Transient shape factors for dual-porosity simulation of tight rocks

Abstract

The shape-factor concept provides an elegant and powerful upscaling method for fractured reservoir simulation. Many different shape-factors, among which the well-known Warren and Root, and Kazemi shape-factors have been proposed in the past. Since different shape-factors can lead to totally different reservoir behavior, selection of the appropriate shape-factor value is critical for accurate fractured reservoir modeling. Constant shape factor is commonly used for simulation of fractured reservoirs by assuming that pressure transient reaches to center of the matrix block within very small time. On the contrary, tight rocks exhibit longer duration of unsteady-state flow such that matrix – fracture transfer is not constant, but rather varies with time until reaching to a constant value. In this regard, dual-porosity simulation of tight rocks using constant shape factor does not capture actual physics of matrix to fracture flow and yields inaccurate performance prediction. In this study, analytical solutions of pressure diffusion and corresponding shape factors are presented for various matrix shapes. The results are compared to those obtained with simple empirical functions. Proposed functions significantly improve accuracy over existing approaches in the prediction of both mean matrix pressure and transfer function. Results of fine grid single-porosity model are compared with two different dual porosity models, one with constant shape factor and one with time dependent shape factor, to verify proposed approach.