Pore-scale Reactive Transport Model Research Articles

Numerical modeling and simulation of microbially induced calcite precipitation on a cement surface at the pore scale

Accurate estimation of contaminant transport in cementitious material using numerical tools plays a key role in the risk assessments of nuclear waste disposal. At the pore scale, the increase of microbial activity, such as microbially induced calcite precipitation on cementitious material, causes changes in solid surface topography, pore network geometry, and pore water chemistry, which affect contaminant transport at the core scale and beyond. Consequently, a meaningful estimation of contaminant migration in the subsurface requires a pore-scale investigation of the influence of microbial activity on transport processes. In this study, a pore-scale reactive transport model is presented to simulate the physicochemical processes resulting from microbially induced calcite precipitation on a cement surface. Numerical investigations focus on modeling the reactive transport in a two-dimensional flow-through cell. The model results are validated by experimental data showing an increase in pH and a decrease in calcium concentration due to microbially induced calcite precipitation. Our results show heterogeneous calcite precipitation under transport-limited conditions and homogeneous calcite precipitation under reaction-limited conditions, resulting in non-uniform and uniform changes in the material surface topography. Moreover, power spectral density analysis of the surface data demonstrates that microbially induced calcite precipitation affects the surface topography via both general changes over the entire frequency and local modifications in the high-frequency region. The sensitivity studies provide a comprehensive understanding of the evolution of surface topography due to the microbially induced calcite precipitation at the pore scale, thus contributing to an improved predictability of contaminant transport at the core scale and beyond.

A reactive transport modeling perspective on the dynamics of interface-coupled dissolution-precipitation

In interface coupled dissolution-precipitation systems, the dynamics of the mineral-fluid interface depends on two intertwining processes: the dissolution of the primary mineral that is needed for subsequent precipitation and the passivation of the dissolution reaction as a result of secondary mineral precipitation. The resulting thickness and texture of the precipitating coating layer will affect the progression of geochemical reactions, flow and transport processes at the macroscopic scale. Understanding the interplay between macroscopic flow regimes and microscopic reaction mechanisms (e.g., nucleation and crystal growth pathways) in controlling the dynamics of the mineral-fluid interface has important implications for predicting natural weathering processes, scaling in the subsurface energy production systems, etc. In this study, we use a micro-continuum pore-scale reactive transport model to investigate the feedback loop between reaction rate and solute transport with explicit consideration of the surface passivation and the diffusion process through the coating layer, as well as the impacts of saturation-dependent nucleation rate on the textures of precipitates that will largely dictate the diffusion properties of the coating layer. Our model results highlight that the drastically different coating behaviors at the macroscopic scale and their dependence on solution supersaturation observed in previous column experiments are primarily controlled by the interplay between mineral reaction rates, advective flow, and diffusion through the dynamically forming coating layer. The diffusion properties of the coating layer also play a secondary but non-negligible role in shaping the evolution of the co-dissolution and precipitation system. The probabilistic nucleation model building on the framework of classical nucleation theory highlights the complex dependence of precipitates’ texture on solution chemistry and substrate properties, which can affect the diffusion process within the precipitates. The modeling observations also underscore the necessity of further investigations to better characterize the properties of the coating layer and to improve modeling descriptions of the nucleation processes.

Pore-Scale Study to Analyze the Impacts of Porous Media Heterogeneity on Mineral Dissolution and Acid Transport Using Darcy–Brinkmann–Stokes Method

Inherent pore structure of rocks has a significant impact on the acid–rock interaction during the acidizing process. In this study, a new pore-scale reactive transport model applying Darcy–Brinkmann–Stokes method has been developed based on the open-source computational fluid dynamics platform, OpenFOAM, and validated with experimental results. By solving the mass balance equation and advection–diffusion equation, the developed numerical simulation model could capture the evolving pore structure and track the distribution of transported acid. The impacts of different grain sizes and distributions on the dissolution rate of mineral (calcite), evolving porosity, and the transport characteristics of acid have been investigated. In addition, sensitivity analysis has been conducted with respect to the various Damkohler numbers and Peclet numbers in the digital rock image model of Niobrara formation. The changing volume fraction of pores could be categorized into three patterns with different dimensionless numbers—linear growth, pseudo-linear growth, and a flat S-curve growth. The simulation cases of Estaillades carbonate, Massangis Jaune carbonate models, and Sample X segmentation showed that their inherent grain distribution was highly influential on the mineral dissolution rate, where 3-D simulation showed the same results. The developed pore-scale reactive transport model can be applied to various systems with complex pore structures, in order to provide a guidance to predict the system responses such as dissolution rates, surface area, and porosity changes during acidizing in large-scale continuum model.

