Cold production of oil leads to degassing of the light species and the formation of a bubbly phase, sometimes called the "foamy oil" effect. This bubbly phase is particularly observed with heavy oils, combining high viscosity and asphaltenes.

Presence and behavior of a foamy-oil effect appears to be critical to the cold production process. This process is not a well-understood production mechanism because a wide range of different petrophysical parameters and experimental factors interact in a rather complex way. Over the past few years, a number of efforts have been made in many institutions, in order to understand and model the solution gas drive mechanism in primary heavy oil recovery. Conventional simulations are not reliable for prediction forecast purposes. The reason is often that conventional modeling requires relative permeabilities tables that are not universal, but depend at least on the depletion rate and possibly on other parameters.

In this paper we keep the conventional Darcy scale point of view and the Darcy law with relative permeabilities. The key difference however is that relative permeabilities are not fit to experiments but obtained through physically-motivated explicit formulas. These expressions or formulas are based on the analysis of the mechanism of gas phase flow based on the geometry of the bubbles and its consequences on their motion. The theory involves a prediction of the aspect ratio of the bubbles and their velocities. The aspect ratio of the bubbles depends on the characteristics of the porous media in terms of pore size distribution and is obtained based on the Invasion Percolation in Gradient theory.

The resulting model is analyzed and solved in two different ways. First we describe a new type of approximate solution assuming extremely slow degassing. A simple partial differential equation similar to a kinematic wave equation results. This approach is more powerful than the asymptotic expansion described in previous wirk of the authirs, as it allows for the stauration to exhibit gradients and even shocks. Second, we solve the full set of Darcy-scale equations by way of a numerical solution, based on a version of the IMPES method based on previous similar numerical approaches. We show comparisons between the two solutions. We discuss how the formation of strong gradients of the gas phase saturation depends on gravity and viscosity.

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