Compute the draw down coefficient (32.11)

in a simple model where the geothermal reservoir is a large cylindrical volume with height h much smaller than the radius r (see Figure 32.17)

Assume that the pressure is constant at p_w in a small cylinder of the radius of the wellbore r_w, and that flow is radial and vertically uniform outside that volume. Show that

Use conservation of mass to show that |u| ∝ 1/r, and note that ∇f (r) = r̂ f ′(r). 

= CDm Pr Pr - Pw wellhead wellbore caprock radial flow reservoir Pur Pr