Nonlocal multicontinuum (NLMC) upscaling of mixed dimensional coupled flow problem for embedded and discrete fracture models

TL;DR

This paper introduces a non-local multicontinuum (NLMC) upscaling method for mixed-dimensional coupled flow problems in fractured porous media, achieving accurate coarse-scale models with reduced computational complexity.

Contribution

The paper develops a novel NLMC-based upscaling approach for mixed-dimensional fracture models, incorporating multiscale basis functions and energy minimization for improved accuracy.

Findings

Upscaled models match fine-grid solutions with high accuracy.

Significant reduction in computational cost and problem dimension.

Effective for various fracture geometries and permeabilities.

Abstract

In this work, we present an upscaled model for mixed dimensional coupled flow problem in fractured porous media. We consider both embedded and discrete fracture models (EFM and DFM) as fine scale models which contain coupled system of equations. For fine grid discretization, we use a conservative finite-volume approximation. We construct an upscaled model using the non-local multicontinuum (NLMC) method for the coupled system. The proposed upscaled model is based on a set of simplified multiscale basis functions for the auxiliary space and a constraint energy minimization principle for the construction of multiscale basis functions. Using the constructed NLMC-multiscale basis functions, we obtain an accurate coarse grid upscaled model. We present numerical results for both fine-grid models and upscaled coarse-grid models using our NLMC method. We consider model problems with (1) discrete fracture fine grid model with low and high permeable fractures; (2) embedded fine grid model for two types of geometries with differnet fracture networks and (3) embedded fracture fine grid model with heterogeneous permeability. The simulations using the upscaled model provide very accurate solutions with significant reduction in the dimension of the problem.