Experimental and numerical evaluation of foam physics in porous media across multiple scales
Keywords: Energy Resources Engineering.

Foaming injected gases with aqueous surfactant solutions has proven to be a successful method in controlling the mobility of injected gases and enhancing oil recovery. Much of this success is attributed to the ability of the foam to make the gaseous phase discontinuous while maintaining the continuity of the wetting liquid in the pore space. This discontinuous microstructure of foam, importantly, deviates its behavior from Newtonian fluids typically present in reservoir rocks. Thus, predictive modeling efforts are hindered by the lack of understanding of this non-Newtonian behavior of foam. This dissertation aims to improve our understanding of the pore-level mechanisms that control the non-Newtonian behavior of foam and to develop ultimately a mechanistic, physics-based model that incorporates these pore-level mechanisms of generation, coalescence, and transport to be able to predict foam behavior at the meter scale. The foam model developed in this thesis is incorporated in the modular, multiphysics simulator \lstinline{AD-GPRS} to provide a general framework where hypotheses or additional foam physics can be readily tested or added. Complementary to the developed model, an experimental investigation of foam flow in a slightly heterogeneous sandstone core is reported and its results are compared to the predictions of the developed model. The snap-off mechanism occurring at the pore-level was chosen to develop a kinetic expression for the rate of foam generation in porous media using a hydrodynamic pore-level corner-flow model. Additionally, the pore-level model evaluates the effect of residual oil on the Roof snap-off criterion and the time of liquid accumulation. The rate of foam generation is found to be sensitive to the liquid and gas velocities, the wetting-liquid content, and the surfactant concentration. Moreover, the presence of residual oil affects foam generation by reducing the number the active germination sites available for foam generation and increasing the time of liquid accumulation in the absence of a large applied liquid pressure gradient. A pore network model is used to investigate the trapped gas fraction and the foam generation mechanisms. The classical invasion percolation algorithm is modified to take into account the existence of generated lamellae into the invasion rule. The model results demonstrate the importance of bubble texture (i.e. the number density of bubbles) to the successful development of strong foam. Moreover, the model shows that the flowing foam fraction increases with pressure but decreases with bubble density. A comparison of the probability of the two most dominant generation mechanisms reveals that snap-off dominates over lamella division in 2D and 3D lattices. Based on the findings of the pore-level as well as the pore network model, a steady-state population balance model of the bubble density is developed. Kinetic expressions of foam generation and coalescence are chosen based on the dominant pore-level mechanisms. The model developed is validated against recent experimental data. Moreover, it is used to elucidate the reasons for hysteresis and backward front movement commonly observed during steady and quasisteady foam flow experiments. An excellent match is found between the model and our experimental data highlighting the importance of the flowing foam fraction to the accurate predictive capability of foam models. Following these investigations that span multiple scales (pore-scale to core-scale), we develop a transient, mechanistic, full-physics bubble density population balance model. The model has a new formulation for the flowing foam fraction that is consistent with the results of the pore network model. Additionally, it is implemented in the modular, multiphysics simulator (\lstinline{AD-GPRS}) to allow flexibility of adding new physics or coupling with more physics in the future. The developed model is tested against experimental data under different conditions. The experimental data used test the model against the rock heterogeneity, the initial saturation state of the rock, and the existence of immobile oil in the core. Excellent agreement is obtained between predictions and experiments. We find that a discontinuous flowing foam fraction is able to simulate heterogeneous cases and that a smaller rate generation constant is sufficient in capturing how foam flows in the presence of immobile oil.