next e ; eth initial condition call listcopy('@yi,'@ye) h:= (x[i]xi)/2 for j=1 to 3 Kj:= 'K[j] call apply(EQ,Kj,'@ye,xi) if mod(j,2) then xi:= xi + h if j=3 then h:= 2*h for e=1 to ne '@ye[e]:= '@yi[e] + h*Kj[e] next e next j call apply(EQ,'K#4,'@ye,xi) for e=1 to ne y[e][i]:= '@yi[e] + ('K#1[e]+2 *('K#2[e]+'K#3[e])+'K#4[e])*h/6 next e next i call delete('@yi) call delete('@ye) for i=1 to 4 call delete('K[i]) next i call delete('K) Function: TWO ;Comment: 1st order equations ;y[1]=dC/dT ;y'[2]=dTs/dt Parameter variables: rho,rhop,ub,Yd,Yi,Yb,Kb, b, 0,db,dp, g, v, s, w,Ti,Tb,Td,hb, ,Dab,r,Cs Input Variables: y`,y,t y`[1]:= (rho*ub*(YdYi)(6*Kb*rho* b/db)*(YbYd))/(rhop*(1)*(1b)) y`[2]:= (rho*ub*( g+Yi* v)*(TiTd)+(6*hb* b/db)*(TbTd)*(rho*ub*(YdYi)(6*Kb+rho* b/dp)*(YbYd)))/(( s+ w*y[1])*(1b)*(10)*rhop) ;y'[1]:=( ^2*Dab/6r^2)*(y[1]Cs) PAGE 150 133 Appendix 2 (Continued) Variables: Name: Unit: Comment: V SCFM operational vol. air flow rate A m operational vibrational amplitude rad/s operational angular frequency dp cm measured mean particle diameter T K temperature s n.d. spericity g cm/s^2 accel due to gravity n.d. pi rhop g/cm^3 particle density rho g/cm^3 air density c n.d. vfb coefficient 0 n.d. bed voidage (static) Hd cm bed height (dynamic) H cm bed height (static) Yi % humidity Ab cm^2 cross sectional bed area k n.d. coeffic of collision elasticity j n.d. lift & fall time / vib. period Kg cal/cm*s*c thermal conductivity of air Dab cm/s binary diffusivity n.d. mole frac. nondiffusing component. Ti K temp in v cal/g*c specific heat g cal/g*c specific heat s cal/g*c specific heat w cal/g*c specific heat cal/g latent heat of vaporization BV ft^3 bed volume vib vibrational factor U cm/s operational air velocity Umf cm/s min. fluidiz. air velocity Vmf SCFM min. fluidiz. vol. air rate Umvf1 cm/s min. vib. fluidiz. air velocity Vmvf1 SCFM min. vib. fluidiz. vol. air rate db cm bubble diameter uT cm/s terminal air velocity ub cm/s bubble air velocity Vd SCFM dense phase vol. air rate PAGE 151 134 Appendix 2 (Continued) Vt SCFM vol. air rate Vb SCFM bubble phase vol. air rate md s^1 dense gas flow rate / unit vol of bed mt s^1 gas flow rate / unit vol of bed mb s^1 bubble gas flow rate / unit vol of bed g m^2/s kinematic viscosity Re n.d. bed reynolds number Sc n.d. bed schmidt number n.d. bed voidage b n.d. bed voidage bubble frac. aif cm^1 interfacial area/bed vol Pwsat Pa saturation pressure Ysat % humidity at saturation Yb % bubble phase humidity Yd % dense phase humidity Kb Cm/s mass transfer coeff dense to bubble Ky Cm/s mass transfer coeff particle to gas hb Cal/cm^2 s C heat transfer coeff bubble to dense To K temp out Tb K temp bubble phase Td K temp dense phase PAGE 152 135 APPENDIX 3 PARTICLE SIZE DISTRIBUTION DATA Table 12 Sieving Data Tabulation 1 gwlog dlogii iWd W= 3.829 mm (37) 1/2 2 logloglogiigw iWdd S W= 1.228E08 non. dim. (38) 1 11 lnln1 loglog 2gwgwSdSS = 2.491E07 mm (39) log di Wi log di log di log dgw Wi(log di log dgw) U.S. Sieve # Sieve Size (mm) Wi (g) Pi (%) Pi (%<) 13.3300.000.00 9.4230.000.00100.001.056 6.6802.556.0793.930.9062.3130.3230.824 44.76011.8328.1165.820.7578.9600.1742.063 63.36013.0330.9734.840.6097.9310.0250.332 102.00011.2226.668.190. 4284.8020.1551.737 161.1682.916.921.260. 2000.5820.3831.117 200.8400.320.750.510. 0020.0010.5810.184 300.5900.110.270.240. 1460.0160.7290.082 400.4200.050.130.110. 2970.0160.8800.048 500.2970.030.070.040. 