A multi-level pore scale reactive transport model for the investigation of combined leaching and carbonation of cement paste

Cementitious materials in underground constructions are exposed to CO2 rich ground waters which leads to combined carbonation and calcium leaching. Complex interplay between leaching, carbonation reaction and changes in transport pathways presents difficulty in parameterizing continuum scale models in a consistent way. Therefore, a novel multi-level pore-scale reactive transport model is presented to capture microstructure changes under combined carbonation and leaching. Model explicitly resolves capillary pores and phases with unresolved porosity as a porous media. Governing equations are solved using a lattice Boltzmann method based reactive transport solver with chemical reaction under thermodynamic equilibrium. The two-dimensional parametric study on idealized microstructures revealed that carbon content and pH of boundary solution strongly affects degradation rates, location and thickness of precipitated calcite layer. Furthermore, reactive surface area plays dominant role and tortuosity of media rather a secondary role. The three-dimensional simulations using virtual cement paste microstructure show that degradation rate exhibit non-linear behaviour with square root of time and time. This implies that simple empirical relations for prediction of progression of reaction fronts are not applicable and use of numerical reactive transport models is inevitable.. The developed model qualitatively captures the development of carbonation, leaching fronts and zonation as observed in experiments. Good quantitative agreement between modelling and experiments is obtained for initial stages. At later times, the modelling result and experimental observations diverge significantly. This discrepancy is likely due to lack of consideration of kinetics of C-S-H dissolution and calcite precipitation.

Evolution of pore-shape and its impact on pore conductivity during CO2 injection in calcite: Single pore simulations and microfluidic experiments

Injection of CO2 into carbonate rocks causes dissolution and alters rock transport properties. The extent of the permeability increases, due to the increased pore volume and connectivity, strongly depends on the regimes of transport and dissolution reactions. Identification of these regimes and their parametrization at the microscopic scale is required for an understanding of the injection processes, and, afterward, for calculating the effective macroscopic parameters for field-scale simulations. Currently, a commonly used approach for calculating the rock effective parameters is the Pore Network Method, PNM, but a better understanding of the validity of its basic assumptions and their areas of applicability is essential. Here, we performed a combined microscopic experimental and numerical study to explore pore-shape evolution over a wide range of transport and dissolution reaction regimes. Experiments were conducted by flowing an acidic solution through a microscopic capillary channel in a calcite crystal at two different flow rates. The experimental results were used to validate our pore-scale reactive transport model that could reproduce the measured effluent composition as well as pore shape changes. Two key stages in pore shape evolution were observed, a transient phase and a quasi-steady-state phase. During the first stage, the shape of the single pore evolved very fast, depending on the flow regime. Under advective-dominant flow, the pore shape remained nearly cylindrical, while under diffusive-dominant transport, the pore shape developed into a half-hyperboloid shape. During the quasi-steady-state stage, the pore volume continued to increase, however, without or with diminutive change of the pore shape. In this stage, only a long period of injection may result in a significant deviation of the pore shape from its original cylinder shape, which is a common assumption in PNMs. Furthermore, we quantitatively evaluated the impact of evolved pore shape spectrum on the conductance calculations and compared it to the formulations currently used for pore network modeling of reactive transport. Under low flow rates, neglecting the developed non-uniform pore shape during the non-steady stage may lead to an overestimation of pore conductance up to 80%.

Three-Dimensional Pore-Scale Modeling of Fracture Evolution in Heterogeneous Carbonate Caprock Subjected to CO2-Enriched Brine.

