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Show Chapter 2 Model for Stratified Aquifer Systems Ground water management modeling generally requires a combination of simulation and management models. The simulation model provides details on aquifer behavior; the management model combines operational and economic considerations to provide an ' optimal' water use plan. Management models, to date, have mostly been concerned with aquifers under purely confined or purely water table conditions. Consideration of stratified aquifer systems in ground water management models has been avoided due to their complex, nonlinear nature. Incorporation of flow equations for confined aquifer systems into management models can be accomplished by use of the principle of linear superposition. The drawdown response of an aquifer to pumping is described by equations which utilize this principle. These equations are then inserted into management models as constraint equations limiting hydraulic head drawdown in the aquifer. An expression of aquifer response to stress in a stratified system, linear on some variable, would allow the principle of linear superposition to be applied in the stratified case. Development of management models for ground water systems of greater complexity follows. For many cases, these models would provide a more realistic picture on which to base operating policies. Development of ground water flow equations leading to a linear description of stratified aquifer response is reviewed. A general formulation of water supply and dewatering management is presented utilizing linear superposition in developing the constraint set for a stratified aquifer system. The management objective of these models is to provide least cost designs; water demands and acceptable drawdowns are considered for water supply, maintenance of hydraulic heads below specified levels is dewatering. Example applications of the dewatering model are included for three objectives aimed at minimizing the cost of the well system. Solution techniques, details of the site, and resulting solutions for the three objectives are provided. Solutions include pump arrangement, pumping levels and drawdown levels at points of concern. 2.1 Stratified Aquifer Flow Equations A linear relationship between pumping and aquifer response enables the development of response matrices. A measure of aquifer response for a stratified aquifer system which meets this criterion is the Girinski potential ( Halek and Svec, 1979). Yeh ( 1982) mathematically completes an analogy between velocity potential for a homogeneous, confined aquifer system and Girinski potential for a complex, homogeneously stratified, unconfined aquifer system Yeh's analysis results in the Girinski potential expressed as a quadratic function of hydraulic head. A simulation model is developed to describe the response of an aquifer system subjected to dewatering measures in terms of the Girinski potential. The general partial differential equation, representing transient flow in an anisotropic non- homogeneous aquifer system, follows from the principle of continuity, and is stated as: V. Kh V h + Q. 8(( x - x*)( y - y*)). R( x, y) = S -^- ( 2- 1) y at where: K is a hydraulic conductivity vector. 11 |