Benchmarks for multicomponent reactive transport across a cement/clay interface

Abstract. Many types of geologic subsurface utilisation are associated with fluid and heat flow as well as simultaneously occurring chemical reactions. For that reason, reactive transport models are required to understand and reproduce the governing processes. In this regard, reactive transport codes must be highly flexible to cover a wide range of applications, while being applicable by users without extensive programming skills at the same time. In this context, we present an extension of the Open Source and Open Access TRANSPORT Simulation Environment, which has been coupled with the geochemical reaction module PHREEQC, and thus provides multiple new features that make it applicable to complex reactive transport problems in various geoscientific fields. Code readability is ensured by the applied high-level programming language Python which is relatively easy to learn compared to low-level programming languages such as C, C++ and FORTRAN. Thus, also users with limited software development knowledge can benefit from the presented simulation environment due to the low entry-level programming skill requirements. In the present study, common geochemical benchmarks are used to verify the numerical code implementation. Currently, the coupled simulator can be used to investigate 3D single-phase fluid and heat flow as well as multicomponent solute transport in porous media. In addition to that, a wide range of equilibrium and nonequilibrium reactions can be considered. Chemical feedback on fluid flow is provided by adapting porosity and permeability of the porous media as well as fluid properties. Thereby, users are in full control of the underlying functions in terms of fluid and rock equations of state, coupled geochemical modules used for reactive transport, dynamic boundary conditions and mass balance calculations. Both, the solution of the system of partial differential equations and the PHREEQC module, can be easily parallelised to increase computational efficiency. The benchmarks used in the present study include density-driven flow as well as advective, diffusive and dispersive reactive transport of solutes. Furthermore, porosity and permeability changes caused by kinetically controlled dissolution-precipitation reactions are considered to verify the main features of our reactive transport code. In future, the code implementation can be used to quantify processes encountered in different types of subsurface utilisation, such as water resource management as well as geothermal energy production, as well as geological energy, CO2 and nuclear waste storage.

Dissolution–precipitation processes in tank experiments for testing numerical models for reactive transport calculations: Experiments and modelling

Reactive transport in unsaturated soil: Comprehensive modelling of the dynamic spatial and temporal mass balance of water and chemical components

Reactive transport modeling involves solving several nonlinear coupled phenomena, among them, the flow of fluid phases, the transport of chemical species and energy, and chemical reactions. There are different ways to consider this coupling that might be more or less suitable depending on the nature of the problem to be solved. In this paper we acknowledge the importance of flexibility on reactive transport codes and how object-oriented programming can facilitate this feature. We present PROOST, an object-oriented code that allows solving reactive transport problems considering different coupling approaches. The code main classes and their interactions are presented. PROOST performance is illustrated by the resolution of a multiphase reactive transport problem where geochemistry affects hydrodynamic processes.

<p>The formation of alkaline magmas observed worldwide requires that low degree-melts, potentially formed in the asthenosphere, were able to cross the overlying lithosphere. Fracturing in the upper, brittle part of the lithosphere may help to extract this melt to the surface. However, the mechanism of extraction in the lower, ductile part of the lithosphere is still contentious. Metasomatic enrichment of the lithospheric mantle demonstrates that such low-degree melts interact with the lithosphere, but the physical aspect of this process remains unclear. The aim of this study is to better understand the percolation of magma in a porous viscous medium at pressure (P) and temperature (T) conditions relevant for the base of the lithosphere. We study such melt percolation numerically with a Thermo-Hydro-Chemical model of reactive transport coupled with thermodynamic data obtained via Gibbs energy minimisation. We perform Gibbs energy minimisation with Matlab using the linprog algorithm. We start with a simple ternary system of Forsterite/Fayalite/Enstatite solids and melts. All variables are a function of T, P and composition of the system (C), and are computed in both the Gibbs energy minimisation and in the reactive transport code, and can therefore vary freely.</p>

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, 2009, 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.

One of the challenging problems in mathematical geosciences is the determination of analytical solutions of nonlinear partial differential equations describing transport processes in porous media. We are interested in diffusive transport coupled with precipitation‐dissolution reactions. Several numerical computer codes that simulate such systems have been developed. Analytical solutions, if they exist, represent an important tool for verification of numerical solutions. We present a methodology for deriving such analytical solutions that are exact and explicit in space and time variables. They describe transport of several aqueous species coupled to precipitation and dissolution of a single mineral in one, two, and three dimensions. As an application, we consider explicit analytical solutions for systems containing one or two solute species that describe the evolution of solutes and solid concentrations as well as porosity. We use one of the proposed analytical solutions to test numerical solutions obtained from two conceptually different reactive transport codes. Both numerical implementations could be verified with the help of the analytical solutions and show good agreement in terms of spatial and temporal evolution of concentrations and porosities.

