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The scale‐dependence of geochemical reaction rates hinders their use in continuum scale models intended for the interpretation and prediction of chemical fate and transport in subsurface environments such as those considered for geologic sequestration of CO2. Processes that take place at the pore scale, especially those involving mass transport limitations to reactive surfaces, may contribute to the discrepancy commonly observed between laboratory‐determined and continuum‐scale or field rates. Here, the dependence of mineral dissolution rates on the pore structure of the porous media is investigated by means of pore scale modeling of flow and multicomponent reactive transport. The pore scale model is composed of high‐performance simulation tools and algorithms for incompressible flow and conservative transport combined with a general‐purpose multicomponent geochemical reaction code. The model performs direct numerical simulation of reactive transport based on an operator‐splitting approach to coupling transport and reactions. The approach is validated with a Poiseuille flow single‐pore experiment and verified with an equivalent 1‐D continuum‐scale model of a capillary tube packed with calcite spheres. Using the case of calcite dissolution as an example, the high‐resolution model is used to demonstrate that nonuniformity in the flow field at the pore scale has the effect of decreasing the overall reactivity of the system, even when systems with identical reactive surface area are considered. The effect becomes more pronounced as the heterogeneity of the reactive grain packing increases, particularly where the flow slows sufficiently such that the solution approaches equilibrium locally and the average rate becomes transport‐limited. Key Points Average reaction rates depend on the pore structure and resulting pore‐scale flow Reactive surface area from pore scale geometry accounts for dependence of rates Direct numerical simulation of the pore scale gives insights into averaged rates

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.

Reactive transport in fractured media is conceptualized as a multi-scale problem that couples a pore-scale component, which comprises Navier–Stokes flow, multi-component transport and aqueous equilibrium in the fracture, and a Darcy-scale component, which comprises multi-component diffusive transport, aqueous equilibrium and mineral reactions in the porous matrix. The model that implements this multi-scale approach builds on an existing pore-scale model and is able to capture complex fracture geometries with the embedded-boundary method. The embedded boundary acts as the interface between pore- and Darcy-scale domains. Adaptive mesh refinement is used to match resolutions at the interface while using coarser resolution away from the interface when not needed in the Darcy-scale domain. The new model is validated and then compared to results from a pore-scale model. Multi-scale model results are shown to be equivalent to pore-scale results under diffusion-controlled reactions in the pore scale and very fast dissolution in the Darcy scale. The multi-scale model provides a more accurate solution for a given resolution as it effectively sets the equilibrium concentrations as boundary conditions. The multi-scale model is capable to capture flow channelization observed in an experimental fractured core and, at the same time, limitations in the dissolution of calcite by diffusive transport through an altered porous layer. Discrepancies in effluent calcium concentrations between the multi-scale results and results from a reduced-dimension Darcy-scale model for this fractured core experiment are attributed to the solution of the flow field and the gradients that develop inside the fracture. Discrepancies in effluent magnesium concentrations exemplify the limitations of the approach because the multi-scale model requires calibration of reactive surface areas as Darcy-scale continuum models.

Reactive transport in fractured media is conceptualized as a multi-scale problem that couples a pore-scale component, which comprises Navier–Stokes flow, multi-component transport and aqueous equilibrium in the fracture, and a Darcy-scale component, which comprises multi-component diffusive transport, aqueous equilibrium and mineral reactions in the porous matrix. The model that implements this multi-scale approach builds on an existing pore-scale model and is able to capture complex fracture geometries with the embedded-boundary method. The embedded boundary acts as the interface between pore- and Darcy-scale domains. Adaptive mesh refinement is used to match resolutions at the interface while using coarser resolution away from the interface when not needed in the Darcy-scale domain. The new model is validated and then compared to results from a pore-scale model. Multi-scale model results are shown to be equivalent to pore-scale results under diffusion-controlled reactions in the pore scale and very fast dissolution in the Darcy scale. The multi-scale model provides a more accurate solution for a given resolution as it effectively sets the equilibrium concentrations as boundary conditions. The multi-scale model is capable to capture flow channelization observed in an experimental fractured core and, at the same time, limitations in the dissolution of calcite by diffusive transport through an altered porous layer. Discrepancies in effluent calcium concentrations between the multi-scale results and results from a reduced-dimension Darcy-scale model for this fractured core experiment are attributed to the solution of the flow field and the gradients that develop inside the fracture. Discrepancies in effluent magnesium concentrations exemplify the limitations of the approach because the multi-scale model requires calibration of reactive surface areas as Darcy-scale continuum models.

