Numerical model of seawater and freshwater fluxes in a carbonate platform

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Numerical model of seawater and freshwater fluxes in a carbonate platform

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Title:
Numerical model of seawater and freshwater fluxes in a carbonate platform
Creator:
Fuller, John R. 1964-
Place of Publication:
Tampa, Florida
Publisher:
University of South Florida
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English
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x, 64 leaves, : ills., 3 folded graphs ; 29 cm.

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Subjects / Keywords:
Dolomite ( lcsh )
Carbonate reservoirs ( lcsh )
Seawater -- Thermodynamics -- Computer simulation ( lcsh )
Dissertations, Academic -- Geology -- Masters -- USF ( FTS )

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General Note:
Thesis (M.S.)--University of South Florida, 1993. Includes bibliographical references (leaves 41-43).

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University of South Florida
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Universtity of South Florida
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All applicable rights reserved by the source institution and holding location.
Resource Identifier:
029494935 ( ALEPH )
29376645 ( OCLC )
F51-00100 ( USFLDC DOI )
f51.100 ( USFLDC Handle )

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NUMERICAL MODEL OF SEAWATER AND FRESHWATER FLUXES IN A CARBONATE PLATFORM by John R. Fuller, Jr. A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in the Department of Geology in the University of South Florida April, 1993 Major Professor: Mark T Stewart

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Graduate Council University of South Florida Tampa, Florida CERTIFICATE OF APPROVAL MASTER'S THESIS This lS to certify that the Master's Thesis of JOHN R. FULLER, JR. with a major in Geology has been approved by the Examining Committee on April 15, 1993 as satisfactory for the thesis requirement for the Master of Science degree. Thesis Committee: Major Professor: Mark T Stewart Member: H. Len Vacher Member: . Terry{ Qui'nn

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DEDICATION For the Fullers, old and new. ii

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ACKNOWLEDGMENTS I would like to thank Dr Mark T. Stewart for his guidance and insight. Dr. Len Vacher and Dr. Terry Quinn deserve thanks for reviewing the manuscript. I am grateful for my parents' support and love. And most of all, my deepest thanks goes to my wife, Mer yl, for her encouragement and patience. iii

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TABLE OF CONTENTS LIST OF TABLES v LIST OF FIGURES vi ABSTRACT vii INTRODUCTION 1 LITERATURE REVIEW 5 MODEL FRAMEWORK 13 METHODS 18 RESULTS 23 DISCUSSION 36 CONCLUSIONS 40 LIST OF REFERENCES 41 APPENDIXES 44 APPENDIX A. C SOURCE CODE TO PLOT VECTORS 45 APPENDIX B. MASS BALANCE OF SIMULATION 51 APPENDIX C. VECTOR MAGNITUDE IN FT/YR 52 APPENDIX D. MAGNESIUM FLUX MAGNITUDE IN MOLE/FT2/YR 58 APPENDIX E. CALCULATION OF MAGNESIUM FLUX 64 iv

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LIST OF TABLES Table Page 1 Assumed model parameters that represent an idealized carbonate platform. 17

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LIST OF FIGURES Figure Page 1 Generalized view of seawater-circulation system in a carbonate platform. 14 2 Geologic setting of the MOCDENS model that represents a half-section of a carbonate platform. 14 3 Boundary conditions of the MOCDENS model. 15 4 Fluctuations in mixing zone concentrations versus time. 19 5 Velocity vectors and relative salinity contours. 24 6 Magnesium fluxes and relative salinity contours. 28 7 Streamtubes, seawater age and velocity vectors. 32 8 Streamtube average residence times, streamtubes and velocity vectors near the seaward margin. 35 9 Distribution of seawater influx versus distance from the center of the platform. 37 vi

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NUMERICAL MODEL OF SEAWATER AND FRESHWATER FLUXES IN A CARBONATE PLATFORM by John R. Fuller, Jr. An Abstract Of a thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in the Department of Geology in the University of South Florida April 1993 Major Professor: Mark T. Stewart, Ph.D. vii

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Seawater and freshwater fluxes in a carbonate platform are simulated using MOCDENS, a two-dimensional, finitedifference, solute-transport, numerical model. The model represents a half-section of a carbonate platform and is used to determine and define the nature of mixing-zoneinduced seawater circulation in a carbonate platform. The modeled platform is 98,000 feet wide, 3240 feet thick and is assumed to rest on an impermeable basement. Mixing-zone-induced seawater circulation has been hypothesized as a possible environment for large-scale platform dolomitization. Model results indicate that such circulation exists and that the ratio of seawater influx to freshwater recharge in the modeled section is 12 to 1. Vector-velocity and stream-tube plots indicate that 50 percent of the total seawater influx is concentrated within the 20 percent of the platform adjacent to the platform margin. Ground-water-flow velocities vary from 4000 feet per year at the platform margin to 4 feet per year at the center of the platform. A contour plot of seawater age indicates that a seawater-circulation system could develop if a similarly sized carbonate platform became emergent for as little as 2,000 years. Thus, sea-level fluctuations with a period of viii

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several thousand years can produce extensive seawater circulation in carbonate platforms. Abstract approved: Major Professor: Mark T. Stewart Professor, Department of Geology Date of Approval X

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INTRODUCTION Dolomite commonly occurs in carbonate platforms as. extensive, thin lenses. Although thin compared to their length, their thickness represents thousands of years of geologic time. The genesis of dolomites in carbonate platforms has received extensive attention from geologists (Hanshaw, 1971; Badiozamani, 1973; Folk, ; Land, 1982; Morrow, 1982b, Saller, 1984; Simms, 1984; Machel, 1986; Aharon and others, 1987; Hardie, 1987; Hardie and others, 1991; Humphrey, 1988; Vahrenkamp, 1988; and Vahrenkamp and others, 1991). 1 Researchers agree that there has to be a favorable chemical environment and a stable source of magnesium ions (Mif+) to sustain the replacement of limestone (calcium carbonate or CaC03 ) by dolomite (calcium magnesium carbonate or CaMg(C03)2) over geologic time. While most studies focus on specific chemical conditions under which dolomite could form, this study examines a ground-water-circulation system that could provide a stable source of Mif+ for thousands of years. Because the dimensions of carbonate platforms are many thousands of feet, practical study of ground-watercirculation patterns in them is most easily accomplished

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2 through computer simulation. Although the geology is generalized and natural systems will exhibit extensive variation from the model, the model will, at a minimum, verify whether such circulation is possible. Because the model is of a general, idealized case, a set of geologically and hydraulically reasonable and realistic aquifer parameters can be assumed. Replacement-dolomitization models must include the mass-transfer processes and ground-water-circulation systems essential for wide-spread dolomitization of platform The dolomite problem is essentially one of explaining the mechanism and environment of formation responsible for the vast amounts of secondary dolomite present throughout the subsurface of modern and ancient carbonate platforms and atolls. Stability of these circulation systems over geologic time is required because of kinetic barriers (Hardie, 1987). Kinetics has a significant influence on dolomitization because the ideal dolomite crystal lattice has a very high degree of order. The degree of order a growing dolomite crystal has is directly affected by the length of time its three constituents have to locate themselves in their proper sites. Differences in disorder, or the degree to which the crystalline structure of dolomite departs from a perfect arrangement of M
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Geologic evidence indicates that replacement dolomitization requires low temperatures, long reaction times and a dependable source of Mif+ (Hardie, 1987) Only very large ground-water-flow systems can transport the quantities of Mif+ that are required to form thick layers of dolomite. The required fluxes are governed by the duration of the dolomitization episode and the stoichiometry, or the extent to which the composition of dolomite departs from a stoichiometric formulation of CaMg(C03)2. 3 The zone of seawater circulation below the freshwater/seawater mixing zone in an emergent carbonate platform is an environment with low temperatures, stable flow conditions and a dependable source of Mif+ ions. While the potential for normal marine seawater to replace limestone with dolomite in carbonate platforms is well documented, (Badiozamani, 1973; Folk, 1975; Land, 1982; Morrow, 1982b and Humphrey, 1988) the mechanism whereby seawater circulation within carbonate platforms occurs is poorly defined due to the vast distances and depths involved. Although direct measurement of such circulation is not practical, computer simulation of this environment can provide finely distributed data on freshwater and seawater circulation within an idealized carbonate platform. The objective of this study is to simulate and analyze mixing-zone-induced seawater circulation beneath an emergent carbonate platform by use of a vertical, two-dimensional, density-driven, solute-transport, numerical model.

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4 Simulation of such circulation allows detailed measurement of the magnitude and distribution of freshwater and seawater fluxes. Fluxes simulated by the model will be plotted as two-dimensional freshwater, seawater, and Mif+ vector fields. It is anticipated that the vector-field profiles of freshwater and seawater fluxes will yield insight into the relationship between the distribution of dolomite and the circulation patterns within carbonate platforms. The principal objective of this study is to determine if freshwater recharge to an emergent carbonate platform can create an extensive seawater flux within the platform. If the circulation of large volumes of seawater is possible, then an estimate of the ratio of freshwater recharge to seawater flux can be calculated. Identification of this ratio will help delimit the range of climates where adequate recharge exists to establish the seawater flux necessary for dolomitization. If seawater fluxes can be discretized into streamtubes then it is possible to determine how deep and how far into the platform seawater flux can extend. The average age of seawater in the platform and the average age of seawater exiting the platform implies the length of time required for an emergent carbonate platform to establish continuous seawater circulation. This period might correspond to sealevel fluctuations that would produce extensive seawater circulation in carbonate platforms.

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LITERATURE REVIEW Many geologic environments have been reported which supply enough Mif+ to replace large quantities of limestone with dolomite. Among the models that satisfy the masstransport requirements are the reflux, sabkah, Coorong, Kohout-convection, dorag or mixing zone, and mixing-zoneinduced seawater circulation models (Hardie, 1987). Because seawater represents the greatest reservoir of Mif+, it is the most important component in each of these three models. Although seawater represents a very large source of Mif+, laboratory observation and experimentation indicate that the chemistry of seawater has many properties that inhibit the replacement of limestone by dolomite (Hardie, 1987). Dolomitization models, therefore, have traditionally relied on geologic circumstances where the chemistry of seawater is modified to produce special solutions derived from seawater. These solutions avoid kinetic factors indigenous to seawater that interfere with or inhibit dolomitization (Morrow, 1982b). The reflux, sabkah, and Coorong models depend exclusively on "special waters" for dolomitization to occur (Hardie, 1987). Although these are workable models, they are based on special circumstances and cannot explain all 5

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6 laterally extensive platform dolomites (Morrow, 1978) The Kohout-convection, dorag or mixing zone, and mixing-zoneinduced seawater circulation models do not depend exclusively on modified solutions of seawater caused by local geologic circumstances and might explain some massive, laterally extensive platform dolomites (Hardie, 1987) Kohout (1965) proposes that a geothermically-driven convection cell within the south-Florida platform includes cold seawater that enters the platform at many locations, including rock outcroppings located in the Straits of Florida. Seawater then invades the platform through hightransmissivity zones extending inland from the east, south, and west sides of the Floridan Plateau. According to Kohout, the circulation is sustained by geothermal heating of Mif+-rich seawater that is continuously circulated into the aquifer to provide the Mif+ for dolomitization. The circulation patterns in the high-transmissivity zones of the Floridan Aquifer are discussed in Kohout (1965, 1967), Henry and Kohout (1972), Cowart (1978), and Fanning and others (1981). An important advantage of this model is that thermallyassisted convection currents are possible in carbonate platforms where there are only normal to depressed geothermal gradients. A study by Aharon and others (1987) on the atoll of Niue in the South Pacific supports the hypothesis that Kohout convection extensively dolomitized the carbonate sediments present there. An analytical model

