Modeling Foam Flow at Achievable Reservoir Flow Rates Using the Population-Balance Approach and Implications for Experimental Design
Authors: Ma Kun , Mateen Khalid , Ren Guangwei , Bourdarot Gilles , Morel Danielle 
Published: November 2016

Abstract
A correct understanding of foam generation, coalescence and transport at achievable reservoir flow rates has been a key issue for its applications in enhanced oil recovery processes. Use of foam models to simulate foam flow in the reservoir requires establishing of the parameters in the lab. This is generally done at relatively high flow rates in a so-called strong-foam state, which covers both high- and low-quality foam regimes that are used to fit foam modeling parameters. In the reservoir, because of the in situ velocities changing between near and far from the wellbore, there is a need for the foam model to be able to predict the foam behavior at two different foam states with high and low velocities, respectively. Depending upon the petrophysical properties of the reservoir, one may not generate and transport strong foam at the low-velocities away from the well.
Bubble population-balance models are considered a useful tool to understand foam flow through porous media by addressing the phenomenon from the first principle of physics. We investigated the capability of available population-balance models to simulate these two foam states over a wide range of velocities. Using an example case, the same set of data was fit to two well-known models at relatively high flow rates. Both models fit the steady-state data at high-flow rates reasonably well through proper tuning of the parameters. One foam model, reported by Afsharpoor and co-workers in 2010, predicted a weak-foam state with much lower apparent viscosity at low flow rates; however, the other model, reported by Chen and co-workers in 2010, predicted much higher pressure gradient at low flow rates with the same set of relative permeability and capillary pressure curves, due to the shear-thinning effect and the foam generation effect in the absence of a minimum pressure gradient (MPG). We observed significantly different foam rheology above the MPG: shear-thinning behavior when the foam texture reaches the maximum and Newtonian behavior when the foam texture is below the maximum. Below the MPG, a shear-thickening behavior, with an abrupt change at the boundary, was predicted by Afsharpoor model as was earlier observed in several experiments reported in the literature. The sensitivity of MPG to the corresponding critical velocity in Afsharpoor model is also studied in this work.
The data acquired in steady-state experiments have to be in the strong-foam state in order to estimate correct parameters in the model to simulate foam behavior in high- and low-quality regimes. However, if the experimental data acquired at low fluid velocities is available and indicates a weak-foam state at low velocities, one can use Afsharpoor model to predict this weak-foam state away from the well. Note that the findings are limited to steady-state foam flows in relatively homogeneous systems, while transient foam modeling and the impact of heterogeneity / pore-network distribution are yet to be investigated.