X-ray microtomography characterization of porosity, permeability and reactive surface changes during dissolution

Abstract. We explore coupling to a configurable subsurface reactive transport code as a flexible and extensible approach to biogeochemistry in land surface models. A reaction network with the Community Land Model carbon–nitrogen (CLM-CN) decomposition, nitrification, denitrification, and plant uptake is used as an example. We implement the reactions in the open-source PFLOTRAN (massively parallel subsurface flow and reactive transport) code and couple it with the CLM. To make the rate formulae designed for use in explicit time stepping in CLMs compatible with the implicit time stepping used in PFLOTRAN, the Monod substrate rate-limiting function with a residual concentration is used to represent the limitation of nitrogen availability on plant uptake and immobilization. We demonstrate that CLM–PFLOTRAN predictions (without invoking PFLOTRAN transport) are consistent with CLM4.5 for Arctic, temperate, and tropical sites.Switching from explicit to implicit method increases rigor but introduces numerical challenges. Care needs to be taken to use scaling, clipping, or log transformation to avoid negative concentrations during the Newton iterations. With a tight relative update tolerance (STOL) to avoid false convergence, an accurate solution can be achieved with about 50 % more computing time than CLM in point mode site simulations using either the scaling or clipping methods. The log transformation method takes 60–100 % more computing time than CLM. The computing time increases slightly for clipping and scaling; it increases substantially for log transformation for half saturation decrease from 10−3 to 10−9 mol m−3, which normally results in decreasing nitrogen concentrations. The frequent occurrence of very low concentrations (e.g. below nanomolar) can increase the computing time for clipping or scaling by about 20 %, double for log transformation. Overall, the log transformation method is accurate and robust, and the clipping and scaling methods are efficient. When the reaction network is highly nonlinear or the half saturation or residual concentration is very low, the allowable time-step cuts may need to be increased for robustness for the log transformation method, or STOL may need to be tightened for the clipping and scaling methods to avoid false convergence.As some biogeochemical processes (e.g., methane and nitrous oxide reactions) involve very low half saturation and thresholds, this work provides insights for addressing nonphysical negativity issues and facilitates the representation of a mechanistic biogeochemical description in Earth system models to reduce climate prediction uncertainty.

PFLOTRAN, a next-generation reactive flow and transport code for modeling subsurface processes, has been designed from the ground up to run efficiently on machines ranging from leadership-class supercomputers to laptops. Based on an object-oriented design, the code is easily extensible to incorporate additional processes. It can interface seamlessly with Fortran 9X, C and C++ codes. Domain decomposition parallelism is employed, with the PETSc parallel framework used to manage parallel solvers, data structures and communication. Features of the code include a modular input file, implementation of high-performance I/O using parallel HDF5, ability to perform multiple realization simulations with multiple processors per realization in a seamless manner, and multiple modes for multiphase flow and multicomponent geochemical transport. Chemical reactions currently implemented in the code include homogeneous aqueous complexing reactions and heterogeneous mineral precipitation/dissolution, ion exchange, surface complexation and a multirate kinetic sorption model. PFLOTRAN has demonstrated petascale performance using 2{sup 17} processor cores with over 2 billion degrees of freedom. Accomplishments achieved to date include applications to the Hanford 300 Area and modeling CO{sub 2} sequestration in deep geologic formations.

Coupled transport-reaction modeling of the long-term interaction between iron, bentonite and Callovo-Oxfordian claystone in radioactive waste confinement systems

<p>Salt deposits host an important industrial raw material and provide storage capacities for energy and nuclear waste. However, leaching zones can seriously endanger the development and utilisation of salt deposits for these purposes, especially if these occur in potash seams. Their increased solubility enables even NaCl-saturated solutions, if present, to deeply penetrate these seams. The resulting salt dissolution processes generate fluid flow paths and affect the mechanical rock integrity. To model the timely evolution of leaching zones and to assess their hazard potential, a reactive transport model has been developed, taking into account not only the complex dissolution and precipitation behaviour of potash salts, but also the resulting porosity and permeability changes as well as density-driven chemical species transport. Additionally, the model makes use of an approach to describe transport and chemical reactions at the interface between impermeable (dry) salt rocks and permeated leaching zones (Steding et al., 2021). In the present study, we focus on the effect of heterogeneity of the mineral distribution within potash seams and on the influence of mineral- and saturation-dependent dissolution rates.</p><p>The applied reactive transport model is based on a coupling of the geochemical module PHREEQC (Parkhurst & Appelo, 2013) with the TRANSport Simulation Environment (Kempka, 2020) as well as the newly developed extension of an interchange approach (Steding et al., 2021). A numerical model has been developed and applied to simulate the leaching process of a carnallite-bearing potash seam due to natural density-driven convection. The results show that both, the mineral composition and dissolution rate of the original salt rock, strongly influence the shape and evolution of the leaching zone (Steding et al., 2021).</p><p>In nature, strong variations of the mineralogy occur within potash seams with random or stratified distributions. Furthermore, dissolution rates depend on the mineral itself as well as on its saturation state. Both may considerably influence the growth rate of a leaching zone. Therefore, the reactive transport model has been extended by mineral- and saturation-dependent dissolution rates. A scenario analysis has been undertaken to compare the impact of homogeneous and heterogeneous rock compositions. For that purpose, the carnallite content in the potash seam was varied from 5 to 25 wt. % including different stratifications and random distributions. The simulations were classified by means of the Péclet and Damköhler numbers, and the long-term behaviour as well as hazard potential are discussed.</p><p> </p><p>

