Non-isothermal Reactive Transport Research Articles

Reactive transport model of the long-term geochemical evolution in a HLW repository in granite at the disposal cell scale: Variants, sensitivities, and model simplifications

The assessment of the long-term performance of the engineered barrier systems of high-level radioactive waste (HLW) repositories requires the use of reactive transport models. Montenegro et al. (2023) presented a non-isothermal reactive transport model of the long-term geochemical evolution of a HLW disposal cell in a granitic host rock corresponding to a generic reference concept. The model accounted for the vitrified waste, the carbon-steel canister, the bentonite buffer and the reference granitic rock. Here we extend their model by considering model variants (V), sensitivity cases (SC) and model abstractions (MA). Variants V1, V2 and V3 consist of considering MX-80 bentonite instead of FEBEX bentonite (V1), a larger groundwater flux through the granite (V2) and the Czech reference crystalline rock as a host rock (V3). Cases SC1 and SC2 consider a decrease of the silica concentration threshold value in the glass dissolution rate (SC1) and an earlier canister failure time (SC2), respectively. Runs MA1 to MA4 consider smectite as an unreactive mineral phase (MA1), the porosity feedback effect on chemical and transport parameters (MA2), a time-varying corrosion rate (MA3), and a coarser finite element grid (MA4), respectively. Model results of V1 show a larger pH, a smaller precipitation of magnetite, siderite and greenalite and a slightly smaller dissolution of ISG and smectite than the base run of Montenegro et al. (2023). Model predictions are very sensitive to the increase in the groundwater flow through the granitic host rock (V2). However, predictions are not sensitive to the chemical composition of the granite porewater (V3). The decrease in the silica saturation threshold from 1·10−3 to 5·10−4 mol/L in SC1 leads to a significant decrease in glass dissolution. Glass dissolution after 50,000 years in SC2 (earlier canister failure) is much larger than that of the base run. Model results are not sensitive to considering smectite as an unreactive mineral phase (MA1). However, model results are very sensitive to the porosity feedback effect (MA2). A 60% volume fraction of Fe(s) remains uncorroded after 50,000 years when a variable corrosion rate is considered in MA3. In this case the precipitation of corrosion products is much smaller than that of the base run. The general patterns of the numerical results in MA4 (coarser grid) are similar to those of the base case.

Phase-field modeling and effective simulation of non-isothermal reactive transport

We consider single-phase flow with solute transport where ions in the fluid can precipitate and form a mineral, and where the mineral can dissolve and release solute into the fluid. Such a setting includes an evolving interface between fluid and mineral. We approximate the evolving interface with a diffuse interface, which is modeled with an Allen–Cahn equation. We also include effects from temperature such that the reaction rate can depend on temperature, and allow heat conduction through fluid and mineral. As Allen–Cahn is generally not conservative due to curvature-driven motion, we include a reformulation that is conservative. This reformulation includes a non-local term that makes the use of standard Newton iterations for solving the resulting non-linear system of equations very slow. We instead apply L-scheme iterations, which can be proven to converge for any starting guess, although giving only linear convergence. The three coupled equations for diffuse interface, solute transport and heat transport are solved via an iterative coupling scheme. This allows the three equations to be solved more efficiently compared to a monolithic scheme, and only few iterations are needed for high accuracy. Through numerical experiments we highlight the usefulness and efficiency of the suggested numerical scheme and the applicability of the resulting model.

Simulation of Reactive Transport in Fractured Porous Media

Numerical simulations of reactive transport in fractured porous media require the solution of coupled physical and chemical processes that depend on the fractures. Such coupled processes are described by a system of nonlinear partial differential-algebraic equations, while strong heterogeneities characterise fractures. This paper presents an approach to simulate single-phase flow and non-isothermal reactive transport with mineral dissolution and precipitation in fractured porous media. Our numerical solution strategy is based on two ingredients. First, the model equations consist of coupled partial differential equations for the fluid flow, heat transfer and solute transport and nonlinear algebraic equations representing the chemical reactions. Second, fractures are explicitly represented and treated as lower-dimensional objects. The partial differential equations are discretised using finite-volume methods, and at each time step, we solve a nonlinear system of equations using Newton’s method. With numerical simulations, we illustrate our model’s ability to accurately describe the two-way interaction between coupled multi-physical processes and two- and three-dimensional porous media with intersecting fractures.

