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This paper presents and discusses the results obtained by the participants to the benchmark described in de Hoop et al, Comput. Geosci. (2024). The benchmark uses a model for CO2 geological storage and focuses on the coupling between two-phase flow and geochemistry. Several test cases of various levels of difficulty are proposed, both in one and two spatial dimensions. Six teams participated in the benchmark, each with their own simulation code, though not all teams attempted all the cases. The codes used by the participants are described, and the results obtained on the various test cases are compared, as well as the performance of the codes. It is shown that the results obtained are widely consistent, giving a good level of confidence in the outcome of the benchmark. The general complexity of two-phase flow coupled with chemical reactions altering porous media means that some differences between the codes remain. Besides, from the convergence study, it is clear that the two-dimensional problem has a relatively high sensitivity to a spatial resolution which adds to the complexity. [ABSTRACT FROM AUTHOR]

This paper proposes a benchmark study for reactive multiphase multicomponent flow in porous media. Modeling such problem leads to a highly nonlinear coupled system of partial differential equations, ordinary differential equations and algebraic constraints, which requires special numerical treatment. The benchmark consists of five test problems in total (both in 1D and in 2D), with varying degrees of difficulty, designed to verify the algorithms and the codes dedicated to simulating coupled isothermal Hydro-Chemical processes during injection and storage of CO2 in the subsurface. It is intended to be used as a basis for comparing codes in order to better understand different couplings such as chemical reactions with two-phase flow, phase behavior with equilibrium reactions, dissolution and precipitation. [ABSTRACT FROM AUTHOR]

In this paper, we present the results of benchmark simulations for plume spreading during CO2 geo-sequestration conducted with the newly developed Australian CO2 Geo-Sequestration Simulator (ACGSS). The simulator uses a hybrid finite element–finite volume (FEFVM) simulation framework, integrating an asynchronous local time stepping method for multi-phase multi-component transport and a novel non-iterative flash calculation approach for the phase equilibrium. The benchmark investigates four standard CO2 storage test cases that are widely used to assess the performance of simulation tools for carbon geo-sequestration: (A) radial flow from a CO2 injection well; (B) CO2 discharge along a fault zone; (C) CO2 injection into a layered brine formation; and (D) leakage through an abandoned well. For these applications, ACGSS gives results similar to well-established compositional simulators. Minor discrepancies can be rationalised in terms of the alternative, spatially adaptive discretisation and the treatment of NaCl solubility. While these benchmarks cover issues related to compositional simulation, they do not address the accurate representation of geologically challenging features of CO2 storage sites. An additional 3D application scenario of a complexly faulted storage site demonstrates the advantages of the FEFVM discretisation used in the ACGSS for resolving the geometric complexity of geologic storage sites. This example also highlights the significant computational benefits gained from the use of the asynchronous time marching scheme. [ABSTRACT FROM AUTHOR]

A specific benchmark has been developed by the French research group MoMas in order to improve numerical solution methods applied by reactive transport models, i.e., codes that couple hydrodynamic flow and mass transport in porous media with geochemical reactions. The HYTEC model has been applied to this benchmark exercise, and this paper summarizes some of the principal results. HYTEC is a general-purpose code, applied by industrials and research groups to a wide variety of domains, including soil pollution, nuclear waste storage, cement degradation, water purification systems, storage of CO2, and valorization of stabilized wastes. The code has been applied to the benchmark test-cases without any specific modification. Apart from the benchmark imposed output, additional information is provided to highlight the behavior of HYTEC specifically and the simulation results in particular. [ABSTRACT FROM AUTHOR]