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of Kohout convection completed by Henry and Hilleke (1972) predicts that although Kohout convection is possible in Florida most of the convective drive is from seawater mixing. 7 A frequently cited model of dolomitization is the Dorag or mixing-zone model as originally proposed by Badiozamani (1973) in his explanation of dolomitization in the Middle Ordovician of Wisconsin. The term "Dorag" is a Farsi word meaning "mixed blood." Badiozamani showed that mixtures of seawater and freshwater containing 5 to 30 percent seawater will dissolve calcite and precipitate dolomite. Because the Ca2+ and carbonate (CO/-) components of dissolved calcite are used to produce dolomite, calcite is being replaced by dolomite. The occurrence of dolomites that have formed through Dorag dolomitization will be affected and controlled by paleo-sea-level fluctuations, paleobathymetry and the configuration and position of the paleo-ground-water lens. Hence, these geologic parameters, once understood, can be used to either dispute or enforce a proposed case of Dorag dolomitization. The mixing zone is potentially an important environment for dolomitization. Many ancient examples of mixing zone dolomite are reported (Land, 1972; and Humphrey, 1988). Several aspects of the mixing-zone environment are regarded as essential for dolomitization to occur. An advantage that is cited frequently in support of the Dorag

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mixing-zone model is the ability of the mixing zone to generate a solution that is undersaturated with respect to calcite and oversaturated with respect to dolomite. This permits "replacement" or the dissolution of limestone concurrent with the precipitation of dolomite. 8 The second most frequently cited advantage is the reduction in the rate of precipitation of dolomite. This allows M
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9 presented by Hardie (1987). Several serious weaknesses in the Dorag model are revealed. In none of the known modern coastal mixing zones that are located in limestones or limesediments has replacement by dolomite been observed. Hardie concludes that any new hypothesis for replacement dolomitization must include the mass-transfer processes and ground-water-circulation systems required to supply the amounts of Mif+ present in platform dolomites. Machel and Mountjoy (1986) caution scientists against uncritical acceptance of mixing-zone dolomitization as a mechanism to form large masses of carbonate-platform dolomite. A hypothetical ground-water-flow system must also include features that explain the heterogeneous distribution and stoichiometry of dolomites in carbonate platforms. The most easily observed and most frequently studied geochemical feature of ground-water-flow systems in carbonate platforms is variations in the degree to which freshwater and seawater mix. Nearly every study of platform dolomites has found that the stoichiometry of dolomite is related to the salinity of the fluid in which it formed (Hanshaw, 1971; Badiozamani, 1973; Folk, 1975; Land, 1982; Morrow, 1982b, Simms, 1984; Machel and Mountjoy, 1986; Hardie, 1987; Humphrey, 1988; Vahrenkamp, 1988; and Vahrenkamp and others, 1991). Because mixing zones are vertically distributed, there should be a correlation between vertical variations in stoichiometry and isotope trends for those isotopes that are indicators of salinity.

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10 Dilution of seawater in the mixing zone reduces the thermodynamic drive toward precipitation of dolomite (Land, 1985) Dolomite that forms in a geochemical environment with a marginal potential for dolomitization has a ratio of Mg2+ to Ca2+ that is closer to the stoichiometric ratio of Mif+ and Ca2+ for perfectly ordered dolomite (Land, 1985) Such solutions include seawater that is depleted in Mg2+ or diluted by freshwater in the mixing zone. The location of well-ordered, stoichiometric dolomite within a platform should correspond to areas within the hypothetical groundwater-flow system where the fluid geochemistry would have allowed such dolomite to form. This should yield wellordered dolomites in mixing zones, while disordered dolomites would form in solutions closer to seawater in composition. In the Bahamas, dolomite located on the edges of the platform where unmixed seawater occurs is more ordered than dolomite located throughout the interior of the platform where a thick mixing zone is present (Vahrenkamp, 1988). Because these data are contradictory with the mixing-zone model, a model based on mixing-zone-induced seawater circulation has been developed. Vahrenkamp (1988) examined the genesis of a large body of Late Tertiary, massive, platform dolomite in the shallow subsurface of Little Bahama Bank. Vahrenkamp' s stableisotope evidence indicates that these dolomites formed in normal seawater and not a mixing zone. Vahrenkamp found

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high-Mif+ dolomites form preferentially where the Mif+ /Ca2+ ratio is high, in contrast to statements by Land (1985). 11 Differences in stoichiometry among these dolomites, or the extent to which the composition of dolomite departs from the stoichiometric formulation of CaMg(C03)2, are dependant on the texture of the carbonate rock that the dolomite has replaced. Bimodality of the Mif+fca2+ ratio in dolomite was observed along the margins of the platform, where the most Mif+-rich dolomite was found. Mode one is Mif+-rich dolomite that has replaced limestone of very low permeability (micrite). Mode two is Ca2+-rich dolomite that has replaced limestone of higher permeability. Also, in the center of the island, dolomites are rich in Ca2+. Changes in the C13 gradient and in major-element composition toward the center of the platform indicate that ground-water flow during diagenesis was toward the platform center. If the ground-water-flow direction during diagenesis was inward, then the fluid at the center of the platform would be depleted in Mif+ and CO/-. Because the dolomite here is Ca2+ rich, the ability of diluted seawater to reduce the rate of dolomitization and the degree of disorder in the dolomite is disputed. Either there are kinetic factors involved which have not been considered or the composition and texture of the dolomite precursor have a controlling influence on the stoichiometry of the resulting dolomite. In the application of a new hypothesis to particular

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12 geologic examples of dolomitization, isotopic dating may outline the length of time represented by the dolomitization process (Vahrenkamp, 1988 and Swart, 1991) Vahrenkamp constrained the time and duration of the dolomitization episode using strontium isotopes and magnetostratigraphy. He demonstrated that the duration of the dolomitization episode corresponds to intervals of time where the platform was emergent. Because short-term periods of emergence do not correspond to dolomitization episodes he proposed that there may be an initiatory length of time during which the ground-water-flow system is active but is not forming dolomite. This hypothesis is supported by evidence that the kinetic factors that inhibit dolomitization do not prevent dolomitization (Morrow, 1982a). Any explanation of a ground-water-flow system that transported a known mass of Mif contained in a particular dolomite body, must include the necessary seawater fluxes to supply such a mass of Mif+ within the duration of the dolomitization episode outlined by the isotopic analysis. The mass of Mif+ required is also dependant on the amount of dolomite that can be converted from limestone by a volume of seawater. Published values range from one to five grams per Liter (Vahrenkamp, 1988). Although there are many kinetic any factors that are not understood, the mi xingzone-induced seawater circulation model is supported by geologic observations and deserves greater consideration as a model of massive replacement dolomitization.

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13 MODEL FRAMEWORK While many carbonate sedimentologists (Hanshaw, 1971; Badiozamani, 1973; Folk, 1975; Land, 1982; Morrow, 1982b, Saller, 1984; Simms, 1984; Machel and Mountjoy, 1986; Aharon and others, 1987; Hardie, 1987; Humphrey, 1988; Vahrenkamp, 1988; Vahrenkamp and others, 1991) have hypothesized about the occurrence and distribution of seawater fluxes within emergent carbonate platforms, few supportive data exist. A two-dimensional, density-driven model was developed to quantify seawater fluxes in carbonate platforms. The purpose of model is to see if a seawater-circulation system exists and how extensive it is. The model is used to determine and define the nature of mixing-zone-induced seawater circulation in a carbonate platform. Figure 1 is a generalized view of the flows within a seawater-circulation system. Seawater and freshwater fluxes in a carbonate platform are simulated using MOCDENS, a two-dimensional, finite-difference, solute-transport, numerical model. An idealized half-section of a carbonate platform provides the geologic setting for the numerical model (Figure 2). The modeled platform is 98,000 feet wide, 3240 feet thick and is assumed to rest on an impermeable basement. Boundary conditions are chosen to simulate the general

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14 Figure 1 Generalized view of seawater-circulation system in a carbonate platform. The greatest amount of dolomite and seawater flow occurs below the mixing zone and near the platform margin. From Vahrenkamp (1988) f t 180 FEET FINITE DIFFERENCE CELL :!Figure 2. Geologic setting of the MOCDENS model that represents a half-section of a carbonate platform. The modeled platform is 98,000 feet wide, 3240 feet thick and is assumed to rest on an impermeable basement.

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15 geometry of a carbonate platform.(Figure 3). Representing sea level, and extending seaward from the shoreline of the platform, is a constant-head boundary with a total dissolved solids (TDS) concentration of 35,000 parts per million (ppm) A constant-head boundary provides the seaward vertical face of the model. Constant heads at this boundary are chosen to represent the continuous increase of pressure with depth in open seawater. Hydrostatic pressures are calculated using the density of normal marine seawater. A zero-flux boundary forms the base of the platform. Opposite the vertical hydrostatic-head boundary is the central axis of the carbonate platform, which is a zero-flux boundary. Landward of the platform margin is a freshwater-recharge boundary that receives ten inches of rain per year and forms the upper boundary of the model. Freshwater recharge is the physical drive for all fluxes in this model. SHOREUNE 1 CONSTANTHEADDOUNO,t.RY MOOEL,t.REA / L'NQ.flOW BOUNO,t.RY Figure 3. Boundary conditions of the MOCDENS model. Seaward from the shoreline and representing sea level is a constant-head boundary. A constant-head boundary representing the continuous increase of pressure with depth in open seawater is the seaward vertical face of the model. The base of the model is a zero-flux boundary. Landward from the shoreline is a freshwater-recharge boundary that receives ten inches of recharge per year.

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16 The modeled area extends 13,000 feet offshore, 84,500 feet onshore and is 3240 feet deep. Discretization of the area utilizes a grid with 100 columns by 20 rows. This configuration requires that certain arrays in the stock MOCDENS code are redimensioned (Sanford, 1985) A constant, rectilinear cell size of 1000 feet horizontally by 180 feet vertically is used (Figure 2) The values of the aquifer parameters used in this study are presented in Table 1. Because the model is of a general, idealized case, a set of geologically and hydraulically reasonable and realistic aquifer parameters are assumed. The values are obtained from several sources that are cited in Table 1. Several parameters are cited as minimizing assumptions. These parameters specify the dispersivity and diffusivity of the model. Because the numerical dispersion in the model is greater than the actual dispersive characteristics of platform carbonates the values of these parameters were minimized. Because many weeks of computer time (microVAX) are required for TDS concentrations in the large 100-by-20 grid to reach steady-state equilibrium after a change in model parameters, an extensive sensitivity analysis was not performed.

