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We will now focus on the salient features or characteristics of typical capillary pressure–saturation curves. First consider the capillary pressure data presented in Figure 8.7, measured by the diaphragm method for the air–water system. Figure 8.7 easily identifies the capillary pressure curve bound within two saturation end points, and corresponding to these two end points, there are capillary pressure end points.

These two end points are some of the most notable features or characteristics of the capillary pressure curves. In order to understand capillary pressure–saturation rela-tionships, the scales of saturation and capillary pressure are examined individually in the following sections.

An important aspect of capillary pressure curves is the noticeable difference between the imbibition and the drainage capillary pressure curves seen in Figure 8.5, based on Leverett’s work on sandpacks, and Figure 8.9, for a North Sea core plug sample. This particular difference in the imbibition and drainage capillary pres-sure curves is due to the phenomenon of capillary hysteresis, which is discussed in Section 8.7.3. Another important characteristic of the capillary pressure curves to be considered is their relationship with permeability. Even though a given rock permeability does not impart any specific or particular characteristic to the capillary pressure curves, it certainly influences the location of the capillary pressure–satura-tion curves when these data are plotted on a single graph for rock samples of differ-ent permeabilities (see Section 8.7.4).

8.7.1 SATURATION SCALE

The saturation scale in Figure 8.9 includes the mercury saturation, S_Hg, or the air saturation, which is (1 – S_Hg), beginning with 0% mercury saturation, or 100% air saturation, which can also be construed as 100% water saturation. This is because, in this case, the wetting phase (air) is being displaced by the nonwetting phase (mercury); that is, the drainage curve can also be carried out with an air–water pair, and the process is designed to mimic the upward migration of hydrocarbons in a reservoir rock. Tracing the saturation–capillary pressure path backward on the curve that begins with 100% water saturation in Figure 8.5 or Figure 8.7 (0% mercury or 100% air in Figure 8.9), a minimum or irreducible wetting-phase saturation, S_wi, is reached. The process starts with 0 capillary pressure, where the water- or wetting-phase saturation is 100% and the wetting-phase is continuous. Because the saturation of the wetting phase is reduced in the drainage process, the wetting phase becomes discon-nected from the bulk wetting phase. Eventually, all of the wetting phase remaining in the pore space becomes completely isolated, where its hydraulic conductivity is lost and it is termed irreducible wetting-phase saturation. The 100% water saturation

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basically represents the conditions that existed prior to the hydrocarbon migration, whereas finite minimum irreducible saturation represents the connate water that resulted from the migration of hydrocarbons in the reservoir rock after gravity and capillary forces equilibrated.

8.7.2 PRESSURE SCALE

Looking at the pressure scale at 100% water saturation in Figure 8.7, we find that a finite capillary pressure is necessary to force the nonwetting phase into capillaries filled with the wetting phase. In other words, a certain pressure must be reached in the nonwetting phase before it can penetrate the sample, displacing the wetting phase contained in it.⁹ This is a pressure that must be built up at the interface between the two phases before drainage of the wetting phase begins. The minimum pressure required to initiate the displacement, that is, the starting point of the capillary pres-sure curve, is known as the displacement or threshold prespres-sure, P_d, and is some-times also referred to as the pore entry pressure. The middle portion of the capillary pressure curve indicates the gradual increase in the capillary pressure, reducing the saturation of the wetting phase. The other end of the capillary pressure scale basi-cally indicates that, irrespective of the magnitude of the capillary pressure, water saturation or the wetting-phase saturation cannot be minimized further. At this end of the capillary pressure curve, all of the remaining wetting phase is discontinu-ous, resulting in the capillary pressure curve becoming almost vertical. Therefore, in summary, at conditions above the capillary pressure at S_wi, capillary forces are entirely dominant, whereas outside the capillary pressure at 100% wetting-phase saturation, the conditions are analogous to the complete dominance of gravity forces, and within these two P_c–S_w end points, both gravity and capillary forces can be con-sidered as being active.

8.7.3 CAPILLARYHYSTERESIS

The drainage process establishes the fluid saturations that are found when the res-ervoir is discovered. In addition to the drainage process, the other principal flow process of interest involves the reversal of the drainage process by displacing the nonwetting phase with the wetting phase, such as the imbibition of water in Leverett’s sandpacks (Figure 8.5) or the withdrawal of mercury (reduction in mercury satura-tion or increase in air saturasatura-tion) shown in Figure 8.9. The two capillary pressure–

saturation curves are not the same. This difference in the two curves is capillary hysteresis. Sometimes, the processes of saturating and desaturating a core are also called capillary hysteresis.¹⁷

Anderson⁷ identified contact angle hysteresis as one cause of capillary pressure hysteresis. In drainage, the wetting fluid is being pushed back from surfaces it pre-viously covered, resulting in a receding contact angle, whereas the opposite occurs during imbibition process as the wetting phase displaces the nonwetting phase, resulting in advancing contact angle. Another mechanism that has been proposed to explain or justify capillary hysteresis is called the ink-bottle effect,^8,17 discussed in Section 8.5. Bear⁹ terms this the geometrical hysteresis effect.

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The hysteresis phenomenon explains why a given capillary pressure corre-sponds to a higher saturation on the drainage curve than on the imbibition curve.

For example, in the case of data reported by Leverett on sandpacks, for a dimen-sionless factor value of 0.4, the difference between the drainage and imbibition saturation values is as high as 60%, whereas in the case of Figure 8.9, for a capillary pressure of 500 psi, the difference between the drainage and imbibi-tion mercury saturaimbibi-tion values is as high as 70%. The other way of looking at capillary hysteresis is to compare the drainage and imbibition capillary pressures for the same fluid saturation (iso-saturation); when, as seen in Figure 8.9, com-pared with a mercury saturation of 68%, it results in the drainage and imbibition capillary pressures of 770 and 380 psi, respectively. However, Bear⁹ states that in most fluid problems, capillary hysteresis is not a serious problem, because the flow regime, that is, drainage or imbibition, usually dictates which curves should be used.

8.7.4 CAPILLARY PRESSURE AND PERMEABILITY

Figure 8.10 shows the air–mercury capillary pressure data as a function of mer-cury saturation for five different core samples varying in absolute permeability in a range of k₁–k₅ mD. The data show decreases in permeability have corre-sponding increases in the capillary pressure at a constant value of mercury satu-ration. In other words, when iso-saturation data are compared, the sample having a permeability of k₁ mD has the lowest capillary pressure, whereas the one with permeability of k₅ mD has the highest capillary pressure. Although the general trend of capillary pressure–saturation curves remains unchanged, the magnitude of the capillary pressures does change when data are compared for samples of dif-ferent permeabilities. Therefore, the capillary pressure–saturation–permeability

0

FIGURE 8.10 Variation of capillary pressure with permeability (k₁>k₂>k₃>k₄>k₅).

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relationship is a reflection of the influence of pore sizes and grain sorting.

Smaller size pores and poorly sorted grains invariably have lower permeabilities and large capillary pressures.

8.8 CONVERTING LABORATORY CAPILLARY PRESSURE