Rigorous vertical averaging for pseudo-3D modeling of precipitation obstructed fluid flow

Abstract

Computing effective hydraulic properties of porous materials with a dynamically changing pore morphology presents a complex and critical challenge in both theoretical and applied sciences. This paper presents a tool to effectively compute the intrinsic permeability k(x,t) for domains with both temporally and spatially varying pore structures, by utilizing a sample of snapshots of microfluidic experiments with calcium carbonate precipitation. To compute large domains at reasonable cost, a pseudo-3D Stokes solver with an additional viscous drag term is employed. In order to simulate the intricate domains with highly heterogeneous pore space, we derive vertically averaged governing equations including a vertically averaged drag term from scratch and without limiting assumptions. For exemplary precipitates (semi-spheres) of varying sizes within a rectangular channel with fixed solid boundaries, results are compared across multiple modeling approaches, each employing different drag force formulations. In addition, the performance of the derived models is examined for segments of an EICP experiment in terms of accuracy (comparison with 3D solvers) and computational efficiency. Finally, an entire experimental domain is used to demonstrate the capabilities offered by the solver thanks to its efficiency as well as accuracy and the permeability tensor k is computed and compared with experimental results. In all these applications, the vertically averaged drag term proves to be the optimal solution in terms of speed and accuracy, thus allowing for an efficient analysis of the non-uniformity of local fluid flow fluctuations resulting from alterations in the pore space.