Estimation of Parameters for the Simulation of Foam Flow through Porous Media: Part 3; Non-Uniqueness, Numerical Artifact and Sensitivity Available to Purchase

In the absence of oil in the porous medium, the STARS™ foam model has three parameters to describe the foam quality dependence, fmmob, fmdry, and epdry. Even for a specified value of epdry, two pairs of values of fmmob and fmdry can sometimes match experimentally measured ft_g and μ^t_foam,app. This non-uniqueness can be broken by limiting the solution to the one for which fmdry <St^t_w. Additionally, a three-parameter search is developed to simultaneously estimate the parameters fmmob, fmdry, and epdry that fit the transition foam quality and apparent viscosity. However, a better strategy is to conduct and match a transient experiment in which 100% gas displaces surfactant solution at 100% water saturation. This transient foam quality scans the entire range of fractional flow and the values of the foam parameters that best match the experiment can be uniquely determined. Finally, a three-parameter fit using all experimental data of apparent viscosity versus foam quality is developed.

The numerical artifact of pressure oscillations in simulating this transient foam process is investigated by comparing finite difference algorithm with method of characteristics. Sensitivity analysis shows that the estimated foam parameters are very dependent on the parameters for the water and gas relative permeability. In particular, the water relative permeability exponent and connate water saturation are important.