4460.0141.0290.032 700.2100.020.0400.5960.0101.1790.020 Summation 42.078100.00 24.532 0.000 PAGE 153 136 APPENDIX 4 INSTRUMENT CALIBRATION STATISTICS Table 13 Regression Statistics for A/D Calibration Input Channel # Number of Observations Correlation Coefficient (R2) Standard Error Upper 95% Confidence Limit Lower 95% Confidence Limit 1 51 1.000 0.0005 1.0006 0.9996 2 41 1.000 0.0002 1.0003 0.9998 3 51 1.000 0.0001 1.0002 0.9999 4 27 1.000 0.0007 1.0001 0.9998 5 39 1.000 0.0029 1.0002 0.9996 6 51 1.000 0.0001 1.0002 0.9999 7 39 1.000 0.0022 1.0002 0.9997 8 39 1.000 0.0011 1.0002 0.9999 Table 14 Regression Analysis of Variance for the A/D Calibration Input Channel # Sum of Square Regression Sum of Square Residual Mean Square of Regression Mean Square of Residual FRatio 1 4.420 1.352E05 4.421 2.7604E07 1.602E+07 2 2.296 1.200E05 2.296 3.060E07 7.491E+07 3 4.421 8.230E05 4.421 1.680E07 2.630E+08 4 102.369 1.090E05 102.369 4.360E07 1.090E88 5 308.689 3.130E04 308.689 8.450E06 1.60E122 6 4.420 6.890E07 4.420 1.410E08 3.140E+08 7 308.703 1.720E04 308.703 4.640E06 6.647E+07 8 308.767 4.580E05 308.766 1.240E06 2.500E+08 PAGE 154 137 Appendix 4 (Continued) Table 15 Regression Statistics for Mass Flow Meter Calibration Number of Observations Correlation Coefficient (R2) Standard Error Upper 95% Confidence Limit Lower 95% Confidence Limit 39 0.994 0.0753 1.0157 0.9996 Sum of Square Regression Sum of Square Residual Mean Square of Regression Mean Square of Residual FRatio 5.013 3.67E2 3.67E2 5.67E3 6.477E5 0 2 4 6 8 10 12 0.002.004.006.008.0010.0012.00 Rotameter or Pitot Reading, SCFMKurz Flow Meter Reading, SCFM 1 Rotamter SCFM 1 Pitot SCFM 2 Rotamter SCFM 2 Pitot SCFM 3 Rotamter SCFM 3 Pitot SCFM Figure 49 Flow Meter Calibration Plot PAGE 155 138 Appendix 4 (Continued) Table 16 Regression Statistics for the Di fferential Pressure Sensor Calibration Number of Observations Correlation Coefficient (R2) Standard Error Upper 95% Confidence Limit Lower 95% Confidence Limit 21 0.9997 0.0329 1.0103 0.9953 Sum of Square Regression Sum of Square Residual Mean Square of Regression Mean Square of Residual FRatio 84.472 2.06E2 84.472 1.0857E3 7.7842E5 4.00000 3.00000 2.00000 1.00000 0.00000 1.00000 2.00000 3.00000 4.00000 4.03.02.01.00.01.02.03.04.0 1 Omega PX138 2 Omega PX138 3 Omega PX138 Figure 50 Differential Pressure Sensor Calibration Plot PAGE 156 139 Appendix 4 (Continued) Table 17 Inlet Thermocouple Calibration Descriptive Statistics Set 1 Set 2 Set 3 Merged Set Mean 23.081100.25920.848100. 62920.140100.25021.357100.379 Standard Error 0.4590.5240. 6500.5160.7410.4710.3920.287 Median 23.010100.55621.493100. 61520.639100.57621.697100.576 Standard Deviation 2.0522.344 2.9062.3073.3122.1053.0342.223 Sample Variance 4.2125.494 8.4445.32210.9674.4319.2064.942 Kurtosis 0.4510.0860.3440 .1622.3920.0142.0010.240 Skewness 0.1950.6670.5400. 6581.4640.1681.0260.489 Range 7.7208.62611.2308. 37912.6958.58615.4629.186 Minimum 19.51195.05214.210 95.52311.76995.65311.76995.052 Maximum 27.231103.67825.441 103.90224.464104.23827.231104.238 Count 2020202020206060 Conf. Level(95.0%) 0.9611.097 1.3601.0801.5500.9850.7840.574 Table 18 Outlet Thermocouple Calibration Descriptive Statistics Set 1 Set 2 Set 3 Merged Set Mean 21.663101.41322.071100.592 21.703100.35021.812100.785 Standard Error 0.5160.5500.4420.5200.5210.5140.2820.306 Median 22.014101.02322.582100.515 22.036100.68022.330100.700 Standard Deviation 2.3092.4621.9772.3282.3312.2972.1812.368 Sample Variance 5.3326.0603.9075.4175.4325.2764.7595.605 Kurtosis 0.6820.9481.1440.160 0.7670.2370.2760.288 Skewness 1.0530.2500.4750.6421 .0580.4570.9040.185 Range 8.3018.3016.0358.5788.2848.5868.33310.692 Minimum 16.16397.81918.40595.428 16.13195.65316.13195.428 Maximum 24.464106.12024.439104.006 24.415104.23824.464106.120 Count 2020202020206060 