Fully Coupled THM Formulations with Two-Phase Fluid Flow in Naturally Fractured Media
Authors: Wang Yarlong , Li Wenda 
Published: September 2022

ABSTRACT:
A coupled formulation is developed, based on a dual-porosity model to simulate a naturally fractured aquifer under non-isothermal and two-phase fluid flow conditions. Two-phase flow coupled to the deformation in a dual-porosity type media, and local thermal non-equilibrium (LTNE) conditions are imposed for the energy transport between and among, respectively, two fluid and porous solid phases. Along and through them conductive and convective mechanisms may dominate. More importantly, different physical parameters reflect different rock types and fracture characteristics are defined and interpreted so that the corresponding rock behaviors may be represented. Models and physical interpretations developed and proposed by different researchers are reviewed and compared. The model is applicable in reservoir simulation of naturally fractured formations with two-phasefluidflow, such as safety design of CO2 injection and sequestration, oil/gas storage injectivity or capacity evaluation, and heat extraction design in geo-thermal reservoir.

1. INTRODUCTION
The coupled thermo-hydro-mechanical (THM) response of a fluid-saturated naturally fractured medium is characterized by bulk skeleton deformation, fluid diffusion and heat transport processes via fluid flux through both matrix and fractures. The hydraulic process of the fluid flowing through the fissured porous skeleton and the mechanical responses to external loading may be calculated by poroelastic theory and the two processes are also coupled with each other simultaneously. When the saturated fissured porous block is heated, the pore pressure inside the porous may rise depending on the formation permeability, solid expands and these two processes shall be interacting with each other following the effective stress principle. Evaluations of THM responses under multiphase fluid flow via the entire porous formation subject to THM loading can be conducted based on their fundamental behaviors following an extended poroelastic constitutive laws with dual porosity and corresponding transport mechanisms in each fluid phase. Either drained moduli for the bulk porous skeleton and those for the matrix and fractured systems separately may be used. Accumulation and dissipation of the thermal potential on and through the fissured porous skeleton and fluid also follow energy conservation equilibrium condition. Separate non-equilibrium thermal energy transport processes may take place along or through the porous matrix and the fracture network, mainly by conduction within the solid matrix phase, depending on its permeability, and by conductive and convective heat transfer through the moving fluid in the fractures system. In an extreme scenario, perhaps typical of Granites and shales, through both the moving fluid and matrix heat flux is completely conductive, whereas in another extreme scenario, perhaps a naturally fractured sandstone, the heat flux along the solid phases (matrix and fracture) and fluid are conductive but a combined conductive and convective is dominating the fluid mass transport through the fracture. In addition, heat exchange between each adjacent system, i.e. between each fluid and solid system are transferable which are typically characterized by heat exchange coefficients assuming an instantaneous equilibrium condition may be reached at the contact areas. A convective components may also be incorporated depending on the hydraulic characteristics such as the fluid velocity between these systems. Simulating naturally fractured formation, early modeling work on the dual-porosity model initialized by Barentblatt et al, 1960 and Warren and Root 1963 assumed porous block is rigid. Studies on deformable skeleton were imposed later by Duguid and Lee, 1977 and a mixture theory is proposed by Aifantis [1977,1979,1980]. In these early work, the cross-coupling between the fracture and pore volume is ignored [Khalili and Valliappan, 1996; Khalili, 2003, 2008]. To improve Aifantis’s early work, improvement and extension of the dual-porosity formulations for single phase fluid flow are developed [Wilson and Aifantis, 1982; Khaled et al, 1984, Valliappan and Khalili-Naghadeh, 1990, Berryman and Wang, 1995; Berryman and Bridge, 2002; Berryman 2002, Khalili-Naghadeh and Valliappan 1991, Chen and Tuefel, 1997. Khalili and Valliappan, 1996, and Khalili and Selvadurai, 2003. The dual-porosity concept to include multiphase flow subject to a number of restrictions are also introduced [Lewis and Ghafouri, 1997; Bai et al., 1998; Pao and Lewis, 2002, and Nair et al. ,2005, Khalili, 2008].