Capillary pressure increment

In this study, a mercury intrusion experiment was performed with a constant injection rate by regulating the intrusion pressure [58]. This is different from the conventional mercury intrusion experiment where the intrusion pressure is initially kept constant to record the mercury intrusion volume, then incremented to record the resultant incremental intrusion. In our experiment, the injection rate was kept extremely low so that the pressure loss due to flow was negligible compared with the capillary pressure. The data from this constant-rate mercury intrusion (CRMI) method, also called APEX [58], was collected through the pressure fluctuations as a function of intrusion volume, shown in Figure 3.7.4. 

It is assumed that, at any relative pressure, P/Po, between 0 and 1, all pores with radii larger than some value r contain an adsorbed layer of thickness t on their walls, while all pores smaller than r are filled, owing to the joint effects of multilayer adsorption and capillary condensation. It is also assumed initially that pores are cylindrical in shape with one end closed, but it can be shown that such a drastic assumption is unnecessary. Although the working equation is derived on the basis of positive pressure increments, it is not the intention to imply that the equation must be applied only to the adsorption branch of the isotherm. 

We present now the extension of the constitutive equation (7) to partially saturated porous media. The material is assumed to be saturated by a liquid phase (noted by index w) and a gas mixture (noted by index g ). The gas mixture is a perfect mixture of dry air (noted by index da) and vapour (noted by index va). Based on most experimental data of unsaturated rocks and soils (Fredlund and Rahardjo 1993), and on the theoretical background of micromechanical analysis (Chateau and Dormieux 1998), the poroelastic behaviour of unsaturated material should be non-linear and depends on the water saturation degree. We consider here the particular case of spherical pores which are dried or wetted under a capillary pressure equal to the superficial tension on the air-solid interface. By adapting the macroscopic non-linear poroelastic model proposed by Coussy al. (1998) to unsaturated damaged porous media, the incremental constitutive equations in isothermal conditions are expressed as follows ... 

Mechanistic interpretations The results of the dynamic and equilibrium displacement experiments are used to evaluate and further define mechanisms by which alkaline floods increase the displacement and recovery of acidic oil in secondary mode and the tertiary mode floods. The data sets used in the mechanistic interpretations of alkaline floods are (a) overall and incremental recovery efficiencies from dynamic and equilibrium displacement experiments, (b) production and effluent concentration profiles from dynamic displacement experiments, (c) capillary pressure as a function of saturation curves and conditions of wettability from equilibrium displacement experiments, (d) interfacial tension reduction and contact angle alteration after contact of aqueous alkali with acidic oil and, (e) emulsion type, stability, size and mode of formation. These data sets are used to interpret the results of the partially scaled dynamic experiments in terms of two-stage phase alteration mechanisms of emulsification followed by entrapment, entrainment, degrees and states of wettability alteration or coalescence. 

WTien historical data are unavailable it is recommended that a capillary pressure curve is measured. The experiment is readily performed in the laboratory and greatly improves the accuracy of later calculations. The necessary equipment is shown in Figure 4.4 and principally comprises a filter at the bottom of a cylindrical funnel (a useful size is about 45 cm long by 10 cm in diameter and the filter cloth should be the same as that intended for use on the actual filter). The funnel is filled with a known volume of suspension at a known solids concentration and is filtered to form a saturated cake. The cake depth and volume of drained filtrate are recorded. A complete capillary pressure curve is obtained by successively incrementing the pressure gradient across the cake and inferring corresponding decrements in the... 

Bridging configurations with these stable orientations of the particles in foam films are now created as another ensemble and subjected to incremental changes in an applied capillary pressure, expressed as an increased curvature of the film surfaces. At each increase in the capillary pressure, the overall surface energy is minimized and the film searched for any points where the opposite sides are touching, indicating film rupture. This procedure therefore makes no allowance for disjoining forces in the film. 

Simulations of drainage in the Finney pack were conducted with the algorithms described above for the different levels of W connectivity. The simulations began with the pore space occupied entirely by W phase and were carried out to irreducible W phase saturation that is, the capillary pressure was increased in increments until no fiirther movement of the meniscus was possible. When W is assumed to be completely connected, the meniscus moves indefinitely at grain contacts with no gap between the spheres, but the area and volume of the pendular rings at these contacts quickly become negligible. 

