<p>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 <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="419_2025_2892_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="10" /> </InlineMediaObject> <EquationSource Format="TEX">$\epsilon $</EquationSource> <EquationSource Format="MATHML"><math> <mi>ϵ</mi> </math></EquationSource> </InlineEquation> used in phase-field approaches, which is directly related to the roughness of the fracture surface. Thus, values for <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="419_2025_2892_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="10" /> </InlineMediaObject> <EquationSource Format="TEX">$\epsilon $</EquationSource> <EquationSource Format="MATHML"><math> <mi>ϵ</mi> </math></EquationSource> </InlineEquation> are proposed for microfluidic devices and different rock types. Furthermore, we apply fully three-dimensional simulations to evaluate the influence of the thickness of thin porous plates on the overall flow resistance, which is typically relevant in microfluidic devices. In a combined numerical–experimental study, we compare results from representative microfluidic experiments and simulations and confirmed the choice of <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="419_2025_2892_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="10" /> </InlineMediaObject> <EquationSource Format="TEX">$\epsilon $</EquationSource> <EquationSource Format="MATHML"><math> <mi>ϵ</mi> </math></EquationSource> </InlineEquation> to correctly predict the flow transition across the porous interface.</p>

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

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2025年9月26日

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Yann Rivas,
Nikolaos Karadimitriou,
Holger Steeb,
Wolfgang Ehlers,
Arndt Wagner

摘要

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 $ $ϵ$ used in phase-field approaches, which is directly related to the roughness of the fracture surface. Thus, values for $\epsilon $ $ϵ$ 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 $ $ϵ$ to correctly predict the flow transition across the porous interface.