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Table 1. Assumed model parameters that represent an idealized carbonate platform. Parameter Value Intrinsic Permeabili ty1 Effective Porosity2 Anisotropy Ratio {Kh/Kv) 2 Longitudinal dispersi vi ty3 Ratio of transverse to longitudinal dispersi vi ty3 Diffusion coefficient3 Width of carbonate platform Thickness of carbonate platform4 Concentration of magnesium ions in seawater5 Total Dissolved Solids in seawater5 Sources: 1 Vahrenkamp, 1988. 2 Freeze and Cherry, 1979 3 Minimizing Assumption 4 Vahrenkamp, 1988 5 Sverdrup, 1942 0 .lE-07 ft2 .20 10:1 1.0 ft 1.0 0.0 40 miles 3,400 feet 1,272 ppm 35,000 ppm 17

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18 METHODS The MOCDENS FORTRAN code was run on a VAX minicomputer and required 4 megabytes of virtual-paged memory to execute. Each model run simulated 250 years of ground-water-flow and required three to five days of computer time to complete. The initial conditions were a rough approximation of a mi xing zone. Many model runs were required with each successive run starting from the final TDS distribution from the previous run. The objective of these simulations was to obtain convergence or equilibrium. This is a solution where the amount of seawater entering the platform balances the amount of seawater leaving the platform. Confirmation that the model had converged was obtained by plotting the concentrations of a node in the mixing zone in 10-year intervals for 200 years. At convergence, the concentrations were fluctuating but linear regression analysis of the data indicated no net trend over the 200-year interval (Figure 4). The method of characteristics particle tracking routine uses the average velocity of an entire cell to calculate particle movement and therefore only a particle in the center of the cell will travel in the truly correct direction. When a particle crosses into an adjacent cell it causes the noise which appears random. The total simulation

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24000 23000 .5. z 0 I= 21000 w 0 z 0 0:.!0000 18000 18000 185 175 185 19 195 211i 235 245 255 MODEL TIME IN YEARS Figure 4. Fluctuations in mixing zone concentrations versus time. The model is at equilibrium because the trend of the concentrations is flat. Noise represents quanta effects caused by the method of characteristics particle tracking routine. time required for concentrations in the mixing zone to attain equilibrium was 4250 years after starting with a rough approximation of the mixing zone. Results were transferred to a personal computer for graphical analysis. Because the MOCDENS code is redimensioned to 100 columns by 20 rows, more detail is present in the results than would be possible with the 20 columns by 20 rows of the stock MOCDENS code. Information obtained directly from the model included horizontal and vertical velocity components. These were reduced to an array of velocity vectors for each calibration run. The

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20 initial vector plots suffered from harmonic noise where the vectors exhibited low-level sinusoidal fluctuations. To remove harmonic noises from the velocity vectors it was necessary to average the velocity components for ten successive runs. Each run simulated 20 years of flow time. Velocity vectors were calculated from the horizontal and vertical components of velocity obtained from MOCDENS. Graphical plotting of the velocity vectors was accomplished through the development of a computer program using the C programming language. The program converts vectors into the graphical Data Exchange File (DXF) format. Source code for this C program is provided in Appendix A. Vector plots of Mif+ flux are also calculated with the C program. Seawater and freshwater fluxes are quantified by calculating the groundwater-flow velocities, converting the velocities into specific discharge or ground-water flux, discretizing these fluxes into streamtubes, and then calculating the average residence time for each streamtube. Mass-balance relationships in the platform were analyzed by summing the horizontal and vertical components of velocity at various sections within the finite-difference grid. The locations of ten streamtubes containing all of the seawater flowing through the platform were calculated by summing horizontal fluxes along rows and columns throughout the platform. These were then graphed as profiles of flux. The total seawater flux was divided into 10 streamtubes. Each streamtube was tracked through the platform using the

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21 profiles of horizontal flux along rows and columns. The zero horizontal flow boundary is outlined this is the boundary that is located below the mixing zone where flow reverses direction and velocity drops sharply. Next, selected points along the zero horizontal flow boundary are recorded relative to the coordinate system used to plot velocity vectors. Total horizontal seawater influx is summed for all finite-difference cells below the outflow cell (all seawater inflows into the platform have to cross here because all inflows into the platform exit through the outflow node) This total is divided by 10 to get flow through each of the 10 streamtubes. The total inward horizontal velocity components are added up in each of 85 columns below the zero horizontal flow boundary. These are plotted versus distance from the center of the platform. This plot is designed so that the y axis is the "percentage of total seawater influx" axis and the x axis is the "distance from the center of the platform." At each multiple of ten percent of the total seawater influx a line is extended horizontally to intercept the curve drawn through the plotted values. At each intercept another line is extended vertically to the x-axis. Each intercepted value on the x axis is the location where a streamtube boundary crosses the zero horizontal flow boundary. The number of streamtubes remaining at each crossing point is the total number of streamtubes minus the

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number of tubes that have crossed the zero horizontal flow boundary. 22 Below each streamtube boundary crossing point along the zero horizontal flow boundary the total influx is summed and plotted versus the vertical distance. Lines are extended to the curve and dropped down to the x axis, similarly to the previous calculations to obtain the vertical distribution of the streamtube boundaries below the zero horizontal flow boundary. This step is repeated nine more times below each streamtube boundary crossing point. Seawater-outflow streamtube boundaries are calculated similarly to the previous step for each of the 10 streamtubes. Streamtube endpoint locations along the constant-head boundary are calculated by summing the influxes, dividing the total by 10 and plotting percentage of total influx versus distance from the outflow node. The final plot of streamtubes is generated by "connecting the dots" with smooth curves between points. The total number of graphs required to complete these calculations is 22 Distribution of seawater age was calculated from ground-water velocities by summing the travel times through each cell along streamlines. Average residence time for each streamtube was calculated by dividing the area of the streamtube by the flux through the streamtube.

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23 RESULTS Results are presented in a format that should be useful to sedimentologists studying dolomite diagenesis. No previous numerical models of this type exist so a verification of the results by comparison with earlier modeling efforts is not possible. Information obtained from the simulation includes velocity vectors of ground-water flow, the distribution of Mif+ fluxes, the distribution of seawater streamtubes, contours of seawater age, the position of the freshwater and seawater mixing zone, and the residence time of seawater for each streamtube. Documenting the precision of these results is the massbalance error in the model. This error represents the error present in the entire model, not just the modeled platform. The chemical-mass-balance error is about 6% and the fluidmass-balance error is about .0000005%. A list of model budget parameters is located in Appendix B. The magnitude of each ground-water velocity vector is listed in Appendix C. Figure 5 contains velocity vectors and relative-salinity contours. Flow is the smallest at the center of the platform. The greatest amount of seawater flow is concentrated at the platform margin The distance between each column of vectors is 1000 feet. For each vector, the

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Figure 5. Velocity vectors and relative salinity contours. Each vector's length is the distance that ground water would flow in one year. Velocities vary from two feet per year at the center of the platform to 4000 feet per year at the platform margin. Flow across the zero horizontal flow boundary is vertical.

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10 -_. 0 PERCENT FROM SHI ...... 40 30 PERCENT DISTANCE FltOM SHORELINE 70 60 PERCENT DISTANCE FROM SHOREUN E ___ __ .;. _____ 0% ;-----=------:------:------=-----=-----:-----:---100 90 PERCENT DISTANCE FROM SHOREUNE

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25 ROMSHOREUNE 10 ---RELINE 20 50 80

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26 origin is drawn as a small circle. Each vector's length is the distance that ground water would flow in one year, and is drawn to the scale of the cross sections. Each vector is oriented parallel to the average direction of flow for the model cell in which it resides. Appendix c contains the magnitude of each vector. Throughout the modeled platform, velocities of inflowing seawater decrease with depth and remain nearly constant with depth in the lower half of the model. Across the platform, velocities of the outflowing freshwater/seawater mixture decrease rapidly with depth until the zero horizontal flow boundary is encountered. Each column of vectors in Figure 5 is an error function (Bear, 1972). Seawater flux at the constant-head boundaries is directed into the platform and flows downward until it crosses under the shoreline. Between these two locations, velocity increases from four feet per year to 600 feet per year. At the platform margin seawater flux is inflected upward into the platform. Seawater flux continues to travel upward into the platform from the margin until it crosses the zero horizontal flow boundary. Between these two locations, velocity decreases from 600 feet per year to two feet per year. The zero horizontal flow boundary is represented by the zone where velocities decrease sharply and the horizontal component of flow reverses. Velocities decrease sharply because the cross-sectional area of the flow increases.

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27 Ground-water flow across this horizontal boundary is vertical. Across the length of the platform, concentrations of the freshwater/seawater mixture along the zero horizonta l flow boundary are greater than 90 percent seawater. This is consistent with the location of the zero.horizontal flow boundary calculated by Bear (1972). Above this boundary, seawater mixes with freshwater as it travels outward and upward toward the platform margin. Between the zero horizontal flow boundary and the platform margin, velocity increases from 20 feet per year to 4000 feet per year. The extent and distribution of Mif+-flux in moles per square foot-year is calculated based on salinity and velocity. Figure 6 contains Mif+-flux vectors and relativesalinity contours. Appendix D contains the magnitude of each Mif+-flux vector. Appendix E contains an explanation for the method used to calculate these fluxes. For each vector, the origin is drawn as a small circle. The length of all Mg2+ vectors is assigned by an arbitrary scale for which a graphical scale is provided. Each vector is oriented parallel to the direction of ground-water flow for the model cell in which it resides. Throughout the platform, the inflowing (platformward) Mif+ flux remains nearly constant relative to depth below the mixing zone. The direction of Mif+ flux is the same as the direction of ground-water flow. The magnitude of the Mif+ flux is proportional to the magnitude of ground-water flow. In the mixing zone is an exception where mixing of

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Figure 6. Magnesium fluxes and relative salinity contours. The length of all vectors is assigned by an arbitrary scale for which a graphical scale is provided. Each vector is oriented parallel to the direction of the groundwater flow. Fluxes of Mg2+ vary from one mole per square footyear at the center of the platform to 600 moles per square foot-year. Flow across the zero horizontal flow boundary is vertical.

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-----:::-::----10 o I I /' / /" PERCENT DISTANCE FROM ----------30 PERCENT DISTANCE FROM SHORE:lll 70 60 PERCENT DISTANCE FROM SHORBJN 0% :-----:-----:-----:-----7-----:----:------:_____ ; _____ 100 90 PERCENT DISTANCE !=ROM SHOREUNE

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I / / / ;E FROM SHOREUNE Mg++ Flux (Moles/ft2/year) 0 500 Mg++ Flu x = 92 (Mole s/ft2/year 15 = I ----)HOREUNE 20 iOREIJNE 50 :UNE 80 29

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30 freshwater and seawater reduces the Mif+ flux. Within about 12,000 feet of the platform margin the Mif+ flux in the freshwater/seawater mixing zone increases rapidly with depth until a concentration of 50 percent seawater is encountered. Below the 50 percent isochlor, Mif+ flux decreases rapidly until the zero horizontal flow boundary is encountered. The concentration of seawater, where the maximum Mif+ flux occurs, decreases from 50 percent seawater at the platform margin to 30 percent seawater at 12,000 feet inland from the platform margin. The Mif+ flux increases from one mole per square footyear at the constant-head boundaries to 150 moles per square foot-year at the platform margin. Fluxes of Mif+ decrease from 200 moles per square foot-year at the platform margin to one mole per square foot-year along the zero horizontal flow boundary. The zero horizontal flow boundary is represented by the zone where Mif+ fluxes decrease sharply and the horizontal component of Mif+ f 1 ux reverses (Figure 6) Mif+ flux across this horizontal boundary is vertical. Above this boundary, seawater mixes with freshwater and ground-water flow is upward toward the platform margin. Although Mif+ concentration is reduced due to dilution, Mif+ flux increases toward the platform margin because fluid velocities increase toward the platform margin. Between these two locations, Mg2+ fluxes increase from one mole per square foot-year to 600 moles per square foot-year.

