A new benchmark reference solution for double-diffusive convection in a heterogeneous porous medium

Time-dependent solution for natural convection in a porous enclosure using the Darcy–Lapwood–Brinkman model

The Fourier-Galerkin (FG) method is used to produce a highly accurate solution for free convection in a square cavity filled with heterogeneous porous medium. To this end, the governing equations are reformulated in terms of the temperature and the stream function. These unknowns are then expanded in infinite Fourier series truncated at given orders. The accuracy of the FG solution is investigated for different truncation orders and compared to the results of an advanced finite-element numerical model using fine-mesh discretization. The obtained results represent a set of high-quality data that can be used for benchmarking numerical models.

Three-dimensional natural convection, entropy generation and mixing in heterogeneous porous medium

The relationship between the scale-dependent dispersivity and heterogeneous sedimentary structures is investigated through conducting non-reactive tracer experiments in a three-dimensional heterogeneous sand tank. The heterogeneous porous media consists of three sedimentary facies of silty, fine, and medium sands collected from the west of the Songnen Plain, China. Moreover, several corresponding individual facies soil columns were constructed for comparison. A conservative tracer was continuously injected from an upstream source. The effective parameters were estimated by inverse modeling of a one-dimensional transport model. The results show that the scale dependence of the estimated dispersivities was discovered in the individual facies column (with relatively weaker effect) and the heterogeneous porous media (with more significant effect). With increasing transport distances, the dispersivities of the individual facies tend to reach an asymptotic value, while those of the heterogeneous media increase continuously. Furthermore, the results show that a power function can describe the relationship between effective dispersivities and transport distances. The exponent of the function is greater than one for the heterogeneous media, but less than one for the individual facies. The results also indicate that the dispersion plume is macroscopically dominated by the distribution of facies. The heterogeneity of hydraulic conductivity causes the variations of flow velocity, which further enhances the scale dependence of dispersivities. The tracer experiment in heterogeneous media provides the fundamental insight into the understanding of contaminant transport processes.

Knowledge of solute transport in heterogeneous porous media is crucial to monitor contaminant fate and transport in soil and groundwater systems. In this study, we present new findings from experimental and mathematical analysis to improve current understanding of solute transport in structured heterogeneous porous media. Three saturated columns packed with different sand combinations were used to examine the breakthrough behavior of bromide, a conservative tracer. Experimental results showed that bromide had different breakthrough responses in the three types of sand combinations, indicating that heterogeneity in hydraulic conductivity has a significant effect on the solute transport in structured heterogeneous porous media. Simulations from analytical solutions of a two-domain solute transport model matched experimental breakthrough data well for all the experimental conditions tested. Experimental and model results show that under saturated flow conditions, advection dominates solute transport in both fast-flow and slow-flow domains. The sand with larger hydraulic conductivity provided a preferential flow path for solute transport (fast-flow domain) that dominates the mass transfer in the heterogeneous porous media. Importantly, the transport in the slow-flow domain and mass exchange between the domains also contribute to the flow and solute transport processes and thus must be considered when investigating contaminant transport in heterogeneous porous media.

Double-diffusive natural convection in a rectangular fluid-saturated porous medium has been studied analytically and numerically. The analysis reveals that there is a range of buoyancy ratios N in which one obtains two types of solutions or oscillating convection. In the case of 0.4 < N < 1.0, there exist two analytical solutions when Rc = 100 and Le = 30. In that case, two solutions, temperature-dominated and concentration-dominated solutions, are calculated when the aspect ratio is small. It is found that the oscillation is due to a temporal formation of a two-roll flow pattern in the cavity when the aspect ratio is sufficiently large. The oscillation of time-dependent Nusselt number and flow patterns are shown. © 1999 Scripta Technica, Heat Trans Asian Res, 28(4): 255–265, 1999

Radial flows in heterogeneous porous media with a linear injection scheme

Preferential flow channeling and viscous fingering are widely observed phenomena in heterogeneous porous media from the pore scale to the core and reservoir scales. The transition from capillary to viscous fingering with increasing injection rate is also a well‐known phenomenon. Based on the previously observed visual similarity of viscous fingers and preferential single‐phase flow paths in 2‐D simulations, we postulate that these single‐ and two‐phase flow patterns should also be interrelated in 3‐D porous media. Capillary fingering is a manifestation of invasion percolation, a process restricted to the subnetwork of pores obtained from the critical path analysis. We investigated single‐phase flow channeling by applying a method similar to critical path analysis to the flow rate field and compared the subnetwork thus determined to the set of invaded pipes in drainage simulations. Our aim is to quantify the relation between preferential flow paths and viscous fingering, its dependence on pore‐scale heterogeneity and pore connectivity, and ultimately to upscale the network observations to the field scale appropriate for the engineering applications involving drainage in heterogeneous media.

