Fractional-Flow Models for Foam Enhanced Oil Recovery

George E. P. Box wrote, "All models are false, but some models are useful." In that spirit, we examine fractionalflow models for foam enhanced oil recovery (EOR). This approach has long fascinated practitioners by transforming a physics problem first into a mathematics problem and then into a geometry puzzle. This approach, sometimes called the method of characteristics (MOC), makes many serious simplifying assumptions and yet provides many useful insights into the complex process of foam EOR. First, we will briefly review fractional-flow theory and its extension to two-phase EOR processes, and then discuss the foam EOR process. The fractional-flow model for a "SAG" (surfactant alternating gas) foam process tells us where to focus experimental studies, and shows how a process with very low mobility can nonetheless give excellent injectivity. This approach allows calculating injectivity to much greater precision than conventional finite-difference simulation. Foam processes can employ a surfactant injected in the "gas" (supercritical fluid) phase rather than water; fractional-flow theory shows the potential advantages for injectivity, but warns of the key role of partitioning of surfactant into water. A related extension of the MOC can predict the distance co-injected gas and water, in conventional gas EOR or foam, flow before complete gravity segregation by transforming variables from position and time to position and stream function. The MOC can be extended to non-Newtonian foam flow by representing each increment in distance from the well as a new porous medium, taking fluid from the inner region and transmitting it outward. Finally, the approach, combined with a "population balance" model for foam generation, shows that the propagation rate of foam may reach zero at some distance from the well, even though foam would be stable beyond that distance. The fractional-flow approach is "false" in that it is not at all a complete representation of foam EOR, but it is clearly useful. Bio William Rossen is Professor in Reservoir Engineering Department of Geoscience and Engineering, Delft University of Technology. Prof. Rossen's current research concerns use of foams for diverting fluid flow in porous media, modeling complex transport processes in networks, and understanding flow in naturally fractured geological formations. Throughout this work runs a search for the simplest, most elegant model to describe a given phenomenon, followed by an exploration of the often-complex implications of that model; often using network or percolation models for flow in porous media.. In 2011 Prof. Rossen was named Best Instructor at Delft University of Technology. In 2012 he was named an IOR Pioneer at the SPE/DOE Symposium on Improved Oil Recovery, Tulsa, OK, USA.