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This work investigates the performance of the on-demand machine learning (ODML) algorithm introduced in Leal et al. ( Transp. Porous Media 133 (2), 161–204, 2020 ) when applied to different reactive transport problems in heterogeneous porous media. This approach was devised to accelerate the computationally expensive geochemical reaction calculations in reactive transport simulations. We demonstrate that even with a strong heterogeneity present, the ODML algorithm speeds up these calculations by one to three orders of magnitude. Such acceleration, in turn, significantly advances the entire reactive transport simulation. The performed numerical experiments are enabled by the novel coupling of two open-source software packages : Reaktoro (Leal 2015 ) and Firedrake (Rathgeber et al. ACM Trans. Math. Softw. 43 (3), 2016 ). The first library provides the most recent version of the ODML approach for the chemical equilibrium calculations, whereas, the second framework includes the newly implemented conservative Discontinuous Galerkin finite element scheme for the Darcy problem, i.e., the Stabilized Dual Hybrid Mixed (SDHM) method Núñez et al. ( Int. J. Model. Simul. Petroleum Industry , 6, 2012 ).

Aims The objective of this research was to develop a three-dimensional (3D) rhizosphere modeling capability for plant-soil interactions by integrating plant biophysics, water and ion uptake and release from individual roots, variably saturated flow, and multicomponent reactive transport in soil. Methods We combined open source software for simulating plant and soil interactions with parallel computing technology to address highly-resolved root system architecture (RSA) and coupled hydrobiogeochemical processes in soil. The new simulation capability was demonstrated on a model grass, Brachypodium distachyon . Results In our simulation, the availability of water and nutrients for root uptake is controlled by the interplay between 1) transpiration-driven cycles of water uptake, root zone saturation and desaturation; 2) hydraulic redistribution; 3) multicomponent competitive ion exchange; 4) buildup of ions not taken up during kinetic nutrient uptake; and 5) advection, dispersion, and diffusion of ions in the soil. The uptake of water and ions by individual roots leads to dynamic, local gradients in ion concentrations. Conclusion By integrating the processes that control the fluxes of water and nutrients in the rhizosphere, the modeling capability we developed will enable exploration of alternative RSAs and function to advance the understanding of the coupled hydro-biogeochemical processes within the rhizosphere.

Simulating reactive transport in fractured porous media is computationally demanding since it requires solving physical and chemical processes that non-linearly affect each other. At the same time, the processes strongly depend on the presence of fractures. Fractures typically behave as shortcuts for flow and transport, while chemical reactions can trigger mineral dissolution or precipitation that might alter the fracture conductivity, thereby modifying the flow regime. The computational demands increase with the number of chemical species, subject to chemical equilibrium and kinetics, and with the complexity of fracture networks. In the case of reservoir simulations, where there are a considerable number of chemical species and fracture networks are highly complex, the computational requirements are severe. In this paper, we present a simulation strategy that handles reactive transport processes with numerous chemical reactions and their two-way interaction with fractures. The governing processes are modelled by conservation equations, joint with ordinary differential equations and non-linear algebraic equations. The fractures are explicitly represented and treated as lower-dimensional objects. We propose a sequential fully implicit procedure to solve the model equations, where the flow and transport equations are solved in a global sense using the open-source code PorePy and the chemical equations are solved using the open-source code Reaktoro. The implementation is established by comparing our simulation results to those from a previously presented study. Moreover, we also show that the presented simulation strategy can handle the coupled processes in porous media with numerous chemical species and intersecting fractures.