We present a second-order accurate finite difference method for numerical solution of the incompressible Navier-Stokes equations in deforming domains. Our approach is a generalization of the Bell-Colella-Glaz predictor-corrector method for incompressible flow. In order to treat the time-dependence and inhomogeneities in the incompressibility constraint introduced by presence of deforming boundaries, we introduce a nontrivial splitting of the velocity field into vortical and potential components to eliminate the inhomogeneous terms in the constraint and a generalization of the Bell-Colella-Glaz algorithm to treat time-dependent constraints. The method is second-order accurate in space and time, has a time step constraint determined by the advective Colella-Friedrichs-Lewy condition, and requires the solution of well behaved linear systems amenable to the use of fast iterative methods. We demonstrate the method on the specific example of viscous incompressible flow in an axisymmetric deforming tube.

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.

We have developed a simulation capability to model multiscale flow and transport in complex biological systems based on algorithms and software infrastructure developed under the SciDAC APDEC CET. The foundation of this work is a new hybrid fluid-particle method for modeling polymer fluids in irregular microscale geometries that enables long-time simulation of validation experiments. Both continuum viscoelastic and discrete particle representations have been used to model the constitutive behavior of polymer fluids. Complex flow environment geometries are represented on Cartesian grids using an implicit function. Direct simulation of flow in the irregular geometry is then possible using embedded boundary/volume-of-fluid methods without loss of geometric detail. This capability has been used to simulate biological flows in a variety of application geometries including biomedical microdevices, anatomical structures and porous media.

The scale-dependence of geochemical reaction rates hinders their use in continuum scale models intended for the interpretation and prediction of chemical fate and transport in subsurface environments such as those considered for geologic sequestration of CO2. Processes that take place at the pore scale, especially those involving mass transport limitations to reactive surfaces, may contribute to the discrepancy commonly observed between laboratory-determined and continuum-scale or field rates. In this study we investigate the dependence of mineral dissolution rates on the pore structure of the porous media by means of pore scale modeling of flow and multicomponent reactive transport. The pore scale model is composed of high-performance simulation tools and algorithms for incompressible flow and conservative transport combined with a general-purpose multicomponent geochemical reaction code. The model performs direct numerical simulation of reactive transport based on an operator-splitting approach to coupling transport and reactions. The approach is validated with a Poiseuille flow single-pore experiment and verified with an equivalent 1-D continuum-scale model of a capillary tube packed with calcite spheres. Using the case of calcite dissolution as an example, the high-resolution model is used to demonstrate that nonuniformity in the flow field at the pore scale has the effect of decreasing the overall reactivity of the system, even when systems with identical reactive surface area are considered. In conclusion, the effect becomes more pronounced as the heterogeneity of the reactive grain packing increases, particularly where the flow slows sufficiently such that the solution approaches equilibrium locally and the average rate becomes transport-limited.

This paper presents a conservative front-tracking method for shocks and contact discontinuities that is second-order accurate. It is based on a volume-of-fluid method that treats the moving front with concepts similar to those of an embedded-boundary method. Special care is taken in the centering of the data to ensure the right order of accuracy at the front, and a redistribution step guarantees conservation. A suite of test problems, for tracking both shocks and contact discontinuities, is presented that confirms that the method is second-order accurate.