Development and testing of hybrid (PNM–CFD) mathematical model and numerical algorithm for description of fluid flows in three-dimensional digital core models

Abstract

Numerical simulation of fluid flow in porous and fractured rocks is an important task for many industrial applications. The most common approaches to constructing such models are direct (CFD or lattice Boltzmann) and porous network (PNM) modeling. Each approach has its own advantages and disadvantages. This paper presents a hybrid mathematical PNM–CFD model for describing fluid flows in three-dimensional digital core models, which has the high speed performance of PNM approaches and high accuracy of CFD models. Numerical technique has been developed for describing fluid flows in three-dimensional digital core models using a hybrid PNM–CFD model. The numerical technique links a one-dimensional pore network solver and a three-dimensional CFD solver into a combined model in original way by constructing a single pressure field for the entire computation domain. To validate the model, several tests were performed, including flow in straight channels and numerical simulation of fluid flow in a microfluidic chip. The test results have shown the adequacy of the hybrid model performance. The hybrid model for determining pressure drop in a branched network with three-dimensional chambers has an error of no more than 5 % when compared to experimental data. Similarly, the error in calculating velocity does not exceed 7 % when compared to the full three-dimensional calculation. The hybrid model has shown an almost twofold increase in calculation speed compared to the full three-dimensional model.