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31 The thickness of the mixing zone, or the vertical distance between water with relative salinity of 0.1 and 0.9, varies from 1000 feet at the center of the platform to several feet at the platform margin. Over the interval of the model where the bulk of the seawater influx occurs, the thickness of the mixing zone averages between 350 and 700 feet thick. The distribution of seawater flux is obtained by grouping the seawater fluxes in Figure 5 into ten discrete, two-dimensional streamtubes. Each streamtube has a seawater flux of 82,000 square feet per year or 10 percent of the total seawater flux. The ratio of total seawater flux to freshwater recharge (70,100 square feet per year) is approximately 12 to 1. Figure 7 contains streamtubes (dashed lines), contours of seawater age, and velocity vectors. Streamtubes follow the same paths in and out of the platform as velocity vectors. Because streamtubes represent zones of equal flux, their width varies inversely with velocity. A streamtube diagram is therefore, a convenient visual representation of the distribution of seawater velocity within carbonate platforms. Narrow streamtubes are areas of high velocities; wide tubes are areas of low velocities. Superimposed on the streamtube diagram are contours of seawater age (thick lines) Seawater entering along the constant-head seawater boundary is assumed to have zero age.

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Figure 7. Streamtubes, seawater age and velocity vectors. Each streamtube has a separate flux of 82,000 square feet per year or 10 percent of the total seawater flux (820,000 square feet per year)

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) z zcaza; ._.. ..... ; _____ 23 ;:ess;;_ ,d / .... "'/ --___.--r c.. _ ......._ r" .:.:.-.---____ 10 0 PERCENT DISTANCE FROM 30 PERCENT DISTANCE FllOM -=--=.. _;::: . -70 60 PERCENT DISTANCE FROM SHORI:UNE 100 90 PERCENT DISTANCE FROM SHOREUNE

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33 ,."" / ------:-------,!,.,"" -=--,.1'/ __ .... _::_. ---::-----;:;-----:-----::_, ___ ....::. ____ ..;::;_----------:-------..... -. .;;------:=----.=.----_;_ ____ ,:_ ____ .;; ___________ ;_ _____ :-----E FROM SHOREUNE 15 G .:= ----------____ ..:_ ____ =._ -------------------.------------....-------------------------------------------iOREUNE 20 =---: _____ ;_ __ -----------------RI;LJNE 50 I E eo

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34 As the seawater enters the platform it becomes progressively older as a function of distance. The age of the seawater increases slowly until the center of the platform is approached. Age slowly increases with depth throughout the platform. An exception to this general trend is located directly below the platform margin. It is a thin horizontal zone where age increases about 50 years and is an artifact of the model geometry. Seawater that is within 25,000 feet of the center of the platform is much older because the seawater velocity is very small near the center of the platform. At the platform margin concentrated flow results in seawater flows with short residence times. Figure 8 is a small-scale profile at the platform margin that shows velocity vectors and streamtubes with their respective residence times. The residence time of a streamtube represents the average length of time required for seawater to travel completely through that particular streamtube. For the ten streamtubes, residence time varies from 6 to 1199 years. The average residence time of the streamtubes is about 300 years. Ninety percent of the seawater flowing through the platform has a residence time of 1000 years or less (Figure 8).

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3 5 6 __ /,.., -///-. / ---?f (__ ----------------3S--__ --------------------20 ------STREAM TUBE AVERAGE RES IDENCE TIME 96 *=""--------1200 1000 200 o 1 k : :t: 6 7 :c 620 ...... Figure 8. Streamtube average residence times, streamtubes and velocity vectors near the seaward margi n T h e residence time of a streamtube represents the average lengt h of time required for seawater to travel completely through that particular streamtube. The average residence time o f the streamtubes is about 300 years.

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36 DISCUSSION A seawater-circulation system in a carbonate platform driven by a mixing-zone has been simulated using a set of boundary conditions aquifer parameters common in carbonate platforms. Model results suggest that a mixing-zone-induced seawater-circulation system could supply quantities of seawater to the interiors of emergent carbonate platforms capable of dolomitizing extensive layers of the platform. The ratio of seawater inflow to freshwater recharge is approximately 12 to 1. It is apparent from these results that the 1:1 ratio of seawater influx to freshwater recharge suggested by Vahrenkamp (1988) is conservative. The a verage age of ground water in the platform by volume is heavily weighted by older, slower-moving ground water that occupies a far greater portion of the platform. An accurate measure of ground water age is the average residence time of the streamtubes (about 300 years). This is the average age of water exiting the platform. Carbonate platforms in climates with low t o moderate annual rainfall could undergo seawater dolomitization because the amount of freshwater recharge required to maintain seawater flow is at least several times less than the volume of the resultant seawater flow. Figure 9 shows

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37 x'IO eo g 150 lz 40 w 0 a: 20 10 0 0 2IXIOO 30WO 40000 10000 10000 DISTANCE FROM CENTER OF PlAlFORM (FT) IW 150 0 PERCENT DISTANCE FROM SHOREUNE Figure 9. Distribution of seawater influx versus distance from the center of the platform. Influx values are calculated by summing the horizontal components of seawater flow. Fifty percent of the seawater influx is concentrated within the 20 percent of the platform adjacent to the platform margin. the distribution of seawater influx versus distance from the platform margin. Influx values are calculated by summing the horizontal component of seawater flux for model cells in a particular column. Because 50 percent of the seawater influx is concentrated within the 20 percent of the platform adjacent to the platform margin, greater quantities of dolomite might occur near the platform margin. Because 90 percent of the seawater flow has a residence time of 1000 years or less, a complete seawater-circulation system could develop if a similarly-sized carbonate platform became

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38 emergent for a few thousand years (Figure 7) Carbonate platforms could undergo dolomitization because of sea-level cycles on the order of several thousand years. Velocity vectors are small around the zero horizontal flow boundary because the area perpendicular to the flow direction (the platform length times 1) is much greater than the area where flow is horizontal (the platform height times 1). In addition, the model is anisotropic so that vertical hydraulic conductivity is smaller than horizontal hydraulic conductivity by a factor of ten. If the hypothesis that slow dolomitization rates result in more stoichiometric and highly ordered dolomite is correct, then, any dolomite that formed near the zero horizontal flow boundary should be stoichiometric and highly ordered because the velocity of seawater flow is very small near the zero horizontal flow boundary. If sea level or recharge were to vary over a period of 100 to 1000 years, thin horizontal beds of alternating ordered/disordered dolomite would result because the greatest Mif+ flux (Figure 6) is concentrated immediately above the mixing zone. Below these strata a thick dolomitized layer should occur with homogeneous or slightly shifting geochemistry. There remain several areas of the simulation that could be improved. A sensitivity analysis was not completed due to limited computer resources. The effects of non symmetrical variations in platform geometry and aquifer parameters were not analyzed.

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39 The calculated 1 to 12 ratio of freshwater recharge to seawater influx may not be conservative because the mixing zone is thick throughout most of the model. However, it is most likely that seawater fluxes are unaffected by thickness. Within 2000 feet of the platform margin the mixing-zone thickness is consistent with that reported by Kohout (1960) of about 100 feet. A thick mixing zone could be caused by dispersion due to coarse discretization of the finite-difference grid.

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40 CONCLUSIONS Mixing-zone-induced seawater-circulation systems can be simulated and may exist. This work adds several pieces of information that are critical to understanding the feasibility of mixing-zone-induced seawater dolomitization. The ratio of seawater flow to freshwater recharge is about 12 to 1. Seawater convection may be possible on carbonate platforms that have low amounts of freshwater recharge. Based on seawater travel time through the model, a lower estimate for the period of emergence required to establish extensive seawater convection in a generalized carbonate platform modeled might be between two and eight thousand years. Fifty percent of the seawater circulation is concentrated within 20 percent of the platform adjacent to the platform margin. As a result, dolomitization may be more intense near the margin. Ninety percent of the flow has a residence time of 1000 years or less. A short period of emergence would be required before the onset of seawater convection.

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41 LIST O F REFERENCES Aharon, P., R.A. Socki, L. Chan, 1987. Dolomitization of atolls by seawater convection flow: test of a hypothesis at Niue, South Pacific. Jour. Geol., v 95 no. 2, pp. 187-203. Badiozamani, K., 1973. The dorag dolomitization model--application to the middle Ordovician of Wisconsin. J. of Sed. Pet., v. 43, no. 4 pp. 965-868. Bear, J., 1972. Dynamics of fluids in porus media, American Elsevier, New York, N.Y., 764 pp. Carpenter, A.B., 1980. The chemistry of dolomite formation I: the stability of dolomite. In: Zenger, D.H., J.B. Dunham, and R.L. Ethington, eds. and models of dolomitization, SEPM, spec. pub. no. 8 pp. 111-121. Cowart, J.B., M.I. Kaufman, and J.K. Osmond, 1978. Uranium isotope variations in groundwaters of the Floridan aquifer and boulder zone of south Florida. J. Hydrology, v. 36 pp. 161-172. Fanning, K.A., R.H. Byrne, J.A. Breland II, P.R. Betzer, W.S. Moore, R.J. Elsinger, and T.E. Pyle, 1981. Geothermal springs of the west Florida continental shelf: evidence for dolomitization and radionuclide enrichment. Earth and Pla. Sci. Let., v 52, pp. 345-354. Folk, R.L. and L.S. Land, 1975. Mg/Ca ratio and salinity: two controls over crystallization of dolomite. AAPG, v. 59, no. 1, pp. 60-68. Freeze, R.A. and J.A. Cherry, 1979. Groundwater, PrenticeHall, New Jersey, 604 p. Friedman, G.H., 1980. Dolomite is an evaporite mineral, in: Zenger, D.H., Dunham, J.B. and Ethington, R.L., eds., Concepts and models of dolomitization, SEPM, spec. pub. No. 28 p.111-121. Garrels, R.M., and C.L. Christ, 1965. Solutions, minerals, and equilibria, Harper and Row, New York, 450 p.