A non-isothermal reactive transport model of the long-term geochemical evolution at the disposal cell scale in a HLW repository in granite

The assessment of the long-term performance of the engineered barrier systems of high-level radioactive waste (HLW) repositories requires the use of reactive transport models. Here a non-isothermal reactive transport model of the long-term geochemical evolution of a HLW disposal cell in a granitic host rock is presented. The model includes the vitrified waste (40 cm in diameter), the carbon-steel canister (5 cm thick), the saturated FEBEX bentonite buffer (75 cm thick) and the reference granitic rock. The model accounts for the thermal transient stage and assumes generalized steel corrosion under anaerobic conditions with a corrosion rate equal to 1.41 m/y. Canister failure is assumed to occur when the remaining canister thickness is equal to 3.5 cm at t = 25,000 years. Canister corrosion caused an increase in pH. The computed pH in the canister just before canister failure (t = 25,000 years) was equal to 9.25 and ranged from 7.82 to 9.25 in the bentonite. Magnetite, the main corrosion product, precipitated in the bentonite and especially in the canister. The thickness of magnetite precipitation band in the bentonite was ≈ 1 cm. Siderite precipitated at both sides of the canister/bentonite interface. The precipitation front penetrated >1 cm into the bentonite. Nuclear glass started dissolving after canister failure (t > 25,000 years). The concentration of dissolved silica increased in the inner part of the glass until t = 30,000 years and decreased in the outer part of the glass due to the out diffusion of dissolved silica into the canister and the bentonite. This diffusive flux caused the precipitation of greenalite at the glass/canister and canister/bentonite interfaces. The pH at the end of the simulation (t = 50,000 years) ranged from 7.93 to 7.89 in the glass, from 7.89 to 8.66 in the canister and from 7.87 to 8.6 in the bentonite. Magnetite precipitated in the canister while there was carbon steel to corrode. Once the canister was fully corroded, magnetite redissolved near the glass/canister interface. Greenalite precipitated in the canister and the bentonite, especially at the glass/canister interface and siderite precipitated at the canister/bentonite interface. The simulation results should be useful for the performance assessment of engineered barriers of radioactive waste repositories in granitic host rocks.

Image-based modelling of coke combustion in a multiscale porous medium using a micro-continuum framework

Non-isothermal reactive transport in complicated porous media is diverse in nature and industrial applications. There are challenges in the modelling of multiple physicochemical processes in multiscale pore structures with various length scales ranging from nanometres to micrometres. This study focuses on coke combustion during in situ crude oil combustion techniques. A micro-continuum model was developed to perform an image-based simulation of coke combustion through a multiscale porous medium. The simulation coupled weakly compressible gas flow, species transport, conjugate heat transfer, heterogeneous coke oxidation kinetics and structural evolution. The unresolved nanoporous coke region was treated as a continuum, for which the random pore model, permeability model and species diffusivity model were integrated as sub-grid models to account for the sub-resolution reactive surface area, Darcy flow and Knudsen diffusion, respectively. A Pe–Da diagram was provided to present five characteristic combustion regimes covering the ignition temperature and air flux in realistic field operations and laboratory measurements. The present model proved to achieve more accurate predictions of the feasible ignition temperature than previous models. Compared with the air flux of $\phi \sim O\textrm{(1) s}{\textrm{m}^\textrm{3}}(\textrm{air})\;{({\textrm{m}^\textrm{2}}\ \textrm{h})^{ - 1}}$ in the field, the increasing air flux in the laboratory transformed the combustion regime from diffusion-limited to convection-limited, which led to an overpredicted burning temperature. Reactive fingering combustion was analysed to understand the potential risks in some experimental measurements. The findings provide a better understanding of coke combustion and can help engineers design sustainable combustion methods. The developed image-based model allows other types of multiscale and nonlinear reactive transport to be simulated.

