Improved mechanistic foam simulation with foam catastrophe theory

  • Kam S
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Abstract

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, Pc*(or the limiting water saturation, Sw*, equivalently) at which foam breaks down abruptly. Capturing the delicate feedback mechanism near Pc*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., Pc*or Sw*) in foam simulation. Results 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 ({down triangle, open}P), known as a minimum pressure gradient ({down triangle, open}Pmin) for lamella mobilization and division, to kick off active bubble generation, and (2) the function should also reach a plateau at high {down triangle, open}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. Simulations 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 Pc*is the key to field performance. Results were compared and verified with fractional flow analysis that was equipped with mechanistic foam mechanisms. © 2007 Elsevier B.V. All rights reserved.

Author-supplied keywords

  • Foam
  • Foam catastrophe
  • Foam simulation
  • Limiting capillary pressure
  • Limiting water saturation

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Authors

  • Seung Ihl Kam

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