A new approach for the linearization of governing equations that describe flow and transport in porous media is proposed in this work. It is based on an approximate representation of the exact physics of the problem, which is similar to an approximate representation of space and time discretization performed in conventional simulation. The governing equations are introduced as a combination of operators, dependent on spatially altered properties and operators, fully controlled by nonlinear properties of fluid and rock. Next, a parametrization in the physics space of the problem is introduced. The property-based operators are approximated using direct interpolation in the space of nonlinear unknowns. The discrete version of the governing equations is constructed as a combination of operators that approximate both nonlinear physics and discretization in time and space. This approach is applied to the reservoir simulation of miscible and immiscible displacement processes. The performance of the method demonstrates a convergence of simulation results by resolution in physical space with the improved performance.
- Compositional simulation
- Compositional space parametrization
- Nonlinear solvers
- Operator-based linearization