Influence of Grain Size Transition on Flow and Solute Transport through 3D Layered Porous Media

Soils and other geologic porous media often have contrasting grain size layers associated with a grain size transition zone between layers. However, this transition zone is generally simplified to a plane of zero thickness for modeling assumption, and its influence has always been neglected in previous studies. In this study, an approach combining a deposition process and a random packing process was developed to generate 3D porous media without and with consideration of the transition zone. The direct numerical models for solving the flow and concentration fields were implemented to investigate the influence of the grain size transition on flow and solute transport. Our results showed that although the transition zone occupied 13.6% of the entire layered porous medium, it had little influence on the distribution of flow velocity at the scale of the entire layered porous medium. However, the transition zone had a significant influence on the local flow field, which was associated with the increased spatial variability of velocity and the varied distribution of flow velocity. This varied local flow field could increase the solute residence time and delay the breakthrough time for solute transport. Although using both the advection-dispersion equation (ADE) and the mobile and immobile (MIM) models to fit the breakthrough curves (BTCs) for solute transport through layered porous media resulted in trivial errors, the ADE model failed to capture the influence induced by the local flow field, especially the influence of the transition zone. In contrast, the MIM model was shown to be able to capture the influence of the transition on solute transport. It was found that the mass transfer rate α, a parameter of the MIM model, was significantly improved by the presence of the transition zone, while it decreased as the transition zone fraction increased. Our study emphasized that the transition zone can vary the local flow field at the pore scale, while it has little influence on the hydraulic properties (e.g., hydraulic conductivity) of the macroscale flow field. However, the local flow field varied by the transition zone has a significant influence on solute transport.

An Improved Picard Iteration Scheme for Simulating Unsaturated Flow in Layered Porous Media

Picard iteration method is commonly used to obtain numerical solution of unsaturated flow in porous media. However, because the system of linear equations derived from Richards equation is seriously ill-conditioned, Picard iteration has slow convergence rate and low computational efficiency, particularly in layered porous media. In this study, control volume method based on non-uniform nodes is used to discrete Richards equation. To improve the convergence rate of Picard iteration, we combine the non-uniform multigrid correction method with the multistep preprocessing technology. Thus, an improved Picard iteration scheme with multistep preconditioner based on non-uniform multigrid correction method (NMG-MPPI(m)) is proposed to model 1D unsaturated flow in layered porous media. Three test cases were used to verify the proposed schemes. The result shows that the condition number of the coefficient matrix has been greatly reduced using the multistep preconditioner. Numerical results indicate that NMG-MPPI(m) can solve Richards equation at a faster convergence rate, with higher calculation accuracy and good robustness. Compared with conventional Picard iteration, NMG-MPPI(m) shows a very high speed-up ratio. As a result, the improved Picard iteration scheme has good application for simulating unsaturated flow in layered porous media.

Modeling Transient Flows in Heterogeneous Layered Porous Media Using the Space–Time Trefftz Method

In this study, we developed a novel boundary-type meshless approach for dealing with two-dimensional transient flows in heterogeneous layered porous media. The novelty of the proposed method is that we derived the Trefftz space–time basis function for the two-dimensional diffusion equation in layered porous media in the space–time domain. The continuity conditions at the interface of the subdomains were satisfied in terms of the domain decomposition method. Numerical solutions were approximated based on the superposition principle utilizing the space–time basis functions of the governing equation. Using the space–time collocation scheme, the numerical solutions of the problem were solved with boundary and initial data assigned on the space–time boundaries, which combined spatial and temporal discretizations in the space–time manifold. Accordingly, the transient flows through the heterogeneous layered porous media in the space–time domain could be solved without using a time-marching scheme. Numerical examples and a convergence analysis were carried out to validate the accuracy and the stability of the method. The results illustrate that an excellent agreement with the analytical solution was obtained. Additionally, the proposed method was relatively simple because we only needed to deal with the boundary data, even for the problems in the heterogeneous layered porous media. Finally, when compared with the conventional time-marching scheme, highly accurate solutions were obtained and the error accumulation from the time-marching scheme was avoided.

