Modeling Foam Displacement With the Local-Equilibrium Approximation: Theory and Experimental Verification

The gas-mobility-control aspects of foamed gas make it highly applicable for improved oil recovery. Gas-bubble size, often referred to as foam texture, determines gas-flow behavior in porous media. A population-balance model has been developed previously for modeling foam texture and flow in porous media. The model incorporates pore-level mechanisms of foam-bubble generation, coalescence, and transport. Here, we propose a simplified foam model to reduce computational costs. The formulation is based on the assumption of local equilibrium of foam generation and coalescence and is applicable to high- and low-quality foams. The proposed foam model is compatible with a standard reservoir simulator. It provides a potentially useful, efficient tool to predict foam flows accurately at the field scale for designing and managing foamed-gas applications. There are three main contributions of this paper. First, foam-displacement experiments in a linear sandstone core are conducted. A visualization cell is employed to measure the effluent foam-bubble sizes for a transient flow as well as to estimate the in-situ foam-bubble sizes along the length of the core during steady-state flow. These appear to be the first measurements of foam-bubble texture in the entrance region of a core. Additionally, the evolution of aqueous-phase saturation is monitored using X-ray computed tomography (CT), and the pressure profile is measured by a series of pressure taps. Second, the population-balance representation of foam generation by gas-bubble snap-off is modified to extend the capability of the population-balance approach to predict foam-flow behaviors in both the so-called high-quality and low-quality regimes. Third, a simplified population-balance model is developed and implemented with the local-equilibrium approximation. Good agreement is found between the experimental results and the predictions of the simplified model, with a minor mismatch in the entrance region.