Numerical Modeling of CO2 Sequestration within a Five-Spot Well Pattern in the Morrow B Sandstone of the Farnsworth Hydrocarbon Field: Comparison of the TOUGHREACT, STOMP-EOR, and GEM Simulators

The objectives of this study were (1) to assess the fate and impact of CO2 injected into the Morrow B Sandstone in the Farnsworth Unit (FWU) through numerical non-isothermal reactive transport modeling, and (2) to compare the performance of three major reactive solute transport simulators, TOUGHREACT, STOMP-EOR, and GEM, under the same input conditions. The models were based on a quarter of a five-spot well pattern where CO2 was injected on a water-alternating-gas schedule for the first 25 years of the 1000 year simulation. The reservoir pore fluid consisted of water with or without petroleum. The results of the models have numerous broad similarities, such as the pattern of reservoir cooling caused by the injected fluids, a large initial pH drop followed by gradual pH neutralization, the long-term persistence of an immiscible CO2 gas phase, the continuous dissolution of calcite, very small decreases in porosity, and the increasing importance over time of carbonate mineral CO2 sequestration. The models differed in their predicted fluid pressure evolutions; amounts of mineral precipitation and dissolution; and distribution of CO2 among immiscible gas, petroleum, formation water, and carbonate minerals. The results of the study show the usefulness of numerical simulations in identifying broad patterns of behavior associated with CO2 injection, but also point to significant uncertainties in the numerical values of many model output parameters.

Growth kinetic and transport of mixed microbial cultures in subsurface environments

Subsurface porous environments harbor various microbial communities that control ecosystem functions such as geochemical cycling, bioremediation and ore formation. To simulate bioprocesses derived by microbial communities, Monod equation and cardinal models are utilized to model growth kinetics dependency on substrate concentration and temperature, respectively. In this work, we illustrate that Monod equation with constant parameters cannot characterize community derived microbial processes. Additionally, the growth-temperature dependency of a community of microorganisms does not follow a specific mathematical model. We suggest an equivalent strain model that can estimate the rate of community-derived metabolisms (RCDM) in non-isothermal reactive transport processes. We consider a one-dimensional flow system with four different simulation scenarios of immobile biomass-limited electron donor, mobile biomass-limited electron donor, immobile biomass-unlimited electron donor and mobile biomass-unlimited electron donor. We illustrate that the equivalent strain can efficiently characterize (with absolute normalized deviation (AND)<4%) the behavior of the test community when electron donor availability is limited. In contrast to the limited electron donor availability cases, we show that the equivalent strain is not capable of characterizing the test community when electron donor is abundant, leading to a maximum AND of 70%. The deviation of the equivalent strain from the test community is due to the inability of the equivalent strain to represent the effects of community evolution on RCDM and biomass deactivation that happens due to temperature variations.

Comprehensive study and comparison of equilibrium and kinetic models in simulation of hydrate reaction in porous media

Coupling hydrate reaction in fluid transport in porous media is essential for simulation of gas hydrate production, as well as carbon sequestration in deep-sea sediments. It can be conceptualized as multiphase, multicomponent, and non-isothermal reactive transport. Two types of models have been developed for the description of hydrate reaction in numerical models. The equilibrium model (EM) assumes instantaneous chemical equilibrium among species, and thus ignores reaction kinetics. The kinetic model (KM) incorporates reaction kinetics by introducing a term of reaction rate dependent on fugacity difference. Although KM achieves a more accurate description of the reaction, it is potentially more computationally intensive due to the increased degree of freedom in the nonlinear equation system. Although several previous studies have investigated the similarities and differences between these two models, inconsistencies exist in their studies, and the mechanisms to distinguish these two models are still not well understood. In our study, in order to identify the reasons for these inconsistencies and elucidate the mechanisms that control the differences between the two reaction models, we provide a comprehensive investigation and comparison of these two models via theoretical analysis and numerical experiments. Through comparing the basic assumptions, mathematical model and the equation systems, we pointed out the basic difference of these two models, which results from the different calculations of physical parameters. Dimensionless analysis of the governing equations of KM yields several characteristic numbers, representing the relative strength of different physical processes. We performed numerical experiments to investigate the effect of characteristic numbers on the difference between the two models, and the results indicate that there exist critical values for these characteristic numbers, lower than which lead to an obvious gap between the results of EM and KM. It turns out that the relative strength of the hydrate reaction and other physical processes controls the magnitude of difference between these two models. EM is essentially a special case of KM when the time scale of the hydrate reaction is sufficiently smaller than other physical processes, such as convective and diffusive transport of mass and heat. Comparison between the time and iteration steps in the two reaction models provides insights into the computational efficiency of the two models.