Conf. Level(95.0%) 1.0811.1520.9251.0891.0911.0750.5640.612 PAGE 157 140 APPENDIX 5 THINLAYER DRYING PARAMETER DETERMINATION y = 2.0568x 5.0396 R2 = 0.9958 2 1.5 1 0.5 0 0.5 1 1.5 00.511.522.533.5 Drying Curve 1 0.000 0.200 0.400 0.600 0.800 1.000 051015202530 Time, min.Moisture Ratio M.R. M.R.predicted Figure 51 Linear Regression for Drying Parameter Determination and Drying Curves, 144.7 C 144.7C PAGE 158 141 Appendix 5 (Continued) y = 2.36x 6.0145 R2 = 0.9774 2.5 2 1.5 1 0.5 0 0.5 1 1.5 2 00.511.522.533.5 Moisture Curve 2 117.7 C0.000 0.200 0.400 0.600 0.800 1.000 1.200 051015202530 Time, min.Moisture Ratio M.R. M.R.predicted Figure 52 Linear Regression for Drying Parameter Determination and Drying Curves, 117.7 C PAGE 159 142 Appendix 5 (Continued) y = 1.9776x 4.2444 R2 = 0.989 1.5 1 0.5 0 0.5 1 1.5 2 00.511.522.533.5 Drying Curve 3 137.73 C0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900 1.000 051015202530 Time, min.Moisture Ratio M.R. M.R.predicted Figure 53 Linear Regression for Drying Parameter Determination and Drying Curves, 137.7 C PAGE 160 143 Appendix 5 (Continued) y = 1.9289x 4.5793 R2 = 0.9855 2 1.5 1 0.5 0 0.5 1 1.5 00.511.522.533.5 Drying Curve 4 152.4 C0.000 0.200 0.400 0.600 0.800 1.000 051015202530 Time, min.Moisture Ratio M.R. M.R.predicted Figure 54 Linear Regression for Drying Parameter Determination and Drying Curves, 152.4 C PAGE 161 144 Appendix 5 (Continued) y = 2.9921x 7.7075 R2 = 0.994 3.5 3 2.5 2 1.5 1 0.5 0 0.5 1 1.5 2 00.511.522.533.5 Drying Curve 5 104.1 C0.000 0.200 0.400 0.600 0.800 1.000 1.200 0510152025 Time, min.Moisture Ratio M.R. M.R.predicted Figure 55 Linear Regression for Drying Parameter Determination and Drying Curves, 104.1 C PAGE 162 145 APPENDIX 6 DRYING MODEL REGRESSION STATISTICS Table 19 Regression Statistics fo r the ThreePhase Model at 144.7 C Number of Observations Correlation Coefficient (R2) Standard Error Upper 95% Confidence Limit Lower 95% Confidence Limit 7 0.9971 0.0234 1.0529 0.9303 Sum of Square Regression Sum of Square Residual Mean Square of Regression Mean Square of Residual FRatio 0.9496 2.75E3 0.9496 5.490E4 1.7289E3 Table 20 Regression Statistics fo r the ThreePhase Model at 117.7 C Number of Observations Correlation Coefficient (R2) Standard Error Upper 95% Confidence Limit Lower 95% Confidence Limit 8 0.9962 0.0268 1.0936 0.9664 Sum of Square Regression Sum of Square Residual Mean Square of Regression Mean Square of Residual FRatio 1.1303 4.31E3 1.1303 7.19E4 1.72E3 Table 21 Regression Statistics fo r the ThreePhase Model at 137.7 C Number of Observations Correlation Coefficient (R2) Standard Error Upper 95% Confidence Limit Lower 95% Confidence Limit 7 0.9991 0.0121 1.0146 0.9488 Sum of Square Regression Sum of Square Residual Mean Square of Regression Mean Square of Residual FRatio 0.8635 7.33E4 0.8635 1.47E4 5.891E3 PAGE 163 146 Appendix 6 (Continued) Table 22 Regression Statistics fo r the ThreePhase Model at 152.4 C Number of Observations Correlation Coefficient (R2) Standard Error Upper 95% Confidence Limit Lower 95% Confidence Limit 7 0.9961 0.02650 1.0714 0.9293 Sum of Square Regression Sum of Square Residual Mean Square of Regression Mean Square of Residual FRatio 0.9203 3.51E3 0.9203 7.02E4 1.310E3 Table 23 Regression Statistics fo r the ThreePhase Model at 104.1 C Number of Observations Correlation Coefficient (R2) Standard Error Upper 95% Confidence Limit Lower 95% Confidence Limit 8 0.9908 0.0425 1.1006 0.9077 Sum of Square Regression Sum of Square Residual Mean Square of Regression Mean Square of Residual FRatio 1.1709 1.083E2 1.1709 1.0804E3 6.488E2 Table 24 Regression Statistics