Compositional Space Parameterization: Multicontact Miscible Displacements and Extension to Multiple Phases

Abstract

We generalize the compositional space parameterization (CSP) approach, which was originally developed for immiscible twophase multicomponent problems, to multicontact miscible displacements. The tie-line based parameterization method improves both the accuracy of the phase-behavior representation as well as the efficiency of equation of state (EOS) computations in compositional flow simulation. For immiscible compositional simulation, compositional space adaptive tabulation (CSAT) can be used to avoid most of the redundant EOS calculations. Because the supercritical region cannot be parameterized using tie-lines, the original CSAT approach is not effective for modeling multicontact miscible gas injection processes. To deal with supercritical compositions, a supercritical state criteria (SSC) algorithm based on adaptive tabulation of the minimal critical pressure (MCP) tie-lines is proposed. For general-purpose simulation of miscible and immiscible compositional displacement processes, we combined the adaptive CSAT strategy in the region of tie-line extensions and the adaptive SSC scheme; we refer to the overall framework as CSAT. Results of several challenging tests of practical interest indicate that the general CSAT strategy is quite robust and that it leads to an order of magnitude gain in computational efficiency. We also describe the extension of the CSP framework for mixtures that form more than two phases. ␣ ␤ = 1 = 1

An Extended Natural Variable Formulation for Compositional Simulation Based on Tie-Line Parameterization

“…It helps to identify when phase behavior should switch from normal tie-lines to the critical tie-lines. Fully adaptive preconditioning strategy is described in Voskov and Tchelepi (2009b). This approach can be successfully used for variable substitution in extended natural formulation for general purpose compositional simulation.…”

Negative Saturation Approach for Non-Isothermal Compositional Two-Phase Flow Simulations

“…22 is independent of the phase density in single-phase regions and, subsequently, we can use the calculated value of z i , temperature T , and pressure P to obtain the density in single-phase regions. This advantage of the NegSat solution approach does not exist in a variable-set based on compositional space parameterization (Voskov and Tchelepi 2009;Voskov 2010) where z i cannot be computed from known values ofŜ g andx i , because the molar fraction of the single-phase (L or V ) should also be known. Consequently, to deal with this issue in the compositional-space-parameterization approach, an additional nonlinear equation with an additional unknown variable (L or V ) is introduced to the system of equations (Voskov 2010), which adds to computational cost.…”

“…There are four methods to deal with phase appearance and disappearance problems: (1) conventional models with switches to be used in grid cells where conversion of single-phase to two-phase or vice versa occurs (Bonnerot and Jamet 1981;Pruess 2004;Zhu et al 2004;Chen et al 2006;Bruining and Marchesin 2007); (2) a non-equilibrium source term in all the equations is used that drives the system toward equilibrium (Ben-Omran and Green 1978;Bruining and Van Duijn 2006); (3) compositional-space-parameterization approach (Voskov and Tchelepi 2009;Voskov 2010), which can be thought of as an extension of the conventional approach; and (4) the negative saturation method (Abadpour and Panfilov 2009;Panfilov and Rasoulzadeh 2010) that avoids the use of switches and separate equations.…”

Generalized negative-flash method for multiphase multicomponent systems

“…Resolving the complex multiphase thermodynamic equilibrium behaviors associated with these subsurface displacement processes poses significant computational challenges [1][2][3]. Here, we propose a multiphase equilibrium method based on a generalized negative-flash strategy.…”

“…In these MoC solutions, tie-lines are used to construct the solution path in compositional space. Motivated by this theory, a general tie-line based Compositional Space Parameterization (CSP) method has been developed in order to improve the computational efficiency and accuracy of isothermal compositional flow simulation [1,2]. The mathematical framework for the extension of the CSP methodology to an arbitrary number of phases has been presented in [3].…”