Equivalence Between Semi-empirical and Population-Balance Foam Models

Models for simulating foam-based displacements in enhanced oil recovery processes fall into two categories: population-balance (PB) models that derive explicitly foam texture, or bubble size, evolution in porous media from pore-level mechanisms related to lamellas generation and coalescence, and semi-empirical (SE) models that account implicitly for foam texture effects through a gas mobility reduction factor that depends on fluid saturation, interstitial velocity, surfactant concentration, and other factors. This mobility reduction factor has to be calibrated from a large number of experiments on a case by case basis in order to match the physical effect of each considered parameter on foam behavior. This paper develops a method for identifying the SE models from the physics of foams as derived from PB models at local equilibrium (LE). The identification of both foam flow models leads to a method for calibrating SE models from the PB model translation of foam flow data. Application to a set of foam quality-scan experiments at fixed total flow rate shows that the SE and PB models at LE match equally well the measurements and generate almost the same results in both the so-called high- and low-quality regimes. We demonstrate that the two approaches are equivalent at local equilibrium and differ only in the way in which the complex dynamic mechanisms of lamellas are handled. This physical approach of foam flow could circumvent some difficulties in the direct calibration of SE models from foam mobility (or apparent viscosity) data.