Mortar coupling and upscaling of pore-scale models

Abstract

Pore-scale models are becoming increasingly useful as predictive tools for modeling flow and transport in porous media. These models can accurately represent the 3D pore-structure of real media. Currently first-principles modeling methods are being employed for obtaining qualitative and quantitative behavior. Generally, artificial, simple boundary conditions are imposed on a model that is used as a stand-alone tool for extracting macroscopic parameters. However, realistic boundary conditions, reflecting flow and transport in surrounding media, may be necessary for behavior that occurs over larger length scales or including pore-scale models in a multiscale setting. Here, pore-scale network models are coupled to adjacent media (additional pore-scale or continuum-scale models) using mortars. Mortars are 2D finite-element spaces employed to couple independent subdomains by enforcing continuity of pressure and flux at shared boundary interfaces. While mortars have been used in the past to couple subdomains of different models, physics, and meshes, they are extended here for the first time to pore-scale models. The approach is demonstrated by modeling single-phase flow in coupled pore-scale models, but the methodology can be utilized to model dynamic processes and perform multiscale modeling in 3D continuum simulators for flow and transport.

A 3D coupled model of organic matter and inorganic matrix for calculating the permeability of shale

“…It decomposes the solution domain into several subdomains, then discretely solves the subdomains with the most suitable method according to their characteristics using a convenient parallel computing. Balhoff et al [23,29] extended Mortar for the first time to pore-scale models (such as coupling PNM to PNM and PNM to continuum). This study follows the idea of Balhoff and uses Mortar to realize the coupling of PNM and continuum which represent kerogen and inorganic matrix, respectively (Fig.…”

“…Mortar method can be referred from Balhoff [23] and it requests that the coupled interface must satisfy: (1) The pressure of the left and right subdomains of the interface is continuous. This rule is guaranteed by the property that the pressure of the boundary nodes of the subdomains is obtained based on their position in Mortar element.…”

“…In the previous literature, Balhoff [23] studied the coupling of 826 and 847 pores at the two sides of the interface. For 1 Â 1, 2 Â 2, 4 Â 4, 8 Â 8 Mortar grids, the maximum flux error is only 1.08% and the maximum pressure error is 0.8%.…”

“…However, those coupling strategies had limitations in terms of flexibility and efficiency. The limitations were avoided in a later work through the introduction of Mortar [23]. The advantages of Mortar are that it allows for different physics, scales, and models in various parts of the domain and is easily parallelizable.…”

High-Performance Modeling of Carbon Dioxide Sequestration by Coupling Reservoir Simulation and Molecular Dynamics

“…Battiatoa et al (2011) treat the flux exchange between the two scales as unknowns and an iterative process is applied at the pore scale to guarantee the flux continuity. Mortars have been also used to handle multiscale problems (Balhoff et al 2008;Sun et al 2012). The heterogeneous multiscale method (E and Engquist 2003) is used to couple the continuum-scale mass-conservation law with a discrete network model for steady-state single-phase flow (Chu et al 2012) and then extended to single-phase flow with nonlinear flux-pressure dependence and two-phase-flow problems (Chu et al 2013).…”