General purpose reservoir simulation is based on the solution of governing equations describing mass and energy transfer in the subsurface. The solution process requires the linearization of strongly nonlinear governing equations. Usually, a Newton-based method is used for the linearization. This method demands the assembly of Jacobian and residual for a fully coupled system of equations. Recently, a new linearization approach was proposed and tested for binary systems. The key idea of the Operator Based Linearization (OBL) approach is to transform the discretized mass and energy conservation equations to an operator form which separates space-dependent and state-dependent properties of governing equations. This transformation provides the opportunity to approximate the representation of exact physics (physical properties) of a problem. Specifically, each term of the conservation equations is presented as the product of two different operators. The first operator depends on the current physical state of a system and contains fluid properties, such as density, viscosity, relative permeability, etc. The second operator captures both spatially altered properties, such as permeability, and the rest of state variables, such as pressure in the discrete approximation of gradient. All state-dependent operators are uniformly parametrized within the physical space of the problem (pressure-composition intervals). During simulation process, a multi-linear interpolation is applied to approximate the first type of operators, while the second type of operators is processed based on conventional approach. In this work, we extended the approach to thermal systems with an arbitrary number of components. Besides, we significantly improved the performance of OBL employing adaptive parametrization technique. We tested the approach for truly multi-component thermal systems of practical interest. The computational performance, accuracy, and robustness of a new method were demonstrated against the conventional approach.
Khait, M., & Voskov, D. V. (2017). Operator-based linearization for general purpose reservoir simulation. Journal of Petroleum Science and Engineering, 157, 990–998. https://doi.org/10.1016/j.petrol.2017.08.009