Fractures in caprocks overlying CO2 storage reservoirs can adversely affect the sealing capacity of the rocks. Interactions between acidified fluid and minerals with different reactivities along a fracture pathway can affect the chemically induced changes in hydrodynamic properties of fractures. To study porosity and permeability evolution of small-scale (millimeter scale) fractures, a three-dimensional pore-scale reactive transport model based on the lattice Boltzmann method has been developed. The model simulates the evolution of two different fractured carbonate-rich caprock samples subjected to a flow of CO2-rich brine. The results show that the existence of nonreactive minerals along the flow path can restrict the increase in permeability and the cubic law used to relate porosity and permeability in monomineral fractured systems is therefore not valid in multimineral systems. Moreover, the injection of CO2-acidified brine at high rates resulted in a more permeable fractured media in comparison to the case with lower injection rates. The overall rate of calcite dissolution along the fracture decreased over time, confirming similar observations from previous continuum scale models. The presented 3D pore-scale model can be used to provide inputs for continuum scale models, such as improved porosity-permeability relationships for heterogeneous rocks, and also to investigate other reactive transport processes in the context of CO2 leakage in fractured seals.

Pore-scale study of reactive transport processes in catalyst layer agglomerates of proton exchange membrane fuel cells

Porous structures of agglomerates in cathode catalyst layers (CLs) of proton exchange membrane fuel cells are reconstructed, in which all the four phases are resolved including Platinum, carbon, ionomer and pore. A pore-scale reactive transport model based on the lattice Boltzmann method is developed, in which oxygen dissolution reaction at pore-ionomer interface, oxygen diffusion inside ionomer, and electrochemical reaction at ionomer-Pt interface are considered. Emphasis is put on structural parameters, especially Pt/C mass ratio, on the reactive transport process and the volumetric reaction rate (or current density). Pore-scale results show that while under high Pt loading oxygen is depleted quite close to the surface of the spherical agglomerate, it has to penetrate deep into the porous agglomerate before it is completely consumed under low Pt loading which is not captured by classical agglomerate model based on homogeneous mixture assumption. Pore-scale results also found that effects of transport inside the agglomerate decreases as reaction rate, porosity or ionomer thickness increases. Finally, local transport resistance inside the agglomerate is evaluated, and it increases as the agglomerate size increases or the dissolution reaction rate decreases.

Numerically accelerated pore-scale equilibrium dissolution

Simulation of dissolution processes with a pore-scale reactive transport model increases insight in coupled chemical-physical-transport processes. However, modelling of dissolution process often requires a large number of time steps especially when the buffering capacity of solid phases is high. In this work we analyze the interplay between solid buffering on one hand and transport on the other. Based on this analysis we propose an approach to reduce the number of required time steps for simulating equilibrium dissolution processes. The underlying idea is that the number of time step iterations can be reduced if the buffering is sufficient to bring the system to a steady state, i.e. that the concentration field around solid is time-invariant. If this condition is satisfied, then it is possible to reduce the physical (and thus also computational) time by adjusting the chemical system appropriately. First we derived a dimensionless value - called buffering number - to determine under which conditions reduction in time can be made. Several examples illustrate that below a certain buffering number, the physical time can be reduced without significant effect on result (e.g. dissolution front) as long as the solid volume fraction is sufficient. This means that for a given solid-liquid system, the calculation time can be reduced either by the reduction of mass in solid or by the increase of equilibrium concentration (solubility). We also show that the calculation time for calcium leaching in cementitious systems can be reduced by 50 times with a negligible error.

Predictions of permeability, surface area and average dissolution rate during reactive transport in multi-mineral rocks

The interactions between minerals and reactive fluids have great impact on the pore structure and hydrologic properties of rocks. A 3D pore-scale reactive transport model is applied to predict multi-mineral reactions in porous rocks. Eight mineral phases are distinguished in 2D slices of a reservoir sandstone by using Quantitative Evaluation of Minerals by SCANning electron microscopy (QEMSCAN) imaging technique. The 2D image is then registered into the corresponding cross-section of the 3D rock image obtained from micro-computed tomography (CT) scanning. Reactive transport with chemical dissolution is simulated directly on the 3D image of the sandstone. In the simulations, each mineral is assigned with a specific intrinsic reaction rate constant. The dissolution-induced changes in the pore structure are measured. The pore size distribution of the rock is analysed to investigate the evolution of the pore space. The changes of surface area and permeability are compared with single mineral simulations to illustrate the importance of mineralogical heterogeneity on reactive transport. The results show that the 3D pore-scale mineralogical heterogeneity causes overestimation of the permeability variations during reactive transport. The average effective dissolution rates for the rock are also measured. The simulations with single mineral assumptions present an overall reaction rate which is 10 times higher than the predictions with multi-mineral dissolution at the start of reactions. Relationships between average reaction rate and time are proposed to characterise the evolution of dissolution rate. A correction is also suggested to reduce the errors in predictions of reaction rates with single mineral assumptions.

