A discrete unified gas kinetic scheme for simulating transient hydrodynamics in porous media with fractures

Abstract

Tight gas reservoirs have typical characteristics of well-developed natural fractures, extremely low permeability, and low porosity. The flow in such media can be described by a dual-porosity dual-permeability (DPDP) model with the consideration of gas slippage and real gas effects. Based on this model, in this study, a discrete unified gas kinetic scheme is developed to describe the transient hydrodynamic behaviors in porous media with fractures. With an interporosity term, two kinetic equations are employed to capture the pressure propagation in matrix and fracture sub-systems, respectively. The proposed DUGKS can correctly recover the DPDP model through the Chapman–Enskog analysis. Unlike the traditional numerical methods, the velocity in DUGKS can be calculated locally by the non-equilibrium distribution functions. The presented method is verified by three typical problems, including the flow in a fractured porous medium, the flow around a vertical production well, and the flow around a fractured horizontal production well. The numerical results are in good agreement with the reference data. In the test, the global relative errors in pressures are on the order of 10−3. Moreover, the transient hydrodynamics in porous media with fractures are evaluated. The simulation results show that the slippage mainly occurs in the matrix, and this effect may result in a 20% increase in permeability. With the consideration of slippage and real gas effects, the predicted production is higher than that predicted by Darcy’s law. In addition, the results indicate that hydraulic fractures have a great impact on production.