A Framework of Coupled Thermal-Hydraulic-Mechanical Analysis for Simulating Hydraulic Fracturing Based on Explicit and Implicit Methods
Authors: Maeda Y. , Ogata S. , Fukuda D. , Inui T. , Yasuhara H. , Kishida K. 
Published: September 2023

ABSTRACT
To design an engineered/enhanced geothermal system (EGS) efficiently, it is essential to develop a coupled thermal-hydraulic-mechanical (THM) simulator, that can track the hydraulic fracturing processes within the rocks including the fracture initiation/propagation and local heat non-equilibrium in the fractures driven by cold injection water or thermal-fluid flow along the fracture surfaces. To realistically capture the coupled THM processes that are sensitive to the presence of rock fractures, a coupled simulator should be based on an analysis method that can insert the explicit fracture surfaces into the computational domain. Currently, as one of such simulators, the Combined Finite-Discrete Element Method (FDEM), which integrates the continuum and discontinuum analysis methods, has been attracting attention. However, FDEM is formulated in the explicit methods and requires extremely small time increment, and it should bring about a difficulty in computing the time-dependent thermal-fluid flow within the rocks corresponding to realistic time scales expected in hydraulic fracturing process at the actual fields. In this study, a novel hydraulic fracturing simulator is developed, capable of application across a wide range of time scales. The simulator employs FDEM based on the explicit methods to solve the mechanical fracturing process and FEM based on the implicit methods, enabling the use of comparatively larger time steps, to solve the thermal-hydraulic process. Furthermore, the performance of the proposed simulator is verified through the numerical experiment for laboratory-scale hydraulic fracturing.

INTRODUCTION
In recent years, a development of an engineered/enhanced geothermal system (EGS) has received significant attention as a promising technology for advancing geothermal power generation. For the efficient design of EGS, a detailed understanding of the hydraulic fracturing process including artificially creating and expanding geothermal reservoirs in deep hot dry rock (HDR) is essential. To achieve the above, it is necessary to develop a coupled Thermal-Hydraulic-Mechanical (THM) simulator that can track the fracture initiation induced by fluid injection into rock mass, the fracture propagation related to the thermal-fluid flow along the fracture surface, and local heat non-equilibrium between the fracture and rock matrix due to temperature reduction caused by a flow of cold injection water. To accurately simulate such phenomena driven by thermal-fluid flow along fractures, an analysis method that can explicitly model fracture surfaces is desirable, and several numerical approaches have been developed (e.g., Wang (2016), Liu et al. (2020)). However, because most of them are formulated the implicit method, which makes it difficult to obtain the calculation convergence for the complex and rapid fracturing processes (e.g. fracture intersections and unstable fracture growth). As a solution to this problem, the Combined Finite-Discrete Element Method (FDEM) (Munjiza (2004)) has attracted significant attention, which is based on the explicit method and integrates continuum-based and discontinuum-based methods, i.e., Finite Element Method (FEM) and Discrete Element Method (DEM). FDEM based on the explicit method can stably solve the complex and rapid fracturing process, which are difficult to deal with in the implicit method and has already applied to hydraulic fracturing analysis (e.g., Lisjak et al. (2014), Yan and Zheng (2016)). However, FDEM formulated in the explicit method, requires extremely small time increment compared to the implicit method. Therefore, it is difficult for FDEM to track the thermal-fluid flow process, which is the main driving force of cracking during the hydraulic fracturing, on realistic time scales. According to previous laboratory-scale and in-situ tests (e.g., Kumari et al. (2018), Hayashi and Ito (1993)), hydraulic fracturing processes at the actual fields should be considered on a time scale of at least several tens of seconds. However, previous hydraulic fracturing FDEM simulators could only calculate for much shorter than 1 second (e.g., Lisjak et al. (2014), Yan and Zheng (2016)).