Dynamics of Viscous Fingering in Porous Media in the Presence of In Situ Formed Precipitates and Their Subsequent Deposition

Abstract

Understanding the dynamics of miscible viscous fingering is of paramount importance in a wide range of applications, from groundwater hydrology to enhanced oil recovery. In this work, we investigate the effect of precipitation and deposition of an initially dissolved component and the subsequent porosity and permeability variations on miscible viscous fingering in porous media. The commonly used stream function-vorticity formulation does not allow for nonsolenoidality of the velocity vector, which is the case when the porosity field varies with time. This is why we develop a velocity-vorticity formulation, making no further simplifications on the flow field. For numerical simulations, the governing equations are solved using the hybridization of pseudospectral and compact finite difference methods, and the time stepping is carried out through high-order semi-implicit schemes. Using our methodology, we tackle the problem of precipitation of an initially dissolved component through an infinitely fast and reversible reaction. It is found that the deposition of the formed precipitates in porous media results in more severe interfacial instabilities, the effect of which is attenuated as the viscosity ratio between the displacing and resident fluids increases. In addition, our results show that the formed precipitates are mostly concentrated around the interface where the two fluids actively mix. We also characterize the alterations of the local and global permeability fields, and interestingly, we find that the ultimate value of the overall permeability of the porous media scales linearly with the log-viscosity ratio at any fixed deposition rate. It is worth mentioning that, without loss of generality, the developed methodology and analysis in this study are applicable to other forms of precipitation reactions (e.g., finite rate and irreversible) in porous media.

Experimental Investigation of the Effects of Porosity, Hydraulic Conductivity, Strength, and Flow Rate on Fluid Flow in Weakly Cemented Bio-Treated Sands

“…The applicability of the findings of this study to hydrology-related applications extends also to theoretical studies of flow equations and flow regimes that have been traditionally used in the field of hydrology (i.e., the Forcheimer equation [13], the Kirchhoff-transformed Richards equation [75], diffusion [14], transient flow equations [76], Darcy and non-Darcy flow [77,78], viscous fingering [79]) in which the particle size effects and in general the porous medium properties are of great importance, as they define porosity and permeability. This study could be used to define semi-empirical correlations, which are usually required in these types of studies.…”

Influences of Dead‐End Pores in Porous Media on Viscous Fingering Instabilities and Cleanup of NAPLs in Miscible Displacements

“…It can be extended to the case considering concentration-dependent diffusion and/or velocity-induced, anisotropic dispersion (Yuan et al, 2017), depending on different scenarios and applications. Previous studies indicate that the dispersion anisotropy does not affect the qualitative features of flow dynamics (Ghesmat & Azaiez, 2008;Jha et al, 2011;Sabet et al, 2020;Zimmerman & Homsy, 1991). Therefore, in this work, we use a constant 𝐴𝐴 𝐴𝐴 and will solve the equations in dimensionless form.…”

“…At the right boundary (outlet), fluids are allowed to flow out freely. In direction, a periodic boundary condition is employed (Islam & Azaiez, 2005; Sabet et al., 2020; Tan & Homsy, 1988).…”

“…The traditional convection‐diffusion/dispersion equation can well characterize such displacement process. Since then, researchers used similar assumption for VF instability in a variety of scenarios for dispersion (Zimmerman & Homsy, 1991), heat transfer (Islam & Azaiez, 2010), mixing (Jha et al., 2011), inertia (Yuan & Azaiez, 2015), gravity effects (Shahraeeni et al., 2015), melting (Sajjadi & Azaiez, 2016), adsorption (Mishra et al., 2007; Rana et al., 2019), reaction (De Wit, 2020), or deposition (Sabet et al., 2020) in a simple Hele‐Shaw cell (Sharma et al., 2020), heterogeneous (Tchelepi & Orr, 1994), or structured porous media (Al‐Housseiny et al., 2012; Rabbani et al., 2018). Conventionally, it is believed that the concentration of injected fluids is nearly 100% behind the VF trailing front in swept area, that is, no displaced fluid is left in this region.…”

Lattice Boltzmann Simulation of Multicomponent Porous Media Flows With Chemical Reaction

“…Continuum models were built to describe fingering properties and classify different fingering regimes under the effects of chemical dissolution [24,25]. In the presence of precipitation reactions, viscous fingering was modeled and found to be intensified [26,27]. In some applications, like in situ combustion for heavy oil recovery, the combustion between hot air and solid fuels, as a typical form of heterogeneous reaction, releases heat to change fluid properties [28].…”