Capillary desaturation curve

Morrow and coworkers (Morrow and Songkran, 1981 Morrow et al., 1988) used the terms capillary number for mobilization and capillary number for prevention of entrapment for (Nc)c and (Nc)max, respectively. In UTCHEM, lower and higher critical capillary numbers are used for (Nc)c and (Nc)max, respectively. Table 7.8 summarizes some of the published experimental data for these critical capillary numbers. In principle, the critical capillary numbers should be system specific. Experiments should always be conducted to determine the capillary desaturation curves (CDC) for the particular application whenever possible. The summarized data could be useful only when no experimental data are available. From Table 7.8, the following observations can be made regarding capillary number ... 

TABLE 7.8 Summary of Experimental Work on Capillary Desaturation Curve ... 

Now we have discussed the two important capillary numbers critical and maximum. The general relationship between residual saturation of a nonaque-ous or aqueous phase and a local capillary number is called capillary desaturation curve (CDC). The residual saturations start to decrease at the critical capillary number as the capillary number increases, and cannot be decreased further at the maximum capillary number. As discussed earlier, the range of capillary numbers for residual phases to be mobilized is, for example, 10 to... 

In a simulation model, we need to input a capillary desaturation curve model. Stegemeier (1977) presented a theoretical equation to calculate CDC based on the capillary number originally proposed by Brownell and Katz (1947). This equation requires several petrophysical quantities. Thus, it would probably be even more difficult to calculate a CDC using the Stegemeier equation than to obtain a CDC in the laboratory. In the laboratory, if several points of residual saturation versus capillary number are measured, we can use those measured points to fit a theoretical model. In UTCHEM, a form of Eq. 7.121 is used ... 

FIGURE 7.36 Example of normalized capillary desaturation curve. 

The grid blocks used are 100 x 1 x 1, which is a ID model, and the length is 0.75 ft. Some of the reservoir and fluid properties and some of the surfactant data are listed in Table 8.1. The viscosity of polymer solutions at different concentrations is presented in Figure 8.5. The polymer adsorption data are shown in Figure 8.6. The microemulsion viscosity is shown in Figure 8.7, and the capillary desaturation curves are shown in Figure 8.8. 

Figure 2. Schematic capillary desaturation curve for a nonwetting phase.

Where surfactant is introduced to the reservoir via some carrying fluid, the relevant capillary pressure curves are from imbibition, both spontaneous and forced. Porous plate/membrane desaturation [26], flow or centrifuge effluent production [27, 28] and direct measurement of saturation in the porous media [29] are capable of measuring the complete imbibition curve. When used with reservoir-like fluids, the results from these methods reflect the wettability state of the porous rock. When surfactant is introduced, these methods should also be able to see the impact of wettability alteration. Two of these methods, the porous plate/membrane and the direct measurement of saturation methods require no modeling to be accurate for laboratory use. 

The capillary number, is related to the residual oil saturation through the desaturation curve illustrated by Figure 2. Nc is defined as the ratio between the viscous and local capillary forces and can be calculated from ... 

Nc)max mean at critical capillary number and maximum desaturation capillary number (Nc) is capillary number and Tp is the parameter used to fit the laboratory measurements. The definition of capillary number used in the preceding equation must be the same as that used in the simulation model. One example of CDC using Eq. 7.121 is shown by the curves in Figure 7.35, and some of the CDC parameters are presented in Table 7.9. The data points in Figures 7.35 and 7.36 are calculated using Eq. 7.124, to be discussed later. 

The thermo-hydrological calculations have indicated that it is possible to choose appropriate hydrological parameters in order to obtain a distribution of saturation similar to the one prevailing in the in situ test. Intrinsic permeability was taken from the fractures and retention curve was taken from the matrix. Relative permeability for gas and for liquid had to be modified. None of the functions valid for the matrix or the fracture were appropriate. The problem in fact, is that relative permeabilities are controlled by degree of saturation in the fracture and this model used a global degree of saturation. Therefore, relative permeability functions should undergo variations near full saturation because the fractures desaturate for low capillary pressures compared to the matrix. 

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