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Conventional concepts for transport in porous media assume that the heterogeneous distribution of hydraulic conductivities is the source for the contaminant temporal and spatial heavy tail. This tailing, known as anomalous or non-Fickian transport, can be captured by the β parameter in the continuous-time random walk framework. This study shows that with the increase in spatial correlation length between these heterogeneous distributions of hydraulic conductivities, the transport’s anomaly reduces; yet, the β value is unchanged, suggesting a topological component of the conductivity field, captured by the β . This finding is verified by an analysis of the solute transport, showing that the changing conductivity values have a moderate effect on the transport shape.

Monotonously stratified porous medium, where the layered medium changes its hydraulic conductivity with depth, is present in various systems like tilled soil and peat formation. In this study, the flow pattern within a monotonously stratified porous medium is explored by deriving a non-dimensional number, Fhp, from the macroscopic Darcian-based flow equation. The derived Fhp theoretically classifies the flow equation to be hyperbolic or parabolic, according to the hydraulic head gradient length scale, and the hydraulic conductivity slope and mean. This flow classification is explored numerically, while its effect on the transport is explored by Lagrangian particle tracking (LPT). The numerical simulations show the transition from hyperbolic to parabolic flow, which manifests in the LPT transition from advective to dispersive transport. This classification is also applied to an interpolation of tilled soil from the literature, showing that, indeed, there is a transition in the transport. These results indicate that in a monotonously stratified porous medium, very low conducting (impervious) formations may still allow unexpected contamination leakage, specifically for the parabolic case. This classification of the Fhp to the flow and transport pattern provides additional insight without solving the flow or transport equation only by knowing the hydraulic conductivity distribution.

We use a particle tracking approach to analyze the dynamics that control bimolecular reactive transport (A + B → C) in porous media. Particle transitions are governed by spatial and temporal distributions to account for the transport within a continuous time random walk framework. Particle tracking simulations are compared to measurements from a laboratory experiment of bimolecular reactive transport in a constant flow field. The simulations capture the experimental sequence of evolving C particle profiles using a marginally Fickian temporal distribution to quantify the particle transitions. The first profile is a fit with the model parameters, and subsequent ones are predictions. The rate of production of reaction product C over time is found to follow a power law. At early times after the injection of A particles into a uniform distribution of B particles, the strong contact and reaction between A and B particles induces the formation of a spatial void between the reactants. At longer times, the production of C is nearly constant and depends on the fluctuations of velocities of reactant particles that can surmount the void. We probe the behavioral dependence of the A, B, and C spatial profiles on the spectra of velocity fluctuations of the reactants. The latter are generated by different temporal distributions, namely, a decaying exponential distribution, which is equivalent to advective‐dispersive (Fickian) transport, and the truncated power law with degrees of non‐Fickian behavior, which is characteristic of transport in heterogeneous media. We demonstrate that the C profile exhibits subtle dynamics because of competition between the dispersion (spreading of the plumes) of A and B and the (power law) production rate.

We characterize the role of preferential pathways in controlling the dynamics of bimolecular reactive transport in a representative model of a heterogeneous porous medium. We examine a suite of numerical simulations that quantifies the irreversible bimolecular reaction A + B → C , in a two-dimensional heterogeneous domain (with log-conductivity, Y ), wherein solute A is injected along an inlet boundary to displace the resident solute B under uniform (in the mean) flow conditions. We explore the feedback between the reactive process and (a) the degree of system heterogeneity, as quantified by the unconditional variance of Y , 1 ≤ σ Y 2 ≤ 7 , representing moderately to strongly heterogeneous media, and (b) the relative strengths of advective and diffusive mechanisms, as quantified by a grid Péclet number, Pe Δ . Our analysis is based on the identification of particle preferential pathways, focusing on particle residence time within cells employed to discretize the flow domain. These preferential pathways are formed mainly by high conductivity cells and generally contain an important component of (sometimes isolated and a relatively small number of) lower conductivity values. A key finding of our analysis is that while the former dominate the behavior, the latter are shown to provide a non-negligible contribution to the global number of reactions taking place in the domain for strongly heterogeneous media, i.e., for the largest investigated values of σ Y 2 . Reactions are detected across the complete simulation time window (of about 5.5 pore volumes) for the strongly advective case. When diffusion plays an important role, the reactive process essentially stops after the injection of a limited amount ( ∼ 2.5) of pore volumes.

