Graduate Thesis Or Dissertation
 

Iterative techniques in linearized free surface flow

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  • The displacement of the free liquid surface in geothermal and hydrologic reservoirs is an important capacitance factor. An iterative approach to determining the drawdown of the free liquid surface for a single sink region in a homogeneous, isotropic, Darcy-type porous mediums is discussed. The iterative approach involves a stepwise adjustment of the pressure on the reference surface which replaces the time-dependent free surface condition by a fixed plane Dirichlet type condition so that readily available, standard techniques can be applied. Grouping of producing wells into a single analogous well may be used to treat multiple well cases with the iterative approach. An analytic solution for the infinite half space situation is used to compare solutions with the iterative technique. The analytic solution is derived for a point sink within an infinite, homogeneous, isotropic, Darcy-type porous half space. It is obtained by linearizing the free liquid boundary condition provided that the free surface deviates from its equilibrium reference position by only a small slowly undulating displacement h. The flow pressure at the equilibrium surface is then approximated by the hydrostatic pressure for a column of height h. A standard model is designed to be analogous to the analytic solution. Testing the iterative-procedure calculations for this model against the derived analytic solution produces very satisfactory results provided that the numerical grid spacing is adequately chosen for the problem. Calculations of the linear and quadratic terms of the free surface condition indicate that the neglected quadratic terms are in general small, and the approximation is reasonable.
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