Numerical upscaling of nonlinear flow in low-permeability sandstone matrix system

The matrix system's apparent permeability model based on nano- and micro-scale mechanism modeling is limited in its role in low-permeability reservoir numerical simulation due to the lack of suitable up-scaling methods. This paper developed a numerical simulation method to evaluate the microporous structure's apparent permeability contribution to total permeability of the heterogeneous representative elementary volume (REV)-scale matrix under macroscopic pressure gradients. First, a local apparent liquid permeability (LALP) model considering the heterogeneous microporous structure and multiple water-transport mechanisms was established to describe the nonlinear seepage behavior of fluid in microscopic computational domain. Then, a multiresolution-image-based REV-scale domain reconstruction method was proposed, in which the microporous structural characteristics were quantified by fractal heterogeneous-porous-media model, and the REV-scale matrix was subsequently stochastic reconstructed based on the porosity distribution characteristics of microporous structures. Finally, the microscopic LALP model and macroscopic continuum model were fully coupled to numerical simulate the nonlinear seepage progress in REV-scale matrix domain. The comparisons between simulation results and experimental results demonstrated that the developed numerical simulation method can effectively predict the nonlinear flow velocity curve of REV-scale sandstone matrix. The influences of internal factors (microporous structural characteristics and seepage fluid properties) and external factors (temperature and pressure) on absolute permeability and apparent permeability of REV-scale matrix were investigated. The results demonstrated that (1) microporous structural characteristics determines the approximate level of intrinsic reservoir permeability, especially the average maximum pore size of discrete domain; (2) with microporous structure's permeability distribution heterogeneity increasing, the macroscopic intrinsic permeability decreases and the differences between apparent permeability and intrinsic permeability increase.