Long-term non-isothermal reactive transport model of compacted bentonite, concrete and corrosion products in a HLW repository in clay

Radioactive waste disposal in deep geological repositories envisages engineered barriers such as carbon-steel canisters, compacted bentonite and concrete liners. The stability and performance of the bentonite barrier could be affected by the corrosion products at the canister-bentonite interface and the hyper-alkaline conditions caused by the degradation of concrete at the bentonite-concrete interface. Additionally, the host clay formation could also be affected by the hyper-alkaline plume at the concrete-clay interface. Here we present a non-isothermal multicomponent reactive transport model of the long-term (1Ma) interactions of the compacted bentonite with the corrosion products of a carbon-steel canister and the concrete liner of the engineered barrier of a high-level radioactive waste repository in clay. Model results show that magnetite is the main corrosion product. Its precipitation reduces significantly the porosity of the bentonite near the canister. The degradation of the concrete liner leads to the precipitation of secondary minerals and the reduction of the porosity of the bentonite and the clay formation at their interfaces with the concrete liner. The reduction of the porosity becomes especially relevant at t=104years. The zones affected by pore clogging at the canister-bentonite and concrete-clay interfaces at 1Ma are approximately equal to 1 and 3.3cm thick, respectively. The hyper-alkaline front (pH>8.5) spreads 2.5cm into the clay formation after 1Ma. Our simulation results share the key features of the models reported by others for engineered barrier systems at similar chemical conditions, including: 1) Pore clogging at the canister-bentonite and concrete-clay interfaces; 2) Narrow alteration zones; and 3) Limited smectite dissolution after 1Ma.

Reactive transport modelling of the long-term interactions of corrosion products and compacted bentonite in a HLW repository in granite: Uncertainties and relevance for performance assessment

Here we present a long-term nonisothermal reactive transport model for the interactions of the corrosion products of a carbon-steel canister and the compacted bentonite of the engineered barrier of a high-level radioactive waste repository in granite. Canister corrosion causes an increase in the pH and the concentration of dissolved Fe2+ of the bentonite porewater. Iron precipitates as magnetite and siderite and sorbs via cation exchange and surface complexation on weak sites. Magnetite precipitation reduces significantly the porosity of the bentonite near the canister. The thickness of the zone of reduced porosity is 7 cm at t = 1 Ma. This thickness increases significantly when the dependence of the corrosion rate on the chemical conditions is considered and decreases 3 cm when smectite dissolution and analcime precipitation are taken into account. Model results are not significantly sensitive to the thermal transient and the effect of temperature on the corrosion rate. The conclusions of our simulations are consistent for the most part with those reported by others for engineered barrier systems at similar chemical conditions.

