Capillary pressure critical

Comparison of the proposed dynamic stability theory for the critical capillary pressure shows acceptable agreement to experimental data on 100-/im permeability sandpacks at reservoir rates and with a commercial a-olefin sulfonate surfactant. The importance of the conjoining/disjoining pressure isotherm and its implications on surfactant formulation (i.e., chemical structure, concentration, and physical properties) is discussed in terms of the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory of classic colloid science. 

These observations are consistent with the concept of a critical capillary pressure for foam to exist in porous media. 

It is now possible to explain the origin of a critical capillary pressure for the existence of foam in a porous medium. For strongly water-wet permeable media, the aqueous phase is everywhere contiguous via liquid films and channels (see Figure 1). Hence, the local capillary pressure exerted at the Plateau borders of the foam lamellae is approximately equal to the mean capillary pressure of the medium. Consider now a relatively dry medium for which the corresponding capillary pressure in a... 

Since, in general, lower permeability media exhibit higher capillary-pressure suction, we argue that it is more difficult to stabilize foam when the permeability is low. Indeed the concept of a critical capillary pressure for foam longevity can be translated into a critical permeability through use of the universal Leverett capillary-pressure J-function (.13) and, by way of example, the constant-charge model in Equation 2 for II ... 

Figure 7 reports calculations of the effect of flow velocity on the critical capillary pressure for the constant-charge electrostatic model and for different initial film thicknesses. 

For Ca < 0.1 in Figure 7 the critical capillary pressure is also independent of the initial film thickness. In this case, the hydrodynamic resistance to fluid filling or draining is small enough that the film reaches the periodic steady state in less than half a pore length. Figure 7 confirms the trend observed by Khatib, Hirasaki and Falls that P falls with increasing flow rate (5). c... 

Figure 7. The effect of gas velocity on the critical capillary pressure.

Figure 9 reports the effect of the pore-body to pore-throat radius ratio, R /R, on the critical capillary pressure for... 

Figure 10 reports as dark circles the critical-capillary-pressure measurements of Khatib, Hirasaki and Falls (5) for foam stabilized by an a-olefin sulfonate of 16 to 18 carbon number... 

For transporting foam, the critical capillary pressure is reduced as lamellae thin under the influence of both capillary suction and stretching by the pore walls. For a given gas superficial velocity, foam cannot exist if the capillary pressure and the pore-body to pore-throat radii ratio exceed a critical value. The dynamic foam stability theory introduced here proves to be in good agreement with direct measurements of the critical capillary pressure in high permeability sandpacks. 

Direct measurements in the porous plate reveal that the capillary pressures are established very quickly (r = 1 min), regardless of the value of the pressure drop. However, the capillary pressure measured at the proximity of the porous plate differs from the equilibrium value. Therefore, if the destruction starts next to the porous plate, it is hardly possible to determine the equilibrium critical capillary pressure with the technique used. 

The concept of the critical capillary pressure considered in Sections 6.5.2. and 6.5.3. has been used in [86-88] for the explanation of the behaviour of a foam flowing through porous media. 

EOR process requires a detail study not only of foam behaviour in porous media but also of the options to control it. Foam flow in porous media during EOR is a complex, multifaceted process. A number of papers are dedicated to that topic, including some reviews [e.g. 13,14,18] which describe the experimental set-up used in the study of foams in porous media. We will focus on those illustrating the efficiency of EOR from oil pools and the role of some important factors, involving the effect of foam properties, especially of the critical capillary pressure. 

The concept of the limiting capillary pressure of foam collapse in porous medium has been introduced by Khatib, Hirasaki and Fall [174] and are based on studies of Kristov, Exerowa and Kruglyakov on the critical capillary pressure in static foams [12,179-182] (see Chapters 6 and 7). 

A third, related limit on the capillary pressure is created by the existence of an upper critical capillary pressure above which the life times of thin films become exceedingly short. Values of this critical capillary number were measured by Khistov and co-workers for single films and bulk foams (72). The importance of this phenomenon for dispersions in porous media was confirmed by Khatib and colleagues (41). Figure 5 shows the latter authors plot of the capillary pressures required for capillary entry by the nonwetting fluid and for lamella stability versus permeability of the porous medium. 

Fig. 6 Schematic of nonwetting phase invasion into a pore (A) schematic representation of a pore formed by four grains (B) low capillary pressure (C) critical capillary pressure for invasion (D) phase distributions after Haines jump (E) high capillary pressure (F) disconnection of the nonwetting phase after snap-off.

In a foam-laden porous medium, the capillary pressure of an equivalent undispersed two-phase system that corresponds to is termed here the critical capillary pressure for rupture. For bulk systems, is a well-documented parameter that controls the stability of the foam (77). As shown in Figure 8, even a very dilute SDS surfactant solution exhibits a critical capillary pressure for rupture greater than 100 kPa (i.e., greater than 1 atm) and creates highly robust foam films. However, not all surfactant-stabilized foam films display an inner branch. In this case, the critical capillary pressure for rupture equals IImax. 

The message from Figure 8 is that static lamellae are stable to small disturbances until a critical capillary pressure is attained then coalescence is catastrophic. In porous media, the liquid saturation, absolute permeability, and surface tension control this critical capillary pressure through the Leverett J-function (75). Of course, static lamellae may coalesce at lower capillary pressures, if they are subjected to large disturbances. Figure 8 also reveals that static lamellae in equilibrium with the imposed capillary pressure are amazingly thin. 

Only when the water saturation exceeds the critical water saturation will foam be allowed to form. In the critical capillary pressure regime the gas relative permeability is reduced exponentially with the slope Si in the critical pressure gradient region, the gas relative permeability is reduced by a factor of u Ugof Fo- This simple model was applied successfully to... 

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