A staggered finite element procedure for the coupled Stokes-Biot system with fluid entry resistance
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ORIGINAL PAPER
A staggered finite element procedure for the coupled Stokes-Biot system with fluid entry resistance E. A. Bergkamp1
· C. V. Verhoosel1 · J. J. C. Remmers1 · D. M. J. Smeulders1
Received: 26 July 2019 / Accepted: 17 December 2019 © Springer Nature Switzerland AG 2020
Abstract We develop a staggered finite element procedure for the coupling of a free viscous flow with a deformable porous medium, in which interface phenomena related to the skin effect can be incorporated. The basis of the developed simulation procedure is the coupled Stokes-Biot model, which is supplemented with interface conditions to mimic interface-related phenomena. Specifically, the fluid entry resistance parameter is used to relate the fluid flux through the interface to the pressure jump across the interface. The attainable jump in pressure over the interface provides an effective way of modeling sharp pressure gradients associated with the possibly reduced permeability of the interface on account of pore clogging. In addition to the fluid entry resistance parameter, the developed simulation strategy also includes the possibility of modeling fluid slip over the porous medium. Sensitivity studies are presented for both the fluid entry resistance parameter and the slip coefficient, and representative two- and three-dimensional test cases are presented to demonstrate the applicability of the developed simulation technique. Keywords Deformable porous media · Stokes-Biot model · Skin effect · Fluid entry resistance · Beavers-Joseph-Saffman condition · Finite element simulation · Interface coupling · Staggered solution procedure
1 Introduction Understanding the interaction of a free fluid flow and a deformable porous medium is essential for many industrial, biological, and geomechanical applications. Examples of industrial and biological applications include filters [22] and the transfer of fluids through the permeable walls of blood vessels to the surrounding tissue [13]. In geomechanics, a variety of both natural and artificial applications can be found. Wave-seabed interactions [25] and surface-ground E. A. Bergkamp
[email protected] C. V. Verhoosel [email protected] J. J. C. Remmers [email protected] D. M. J. Smeulders [email protected] 1
Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands
water systems [34] are among many naturally occurring phenomena that are controlled by the interaction between fluids and porous media. A detailed understanding of this interaction can be used to our advantage, for example to increase the production of geothermal energy through Enhanced Geothermal Systems [24], or to control the extraction of oil and gas from fractured reservoirs [29]. The ability to accurately model the interaction between a free flow and a deformable porous medium increases our understanding of processes that cannot be observed in practice, such as the flow through fractures deep in the subsurface. The analysis presented in this manuscript is aimed specifically at this applica
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