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42 Hardie, L.A., 1987. Perspectives Dolomitization: a critical view of some current views. Jour. Sed. Pet., v. 57, no.l, pp. 166-183. Hardie, L.A., P.A. Dunn, and R.K. Goldhammer, 1971. Field and modelling studies of Cambrian carbonate cycles, Virginia Appalachians -Discussion. Jour. Sed. Pet., v 61, no. 4, pp.636-646. Hanshaw, B.B., W. Back, and R.G. Dieke, 1971 A geochemical hypothesis for dolomitization by ground-water. Econ. Geol., v. 66, pp. 710-723. Henry, H.R. and J.B. Hilleke, 1972. Expansion of multiphase fluid flow in saline aquifer system affected by geothermal heating. Univ. of Alab. Bur. Eng. Report, 118 p. Henry, H.R. and F.A. Kohout, 1972. Circulation pattern of saline ground-wateraffected by geothermal heating--as related to waste disposal. Symposium on underground waste management and environmental implications, AAPG Memoir 18, pp. 202-221. Humphrey, J.D., 1988. Late Pleistocene m1x1ng zone dolomitization, Southeastern Barbados, West Indies. Sedimentology, v. 35, pp. 327-348. Kinsman, D.J.J., 1966. Gypsum and anhydrite of recent age, Trucial Coast, Persian Gulf: in J.L. Rau, ed., Second symposium on salt, v.l, Northern Ohio Geol. Soc., p.302-326. Kohout, F.A., 1960. Cyclic flow of salt water in the Biscayne aquifer of southeastern Florida. Jour. Geophys. Research, v. 65, no. 7, pp. 2133-2141. Kohout, F.A., 1965. A hypothesis concerning cyclic flow of salt water related to geothermal heating in the Floridan Aquifer. New York Acad. of Sci. Trans., pp. 249-271. Kohout, F.A., 1967. Ground-water flow and the geothermal regime of the Floridan plateau. Trans. Gulf Coast Assoc. Geol. Soc., v. 17, pp. 339-354. Land, L.S., 1982. Dolomitization. AAPG short course notes No. 14, 20 p. Land, L.S., 1985. The or1g1n of massive dolomite. Jour. Geol. Ed., v 33, pp. 112.

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43 Machel, H.G., and E.W. Mountjoy, 1986. Chemistry and environments of dolomitization -a reappraisal. Earth Sci. Rev., v. 23, pp. 175-222. Morrow, D.W., 1978. The influence of the Mg/Ca ratio and salinity on dolomitization in evaporite basins. Petroleum Geol. Bull., v. 26, pp. 389-392. Morrow, D.W., 1982a. Diagenesis 1. Dolomite -part 1: the chemistry of dolomitization and dolomite precipitation. Geoscience Canada, v. 9, no. 1, pp. 5-13. Morrow, D.W., 1982b. Diagenesis 2. Dolomite -part 2: dolomitization models and ancient dolostones. Geoscience Canada, v. 9, no. 2, pp. 95-107. Saller, A.H., 1984. Petrologic and geochemical constraints on the origin of subsurface dolomite, Enewetak Atoll: An example of dolomitization by normal seawater. Geology, v. 12. pp. 217-220. Sanford, W.E. and L.F. Konikow, 1985. A two-constituent solute-transport model for ground-water having variable density. U.S. Geol. Survey, Water Res. Invest. 85-4279, 88 p. Simms, M., 1984. Dolomitization by ground-water-flow systems in carbonate platforms. Trans. Gulf Coast Assoc. Geol. Soc., v. 34. pp. 411-420. Stoessel!, R.K., W.C. Ward, B.H. Ford, and J.D. Schuffert, 1989. Water chemistry and CaC03 dissolution in the saline part of an open-flow mixing zone, coastal Yucatan Peninsula, Mexico. Geol. Soc. Am. Bull., 101(2) :159-169. Sverdrup, Johnson, and Fleming, 1942. The Oceans, Prentice Hall. Vahrenkamp, V.C, 1988. Constraints on the formation of platform dolomites: a geochemical study of LateTertiary dolomite from Little Bahama Bank, Bahamas. unpub. PhD dissertation, Univ. of Miami, Florida, Vahrenkamp, V.C., P.K Swart, and J. Ruiz, 1991. Episodic dolomitization of Late Cenozoic carbonates in the Bahamas: evidence from strontium isotopes. Jour. Sed. Pet., v. 61, no. 6, pp. 1002-1014.

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44 APPENDIXES

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45 APPENDIX A. C SOURCE CODE TO PLOT VECTORS Explanation: The horizontal and vertical components of velocity are identified as particular files on the hard drive. The dimensions of those files are read from the dimensioning file. Each set of horizontal and vertical velocities is read from the input files and scaled to convert feet per second to feet per year. The location of that vector relative to the lower-left corner of the model is calculated. At this point a small, solid circle is drawn and a line is plotted to the vector sum of the two velocity components using the same distance units as the model. The length of the vector is now unitless as its scale is identical to that of the model. /* *Preprocessor Directives Area *I #include #include #include #include J *Declaration Area *I char d imfilename(81), t Name of model and plot dimensions file t xvelofilename(81), t Name of x-component velocity file t zvelofilename(81), t Name of z-component velocity file t dxffilename(81), t Name of Data interchange (Autocad) fila t chemfilename(81),/" Name of solute concentration file t yesorno, t Y(es) or n(o) t dxf, t Plot to date exchange file? (Y or N) t cham, t Include 11 solute concentration file? (Y or N) t buffer1(81), t Buffer #1 for multiple assignments t buffer2(81); t Buffer #2 for multiple assignments t FILE "dimfileaddr, xvelofileaddr, zvelofileaddr, dxffileaddr, chemfileaddr; nt x1,z1,x2,z2, rofcpixals, scanband, scanlayer, currband, currlayer, grephdriver, graphmode, g_ errorcode, grOK, t File pointer to model and plot dimensions file t t File pointer to x-component velocity file t File pointer to z-component velocity file t File pointer to data interchange file t File pointer to solute concentration file t End points of vectors t Radius of circle in pixels ,. Band that file scanner (loop) is in t Layer that file scanner (loop) is in t Band that the current plot is in t Layer that the current plot is in t Graphics driver t Graphics video mode t Graphics error code t Graphics error condition OK ., ., ., ., ., ., ., ., ., ., ., ., ., .,

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APPENDIX A. CONTINUED numlayars, I" Number of plot layers ., plotnumbar, I" Number of the plot baing plotted ., xasp. zasp, J Aspect ratio values in the x and z directions ., numplots, I" Number of plots ., plotsparlayer; I" Number of plots in each layer ., long maxx, maxz, I" Largest pixel numbers on the x and z axes ., columns, rows, I" Number of columns and rows in model ., width, height, t Call dimensions ., columncountar, t Index counter for columns ., rowcountar; t Index counter for rows ., float xl f,x2f,z1 f,z2f, t Endpoints of vectors ., vlx,v2x, /" Verticias of polytinas in data interchange file ., xval, zval, J X-and z-componant velocities ., maxxfloat, J Largest pixel number on the x axis ., maxzfloat, I" Largest pixel number on the z axis ., zpixeldist, I" Haight of one pixel in modal's units ., xpixeldist, /" Length of one pixel in model's units ., xaspfloat, I Aoating value of xasp ., dansadist, I Distance between nodes along densest axis ., widthfloat, I* Column Width ., heightfloat, t Row Haight ., columnsfloat, J Total number of columns ., rowsfloat, I* Total number of rows ., concentration, J Concentration of solute throughout plot ., vactorscale. I" Velocity scaling & unit convers ion factor ., radiusofcircle. /* Radius of the circle at vectors origin coordinatescale. t Unit conversion factor for width & height ., zaspfloat t Aoating value of zasp ., zaxisvnum = 18; t Number of vectors plotted on z-axis ., double xaxisvnum; /" Number of vectors plotted on x-axis ., J Main Program Area *I main() { I" Get the names of the input files and open them t printf("Enter name of input fila that dimensions the model:\n"); gets(dimfilenamal; if ((dimfilaaddr = fopen(d i mfilename. "r")) = = NULL) { } printf("Error opening fila: %s\n", dimfilename); axit(O); printf("Entar name of fila with node-cantered x-direction velocities:\n") ; gats(xvelofilaname); if ((xvelofileaddr = fopen(xvelofilaname, "r")) = = NULL) { } printf("Error opening fila: %s\n", xvelofilaname); axit(O}; printf("Entar name of fila with node-centered z direction velocities : \n"); gata(zvalofilename) ; if ((zvelofileaddr = fopan(zvelofilename, "r")) = = NULL) { printf("Error opening file: %s\n", zvalofilename); axit(O); 46

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APPENDIX A. CONTINUED while(yesorno = 'y' && yesorno I= y && yesorno I= 'n' && yesorno I= 'N') { printWWould you like to plot to a .dxf file?\n"l; yesorno = getch(); } if (yesorno = = 'y' II yesorno = = 'Y') { printf("Enter name of drawing interchange file (include extension .dxf, in name):\n" ); gets(dxffilename); if ((dxffileaddr = fopen(dxffilename, "w")) = = NULL) { printf("Error opening file: %s\n", dxffilename); exit(O); dxf = 'Y'; yesorno = ; while(yesorno I= 'y' && yesorno I= 'Y' && yesorno I= 'n' && yesorno I= 'N') { printf("Would you like to scale vectors to a solute concentration file?\n"); yesorno = getch() ; if (yesorno = = 'y' II yesorno = = 'Y') { printf("Enter name of solute concentration file :\n"l; gets(chemfilename); if ((chemfileaddr = fopen(chemfilaname, "w")) = = NULL) ( printf("Error opening fila: %s\n", chemfilaname); exit(O) ; cham= 'Y'; yesorno = "; t Get the dimensions of the model and t determine axis of greatest density if (fscanf(dimfileaddr, "%0", &columns) = = EOF) ( printf("%s file Emptyl\n", dimfilenama); exit(O); } fscanf(dimfileaddr ,"%D%D%D%f%f%f", &rows, &width, &height, &vectorscale, &radiusofcircle, &coordinatascale); if (cham = 'Y') ( t New variables declared herel float chemscale =vectorscale,t Keeps track of vectorscale formulamass r Atomic mass of solute porosity; t Porosity of sediments fscanf(dimfileaddr "%f%f", &formulamass, &porosity; columnsfloat = columns; rowsfloat = rows; widthfloat = coordinatescala width; heightfloat = coordinatescale height; densedist = (widthfloat > heightfloat?heightfloat:widthfloat); if (dxf = = 'Y'l ( t Plot to data interchange file fprintf(dxffileaddr, 0\nSECTION\n 2\nENTITIES\n"l; 47

