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<br />('t) _ <br />~ <br />C\l . <br />C\l <br />c.::' <br />a <br /> <br />, . <br /> <br />The governing equations describing fluxes of fluid and solute mass are solved using standard finite- <br />element approximations, Other non-flux tenns are approximated with a finite-element grid using integrated <br />finite-difference methods. Voss (1984, p, 95-129) gives a comprehensive explanation of the numerical <br />technique used to solve the governing equations. <br /> <br />Now thaI the mechanisms and processes of flow and transport used by the numerical program have <br />been defined, the three conceptual and mathematical models can be developed with a clearer understanding <br />of the information necessary to represent actual processes in the study area, Metric units have been used <br />in developing the mathematical model because chemical quantities used in the model are in metric uni~, <br />All model output has been converted to inch-pound units for discussion, illustrations, ~9' tables so that <br />consistency is maintained with earlier sections of this report. <br /> <br />Planimetric Model of Ground-Water Flow <br /> <br />The main purpose of developing a generalized conceptual planimetric flow model was to detennine <br />whether the hydraulic heads within the detention basin would be significantly altered by the presence of the <br />slurry wall, resulting in a diversion of flow around the detention basin. The success of the detention basin <br />requires uninhibited inflow; if flow is diverted around the basin. then the potential for salt reduction <br />diminishes. <br /> <br />The generalized conceptual model used to examine the effectiveness of the slurry wall assumes a <br />uniform aquifer thickness throughout the Whitney area. The areal extent of the model was selected to <br />minimize the model's influence on the direction or magnitude of flow or the altitude of water levels in the <br />vicinity of the detention basin. Upgradient ground-water inflow to the area of the detention basin was <br />assumed to be constant. Surface-water inflow to the area was assumed to be insignificant for this particular <br />conceptualization of the system. The average horizontal hydraulic conductivity was estimated to be about <br />30 ftId for the entire area, on the basis of slug-test analyses. A "U"-shaped detention basin (open end of <br />U facing upgradient) representing the proposed impermeable dike and slurry wall, similar in size to the <br />actual 0-14 detention basin, was incorporated into the conceptual model. The detention basin was designed <br />to release water only by topping the dike, which was assumed to extend 6 ft above the adjacent land <br />surface, on the downgradient side. and to taper to only 1 ft above land surface at its farthest upgradient <br />extent; no outlet Structures were incorporated in the conceptual model of the detention basin, <br /> <br />Constructing the Mathematical Model <br /> <br />For these simulations. the governing equation (eqn. 3) for the planimetric model is simplified because <br />only steady-state ground-water flow is considered; thus, all terms involving solute concentration can be <br />ignored, A finite-element grid, consisting of 20 rowS and 40 columns of elements connected by 861 nodes, <br />was used in the mathematical model to conceptualize ground-water flow in the Whitney area (fig. l2A). <br />The elements of the planimetric grid differ in areal dimension, but have a constant thickness of 30 fl. Three <br />bands of elements, each 1 ft wide, were used to represent the dike and slurry wall, the permeability of <br />which was varied to analyze its effect on flow fields. A constant-head boundary was specified along the <br />bottom row of nodes in the model grid to approximately represent Las Vegas Wash; that is. the water-table <br />altitude (relative to an arbitrary datum) was specified to be constant at this boundary, TIlls constant altitude <br />allows the fluid-mass flux to vary across the boundary in the simulation, The nodes along the top row of <br />the grid were specified as a constant-flux boundary representing the assumed constant ground-water flow <br />into the study area, Specifically, a constant rate of 1.0 ft3/s was assigned for total ground-water inflow to <br />this top row of nodes, and it is proportionately divided between each element on the basis of its width, <br /> <br />-29- <br />