Changes of porosity, permeability, and tortuosity due to physical and geochemical processes are of vital importance for a variety of hydrogeological systems, including passive treatment facilities for contaminated groundwater, engineered barrier systems (EBS), and host rocks for high-level nuclear waste (HLW) repositories. Due to the nonlinear nature and chemical complexity of the problem, in most cases, it is impossible to verify reactive transport codes analytically, and code intercomparisons are the most suitable method to assess code capabilities and model performance. This paper summarizes model intercomparisons for six hypothetical scenarios with generally increasing geochemical or physical complexity using the reactive transport codes CrunchFlow, HP1, MIN3P, PFlotran, and TOUGHREACT. Benchmark problems include the enhancement of porosity and permeability through mineral dissolution, as well as near complete clogging due to localized mineral precipitation, leading to reduction of permeability and tortuosity. Processes considered in the benchmark simulations are advective-dispersive transport in saturated media, kinetically controlled mineral dissolution-precipitation, and aqueous complexation. Porosity changes are induced by mineral dissolution-precipitation reactions, and the Carman-Kozeny relationship is used to describe changes in permeability as a function of porosity. Archie's law is used to update the tortuosity and the pore diffusion coefficient as a function of porosity. Results demonstrate that, generally, good agreement is reached amongst the computer models despite significant differences in model formulations. Some differences are observed, in particular for the more complex scenarios involving clogging; however, these differences do not affect the interpretation of system behavior and evolution. [ABSTRACT FROM AUTHOR]

The benchmark problem presented in this paper deals with the leaching of calcium from hardened cement paste. The leaching of calcium results in the dissolution of the cement minerals which affects physical, chemical and mechanical properties of porous cement matrix. The dissolution of cement minerals in this case progresses heterogeneously as a consequence of a small-scale geometrical feature (crack) within a domain. Complexity of transport through cracked porous media combined with complex cement chemistry can lead to considerable modelling uncertainties. One possible way to get an insight into the robustness of modelling results is to perform benchmark based on (i) different transport models and solution methods (finite volume, finite element, etc.), (ii) different geochemical solvers and (iii) different coupling algorithms (sequential iterative and non-iterative). This benchmark is designed to gradually increase the complexity of the problem and in this way recognize modelling elements that are the most sensitive in terms of modelling results, e.g. evolution of physical and chemical properties. Five international teams participated in this benchmark exercise. The reactive transport codes used (HYTEC, MIN3P, OGS-GEM, ORCHESTRA, COMSOL Multiphysics-iPHREEQC) give similar patterns in terms of predicted concentrations of elements and the mineralogy. The level of agreement depends on the problem complexity related mainly to the weighting and conservation properties of different numerical methods, to the coupling between transport and reactive solver and the agreement of thermodynamic database. [ABSTRACT FROM AUTHOR]

Bioremediation efforts in aquifers contaminated with redox-sensitive contaminants often rely on in situ reductive immobilization. The bioremediation treatment usually involves injection of organic carbon into the subsurface (e.g., acetate) to stimulate the growth of indigenous bacteria that mediate the relevant redox processes that immobilize the target contaminant. Batch and flow-through column experimental studies are conducted to elucidate reaction networks associated with specific electron acceptor pathways and/or specific bacterial isolates. The proposed benchmark involves the simulation of microbially mediated chromium reduction under denitrifying conditions in biostimulated batch and flow-through column experiments. Simulated reactive processes include multicomponent aqueous complexation, kinetically controlled mineral precipitation and dissolution, biologically mediated reactions, and biomass growth and decay. The focus of the benchmark problem set is on the simulation of microbially mediated redox reactions with the explicit inclusion of the microbial community dynamics and the impacts on reaction rates. Rate expressions for microbially mediated redox reactions include kinetic limitations (Monod and inhibition terms) as well as thermodynamic limitations. Both catabolic (energy) and anabolic pathways (biomass growth) are considered in the microbially mediated reactions. Microbial biomass is assumed to be bound to the sediment (non-planktonic). Any reactive transport model used to reproduce results of this benchmark problem must be capable of simulating multicomponent aqueous complexation, kinetically controlled mineral precipitation and dissolution and kinetically controlled aqueous reactions. Though convenient, it is not necessary to allow for specific stoichiometric relationships for catabolic and anabolic pathways; only the overall reaction stoichiometry is used. Rate expressions for microbially mediated reaction must include a rate constant, the biomass concentration, and a number of Monod and inhibition terms. To ensure that the results presented in this paper were the correct solutions to the problems posed, the general-purpose reactive transport codes CrunchFlow, PHT3D, ToughReact, and MIN3P were used to perform the simulations. In general, results obtained with all codes show excellent agreement. [ABSTRACT FROM AUTHOR]

