Anisotropy of the permeability tensor in statistically uniform porous media of sizes used in typical computer simulations is studied. Although such systems are assumed to be isotropic by default, we show that de facto their anisotropic permeability can give rise to significant changes of transport parameters such as permeability and tortuosity. The main parameter controlling the anisotropy is $a/L$, being the ratio of the obstacle to system size. Distribution of the angle $α$ between the external force and the volumetric fluid stream is found to be approximately normal, and the standard deviation of $α$ is found to decay with the system size as $(a/L)^{d/2}$, where $d$ is the space dimensionality. These properties can be used to estimate both anisotropy-related statistical errors in large-scale simulations and the size of the representative elementary volume.
The emerging instability of a forced throughflow in a fluid saturated horizontal porous duct of rectangular cross section is investigated. The duct is heated from below by assuming the horizontal boundaries to be at different temperatures. Both the horizontal and the vertical boundaries are impermeable and the basic flow is parallel to such boundaries. The porous medium is anisotropic with different permeabilities in the vertical and horizontal directions. The effect of the anisotropy on the onset of the buoyancy driven modal instability and absolute instability is analysed. The parametric con…
Using a Cauchy integral formulation of the boundary integral equations, we simulate the erosion a porous medium comprised of up to 100 solid bodies embedded in a Stokes flow. The grains of the medium are resolved individually and erode under the action of surface shear stress. Through nonlinear feedback with the surrounding flow fields, microscopic changes in grain morphology give way to larger-scale features in the medium such as channelization. The Cauchy-integral formulation and associated quadrature formulas enable us to resolve dense configurations of nearly contacting bodies. We observe …
Fully developed forced convective flow in a channel filled with porous material bounded by two impermeable walls subject to constant heat flux is considered. We consider Brinkman-Forchhimer equation to govern the flow inside the porous medium which accounts for the presence of inertial term. We assume that the porous medium is anisotropic in nature and permeability is varying along all the directions, correspondingly, permeability will be a matrix which appear as a positive semi-definite matrix in the momentum equation. The anisotropic nature of the porous medium is characterized by anisotropi…
We explore the motion of an axisymmetric gravity current in an anisotropic porous medium in which the horizontal permeability is larger than the vertical permeability. It is well known that the classical axisymmetric gravity current supplied by a constant point source of fluid has an unphysical singularity near the origin. We address this by considering a pressure-dominated region near the origin which allows for vertical flow from the source, such that the current remains of finite depth, whilst beyond this region the flow is gravity-dominated. At early times the inner pressure-driven region …
In this work, we study non-Newtonian fluid flow in heterogeneous porous media. We are interested in fluids presenting a specific change in rheology: Newtonian below a certain shear rate and power law above. Since porous media generally exhibit strong spatial heterogeneity at large geological scales, we study the interaction between such inhomogeneity and the nonlinear rheology of the fluid. The coupling between permeability heterogeneity and nonlinear rheology significantly affects the flow. We are particularly in the statistical properties of the velocity field (mean, variance, correlation, e…
Microscale turbulence in porous media is a new physical phenomenon that exhibits unique properties unlike those in classical turbulence flows. At low values of porosity, the surface forces on the solid obstacles compete with the inertial force of the fluid flow to result in the formation of flow instabilities. In this paper, we report the origin and mechanism of a symmetry-breaking phenomenon in periodic porous media that causes a deviation in the direction of the mean flow from that of the applied pressure gradient. Large Eddy Simulation (LES) is used to simulate turbulent flow in a homogeneo…
We investigate the effect of dispersion on convection in porous media by performing direct numerical simulations (DNS) in a two-dimensional Rayleigh-Darcy domain. Scaling analysis of the governing equations shows that the dynamics of this system are not only controlled by the classical Rayleigh-Darcy number based on molecular diffusion, $Ra_m$, and the domain aspect ratio, but also controlled by two other dimensionless parameters: the dispersive Rayleigh number $Ra_d = H/α_t$ and the dispersivity ratio $r = α_l/α_t$, where $H$ is the domain height, $α_t$ and $α_l$ are the transverse and longit…
We report and discuss, by means of pore-scale numerical simulations, the possibility of achieving a directional-dependent two-phase flow behaviour during the process of invasion of a viscous fluid into anisotropic porous media with controlled design. By customising the pore-scale morphology and heterogeneities with the adoption of anisotropic triangular pillars distributed with quenched disorder, we observe a substantially different invasion dynamics according to the direction of fluid injection relative to the medium orientation, that is depending if the triangular pillars have their apex ori…
Convective dissolution is the process by which CO$_2$ injected in deep geological formations dissolves into the aqueous phase, which allows storing it perennially by gravity. The process results from buoyancy-coupled Darcy flow and solute transport. Proper theoretical modeling of the process should consider in the transport equation a diffusive term accounting for hydrodynamics (or, mechanical) dispersion, with an effective diffusion coefficient that is proportional to the local interstitial velocity. A few two-dimensional (2D) numerical studies, and three-dimensional (3D) experimental investi…
