Interpolation Strategies for Complex Thermal-Multiphase-Reactive Modeling with Operator-Based Linearization

Summary The effective management of geoenergy systems heavily relies on robust modeling frameworks that integrate diverse simulation capabilities, including flow and transport, phase equilibrium, geochemistry, and geomechanics. While a multiphysics simulation engine within a unified framework has its advantages, integrating specialized modeling packages often enhances viability. Efficient and seamless communication between these engines becomes crucial for improving the performance and scalability of the integration. Advanced parametrization techniques can facilitate this integration by efficiently approximating and interpolating coupling data, ensuring both speed and accuracy. In this study, we compare the efficiency of different interpolation techniques used for the parametrization of complex many-component fluid systems in compositional simulation. We use an operator-based linearization (OBL) framework that leverages the general formulation of the corresponding conservation laws. OBL effectively learns the operators required for the assembly of these laws, while interpolation delivers fast evaluation of operators and their derivatives for all physical states in a simulation domain. Multilinear interpolation is a simple and robust approach, yet it has poor scaling properties with respect to the dimension of the physical state. To alleviate interpolation costs in multiple dimensions, we study the performance and accuracy of other interpolation techniques, including linear interpolation with standard and Delaunay triangulation. Overall, this approach provides great flexibility, saves development costs, and simplifies the incorporation of thermodynamics and geochemistry engines for precise modeling of phase equilibrium, reactive transport, dissolution-precipitation, and kinetics of chemical reactions. We investigate the efficiency of the aforementioned interpolation strategies in terms of robustness, accuracy, performance, and scalability. As test models, we consider a multicomponent fluid model with thermal and reactive effects relevant to carbon dioxide (CO2) sequestration applications. As expected, we observe the performance gain of linear interpolation compared with multilinear interpolation, increasing with the number of components. We investigate the robustness and efficiency of standard and Delaunay triangulations for systems with a significant number of components. This research extends the scalability of the OBL framework and addresses the challenges of high dimensionality in compositional modeling. Consequently, this approach holds significant potential for integrating various complex multiphysics problems, advancing the development of more comprehensive digital twins for geoenergy systems management.