We propose a new capillary number for flow in fractures starting with a force balance on a trapped ganglion in a fracture. The new definition is validated with laboratory experiments using five distinctive model fractures. Capillary desaturation curves were generated experimentally using water-air forced imbibition. The residual saturation-capillary number relationship obtained from different fractures, which vary in aperture and roughness, can be represented approximately by a single curve in terms of the new definition of the capillary number. They do not fit a single trend using the conventional definition of the capillary number.@en

Naturally fractured reservoirs (NFRs) are found in many countries around the globe, in almost every lithology. These reservoirs can be carbonates, sandstones, or shale, in the case of unconventional or basement reservoirs. NFRs have been explored and exploited globally for groundwater, geothermal energy, hydrocarbon production, coalbedmethane production, and nuclear-waste sequestration. They have unique characteristics in their flow behavior. Short-circuiting is encountered in these reservoirs during fluid-displacement processes. This unfavourable behavior leads to considerable unrecovered hydrocarbons. Injection of gas into these reservoirs to enhance oil recoverywithout mobility control can greatly reduce the efficiency of the enhanced oil recovery process. Foam greatly reduces the mobility of gas in non-fractured porous media and improves sweep efficiency. However, the knowledge of foam in fractured porous media is far less complete [Chapter 1].@en

Gas is used in petroleum reservoirs to displace oil for enhanced oil recovery. The microscopic displacement efficiency of gas is very good, but at the reservoir scale the process suffers from poor sweep efficiency, especially in naturally fractured reservoirs. Foam can improve the sweep. There have been considerable scientific contributions toward understanding foam flow in nonfractured porous media, with relatively little work on foam flow in fractured porous media. We investigate foam-generation mechanisms in five fully characterized glass models of fractures with different apertures and correlation lengths of the aperture distribution. We also study the rheology of the in situ-generated foam by varying the superficial velocities of the gas and surfactant solution. We compare the measured pressure gradient against the fracture attributes, aperture, and the correlation length of the aperture. We also compare foam texture as a function of position within the fracture as the generated foam propagates through the fracture. Gas mobility was greatly reduced as a result of in situ foam generation in our model fractures. Foam was generated predominantly by capillary snap-off and lamella division. The measured mobility reduction depends on fracture attributes. Fracture-wall roughness, represented by both the hydraulic aperture and the correlation length of the aperture, plays an important role in foam generation and mobility. The average bubble size increases as the aperture increases, which results in a significant decrease in pressure gradient. Two model fractures show the same two foam-flow regimes central to the understanding of foam in nonfractured porous media: a low-quality regime where pressure gradient is independent of liquid velocity and a high-quality regime where pressure gradient is independent of gas velocity. The mechanisms thought to be behind these two regimes in nonfractured porous media do not apply to these experiments, however.@en

Foam greatly reduces gas mobility for gas enhanced-oil-recovery (EOR) projects. It substantially increases both the effective viscosity of gas and gas trapping. Numerous studies have been conducted to understand foam rheology in rock matrix both theoretically and experimentally. The knowledge of foam flow in fractured porous media is incomplete, however. This study aims to contribute to the understating of foam generation and propagation in a fully characterized physical-model fracture. We investigate foam-generation mechanisms and the propagation of pre-generated foam. Gas mobility was greatly reduced as a result of in-situ foam generation. Foam-generation mechanisms similar to those seen in 3D porous media were observed on this model fracture. Foam was generated predominantly by capillary snap-off and lamella division. Lamella division was observed at high gas fractional flow at two different superficial velocities. Fracture wall roughness played an important role in foam generation. In the case of pre-generated foam, two very distinct bubble sizes were injected: fine-textured bubbles much smaller than the roughness scale and coarse-textured foam with bubbles much larger than the roughness scale. The first case did not show any significant change in bubble size as foam propagated through the model fracture, while in the second case, the fracture played a role in reducing bubble size. Inter-bubble diffusion did not regulate bubble size in our apparatus because residence time in the fracture is relatively short. We cannot confirm that foam reached local equilibrium in our experiments, but we believe that local equilibrium lies between the cases of in-situ- and pre-generated foams.@en

