A two-pressure model for slightly compressible single phase flow in bi-structured porous media

Problems involving flow in porous media are ubiquitous in many natural and engineered systems. Mathematical modeling of such systems often relies on homogenization of pore-scale equations and macroscale continuum descriptions. For single phase flow, Stokes equations at the pore-scale are generally approximated by Darcy’s law at a larger scale. In this work, we develop an alternative model to Darcy’s law that can be used to describe slightly compressible single phase flow within bi-structured porous media. We use the method of volume averaging to upscale mass and momentum balance equations with the fluid phase split into two fictitious domains. The resulting macroscale model combines two coupled equations for average pressures with regional Darcy’s laws for velocities. In these equations, effective parameters are expressed via integrals of mapping variables that solve boundary value problems over a representative unit cell. Finally, we illustrate the behaviour of these equations in a two-dimensional model porous medium and validate our approach by comparing solutions of the homogenized equations with computations of the exact microscale problem

Multiphase flow modeling in multiscale porous media: An open-source micro-continuum approach

International audienceA multiphase Darcy-Brinkman approach is proposed to simulate two-phase flow in hybrid systems containing both solid-free regions and porous matrices. This micro-continuum model is rooted in elementary physics and volume averaging principles, where a unique set of partial differential equations is used to represent flow in both regions and scales. The crux of the proposed model is that it tends asymptotically towards the Navier-Stokes volume-of-fluid approach in solid-free regions and towards the multiphase Darcy equations in porous regions. Unlike existing multiscale multiphase solvers, it can match analytical predictions of capillary, relative permeability, and gravitational effects at both the pore and Darcy scales. Through its open-source implementation, hybridPorousInterFoam, the proposed approach marks the extension of computational fluid dynamics (CFD) simulation packages into porous multiscale, multiphase systems. The versatility of the solver is illustrated using applications to two-phase flow in a fractured porous matrix and wave interaction with a porous coastal barrier

Orange hydrogen is the new green

International audienceMaintaining global warming well below 2 °C, as stipulated in the Paris Agreement, will require a complete overhaul of the world energy system. Hydrogen is considered to be a key component of the decarbonization strategy for large parts of the transport system, as well as some heavy industries. Today, about 96% of current hydrogen production comes from the steam reforming of coal or natural gas (labelled black and grey hydrogen, respectively). If hydrogen is to become a solution, then black and grey hydrogen need to be replaced by a low-carbon option. One method that has received much attention is to produce so-called green hydrogen by coupling water electrolysis with renewable energies. However, green hydrogen is expensive and energy-intensive to produce. Here, we explore an alternative option and highlight the benefits of rock-based hydrogen (white and orange) compared with classic electrolysis-based technologies. We show that the exploitation of native hydrogen and its combination with carbon sequestration has the potential to fuel a large part of the energy transition without the substantial energy and raw material cost of green hydrogen

Multiphase micro-continuum models: a hybrid-scale approach

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A benchmark for the numerical simulation of pore-scale mineral dissolution with fluid-solid interface evolution

International audienceThis talk 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, dissolution-driven geometry evolution in two dimensions, and a three-dimensional dissolution-driven geometry evolution including an experimental validation. Five codes are used to obtain the solution to this benchmark problem, including Chombo-Crunch, OpenFOAM-DBS, a lattice Boltzman code, Vortex method, 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. Among the discretization methods, one can find finite volumes, Lagrangian methods, grid based methods (stochastic and deterministic). 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.References[1] S. Molins, C. Soulaine, N. I. Prasianakis, A. Abbasi, P. Poncet, A. J. C. Ladd, V.Starchenko, S. Roman, D. Trebotich, H. A. Tchelepi, and C. I. Steefel,Simulation ofmineral dissolution at the pore scale with evolving fluid-solid interfaces: Review of ap-proaches and benchmark problem set, to appear in Computational Geosciences, 2019

Simulation of mineral dissolution at the pore scale with evolving fluid-solid interfaces: review of approaches and benchmark problem set

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