Capillary Flow Rheometry Next we examine the experimentally obtained results with the capillary flow rheometer shown in Fig. 3.1, which are directly relevant to polymer processing flows, since the attainable shear rate values are in the range encountered in polymer processing. The required pressure drop AP does not increase linearly with increases in the volumetric flow rate Q, as is the case with Newtonian fluids. Rather, increasingly smaller increments of AP are needed for the same increases in Q. The Newtonian Poiseuille equation, relating flow rate to pressure drop in a tube, is linear and given by... 

Microporous membranes will fill their pores with wetting fluids by imbibing that fluid in accordance with the laws of capillary rise. The retained fluid can be forced from the filter pores by air pressure applied from the upstream side. The pressure is increased gradually in increments. At a certain pressure level, liquid will be forced first from the set of largest pores, in keeping with the inverse relationship of the applied air pressure P and the diameter of the pore, d, described in the bubble point equation ... 

Existing ceramic, mesoporous membranes (with a 4 nm pore diameter) perform most gas separations according to Knudsen diffusion. The obtainable separation factors (Section 9.3.2.) are usually not economical for most gas separations and provide incremental but limited conversion enhancement in catalytic membrane reactor applications. Capillary condensation and preceding surface flow yield economically interesting separation factors but this mechanism is limited to easily condensable gases and is limited to rather low pressure drops due to stability problems (Sections 9.2.3. and 9.3.3.). 

The increase of the bulk pressure at a small increment after achievement of the equihbrium density distribution allows obtaining the adsorption branch of the isotherm. If the pore is wide enough, the capillary condensation will occur, with the pressure of the condensation being corresponded to the vapor-like spinodal point. Similarly, desorption branch of the isotherm will be obtained at the decrease of pressure. In this case, the capillary evaporation will occur at a hquid-like spinodal point. The equilibrium transition pressure is obtained by comparing the grand thermodynamic potentials corresponding to the adsorption and the desorption branches of the isotherm. It corresponds to the equality of these values of the grand thermodynamic potential. 

Equation (18.9) expresses the fundamental result that the pressure inside a phase which has a convex surface is greater than that outside. The difference in pressure in passing across a curved surface is the physical reason for capillary rise and capillary depression, which we consider in the next section. Note that in the case of a bubble the increment in pressure in moving from the outside to the inside is 4y/R, or twice the value given by Eq. (18.9), because two convex interfaces are traversed. 

With regard to interstitial mechanisms, increments of pulmonary arterial pressure with increased cardiac output may aggravate capillary leaks, increasing interstitial edema. Inflammatory cells may accumulate in the interstitium, creating local toxicity as they degenerate. 

Figure 2.16 Typical nitrogen adsorption-desorption isotherms at 77K for (a) MCM-41 materials templated with alkyltrimethylammonium bromide surfactants with hydrophobic tails of different lengths as indicated (volumes adsorbed for C12, C14, C16 and C18 were incremented by 200, 400, 600 and 800 ml(STP) g, respectively) and (b) nonionic triblock copolymer templated SBA-15 silicas synthesised at different temperatures (volumes adsorbed for 353 K and 373 K were incremented by 200 and 400 ml(STP) respectively). The hysteresis loops observed in this case are typical of the larger mesopores in these materials. Desorption points are represented by closed symbols. Reprinted with permission from Morishige, K. Tateishi, M., Accurate relations between pore size and the pressure of capillary condensation and the evaporation of nitrogen in cylindrical pores, Langmuir, 22, 4165 169. Copyright (2006) American Chemical Society...

To determine the distribution of pores with diameters smaller than 20 nm, a nitrogen desorption technique is employed which utilizes the Kelvin equation to relate the pore radius to the ambient pressure. The porous material is exposed to high pressures of N2 such that P/Po 1 and the void space is assumed to be filled with condensed N2, then the pressure is lowered in increments to obtain a desorption isotherm. The vapor pressure of a liquid in a capillary depends on the radius of curvature, but in pores larger than 20 nm in diameter the radius of curvature has little effect on the vapor pressure however, this is of little importance because this region is overlapped by the Hg penetration method. 

Vacuum is carefully applied to remove physically adsorbed gases. Degassing times vary decoding on the sample and can be greatly reduced if the samples are oven dried before testing. Triple distilled mercury is slowly introduced until it completely covers the sample and fills the sample chamber any excess is drained off. Air is introduced to raise the pressure to O.S psia from which point the analysis begins. The pressure is raised manually or automatically in steps of about 1 psia to atmospheric pressure. As the pressure on the filled penetrometer is increased, mercury intrudes into tlK sample container and recedes in the capillary. After each increment the pressure is monitored, and may be maintained by the addition of additional pressure until the system... 

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