A semi-analytical model for multiple-fractured horizontal wells in heterogeneous gas reservoirs

Most gas reservoirs are not homogeneous in practice. Due to the influences of the nonlinearity and heterogeneity, little work has focused on the behavior of multiple-fractured horizontal wells (MFHWs) in heterogeneous gas reservoirs. In this study, a semi-analytical model based on a detailed analytical method for MFHWs in heterogeneous gas reservoirs is established. The source functions, boundary element method and Green's solution are used to build the model in Laplace space. To solve the problem that the combination of the pseudofunction approach with the material balance equation describing homogeneous gas reservoirs cannot be effectively linearize the nonlinearity in heterogeneous gas reservoirs, a multi-region material balance equation for heterogeneous gas reservoirs is derived. Then, the performance of an MFHW in a two-block gas reservoir is calculated. The pressure behavior and the flux distribution are influenced by the crossflow coefficient, fracture conductivity, size of the gas reservoir, fracture half-length and storage ratio. A high crossflow coefficient increases the flux of the interface and the difference in flux between fractures in different blocks. The effects of the crossflow can be weakened by a high fracture conductivity and large fracture half-length. This study provides a theoretical basis for MFHWs in heterogeneous gas reservoirs.