Oil production through cold depletion 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 asphaltènes. We have modeled depletion experiments on laboratory-scale cores using a one-dimensional model at the Darcy scale, describing the multiphase flow of the oil and gas. The oil and gas phases move with a classical relative permeability model. <br><br> Initially, the gas phase is in the form of very small bubbles, which are physically viewed as stabilized in crevices of the solid phase or as small germs surrounded by a coating skin. <br>When surface tension is taken into account in the phase equilibrium a Gibbs radius appears<br>so that bubbles grow rapidly above the Gibbs radius and collapse below it. <br><br> As a result, the solution of the partial differential equations describing mass conservation display nonlinear fronts that connect two regions of almost constant concentration and velocity, in a manner analogous to shock waves. We describe an asymptotic theory that allows understanding the formation of the fronts and connects them to the dynamics of bubble activation at nucleation sites.<br>


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