Closed-form solution for determination of pore pressure field around horizontal wellbore

Wellbores are usually located in saturated geological layers. The determination of pore water pressure field around the wellbore is necessary during the design calculation and drilling stages. This paper presents analytical approach to determine the pore water pressure field around a horizontal wellbore at deep geological layer that exhibits heterogeneous, isotropic or transversely isotropic behavior. Thus, the wellbore is considered to be in an infinite medium. The pore water pressure at the well wall, equal to the drilling mud pressure, together with the pore water pressure at infinity is assumed to be constant. The closed-form solutions are based on the theory of fluid transport in porous medium and the conformal mapping technique of the complex variable method. The closed-form solutions are established with the condition of transient fluid flow for the case of isotropic medium and with the condition of steady state fluid flow for the case of transversely isotropic medium. The accuracy of the closed-form solutions is validated by numerical solutions based on the finite element method. The obtained solutions can be used as tools to determine quickly and accurately the pore pressure field around the horizontal wellbore, which serves to evaluate the stability of the well wall in preliminary design of the wellbore, as well as the amount of water inflow into it. Furthermore, the closed-form solutions are also considered as reference solutions to evaluate the accuracy and reliability of numerical models.