Porous media Relative permeability

It is now possible to explain the origin of a critical capillary pressure for the existence of foam in a porous medium. For strongly water-wet permeable media, the aqueous phase is everywhere contiguous via liquid films and channels (see Figure 1). Hence, the local capillary pressure exerted at the Plateau borders of the foam lamellae is approximately equal to the mean capillary pressure of the medium. Consider now a relatively dry medium for which the corresponding capillary pressure in a... 

These tests show that CC -foam is not equally effective in all porous media, and that the relative reduction of mobility caused by foam is much greater in the higher permeability rock. It seems that in more permeable sections of a heterogeneous rock, C02-foam acts like a more viscous liquid than it does in the less permeable sections. Also, we presume that the reduction of relative mobility is caused by an increased population of lamellae in the porous medium. The exact mechanism of the foam flow cannot be discussed further at this point due to the limitation of the current experimental set-up. Although the quantitative exploration of this effect cannot be considered complete on the basis of these tests alone, they are sufficient to raise two important, practical points. One is the hope that by this mechanism, displacement in heterogeneous rocks can be rendered even more uniform than could be expected by the decrease in mobility ratio alone. The second point is that because the effect is very non-linear, the magnitude of the ratio of relative mobility in different rocks cannot be expected to remain the same at all conditions. Further experiments of this type are therefore especially important in order to define the numerical bounds of the effect. 

Here the relative permeability, kri, is the fraction by which the fluid conductivity of the porous medium has to be modified to account for the presence of the other fluid. For a given fluid, kri increases with concentration, but is always less than or equal to one. Since the porous medium will usually have a wetting preference for one fluid over others, there will be a distribution of fluids among the different sizes of pores. Some of the factors that can influence the relative permeability of a particular fluid include [108,417-419] ... 

Gas mobility depends on the permeability of the porous medium. In the presence of foam gas mobility is the mobility of the continuous gas phase through the free channels and the mobility of the confined gas along with the liquid. Formally the relative permeability of each phase (liquid or gas) can be expressed by Darcy s equation. 

Fig. 10.18. Effect of gas fractional flow on relative gas mobility (A) porous medium - 0.6 cm glass beads L = 60 cm permeability - 270 pm2 porosity - 0.36 surfactant - 1% Siponate DS-10.

For the tortuous and irregular capillaries of porous media, it has been reported theoretically and experimentally that a minimum in the permeability of adsorbates at low pressures is not expected to appear. In our study of n-hexane in activated carbon, however, a minimum was consistently observed for n-hexane at a relative pressure of about 0.03, while benzene and CCI4 show a monotonically increasing behavior of the permeability versus pressure. Such an observation suggests that the existence of the minimum depends on the properties of permeating vapors as well as the porous medium. In this paper a permeation model is presented to describe the minimum with an introduction of a collision-reflection factor. Surface diffusion permeability is found to increase sharply at very low pressure, then decrease modestly with an increase in pressure. As a result, the appearance of a minimum in permeability was found to be controlled by the interplay between Knudsen diffusion and surface diffusion for each adsorbate at low pressures. 

The symbols Ko/K, Kg/K, and K /K are used to represent the relative permeabilities to oil, gas, and water, respectively. Obviously, relative permeability values range between 0 and 1. It has been found that, for a given porous medium, the relative permeability is a junction of saturation. Consider a system in which both oil and gas... 

A comprehensive review of the important factors that affect the flow of emulsions in porous media is presented with particular emphasis on petroleum emulsions. The nature, characteristics, and properties of porous media are discussed. Darcy s law for the flow of a single fluid through a homogeneous porous medium is introduced and then extended for multiphase flow. The concepts of relative permeability and wettability and their influence on fluid flow are discussed. The flow of oil-in-water (OfW) and water-in-oil (W/O) emulsions in porous media and the mechanisms involved are presented. The effects of emulsion characteristics, porous medium characteristics, and the flow velocity are examined. Finally, the mathematical models of emulsion flow in porous media are also reviewed. 

Relative Permeability. A comparison of equation 7 with equation 1 also shows that for the two-phase system we have used fc, the effective permeability for the fluid, in place of the absolute permeability k, which is a property of the porous medium alone. This effective permeability term, depends on the absolute permeability, the type of fluid involved, and the saturation of this fluid. 

