Tie‐simplex based compositional space parameterization: Continuity and generalization to multiphase systems

Abstract

A theoretical analysis is provided of the continuity of multiphase compositional space parameterization for thermalcompositional reservoir simulation. It is shown that the tie-simplex space changes continuously as a function of composition, pressure, and temperature, and this justifies the Compositional Space Adaptive Tabulation (CSAT) framework, in which a discrete number of tie-simplexes are constructed, tabulated, and reused in the course of a simulation. The CSAT is extended for thermal-compositional displacements for mixtures that can form an arbitrary number of phases. In particular, the construction is described of three-phase tie-simplex tables, and it is shown how the degeneration of multiphase regions can be accurately captured over wide ranges of temperature and pressure. Several challenging multiphase examples are used to demonstrate the accuracy and effectiveness of phase-state identification using tabulated tie-simplexes.

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

“…An example of a simple error estimator applied for a limited case of property interpolation can be found in [17]. The extension to systems with more than two-phases can be performed based on a tie-simplex parametrization approach [32,33].…”

Numerical Simulation of Three-Hydrocarbon-Phase Flow with Robust Phase Identification

“…This global characteristic of thermodynamic problems (which cannot be solved robustly only from local information) can be also seen in multiphase flash; i.e., global minimization of the Gibbs free energy. Use of tie simplex information tabulated prior to simulation has been shown to be effective in speeding up fully implicit reservoir simulations (Voskov and Tchelepi 2009ab;Iranshahr et al 2012Iranshahr et al , 2013.…”

Tie-Simplex Parametrization For Operator-Based Linearization For Non-Isothermal Multiphase Compositional Flow In Porous

“…We show the application of tie-line parametrization for a three-component isothermal system with two hydrocarbon phases for the sake of simplicity. However, similar parametrization techniques can be extended for multi-dimensional parameter space with multiple phases (Zaydullin et al, 2013;Iranshahr et al, 2013). For each pressure within the interval of interest, we construct a ternary diagram for phase behavior representation in compositional space.…”