A New Triple-Porosity Model for Rate and Pressure Transient Analysis of Unconventional Gas Reservoirs with Multivariate Bimodal Matrix Property Distribution

Unconventional gas reservoirs (UGRs), such as shale and coal formations, are characterized by ultratight matrix properties and complex natural fracture networks. Accurately modeling flow behavior in such reservoirs requires accounting for both their intrinsic heterogeneity and pressure-dependent flow mechanisms. This study introduces a novel semianalytical model for rate and pressure transient analysis (RTA/PTA) of a UGRs, incorporating a triple-porosity representation enabled by bimodal distributions of matrix block size, porosity, and permeability. The model integrates multivariate statistical approaches (univariate, bivariate, and trivariate) to represent reservoir heterogeneity realistically. It also accounts for key non-Darcy flow mechanisms relevant in shale and coal reservoirs, including gas sorption, surface diffusion, slip flow, Knudsen diffusion, and pore-scale confinement effects, alongside porosity and permeability stress sensitivity. The proposed model is validated against numerical simulations, demonstrating excellent agreement with normalized root-mean square error (NRMSE) values of 0.17% for pseudopressure and 6.93% for bottomhole pressure. Type curve analysis revealed that the characteristic two-stage descent observed in derivative plots—a hallmark of triple-porosity systems—is primarily attributed to bimodal block-size distributions. Furthermore, sensitivity analysis indicated that Knudsen and surface diffusion coefficients have comparable impact on transient behavior during the interporosity flow period. This work contributes a robust, physics-informed framework for transient flow modeling in a UGRs with realistic geological complexity. The methodology offers practical insights into interpreting transient data from hydraulically fractured horizontal wells and supports improved reservoir characterization and production forecasting in heterogeneous unconventional gas systems. The model is applicable to shale gas, coal seam gas, and tight gas reservoirs, and supports both PTA type-curve analysis and practical RTA curve-matching workflows across varying levels of matrix heterogeneity.