Typical gas relative permeability measured during primary depletion of sand packs filled with heavy oil is in the order of 1E-6 - 1E-5. This is much lower than what is found in similar experiments with light oil. We think that the reason for this difference is that in heavy oil depletion, free gas flows in the form of small bubbles (dispersed flow) and not as connected gas. For dispersed flow, the velocity of the gas phase would not be inversely proportional to the gas viscosity, as would result from applying conventional Darcy's law.

This discrepancy indicates that a different type of model might be needed. We suggest the use of effective phase viscosities that should replace the relative permeabilities. We study a special case, in which the velocities of oil and gas are supposed to be equal. This leads to a model with one continuity equation and a Darcy law for the gas-oil mixture, depending on one effective viscosity.

We solve the model for steady flow in a core, obtaining good agreement with experimental measurements. Matching experimental data, an expression for the effective viscosity is obtained. The model is a first step in an attempt to obtain a new model for viscous gas-liquid flows in porous media. Such a model would reduce the uncertainty in forecasts of the oil production and recovery factors in heavy oil reservoirs such as the Venezuelan Orinoco belt.

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