fo r the ThinLayer Model at 144.7 C Number of Observations Correlation Coefficient (R2) Standard Error Upper 95% Confidence Limit Lower 95% Confidence Limit 7 0.9941 0.0340 1.0934 0.9157 Sum of Square Regression Sum of Square Residual Mean Square of Regression Mean Square of Residual FRatio 0.9744 5.769E3 0.9745 1.154E3 8.446E2 Table 25 Regression Statistics fo r the ThinLayer Model at 117.7 C Number of Observations Correlation Coefficient (R2) Standard Error Upper 95% Confidence Limit Lower 95% Confidence Limit 8 0.9914 0.0363 1.0833 0.9112 Sum of Square Regression Sum of Square Residual Mean Square of Regression Mean Square of Residual FRatio 1.0595 8.899E2 1.0595 1.317E3 8.048E2 PAGE 164 147 Appendix 6 (Continued) Table 26 Regression Statistics fo r the ThinLayer Model at 137.7 C Number of Observations Correlation Coefficient (R2) Standard Error Upper 95% Confidence Limit Lower 95% Confidence Limit 7 0.9987 0.0145 1.0224 0.9439 Sum of Square Regression Sum of Square Residual Mean Square of Regression Mean Square of Residual FRatio 0.8659 1.045E3 0.8659 2.090E4 4.1413E3 Table 27 Regression Statistics fo r the ThinLayer Model at 152.4 C Number of Observations Correlation Coefficient (R2) Standard Error Upper 95% Confidence Limit Lower 95% Confidence Limit 7 0.9962 0.0264 1.0641 0.9224 Sum of Square Regression Sum of Square Residual Mean Square of Regression Mean Square of Residual FRatio 0.9074 3.491E3 0.9074 6.980E4 1.2994E3 Table 28 Regression Statistics fo r the ThinLayer Model at 104.1 C Number of Observations Correlation Coefficient (R2) Standard Error Upper 95% Confidence Limit Lower 95% Confidence Limit 8 0.9971 0.0218 1.0518 0.9527 Sum of Square Regression Sum of Square Residual Mean Square of Regression Mean Square of Residual FRatio 1.1666 2.863E3 1.1666 4.770E4 2.4449E3 PAGE 165 148 APPENDIX 7 MULTIMEDIA Included in this dissertation are 3 videos produced to help illustrate the dissertation research. The first (D rying.wmv), is a timecompressed representation of a typical dr ying trial. It is 3:47 minut es long, and utilizes a split screen format. This allows the viewer to watch the vibrofluidized bed drying process while graphs of t he data are generated in the side panel. It is useful for linking the observed bed hydrodynamic behav ior to the acquired data, throughout a trial. The second (Vfbd.wmv ), is a lowresolu tion 31 second clip of the citrus processing residue being dried in the vibrof luidized bed dryer. This video allows the viewer an opportunity to quickly view t he quality of fluidization achieved in the bed, at the conditions used for the experim ental drying trials. The viewer can observe that stable fluidization is achi eved, the bed is well mixed, and there are no agglomeration or el utriation problems. The third video (Intro.wmv), is a video produced for the dissertation defense. It is 6:20 minutes in lengt h and uses video foot age from actual processing plants, as well as from the laboratory. It prov ides the viewer an introduction to the citrus industry, the c hallenges associated with the disposal of the processing residue, an overview of the existing feedmill process and an introduction to the proposed vibrof luidized bed drying process. PAGE 166 ERIC ROE is a Ph.D. candidate in Chemic al Engineering at the University of South Florida (USF). He received his MS in Chemical Engi neering from USF. During his time at USF, and in addition to his research into fluidized bed drying, he has been a consultant to the Citrus Industry, and has wo rked on the State Test Lab Sampler project funded by the Florida Department of Citrus, the High