Solutal Convection in Layered Sorbing Porous Media

<p>We study convective instability in the vertically layered porous media saturated with mixture. The mixture consists of a carrier fluid and solid nanoparticles. The nanoparticles are considered as solute within the continuous approach. The porous media are two horizontal sublayers with different permeabilities. The solute concentration is maximal near the upper boundary and is zero near the lower boundary of the superposed sublayers. Thus, one has suitable conditions for the onset of solutal convection in the gravitational field.</p><p>The porous sublayers are reactive media, which can absorb nanoparticles. The mixture transport here is accompanied by immobilization. It is described by the mobile/immobile media model. The mobile phase is carried by fluid flow, while the immobile phase is absorbed by porous matrix. The linear kinetic equation for the mixture redistribution between the phases is applied. The Boussinesq approximation is used in the equations for convection in each of the sublayers. Numerical simulation is performed by the shooting method.</p><p>We apply a linear stability theory to find the threshold Rayleigh-Darcy number for the onset of solutal convection. This similarity criterion is determined through the average permeability and porosity of uncontaminated porous sublayers. For the first time, we introduce a solutal pore shrinkage coefficient, which is analogous to the thermal expansion coefficient for thermal natural convection. This coefficient shows that porosity decreases as the concentration of immobile phase grows in the presence of sorption. Particles in this case join the surface of pores and shrink the void space.</p><p>Firstly, we find the permeability ratios for bimodal marginal stability curves in the uncontaminated sublayers. Here, the sublayer permeabilities differ by approximately 100 times. The bimodal curves demonstrate the competition between two convective instabilities. One of them is for the local convective rolls that generate within the more permeable layer and the other is for the large-scale rolls penetrating both layers. The rolls are similar to thermal natural convection in the multi-layered porous media studied by McKibbin and O'Sullivan (1980). For sorbing porous media, the type of convective rolls strongly depends on the solutal pore shrinkage coefficient. Even a small change in its value can produce a large variation of flow streamlines from the convective rolls localized within the upper highly permeable sublayer to the rolls covering both the upper and lower sublayers. The observed sorption effect on the transition from local to large-scale convection is due to the fact that the permeability ratio depends on the solutal pore shrinkage coefficient. It is also found that sorption effect delays the onset of solutal convection.</p><p>The work was supported by the Russian Science Foundation (Grant No. 20-11-20125).</p>

Solute Driven Transient Convection in Layered Porous Media

CO2 geological sequestration has been proposed as a climate change mitigation strategy that can contribute towards meeting the Paris Agreement. A key process on which successful injection of CO2 into deep saline aquifer relies on is the dissolution of CO2 in brine. CO2 dissolution improves storage security and reduces risk of leakage by (i) removing the CO2 from a highly mobile fluid phase and (ii) triggering gravity-induced convective instability which accelerates the downward migration of dissolved CO2. Our understanding of CO2 density-driven convection in geologic media is limited. Studies on transient convective instability are mostly in homogeneous systems or in systems with heterogeneity in the form of random permeability distribution or dispersed impermeable barriers. However, layering which exist naturally in sedimentary geological formations has not received much research attention on transient convection. Therefore, we investigate the role of layering on the onset time of convective instability and on the flow pattern beyond the onset time during CO2 storage. We find that while layering has no significant effect on the onset time, it has an impact on the CO2 flux. Our findings suggest that detailed reservoir characterisation is required to forecast the ability of a formation to sequester CO2.

Study of Polymer Flooding Behavior in Heterogeneous Two-Layered Porous Media

<em>In this paper, a numerical study was conducted to investigate the effect of spatial heterogeneity of multiple porosity fields on oil recovery, residual oil saturation, polymer retained, and polymer adsorption. The generated porosity fields were applied to UTCHEM for simulating polymer and water flooding in heterogeneous two-layered porous media. From the analysis, the increase of reservoir heterogeneity resulted in higher polymer retention and lower polymer adsorption. In general, polymer flooding results in more balance residual oil saturation in the upper and lower layer than water flooding. This indicated that the vertical sweep efficiency of polymer flooding was better than water flooding. Residual oil saturation ratio between layers after water or polymer flooding was about equal along with the increase of reservoir heterogeneity. Spatial heterogeneity of multiple porosity fields had only a small effect on recovery factor. The variation of the recovery factor of polymer and water flooding due to the reservoir heterogeneity was under 1%</em>.