Pressure Transient Solutions for Vertically Slotted-Partially Penetrated Vertical Wells in Porous Media

Abstract

In this paper, we present semi-analytical pressure transient solutions for vertically slotted-limited entry or partially penetrated vertical wells. These solutions are needed for interpretation of the pressure transient tests conducted with the Wireline Formation Testing vertically slotted-packer configuration, and in wells with vertically slotted-liner completions. These slots have limited size openings and are vertically placed on a non-permeable cylindrical wellbore in a porous medium. The fluid from the formation is produced through these slots into the wellbore. Pressure transient solutions are not readily available for the uniform pressure boundary condition on the surface of the slots because such a condition creates a mixed boundary value problem, which is difficult to solve. Here we present exact pressure transient solutions obtained under the assumption that the pressure on the slot surface is uniform but a priori unknown, and the rest of the wellbore surface is non-permeable (no-flow condition). Furthermore, we generalize our solution for the case of multiple slots (open sections) on the wellbore for both well testing and Wireline formation tester packer modules. Our solutions are compared with the existing solutions. A new formula for obtaining the drawdown horizontal mobility is presented for anisotropic media.