A Dynamic Model to Simulate Foamy Oil Flow in Porous Media
Authors: Sheng J.J. , Hayes R.E. , Maini B.B. , Tortike W.S. 
Published: December 2007

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. Currently, numerical simulation of primary depletion in foamy oil reservoirs is based primarily on empirical adjustments to the conventional solution gas drive models. This paper presents a numerical model including the rate processes related to the nucleation, bubble growth and coalescence. The rate of nucleation is assumed to be instantaneous; the rate of bubble growth is a function of supersaturation and time; and the rate of coalescence is proportional to the amount of gas bubbles dispersed in the oil phase. The two-phase flow of oil and gas is modelled with the normal two-phase relative permeability-saturation relationship. The dispersed gas is assumed to flow with the oil as if it was a part of the liquid phase.
The model satisfactorily matched the primary depletion tests in a sand-pack. It was observed that the solution gas drive recovery factor increased dramatically as the rate of pressure decline was increased.
This model adequately accounts for the rate processes under solution gas drive in heavy oil reservoirs. It can be extended to investigate the effects of various process parameters on oil recovery and it may provide more reliable prediction of field performance. It also provides a tool to evaluate the significance of dynamic processes under various operation conditions.

Introduction
A number of heavy oil reservoirs under solution gas drive show anomalously good primary performance: high oil production rate, low produced GOR and high recovery. These reservoirs show "foamy oil" behaviour in wellhead samples. The oil is produced in the form of an oil-continuous foam. The term, "foamy oil", has been used to describe such heavy oils. Foamy oil was defined as a heavy oil containing dispersed gas bubbles.
The foamy oil flow involves a complex interplay of several rate processes related to the nucleation, growth and coalescence of gas bubbles with the fluid mechanics of multiphase flow through porous media. However, numerical simulation of primary depletion in foamy oil reservoirs is still based primarily on empirical adjustments to the conventional solution gas drive models. Published models include the pseudo-bubblepoint model, the modified fractional flow model, and the reduced oil viscosity model. Maini gave a detailed review and discussion of these models. These models have been used to history match heavy oil production, but their common weakness is that the dynamic processes which are the important features of foamy oil flow were not included properly. Although it may be possible to get an acceptable history match using these models, the predictive ability is likely to be limited.
This paper presents a model which includes these rate processes. The proposed model was used to match the primary depletion tests in a laboratory scale sand pack.

Description of the Proposed Dynamic Model
This proposed model incorporates two rate processes:the process which controls the rate of transfer from solution gas to evolved gas; andthe process which controls the rate of transfer from dispersed gas to free gas.
Note that a fraction of the evolved gas can remain dispersed in oil phase as dispersed gas and the rest of it becomes free gas directly. The sum of dispersed gas and free gas is equal to the amount of evolved gas.
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