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APPENDIX A. CONTINUED for (rowcounter = 1; rowcounter < = rows; rowcounter + +) { for (columncounter = 1 ; columncounter < = columns; columncounter + +I fscanf(xvelofileaddr, "% 1 Oe , &xvel); fscanf(zvelofileaddr, "% 1 Oe , &zvel); x1f = (columncounter-.51 widthfloat; z1f = (rowcounter. 5) heightfloat; if (cham = 'Y'I { fscanf(chemfileaddr, "% 1 Oe , &concentration); vectorscale = porosity concentration molespermilligram x2f = x1f + vectorscale*xvel; z2f = z1f + vectorscale zvel; v1x = x1f-radiusofcircle/2; v2x = x1 f + radiusofcircle/2; fprintf(dxffileaddr, 0\nLINE\n 8\nO\n 10\n%g\n 20\n%g\n 11\n%g\n 21 \n%g\n" x1 f,z1 f ,x2f,z2f); 0\nPOLYLINE\n 8\nO\n 66\n 1 \n\ 70\n 1\n 48 fprintf(dxffileaddr, 40\n%g\ n 41 \n%g\n", radiusofcircle. radiusofcircle); fprintf(dxffileaddr, v1x, z1f); fprintf(dxffileaddr, v2x, z1fl; fpri ntf(dxffileadd r, 0\nVERTEX\n 8\nO \ n 1 O \n%g\n 20\n%g\n\ 42\n1 0 \n", 0\nVERTEX\n 8\nO\n 1 0\n%g\n 20\n%g\ n \ 42\n1.0\n", 0\nSEQEND\n 8\nO\n"l; fprintf(dxffileaddr, 0\nENDSEC \ n 0\nEOF\n"); rewind(xvelofileaddr); rewind(zvelofileaddr); yesorno = "; while(yesorno I= 'y' && yesorno I= 'Y' && yesorno I= 'n' && yesorno I= 'N' ) { printf("Would you like to plot to the screen7\n"l; yesorno = getch(); if (yesorno = = 'y' II yesorno = = 'Y'I { t Register BGI drivers as linked, detect */ t adapter, load driver, select best mode, and *I t return error message if needed. Last argument t t in initgraph() is directory name where BGI t t fil es reside. t if(registerbgidriver(EGAVGA_driver) < 0) { } printf("Error registering driver: EGAVGA\n") ; exit(1); if(registerfarbgidriver(Herc_driver_far) < 01 { } printf("Error registering driver: HERC\n"); exit(1); if(registerfarbgidriver(CGA_driver_far) < 0) { printf("Error registering driver: CGA\n"); exit(1);

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APPENDIX A. CONTINUED zaxisvnum); if(registerfarbgidriver(IBM8514 driver far) < 01 { --printf("Error registering driver: IBM851 4\n"); exit(1); if(registerfarbgidriver(PC3270 driver far) < 0) { --printf("Error registering driver : PC3270\n"); exit(1 ); if(registerfarbgidriver(ATT driver far) < 0) { --printf("Error registering driver : Amn"l; exit(1); graphdriver = DETECT; initgraph(&graphdriver, &graphmode, "C:\\TC"); g_errorcode = graphresultO; if (g_errorcode I= grOKI { printf("Graphics error: %s\n", grapherrormsg(g_errorcode)); exit(1); t Get aspect ratio and display on screen maxx = getmaxx(); maxz = getmaxy(); maxxfloat = maxx; maxzfloat = maxz; getaspectratio( &xasp, &zasp ); xaspfloat = (long)xasp; zaspfloat = (long)zasp ; sprintf(bufferl," Aspect ratio: xasp = %d, zasp = %d", xasp, zasp); outtextxy(1 0, 10, bufferl); sprintf(bufferl, "Monitor resolution = %1d pixels by %1d pixels", maxx + 1, maxz + 1 ); outtextxy(1 0, 20, bufferl ); sprintf (buffer1, "Total columns = %1d Total rows = %1d\ Width = %.3f Height = % .3f", columns, rows, widthfloat, heightfloat); outtextxy(10, 30, buffer1); sprintf (buffer1," Aspect = %If lnvaspect = %If", zaspfloat/xaspfloat, xaspfloat/zaspfloat); outtextxy(10, 40, buffer1); setfillstyle(1,WHITE); setcolor(WHITEI; setbkcolor(LIGHTBLUE); t Calculate the size and the t discretization scheme of plotting area zpixeldist = ((zaxisvnum1 I "heightfloat + (2 "densedist))f(maxzfloat + 1 ); xpixeldist = zpixeldist xaspfloat/zaspftoat; xaxisvnum = (int)floor((xpixeldist"(maxxftoat + 1 1-densedist 2)/(widthfloat)); plotsperlayer = (int)cail(columns/xaxisvnuml; numlayers = (int)ceil(rows/zaxisvnum); numplots = plotsperlayernumlayers; rofcpixels = radiusofcircle/zpixeldist; t Plot vectors sprintf(buffer1, "Press any key to draw a % .3f by % .3f grid of\ vectors. , xaxisvnum, sprintf(buffer2, "where each cell measures %.3f by %.3f:", widthfl oat, heightfloat); outtextxy(10, maxz20, bufferll; outtextxy(10, maxz10, buffer2); getchO; t Wait until a key is pressed t 49

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APPENDIX A. CONTINUED cleardevica(); plotnumbar = 1; while (plotnumber < = numplots) { currlayer = (int)floor(plotnumbar/plotsparlayer) + 1; currband = plotnumbar-(currlayer-1)"plotsparlayer; for (rowcounter = 1; rowcountar < = rows; rowcountar + +) { 50 for (columncountar = 1 ; columncounter < = columns; columncounter + + l { scanband = (inti ceil(columncounter/xaxisvnum); scanlayer = (int) ceil(rowcounter/zaxisvnum) ; fscanf(xvalofileaddr, % 1 Oa , &xvell; fscanf(zvalofilaaddr, % 1 Oa , &zvel); if ((scanband = = currband) && (scanlayer = = currlayerll { x1 = (columncountar(xaxisvnum (scanband-1 )))" widthfloat/ xpixeldist; z1 (rowcounter-(zaxisvnum (scanlayer-1 Ill" heightfloat/ closegraph(); rawind(xvalofilaaddr) ; rewind(zvalofileaddr); plotnumber + + ; zpixeldist ; x2 = x1 + vactorscala"xvel/ xpixeldist; z2 = z1 + vectorscala zvel/zpixeldist; lina(x1 ,z1, x2,z21; fillallipsa(x 1,z 1,rofcpixels,rofcpixelsl; outtextxy(maxx/2, maxz 10;prass any key for next ploe); gatch(); claardavice() ; J End of Program I

PAGE 64

APPENDIX B. MASS BALANCE OF SIMULATION CHEMICAL MASS BALANCE DENSITY-CONTROLLING SOLUTE MASS IN BOUNDARIES = 6.96545e+14 MASS OUT BOUNDARIES = -6.52996e+l4 MASS PUMPED IN = O.OOOOOe+OO MASS PUMPED OUT = O.OOOOOe+OO INFLOW MINUS OUTFLOW = 4.35485e+13 INITIAL MASS STORED = 6.08601e+14 PRESENT MASS STORED = 6.09122e+14 CHANGE MASS STORED = 5.21582e+ll COMPARE RESIDUAL WITH NET FLUX AND MASS ACCUMULATION: MASS-BALANCE RESIDUAL = 4.30269e+13 ERROR (AS PERCENT) = 6.17720e+OO 51 COMPARE INITIAL MASS STORED WITH CHANGE IN MASS STORED: ERROR (AS PERCENT) = 7.61469e+OO CUMULATIVE MASS BALANCE RECHARGE DISCHARGE CUMULATIVE NET RECHARGE WATER RELEASE FROM STORAGE LEAKAGE INTO AQUIFER LEAKAGE OUT OF AQUIFER CUMULATIVE NET LEAKAGE MASS-BALANCE RESIDUAL ERROR (AS PERCENT) (IN LB) = -3.49602e+ll = O.OOOOOe+OO = -3.49602e+ll = O.OOOOOe+OO = -1.27547e+12 = 1. 62496e+12 = 3.49484e+ll = -8633.2 = -0.53129e-06 RATE MASS BALANCE -(IN LB/SEC) LEAKAGE INTO AQUIFER = -1.64282e+02 LEAKAGE OUT OF AQUIFER = 2.08107e+02 NET LEAKAGE (QNET) = 4.38253e+Ol RECHARGE = -4.43128e+Ol DISCHARGE = O.OOOOOe+OO NET WITHDRAWAL (TPUM) = -4.43128e+Ol

PAGE 65

ROW NUMBER 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 COLUMN NUMBER 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 6 9 28 17 13 32 52 72 90 85 78 87 93 95 103 117 140 13 6 33 21 23 53 50 3 5 53 64 59 80 87 88 95 109 131 28 16 16 17 29 33 24 46 71 54 50 76 86 84 91 102 108 4 4 5 41 42 5 14 20 26 39 54 68 80 92 100 101 89 2 20 33 26 16 16 33 25 13 23 45 44 56 80 87 76 72 5 8 4 3 4 10 10 34 22 10 23 18 29 43 42 35 41 6 17 8 4 4 4 9 12 12 8 13 6 6 11 21 28 22 10 14 11 17 25 16 9 9 2 8 6 5 11 11 4 9 4 9 21 25 20 2 0 19 12 14 14 10 8 5 8 14 17 11 6 11 3 12 16 14 16 1 9 19 23 18 15 17 19 2 3 25 22 17 5 7 4 1 2 1 10 12 16 18 18 20 21 24 27 28 25 3 4 5 5 7 8 5 3 5 10 13 15 18 23 26 28 28 2 4 5 5 6 7 5 2 2 4 7 10 14 19 22 25 27 2 3 4 5 5 5 4 2 2 3 6 8 12 16 20 23 26 1 3 3 4 5 4 3 2 1 3 6 8 1 1 15 18 21 25 1 2 3 4 4 4 3 1 1 3 6 8 1 1 14 18 21 25 1 2 3 4 4 3 2 1 1 3 6 8 11 14 18 21 25 1 2 3 3 4 3 2 1 1 3 6 8 11 14 18 21 25 DISTANCE FROM SHORELINE (FEET) 84000 83000 82000 81000 80000 79000 78000 77000 76000 75000 74000 73000 72000 71000 70000 69000 68000 N 8 : Ea c h column is 1000 feet across, each row is 180 feet high t't:J t't:J trl z tj H X n ;3 n 1-3 0 ::0 z H 1-3 trl H z t'
PAGE 66

ROW NUMBER 1 2 3 4 6 6 7 8 9 10 11 12 13 14 15 16 11 18 VECTOR MAGNITUDE IFEETNEARI COLUMN NUMBER 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 161 177 183 185 197 216 220 220 242 236 248 310 342 345 361 348 386 145 161 162 161 176 200 198 189 221 200 208 288 336 322 320 320 301 117 133 164 188 181 153 149 168 171 162 185 254 285 289 292 273 270 94 101 114 129 114 123 163 173 141 165 191 189 188 208 230 223 244 83 85 65 53 64 109 134 123 121 159 172 123 102 114 115 142 146 41 43 47 56 72 69 59 68 72 92 101 71 56 67 61 88 90 10 8 9 22 33 32 32 44 51 52 45 25 25 42 47 72 76 5 7 5 8 10 9 3 13 31 42 41 19 7 1 1 10 13 7 8 1 5 8 4 1 5 9 11 17 13 12 31 45 40 50 67 15 16 15 15 10 8 8 9 17 28 46 65 67 70 79 80 75 24 25 23 22 22 23 30 38 46 58 66 68 70 73 78 79 75 29 31 30 29 33 41 49 56 56 60 66 67 70 73 76 77 76 29 33 35 37 43 53 55 56 57 61 64 67 71 72 74 76 76 29 32 37 43 50 54 55 57 58 61 64 67 70 72 74 75 75 28 32 38 46 51 54 55 57 60 61 64 67 69 71 73 74 75 28 33 39 46 51 53 55 57 60 61 64 67 69 71 73 74 75 29 33 39 46 50 53 55 57 60 62 63 67 68 70 73 74 75 29 33 39 45 50 53 55 57 60 62 63 67 68 70 72 74 75 DISTANCE FROM SHORELINE IFEETI 67000 66000 66000 64000 63000 62000 61000 60000 69000 58000 57000 56000 55000 54000 53000 62000 61000 N B.: Each column i s 1000 feet acrou, each row is 180 feet high. tU tzj s H :>< (') (') H tJ (.11 w

