Improved mechanistic foam simulation with foam catastrophe theory

Recent experimental studies discovered that foam exhibits three different states (weak-foam, intermediate, and strong-foam states) reminiscent of catastrophe theory, and the strong-foam state consists of two distinct flow regimes (high-quality and low-quality regimes). No existing foam simulators can handle these concepts properly, especially when the simulation comes to near the limiting capillary pressure, P c * (or the limiting water saturation, S w * , equivalently) at which foam breaks down abruptly. Capturing the delicate feedback mechanism near P c * has been a great challenge in mechanistic foam simulations. This study presents how to build a mechanistic foam simulator consistent with foam catastrophe theory and two steady-state strong-foam regimes. More importantly, this study for the first time resolves the issues on the instability and divergence of numerical simulation that take place near the physical discontinuity (i.e., P c * or S w * ) in foam simulation. s showed that it was necessary to choose an appropriate lamella-creation function to ensure the stability and convergence. Specifically (1) the lamella-creation function should increase rapidly above a certain pressure gradient (▿P), known as a minimum pressure gradient (▿Pmin) for lamella mobilization and division, to kick off active bubble generation, and (2) the function should also reach a plateau at high ▿P at which foam rheology is governed by bubble coalescence rather than bubble generation. This new mechanistic simulator required five parameters to fit the steady-state foam catastrophe, the two flow regimes, and dynamic foam coreflood data, each of which was determined uniquely. The foam model in this study manifested that active (or, inactive) lamella-creation mechanism could be compensated by active (or, inactive) lamella-coalescence mechanism in the modeling process. The level of how active these mechanisms were, however, had a significant impact on the shift from weak-foam to strong-foam propagation during dynamic foam displacement. tions were extended not only to simultaneous injection of gas and surfactant solutions in a wide range of injection velocities, but also to alternating gas and surfactant solutions in which the dynamic mechanisms near P c * is the key to field performance. Results were compared and verified with fractional flow analysis that was equipped with mechanistic foam mechanisms.