Analytical dual-porosity gas model for reserve evaluation of naturally fractured gas reservoirs using a density-based approach

The development of naturally fractured gas reservoirs often requires the deployment of rigorous techniques for production data analysis incorporating dual-porosity gas behavior. It has been a prominent problem to linearize and analytically solve the governing equations for dual-porosity gas systems. This study applies a pseudo-pressure-based interporosity flow equation to derive a density-based rate-transient analysis method to accurately predict the gas production rate and estimate the amount of original gas in place (G_i) for the systems. The methodology also predicts the gas production rate by transforming the response of its liquid counterpart via a decoupling of the pressure-dependent effects using dimensionless depletion-driven parameters. For the first time, the density-based flowing material balance method is derived for the dual-porosity gas reservoir. More than that, an innovative fracture productivity equation that was missing for the dual-porosity system is derived as well. This study provided detailed derivations for the model and relationship used in past density-based dual-porosity rate-transient analysis. The dual-porosity productivity equation and the relationship between average matrix pseudopressure and average fracture pseudopressure are rigorously derived. The rescaling relationship between the dual-porosity liquid solution and the dual-porosity gas solution is also demonstrated in detail. An appropriate interporosity flow equation for gas is used. Based on that, the results show that the density-based approach is able to successfully capture the dual-porosity behavior of gas for constant bottomhole pressure condition.