Gas is very efficient in displacing oil for enhanced-oil-recovery projects because of its high microscopicdisplacement efficiency. However, the process at the reservoir scale suffers from poor sweep efficiency due to density and viscosity differences compared to in-situ fluids. Foam substantially reduces the viscosity of injected gas and hence improves the sweep. Foam rheology in 3D geological porous media has been characterized both theoretically and experimentally. In contrast, the knowledge of foam flow in fractured porous media is far less complete. We study foam rheology in a fully characterized model fracture. This investigation is conducted by varying superficial velocities of gas and surfactant solution. We find in this model fracture the same two foam-flow regimes central to the understanding of foam in 3D porous media: a low-quality regime where pressure gradient is independent of liquid velocity and a high-quality regime where pressure gradient is independent of gas velocity. The transition between regimes is less abrupt than in 3D porous media. Direct observation of bubble size, bubble trapping and mobilization, and foam stability as functions of superficial velocities allows comparison with our understanding of the mechanisms behind the two flow regimes in 3D porous media. Additionally, foam is shear-thinning in both regimes. But in other important respects the mechanisms thought to be behind the two flow regimes in 3D media do not appear in our model fracture. Foam is not at the limit of stability in the high-quality regime. Mobility in the high-quality regime instead reflects reduced and fluctuating foam generation at high foam quality. @en

The displacement of a nonwetting phase by a wetting phase is characterized by the capillary number. Different forms of capillary number have been used in the literature for flow in porous media. A capillary number for a single rock fracture has been defined in the literature, using the mean aperture to characterize the trapping and mobilization in a fracture. We propose a new capillary-number definition for fractures that incorporates geometrical characterization of the fracture, dependent on the force balance on a trapped ganglion. The new definition is validated with laboratory experiments using five distinctive model fractures. The model fractures are made of glass plates, with a wide variety of hydraulic apertures, degrees of roughness, and correlation lengths of the roughness. The fracture surfaces were characterized in detail and statistically analyzed. The aperture distribution of each model fracture was represented as a 2D network of pore bodies connected by throats. The hydraulic aperture of each model fracture was measured experimentally. Capillary desaturation curves (CDCs) were generated experimentally using water/air in forced imbibition. The transparent nature of the system permits us to determine the residual air saturation as a function of pressure gradient from the captured images. The residual nonwetting saturation/capillary-number relationship obtained from different fractures varying in aperture and roughness can be represented approximately by a single curve in terms of the new definition of the capillary number. They do not fit a single trend using the conventional definition of the capillary number.@en

Gas is used in displacing oil for enhanced oil recovery because of its high microscopic-displacement efficiency. However, the process at the reservoir scale suffers from poor sweep efficiency due to density and viscosity differences compared to in-situ fluids. Foam substantially increases the viscosity of injected gas and hence improves the sweep. Foam rheology in 3D geological porous media has been characterized both theoretically and experimentally. In contrast, the knowledge of foam flow in fractured porous media is far less complete. A companion paper (AlQuaimi and Rossen, 2017c), We focused on foam generation and propagation in a fully characterized model fracture. Here we focus on foam rheology in the same model fracture. This investigation is conducted by varying superficial velocities of gas and surfactant solution. We find in this model fracture the same two foam-flow regimes central to the understanding of foam in 3D porous media: a low-quality regime where pressure gradient is independent of liquid velocity and a high-quality regime where pressure gradient is independent of gas velocity. The transition between regimes is less abrupt than in 3D porous media. Our study directly relates flow regime to foam texture through observation of bubble size, bubble trapping and mobilization, and foam stability as functions of superficial velocities which allows comparison with our understanding of the mechanisms behind the two flow regimes in 3D porous media. Additionally, foam is shear-thinning in both regimes. However, the mechanisms thought to be behind the two flow regimes in 3D porous media do not appear in our model fracture. Foam is not at the limit of stability in the high-quality regime. Mobility in the high-quality regime, instead, reflects reduced and fluctuating foam generation at high foam quality. Moreover, bubble size is not fixed at approximately pore size, the mechanism thought to control the low-quality regime in 3D porous media. Instead, bubbles are much smaller than pores. Finally, for this model fracture, the investigation of vertical flow reaches the same findings as for horizontal flow, with somewhat lower pressure gradient.@en