A Sequentially Coupled THM Model for Fractured Enhanced Geothermal Systems using XFEM and Hybrid EDFM and MINC Models

Abstract

The long-term fluid circulation of Enhanced Geothermal Systems (EGS) involves complex coupled Thermal-Hydrological-Mechanical (THM) processes dominated by hydraulic and induced natural fractures. The hydraulic fracture of arbitrary shape in response to pressure changes and thermal strains can be handled by the three-dimensional (3D) eXtended Finite Element Method (XFEM). The induced/natural fractures are incorporated into the model and treated as one continuum of the Multiple INteracting Continua (MINC) for the investigation of their impacts. A TOUGH-code-based program, TOUGH2-EGS, is utilized to simulate the Thermal-Hydrological processes. The 3D Embedded Discrete Fracture Method (EDFM), compatible with the 3D XFEM, is adopted to model the hydraulic fracture. TOUGH2-EGS is then coupled with an XFEM simulator by the sequentially coupled fixed-stress split approach. The convergence performance of this coupling scheme is firstly analyzed by introducing the fracture stiffness coefficient into a single-fracture model. Sensitivity analyses are performed for this model in terms of injection temperature and thermal expansivity. The hybrid EDFM and MINC model is established and analyzed for an EGS with both hydraulic and induced/natural fractures. The convergence performance of the single-fracture model shows that an appropriate stiffness coefficient is essential for this model and different choices of the coefficient value result in distinct performances. The sensitivity analyses for injection temperatures and thermal expansivity are conducted by comparing effective stresses, pressure, temperature, and porosity/permeability distributions, as well as dynamic production temperature, outflow rate, and injection fracture permeability. The results illustrate that the fracture aperture is opened by the cold fluid injection and the reservoir is dominated by the thermal stress/strain. The temperature and pressure distribution are both affected by the thermal-hydrological-mechanical processes through the dynamic porosity, permeability, stress/strain, and fluid viscosity. The thermal breakthrough curves reflect that the conduction contributes the most to heating the fluid while the outflow rates demonstrate the mass loss due to the porosity/permeability altered by thermo-poro-elasticity. In the hybrid model, the enhancement of the natural fracture permeability notably delays the thermal breakthrough by allowing injected fluid to contact more hot reservoirs. Natural fracture spacing, MINC partition numbers are also varied to investigate their influence on the production behavior: the increased spacing delays the thermal breakthrough and needs more MINC partitions for modeling accuracy. Traditional coupled THM models are only applicable under the assumption of infinitesimal strains which does not hold in hydraulically fractured EGS reservoirs. The introduction of fracture stiffness stabilizes the numerical solution. The combined 3D XFEM and EDFM is capable of handling arbitrary fracture shapes in a 3D EGS model. Moreover, the hybrid hydraulic and induced/natural fracture model enables us to establish the stimulated reservoir volume of the EGS and investigate the operational and geological parameters.

Sequential formulation of all‐way coupled finite strain thermoporomechanics for largely deformable gas hydrate deposits

“…where 𝒅 can be decomposed into the volumetric and deviatoric parts (i.e., ε 𝑣 and ė, respectively), which satisfies 𝟏 ∶ 𝗰 𝑡 ∶ 𝒆 = 0. By substituting Equation ( 57) into Equation (36), we obtain…”

“…30 In time discretization, we take the fixed stress sequential implicit method, where individual problems of flow and geomechanics are solved implicitly and sequentially. Specifically, the fixed stress method solves the flow problem first by fixing the total stress rate locally and the geomechanics problem is solved at the next step [31][32][33][34][35][36] In this sequential approach, one may iterate this sequential procedure at each time step until convergence, where the solution is then identical to that from the monolithic approach, or perform a fixed number of iterations per time step. It is common to employ a staggered method (one iteration per time step), similar to the fractional step method.…”