Capillary Pressure Curves

Fig. 6. Typical capillary pressure curves in air displacement cake dewatering of a fine coal suspension at varying dewatering times from top curve down the...

The relaxation time for each pore will still be expressed by Eq. (3.6.3) where each pore has a different surface/volume ratio. Calibration to estimate the surface relaxivity is more challenging because now a measurement is needed for a rock sample with a distribution of pore sizes or a distribution of surface/volume ratios. The mercury-air or water-air capillary pressure curve is usually used as an estimator of the cumulative pore size distribution. Assuming that all pores have the same surface relaxivity and ratio of pore body/pore throat radius, the surface relaxivity is estimated by overlaying the normalized cumulative relaxation time distribution on the capillary pressure curve [18, 25], An example of this process is illustrated in Figure 3.6.5. The relationship between the capillary pressure curve and the relaxation time distribution with the pore radii, assuming cylindrical pores is expressed by Eq. (3.6.5). 

Although the capillary pressure curve cannot be predicted from the fundamental properties of the particulate bed, a crude estimate of the entry suction for wetting liquids is given by (N2)... 

These problems can be avoided by measuring capillary pressure curves of GDMs directly with water as the working fluid. A number of techniques have been recently proposed. Of the different types of GDM (carbon paper, carbon cloth, metal foam/mesh, etc.), only carbon paper GDMS have been studied to any appreciable extent using these methods. An ideal capillary pressure measurement technique must be able to vary water saturation in directions of increasing saturation from Sw = 0 to Sw -> 1 and decreasing saturation from Sw = 1 to Sw -> 0. This requires the application... 

The method of standard porosimetry (MSP)41-43 was one of the first approaches used to obtain air-water capillary pressure curves for GDMs.16 In this test, a GDM sample is initially saturated with water and contacted with a water-saturated porous disc, which is a standard with known Pc(Sw) behavior. The capillary pressure of the sample-standard system is varied by allowing the liquid to evaporate from the standard and sample while in contact. If the two media can be assumed to be in capillary equilibrium, their capillary pressures are equal. Saturation is determined by measuring the weights of the sample and standard periodically. The capillary pressure of the system is found by reference to the known capillary pressure curve of the standard. This method is limited to scanning... 

Figure 2. Comparison of air-water capillary pressure curves available in the literature for Toray TGP-H-090 or similar material without PTFE coating (a) and with PTFE coating (b). Triangles indicate direction of saturation change.

Figure 4. Left Schematic of pressure profile reported by Fairweather et al40 Right Capillary pressure curve obtained from pressure profile showing pressure decay at constant saturation. Dotted line shows envelope of peak pressures corresponding to pressure-controlled injection2 53,54 while dashed fine shows envelope of decayed pressures corresponding to the data of Fairweather et al4,3...

Figure 6. Air-water capillary pressure curves for treated Toray TGP-H-120 (10 wt%) showing internal withdrawal scanning loops obtained using the method...

The effect of GDM thickness on the capillary pressure curves has also been investigated.21 A pronounced shoulder was observed at low capillary pressures in the curves obtained for very thin samples. This feature was diminished for thicker samples and virtually non-existent in the capillary pressure curves obtained from multilayer stacks. The dependence of this feature on the sample surface area-to-volume ratio is a clear demonstration of finite-size effects.70... 

The capillary pressure response, a direct manifestation of the underlying pore morphology, can be evaluated from the two-phase LB drainage simulation and the corresponding transport relation as function of liquid water saturation can be devised as shown in Fig. 20 for the reconstructed CL micro structure.21 The overall shape of the capillary pressure curve agrees well with those reported in the literature for synthetic porous medium.55 The capillary... 

Wettability Index (W), (based on the U.S. Bureau of Mines wettability test), in which the forced (pressure) imbibition of water is compared to forced imbibition of oil via capillary pressure curves. The wettability index varies from -oo for complete oil-wetting, to zero for neutral, to +°° for complete water-wetting. For practical purposes, W usually varies between about -1.5 and +1.0. 

Yu, L. Wardlaw, N.C. Quantitative Determination of Pore Structure from Mercury Capillary Pressure Curves in Interfacial Phenomena in Petroleum Recovery, Morrow, N.R. (Ed.), Dekker New York, 1991, pp. 101-156. 

