Determining Pressure Recovery Time for Non-Steady-State Spherical Flow of Viscoplastic Oil in a Homogeneous Formation

Abstract

The paper solves a non-steady-state hydrodynamic problem concerning a spherical flow of viscoplastic oil in a homogeneous formation. Pressure recovery in the formation occurs in two stages after well operation stops instantaneously. At the first stage the perturbation region appears at the well, expands and eventually reaches the external boundary, and keeps expanding during the second stage until steady-state pressure is reached in every formation region. We solved the differential equations for specific initial and boundary conditions, assuming pressure distribution laws over the formation and respective integral relations, and derived equations to determine pressure recovery time. At each stage pressure in the formation is a function of two variables, that is, a spatial coordinate and time. We assume that the first variable equals zero. We derived an expression for recovering the bottomhole pressure in the wellbore. We used the transient flow method to study the wells, plotted the pressure recovery curve (PRC) and determined formation parameters.