Computationally Inexpensive Incorporation of Solute Transport Physics into Pore-Network Models

Several modeling approaches have been developed in the literature for simulating solute transport at the pore scale. This includes "direct modeling" where the fundamental equations are solved directly on the actual pore-scale geometry (obtained from digital images). These methods, even though very accurate, come at a high computational cost. A pore-network representation of the pore-scale geometry is a first step in reducing the computational cost. However, the geometric simplification is typically accompanied by a secondary simplification of the physics of the problem (contributing to their inaccuracy). This is seen in the widely-used "mixed-cell method" which has simplifications in two key components: 1) intra-pore mixing, and 2) inter-pore rate expressions. Nevertheless, the method is popular because it is computationally inexpensive, allowing for examining larger and more representative computational domains. In this work, we explore two novel methods for circumventing the aforementioned limitations of the mixed-cell method (intra-pore mixing and inter-pore rate expressions); all while making an effort to keep the computational cost low. We show that while intra-pore mixing can be accurately taken into account, correcting for the inter-pore rate expressions has fundamental implications on the applicability of Eulerian pore-network models and the interpretation of the results obtained therefrom. Despite recent important progress in the development of accurate and robust direct modeling tools, there is a need in the literature for simple, accurate, and inexpensive models both from a scientific as well as a practical point of view.