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Abstract
AbstractA two‐scale numerical model is developed for fluid flow in fractured, deforming porous media. At the microscale the flow in the cavity of a fracture is modelled as a viscous fluid. From the micromechanics of the flow in the cavity, coupling equations are derived for the momentum and the mass couplings to the equations for a fluid‐saturated porous medium, which are assumed to hold on the macroscopic scale. The finite element equations are derived for this two‐scale approach and integrated over time. By exploiting the partition‐of‐unity property of the finite element shape functions, the position and direction of the fractures is independent from the underlying discretization. The resulting discrete equations are non‐linear due to the non‐linearity of the coupling terms. A consistent linearization is given for use within a Newton–Raphson iterative procedure. Finally, examples are given to show the versatility and the efficiency of the approach, and show that faults in a deforming porous medium can have a significant effect on the local as well as on the overall flow and deformation patterns. Copyright © 2006 John Wiley & Sons, Ltd.
Highlights
Flow of fluids in deforming porous media has been a topic of attention in engineering science ever since the seminal works of Terzaghi [1] and Biot [2], see [3] for a recent account
Porous Medium pore fluid solid grain free fluid functioning of human tissues, the classical two-phase theory has been extended in recent times to three- and four-phase media, taking into account ion transport and electrical charges as well [4,5,6]
Building on earlier work in which we have constructed a numerical model for fracture propagation in deforming, fluid-saturated porous media [8], we extend the theory to include flow inside such cavities directed tangentially to the discontinuity
Summary
Flow of fluids in deforming porous media has been a topic of attention in engineering science ever since the seminal works of Terzaghi [1] and Biot [2], see [3] for a recent account. Building on earlier work in which we have constructed a numerical model for fracture propagation in deforming, fluid-saturated porous media [8], we extend the theory to include flow inside such cavities directed tangentially to the discontinuity. This is achieved by a priori adopting a two-scale approach. Apart from demonstrating the effectiveness of the two-scale approach, the calculations show that the influence of the presence of discontinuities on flow and deformation patterns can be significant
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