PAGE 67

ROW NUMBER 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 VECTOR MAGNITUDE (FEETIYEARI COLUMN NUMBER 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 61 410 382 382 382 396 438 484 480 477 515 523 554 621 638 603 645 691 342 398 393 364 390 438 431 432 421 453 516 523 526 558 554 572 638 314 323 316 340 364 361 360 372 382 386 411 403 393 424 471 488 498 253 208 203 253 242 224 249 266 293 282 249 264 291 292 332 344 337 128 142 142 140 139 145 148 169 192 188 192 206 201 181 198 192 159 59 66 85 96 99 95 82 88 116 119 123 132 119 104 105 94 64 45 50 64 65 61 64 40 11 11 5 5 7 7 7 7 18 2 2 5 3 2 8 14 21 25 43 62 70 75 83 88 96 102 109 120 69 65 63 67 72 87 87 73 77 83 88 93 99 104 109 113 116 75 73 72 74 78 85 86 80 81 86 89 95 99 104 108 110 112 75 74 74 76 79 83 84 82 83 86 91 95 99 102 106 108 109 75 75 75 78 80 83 84 84 85 88 91 95 98 101 105 106 107 76 76 77 78 79 81 84 84 86 88 91 95 98 101 103 105 106 76 76 77 78 80 81 84 85 86 88 92 95 97 100 103 104 105 76 76 77 79 80 82 83 85 87 89 91 94 96 100 102 102 104 76 76 77 79 80 82 83 85 87 89 91 94 96 100 101 102 103 76 76 77 79 80 82 83 85 87 89 91 94 96 100 101 102 103 76 76 77 79 80 82 83 85 87 89 91 94 96 100 101 102 103 DISTANCE FROM SHORELINE (FEETI 50000 49000 48000 47000 46000 45000 44000 43000 42000 41000 40000 39000 38000 37000 36000 35000 34000 N B .: Each column is 1000 feet across, eac h row is 180 feet high. I'd tzj z t:l H :>< () (1 0 z 1-'3 H t:l (J1 ,I:>.

PAGE 68

ROW NUMBER 1 2 3 4 6 6 7 8 9 10 11 12 13 14 16 16 17 18 VECTOR MAGNITUDE IFEETNEARI COLUMN NUMBER 52 53 54 55 56 57 68 69 60 61 62 63 64 65 66 67 68 673 649 680 733 796 852 880 912 919 929 1020 1076 1055 1059 1150 1266 1287 600 675 607 645 698 715 733 726 761 828 836 835 845 887 915 961 1038 499 519 508 487 509 537 554 640 572 614 610 665 686 617 693 696 656 365 376 340 306 306 335 350 361 368 338 356 366 371 342 349 354 316 171 180 189 192 176 159 163 176 173 163 150 173 178 143 129 92 42 66 68 57 59 35 11 6 10 9 16 32 32 17 32 72 124 142 24 33 48 58 73 92 102 100 104 113 130 133 129 120 116 136 145 106 85 82 86 95 107 113 113 116 122 131 134 132 127 125 135 140 108 95 92 93 100 108 113 115 118 123 129 131 131 128 128 134 137 106 99 96 99 102 108 1 12 115 118 122 127 129 130 129 130 133 135 106 101 99 101 104 108 112 115 118 122 126 128 129 129 130 133 135 105 102 101 103 105 108 113 115 118 122 126 127 129 129 131 133 134 104 103 103 103 106 109 113 115 119 121 124 126 128 129 131 132 134 104 104 104 105 107 110 112 115 119 121 124 126 127 129 130 13 2 134 105 104 104 106 108 110 112 115 119 121 123 126 127 1 29 130 132 134 105 104 105 107 1 0 8 1 10 1 13 1 16 118 120 123 126 127 128 13 0 132 133 104 104 106 107 108 1 10 113 115 118 120 123 125 127 128 130 132 133 104 105 101? 107 108 1 1 1 113 115 118 120 123 125 127 128 130 132 133 DISTANCE FROM SHORELINE IFEETI 33000 32000 31000 30000 29000 28000 27000 26000 25000 24000 23000 22000 20000 19000 18000 17000 N.B. : Each column Is 1000 feet across, each row Is 180 feet high 1-0 t:r:l z t:J H X () () 0 z t-,3 H t:J Ul Ul

PAGE 69

VECTOR MAGNITUDE IFEET/YEARI ROW COLUMN NUMBER NUMBER 69 70 71 72 73 74 75 76 77 78 79 1 1297 1364 1385 1350 1410 1504 1595 1718 1715 1827 2079 2 1052 1041 1084 1076 1115 1203 1217 1227 1238 1277 1368 3 677 659 663 712 709 702 698 635 666 675 561 4 291 289 262 291 270 201 188 155 154 134 35 5 7 18 17 10 31 64 91 100 92 123 144 6 115 114 118 117 127 139 145 132 124 136 150 7 131 127 129 129 134 141 144 138 134 142 154 8 134 131 132 133 136 141 143 140 140 147 156 9 135 133 134 134 137 141 142 143 145 150 159 10 135 134 135 136 139 141 144 145 148 153 161 11 135 134 135 137 139 142 145 147 150 155 161 12 135 136 137 139 140 142 145 147 152 157 163 13 135 136 136 139 141 143 146 149 153 158 163 14 135 136 136 139 141 144 146 150 154 159 163 15 135 136 137 140 141 144 147 151 155 159 164 16 135 136 138 140 142 145 148 151 155 159 164 17 135 136 138 140 142 145 148 151 155 160 164 18 135 136 138 140 142 145 148 151 155 160 164 DISTANCE FROM SHORELINE IFEETI 16000 15000 14000 13000 12000 11000 10000 9000 8000 7000 6000 N B.: Each column is 1000 feet across each row is 180 feet h i gh. 80 81 82 2346 2591 2914 1464 1498 1476 454 382 263 81 131 160 165 175 183 165 178 191 167 179 193 168 180 194 169 180 192 169 180 190 170 179 188 169 178 185 170 176 183 169 175 181 169 175 180 169 174 179 169 173 178 169 173 177 5000 4000 3000 83 84 3321 4174 1440 1099 129 160 193 272 211 272 216 261 215 248 212 234 208 223 201 214 197 205 193 198 189 193 186 189 184 185 182 183 181 181 180 181 2000 1000 85 2425 525 595 457 373 311 280 254 235 220 208 200 193 188 184 181 181 179 0 t"tj tz:l z t::l H :>< () () 0 z 1-3 H t::l (Jl 0\

PAGE 70

VECTOR MAGNITUDE IFEET!YEARI ROW COLUMN NUMBER NUMBER 86 87 88 89 90 91 92 93 94 95 96 97 98 1 188 90 55 40 29 22 17 13 10 7 5 3 4 2 928 282 139 90 64 49 38 29 23 17 12 6 8 3 654 320 175 1 12 78 59 45 36 29 23 18 4 12 4 485 310 195 130 93 70 55 45 36 31 28 38 21 5 388 288 201 143 106 82 65 54 45 39 35 38 22 6 325 264 201 151 1 16 91 75 62 53 46 42 39 21 7 280 243 196 155 124 100 83 70 60 53 47 39 18 8 251 226 190 157 129 107 90 77 67 59 53 37 17 9 232 212 185 156 132 1 12 96 83 73 66 62 70 42 10 217 201 179 156 134 1 1 6 100 88 79 72 67 67 35 11 204 192 174 155 136 119 105 93 83 77 71 65 32 12 196 185 170 153 137 121 108 96 88 81 75 61 28 13 189 180 167 152 137 124 1 1 1 100 91 85 83 92 53 14 184 176 164 151 137 124 113 102 94 87 85 88 46 15 181 173 162 150 137 125 1 14 104 96 89 86 83 41 16 177 171 160 149 137 126 1 15 105 98 92 86 77 37 17 175 168 160 149 137 127 1 16 106 99 93 86 71 32 18 174 168 158 149 137 127 116 107 99 93 90 99 57 DISTANCE FROM SHORELINE (FEET) -1000 -2000 -3000 -4000 -5000 -6000 -7000 -8000 -9000 -10000 -11000 -12000 -13000 N.B.: Each column Is 1000 feet across, each row is 180 feet high. r; '""'d t:<:l z t:1 H X 0 0 0 z t-3 H t:1 (J1 -....1

PAGE 71

t"'cJ t"'cJ tz:l z t:1 H :X: t:1 ROW COLUMN NUMBER NUMBER 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 2 1 0 2 1 1 2 2 2 2 3 3 4 4 4 4 5 6 3 3 2 1 2 3 3 2 4 6 5 5 7 8 8 8 9 10 4 1 1 1 6 6 1 2 3 4 6 8 10 12 14 15 15 14 5 0 4 7 5 3 3 7 5 3 5 9 9 11 16 18 16 15 C/l H 6 1 2 1 1 1 2 2 8 5 2 6 4 7 10 10 8 10 7 2 4 2 1 1 1 2 3 3 2 3 1 2 3 5 7 6 8 3 4 3 5 7 4 3 3 2 2 1 3 3 2 1 9 3 6 7 6 6 6 4 4 4 3 2 2 2 4 5 3 2 10 3 1 4 5 4 5 6 6 7 5 4 5 6 7 7 6 5 11 2 1 0 0 3 4 5 5 6 6 6 7 8 8 7 12 1 1 2 2 3 2 2 3 4 4 5 7 8 8 8 hj t"i 13 1 1 2 2 2 2 1 , 2 3 4 6 7 8 8 14 1 1 1 2 2 1 0 2 2 3 5 6 7 8 15 0 1 , 1 1 1 0 1 2 2 3 4 5 6 7 16 0 1 , 1 1 0 0 2 2 3 4 5 6 7 17 0 1 1 , 1 1 0 0 2 3 3 4 5 6 7 18 0 1 1 1 1 1 0 0 2 2 3 4 5 6 7 z H 1-3 c:: DISTANCE FROM SHORELINE (FEET) t:1 tz:l 84000 83000 82000 81000 80000 79000 78000 77000 76000 75000 74000 73000 72000 71000 70000 69000 68000 H N.B.: Eac h column is 1000 feet a c ross, each row is 180 f eet high z 0 t"i tz:l {I) .......... C/l 10 hj 1-3 .......... t-< (J1 CD

