A Mechanistic Population Balance Model For Transient and Steady-State Foam Flow in Boise Sandstone
byA. R. Kovscek, Tad W. Patzek, Clayton J. Radke
Kovscek, A. R., T. W. Patzek, and C. J. Radke. "A mechanistic population balance model for transient and steady-state foam flow in Boise sandstone." Chemical Engineering Science 50, no. 23 (1995): 3783-3799.
Foam in porous media is discontinuous on a length scale that overlaps with pore dimensions. This foam-bubble microstructure determines the flow behavior of foam in porous media and, in turn, the flow of gas and liquid. Modeling of foam displacement has been frustrated because empirical extensions of the conventional continuum and Newtonian description of fluids in porous media do not reflect the coupling of foam-bubble microstructure and foam rheology. We report a mechanistic model for foam displacement in porous media that incorporates pore-level mechanisms of foam generation, coalescence, and transport in the transient flow of aqueous foams. A mean-size foam-bubble conservation equation, along with the traditional reservoir/groundwater simulation equations, provides the foundation for our mechanistic foam-displacement simulations. Since foam mobility depends heavily upon its texture, the bubble population balance is both useful and necessary, as the role of foam texture must be incorporated into any model which seeks to predict foam flow accurately. Our model employs capillary-pressure-dependent kinetic expressions for lamellae generation and coalescence, and incorporates trapping of lamellae. Additionally, the effects of surfactant chemical transport are included. All model parameters have clear physical meaning and, consequently, are independent of flow conditions. Thus, for the first time, scale up of foam-flow behavior from laboratory to field dimensions appears possible. The simulation model is verified by comparison with experiment. In situ, transient, and steady aqueous-phase liquid contents are garnered in a 1.3 μm2 Boise sandstone using scanning gamma-ray densitometry. Backpressures exceed 5 MPa, and foam quality ranges from 0.80 to 0.99. Total superficial velocities range from as little as 0.42 to 2.20 m/d. Sequential pressure taps measure flow resistance. Excellent agreement is found between experiment and theory. Further, we find that the bubble population balance is the only current means of describing all flow modes of foam self-consistently.