The use of the subsurface for CO storage, geothermal energy generation, and nuclear waste disposal will greatly increase the interaction between clay(stone) and concrete. The development of models describing the mineralogical transformations at this interface is complicated, because contrasting geochemical conditions (Eh, pH, solution composition, etc.) induce steep concentration gradients and a high mineral reactivity. Due to the complexity of the problem, analytical solutions are not available to verify code accuracy, rendering code intercomparisons as the most efficient method for assessing code capabilities and for building confidence in the used model. A benchmark problem was established for tackling this issue. We summarize three scenarios with increasing geochemical complexity in this paper. The processes considered in the simulations are diffusion-controlled transport in saturated media under isothermal conditions, cation exchange reactions, and both local equilibrium and kinetically controlled mineral dissolution-precipitation reactions. No update of the pore diffusion coefficient as a function of porosity changes was considered. Seven international teams participated in this benchmarking exercise. The reactive transport codes used (TOUGHREACT, PHREEQC, with two different ways of handling transport, CRUNCH, HYTEC, ORCHESTRA, MIN3P-THCm) gave very similar patterns in terms of predicted solute concentrations and mineral distributions. Some differences linked to the considered activity models were observed, but they do not bias the general system evolution. The benchmarking exercise thus demonstrates that a reactive transport modelling specification for long-term performance assessment can be consistently addressed by multiple simulators. [ABSTRACT FROM AUTHOR]

This paper summarizes the governing equations as implemented in the MIN3P multicomponent flow and reactive transport code (Mayer et al., Water Resour Res 38:1174, ) and introduces the equations in discretized form. Linearization and solution methods are presented including adaptive time stepping and update modification schemes. Code-specific details for the implementation of the GdR MoMaS benchmark simulations (Carrayrou et al., Comput Geosci, ) are presented. The standard version of the MIN3P code was used to solve the Easy, Medium, and Hard Test Cases, in one and two spatial dimensions, for both advection- and diffusion-dominated conditions. An analysis of the sensitivity of the solution in relation to spatial and temporal discretization parameters is provided for the Easy Test Case, selected results are presented for the Medium and Hard Test Cases, and the performance of the code as a function of discretization parameters is evaluated for all test cases. [ABSTRACT FROM AUTHOR]

Sophisticated modeling of the migration of sorbing radionuclides in compacted claystones is needed for supporting the safety analysis of deep geological repositories for radioactive waste, which requires robust modeling tools/codes. Here, a benchmark related to a long term laboratory scale diffusion experiment of cesium, a moderately sorbing radionuclide, through Opalinus clay is presented. The benchmark was performed with the following codes: CORE2DV5, Flotran, COMSOL Multiphysics, OpenGeoSys-GEM, MCOTAC and PHREEQC v.3. The migration setup was solved with two different conceptual models, i) a single-species model by using a look-up table for a cesium sorption isotherm and ii) a multi-species diffusion model including a complex mechanistic cesium sorption model. The calculations were performed for three different cesium boundary concentrations (10−3, 10−5, 10−7 mol / L) to investigate the models/codes capabilities taking into account the nonlinear sorption behavior of cesium. Generally, good agreement for both single- and multi-species benchmark concepts could be achieved, however, some discrepancies have been identified, especially near the boundaries, where code specific spatial (and time) discretization had to be improved to achieve better agreement at the expense of longer computation times. In addition, the benchmark exercise yielded useful information on code performance, setup options, input and output data management, and post processing options. Finally, the comparison of single-species and multi-species model concepts showed that the single-species approach yielded generally earlier breakthrough, because this approach accounts neither for cation exchange of Cs+ with K+ and Na+, nor K+ and Na+ diffusion in the pore water. [ABSTRACT FROM AUTHOR]

