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r <br /> APPENDIX D <br /> DARCY FLOW MODEL <br /> This appendix includes a description of the Darcy flow model The steady-state form of Darcy's <br /> equation as applied to radial flow conditions is used to model air flow through the subsurface and <br /> Y to estimate the soil parameters. <br /> DARCY FLOW MODEL CONDITIONS <br /> Steady-state conditions prevail, after a transient period, for a well extracting a drainage area <br /> a (cell) with a completely open outer boundary The steady-state conditions assume that wr <br /> extracted from the soil will be exactly balanced by air entering the soil at the outer boundary <br /> In the Darcy model, the radius of influence is defined as the outer radius of the drainage area <br /> at which point the pressure is always equal to the initial (atmospheric) pressure once steady-state <br /> flow conditions prevail. <br /> GOVERNING EQUATIONS FOR THE DARCY FLOW MODEL <br /> The general form of the compressible-flow radial diffusivity equation is. <br /> 1 S (p— r Spy = � L(p) (1} <br /> r Sr pz Sr k at z <br /> where p = pressure <br /> r = radius <br /> = porosity <br /> k = permeability <br /> Ju = viscosity <br /> z = gas compressibility factor (z=1 for ideal gas flow) <br /> For steady state, the following boundary conditions apply <br /> p = p. = pressure at r = r, (outer boundary) <br /> b = 0 for all rand t (z = 1) <br /> at <br />. The general form of Darcy's law for radial flow is: <br /> q k 27rrh dp (2) <br /> p dr <br /> + D-1 III <br />