This paper describes a preliminary hydrochemical study of a Triassic Sandstone aquifer in the UK East Midlands which is contaminated by coal tar waste products from a former coal-carbonization plant. Processes controlling the attenuation of inorganic species within the identified plume are examined, supported by equilibrium and reactive transport modelling of contaminant fate. The study forms part of a more detailed research programme examining the long term fate of pollutants from this site in the aquifer. Groundwater beneath the site is polluted with NH 4 (up to 350 mg l -1 ), SO 4 and NVOC from the plant and nearby coal mining operations. Concentrations of organic chemicals within the plume are not significant. The aquifer is calcareous, (Fe) oxide-rich and aerobic, and geochemical modelling suggests that the native groundwater chemistry is primarily controlled by carbonate equilibria. Anaerobic conditions are sustained within the plume by microbial oxidation of the NH 4 and NVOC load which is coupled to the reduction of native Fe oxides. Sulphate is transported conservatively within the plume. The NH 4 load is primarily attenuated by cation exchange reactions with the aquifer sediments. This is supplemented by nitrification at the plume margins under conditions of higher oxygen flux which generates locally elevated NO 3 concentrations and depressed pH in the contaminated groundwater. Elevated alkalinity within the plume is consistent with dissociation of the ammonia waste stream during groundwater transport and is an important control on the increased porewater Ca and Fe load mobilized by cation-exchange and redox reactions. A conceptual model of the key processes affecting contaminant fate within the plume is presented and the implications for aquifer clean-up are discussed.

Two types of fluids are encountered in the Onikobe geothermal reservoir (Japan): one is neutral and the other is acidic. It is hypothesized that acidic fluid might be upwelling along a fault zone from magma and that an impermeable barrier might be present between the acidic and neutral fluid zones. To test such a conceptual model and to study the geochemical behavior due to mixing of the two fluids, reactive geothermal transport simulations under both natural and production conditions were carried out using the code TOUGHREACT. Results indicate Mn‐rich smectite precipitates near the mixing front. Precipitation of sphalerite and galena occurs in a similar region as the Mn‐rich smectite. Precipitation of these minerals depends on pH and temperature. In addition, quartz, pyrite, and calcite precipitate in the shallow zone resulting in further development of caprock. The changes in porosity and permeability due to precipitation of Mn‐rich smectite are small compared with that of quartz, calcite, and pyrite. However, the smectite precipitation is likely to fill open fractures and to form an impermeable barrier between acidic and neutral fluid regions. The simulated mineral assemblage is generally consistent with observations in the Onikobe field. The numerical simulations described here provide useful insight into geochemical behavior and formation of impermeable barriers from fluid mixing. The method presented in this paper may be useful in fundamental analysis of hydrothermal systems and in the exploration of geothermal reservoirs, including chemical evolution, mineral alteration, mineral scaling, and changes in porosity and permeability.

Weathering of rocks as a result of exposure to water and the atmosphere can cause significant changes in their chemistry and porosity. In low‐porosity rocks, such as basalts, changes in porosity, resulting from chemical weathering, are likely to modify the rock's effective diffusivity and permeability, affecting the rate of solute transport and thus potentially the rate of overall weathering to the extent that transport is the rate limiting step. Changes in total porosity as a result of mineral dissolution and precipitation have typically been used to calculate effective diffusion coefficients through Archie's law for reactive transport simulations of chemical weathering, but this approach fails to account for unconnected porosity that does not contribute to transport. In this study, we combine synchrotron X‐ray microcomputed tomography (μCT) and laboratory and numerical diffusion experiments to examine changes in both total and effective porosity and effective diffusion coefficients across a weathering interface in a weathered basalt clast from Costa Rica. The μCT data indicate that below a critical value of ∼9%, the porosity is largely unconnected in the basalt clast. The μCT data were further used to construct a numerical pore network model to determine upscaled, effective diffusivities as a function of total porosity (ranging from 3 to 30%) for comparison with diffusivities determined in laboratory tracer experiments. By using effective porosity as the scaling parameter and accounting for critical porosity, a model is developed that accurately predicts continuum‐scale effective diffusivities across the weathering interface of the basalt clast.