Multiphase Linear Flow in Tight Oil Reservoirs

Abstract

Summary The main objective of this work is to gain a general understanding of the performance of tight oil reservoirs during transient linear two-phase flow producing at constant flowing pressure. To achieve this, we provide a theoretical basis to explain the effect of different parameters on the behavior of solution-gas-drive unconventional reservoirs. It is shown that, with the Boltzmann transformation, the highly nonlinear partial-differential equations (PDEs) governing two-phase flow through porous media can be converted to two nonlinear ordinary-differential equations (ODEs). The resulting ODEs simplify the calculation of the reservoir performance and avoid the tedious calculation inherent in solving the original PDEs. Thus, the proposed model facilitates sensitivity studies and rapid evaluation of different hypotheses. Moreover, successful conversion of the highly nonlinear PDEs (in terms of distance and time) to the ODEs (in terms of the Boltzmann variable) implies that the saturation and pressure are unique functions of the Boltzmann variable, and as a result, saturation is a unique function of pressure. This transformation enables us to explain (a) the constant gas/oil ratio (GOR) that has been observed in some hydraulically fractured tight oil reservoirs and (b) the straight-line plot of 1/qo and 1/qg vs. t during constant-pressure two-phase production. An approximate analytical model is also developed. It is shown that the proposed approximate solution can be converted to a form similar to the well-known equations for single-phase flow, which enhances our understanding of two-phase-flow behavior. Extensive sensitivity studies are performed to examine the utility of the proposed model in predicting the performance of tight oil reservoirs. The applicability of the conclusions to the boundary-dominated flow period is investigated. On the basis of numerous simulation studies, it is shown that the impact of various parameters on boundary-dominated flow can be predicted with the transient solution, without the need for running multiple numerical simulations.