Efficient Prediction of Multidomain Flow and Transport in Hierarchically Structured Porous Media

Structural hierarchy is a fundamental characteristic of natural porous media. Yet it provokes one of the grand challenges for the modeling of fluid flow and transport since pore‐scale structures and continuum‐scale domains often coincide independent of the observation scale. Common approaches to represent structural hierarchy build, for example, on a multidomain continuum for transport or on the coupling of the Stokes equations with Darcy's law for fluid flow. These approaches, however, are computationally expensive or introduce empirical parameters that are difficult to derive with independent observations. We present an efficient model for fluid flow based on Darcy's law and the law of Hagen‐Poiseuille that is parameterized based on the explicit pore space morphology obtained, for example, by X‐ray μ‐CT and inherently permits the coupling of pore‐scale and continuum‐scale domain. We used the resulting flow field to predict the transport of solutes via particle tracking across the different domains. Compared to experimental breakthrough data from laboratory‐scale columns with hierarchically structured porosity built from solid glass beads and microporous glass pellets, an excellent agreement was achieved without any calibration. Furthermore, we present different test scenarios to compare the flow fields resulting from the Stokes‐Brinkman equations and our approach to comprehensively illustrate its advantages and limitations. In this way, we could show a striking efficiency and accuracy of our approach that qualifies as general alternative for the modeling of fluid flow and transport in hierarchical porous media, for example, fractured rock or karstic aquifers. Key Points A model for the simulation of pore‐scale and continuum‐scale flow in hierarchically structured porous media is developed Explicit pore space morphology obtained by image analysis of X‐ray micro‐CT images is used for parameterization Predictions of solute breakthrough obtained by particle tracking perfectly match observations