A MULTI-LINEAR FRACTAL MODEL FOR PRESSURE TRANSIENT ANALYSIS OF MULTIPLE FRACTURED HORIZONTAL WELLS IN TIGHT OIL RESERVOIRS INCLUDING IMBIBITION

Abstract

Most models for multiple fractured horizontal wells (MFHWs) in tight oil reservoirs (TORs) are based on classical simplified dual-porosity model that ignores the influence of imbibition, while the distribution of fracture system is heterogeneous, multi-scale and self-similar, which can be described by fractal dual-porosity model on fractal theory, and imbibition production is the important part of fracture system production. In this paper, a multi-linear fractal model (MFM) considering imbibition for MFHWs in TORs was established based on fractal theory and semi-analytical method. In this model, fractal theory was used to describe the heterogeneous, complex fracture network, and imbibition was considered by analogy of fluid crossflow law in fractured-porous dual media. And the approximate analytic solution was given by using the Laplace transformation and iteration method. The pressure responses in the domain of real time were obtained with Stehfest numerical inversion algorithms. The pressure transient and production rate were used to analyze, and sensitivity analysis of some related parameters were discussed. The results show that the fluid flow in MFHWs can be divided into nine main flow periods by analysis of type curves, and the fractal parameters of fracture system have great effect on the middle and later periods and imbibition influences the period of crossflow.