Microbially mediated sulfate reduction is a ubiquitous process in many subsurface systems. Isotopic fractionation is characteristic of this anaerobic process, since sulfate-reducing bacteria (SRB) favor the reduction of the lighter sulfate isotopologue (S32O42−) over the heavier isotopologue (S34O42−). Detection of isotopic shifts has been utilized as a proxy for the onset of sulfate reduction in subsurface systems such as oil reservoirs and aquifers undergoing heavy metal and radionuclide bioremediation. Reactive transport modeling (RTM) of kinetic sulfur isotope fractionation has been applied to field and laboratory studies. We developed a benchmark problem set for the simulation of kinetic sulfur isotope fractionation during microbially mediated sulfate reduction. The benchmark problem set is comprised of three problem levels and is based on a large-scale laboratory column experimental study of organic carbon amended sulfate reduction in soils from a uranium-contaminated aquifer. Pertinent processes impacting sulfur isotopic composition such as microbial sulfate reduction and iron-sulfide reactions are included in the problem set. This benchmark also explores the different mathematical formulations in the representation of kinetic sulfur isotope fractionation as employed in the different RTMs. Participating RTM codes are the following: CrunchTope, TOUGHREACT, PHREEQC, and PHT3D. Across all problem levels, simulation results from all RTMs demonstrate reasonable agreement. [ABSTRACT FROM AUTHOR]

This manuscript presents a benchmark problem for the simulation of single-phase flow, reactive transport, and solid geometry evolution at the pore scale. The problem is organized in three parts that focus on specific aspects: flow and reactive transport (part I), dissolution-driven geometry evolution in two dimensions (part II), and an experimental validation of three-dimensional dissolution-driven geometry evolution (part III). Five codes are used to obtain the solution to this benchmark problem, including Chombo-Crunch, OpenFOAM-DBS, a lattice Boltzman code, Vortex, and dissolFoam. These codes cover a good portion of the wide range of approaches typically employed for solving pore-scale problems in the literature, including discretization methods, characterization of the fluid-solid interfaces, and methods to move these interfaces as a result of fluid-solid reactions. A short review of these approaches is given in relation to selected published studies. Results from the simulations performed by the five codes show remarkable agreement both quantitatively—based on upscaled parameters such as surface area, solid volume, and effective reaction rate—and qualitatively—based on comparisons of shape evolution. This outcome is especially notable given the disparity of approaches used by the codes. Therefore, these results establish a strong benchmark for the validation and testing of pore-scale codes developed for the simulation of flow and reactive transport with evolving geometries. They also underscore the significant advances seen in the last decade in tools and approaches for simulating this type of problem. [ABSTRACT FROM AUTHOR]

The aim of this study is to compare numerical methods for the simulation of single-phase flow and transport in fractured media, described here by means of the discrete fracture network (DFN) model. A Darcy problem is solved to compute the advective field, then used in a subsequent time-dependent transport-diffusion-reaction problem. The numerical schemes are benchmarked in terms of flexibility in handling geometrical complexity, mass conservation, and stability issues for advection-dominated flow regimes. To this end, two benchmark cases, along with an additional one from a previous work, have been specifically designed and are here proposed and investigated, representing some of the most critical issues encountered in DFN simulations. [ABSTRACT FROM AUTHOR]

ReactMiCP, a new reactive transport simulator was developed based on the semismooth speciation solver SpecMiCP. Its main feature is a sequential iterative operator splitting algorithm where macroscopic model parameters are explicitly included in the formulation. Its correctness, robustness, and efficiency are tested against the MoMaS benchmark and two sets of cement paste lab experiments. We show that a robust speciation solver is a key requirement for good performance of the reactive transport simulator. We also demonstrate that a sequential iterative solver should be preferred over non-iterative solvers when using operator splitting. The flexibility and the speed of the simulator are used to test the influence of the database, the initial condition, and the diffusion coefficient model for the cement paste simulations. [ABSTRACT FROM AUTHOR]

