Leverett J-function

The Leverett J-function is used in reservoir engineering (22) to relate the permeability k, porosity < >, and wetting characteristics to water saturation S... 

The values of the effective permeabilities vary over orders of magnitude, and this corresponds to the different results of the models. Furthermore, as discussed in various papers,the effective permeability of Natarajan and Nguyen (curve e) varies significantly over a very small pressure range, although they state that their capillary-pressure equation mimics data well. With respect to the various equations, the models that use the Leverett J-function all have a similar shape except for that of Berning and Djilali (curve a), who used a linear variation in the permeability with respect to the saturation. The differences in the other curves are due mainly to different values of porosity and saturated permeability. As mentioned above, only the models of Weber and Newman (curve d) and Nam and Kaviany (curve f) have hydrophobic pores, which is why they increase for positive capillary pressures. For the case of Weber and Newman, the curve has a stepped shape due to the integration of both a hydrophilic and a hydrophobic pore-size distribution. 

Here J denotes the Leverett J function, and is the porosity.) Khatib and co-workers used Equation 9 in their demonstration of the dependence of coalescence and gas mobility on the limiting capillary number (41). 

The message from Figure 8 is that static lamellae are stable to small disturbances until a critical capillary pressure is attained then coalescence is catastrophic. In porous media, the liquid saturation, absolute permeability, and surface tension control this critical capillary pressure through the Leverett J-function (75). Of course, static lamellae may coalesce at lower capillary pressures, if they are subjected to large disturbances. Figure 8 also reveals that static lamellae in equilibrium with the imposed capillary pressure are amazingly thin. 

Next, by assuming that the Leverett J function is applicable and that Krf and Krg can be given as functions of s only, Eq. 9.137 can be written in terms of the saturation only. Udell [90] uses the pc correlation given in Table 9.9 and the relative permeabilities suggested by Wyllie [93] as given in Table 9.10. By using these, Eq. 9.137 becomes... 

Thus, we have two linear equations in the unknowns k/((), a useful lithology indicator related to the well-known Leverett J-function, and the viscosity P2. This simple 2x2 system can be solved using elementary algebra. If the porosity of the formation were known from a separate logging measurement, or from late-time-invasion based porosity extrapolation, then these equations would yield solutions for formation permeability and hydrocarbon viscosity. 

Since, in general, lower permeability media exhibit higher capillary-pressure suction, we argue that it is more difficult to stabilize foam when the permeability is low. Indeed the concept of a critical capillary pressure for foam longevity can be translated into a critical permeability through use of the universal Leverett capillary-pressure J-function (.13) and, by way of example, the constant-charge model in Equation 2 for II ... 

In addition to these equations, one can set up a constitutive relationship between Pg and Pl (Pg Pl = Pc, capillary pressure) by means of the so-called Leverett s J function ... 

Modified Leverett Function Appropriate for Fuel Cell Media The standard Leverett function has been found to be appropriate for qualitative matching of the flow characteristics through the media however, actual measurements of PEFC diffusion media show different quantitative behavior. Kumbur et al. [47] presented a modified Leverett function appropriate for thin-film fuel cell DM to estimate the capillary pressure as a function of liquid saturation and hydrophobic additive content This empirical fit was derived from the direct measurement of capillary pressure-saturation for different types of DMs (cloth and paper) with PTFE content ranging from 0 to 20% of weight and a nnicrop-orous layer. Figure 5.35 depicts the measured capillary pressure (Pc) versus nonwetting liquid saturation for carbon paper DM tailored with 20% PTFE content. The nature of the capillary pressure-saturation curves exhibits a continuous S shape, rather than J shape, and yields four inflection points. For saturation leads under 0.5, the capillary pressure in the DM was fit to a modified Leverett function, appropriate for the hydrophobic pores ... 

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