Fluid injection into underground rocks plays a crucial role in various geoengineering applications. While injection‐induced deformation is often associated with tensile and shear failures, the feasibility of flow‐driven compaction localization remains largely unexplored. In this study, we investigate the formation of compaction localizations in a rock‐like porous medium composed of sintered polymethyl methacrylate beads, using high‐resolution image analysis. By tracking deformation in real‐time, we reveal a complex localization process that couples compaction with shear. Moreover, following the initial localization, we observe a transient loss and subsequent recovery of stiffness within the medium. These findings suggest that flow‐induced compaction localizations likely play a significant role in field‐scale deformation processes, particularly in high‐porosity rock formations subjected to pressurized flow.

Chemical weathering of soil and rock is a complex geophysical process during which the reaction and transport processes in the porous medium interact, causing erosion of the medium. This process is ubiquitous in geophysical systems and can be encountered, among others, in formation of karst systems, subsurface carbon sequestration and surface weathering of river beds. A common outcome of chemical weathering is the emergence and intensification of preferential flow paths, where the weathering alters the transport properties of the rock, thus introducing coupling between transport and reaction. While numerous approaches have been undertaken to simulate this complex interaction, still a need exists for a unified framework able to correlate the emergence of preferential flow paths due to reaction-transport interaction with the associated dissipative dynamics. Here we propose such a framework considering the case of subsurface chemical weathering of calcite porous rock undergoing reversible dissolution-precipitation reaction, and apply non-equilibrium thermodynamics to analyze the ensuing reaction-transport interaction in this geophysical scenario. We identify the entropy generation sources, attributed to the dissipative processes inherent to this physical scenario and show a clear correlation between the emergence and intensification of preferential flow paths and the accompanying dissipative dynamics, where the evolution of the emerging paths leads to a decrease in the free-energy dissipation rate due to flow percolation, mixing of chemical constituents and reaction. This indicates that the emergence of preferential flow paths due to chemical weathering in geophysical systems represents an energetically-preferred state of the system that can be considered a manifestation of the minimum energy dissipation principle. Our analysis implies that, for a given pressure head, a more homogeneous porous matrix will result in less pronounced preferential flow paths, along with lower flow and higher mineralization rates. On the other hand, for a highly heterogeneous matrix dominant preferential flow paths will be obtained, along with higher flow and lower mineralization rates. Considering these aspects for carbon sequestration where acidified brine leads to carbon mineralization, we conclude that, for a given pressure head, an injection into a more heterogeneous matrix will result in a higher injection rate, while a more homogeneous domain will yield a higher mineralization rate, thus exemplifying the resulting trade-off in the injection strategy.

Dissolution and precipitation processes in reactive transport in porous media are ubiquitous in a multitude of contexts within the field of Earth sciences. In particular, the dynamic interaction between the reactive dissolution and precipitation processes and the solute transport is of interest as it is capable of giving rise to the emergence of preferential flow paths in the porous host matrix. It has been shown that the emergence of preferential flow paths can be considered to be a manifestation of transport self-organization in porous media as these create spatial gradients that distance the system from the state of perfect mixing and allow for a faster and more efficient fluid transport through the host matrix. To investigate the dynamic feedback between the transport and the reactive processes in the field and its influence on the emergence of transport self-organization, we consider a two-dimensional Darcy-scale formulation of a reactive-transport setup, where the precipitation and dissolution of the host matrix are driven by the injection of an acid compound, establishing local equilibrium with the resident fluid and an initially homogeneous porous matrix, composed of a calcite mineral. The coupled reactive process is simulated in a series of computational analyses employing the Lagrangian particle-tracking (LPT) approach, capable of capturing the subtleties of the multiple-scale heterogeneity phenomena. We employ the Shannon entropy to quantify the emergence of self-organization in the field, which we define as a relative reduction in entropy compared to its maximum value. Scalability of the parameters, which characterize the evolution of the reactive process, with the Peclet number in an initially homogeneous field is derived using a simple one-dimensional ADRE model with a linear adsorption reaction term and is then confirmed through numerical simulations, with the global reaction rate, the mean value, and the variance of the hydraulic-conductivity distribution in the field all exhibiting dependency on the reciprocal of the Peclet number. Our findings show that transport self-organization in an initially homogeneous field increases with time, along with the emergence of the field heterogeneity due to the interaction between the transport and reactive processes. By studying the influence of the Peclet number on the reactive process, we arrive at a conclusion that self-organization is more pronounced in diffusion-dominated flows, characterized by small Peclet values. The self-organization of the breakthrough curve exhibits the opposite tendencies, which are observed from the perspective of a thermodynamic analogy. The hydraulic power, required to maintain the driving head pressure difference between the inlet and outlet of the field, was shown to increase with the increasing variance, as well as with the increasing mean value of the hydraulic-conductivity distribution in the field, using a simple analytic model. This was confirmed by numerical experiments. This increase in power, supplied to the flow in the field, results in an increase in the level of transport self-organization. Employing a thermodynamic framework to investigate the dynamic reaction–transport interaction in porous media may prove to be beneficial whenever the need exists to establish relations between the intensification of the preferential flow path phenomenon, represented by a decline in the Shannon entropy of the transport, with the amount of reaction that occurred in the porous medium and the change in its heterogeneity.