School Technology Initiative funded by the National Science Foundation (NSF), and the Florida Center for Manufacturing E ducation project also funded by NSF. Prior to his study at USF, he was employed as a technologist in Research and Development at Tropicana Products, Inc ., with process and product development responsibilities. His research interest s are food engineering, fluidized bed drying, and the integration of engineering and education. xml version 1.0 encoding UTF8 standalone no record xmlns http:www.loc.govMARC21slim xmlns:xsi http:www.w3.org2001XMLSchemainstance xsi:schemaLocation http:www.loc.govstandardsmarcxmlschemaMARC21slim.xsd leader nam Ka controlfield tag 001 001681117 003 fts 005 20060215071250.0 006 med 007 cr mnuuuuuu 008 060105s2003 flu sbm s000 0 eng d datafield ind1 8 ind2 024 subfield code a E14SFE0000628 035 (OCoLC)62784571 SFE0000628 040 FHM c FHM 049 FHMM 090 TP145 (Online) 1 100 Roe, Eric A. 0 245 Vibrofluidized bed drying of citrus processing residue for byproduct recovery h [electronic resource] / by Eric A. Roe. 260 [Tampa, Fla.] : b University of South Florida, 2003. 502 Thesis (Ph.D.)University of South Florida, 2003. 504 Includes bibliographical references. 516 Text (Electronic thesis) in PDF format. 538 System requirements: World Wide Web browser and PDF reader. Mode of access: World Wide Web. 500 Title from PDF of title page. Document formatted into pages; contains 166 pages. Includes vita. 520 ABSTRACT: Approximately 44% of the citrus that is processed becomes processing residue. The residue consists of the nonjuice components of a citrus fruit, primarily peel and pulp, and is recovered by conversion to animal feed. The material is hygroscopic, agglomerating, has a wide particle size distribution, and must be carefully dried to avoid thermal damage to nutrients and flavors. This dissertation evaluates the possibility of utilizing a vibrofluidized bed dryer for citrus processing residue. Results demonstrate that it is possible to overcome the agglomeration difficulties associated with this material, offering an economically viable alternative processing methodology. To properly analyze this proposed system, a benchtop vibrofluidized bed dryer was designed, constructed and instrumented. Vibrofluidization and batch drying trials were conducted and analyzed. An economic evaluation of the proposed process was undertaken.Two mathematical models of the drying process were developed and validated. Characteristics that describe the vibrofluidized bed drying of the residue were determined. The conditions that facilitated fluidization were: 1) A particle size distribution of the dried residue that was lognormal, had a geometric mean diameter, dgw, of 3.829 mm, and a geometric standard deviation, Sgw, of 2.49x1007 mm. 2) A vibrational acceleration, Aw2/g, of 2.54. 3) A minimum vibrofluidization velocity, Umvf, of 4.2 cm/s. The controlling mechanism of the falling rate period was determined to be diffusion, with an effective diffusion coefficient, Deff, of 2.85x105 cm/s, and critical moisture content, Mc, of 30%. Economic evaluation of the proposed method has a payback period of 4.34 years, and an estimated processing cost of $33 per ton of dried material. Models were developed based on bed hydrodynamics and threephase drying kinetics, and thinlayer drying. 590 Adviser: Gilbert, Richard A. 653 Vibrating fluidized bed. Dried citrus pulp. Fluidized bed. Animal feed. Citrus byproducts. 690 Dissertations, Academic z USF x Chemical Engineering Doctoral. 773 t USF Electronic Theses and Dissertations. 4 856 u http://digital.lib.usf.edu/?e14.628 