A fully-implicit parallel framework for complex reservoir simulation with mimetic finite difference discretization and operator-based linearization

• Published in: Computational geosciences 2022-08, Vol.26 (4), p.915-931
• Main Authors: Li, Longlong, Abushaikha, Ahmad
• Format: Article
• Language: English
• Subjects: Computer applications; Computing time; Conservation laws; Development strategies; Discretization; Earth and Environmental Science; Earth Sciences; Exact solutions; Finite difference method; Frameworks; Geotechnical Engineering & Applied Earth Sciences; Hydrogeology; Interpolation; Linearization; Mathematical Modeling and Industrial Mathematics; Operators (mathematics); Original Paper; Properties; Reservoirs; Simulation; Soil Science & Conservation; Tabulation; Tensors; Unstructured grids (mathematics)
• ISSN: 1420-0597; 1573-1499
• DOI: 10.1007/s10596-021-10096-5

As the main way to reproduce flow response in subsurface reservoirs, the reservoir simulation could drastically assist in reducing the uncertainties in the geological characterization and in optimizing the field development strategies. However, the challenges in providing efficient and accurate solutions for complex field cases constrain further utilization of this technology. In this work, we develop a new reservoir simulation framework based on advanced spatial discretization and linearization schemes, 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 unknowns is treated in a piece-wise manner 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 first coupling these two schemes within a parallel framework, we can solve large and complex reservoir simulation problems in an efficient manner. Finally, we present a benchmark case that compares the numerical solutions to a Buckley-Leverett analytical solution to assure their accuracy and convergence. Moreover, we test three challenging field cases to demonstrate the performance of the advanced parallel framework for complex reservoir simulation.