Network Modelling of Apparent-Relative Permeability of Gas in Heavy Oils
Authors: Javadpour F. , Pooladi-Darvish M. 
Published: March 2010

Abstract
Some of the solution-gas drive heavy oil reservoirs known as foamy oil reservoirs, in Canada, Venezuela, and other countries have demonstrated a high primary oil recovery factor (&gt;10%), a low producing gas-oil ratio, a low reservoir pressure decline, and a high oil production rate. One of the hypotheses to explain these unusual behaviours is that the gas mobility in a foamy oil flow is much lower than that in conventional oil, leading to improved recovery performance. In this study, the immiscible two-phase micro-displacement in porous media is modelled by using a network of pores of converging-diverging geometry. The effect of viscosity of one phase (oil) on the mobility of another phase (gas) is included in the model. The developed model is used to simulate the motion of the dispersed bubbles in an initially oil-filled network, and to determine bubble mobility. The obtained results showed that bubble mobility decreased drastically by increasing the oil viscosity. The results also showed that dispersion of gas leads to lower mobility of bubbles. Dispersed gas flow and low bubble mobility are believed to lead to improved recovery in foamy oil reservoirs.

Introduction
Some of the solution-gas drive heavy oil reservoirs in Canada, Venezuela, China, and Oman have demonstrated unusually high primary production rates, high primary oil recovery factors (&gt;10%), low producing gas-oil ratios, and low reservoir pressure declines(1, 2). To explain these unusual behaviours, three fundamental reasons have been suggested: geomechanical effects(3), special fluid properties(4), and unusual flow dependent properties of oil and gas(5). Most researchers now believe that the low mobility of gas is the main reason for low producing GOR and high recoveries obtained(1, 2). Gas mobility in a heavy oil system is investigated in this paper.
In one study, solution-gas drive experiments were performed in an identical sand-pack, using light oil and heavy oil(5). The experimental studies clearly showed that gas mobility in the two experiments differed by about four orders of magnitude.
It has been observed that matching of field(6) and laboratory depletion data(5) required assigning extremely low values of gas relative permeability. The relative permeability functions of these studies, however, were obtained through history matching. Of primary interest is, how can relative permeability functions be determined for a particular system a priori? Following this question, the first step is to find what parameters affect relative permeability functions; the second is to find how these factors are ranked in their importance. These steps are investigated in this paper. A microscopic scale (network) model is developed and used to investigate the effects of different parameters, in particular, oil viscosity on gas mobility in porous media.
Network models are simplified mathematical representations of real porous material. The objective of a porous network model is to provide a reasonable idealization of the complex geometry of a real porous medium on a microscopic scale, so that the related fluid flow can be treated mathematically at a manageable level of complexity.