A benchmark problem set consisting of four problem levels was developed for the simulation of Cr isotope fractionation in 1D and 2D domains. The benchmark is based on a recent field study where Cr(VI) reduction and accompanying Cr isotope fractionation occurs abiotically by an aqueous reaction with dissolved Fe (Wanner et al., 2012., Appl. Geochem., 27, 644-662). The problem set includes simulation of the major processes affecting the Cr isotopic composition such as the dissolution of various Cr(VI) bearing minerals, fractionation during abiotic aqueous Cr(VI) reduction, and non-fractionating precipitation of Cr(III) as sparingly soluble Cr-hydroxide. Accuracy of the presented solutions was ensured by running the problems with four well-established reactive transport modeling codes: TOUGHREACT, MIN3P, CRUNCHFLOW, and FLOTRAN. Results were also compared with an analytical Rayleigh-type fractionation model. An additional constraint on the correctness of the results was obtained by comparing output from the problem levels simulating Cr isotope fractionation with the corresponding ones only simulating bulk concentrations. For all problem levels, model to model comparisons showed excellent agreement, suggesting that for the tested geochemical processes any code is capable of accurately simulating the fate of individual Cr isotopes. [ABSTRACT FROM AUTHOR]

A reactive transport benchmark problem set has been developed based on in situ uranium bio-immobilization experiments that have been performed at a former uranium mill tailing site in Rifle, CO, USA. Acetate-amended groundwater stimulates indigenous microorganisms to catalyze the reduction of U(VI) to a sparingly soluble U(IV) mineral. The interplay between the flow, acetate loading periods and rates, and microbially mediated and geochemical reactions leads to dynamic behavior in metal- and sulfate-reducing bacteria, pH, alkalinity, and reactive mineral surfaces. The benchmark is based on an 8.5 m long one-dimensional model domain with constant saturated flow and uniform porosity. The 159-day simulation introduces acetate and bromide through the upgradient boundary in 14- and 85-day pulses separated by a 10 day interruption. Acetate loading is tripled during the second pulse, which is followed by a 50 day recovery period. Terminal electron-accepting processes for goethite, phyllosilicate Fe(III), U(VI), and sulfate are modeled using Monod-type rate laws. Major ion geochemistry modeled includes mineral reactions as well as aqueous and surface complexation reactions for UO $_{2}^{2+}$, Fe, and H. In addition to the dynamics imparted by the transport of the acetate pulses, U(VI) behavior involves the interplay between bioreduction, which is dependent on acetate availability, and speciation-controlled surface complexation, which is dependent on pH, alkalinity, and available surface complexation sites. The general difficulty of this benchmark is the large number of reactions (74), multiple rate law formulations, a multisite uranium surface complexation model, and the strong interdependency and sensitivity of the reaction processes. Results are presented for three simulators: HYDROGEOCHEM, PHT3D, and PHREEQC. [ABSTRACT FROM AUTHOR]

Acid rock drainage (ARD) is a problem of international relevance with substantial environmental and economic implications. Reactive transport modeling has proven a powerful tool for the process-based assessment of metal release and attenuation at ARD sites. Although a variety of models has been used to investigate ARD, a systematic model intercomparison has not been conducted to date. This contribution presents such a model intercomparison involving three synthetic benchmark problems designed to evaluate model results for the most relevant processes at ARD sites. The first benchmark (ARD-B1) focuses on the oxidation of sulfide minerals in an unsaturated tailing impoundment, affected by the ingress of atmospheric oxygen. ARD-B2 extends the first problem to include pH buffering by primary mineral dissolution and secondary mineral precipitation. The third problem (ARD-B3) in addition considers the kinetic and pH-dependent dissolution of silicate minerals under low pH conditions. The set of benchmarks was solved by four reactive transport codes, namely CrunchFlow, Flotran, HP1, and MIN3P. The results comparison focused on spatial profiles of dissolved concentrations, pH and pE, pore gas composition, and mineral assemblages. In addition, results of transient profiles for selected elements and cumulative mass loadings were considered in the intercomparison. Despite substantial differences in model formulations, very good agreement was obtained between the various codes. Residual deviations between the results are analyzed and discussed in terms of their implications for capturing system evolution and long-term mass loading predictions. [ABSTRACT FROM AUTHOR]