Application of a pore-scale reactive transport model to a natural analog for reaction-induced pore alterations

Dissolved CO2 in the subsurface resulting from geological CO2 storage may react with minerals in fractured rocks, confined aquifers, or faults, resulting in mineral precipitation and dissolution. The overall rate of reaction can be affected by coupled processes including hydrodynamics, transport, and reactions at the (sub) pore-scale. In this work pore-scale modeling of coupled fluid flow, reactive transport, and heterogeneous reactions at the mineral surface is applied to account for permeability alterations caused by precipitation-induced pore-blocking. This work is motivated by observations of CO2 seeps from a natural CO2 sequestration analog, Crystal Geyser, Utah. Observations along the surface exposure of the Little Grand Wash fault indicate the lateral migration of CO2 seep sites (i.e., alteration zones) of 10–50m width with spacing on the order of ~100m over time. Sandstone permeability in alteration zones is reduced by 3–4 orders of magnitude by carbonate cementation compared to unaltered zones. One granular porous medium and one fracture network systems are used to conceptually represent permeable porous media and locations of conduits controlled by fault-segment intersections and/or topography, respectively. Simulation cases accounted for a range of reaction regimes characterized by the Damköhler (Da) and Peclet (Pe) numbers. Pore-scale simulation results demonstrate that combinations of transport (Pe), geochemical conditions (Da), solution chemistry, and pore and fracture configurations contributed to match key patterns observed in the field of how calcite precipitation alters flow paths by pore plugging. This comparison of simulation results with field observations reveals mechanistic explanations of the lateral migration and enhances our understanding of subsurface processes associated with the CO2 injection. In addition, permeability and porosity relations are constructed from pore-scale simulations which account for a range of reaction regimes characterized by the Da and Pe numbers. The functional relationships obtained from pore-scale simulations can be used in a continuum scale model that may account for large-scale phenomena mimicking lateral migration of surface CO2 seeps.

Changes in porosity, permeability and surface area during rock dissolution: Effects of mineralogical heterogeneity

Effects of heterogeneity of mineral distribution and reaction rate on the rock dissolution process are investigated using a pore-scale reactive transport model based on the lattice Boltzmann method. Coupled fluid flow, species transport, chemical reaction and solid structure alternation due to dissolution are simulated. Effects of mineral distributions and chemical heterogeneity on the dissolution behaviors and evolutions of hydrologic properties are studied under different reactive transport conditions. Simulation results show that the coupling between advection, diffusion and reaction as well as the mineralogical heterogeneity leads to complex reactive transport behaviors and complicated temporal evolutions of hydrologic properties including porosity, permeability and reactive surface. Diverse relationships between surface area and volume are predicted, which cannot be described by simple models such as the spherical-grain model. Porosity-permeability relationships also differ under different mineral distributions and reactive transport conditions. Simulation results indicate that it is extremely challenging to propose general relationships for hydrologic properties for dissolution of rocks with mineralogical heterogeneity, due to the complicated interactions between reactive transport and mineralogical heterogeneity.

Metabolism-Induced CaCO3 Biomineralization During Reactive Transport in a Micromodel: Implications for Porosity Alteration.

The ability of Pseudomonas stutzeri strain DCP-Ps1 to drive CaCO3 biomineralization has been investigated in a microfluidic flowcell (i.e., micromodel) that simulates subsurface porous media. Results indicate that CaCO3 precipitation occurs during NO3(-) reduction with a maximum saturation index (SIcalcite) of ∼1.56, but not when NO3(-) was removed, inactive biomass remained, and pH and alkalinity were adjusted to SIcalcite ∼ 1.56. CaCO3 precipitation was promoted by metabolically active cultures of strain DCP-Ps1, which at similar values of SIcalcite, have a more negative surface charge than inactive strain DCP-Ps1. A two-stage NO3(-) reduction (NO3(-) → NO2(-) → N2) pore-scale reactive transport model was used to evaluate denitrification kinetics, which was observed in the micromodel as upper (NO3(-) reduction) and lower (NO2(-) reduction) horizontal zones of biomass growth with CaCO3 precipitation exclusively in the lower zone. Model results are consistent with two biomass growth regions and indicate that precipitation occurred in the lower zone because the largest increase in pH and alkalinity is associated with NO2(-) reduction. CaCO3 precipitates typically occupied the entire vertical depth of pores and impacted porosity, permeability, and flow. This study provides a framework for incorporating microbial activity in biogeochemistry models, which often base biomineralization only on SI (caused by biotic or abiotic reactions) and, thereby, underpredict the extent of this complex process. These results have wide-ranging implications for understanding reactive transport in relevance to groundwater remediation, CO2 sequestration, and enhanced oil recovery.