The Method of Finite Averages: A rigorous upscaling methodology for heterogeneous porous media

Discontinuous Galerkin approximation of two-phase flows in heterogeneous porous media with discontinuous capillary pressures

Finite analytic numerical method for two-dimensional fluid flow in heterogeneous porous media

Mixing is the process that homogenizes initially segregated miscible constituents, increases the volume occupied by a solute, and decreases concentration peaks. It is important for the assessment of contamination levels and biogeochemical reactions in groundwater and soils. Mixing processes are governed by the interplay of fluid advection, molecular diffusion and local-scale dispersion at Darcy scale. Here we study the mechanisms of mixing in three-dimensional Darcy scale porous media with different heterogeneity structure. We analyze the role of medium and flow topology on the mixing and dispersion behavior. To this end, we perform Darcy-scale numerical simulations of incompressible flow and transport in heterogeneous three-dimensional porous media. Hydraulic conductivity is represented as a multi-Gaussian random field with lognormal marginal distribution. We consider isotropic and anisotropic correlation structures and scalar and tensorial conductivity. Flow is solved using a finite volume two-point method and transport using a Lagrangian approach. The flow topology is quantified by the helicity of the velocity field. We consider a planar injection of particles. Dispersion is quantified by the longitudinal and transverse dispersion coefficient, which are determined by the evolution along time of the position&amp;#8217;s variance in the respective direction divide by two. It is also quantified by the breakthrough curves, which measure the distribution of arrival times at a given position from the initial one. Mixing is quantified by the ability of the flow to stretch and elongate a fluid strip which enhances diffusion through the creation and sustaining of concentration gradients. Results show that for a helical flow, a finite transverse dispersion coefficient is observed at long times and that the elongation of elemental strips follow an exponential stretching &amp;#160;(for large logK variances). On the contrary, on non-helical flows, transverse dispersion tends asymptotically to zero and the stretching rate is algebraic. The longitudinal dispersion coefficient seems unaffected by the helicity of the flow. These results shed light on the relation between medium structure and flow topology on mixing, making an important step towards the control, upscaling and large scale representation of mixing in porous media . &amp;#160;

Density driven flow in CO2 storage sites: A new formulation for heterogeneous layered porous media

Simulating solute transport in heterogeneous porous media poses computational challenges due to the high-resolution meshing required for traditional solvers. To overcome these challenges, this study explores a mesh-free method based on deep learning to accelerate solute transport simulation. We employ Physics-informed Neural Networks (PiNN) with a periodic activation function to solve solute transport problems in both homogeneous and heterogeneous porous media governed by the advection-dispersion equation. Unlike traditional neural networks that rely on large training datasets, PiNNs use strong-form mathematical models to constrain the network in the training phase and simultaneously solve for multiple dependent or independent field variables, such as pressure and solute concentration fields. To demonstrate the effectiveness of using PiNNs with a periodic activation function to resolve solute transport in porous media, we construct PiNNs using two activation functions, sin and tanh, for seven case studies, including 1D and 2D scenarios. The accuracy of the PiNNs’ predictions is then evaluated using absolute point error and mean square error metrics and compared to the ground truth solutions obtained analytically or numerically. Our results demonstrate that the PiNN with sin activation function, compared to tanh activation function, is up to two orders of magnitude more accurate and up to two times faster to train, especially in heterogeneous porous media. Moreover, PiNN’s simultaneous predictions of pressure and concentration fields can reduce computational expenses in terms of inference time by three orders of magnitude compared to FEM simulations for two-dimensional cases.

Vadose Zone JournalVolume 15, Issue 4 vzj2016.01.0008br p. 1-3 Book Review Review of Flow Through Heterogeneous Geologic Media Hongbin Zhan, Hongbin Zhan zhan@geos.tamu.edu Dep. of Geology and Geophysics, Texas A& M University, College Station, TX, 77843-3115Search for more papers by this author Hongbin Zhan, Hongbin Zhan zhan@geos.tamu.edu Dep. of Geology and Geophysics, Texas A& M University, College Station, TX, 77843-3115Search for more papers by this author First published: 15 April 2016 https://doi.org/10.2136/vzj2016.01.0008brCitations: 1 All rights reserved. Read the full textAboutRelatedInformationPDFPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessClose modalShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL No abstract is available for this article.Citing Literature Volume15, Issue4April 2016Pages 1-3 RelatedInformation RecommendedFlow Through Heterogeneous MediaLarry G. King, Drainage for Agriculture, [1]Characterizing Heterogeneous Processes of Water Flow and Solute Transport in Soils Using Multiple Tracer ExperimentsKang Wang, Renduo Zhang, Feng Sheng, Vadose Zone JournalNonaqueous‐Phase Liquid Infiltration and Immobilization in Heterogeneous Media: 2. Application to Stochastically Heterogeneous FormationsF. Fagerlund, T.H. Illangasekare, A. Niemi, Vadose Zone JournalField‐Scale Analysis of Flow Mechanisms in Highly Heterogeneous Mining MediaG. Webb, S.W. Tyler, J. Collord, D. Van Zyl, T. Halihan, J. Turrentine, T. Fenstemaker, Vadose Zone JournalSimulation of Channelized Gas Flow Pattern in Heterogeneous Porous Media: A Feasibility Study of Continuum Simulation at Bench ScaleShirin Samani, Helmut Geistlinger, Vadose Zone Journal