Capillary pressure maximum

The stability of pseudoemulsion film was studied directly in our laboratory, by forming such a film from a surfactant solution (0.06 M sodium dodecyl sulfate) on the tip of a capillary (Figure 33). The tip of the capillary, which was filled with antifoam oil, was covered with a small pseudoemulsion film from the surfactant solution. Then, the oil was slowly pushed out of the capillaiy. In this way, the area of the pseudoemulsion film and the capillary pressure was increased. The pseudoemulsion film between silicone oil containing no particles and air was relatively stable, and it did not rupture before the capillary pressure maximum, (i.e., hemispherical shape). However, when the oil contained hydrophobic silica particles, the film was much less stable. At high particle concentrations (1—6 wt%), the film ruptured shortly after it was formed, (i.e., at very low capillary pressures). 

With the progressive removal of the liquid, the curve at first rises almost vertically but subsequently tapers off to acquire a gradual slope. The intersection of the tangents extended from the steep and the flat portions of the curve occurs at about S = 0.9. At this saturation, the capillary pressure is known as entry suction Pe, and the pellet strength attains its maximum (R5). 

Fig. 4.8). At maximum pressure, the radius of the bubble is equal to the radius of the capillary rK on further increasing the pressure the difference decreases, and the gas bubble is released from the capillary. This maximum pressure pmax can be measured and correlates to the surface tension ydyn via the modified LAPLACE-equa-tion ...

Fig. 4.8 Schematic illustration of the working principle of the dynamic bubble pressure method. If the bubble radius equals the capillary radius, maximum pressure is detected. The pressure minimum occurs on bubble detachment.

When suction is generated within the sampling system, water is sucked inwards through the pores of the sampler until a corresponding capillary pressure occurs in the pores. If the capillary pressure in the sampler is lower than that in the soil, water flows from the soil into the sampler until the capillary pressure in the sampler and in the soil are equal. The maximum capillary pressure in a pore can be calculated by the following equation (Schubert, 1982) ... 

Fig. 2.4 presents a measuring cell with a porous plate made of sintered glass (similar to variant C, Fig. 2.2). Porous plates of various pore radii can be used (usually the smallest radius is about 0.5 p.m) [23]. In this case the meniscus penetrates into the pores and their radius determines the radius of curvature, i.e. the small pore size allows to increase the capillary pressure until the gas phase can enter in them. The radius of the hole in which the film is formed is usually 0.025 - 0.2 cm. To provide a horizontal position of the film the whole plate is made very thin. In the porous plate measuring cell (Fig. 2.4) the capillary pressure can be varied to more than 10s Pa, depending on the pores size and the surface tension of the solution. When the maximum pore radius is 0.5 (tm, the capillary pressure is 3- 10s Pa at a - 70 mN/m.

A block-scheme of the apparatus for the study of foam films under applied pressure is shown in Fig. 2.11. The films are formed in the porous plate of the measuring cell (Fig. 2.4, variant D and E). The hydrodynamic resistance in the porous plate is sufficiently small and the maximum capillary pressure which can be applied to the film is determined by the pore material. The porous plate measuring cell (Fig. 2.4, variants D and E) permits to increase the capillary pressure up to 105 Pa, depending on the pore size and the surface tension of the solution. When the maximum pore size is 0.5 pm, the capillary pressure is 310s Pa (at cr = 70 mN/m). The cell is placed in a thermostating device, mounted on the microscopic table. 

The maximum capillary pressure p max in a 1.5 cm layer of a NaDoS foam, calculated from Eq. (6.41) using the value of the maximum expansion ratio, is 13 kPa. It is slightly lower than the maximum pressure obtained earlier for a foam at the moment of its destruction, studied with the porous plate cells [84],... 

The first results about foam electrokinetics have been reported by Sharovamikov [62,63]. An electroosmotic liquid transport is observed in foams from solutions of ionic surfactants (NaDoS, CTAB, PO-3A, etc.) and it is larger than in systems with solid capillaries (specific transport from 1.6-1 O 6 to 210 6 m3 C 1). The maximum electroosmotic pressure depends on the initial pressure in borders and reaches 1 Pa. The addition of dedecanol to the NaDoS solution sharply decreases the electroosmotic transport but increases the electroosmotic pressure. To reduce the influence of border and film non-homogeneity that originates in a static foam under gravity, the electrokinetic studies have been performed in an advancing foam [62]. The specific electroosmotic transport depends on the capillary pressure and reaches a maximum value at pg = 0.5 kPa. The streaming potential (up to 10 mV)... 