In multicomponent electrolyte solutions, the tendency of ions to diffuse at different rates results in a charge imbalance that is counteracted by the electrostatic coupling between charged species leading to a process called 'electrochemical migration' or 'electromigration.' Although not commonly considered in solute transport problems, electromigration can strongly affect mass transport processes. The number of reactive transport models that consider electromigration has been growing in recent years, but a direct model intercomparison that specifically focuses on the role of electromigration has not been published to date. This contribution provides a set of three benchmark problems that demonstrate the effect of electric coupling during multicomponent diffusion and electrochemical migration and at the same time facilitate the intercomparison of solutions from existing reactive transport codes. The first benchmark focuses on the 1D transient diffusion of HNO (pH = 4) in a NaCl solution into a fixed concentration reservoir, also containing NaCl-but with lower HNO concentrations (pH = 6). The second benchmark describes the 1D steady-state migration of the sodium isotope Na triggered by sodium chloride diffusion in neutral pH water. The third benchmark presents a flow-through problem in which transverse dispersion is significantly affected by electromigration. The system is described by 1D transient and 2D steady-state models. Very good agreement on all of the benchmarks was obtained with the three reactive transport codes used: CrunchFlow, MIN3P, and PHREEQC. [ABSTRACT FROM AUTHOR]

We present here the definition of the reactive transport benchmark of Groupement Mathematical Modeling and Numerical Simulation for Nuclear Waste Management Problems. The aim of this benchmark is to propose a challenging test for numerical methods used for reactive transport modeling in porous media. In order to focus on numerical methods, the problem presented here is of quite a small size, both from a hydrodynamical and from a geochemical point of view. Though the chemical coefficients used in this benchmark are not taken from a real chemical system, they are realistic, and the test case is quite challenging. [ABSTRACT FROM AUTHOR]

Numerical benchmark can be an efficient way to validate reactive transport codes. The reactive transport benchmark of GNR MoMaS is here presented and solved on its easy 1D version. The reactive transport code SPECY is presented with a brief description of its main numerical methods: discontinuous finite elements for solving advection, mixed hybrid finite elements for solving dispersion and Newton–Raphson method to linearise the equilibrium chemistry and respect of the chemically allowed interval and positive continuous fractions methods to increase the robustness of the chemistry resolution. By successive mesh and time step refinement, we use the reactive transport code SPECY to look for a reference solution to this problem. [ABSTRACT FROM AUTHOR]

Although multicomponent reactive transport modeling is gaining wider application in various geoscience fields, it continues to present significant mathematical and computational challenges. There is a need to solve and compare the solutions to complex benchmark problems, using a variety of codes, because such intercomparisons can reveal promising numerical solution approaches and increase confidence in the application of reactive transport codes. In this contribution, the results and performance of five current reactive transport codes are compared for the 1D and 2D subproblems of the so-called easy test case of the MoMaS benchmark (Carrayrou et al., Comput Geosci, , this issue). This benchmark presents a simple fictitious reactive transport problem that highlights the main numerical difficulties encountered in real reactive transport problems. As a group, the codes include iterative and noniterative operator splitting and global implicit solution approaches. The 1D easy advective and 1D easy diffusive scenarios were solved using all codes, and, in general, there was a good agreement, with solution discrepancies limited to regions with rapid concentration changes. Computational demands were typically consistent with what was expected for the various solution approaches. The differences between solutions given by the three codes solving the 2D problem are more important. The very high computing effort required by the 2D problem illustrates the importance of parallel computations. The most important outcome of the benchmark exercise is that all codes are able to generate comparable results for problems of significant complexity and computational difficulty. [ABSTRACT FROM AUTHOR]