The term in equation 9 is called relative permeability of the fluid i. It represents the fraction by which the fluid conductivity of the porous medium must be modified to account for the presence of the other fluid. The presence of the other fluid implies that some of the flow paths would not be available to this fluid, thus the term k in equation 9 must always be less than, or at most equal to, 1. Furthermore, when more of the fluid i is present in the medium, it will occupy more of the available channels, and hence its effective permeability will be higher. Therefore, the relative permeability term is expected to increase with increasing saturation of this fluid. 

A porous medium in general will have flow channels of many different sizes consequently, the relative permeability of a given fluid will depend not only on what fraction of the available pore space it occupies but also on what types of flow channels it occupies. If the fluid occupies smaller channels, its relative permeability will be smaller. Therefore, the distribution of the fluids is an important factor in determining relative permeability. 

To develop an understanding of the emulsion flow in porous media, it is useful to consider differences and similarities between the flow of an OAV emulsion and simultaneous flow of oil and water in a porous medium. As discussed in the preceding section, in simultaneous flow of oil and water, both fluid phases are likely to occupy continuous, and to a large extent, separate networks of flow channels. Assuming the porous medium to be water-wet, the oil phase becomes discontinuous only at the residual saturation of oil, where the oil ceases to flow. Even at its residual saturation, the oil may remain continuous on a scale much larger than pores. In the flow of an OAV emulsion, the oil exists as tiny dispersed droplets that are comparable in size to pore sizes. Therefore, the oil and water are much more likely to occupy the same flow channels. Consequently, at the same water saturation the relative permeabilities to water and oil are likely to be quite different in emulsion flow. In normal flow of oil and water, oil droplets or ganglia become trapped in the porous medium by the process of snap-off of oil filament at pore throats (8). In the flow of an OAV emulsion, an oil droplet is likely to become trapped by the mechanism of straining capture at a pore throat smaller than the drop. 

Wettability. Wettability of the porous medium controls the flow, location, and distribution of fluids inside a reservoir (7, 28). It directly affects capillary pressure, relative permeability, secondary and tertiary recovery performances, irreducible water saturations, residual oil saturations, and other properties. 

In the original Buckley-Leverett theory, gravitational, compressibility and capillarity are ignored. Devereux (36) presents the solution for the case of constant pressure, and the constant-velocity case was derived by Soo and Radke 12). The model requires a knowledge of the capillary retarding force per unit volume of the porous medium, and the relative permeabilities of the oil droplets in the emulsion and the continuous water phase. These relative permeabilities are assumed to be functions of the oil saturation in the porous medium. These must be determined before the model can be used. 

The formation and displacement of the oil bank depends upon the nature of the phases formed in the porous medium and their relative permeabilities, which may also change as a result of changes in wettability. Detailed discussion of these factors is beyond the scope of this chapter Chapter 6 and references 37 and 38 address this topic. 

Gas relative permeability, Pk, is defined as the permeability of a fluid through a porous medium partially blocked by a second fluid, normalized by the permeability when the pore space is free of this second fluid. This property diminishes at the percolation threshold , at which a significant portion of the pores are still conducting but they do not form a continuous path along the flow direction. It is obvious that only the network model, can provide a satisfactory analysis of the percolation threshold problem. Nicholson et al. [3] introduced a simple network model, and applied it on gas relative permeability [4]. For the gas relative permeability, an explicit approximate analytical relation between the relative permeability and the two network parameters, namely z and the first four moments of, f(r), has been developed, based on the Effective Medium Approximation (EMA) [5]. If a porous... 

Clearly, the relative permeability of the trapped foam is zero. However, knowledge of the fraction of foam trapped in the porous medium is needed to complete the flow model. In general, the fraction of foam... 

Equations 40.6 and 40.7 must be consistent with Darcy s law (Equation 40.5) when one single-fluid phase occupies the porous medium. Consequently, the relative permeability functions fulflll the following conditions ... 

FIGURE 1 Typical water-oil relative permeability curves for a porous medium. 

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