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' APPENDIX D <br /> DARCY FLOW MODEL <br /> 1 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 /> to estimate the soil parameters. <br /> DARCY FLOW MODEL CONDITIONS <br />' Steady-state conditions prevail, after a transient period, for a well extracting a drama a area <br /> (cell) with a completely open outer boundary. The steady-state conditions assume that air <br /> extracted from the soil wiII 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 />' GOVEMNING EQUATIONS FOR THE DARCY <br /> FLOW MODEL <br /> The general form of the compressible-flow radial diffusivity equation is- <br /> 1 S (PrSp) = IS (P) (1) <br />' r ar uz Sr k at z <br /> where p = pressure <br /> r = radius <br /> = porosity <br />' k = permeability <br /> U = 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 /> 5 = 0 for all r and t (z = I) <br />' at <br />' The general form of Darcy's law for radial flow is: <br /> q = k 2nrh dR (Z) <br /> µ dr <br />' r D-1 <br />