PAGE 72

ROW NUMBER 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 MAGNESIUM FLUX (MOLES/SQUARE FOOT /YEAR I COLUMN NUMBER 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 1 1 1 1 1 2 2 2 2 2 2 3 3 4 4 4 5 7 7 7 7 8 9 9 9 10 9 10 14 16 15 15 16 15 11 12 15 17 17 14 14 16 16 15 18 24 27 28 28 26 27 14 15 17 20 17 19 25 27 21 25 30 30 30 33 36 38 40 17 18 14 11 13 22 28 25 26 34 37 26 22 25 25 31 32 10 11 12 14 18 17 14 17 18 23 25 18 14 17 17 22 23 3 2 2 6 9 8 9 12 14 14 12 7 7 12 13 20 21 1 2 1 2 3 2 1 4 9 12 11 5 2 3 3 4 2 2 2 2 2 1 2 1 3 3 5 4 4 9 13 12 15 20 5 5 4 4 3 2 2 3 5 8 14 19 20 21 24 24 22 7 8 7 7 7 7 9 11 14 17 20 20 21 22 23 24 23 9 9 9 9 10 12 15 17 17 18 20 20 21 22 23 23 23 9 10 10 11 13 16 17 17 17 18 19 20 21 22 22 23 23 9 10 11 13 15 16 17 17 18 18 19 20 21 22 22 22 23 9 10 12 14 15 16 17 17 18 18 1 9 20 21 21 22 22 23 9 10 12 14 15 16 17 17 18 18 19 20 21 21 22 22 23 9 10 12 14 15 16 16 17 18 19 19 20 21 21 22 22 23 9 10 12 14 15 16 16 17 18 19 19 20 21 21 22 22 23 DISTANCE FROM SHORELINE (FEET) 67000 66000 65000 64000 63000 62000 61000 60000 59000 58000 57000 56000 55000 54000 53000 52000 51000 N B : Each column is 1000 feet across, each row is 180 feet high. tU tzj z t:J H X t:J (') 0 z H t:J (.Jl \0

PAGE 73

ROW NUMBER 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 MAGNESIUM FLUX (MOLES/SQUARE FOOTNEARI COLUMN NUMBER 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 60 51 5 5 5 5 5 6 7 7 7 8 8 9 11 11 11 12 13 17 20 20 19 20 23 22 22 22 24 27 28 29 32 32 35 37 32 34 33 36 38 39 37 40 41 42 45 44 44 47 56 60 59 42 34 33 41 40 37 42 47 51 50 44 47 54 54 60 66 65 27 31 31 31 31 33 34 38 43 42 44 48 47 42 47 45 37 15 17 22 25 25 24 21 23 30 31 32 35 32 27 28 25 17 12 13 17 17 17 17 11 3 3 1 1 2 2 2 2 5 6 1 1 1 2 4 6 7 13 19 21 22 25 26 29 31 33 36 21 20 19 20 22 26 26 22 23 25 26 28 30 31 33 34 35 22 22 22 22 23 26 26 24 24 26 27 28 30 31 32 33 34 23 22 22 23 24 25 25 25 25 26 27 28 30 31 32 33 33 23 23 23 23 24 25 25 25 26 26 27 28 30 30 31 32 32 23 23 23 23 24 24 25 25 26 27 27 28 29 30 31 32 32 23 23 23 24 24 24 25 25 26 26 28 28 29 30 31 31 32 23 23 23 24 24 25 25 26 26 27 27 28 29 30 31 31 31 23 23 23 24 24 25 25 26 26 27 27 28 29 30 30 31 31 23 23 23 24 24 25 25 26 26 27 27 28 29 30 30 31 31 23 23 23 24 24 25 25 26 26 27 27 28 29 30 30 31 31 DISTANCE FROM SHORELINE (FEET) 50000 49000 48000 47000 46000 45000 44000 43000 42000 41000 40000 39000 38000 37000 36000 35000 34000 N.B.: Each column is 1000 feet across, each row is 180 feet high. 1"0 1"0 t<:l z 0 H :><: 0 () 0 z 8 H t<:l 0 0"1 0

PAGE 74

ROW NUMB E R 1 2 3 4 5 6 7 8 9 1 0 11 12 1 3 1 4 1 5 1 6 1 7 18 MAGNESIUM FLUX ( MOLES / SQUARE FOOT/YEARI COLUMN NUMBER 5 2 53 54 5 5 56 5 7 58 5 9 60 61 6 2 6 3 6 4 6 5 66 67 68 1 3 13 1 4 17 1 9 21 23 26 28 30 33 36 39 40 43 50 5 3 34 3 4 39 46 48 50 53 5 2 56 63 66 72 75 7 6 82 92 103 62 66 65 62 69 71 76 77 83 92 92 85 91 102 1 0 1 100 114 70 74 6 7 61 61 68 70 7 3 77 7 1 77 82 83 78 8 1 84 75 41 44 46 47 43 39 4 1 45 44 42 39 45 47 38 35 25 1 2 18 1 8 1 5 16 10 3 2 3 2 5 9 9 5 9 21 3 7 42 7 10 14 1 7 22 27 3 1 3 0 31 34 39 40 39 36 35 4 1 44 32 25 25 26 29 32 34 34 35 37 40 40 40 38 38 41 42 32 28 28 28 30 33 34 3 4 35 37 39 39 39 39 39 40 4 1 32 30 29 30 31 32 34 34 36 37 38 39 39 39 39 40 40 32 30 30 30 31 3 3 34 35 36 37 38 38 39 39 39 40 40 32 31 30 31 3 2 33 34 35 36 37 37 38 39 39 39 40 40 31 31 3 1 31 32 33 34 35 3 6 36 37 38 38 39 39 40 40 31 3 1 3 1 32 32 33 34 35 36 36 3 7 38 38 39 39 40 40 32 31 3 1 32 32 33 34 35 36 3 6 37 38 3 8 39 39 40 40 32 31 32 32 33 33 34 35 3 5 36 37 38 3 8 39 39 4 0 40 31 3 1 32 32 33 33 34 35 35 36 3 7 38 38 39 39 40 40 31 32 32 32 3 3 33 34 35 35 36 37 38 3 8 39 39 40 40 DISTANCE FROM SHORELINE (FEETI 3 3000 3 2000 31000 3000 0 29000 2800 0 27000 260 0 0 25000 24000 2300 0 22000 21000 20000 19000 1 8000 17000 N B : Each colum n i s 1 0 0 0 feet across, each row is 180 feet high "'d tx:l z t:l H :><: t:l () 0 z 1-3 H a t
PAGE 75

MAGNESIUM FLUX IMOLES/SQUARE FOOTJYEARI ROW COLUMN NUMBER NUMBER 69 70 71 72 73 74 75 76 77 78 79 80 1 56 62 67 70 86 90 100 115 134 142 167 250 2 115 110 124 129 144 145 166 172 166 197 244 290 3 119 121 129 138 144 148 153 142 155 163 142 119 4 71 72 66 75 69 54 51 42 43 39 10 24 5 2 5 5 3 9 19 27 30 28 37 43 50 6 35 34 35 35 38 42 43 40 37 41 45 50 7 40 38 39 39 40 43 43 41 40 43 46 50 8 40 39 40 40 41 42 43 42 42 44 47 51 9 40 40 40 40 41 42 43 43 43 45 48 51 10 40 40 40 41 42 42 43 43 44 46 48 51 11 40 40 41 41 42 43 43 44 45 47 49 51 12 40 41 41 42 42 43 44 44 46 47 49 51 13 40 41 41 42 42 43 44 45 46 47 49 51 14 40 41 41 42 42 43 44 45 46 48 49 51 15 40 41 41 42 42 43 44 45 47 48 49 51 16 41 41 41 42 43 44 44 45 47 48 49 51 17 41 41 42 42 43 44 44 45 47 48 49 51 18 41 41 42 42 43 44 44 46 47 48 49 51 DISTANCE FROM SHORELINE IFEETl 16000 15000 14000 13000 12000 11000 10000 9000 8000 7000 6000 5000 N B.: Each column is 1000 feet across, each row is 180 feet high. 81 82 83 269 293 474 281 313 359 107 76 38 39 48 58 53 55 63 53 57 65 54 58 65 54 58 64 54 58 62 54 57 61 54 56 59 53 56 58 53 55 57 53 54 56 53 54 55 52 54 55 52 53 54 52 53 54 4000 3000 2000 84 620 304 48 82 82 78 75 71 67 64 62 60 58 57 56 55 55 54 1000 85 533 155 179 137 112 94 84 76 71 66 63 60 58 57 55 54 54 54 0 'i:l tr:l z t:1 H :X: t::1 0 0 z 1-3 H a t:<:! t::1 0'1 N

PAGE 76

ROW NUMBER 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 MAGNESIUM FLUX (MOLES/SQUARE FOOT/YEAR) COLUMN NUMBER 86 87 88 89 90 91 92 93 94 95 96 97 98 56 27 17 12 9 7 5 4 3 2 1 1 1 279 85 42 27 19 15 11 9 7 5 4 2 3 197 96 53 34 23 18 14 11 9 7 5 1 4 146 93 59 39 28 21 17 13 11 9 9 11 8 117 87 61 43 32 25 20 16 13 12 11 11 7 98 79 60 45 35 27 23 19 16 14 12 12 6 84 73 59 47 37 30 25 21 18 16 14 12 6 76 68 57 47 39 32 27 2 3 20 18 16 11 5 70 64 55 47 40 34 29 25 22 20 19 21 13 65 60 54 47 40 35 30 26 24 22 20 20 11 61 58 52 47 41 36 32 28 25 23 21 20 10 59 56 51 46 41 36 3 2 29 26 24 23 18 8 57 54 50 46 41 37 33 30 27 26 25 28 16 55 53 49 45 41 37 34 31 28 26 26 26 14 54 52 49 45 41 37 34 31 29 27 26 25 12 53 51 48 45 41 38 34 32 29 28 26 23 11 53 50 48 45 41 38 35 32 30 28 26 21 10 52 50 48 45 41 38 35 32 30 28 27 30 17 DISTANCE FROM SHORELINE (FEET) -1000 -2000 -3000 -4000 -5000 -6000 -7000 -8000 -9000 -10000 -1 1000 -12000 -13000 N B .: Each column is 1000 feet across, each row is 180 feet high. t-el (%:1 z t1 H X t1 n 0 z t-3 H t1 0"\ w

PAGE 77

APPENDIX E. CALCULATION OF MAGNESIUM FLUX (assumes that freshwater recharge contains no magnesium) Definitions : v = velocity in meters per year (m/yr) 1 cubic meter (m 3 ) = 1 000 Liters (L) TDS = Total Dissolved Solids in milligrams per Liter (mg /L) n = poros ity atomic weight of magnesium (Mg + + ) = 24.3 = 24,300 mg Mg + + p er mole TDS in normal seawater = 35,000 mg / L Mg + + co n centration in normal seawater = 1 290 mg / L Example : TDS = 11 ,200 mg / L (m ixi ng zone) v = 300 m /yr n = 0.20 % seawater = 11 ,200 35,000 0.32 (32 percent seawater) Mg + + concen tration in mixing zone = 1290 mg / L 0.32 = 413 mg / L specific dis c harge (Darcy v e locity) = q = vn = 300 m/yr 0.20 = 60 m/yr di sc harge = Q = 60 m 3 / m 2/yr Q = 60 m3f m2 /yr 1000 L/1 m 3 = 60,000 L/m 2 /yr Mg + + Flu x = QMg + + = 413 mg / L 60,000 L/m 2/yr = 24,800,000 mg / m 2 /yr Q 24,800,000 mg / m 2 /yr = 1 ,020 moles / m 2 /yr Mg + + = =.c-24,300 mg / mole 64


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