Physical Mechanisms for Bubble Growth during Solution Gas Drive
Authors: El Yousfi A. , Zarcone C. , Bories S. , Lenormand R. 
Published: December 2007

Physical Mechanisms for Bubble Growth during Solution Gas Drive.

Abstract
A series of experiments were performed in transparent micromodels to understand the mechanism of nucleation by pressure decline in a CO2-water solution. All our observations can be interpreted by a process that consists in the following succession of steps:pre-existence of stabilized microbubbles (order of magnitude of one micron),growth of the microbubbles in a very large number of sites and trapping by capillary forces,activation of some of these sites when pressure drawdown balances capillary trapping,growth of these bubbles by gas diffusion to a size allowing observation (around 30 microns).
The above process is similar to the one found in literature explaining boiling on heated surfaces.

Introduction
In petroleum engineering, there is a need for modelling gas production in reservoirs when pressure decreases below the bubble point. Modelling of gas production requires an accurate description of the three physical mechanisms involved in the process:the rate of appearance of gas bubbles,the growth of bubbles inside the pores,the formation of a continuous gas phase which will invade the medium.
The physical mechanisms governing the second and third steps are quite well understood. For instance, bubble growth inside pores is described by molecular diffusion with some correction factors to account for the presence of the porous medium (Li and Yortsos). However, the understanding of the first step, bubble formation inside a porous medium, is quite poor. The few existing models found in petroleum literature are contradictory. The classical model is derived from "homogeneous nucleation" (Wilt, Li and Yortsos). A recent paper by Firoozabadi and Kashiev, propose a completely different approach based on instantaneous nucleation. In order to improve the understanding of bubble appearance, we performed visualisations and measurements in transparent micromodels. The conclusion of our work is that nucleation is instantaneous, but not so simple than the model proposed by Firoozabadi and Kashiev. In fact, there is an additional step of trapping due to capillary force that explains the observed threshold and the progressive appearance of the bubbles.
Heterogeneous nucleation. We will first recall the principle of "homogeneous" nucleation, when the liquid is pure, without any solid or liquid interface.
When pressure is decreased under the bubble point, a transient gas "nucleus" appears by thermal fluctuations. This nucleus will grow in order to form a bubble only if its radius r is larger than a critical value. Otherwise, the nucleus will collapse under capillary pressure proportional to l/r (Laplace's law). The appearance of bubbles is therefore a random process such as photon emission, characterized by a rate of nucleation J (number of bubble per unit time and unit volume of liquid). J is an exponential function of the supersaturation P=P(equilibrium)-P
(1)
where N is the number of molecules per unit volume, m the mass of a molecule, kT is thermal energy, interfacial tension and B a parameter close to 2/3. It is now well established that homogeneous nucleation requires a very high supersaturation ratio P/P. Wilt gave the example of 1100 to 1700 for CO2 solutions near room conditions. Consequently, homogeneous nucleation cannot occur during pressure decline in porous media (Li and Yortsos). Instead, gas formation with low supersaturation rates can only be explained by "heterogeneous" nucleation.
In heterogeneous nucleation, the nucleus is formed on a solid interface. The nucleus is stabilized by the combined effect of surface roughness and wettability (Wilt, Li and Yortsos). For instance, it is simple to show that in a site of conical geometry with an angle, the interface between liquid and gas is flat when the contact angle is equal to /2- /2. There is no curvature of the interface and therefore there is no capillary pressure to collapse the nucleus. Consequently, hydrophobic sites reduce the energy involved for nucleus formation and can explain gas nucleation at low supersaturation rate. P. 805^