A numerical framework for coupled flow, large deformation, and large slip for fractured and faulted reservoirs
Keywords: Energy Resources Engineering.

Many applications of the numerical modeling of coupled flow and deformation for subsurface reservoirs are based on the assumption of small deformation. This approximation makes two assumptions: the displacement gradients in the reference configuration are infinitesimal, and the displacement itself is very small compared to the characteristic length of the problem of interest. The small deformation approximation is usually valid in subsurface reservoirs because a typical reservoir rock is stiff and, therefore, exhibits small deformation. However, this assumption may not be valid in some subsurface reservoirs that experience substantial compaction or shear. Some examples demonstrate the substantial subsidence due to a large amount of hydrocarbon production, underground water removal, and softening of the rock due to thermal injections. Accounting for large deformations can be particularly important in fractured or faulted reservoirs. There, fractures can have a significant impact on the fluid flow by acting as flow conduits or flow barriers. Considering that fractures and faults typically have a very small aperture, even small deformation or small tangential slip of the fracture could significantly impact the flow by changing flow directions or fracture permeability. Therefore, a new numerical framework for coupled fluid flow, large deformation, and large slip for fractured and faulted reservoirs is developed by employing the mixed standard Galerkin finite element and two-point flux approximation finite volume methods. The developed framework models the fracture as a large deformation frictional contact using the Node-To-Segment (NTS) contact element with the penalty formulation. The algorithms to dynamically update flow connections around the fracture and their transmissibility are presented for non-matching grids along the fracture due to the tangential slip. The coupled equations are solved in a fully coupled way using the Newton-Raphson method with the active set strategy. In order to model the realistic behavior of the fracture, fracture permeability is updated depending on the fracture states, stress, and deformation. The linear slip-weakening model and gravity are also incorporated in the model. The developed framework is verified with several benchmark problems having analytical solutions, including the single fracture slip problem, the Mandel problem, and the strip footing problem. Afterward, the relative errors of the coupled flow and small deformation model are computed for various model problems with various material properties in order to investigate the applicability of the coupled small deformation model. Finally, the developed framework was applied to model fluid injection into the faulted overburden-reservoir-underburden system in order to model the reactivation of the fault. Even though the stiffness of the system is high and deformation is indeed small, the coupled large deformation model indicates a faster increase in the fault slip area compared to the small deformation model. A separate section of the dissertation presents a framework to solve the small deformation frictional contact problem using the method of augmented Lagrangian with the polynomial pressure projection (PPP) stabilization. This method successfully suppresses spurious oscillations on the normal contact traction and demonstrates the capability to precisely apply the constraints on the contact without introducing additional global degrees of freedom