A Non-Equilibrium Equation-of-State Compositional Simulator
Authors: Nghiem Long X. , Sammon Peter H. 
Published: December 2007

Abstract
This paper describes an equation-of-state compositional simulator where the oil and gas approach thermodynamic equilibrium through a rate process. Thermodynamic equilibrium prevails only at the interface between the oil and gas phases, and a diffusion process drives the oil and gas composition towards these equilibrium values. A simulation of a gas-injection core displacement shows the effects of such non-equilibrium phenomena.

Introduction
It is well documented that bypassing of injected gas may occur during gas injection processes. This bypassing can take place in both field and laboratory core displacements, and can be caused by various mechanisms, including viscous fingering, channeling due to heterogeneities, or gravity segregation.
Current compositional simulators assume that fluids are completed mixed in grid blocks and that thermodynamic equilibrium exists between the oil and gas phases. These assumptions may not be applicable when bypassing is caused by effects such as those noted above. Nor are these assumptions valid for any particular length scale since bypassing has been reported at both the field scale 5 and laboratory scale (core displacement).
Several methods have been proposed to model bypassing in compositional simulation. References 7, 8 and 9 describe the implementation of a viscous fingering model proposed by Fayers in a compositional simulator. This technique involves the use of transport coefficients that modify the component flow terms, and a density coefficient that modifies the accumulation terms, to account for the incomplete mixing of fluids. This method is similar to the Todd and Longstaff technique for first-contact miscible floods. Another method, proposed by Young, consists of using an empirical model for longitudinal dispersion to simulate finger growth in adverse mobility displacements.
The above approaches are empirical in nature as they attempt to reproduce the observed bypassing effect due to viscous fingering by altering the flow characteristics and accumulation terms for each component. The applicability of these techniques to bypassing due to heterogeneities and gravity segregation has not been fully investigated.
This paper describes a compositional simulator with a mechanistic model for the transfer of components between the oil and the displacing fluid. Recall that in a gas injection process, the injected gas typically moves faster than the oil. Several mechanisms are responsible for the mixing of fluids between zones of fast flow (the gas) and slow flow (the oil). These include diffusion, transverse dispersion, viscous crossflow, capillary crossflow, and density driven cross flow. The framework of a non-equilibrium equation-of-state compositional simulator is described here that uses a transfer based on a diffusion model of fluid mixing. A compositional simulation of a typical core displacement is presented to illustrate the non-equilibrium effects on displacement efficiency.

Formulation
Current compositional simulators solve for the combined flow of each component in the oil and gas phases to obtain the global composition in every grid block. A flash calculation is performed to determine the respective oil and gas saturations and compositions. The component flow and flash equations are solved simultaneously. The main differences between the different simulators are the selection of equations and primary variables.