Snap-off mechanism

The three dispersion types described by Wellington et al. are important mechanistically, in view of the apparent importance of capillary snap-off. Extant descriptions of the snap-off mechanism explicitly treat the first type of dispersion, and they should be able to accommodate the second dispersion type by addition of a second fluid that does not wet the porous medium. However, if the aqueous phase of the first two dispersion types wets the porous... 

We point out the existence of an additional potential snap-off mechanism due to piston-like advance of an invading meniscus [termed by Mason Morrow (1991) as the main terminal meniscus MTM] in direction perpendicular to the cross-sectional plane of the unit cell. This snap-off mechanism is only important for very high flow rates and when the liquid front is very well connected (Blunt Scher, 1995). 

Figure 5. Schematic of snap-off mechanism (gas is unshaded) showing (a) gas entry into liquid filled pore-throat (b) gas finger and wetting collar formation prior to breakup, and (c) liquid lens after snap-off. (Reproduced with permission from reference 60. Copyright 1989 Society of Petroleum Engineers.)...

Barring direct measurement of foam texture, we adopt the following reasoning. Because of the generation of foam bubbles by the snap-off and division mechanisms (4), bubble sizes are expected to be approximately that of pore bodies. Thus, the linear bubble density should scale roughly as n 6/Dwhere... 

In a third paper by the Bernard and Holm group, visual studies (in a sand-packed capillary tube, 0.25 mm in diameter) and gas tracer measurements were also used to elucidate flow mechanisms ( ). Bubbles were observed to break into smaller bubbles at the exits of constrictions between sand grains (see Capillary Snap-Off, below), and bubbles tended to coalesce in pore spaces as they entered constrictions (see Coalescence, below). It was concluded that liquid moved through the film network between bubbles, that gas moved by a dynamic process of the breakage and formation of films (lamellae) between bubbles, that there were no continuous gas path, and that flow rates were a function of the number and strength of the aqueous films between the bubbles. As in the previous studies (it is important to note), flow measurements were made at low pressures with a steady-state method. Thus, the dispersions studied were true foams (dispersions of a gaseous phase in a liquid phase), and the experimental technique avoided long-lived transient effects, which are produced by nonsteady-state flow and are extremely difficult to interpret. 

A key factor in the commercialization of surfactant-based mobility control will be the ability to create and control dispersions at distances far from the injection well (TJ ). Capillary snap-off is often considered to be the most important mechanism for dispersion formation, because it is the only mechanism that can form dispersions directly when none are present (39,40). The only alternative to snap-off is either leave-behind, or else injection of a dispersion, followed by adequate rates of thread breakup and division to maintain the injected lamellae. 

Countering snap-off and division, there are two mechanisms by which droplets of noncondensible fluids can become larger and dispersions can coarsen and disappear. 

When the lamella between two droplets thins and breaks, the droplets on either side coalesce into a single, larger droplet (41,72). Continuation of this backward" process eventually leads to the disappearance of the dispersion, if it is not balanced by the forward" mechanisms of snap-off and division. Lamellae are thermodynamically metastable, and there are many mechanisms by which static and moving thin films can rupture. These mechanisms also depend on the molecular packing in the film and, thus, on the surfactant structure and locations of the dispersed and dispersing phases in the phase diagram. The stability and rupture of thin films is described in greater detail in Chapter 7. 

Effects of Capillary Number, Capillary Pressure, and the Porous Medium. Since the mechanisms of leave-behind, snap-off, lamella division and coalescence have been observed in several types of porous media, it may be supposed that they all play roles in the various combinations of oil-bearing rocks and types of dispersion-based mobility control (35,37,39-41). However, the relative importance of these mechanisms depends on the porous medium and other physico-chemical conditions. Hence, it is important to understand quantitatively how the various mechanisms depend on capillary number, capillary pressure, interfacial properties, and other parameters. 

The population balance simulator has been developed for three-dimensional porous media. It is based on the integrated experimental and theoretical studies of the Shell group (38,39,41,74,75). As described above, experiments have shown that dispersion mobility is dominated by droplet size and that droplet sizes in turn are sensitive to flow through porous media. Hence, the Shell model seeks to incorporate all mechanisms of formation, division, destruction, and transport of lamellae to obtain the steady-state distribution of droplet sizes for the dispersed phase when the various "forward and backward mechanisms become balanced. For incorporation in a reservoir simulator, the resulting equations are coupled to the flow equations found in a conventional simulator by means of the mobility in Darcy s Law. A simplified one-dimensional transient solution to the bubble population balance equations for capillary snap-off was presented and experimentally verified earlier. Patzek s chapter (Chapter 16) generalizes and extends this method to obtain the population balance averaged over the volume of mobile and stationary dispersions. The resulting equations are reduced by a series expansion to a simplified form for direct incorporation into reservoir simulators. 

A study of the effect of pore geometry on foam formation mechanisms shows that snap-off" bubble formation is dominant in highly heterogeneous pore systems. The morphology of the foams formed by the two mechanisms are quite different. A comparison of two foam injection schemes, simultaneous gas/surfactant solution injection (SI) and alternate gas/surfactant solution injection (GDS), shows that the SI scheme is more efficient at controlling gas mobility on a micro-scale during a foam flood. 

