An advanced parallel framework for reservoir simulation with mimetic finite difference discretization and operatorbased linearization

Reservoir simulation is the only way to reproduce flow response in subsurface reservoirs that drastically assists in reducing the uncertainties in the geological characterization and in optimizing the field development strategies. However, it is always challenging to provide efficient and accurate solutions for field cases which in turn further constrains the utilization of reservoir simulation. In this work, we develop a novel reservoir simulation framework based on advanced spatial discretization and linearization scheme, the mimetic finite difference (MFD) and operator-based linearization (OBL), for fully implicit temporal discretization. The MFD has gained some popularity lately since it was developed to solve for unstructured grids and full tensor properties while mimicking the fundamental properties of the system (i.e. conservation laws, solution symmetries, and the fundamental identities and theorems of vector and tensor calculus). On the other hand, in the OBL the mass-based formulations are written in an operator form where the parametric space of the nonlinear unknowns is treated piece-wisely for the linearization process. Moreover, the values of these operators are usually precomputed into a nodal tabulation and with the implementation of multi-linear interpolation, the values of these operators and their derivatives during a simulation run can be determined in an efficient way for the Jacobian assembly at any time-step. This saves computational time during complex phase behavior computations. By coupling these two novel schemes within a parallel framework, we can solve large and complex reservoir simulation problems in an efficient manner. Finally, we benchmark these methods with analytical solutions to assure their robustness, accuracy, and convergence. We also test several field cases to demonstrate the performance and scalability of the advanced parallel framework for reservoir simulation.