Title : A (real) multi-scale solver for two-phase flow: a micro-continuum approach
Speaker: Dr. Cyprien Soulaine
Affiliation: Associate Scientist at CNRS
Abstract:
Micro-continuum approaches are intermediate between a pure Navier-Stokes description of flow and transport and a continuum-scale model using Darcy’s law [1]. They use an unique formulation regardless the content of a grid cells, i.e. the same set of partial differential equations handles both pore-scale and Darcy-scale physics. Micro-continuum approaches are intrisincally two-scale allowing simulations with resolved and unresolved porosity in the same computational domain. For example, this hybrid-scale framework allows simulations in fractures (Stokes flow) surrounded by a porous matrix (Darcy’s law) [1]. It is therefore well-suited to simulate flow and transport in microtomography images that contain sub-voxel porosity [2]. The technique can also move fluid / solid boundaries in presence of geochemical processes such as dissolution or precipitation [3,4]. Recently, solid mechanics have been introduced into the framework to model the hydrology of soft porous media such as clays and elastic membranes [5].
The micro-continuum frameworks so far were limited to single-phase flow only. In this work, we propose a multi-scale solver for two-phase flow in porous media based on a multi-phase micro-continuum model. The model is rooted on the elementary physical principles and rigorously derived using the method of the volume averaging. Eventually, we obtain a single set of partial differential equations that can be used both at the pore-scale and the continuum-scale and also in hybrid-scale modeling for which the porosity in some regions of the computational domain is fully resolved while some other regions are unresolved. A particular attention is paid to derive an comprehensive physics in the porous domain including unsaturated conditions, capillary and gravity effects. The two-phase micro-continuum framework is verified through a series of test cases where reference solutions exist. We show that the multi-scale solver converges to the standard Darcy-scale solutions (Buckley-Leverett, capillary-gravity equilibrium, drainage in heterogeneous reservoir) when it is used in a coarse grid, and converges to the two-phase Navier-Stokes solutions (droplet in a flat surface, capillary rise, drainage with film deposition, two-phase flow in a complex porous structure) when it is used at the pore-scale.
[1] Soulaine and Tchelepi, Micro-continuum approach for pore-scale simulation of subsurface processes, Transport In Porous Media, 2016, 113, 431-456
[2] Soulaine, Gjetvaj, Garing, Roman, Russian, Gouze, Tchelepi, The impact of sub-resolution porosity of X-ray microtomography images on the permeability, Transport in Porous Media, 2016, 113(1), 227-243
[3] Soulaine, Roman, Kovscek, Hamdi, Mineral dissolution and wormholing from a pore-scale perspective, Journal of Fluid Mechanics, 2017, 827, 457--483
[4] Molins, Soulaine, Prasianakis, Abbasi, Poncet, Ladd, Starchenko, Roman, Trebotich, Tchelepi, Steefel, Simulation of mineral dissolution at the pore scale with evolving fluid-solid interfaces: Review of approaches and benchmark problem set, Computational Geosciences, 2019
[5] Carrillo and Bourg, A Darcy-Brinkman-Biot Approach to Modeling the Hydrology and Mechanics of Porous Media Containing Macropores and Deformable Microporous Regions, Water Resources Research, 2019
[6] Soulaine, Roman, Kovscek, Tchelepi, Pore-scale modelling of multiphase reactive flow. Application to mineral dissolution with production of CO2, Journal of Fluid Mechanics, 2018, 855, 616–645
[7] Soulaine, Creux, Tchelepi, Micro-Continuum Framework for Pore-Scale Multiphase Fluid Transport in Shale Formations, Transport in Porous Media, 2019
