Modeling foam displacement in fractures

The use of the population-balance approach is extended to include the description of foam transport in fractures. We study numerically foam flow resistance as a function of gas and liquid velocities and the degree of fracture heterogeneity. The mechanisms of foam flow resistance, generation, and coalescence are similar among fractured and unfractured media but the macroscopic expression of non-linear foam physics is different. The possibility of continuously varying gas–liquid curvature in response to capillary pressure and the relationship of curvature to foam apparent viscosity, however, results in different pressure drop behavior in fractures as gas flow rate and foam quality are varied. The full physics foam model is modified to incorporate this relationship in the simulations. The foam flow resistance parameter is then calculated locally. The simulated fracture models include one- and two-dimensional heterogeneous and a radial homogeneous model. Model predictions compare favorably to experimental literature data.