| Summary: | 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. === Graduation date: 1981
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