Using Laboratory Flow Experiments and Reactive Chemical Transport Modeling for Designing Waterflooding of the Agua Fria Reservoir, Poza Rica-Altamira Field, Mexico

Summary Waterflooding for enhanced oil recovery requires that injected waters must be chemically compatible with connate reservoir waters, in order to avoid mineral dissolution-and-precipitation cycles that could seriously degrade formation permeability and injectivity. Formation plugging is a concern especially in reservoirs with a large content of carbonates, such as calcite and dolomite, as such minerals typically react rapidly with an aqueous phase, and have strongly temperature-dependent solubility. Clay swelling also can pose problems. During a preliminary waterflooding pilot project, the Poza Rica-Altamira oil field, bordering the Gulf coast in the eastern part of Mexico, experienced injectivity loss after 5 months of reinjection of formation waters into Well AF-847 in 1999. Acidizing with hydrochloric acid (HCl) restored injectivity. We report on laboratory experiments and reactive-chemistry modeling studies that were undertaken in preparation for long-term waterflooding at the Agua Fría reservoir. Using analogous core plugs obtained from the same reservoir interval, laboratory core-flood experiments were conducted to examine the sensitivity of mineral-dissolution and -precipitation effects to water composition. Native reservoir water, chemically altered waters, and distilled water were used, and temporal changes in core permeability, mineral quantities, and aqueous concentrations of solutes were monitored. The experiments were simulated with the multiphase, nonisothermal reactive transport code TOUGHREACT™ (Lawrence Berkeley National Laboratory, Berkeley, California, 2004), and reasonable-to-good agreement was obtained for changes in solute concentrations. Clay swelling caused an additional impact on permeability behavior during coreflood experiments, whereas the modeled permeability depends exclusively on chemical processes. TOUGHREACT was then used for reservoir-scale simulation of injecting ambient-temperature water (30°C, 86°F) into a reservoir with initial temperature of 80°C (176°F). Untreated native reservoir water was found to cause serious porosity and permeability reduction because of calcite precipitation, which is promoted by the retrograde solubility of this mineral. Using treated water that performed well in the laboratory flow experiments was found to avoid excessive precipitation and allowed injection to proceed.

A coupled non-isothermal reactive transport model for long-term geochemical evolution of a HLW repository in clay

A numerical model of coupled saturated/unsaturated water flow, heat transfer and multi-component reactive solute transport is presented to evaluate the long-term geochemical evolution in bentonite, concrete and clay formation for a potential geological radioactive waste repository. Changes in formation porosity caused by mineral dissolution/precipitation reactions are taken into account. Simulations were carried out with a general-purpose multicomponent reactive transport code, CORE2D V4. Numerical results show that pH in the bentonite porewater can vary from neutral to up to 13 over a time scale of 1 Ma although dissolution of silica minerals and precipitation of secondary calcium silicate hydrate (CSH) minerals in bentonite buffer the effect of the hyperalkaline plume. Mineral precipitation reduces the volume of pore space in bentonite close to the bentonite–concrete interface due to the precipitation of CSH minerals. Model results indicate that bentonite porosity decreases less than 25%. The hyperalkaline plume from the concrete only extends to a distance of 0.7 m in the clay formation over the time range of 1 Ma.

Numerical simulation of reactive processes in an experiment with partially saturated bentonite

Bentonites are preferred materials for use as engineered barriers for high-level nuclear waste repositories. Simulation of geochemical processes in bentonite is therefore important for long-term safety assessment of those repositories. In this work, the porewater chemistry of a bentonite sample subject to simultaneous heating and hydration, as studied by Cuevas et al. [Cuevas, J., Villar, M., Fernández, A., Gómez, P., Martín, P., 1997. Porewaters extracted from compacted bentonite subjected to simultaneous heating and hydration. Applied Geochemistry 12, 473–481.], was assessed with a non-isothermal reactive transport model by coupling the geochemical software PHREEQC2 with the object-oriented FEM simulator GeoSys/RockFlow. Reactive transport modelling includes heat transport, two-phase flow, multicomponent transport and geochemical reactions in the liquid phase, i.e. ion exchange, mineral dissolution/precipitation and equilibrium reactions. Simulations show that the easily soluble minerals in bentonite determine the porewater chemistry. Temperature affects both two-phase flow and geochemical reactions. Porosity change due to dissolution/precipitation is low during the experiment. However, changes of the effective porosity caused by bentonite swelling can be very large. The simulated results agree well with the experimental data.