Larger values of the accumulation ratio can be reached in dry foams [24,25,47,73,74,76-78]. Kruglyakov and Kuznetsova [47,71] have studied the effect of capillary pressure, foam expansion ratio and dispersity on / mjn. The foam was prepared from NaDoBS and NP20 solutions. The accumulation ratio //m,n increased directly proportional to the expansion ratio (at a = const) and inversely proportional to the parameter a (at n = const) (Fig. 10.4). The maximum degree of accumulation in a NaDoBS solution (0.3 g dm 3 + 0.4 mol dm 3 NaCl) which could be achieved was = 1050 at Ap = 102 kPa. Further increase in... 

Once a discontinuous nonwetting phase is formed, the capillary forces opposing ganglia motion must be overcome, or the ganglia will be trapped. The maximum capillary pressure rise exhibited by ganglia of any length in a porous medium can be estimated in terms of throat radius r. and body radius... 

In laboratory experiments and field applications the gas is delivered to the rock face either as continuous gas or as a course gas-liquid dispersion. In both cases, for the gas to move into the porous medium, the gas pressure at the rock face must be higher than the capillary entry pressure. For a gas finger or a bubble train to advance through the porous medium, the face pressure must be maintained at a level above the maximum capillary pressure that the gas finger or bubble train will experience along its path through the medium. 

In the method of the Jailing meniscus a liquid-wetted tapering tube is placed vertically in a reservoir, as in fig. 1.26. Inside the tube liquid is held by the capillary pressure. The tube is now moved upwards - or the liquid in the vessel downwards - to increase the hydrostatic pressure head, and this is continued until the liquid in the capillary collapses. From the hydrostatic head the Laplace pressure is obtained and from that the surface tension. The method is very simple and may be considered as the counterpart of the maximum bubble pressure technique there are also similarities to the situation sketched in fig. 1.8a. The idea is rather old... 

If the wavelength of the ultrasound exceeds 8 mm, the maximum volume of a liquid drop is no longer dictated by the above-described ratio but by that between hydrostatic pressure and the capillary pressure due to surface tension inside the drop. If this ratio, which is referred to as the Bond number of the levitated drop, exceeds 1.5, the drop disintegrates. Therefore, the maximum volume of a drop is a function of the surface tension and specific density of the liquid. For example, the maximum volume of a water drop is 155 pi for most organic solvents, it is about 40 pi [111]. 

Under the assumption that the capillary pressure gradient across the carrier rock-barrier rock interface is the only significant resistant force affecting hydrocarbon accumulation in a conventional hydrostatic trap, i.e. the influence of the hydrodynamic condition in the barrier rock on its sealing capacity can be considered to be negligible, the maximum height of the hydrocarbon column below the barrier rock can be given by Equation 4.22... 

Under hydrostatic conditions, the hydrocarbons will become trapped in the reservoir rock when buoyancy-induced lateral upward hydrocarbon migration in the carrier-reservoir rock is stopped by a capillary pressure boimdary. Hydrostatic trapping positions include structural traps, stratigraphic traps and combination traps. The maximum height of a hydrocarbon column that can be contained in a hydrostatic trap is determined by the sealing capacity and geometry of the rocks, or rocks and faults, that form the trap. 

Laboratory measurements of capillary entry pressures are commonly performed on Hg-air systems. To calculate maximum hydrocarbon column heights, mercury-air capillary pressure data must first be converted to hydrocarbon-water pressures, using the following equation (Watts, 1987) ... 

Equation (6.39) is only valid when the wetting front in the substrate is smooth, which depends on the (pore) homogeneity of the substrate. Tiller and Tsai [52] showed that there is an optimum pore size of the substrate which produces the maximum pressure drop across the cake. This is shown by Eqn. (6.37). A smaller pore size gives a larger capillary pressure AP,but also a smaller substrate permeability Ki. As a consequence, local differences in growth kinetics may arise, which limit the minimum layer thickness and are a source of defects. 

Note that the difference in pressure through the thickness of the body, giving rise to the stress, is usually much smaller than the value of the capillary pressure Pc at the critical point but there is a relation between them. The greater the capillary pressure, and the lower the permeability, the greater is the stress at the critical point. The maximum stress at the critical point approaches Pr when the evaporation rate is very high and cracking is most likely at the end of the CRP and the beginning of the FRPl. 

The maximum capillary pressure is obtained when 9 = 0 and Ap is proportional to Y y> which means that a high y v i required. Thus, to achieve wetting of the internal surface a compromise is needed since the contact angle only goes down as Xlv goes down. Hence, there is a need to make 9 as close as possible to 0 while not having a too- low liquid surface tension. 

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