A Non-equilibrium Model to Calculate Foamy Oil Properties
Authors: Sheng J.J. , Maini B.B. , Hayes R.E. , Tortike W.S. 
Published: March 2010

Abstract
A number of heavy oil reservoirs under solution gas drive show anomalously good primary performance. Foamy oil behaviour is believed to be one of the reasons. Several previous investigators have developed numerical models to simulate the foamy oil flow. These models account for the presence of foamy oil effects by modifying the equilibrium properties of the rock-fluid system, such as the PVT characteristics and relative permeability. Their approach does not account for the time (or rate) dependent changes in foamy oil characteristics. This paper proposes a methodology for including the non-equilibrium processes in calculating the foamy oil properties.
The basic foundation of this model rests on theories of bubble nucleation and bubble growth. However, several simplifying assumptions have been used to keep the mathematical treatment tractable and to maintain consistency with reported experimental observations. The model is verified by matching our calculated results with the experimental data.
The results calculated from this model show how the foamy oil properties vary with pressure and time. The volumes and compressibilities of foamy oil increase to their maximum values before they decrease with time. The maximum values strongly depend on the amount of the gas that can be entrained in the liquid oleic phase. The amount of entrained gas is a key parameter in foamy oil flow.
This method of calculating foamy oil properties provides the basics for developing numerical simulation models of foamy oil flow. The results from this model may also be useful for well testing analysis in foamy oil reservoirs.

Introduction
A number of heavy oil reservoirs under solution gas drive show anomalously good primary performance: high oil production rates, low produced GOR and high recovery(1, 2). These reservoirs show "foamy-oil" behaviour in wellhead samples produced under solution gas drive. The oil is produced in the form of an oil-continuous foam which has the appearance of chocolate mousse and contains a high volume fraction of gas(3).
Foamy oil may be defined as a heavy oil containing dispersed gas bubbles(4). In the context of solution gas drive, its physical form could be a dispersion of gas bubbles flowing with the oil; a foam in which the continuous phase is oil; or any other form which causes trapping of a large volume of gas within porous media. Foamy oil flow was defined by Maini(5) as an unusual form of two-phase (oil/gas) flow in porous media which can be invoked to explain the high solution-gas-drive recovery in some heavy oil reservoirs. To study the foamy oil flow, it is important to first understand the foamy oil properties. The most important properties related to flow are the compressibility and viscosity.
The compressibility of a foamy oil (oil containing dispersed gas bubbles) would obviously be much higher than the compressibility of the same oil containing only dissolved gas. Since the gas compressibility is much higher than the liquid compressibility, the total compressibility of the dispersion would be dominated by the gas, once a significant volume fraction of gas has evolved.