Modeling of Foamed Gas Mobility in Permeable Porous Media

Abstract

In mechanistic modeling of foam in porous media, reduced gas mobility is attributed to viscous resistance of flowing foam lamellas to gas flow, while gas trapping significantly modifies relative permeability. By using pore-network models representative of real porous media, we previously developed a relationship between flowing gas fraction and pressure gradient for strong foam (high lamella density). In this study, we expand our model to describe the effects of foam strength and pore-scale apparent gas viscosity models on both relative gas permeability and effective gas viscosity. Dimensional analysis in scaling of these two rheological quantities with pressure gradient and lamella density is discussed. One of our important findings is that relative gas permeability is poorly sensitive to total lamella density while it is a strong non-linear function of flowing gas fraction, opposing to most of the existing theoretical models describing the effect of gas trapping on relative gas permeability. This is consistently observed for all the pore-scale apparent gas viscosity models. It is also found that effective gas viscosity increases exponentially with flowing lamella density. This result implies that the use of the commonly used apparent gas viscosity model for straight capillary tubes is not accurate for foam flow in porous media. In addition, shear thinning foam flow is more obvious at high flowing lamella density while Newtonian flow becomes significant at relatively low flowing lamella density. Furthermore, scaling of effective gas viscosity with flowing lamella density depends on how the later quantity is defined. Both empirical and mechanistic pore-scale apparent gas viscosity models give almost the same functional relationship between flowing gas fraction and pressure gradient. This would facilitate scaling of flow rate with pressure gradient and testing a range of shear-thinning and yield-stress behavior in a simple format. Our results necessitate the need for further improving the existing mechanistic foam modeling methods with focus on process upscaling.

Laboratory Investigation of Low-Tension-Gas Flooding for Improved Oil Recovery in Tight Formations

“…In this regime, lamellae generation is primarily driven by snap off and leave behind mechanisms that are only poorly dependent on pressure gradient or capillary pressure. These lamellae will primarily be of the immobile variety because of the high in-situ capillary pressures demonstrated at the small pore throats and should provide a reduced but still sufficient resistance to flow [Balan et al (2012) has shown that gas relative permeability is exponentially reduced with trapped-gas saturation].…”

Flow of non‐Newtonian fluids in converging–diverging rigid tubes

“…In this respect, pore-scale network modeling is the main candidate and the most natural approach to accommodate such flow-structure features [19][20][21][22][23][24]. The effect of varying cross section in the flow direction can be particularly important for modeling certain flow phenomena such as extensional flows, viscoelastic effects and yield-stress dynamics which are essential for various scientific and technological purposes like enhanced oil recovery as well as many other applications [25][26][27][28][29][30][31][32][33][34][35][36].…”