Combined Effects of Shut-in and Production: Solution with a New Inner Boundary Condition

Abstract

ABSTRACT A new approach was used to solve the the problem of pressure buildup following constant bottom hole pressure production. Previous methods of solution involve finite difference solution or numerical evaluation of the superposition integral. An analytical solution correct for both the flowing and shut-in periods was obtained by solving the diffusivity equation with a single inner boundary condition which included the mixed conditions for flow and buildup. Both a skin effect and wellbore storage were included even though the production period was at constant wellbore pressure. Solution was obtained by Laplace transformation. The procedure presented in this paper may be used to solve other interesting problems. One example presented is the joint solution of constant rate production and shut-in with wellbore storage and skin effect. The procedure used does not involve superposition.