A Streamline Splitting Pore-Network Approach for Computationally Inexpensive and Accurate Simulation of Species Transport in Porous Media

Several modeling approaches have been developed in the literature for solving flow and transport problems at the pore-scale. Some use a direct modeling approach where the fundamental flow and transport equations are solved in detail on the actual (or a simplified representation of the) pore-scale geometry. Such direct modeling captures a great deal of the pore-level details, but comes at a great computational cost. Network models, however, are computationally more efficient because the pore-space morphology is approximated. Additionally, a mixed cell method (MCM) is typically employed for solving the flow and transport system, which assumes a single concentration value per pore, and therefore pore-level perfect mixing. However, large concentration gradients exist at the pore-level for moderate to high Peclet regimes and MCM can be restrictive in the model's predictive capabilities. In this work, a novel perspective on modeling flow and transport at the pore-scale is presented. The new streamline splitting method (SSM) allows for circumventing the pore-level perfect mixing assumption, while maintaining the computational efficiency of pore-network models. The model was verified with direct simulations, and excellent matches were obtained against micromodel experiments across a wide range of pore-structure and fluid-flow parameters. The number of unknowns in the SSM model is typically only ~2 times more than those of the MCM method. However, the accuracy of SSM is much higher than that of MCM and in most cases comparable to direct modeling approaches. Therefore, SSM can be regarded as an appropriate balance between incorporating detailed physics and controlling computational cost. The truly predictive capability of the model allows for the study of interactions between fluid flow and species transport in more complicated 3D media.