Modeling of Foam Flow in Porous Media by the Population Balance Method
byTad W. Patzek
Patzek, T. W., "Modeling of Foam Flow in Porous Media by the Population Balance Method," Chapter 16 in the Surfactant-Based Mobility Control, D. H. Smith, Editor, American Chemical Society, Symposium Series, Volume 373, Washington, D.C., 1988.
The mobility of foams in porous media is dominated by foam texture (i.e. foam bubble size). The effect of bubble size can be incorporated into a reservoir simulator by adding balances on the number density of bubbles in flowing and stationary foam to the equations of mass, momentum, and energy conservation. These balances account for changes in foam texture caused by mechanisms which create, destroy, or transfer bubbles, e.g., capillary snap-off, bubble division, coalescence, diffusion, evaporation or condensation, as well as bubble trapping and mobilization. The population balance of the number bubble density is volume-averaged and the resulting equations are simplified by a series expansion in the moments of bubble mass. The zeroth order moment equations have a form directly applicable to reservoir simulations, but they cannot be solved without some knowledge or assumptions about the higher order (≥ 2) moments.