Multiscale formulation for coupled flow-heat equations arising from single-phase flow in fractured geothermal reservoirs

Abstract

Efficient heat exploitation strategies from geothermal systems demand for accurate and efficient simulation of coupled flow-heat equations on large-scale heterogeneous fractured formations. While the accuracy depends on honouring highresolution discrete fractures and rock heterogeneities, specially avoiding excessive upscaled quantities, the efficiency can be maintained if scalable model-reduction computational frameworks are developed. Addressing both aspects, this work presents a multiscale formulation for geothermal reservoirs. To this end, the nonlinear time-dependent (transient) multiscale coarse-scale system is obtained, for both pressure and temperature unknowns, based on elliptic locally solved basis functions. These basis functions account for fine-scale heterogeneity and discrete fractures, leading to accurate and efficient simulation strategies. The flow-heat coupling is treated in a sequential implicit loop, where in each stage, the multiscale stage is complemented by an ILU(0) smoother stage to guarantee convergence to any desired accuracy. Numerical results are presented in 2D to systematically analyze the multiscale approximate solutions compared with the fine scale ones for many challenging cases, including the outcrop-based geological fractured field. These results show that the developed multiscale formulation casts a promising framework for the real-field enhanced geothermal formations.

Upscaling of the single-phase flow and heat transport in fractured geothermal reservoirs using nonlocal multicontinuum method

“…In general subsurface problems, to reduce the dimension of fine-scale system, multiscale methods or upscaling techniques are used [16,27,28,33,56]. Also recently, the multiscale methods have been adapted for geothermal and EGS problems [25,26,29,30,35,39,43].…”

“…The coarse-scale advective term is constructed from sums of fine-scale fluxes, whereas the coarse-scale conductive term is constructed based on numerically computed basis functions. Praditia et al [39] obtained a nonlinear time-dependent (transient) multiscale coarse-scale system for both pressure and temperature unknowns based on locally solved elliptic basis functions.…”

A Galerkin‐free/equation‐free model reduction method for single‐phase flow in fractured porous media

“…According to the different solving algorithms, the framework of multiscale methods, it can be divided into the multiscale finite element method (MsFEM), multiscale mixed finite element (MsMFEM) and multiscale finite volume method (MsFVM) . Lunati et al pointed out that in general, the MsFEM can obtain a nonconservative flux field, and the MsMFEM is conservative but involves more degrees of freedom.…”

“…The MsFVM was first proposed by Jenny in 2003 to simulate subsurface flow. Now, it has been extended to simulate two‐phase flow and fracture‐dominated flow in porous media . As indicated by previous studies, the solution procedures of the multiscale method include two main steps.…”

Nonlocal multicontinua upscaling for multicontinua flow problems in fractured porous media

“…The definition of these transfer functions is a key issue for multicontinuum approach, since the construction of the exchange term is based on additional assumptions. In the case of the large fractures, the fracture networks should be considered explicitly using Discrete Fracture Model (DFM) or Embedded Fracture Model (EFM) [24,27,17,18]. Accurate and explicit consideration of the fracture flow and complex interaction with porous matrix leads to the large system of equations and is computationally expensive.…”