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| Fig. 1: Foam in porous media. It consists of a flowing part and a trapped part. (Source: M. Almajid) |
Gas injection into oil-bearing reservoirs is a practical method that is widely used to enhance oil recovery. [1] It has, however, some shortcomings because of the viscosity and density contrast between the injected gas and the resident fluids in the reservoir. Foam provides one means to circumvent these shortcomings. Foam is defined as a dispersion of a non- wetting phase in a continuous wetting phase as shown in Fig. 1. The non-wetting phase is gas and the wetting phase is water that contains surfactant at a particular concentration that is above the critical micelle concentration. Foam has been shown to reduce the gas relative permeability by trapping a large fraction of gas. [2,3] Additionally, the drag forces exerted by the moving bubbles on pore walls increases the gas apparent viscosity. [4,5] Therefore, a more favorable mobility ratio than pure gas injection is obtained, where the mobility ratio is defined as:
| M | = | λdisplacing λdisplaced |
= | krg/μg kro/μo |
In the above equation, λ is the phase mobility, kri denotes the relative permeability of phase i, and μi denotes the phase viscosity. Having a more favorable mobility ratio means that more oil can be produced because viscous fingering (due ot differences in viscosity) and fluid channeling (due to high permeability streaks) are greatly reduced, see Fig. 2. Foam in porous media is different than bulk foam in that it can get generated and destroyed by various mechanisms that are largely induced by the porous media topology and heterogeneity. In this report, we review these mechanisms.
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| Fig. 2: Top schematic shows viscous fingering of CO2 when it is injected into an oil-bearing reservoir, while the bottom one shows how this is modified by foam injection. (Source: M. Almajid) |
Snap-off is a mechanical process where the wetting phase forms collars in the pore throat that snaps off the gas bubble as it moves through the pore throat. This is similar to the process that was introduced by Roof to account for the formation of residual oil droplets in a water-wet porous medium. [6] The static condition for snap-off to happen is that the ratio of the pore throat to the pore body be 1:2.67. [6] This ratio ensures that the capillary pressure at the front of the interface, as it moves from the pore throat to the body, is less than the capillary pressure at the throat. The difference in capillary pressure induces the wetting phase (water) to flow back and helps the collar grow and snap-off the oil. The same conditions apply to foam generation by snap-off. Fig. 3 shows a schematic of snap-off in porous media. The gray circles represent the rock grains, the white-colored fluid represents gas, and the blue-colored fluid represents water with some surface active agents.
Lamella division generally occurs when a foam bubble that has a size larger than that of the pore body approaches a "branching point" as depicted in Fig. 4. The lamella division mechanism requires the existence of a lamella, and a branching point in the porous media that exhibits the same conditions in each way. If the lamella is at a branching point where the available paths require the same pressure drop for the lamella to enter them, the lamella divides into two lamellae as shown in Fig. 4.
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| Fig. 3: Snap-off mechanism. a) gas invades the pore body, b) gas enters the pore body, and c) wetting fluid moves back to snap off the gas thread. (Source: M. Almajid) |
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| Fig. 4: Lamella division in porous media. (Source: M. Almajid) |
A leave-behind mechanism can occur when two gas bubbles approach a pore body. The two bubbles converge together downstream leaving behind a lens. These lenses can also occur if one bubble approaches a pore body and wraps around that body. Foam that is generated only by a leave- behind mechanism is considered weak. However, this could be the way foam generation starts as the lenses later get transported and divided by the lamella division mechanism.
Understanding foam generation mechanisms is important and equally so is understanding mechanisms of foam coalescence. Achieving gas mobility control is dependent on the bubble density, which is dependent on the rates of generation and coalescence. If the rate of generation is greater than the rate of coalescence, then gas mobility is achieved and vice versa. There are two main mechanisms that describe foam coalescence in porous media in the absence of oil: capillary-suction coalescence and gas diffusion. The former is more dominant than the latter.
Churaev et al. introduced the idea of capillary-suction coalescence when they discussed the disjoining pressure of a film. [7] The disjoining pressure curve of a foam film is the net result of repulsive forces (electrostatic forces) and attractive forces (Van der Waals forces). Repulsive forces help keep the lamella stable while attractive forces induce lamella instability and, hence, rupture. Foam films are often referred to as metastable. Disjoining pressure only explains the behavior of static lamellae but we are more interested in dynamic flowing lamellae in porous media. It turns out that flowing foam have a limiting capillary pressure (Pc*) implying the existence of a critical water saturation (Sw*) below which flowing foam cannot exist. [8]
Gas diffusion is another process that describes foam coalescence mostly in the trapped gas region. Based on the Young-Laplace equation, the gas diffuses from bubbles of larger curvature to bubbles of smaller curvature. The bubbles with larger curvature are, therefore, filled at the expense of the bubble with smaller curvature disappearing. Gas diffusion is more predominant in trapped gas regions, where the gas is static. Coalesced static bubbles can eventually form a long bubble that is able to flow as the pressure needed to flow it is reduced then.
Foam provides one way of reducing the gas mobility but generating more bubbles in the reservoir. As the bubble density increases, the gas mobility is reduced. In this brief report, we showed how pore-scale phenomena can determine large-scale behavior (in reservoir-scale). This report only reviews the tip of the iceberg. The literature is filled with studies of foam inside and outside of porous media.
© Muhammad Almajid. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.
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