A streamline splitting pore-network approach for computationally inexpensive and accurate simulation of transport in porous media

Several approaches have been developed in the literature for solving flow and transport at the pore scale. Some authors use a direct modeling approach where the fundamental flow and transport equations are solved on the actual pore-space geometry. Such direct modeling, while very accurate, comes at a great computational cost. Network models are computationally more efficient because the pore-space morphology is approximated. Typically, a mixed cell method (MCM) is employed for solving the flow and transport system which assumes pore-level perfect mixing. This assumption is invalid at moderate to high Peclet regimes. In this work, a novel Eulerian perspective on modeling flow and transport at the pore scale is developed. The new streamline splitting method (SSM) allows for circumventing the pore-level perfect-mixing assumption, while maintaining the computational efficiency of pore-network models. SSM was verified with direct simulations and validated against micromodel experiments; excellent matches were obtained across a wide range of pore-structure and fluid-flow parameters. The increase in the computational cost from MCM to SSM is shown to be minimal, while the accuracy of SSM is much higher than that of MCM and 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 pore-level interactions of fluid flow and transport in different porous materials. In this paper, we apply SSM and MCM to study the effects of pore-level mixing on transverse dispersion in 3-D disordered granular media.