High‐resolution, three‐dimensional, reactive flow and transport simulations are carried out to describe the migration of hexavalent uranium [U(VI)] at the Hanford 300 Area bordering the Columbia River and to better understand the persistence of the uranium plume at the site. The computer code PFLOTRAN developed under a DOE SciDAC‐2 project is employed in the simulations that are executed on ORNL's Cray XT4/XT5 supercomputer Jaguar. The conceptual model used in the simulations is based on the recognition of three distinct phases or time periods in the evolution of the U(VI) plume. These correspond to (1) initial waste emplacement; (2) initial presence of both labile and nonlabile U(VI) with an evolved U(VI) plume extending from the source region to the river boundary, representing present‐day conditions; and (3) the complete removal of all nonlabile U(VI) and labile U(VI) in the vadose zone. This work focuses primarily on modeling Phase II using equilibrium and multirate sorption models for labile U(VI) and a continuous source release of nonlabile U(VI) in the South Process Pond through dissolution of metatorbernite as a surrogate mineral. For this case, rapid fluctuations in the Columbia River stage combined with the slow release of nonlabile U(VI) from contaminated sediment are found to play a predominant role in determining the migration behavior of U(VI) with sorption only a second‐order effect. Nevertheless, a multirate model was essential in explaining breakthrough curves obtained from laboratory column experiments using the same sediment and is demonstrated to be important in Phase III. The calculations demonstrate that U(VI) is discharged to the river at a highly fluctuating rate in a ratchet‐like behavior as the river stage rises and falls. The high‐frequency fluctuations must be resolved in the model to calculate the flux of U(VI) at the river boundary. By time averaging the instantaneous flux to average out noise superimposed on the river stage fluctuations, the cumulative U(VI) flux to the river is found to increase approximately linearly with time. The flow rate and U(VI) flux are highly sensitive to the conductance boundary condition that describes the river‐sediment interface. By adjusting the conductance coefficient to give a better match to the measured piezometric head, good agreement was obtained with field studies for both the mean flux of water of 109 kg/yr and U(VI) of 25 kg/yr at the river‐aquifer boundary for a computational domain encompassing the South Process Pond. Finally, it is demonstrated that, through global mass conservation, the U(VI) leach rate from the source region is related to the U(VI) flux at the river boundary.

This study explores field‐scale modeling of U(VI) reactive transport through incorporation of laboratory and field data. A field‐scale reactive transport model was developed on the basis of laboratory‐characterized U(VI) surface complexation reactions (SCRs) and multirate mass transfer processes, as well as field‐measured hydrogeochemical conditions at the U.S. Department of Energy, Hanford 300 Area (300 A), Washington. The model was used to assess the importance of multirate mass transfer processes on U(VI) reactive transport and to evaluate the effect of variable geochemical conditions caused by dynamic river water‐groundwater interactions on U(VI) plume migration. Model simulations revealed complex spatiotemporal relationships between groundwater composition and U(VI) speciation, adsorption, and plume migration. In general, river water intrusion enhances uranium adsorption and lowers aqueous uranium concentration because river water dilution increases pH and decreases aqueous bicarbonate concentration, leading to overall enhanced U(VI) surface complexation. Strong U(VI) retardation was computed for the field‐measured hydrogeochemical conditions, suggesting a slow dissipation of the U(VI) plume, a phenomenon consistent with field observations. The simulations also showed that SCR‐retarded U(VI) migration becomes more dynamic and synchronous with the groundwater flow field when multirate mass transfer processes are involved. Breakthrough curves at selected locations and the temporal changes in the calculated mass during the 20 year simulation period indicated that uranium adsorption/desorption never attained steady state because of the dynamic flow field and groundwater composition variations caused by river water intrusion. Thus, the multirate SCR model appears to be a crucial consideration for future reactive transport simulations of uranium contaminants at the Hanford 300 A site and elsewhere under similar hydrogeochemical conditions.

For the purpose of geological carbon storage, it is necessary to understand the long-term effects of introducing CO2 and sulfur-species into saline aquifers. CO2 stripped from the flue gas during the carbon capture process may contain trace SO2 and H2S and it may be economically beneficial to inject S-bearing CO2 rather than costly purified CO2. Furthermore, reactions between the S-CO2-bearing formation brines and formation minerals will increase pH and promote further dissolution and precipitation reactions. To investigate this we model reactions in a natural analog where CO2- and SO4-H2S bearing fluids have reacted with clay-rich siltstones. In the Mid-Jurassic Carmel formation in a cap rock to a natural CO2-bearing reservoir at Green River, Utah, a 3.1 mm wide bleached alteration zone is observed at the uppermost contact between a primary gypsum bed and red siltstone. Gypsum at the contact is ∼1 mm thick and shows elongate fibers perpendicular to the siltstone surface, suggesting fluid flow along the contact. Mineralogical concentrations, analyzed by Quantitative Evaluation of Minerals by SCANning electron microscopy (QEMSCAN), show the altered siltstone region comprises two main zones: a 0.8 mm wide, hematite-poor, dolomite-poor, and illite-rich region adjacent to the gypsum bed; and a 2.3 mm wide, hematite-poor, dolomite-poor, and illite-poor region adjacent to the hematite alteration front. A one-component analytical solution to reactive-diffusive transport for the bleached zone implies it took less than 20 yr to form before the fluid self-sealed, and that literature hematite dissolution rates between 10-8 and 10-7 mol/m2/s are valid for likely diffusivities. Multi-component reactive-diffusive transport equilibrium modeling for the full phase assemblage, conducted with PHREEQC, suggests dissolution of hematite and dolomite and precipitation of illite over similar short timescales. Reaction progress with CO2-bearing, SO4-rich, and minor H2S-bearing fluids is shown to be much faster than with CO2-poor, SO4-rich with minor H2S-bearing fluids. The substantial buffering capacity of mineral reactions demonstrated by the S- and CO2-related alteration of hematite-bearing siltstones at the Green River CO2 accumulation implies that corrosion of such a cap rock are, at worst, comparable to the 10 000 yr timescales needed for carbon storage.

