Pore constriction

Upon moving from the pore constriction (f=0) to the pore body (f = A/2), the lamella is stretched as it conforms to the wall. To achieve the requisite volume rearrangement a radial pressure differential is induced which thins the film but results in no net fluid efflux into the Plateau borders. The converse occurs when the film is squeezed upon moving from a pore body to a pore constriction. If R /R, or equivalently a, is large enough... 

Homogenous (multi) layers in the pores Plugs in the pores (constrictions) Plugs/layers on top of the pores... 

As Ca is increased further, drop size continues to decrease, falling below the diameter of the pore throats and eventually becoming small enough for several drops to pass through a single pore constriction concurrently. In this last situation the drops are also somewhat elongated in the direction of flow. 

This equation assumes a contact angle of zero, a good approximation for the glass micromodel used here where the oleic phase has been observed flowing through pore constrictions without forming contact lines. 

In the present paper, pore level descriptions of bubble and bubble train displacement in simple constricted geometries are used in developing mobility expressions for foam flow in porous media. Such expressions provide a basis for understanding many of the previous core flood observations and for evaluating the importance of foam texture and interfacial mobility. Inclusion of the effects of pore constrictions represents an extension of the earlier efforts of Hirasaki and Lawson (1). 

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. 

Once in the medium, bubbles can be displaced through pore constrictions only by the concerted action of long, continuous bubble trains. As illustrated in Figure 1(a), bubble 1 will not move through constriction E until the bubble train behind it catches up and pushes it through the constriction. The latter is possible since the pressure drop across the long continuous train is much larger than across the individual bubble. 

A somewhat different interpretation of such phenomena has been given recently by Falls et al. (14). These investigators use energy arguments to account for the work associated with moving lamellae into the constrictions along the bubble train path. Such an approach is attractive from a mechanistic standpoint however, it predicts that the capillary resistance increases with the length of the porous medium, which has not been observed experimentally. Obviously, more extensive analysis and experimentation are required before such pore constriction effects are fully understood and accurately represented. 

Although the current permeability model properly reflects many of the important features of foam displacement, the authors acknowledge its limitations in several respects. First, the open pore, constricted tube, network model is an oversimplification of true 3-D porous structures. Even though communication was allowed between adjacent pore channels, the dissipation associated with transverse motions was not considered. Further, the actual local displacement events are highly transient with the bubble trains moving in channels considerably more complex than those used here. Also, the foam texture has been taken as fixed the important effects of gas and liquid rates, displacement history, pore structure, and foam stability on in situ foam texture were not considered. Finally, the use of the permeability model for quantitative predictions would require the apriori specification of fc, the fraction of Da channels containing flowing foam, which at present is not possible. Obviously, such limitations and factors must be addressed in future studies if a more complete description of foam flow and displacement is to be realized. 

Ro radius, front pore constriction of bubble train... 

Complete pore blockage Intermediate pore blockage Cake filtration Pore constriction... 

When the pressure drop across the pore throat is larger than that predicted by equation 10, the oil droplet undergoes distortions to pass through the pore constriction. The droplets pass undistorted through those pore constrictions that have diameters larger than the droplet diameter. Thus, when the droplet diameter is much smaller than pore throat size (a microemulsion, for example), the rock sees the fluid as a homogeneous fluid. 

Soo and Radke (11) confirmed that the transient permeability reduction observed by McAuliffe (9) mainly arises from the retention of drops in pores, which they termed as straining capture of the oil droplets. They also observed that droplets smaller than pore throats were captured in crevices or pockets and sometimes on the surface of the porous medium. They concluded, on the basis of their experiments in sand packs and visual glass micromodel observations, that stable OAV emulsions do not flow in the porous medium as a continuum viscous liquid, nor do they flow by squeezing through pore constrictions, but rather by the capture of the oil droplets with subsequent permeability reduction. They used deep-bed filtration principles (i2, 13) to model this phenomenon, which is discussed in detail later in this chapter. 

Straining capture refers to the condition that results when a particle lodges in a pore throat of size smaller than its own. The rate of capture is directly proportional to the velocity. Re-entrainment of strained droplets occurs either by squeezing of droplets through pore constrictions due to locally high pressures or by breakup of the oil droplets. 

Filtration Model. A model based on deep-bed filtration principles was proposed by Soo and Radke (12), who suggested that the emulsion droplets are not only retarded, but they are also captured in the pore constrictions. These droplets are captured in the porous medium by two types of capture mechanisms straining and interception. These were discussed earlier and are shown schematically in Figure 22. Straining capture occurs when an emulsion droplet gets trapped in a pore constriction of size smaller than its own diameter. Emulsion droplets can also attach themselves onto the rock surface and pore walls due to van der Waals, electrical, gravitational, and hydrodynamic forces. This mode of capture is denoted as interception. Capture of emulsion droplets reduces the effective pore diameter, diverts flow to the larger pores, and thereby effectively reduces permeability. 

Yoshimura K, Batiza A, Kung C (2001) Chemically charging the pore constriction opens the mechanosensitive channel MscL. Biophys J 80 2198-2206... 

A schematic picture of different t5q)es of pores is given in Fig. 9.1 and of main types of pore shapes in Fig. 9.2. In single crystal zeolites the pore characteristics are an intrinsic property of the crystalline lattice [3] but in zeolite membranes other pore types also occur. As can be seen from Fig. 9.1, isolated pores and dead ends do not contribute to the permeation under steady conditions. With adsorbing gases, dead end pores can contribute however in transient measurements [1,2,3]. Dead ends do also contribute to the porosity as measured by adsorption techniques but do not contribute to the effective porosity in permeation. Pore shapes are channel-like or slit-shaped. Pore constrictions are important for flow resistance, especially when capillary condensation and surface diffusion phenomena occur in systems with a relatively large internal surface area. 

This hypothesis is supported by additional experimental data. Therefore, when sample SI300 (obtained at 1300°C) is mildly gasified up to 1% burn-off the benzene/cyclohexane ratio clearly decreases (142.6). Moreover, when the gasification is increased up to a medium burn- off (6%) the molecular sieve effect disappears (benzene/cyclohexane ratio, 0.93), and Vs for 2,2 DMB is far from the gas hold-up time and can be measured (0.75 cm /m ). This means that this treatment produced carbon removal which enlarged the pore constrictions. This fact is consistent with Vs values of linear hydrocarbons rising with increasing burn-off... 

The diffusion equations just used are simplifications of more complex processes. The F factor was empirically derived and must take into account those matrix pore geometric factors contributing to decreases in diffusion rates. Such factors may include pore tortuosity, dead-end pores, and pore constrictions. Initial modeling studies suggest that constrictions, in particular, have large effects in retarding release (8,9). 

Two notable approaches have been used to include the role of pore constrictions in the pressure gradient required to drive lamellae through porous media. Falls et al. (48) added a viscous resistance that accounted for pore constrictions and that acted in series with the straight-tube flow resistance of Hirasaki and Lawson (18). Prieditis (41) and Rossen (42—44, 46) computed the static curvature resistance to the movement of a single bubble and also trains of bubbles through a variety of constricted geometries. Rossen considered the role of bubble compressibility (43), asymmetric lamella shapes (44), and stationary lamellae (46) on foam mobilization. 

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