The majority of the bubbles in the GDS experiment were formed in this manner. Bubbles formed by this second mechanism are several times larger than the pore radius, whereas bubbles formed by snap-off tend to be the same size as the pore throat radius. 

The first mechanism is snap-off, studied by Roof (22), and discussed in more detail recently by Mohanty et (23), and Falls et (5). Basically a thermodynamic instability arises as curvature and hence capillary pressure variations cause the wetting fluid to... 

A heterogeneous pore structure with varying aspect ratio would increase the frequency of breakup and coalescence, which should increase the observed mobile ganglia size distribution. However, the basic flow mechanism should remain unchanged. Also the relative importance of snap-off as a breakup mechanism would be increased relative to dynamic splitting. Here too a detailed study seems desirable. 

Arriola (8) and Ni (5) have observed a second mechanism for snap off in strongly constricted square capillaries. At low liquid flow rates, a bubble is trapped in the converging section of the constriction and liquid flows past the bubble. As liquid flow rate increases, waves developed in the film profile and at some critical liquid flow rate these oscillations become unstable and bubbles snap off. In these experiments, the bubble front is located upstream of the constriction neck. Therefore, no driving force for the drainage mechanism exists. Bubbles formed by this mechanism are produced at a high rate and have a radius on the order of the constriction neck. No attempt has previously been made to model snap-off rate by this mechanism in noncircular constrictions. 

Snap off by the instability mechanism may occur in the following way. A bubble in an angular constriction such as a square channel will flatten against the walls as shown in Figure 2. The radius of the circular arcs in the corners for a static bubble is about one half of the tube half width. At low liquid flow rates, a bubble trapped behind a constriction has this nonaxisymmetric shape. As liquid flow rate increases, the bubble moves farther into the constriction and the fraction of cross sectional area open to liquid flow at the front of the bubble increases until the thread becomes axisymmetric at some point near the bubble front. 

In addition to this thread breakup mechanism, gas fingers and large bubbles can also experience bubble snap-off when passing through narrow pore constrictions (20,21). Although snap-off phenomena can be quite complex (21-24), the static analysis of Roof (20) indicates that the resulting bubble diameters are at least twice the pore constriction diameter. 

To develop an understanding of the emulsion flow in porous media, it is useful to consider differences and similarities between the flow of an OAV emulsion and simultaneous flow of oil and water in a porous medium. As discussed in the preceding section, in simultaneous flow of oil and water, both fluid phases are likely to occupy continuous, and to a large extent, separate networks of flow channels. Assuming the porous medium to be water-wet, the oil phase becomes discontinuous only at the residual saturation of oil, where the oil ceases to flow. Even at its residual saturation, the oil may remain continuous on a scale much larger than pores. In the flow of an OAV emulsion, the oil exists as tiny dispersed droplets that are comparable in size to pore sizes. Therefore, the oil and water are much more likely to occupy the same flow channels. Consequently, at the same water saturation the relative permeabilities to water and oil are likely to be quite different in emulsion flow. In normal flow of oil and water, oil droplets or ganglia become trapped in the porous medium by the process of snap-off of oil filament at pore throats (8). In the flow of an OAV emulsion, an oil droplet is likely to become trapped by the mechanism of straining capture at a pore throat smaller than the drop. 

Two models help to explain the mechanisms by which oil is entrapped in porous media the pore doublet and the snap-off models. 

Foam Formation. Three fundamental pore-level generation mechanisms exist snap-off, division, and leave-behind. 

Snap-off. Snap-off is a very significant mechanism for bubble generation in porous media. This phenomenon was first identified and explained by Roof (54) to understand the origin of residual oil. Snap-off is not restricted to the creation of trapped oil globules. It repeatedly occurs during multiphase flow in porous media regardless of the presence or absence of surfactant. Hence, snap-off is recognized as a mechanical process. 

Nevertheless, it is important to point out that a lamella cannot be created directly at a pore-throat. Rather, a lens forms first with lamella creation occurring upon expansion into the adjacent pore-body, provided surfactant is available (see the discussion of foam-generation mechanisms). During two-phase flow without stabilizing surfactant present, lenses are still created by snap-off in Roof sites (54, 60) followed by expansion and rapid coalescence in the downstream pore-body, once the lens thins to a film. If stabilized lamellae are pictured to rupture before exiting the immediate downstream pore-body, they are not much longer lived than unstable lenses. Such processes are accounted for in measurements of continuum relative permeabilities. 

A porous medium shapes foam to its own liking as confined, porefilling bubbles and lamellae. Foam in porous media is not a continuous fluid. The three mechanisms of foam generation (snap-off, division, and leave-behind) are all pore geometry specific. Snap-off is a mechanical process that occurs in multiphase flow without surfactant. For successful gas-bubble snap-off, the pore-body to pore-throat constriction ratio must be sufficiently large (roughly 2) and gently sloped. Otherwise stable wet-... 

---