The Effect of Pore-Scale Two-Phase Flow on Mineral Reaction Rates

In various natural and engineered systems, mineral–fluid interactions take place in the presence of multiple fluid phases. While there is evidence that the interplay between multiphase flow processes and reactions controls the evolution of these systems, investigation of the dynamics that shape this interplay at the pore scale has received little attention. Specifically, continuum scale models rarely consider the effect of multiphase flow parameters on mineral reaction rates or apply simple corrections as a function of the reactive surface area or saturation of the aqueous phase, without developing a mechanistic understanding of the pore-scale dynamics. In this study, we developed a framework that couples the two-phase flow simulator of OpenFOAM (open field operation and manipulation) with the geochemical reaction capability of CrunchTope to examine pore-scale dynamics of two phase flow and their impacts on mineral reaction rates. For our investigations, flat 2D channels and single sine wave channels were used to represent smooth and rough geometries. Calcite dissolution in these channels was quantified with single phase flow and two phase flow at a range of velocities. We observed that the bulk calcite dissolution rates were not only affected by the loss of reactive surface area as it becomes occupied by the non-reactive non-aqueous phase, but also largely influenced by the changes in local velocity profiles, e.g., recirculation zones, due to the presence of the non-aqueous phase. The extent of the changes in reaction rates in the two-phase systems compared to the corresponding single phase system is dependent on the flow rate (i.e., capillary number) and channel geometry, and follows a non-monotonic relationship with respect to aqueous saturation. The pore-scale simulation results highlight the importance of interfacial dynamics in controlling mineral reactions and can be used to better constrain reaction rate descriptions in multiphase continuum scale models. These results also emphasize the need for experimental studies that underpin the development of mechanistic models for multiphase flow in reactive systems.

Continuum-Scale Gas Transport Modeling in Organic Nanoporous Media Based on Pore-Scale Density Distributions

This paper presents a continuum-scale diffusion-based model informed by pore-scale data for gas transport in organic nanoporous media. A mass transfer and adsorption model is developed by considering multiple transport and storage mechanisms, including bulk diffusion and Knudsen diffusion for free phase, surface diffusion for sorbed phase, and multilayer adsorption. The continuum-scale diffusion-based governing equation is developed solely based on free phase concentration for the overall mass conservation of free and sorbed phases, carrying a newly-defined effective diffusion coefficient and a capacity factor to account for multilayer adsorption. Diffusion of free and sorbed phases is coupled through the pore-scale simplified local density method based on the modified Peng-Robinson equation of state for confinement effects. The model is first utilized to analyze pore-scale adsorption data from the krypton (Kr) gas adsorption experiment on graphite. Then we implement the model to conduct sensitivity analysis for the effects of pore size on gas transport for Kr-graphite and methane-coal systems. The model is finally used to study Kr diffusion profiles through a coal matrix obtained through X-ray micro-CT imaging. The results show that the sorbed phase occupies most of the pore space in organic nanoporous media due to multilayer adsorption, and surface diffusion contributes significantly to the total mass flux. Therefore, neglecting the volume of sorbed phase and surface diffusion in organic nanoporous rocks may result in considerable errors. Furthermore, the results reveal that implementing a Langmuir-based model may be erroneous for an organic-rich reservoir with nanopores during the early depletion period when the reservoir pressure is high.

Continuum Scale Non Newtonian Particle Transport Model for Hæmorheology

We present a continuum scale particle transport model for red blood cells following collision arguments, in a diffusive flux formulation. The model is implemented in FOAM, in a framework suitable for haemodynamics simulations and adapted to multi-scaling. Specifically, the framework we present is able to ingest transport coefficient models to be derived, prospectively, from complimentary but independent meso-scale simulations. For present purposes, we consider modern semi-mechanistic rheology models, which we implement and test as proxies for such data. The model is verified against a known analytical solution and shows excellent agreement for high quality meshes and good agreement for typical meshes as used in vascular flow simulations. Simulation results for different size and time scales show that migration of red blood cells does occur on physiologically relevany timescales on small vessels below 1 mm and that the haematocrit concentration modulates the non-Newtonian viscosity. This model forms part of a multi-scale approach to haemorheology and model parameters will be derived from meso-scale simulations using multi-component Lattice Boltzmann methods. The code, haemoFoam, is made available for interested researchers.

Linking rhizosphere processes across scales: Opinion

Purpose Simultaneously interacting small-scale rhizosphere processes determine emergent plant-scale behaviour, including growth, transpiration, nutrient uptake, soil carbon storage and transformation by microorganisms. Current advances in modelling and experimental methods open the path to unravel and link those processes. Methods We present a series of examples of state-of-the art simulations addressing this multi-scale, multi-process problem from a modelling point of view, as well as from the point of view of integrating newly available rhizosphere data and images. Results Each example includes a model that links scales and experimental data to set-up simulations that explain and predict spatial and temporal distribution of rhizodeposition as driven by root architecture development, soil structure, presence of root hairs, soil water content and distribution of soil water. Furthermore, two models explicitly simulate the impact of the rhizodeposits on plant nutrient uptake and soil microbial activity, respectively. This exemplifies the currently available state of the art modelling tools in this field: image-based modelling, pore-scale modelling, continuum scale modelling and functional-structural plant modelling. We further show how to link the pore scale to the continuum scale by homogenisation or by deriving effective physical parameters like viscosity from nano-scale chemical properties. Conclusion Modelling allows to integrate and make use of new experimental data across different rhizosphere processes (and thus across different disciplines) and scales. Described models are tools to test hypotheses and consequently improve our mechanistic understanding of how rhizosphere processes impact plant-scale behaviour. Linking multiple scales and processes is the logical next step for future research.