In this paper we present an improved method for handling Neumann or Robin boundary conditions in smoothed particle hydrodynamics. The Neumann and Robin boundary conditions are common to many physical problems (such as heat/mass transfer), and can prove challenging to model in volumetric modeling techniques such as smoothed particle hydrodynamics (SPH). A new SPH method for diffusion type equations subject to Neumann or Robin boundary conditions is proposed. The new method is based on the continuum surface force model [1] and allows an efficient implementation of the Neumann and Robin boundary conditions in the SPH method for geometrically complex boundaries. The paper discusses the details of the method and the criteria needed to apply the model. The model is used to simulate diffusion and surface reactions and its accuracy is demonstrated through test cases for boundary conditions describing different surface reactions.

Geophysical models for pressure solution are typically developed for diffusion-controlled or reaction-controlled scenarios. We present a unified analytical model that considers fully coupled diffusion and reaction during pressure solution. The model recovers the diffusion-controlled and reaction-controlled models in the literature as specific limiting cases. When diffusion and reaction exhibit comparable influences, we validate the proposed model against independent numerical simulations. The proposed model is then employed in interpreting experimental measurements, demonstrating a better agreement compared to previous interpretations.

The diverse range of patterns in porous media formed by dissolution processes depends on the relative magnitude of flow, transport, and chemical reactions at pore surfaces. However, distinguishing between regimes often relies solely on qualitative, visual comparisons of emergent structures. Here, we propose a quantitative measure capable of identifying different regimes using the concept of the spatial flow focusing profile, which segments the medium into cross sections along the flow direction to calculate the flow focusing index for each section. We employ this measure in numerical simulations of a dissolving porous medium using a pore network model. We obtain a morphological phase diagram of dissolution patterns, which we characterize using the flow focusing profile. In particular, we demonstrate that analyzing the temporal changes in the profile allows one to quantitatively distinguish between wormholing and channeling. The transition between them is shown to be affected by the heterogeneity of the system.

A laboratory‐derived conceptual and numerical model for U(VI) transport at the Hanford 300A site, Washington, USA, was applied to a range of field‐scale scenarios of different geochemical complexity to identify the importance of individual processes in controlling the fate of U(VI), as well as to elucidate the characteristic differences between well‐defined laboratory and the more complex field‐scale conditions. Therefore, a rigorous sensitivity analysis was carried out for the various simulation scenarios. The underlying conceptual and numerical model, originally developed from column experiment data, includes distributed rate surface complexation kinetics of U(VI), aqueous speciation, and physical nonequilibrium transport processes. The field scenarios accounted additionally for highly transient groundwater flow and variable geochemical conditions driven by frequent water level changes of the nearby Columbia River. The results of the sensitivity analysis showed not only similarities but also important differences in parameter sensitivities between the laboratory and field‐scale models. It was found that the actual degree of sorption disequilibrium, actual concentration of sorbed U(VI), and the sorption extent (i.e., theoretical concentration of sorbed U(VI) at equilibrium) are the major controls for the magnitude of the calculated parameter sensitivities. These internal model variables depended mainly on (1) the groundwater flow conditions, i.e., the relatively long phases of limited groundwater movement in the field scale (intercepted by short peak flow events) and the long sustained flow phases in the column experiment (intercepted by relatively short stop flow events), and (2) the sampling location in the field‐scale model, i.e., plume fringe versus plume center.