Transport analysis in deformable porous media through integral transforms

Abstract

Geomechanical deformation can alter the flow field that impacts solute mass fluxes. Despite its importance, the effects of the coupling between geomechanical deformation and the flow field on solute transport behavior are not fully known. In this paper, we study the impact of this coupling on the solute concentration distribution. The concentration field is semianalytically derived by making use of the generalized integral transform technique. We apply the semianalytical solution to two uniaxial consolidation problems, the classical Terzaghi's problem with a constant load and the case of periodic loading of a porous deformable layer. Our results indicate that geomechanical parameters, such as the Skempton's coefficient and the soil compressibility, can affect the peak concentration as well as the spatial moments of solute plume. In case of periodic loading, we show that the frequency of loading also plays a key role in regulating the temporal dynamics of the concentration field.

Effect of Poroelastic Coupling and Fracture Dynamics on Solute Transport and Geomechanical Stability

“…The volumetric effective stress is related to the volumetric strain as , where in 2D. Mass conservation of the solid component yields the porosity evolution equation in terms of the volumetric strain and the fluid pressure (Bonazzi et al., 2020; Coussy, 2004): …”

“…Injection of fluids into naturally or hydraulically fractured formations has been an important research topic due to its relevance in a vast number of engineering applications: waste disposal (Cornaton et al., 2008; McCarthy & Zachara, 1989; Witherspoon et al., 1981), carbon sequestration (Iding & Ringrose, 2010), contaminant transport (Sahimi, 2011), enhanced oil recovery (Jiménez‐Martínez et al., 2016), and tracer surveillance (Hu & Moran, 2005; Rugh & Burbey, 2008; Warner et al., 2014). In many applications, a key objective of the numerical model built to simulate the processes is to quantify the mixing between the injected and resident fluids and quantify the extent of the associated mixing zone (Bonazzi et al., 2020, 2021; Cirpka & Valocchi, 2007; Dentz et al., 2011; Jha et al., 2011a; Z. Zhao et al., 2011). In cyclic well operations, where the well alternates or cycles through injection and production/withdrawal stages, the evolution of fluid mixing is complicated by short time scale variations in the pore pressure field.…”

Analytical solution for one‐dimensional steady‐state contaminant transport through a geomembrane layer (GMBL)/compacted clay layer (CCL)/attenuation layer (AL) composite liner considering consolidation

“…38,39 The existing analytical solutions for coupling consolidation and solute transport are mainly for single CCLs. 23,24,27,40,41 Yan et al 23 developed an analytical model to study the migration of contaminant through deforming composite liner under the assumption of quasi-steady-state small deformation of the CCL. The model was then extended to consider the effects of transient consolidation processes on contaminant transport in a deforming liner system.…”

“…This implies that a better understanding of the mechanism involved in the contaminant transport process may be obtained by using the analytical solution, which is mathematically derived from the basic physical principles 38,39 . The existing analytical solutions for coupling consolidation and solute transport are mainly for single CCLs 23,24,27,40,41 . Yan et al 23 .…”

Dynamic soil consolidation model using a nonlocal continuum poroelastic damage approach

“…These class of problems are not yet well understood, and available experiments are extremely limited. Thus, there is an urgent need for appropriate dynamic poroelastic models that can reliably describe and predict complex hydro‐mechanical coupling processes in porous media 19–21 . In this work, we have chosen a nonlocal integral damage approach as it provides (i) reliability (mesh independent results), (ii) efficiency (does not require additional degrees of freedom as for example in XFEM 22 or phase field methods 23 ), and (iii) flexibility (any damage model can be calibrated and employed as opposed for example to phase field methods, which are limited by certain mathematical constraints 24 ).…”