Transient pressure solution in the presence of pressure drop in the wellbore

摘要

Horizontal qand multi-lateral wells are increasingly used in reservoir engineering to improve the oil recovery. To optimise the effeciency of these wells, it is necessary to develop semianalytical methods which are simple, fast and accurate, to study the transient pressure behavior. Moreover, the pressure drop in the wellbore, which has sometimes a strong impact on the pressure transient behavior, has to be incorporated in the modelling. In this paper, the boundary integral equation, based on single layer heat potential, is used at the wellbore boundary to describe the transient phenomena. The pressure drop along the well length is considered. The Galerkin type approach is used to solve the boundary integral equation. Using linear Galerkin approach allows to give good approximation for the extemity effect, especially in the presence of the pressure drop in the wellbore. The pressure drop along the well length can be quickly and accurately evaluated using the linear Galerkin approach then using the commonly used line source method. The implicit Newton's technique is discussed to solve the nonlinear flow equation in the wellbore. The proposed method can be used to study the pressure solution for any number of multilateral wells, as well as selectively perforated wells.