Fluid flow in thin fractured porous media using a TPM-phase-field model and microfluidic experiments

Abstract The Theory of Porous Media (TPM) with an embedded phase-field approach to fracture provides an elegant opportunity to study complex flow phenomena in fractured porous materials in a unified single-domain approach. On this basis, the interactive flow behaviour between free flow and porous-media flow is studied using the example of flow through a thin porous plate containing a rectangular channel. By considering different boundary conditions and investigating the flow behaviour for a range of hydraulic conductivities, our study is designed to reveal insights into phenomena which are relevant for various sub-surface geo-engineered applications. Furthermore, we show that the applied macroscopic single-domain approach is able to reveal local flow effects near the porous interface (channel walls), namely the so-called velocity profile inversion phenomenon. Moreover, we introduce a geometrically motivated estimation of the length-scale parameter $$\epsilon $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ϵ</mml:mi> </mml:math> used in phase-field approaches, which is directly related to the roughness of the fracture surface. Thus, values for $$\epsilon $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ϵ</mml:mi> </mml:math> are proposed for microfluidic devices and different rock types. Furthermore, we apply fully three-dimensional simulations to evaluate the influence of the thickness of thin porous plates on the overall flow resistance, which is typically relevant in microfluidic devices. In a combined numerical–experimental study, we compare results from representative microfluidic experiments and simulations and confirmed the choice of $$\epsilon $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ϵ</mml:mi> </mml:math> to correctly predict the flow transition across the porous interface.