An Efficient Method For Modelling Gas Solubility In The Aqueous Phase For Compositional Simulators
Authors: Agarwal Rajeev , Li Yau-Kun , Nghiem Long 
Published: March 2010

Abstract
The modelling of gas solubility in the aqueous phase is important in CO(2) flooding. In this paper, an efficient method for modelling this effect in a compositional simulator is presented.
The oil and gas phases are modelled with an equation-of-state and the aqueous phase with Henry's Law. By assuming that the water component is present only in the aqueous phase and by all appropriate choice of primary variables, a compositional simulator with a two-phase flash-calculation module can be modified to handle gas solubility in the aqueous phase without the need of a three-phase flash-calculation module.
Example runs of CO(2) flooding and WAG processes show that gas-solubility effects on the recovery are significant.

Introduction
Because water exists abundantly in hydrocarbon reservoirs either as a fluid originally in place or as an injected fluid, it becomes important [0 model the effects or gas solubility in the aqueous phase during miscible displacements, This is particularly important for CO(2) injection because CO(2) is more soluble in water than the other light gases.
Most compositional simulators assume thermodynamic equilibrium between the hydrocarbon phases (oil and gas) only and consider water as an inert fluid that does not contribute to the phase behaviour. This limits the utility of these simulators especially for CO(2)-injection studies where a significant portion of the injection CO(2): may dissolve in the aqueous phase.
It was shown by Li and Nghiem(1) that the solubility of gases in the aqueous phase can be modelled successful using Henry's Law. They also provided correlations for the calculation of Henry's Law constant for reservoir gases.
In this paper, an efficient method for modelling the gas solubility using Henry's Law is presented. The advantage of using Henry's Law for modelling gas solubility in water is that it eliminates the need for a tedious and time consuming three-phase (oil-gas-aqueous) equation-of-state (EOS) fIash-calculation module. This is accomplished by modelling the oil and gas phases with an EOS and the aqueous phase with Henry's Law. By assuming that the water component is present only in the aqueous phase and by an appropriate choice of primary variables, a compositional simulator with a two-phase flash-calculation can be modified to handle gas solubility in the aqueous phase without the requirement of a three-phase flash-calculation module.

Formulation and Equations
In all subsequent discussions, the gas and oil phases are modelled with a cubic EOS and the solubility in the aqueous phase is modelled with Henry's Law. It is further assumed that the water component exists only in the aqueous phase.
Henry's Law
Henry's Law gives the following expression for the fugacity or Component i in the aqueous phase:
Equation (1) Available In Full Paper.
where the subscript i denotes a non-water component, and w the water component. Hi is the Henry's Law constant of Component i, yia is the mole fraction of Component i in the aqueous phase and fia is the fugacity of Component i in the aqueous phase. The variation of Henry's Law constant, Hi with respect to pressure and temperature is given by