A Fully-Coupled, Implicit, Finite Element Model for Simultaneously Solving Multiphase Fluid Flow, Heat Transport, and Rock Deformation

Abstract

Creation of enhanced geothermal system reservoirs requires fracturing of a sufficient volume of the subsurface to enable commercial- scale heat transfer from the reservoir rocks to the working fluid. A key assumption associated with reservoir stimulation/ fracturing is that sufficient rock volumes can be hydraulically fractured via both tensile and shear failure to create the reservoir. The advancement of enhanced geothermal systems greatly depends on our understanding of the dynamics of the intimately coupled rockfracture- fluid-heat system and our ability to reliably predict how reservoirs behave under stimulation and production. This paper details our efforts to better understand how enhanced geothermal system reservoirs behave under conditions of stimulation and longterm production. In order to describe all the processes involved with an enhanced geothermal reservoir, we are developing a hybrid finite element-discrete element model where the physics of rock deformation and fracture propagation are solved using discrete element methods while continuum multiphase fluid flow and heat transport are solved using finite element methods. All governing equations are solved in a fully implicit, fully coupled manner. In this approach, the continuum flow and heat transport equations are solved on an underlying finite element mesh with evolving porosity and permeability for each element that depends on the local structure of the discrete element network. Reliable performance predictions of enhanced geothermal system reservoirs require accurate and robust modeling for the coupled thermalhydrological- mechanical processes. Conventionally, these types of problems have been solved using operator-splitting methods, usually by coupling a subsurface flow and heat transport simulators with a solid mechanics simulator via input files. An example of this approach is presented by Rutquist et al. (2002), where a widely used flow and heat transport simulator TOUGH2 (Pruess et al., 1999) is coupled to the commercial rock mechanics simulator FLAC (Itasca Consulting Group Inc, 1997) via input files. During each time step, TOUGH2 and FLAC run sequentially with the output from one code as input to the other. Iterations between the codes during each time step might be necessary if there is a strong dependence among processes. An alternative approach is to solve the system of nonlinear partial differential equations that govern multiphase fluid flow, heat transport, and rock mechanics simultaneously, using a fully coupled solution procedure. This procedure solves for all solution variables (pressure, enthalpy, and rock displacement fields) simultaneously, which leads to a large single nonlinear algebraic system that is solved using a strongly convergent nonlinear solver. Developments over the past decade in the area of physics-based conditioning, strongly convergent nonlinear solvers (such as Jacobian Free Newton methods) and efficient linear solvers, such as GMRES, make such an approach competitive compared to more traditional methods in terms of both computational burden and solution time. This paper describes the development of the code and details the governing equations, solution procedures, and numerical methods used to solve for fully coupled, implicit, multiscale geothermal-geomechanical systems. Simulations are presented to compare model results to both analytical solutions for simple systems and for more complex cases, to other simulation.