Patterns of distinct preferential pathways for fluid flow and solute transport are ubiquitous in heterogeneous, saturated and partially saturated porous media. Yet, the underlying reasons for their emergence, and their characterization and quantification, remain enigmatic. Here we analyze simulations of steady-state fluid flow and solute transport in two-dimensional, heterogeneous saturated porous media with a relatively short correlation length. We demonstrate that the downstream concentration of solutes in preferential pathways implies a downstream declining entropy in the transverse distribution of solute transport pathways. This reflects the associated formation and downstream steepening of a concentration gradient transversal to the main flow direction. With an increasing variance of the hydraulic conductivity field, stronger transversal concentration gradients emerge, which is reflected in an even smaller entropy of the transversal distribution of transport pathways. By defining “self-organization” through a reduction in entropy (compared to its maximum), our findings suggest that a higher variance and thus randomness of the hydraulic conductivity coincides with stronger macroscale self-organization of transport pathways. Simulations at lower driving head differences revealed an even stronger self-organization with increasing variance. While these findings appear at first sight striking, they can be explained by recognizing that emergence of spatial self-organization requires, in light of the second law of thermodynamics, that work be performed to establish transversal concentration gradients. The emergence of steeper concentration gradients requires that even more work be performed, with an even higher energy input into an open system. Consistently, we find that the energy input necessary to sustain steady-state fluid flow and tracer transport grows with the variance of the hydraulic conductivity field as well. Solute particles prefer to move through pathways of very high power in the transversal flow component, and these pathways emerge in the vicinity of bottlenecks of low hydraulic conductivity. This is because power depends on the squared spatial head gradient, which is in these simulations largest in regions of low hydraulic conductivity.

pH-induced reactive transport in porous environments is a critical factor in Earth sciences, influencing a range of natural and anthropogenic processes, such as mineral dissolution and precipitation, adsorption and desorption, microbial reactions, and redox transformations. These processes, pivotal to carbon capture and storage (CCS) applications to groundwater remediation, are determined by pH transport. However, the uncertainty in these macroscopic processes’ stems from pore-scale heterogeneities and the high diffusion value of the ions and protons forming the pH range. While practical for field-scale applications, traditional macroscopic models often fail to accurately predict experimental and field results in reactive systems due to their inability to capture the details of the pore-scale pH range. This study investigates the interplay between transverse mixing and pH-driven reactions in porous media. It focuses on how porous structure and flow rate affect mixing and chemical reaction dynamics. Utilizing confocal microscopy, the research visualizes fluorescently labeled fluids, revealing variations in mixing patterns from diffusive in homogeneous to shear-driven in heterogeneous media. However, pH-driven reactions show a different pattern, with a faster reaction rate, suggesting quicker pH equilibration between co-flowing fluids than predicted by transverse dispersion or diffusion. The study highlights the unique characteristics of pH change in water, which significantly influences reactive transport in porous media.

Our study investigates interplays between dissolution, precipitation, and transport processes taking place across randomly heterogeneous conductivity domains and the ensuing spatial distribution of preferential pathways. We do so by relying on a collection of computational analyses of reactive transport performed in two-dimensional systems where the (natural) logarithm of conductivity is characterized by various degrees of spatial heterogeneity. Our results document that precipitation and dissolution jointly take place in the system, with the latter mainly occurring along preferential flow paths associated with the conductivity field and the former being observed at locations close to and clearly separated from these. High conductivity values associated with the preferential flow paths tend to further increase in time, giving rise to a self-sustained feedback between transport and reaction processes. The clear separation between regions where dissolution or precipitation takes place is imprinted onto the sample distributions of conductivity which tend to become visibly left skewed with time (with the appearance of a bimodal behavior at some times). The link between conductivity changes and reaction-driven processes promotes the emergence of non-Fickian effective transport features. The latter can be captured through a continuous-time random-walk model where solute travel times are approximated with a truncated power law probability distribution. The parameters of such a model shift towards values associated with increasingly high non-Fickian effective transport behavior as time progresses.