Compositional Space Parameterization for Flow Simulation
Authors: Voskov Denis , Tchelepi Hamdi A. 
Published: December 2007

Abstract
Thermodynamic equilibrium (flash) calculations in compositional simulators are used to find the partitioning of components among fluid phases. The basic idea is to solve the nonlinear thermodynamic equilibrium relations for each gridblock separately from hydrodynamic flow. This step can be the most time consuming kernel in a compositional flow simulation. We describe a compositional space parameterization approach for dealing with gas injection displacement processes involving large numbers of components.
The multi-component multiphase equilibrium problem can be recast rigorously in terms of this parameterized compositional space, in which the compositional path of a near-miscible displacement is naturally represented.
We use this parameterization space to speed up the phase behavior calculations in standard compositional simulation. Flash calculations are performed and their results stored as a preprocessing step. During the course of a simulation, the flash calculation procedure is replaced by the solution of an optimization problem of a multidimensional equilibrium table in terms of the parameterized space. For processes where significant changes in pressure and temperature take place, this optimization procedure is combined with linear tie-line interpolation. We demonstrate our approach using one-dimensional numerical examples of near-miscible gas injection into multicomponent hydrocarbon systems. Extension of this approach to large-scale multi-dimensional problems is discussed.
The use of compositional space parameterization to speed up the standard phase split calculation is also presented. In gas injection processes, the displacement path in compositional space takes place along a limited number of tie-lines. This fact is used to avoid redundant stability checks. Specifically, given a composition, we check if it belongs to one of the pre-calculated tie-lines, or their extensions. If not, a new tie-line is computed and added to the compositional-space table. This Compositional Space Adaptive Tabulation (CSAT) technique was implemented in a general-purpose research simulator (GPRS), which is designed for compositional flow modeling on unstructured grid. Using a variety of challenging models, we show that for compositional processes, CSAT leads to significant speed up (at least a several-fold improvement) of the flash calculations compared to standard techniques.

Introduction
Gas injection processes for enhanced oil recovery are described using compositional models that account for the transfer of components between multiple fluid phases. Compositional reservoir simulators usually employ an Equation of State (EOS) model to describe the phase behavior.1–4 For each computational cell (control volume) in the reservoir model, given temperature, pressure, and the overall composition of each component in the mixture, EOS computations are used to determine the phase state (liquid, vapor, or both) and the phase compositions at thermodynamic equilibrium. These EOS calculations are time consuming, and several challenges remain. These include dealing with mixtures made up of large numbers of components in the near-critical region and accurate modeling of thermal-compositional processes.