Early-Time 1D Analysis of Shale-Oil and -Gas Flow

Abstract

Summary We present a new semianalytic method to solve the nonlinear pressure-diffusion equation at early time, before reservoir boundaries are encountered, and under constant bottomhole pressure (BHP), applicable to the analysis of unconventional reservoirs. We assume that the flow rate is inversely proportional to the square root of time since the beginning of production. The method is an extension of the semianalytic solution proposed by Schmid et al. (2011) for spontaneous imbibition; we replace the solution for saturation with one for pressure, while extending the functional form of the governing diffusion equation. The solution can accommodate arbitrary pressure-dependent nonlinear rock and fluid properties as well as production caused by desorption. The mathematical formulation is presented for a general nonlinear case and tested by use of synthetic data. Field production from the Barnett Shale is then used to estimate effective matrix permeability. The model can be used to predict production if the rock and fluid properties are known, or can be used to constrain reservoir properties from production data. It is a complement to traditional pressure- or rate-transient analysis; if the response of a well for constant-pressure production can be determined, our method can be used to determine reservoir properties, without any approximations inherent in linearizing the flow equations.