A Hybrid-Dimensional Coupled Pore-Network/Free-Flow Model Including Pore-Scale Slip and Its Application to a Micromodel Experiment

Abstract

Modeling coupled systems of free flow adjacent to a porous medium by means of fully resolved Navier–Stokes equations is limited by the immense computational cost and is thus only feasible for relatively small domains. Coupled, hybrid-dimensional models can be much more efficient by simplifying the porous domain, e.g., in terms of a pore-network model. In this work, we present a coupled pore-network/free-flow model taking into account pore-scale slip at the local interfaces between free flow and the pores. We consider two-dimensional and three-dimensional setups and show that our proposed slip condition can significantly increase the coupled model’s accuracy: compared to fully resolved equidimensional numerical reference solutions, the normalized errors for velocity are reduced by a factor of more than five, depending on the flow configuration. A pore-scale slip parameter $$\beta _{{{{\rm pore}}}}$$ β pore required by the slip condition was determined numerically in a preprocessing step. We found a linear scaling behavior of $$\beta _{{{{\rm pore}}}}$$ β pore with the size of the interface pore body for three-dimensional and two-dimensional domains. The slip condition can thus be applied without incurring any run-time cost. In the last section of this work, we used the coupled model to recalculate a microfluidic experiment where we additionally exploited the flat structure of the micromodel which permits the use of a quasi-3D free-flow model. The extended coupled model is accurate and efficient.

A Dynamic and Fully Implicit Non‐Isothermal, Two‐Phase, Two‐Component Pore‐Network Model Coupled to Single‐Phase Free Flow for the Pore‐Scale Description of Evaporation Processes

“…The momentum interface conditions are explained in detail in Weishaupt et al (2020). We require mechanical equilibrium at the interface and assume creeping flow (Re < 1), yielding…”

“…for the normal force component. The tangential momentum transfer from the pore-network model to the free-flow domain is described by an approximation similar to the widely used Beavers-Joseph interface slip condition for REV-scale models (Beavers & Joseph, 1967), adapted for a pore-local description of the slip (Weishaupt et al, 2020).…”

“…Note that Equation 23does not impair mass conservation as it is only used for the approximation of the tangential momentum transfer. The material parameter β pore is determined numerically in a preprocessing step (Weishaupt et al, 2020).…”

“…This means that no coupling iterations are required and the scheme inherently conserves mass, momentum and energy. Details on the system matrix can be found in Weishaupt et al (2020).…”

Fully Implicit Dynamic Pore‐Network Modeling of Two‐Phase Flow and Phase Change in Porous Media

“…More generally, other physical and chemical processes such as heat transfer and reactive processes can also be included in the current framework through either sequential coupling after the flow and transport are solved, or via direct fully implicit coupling together with the flow and transport. For example, Weishaupt et al (2019Weishaupt et al ( , 2020 have coupled a fully implicit PNM to a DNS model of the Navier-Stokes equation under single-phase conditions. While finalizing the revision of our manuscript, we learned that Weishaupt (2020) has further extended 10.1029/2020WR028510 their modeling framework to two-phase flow conditions to simulate heat transfer and water evaporation (using Henry's law) at the interface between free flow and air-water two-phase flow in a porous medium.…”