P.G., Toledo, L.E., Scriven, H.T., Davis, 1994. Pore-space statistics and capillary pressure curves from volume-controlled, ed. Society of Petroleum Engineers, pp. 61-65. 

Fig. 4. Capillary pressure curves for two fault rocks. The data emphasise that while a single entry pressure does describe the properties of material with a simple pore structure, e.g., (a), the complex mixing of grain and pore sizes in the cataclastic shown in (b) generates a more complex pressure curve where a single characteristic entry pressure is more difficult to define, i.e., reflects more of a membrane behaviour.

Several analytical equations have been proposed to describe capillary pressure-saturation relationships in porous media, and Fig. 4 presents one of the equations commonly used, the van Genuchten model.The water release curve shown is based on the data presented by Schroth et al. for 20/30 and 40/50 silica sand. The saturation-capillary pressure curve can be viewed as a cumulative distribution of pore sizes. 

Because mercury is nonwetting, mercury porosimetry is used to obtain capillary pressure curves during injection (see section on Immiscible Displacement ). This technique allows estimates of pore-size distribution to be made. 

Despite the suddenness of these pore-scale events, the displacement process appears smooth at the macroscopic scale As the capillary pressure is increased, the nonwetting phase flows into increasingly smaller pore spaces, and is thereby reduced. The macroscopic functionality (capillary pressure vs. saturation) is the capillary pressure curve mentioned previously. Fig. 7 is an example capillary pressure curve obtained by injecting mercury into a dry packing of glass... 

Fig. 7 Capillary pressure curve for mercury (nonwetting phase) intrusion into a packing of glass spheres. (From...

Paw Two auxiliary equations complete the system of equations S, + Saw = L and Pnw = Pw + Pc(Sw)-The capillary pressure functionality in the second equation is obtained from the macroscopic capillary pressure curve. The equations also contain relative permeabilities that require explicit evaluation. 

Dullien, F.A.L. Zarcone, C. Macdonald, I.F. Collins, A. Bochard, R.D.E. The effects of surface roughness on the capillary-pressure curves and the heights of capillary rise in glass bead packs. J. Colloid Interf. Sci. 1989, 127, 362. 

Figure 64(a) shows schematically the maximally transferable tensile stress as a function of the liquid saturation The capillary pressure curve (Figure 64b) is used to calculate (Jtc = LPc for lc l The capillary state ends when liquid bridges between the particles start to form (t/ L lc)- The funicular state exists in the region J Lb / l / lc Tor the pendular state (i/ Ldiscussed equation (45) is valid. 

Zhou, D., and E.H. Stenby. 1993. Interpretation of capillary pressure curves using invasion percolation theory. Transp. Por. Media 11 17-31. 

Figure 4. Typical capillary pressure curves for a porous medium.

Wettability Index A measure of wettability based on the U.S. Bureau of Mines wettability test in which the wettability index (W) is determined as the logarithm of the ratio of areas under the capillary pressure curves for both increasing and decreasing saturation of the wetting phase. Complete oil-wetting occurs for W = —oo (in practice about —1.5), and complete water-wetting occurs for W = oo (in practice about 1.0). Another wettability index is derived from the Amott-Harvey test. See also reference 8, Amott Test, Wettability. 

Pittman, E. D. 1992. Relationship of porosity and permeability to various parameters derived from mercury injection-capillary pressure curves for sandstone. American Association of Petroleum Geologists Memoir, 76(2), 191-198. 

This test has been modeled with RockFlow/ RockMech in ID to check the chosen hydraulic parameters for the modeling of the FEBEX in situ experiment. The capillary pressure curve has been set as shown in Figure 3. Relative permeability for gas has been developed from the experimental results shown in Figure 4. Relative permeability for water has been assembled from the dependency on saturation and swelling pressure and an additional factor c. 

To compute a capillary pressure curve, Spolek and Plumb (1981) have developed the geometrical model of the tracheid shape proposed by Comstock (1970). Although it may be simplistic to assume that all tra-cheids have exactly the same shape, they obtained a good trend for the capillary pressnre fnnction by this means. 

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