An Approximate Solution for the Potential Flow of a Pore Fluid Into a Slotted Cylinder

Abstract

Conformal mapping may be used to approximate the two-dimensional pore pressure distribution around a cylinder with a single longitudinal slot. A nonsymmetric flow field can significantly affect the stress distribution around a slotted casing. In order to investigate analytically the importance of such asymmetry on incipient rock yielding and casing collapse in producing wells, an approximate solution is obtained for the pore pressure distribution in the extreme case of a cylinder with a single slot. The derived solution does not employ the Schwartz-Christoffel transformation used in previous work. Hence the resulting expression gives the pore pressure as an explicit function of position. Comparison with the exact solution for typical reservoir radius to casing radius ratios gives predicted flow rates correct to within one percent.