Pore and continuum scale study of the effect of subgrid transport heterogeneity on redox reaction rates

A micromodel system, which corresponds to one or part of a numerical grid in the continuum model, was used to investigate the effect of subgrid transport heterogeneity on redox reaction rates. Hematite reductive dissolution by injecting a reduced form of flavin mononucleotide (FMNH2) at variable flow rates was used as an example to probe the variations of redox reaction rates in different subgrid transport domains. Experiments, pore-scale simulations, and macroscopic continuum modeling were performed to measure and simulate in-situ hematite reduction and to evaluate the scaling behavior of the redox reaction rates from the pore to continuum scales. The results indicated that the measured pore-scale rates of hematite reduction were consistent with the predictions from a pore-scale reactive transport model. A general trend is that hematite reduction followed reductant transport pathways, starting from the advection-dominated pores toward the interior of diffusion-dominated domains. Two types of diffusion domains were considered in the micromodel: a micropore diffusion domain, which locates inside solid grains or aggregates where reactant transport is limited by diffusion; and a macropore diffusion domain, which locates at wedged, dead-end pore spaces created by the grain-grain contacts. The rate of hematite reduction in the advection-dominated domain was faster than those in the diffusion-controlled domains, and the rate in the macropore diffusion domain was faster than that in the micropore domain. The reduction rates in the advection and macropore diffusion domains increased with increasing flow rate, but were affected by different mechanisms. The rate increase in the advection domain was controlled by the mass action effect as a faster flow supplied more reactants, and the rate increase in the macropore domain was more affected by the rate of mass exchange with the advection domain, which increased with increasing flow rate. The hematite reduction rate in the micropore domain was, however, not affected by the flow rate because molecular diffusion limits reductant supply to the micropore domain interior. Domain-based macroscopic models were evaluated to scale redox reaction rates from the pore to continuum scales. Simulation results from the single domain model, which ignores subgrid transport heterogeneity, deviated significantly from the pore-scale results. Further analysis revealed that the rate expression for hematite reduction was not scalable from the pore to porous media using the single domain model. A three-domain model, which effectively considers subgrid reactive diffusion in the micropore and macropore domains, significantly improved model description. Overall this study revealed the importance of subgrid transport heterogeneity in the manifestation of redox reaction rates in porous media and in scaling reactions from the pore to porous media. The research also supported that the domain-based scaling approach can be used to directly scale redox reactions in porous media with subgrid transport heterogeneity.

Effects of Pore-Scale Heterogeneity and Transverse Mixing on Bacterial Growth in Porous Media

Microbial degradation of contaminants in the subsurface requires the availability of nutrients; this is impacted by porous media heterogeneity and the degree of transverse mixing. Two types of microfluidic pore structures etched into silicon wafers (i.e., micromodels), (i) a homogeneous distribution of cylindrical posts and (ii) aggregates of large and small cylindrical posts, were used to evaluate the impact of heterogeneity on growth of a pure culture (Delftia acidovorans) that degrades (R)-2-(2,4-dichlorophenoxy)propionate (R-2,4-DP). Following inoculation, dissolved O2 and R-2,4-DP were introduced as two parallel streams that mixed transverse to the direction of flow. In the homogeneous micromodel, biomass growth was uniform in pore bodies along the center mixing line, while in the aggregate micromodel, preferential growth occurred between aggregates and slower less dense growth occurred throughout aggregates along the center mixing line. The homogeneous micromodel had more rapid growth overall (2 times) and more R-2,4-DP degradation (9.5%) than the aggregate pore structure (5.7%). Simulation results from a pore-scale reactive transport model indicate mass transfer limitations within aggregates along the center mixing line decreased overall reaction; hence, slower biomass growth rates relative to the homogeneous micromodel are expected. Results from this study contribute to a better understanding of the coupling between mass transfer, reaction rates, and biomass growth in complex porous media and suggest successful implementation and analysis of bioremediation systems requires knowledge of subsurface heterogeneity.