Operator-based Linearization for Non-isothermal Multiphase Compositional Flow in Porous Media

Abstract

SUMMARYNon-isothermal multiphase compositional simulation is based on the solution of governing equations describing mass and energy transfer in the subsurface. The solution strategy requires a linearization of strongly nonlinear governing equations describing the process. Usually, a Newton-based method is used for the linearization that demands an assembly of a Jacobian matrix and residuals for a fully coupled system of equations. Recently, a new linearization approach was proposed for compositional problems and tested for simulation of binary compositional and low-enthalpy geothermal flow. The key idea of the approach is the transformation of discretised mass conservation equations to an operator form with separate space-dependent and state-dependent components. This transformation provides an opportunity for an approximate representation of exact physics (physical properties) of the problem. Specifically, each term of conservation equations is represented as a product of two different operators. The first operator depends on a current physical state of a system and contains different 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 the gradient. At the pre-processing stage, all state-dependent operators are uniformly parametrized within the physical space of the problem (pressure-composition intervals). During the 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 the conventional approach. In this work, we have extended this approach to general purpose simulation. We introduced the operator-based parametrization of mass and energy conservations equation based on the pressure, composition, temperature, and porosity. In addition, the approach has been extended and tested on truly multi-component systems of practical interest. The accuracy and robustness of the new method have been tested against the results of simulations based on the conventional approach.

Operator-based linearization approach for modeling of multiphase multi-component flow in porous media

“…Notice, that transport in binary systems is always hyperbolic since the only eigenvalue is always real. For systems with a larger number of components, the simulation for a coarse resolution of parameter space with uniform parametrization may fail to converge, as was observed by Khait and Voskov in [26]. This can be explained by the potential loss of hyperbol-icity in systems with a large number of components.…”

“…For a general purpose simulation, it is possible to apply this approach adaptively, following the idea of a compositional space parametrization [18,12]. The example of adaptive interpolation applied to the Operator-Based Linearization is described by Khait and Voskov [26].…”