Relative permeability ratio

A useful way of expressing relative permeability data as a function of saturation is by means of the relative permeability ratio. The gas-oil relative permeability ratio is defined as... 

Fig. 100. Typical gas-oil relative permeability ratio versus saturation curve for a system containing oil and gas only.

Step s. The value of So computed in step 2 determines the relative permeability ratio at that saturation. Using this value of Kg/Kg compute the producing gas-oil ratio using equation 20... 

At this oil saturation the relative permeability ratio is zero, as shown in Figure 101. Consequently, the producing gas-oil ratio is given by... 

Calculate the gas-oil relative permeability ratio and the oil saturation. Ansvier Kg/Ko = 0.0567. 

Relative permeability ratio, 168 Reservoir saturation equation, 160 ff. Retrograde phenomena, 60 ff., 75... 

This equation shows that the fraction is a function of the relative permeability ratio, k /kio- It increases as the ratio is increased. We would be interested to know how the ratio changes as the IFT is decreased or the capillary number is increased. 

The ratio of the permeability of any material to the permeability of free space is termed the relative permeability (p ). 

FIG. 13 Reduction of the relative permeability coefficient is dependent on the clay platelet aspect ratio in the system of polyimide-clay hybrid with water vapor as the permeate. Each hybrid contains 2 wt% clay. The aspect ratios for hectorite, saponite, montmorillonite, and synthetic mica are 46, 165, 218, and 1230, respectively. (From Ref. 71.)... 

Key mechanisms important for improved oil mobilization by microbial formulations have been identified, including wettability alteration, emulsification, oil solubilization, alteration in interfacial forces, lowering of mobility ratio, and permeability modification. Aggregation of the bacteria at the oil-water-rock interface may produce localized high concentrations of metabolic chemical products that result in oil mobilization. A decrease in relative permeability to water and an increase in relative permeability to oil was usually observed in microbial-flooded cores, causing an apparent curve shift toward a more water-wet condition. Cores preflushed with sodium bicarbonate showed increased oil-recovery efficiency [355]. 

Relative permeability and capillary pressure functions, collectively called multiphase flow functions, are required to describe the flow of two or more fluid phases through permeable media. These functions primarily depend on fluid saturation, although they also depend on the direction of saturation change, and in the case of relative permeabilities, the capillary number (or ratio of capillary forces to viscous forces). Dynamic experiments are used to determine these properties [32]. 

Relative permeability is the reduction of mobility between more than one fluid flowing through a porous media, and is the ratio of the effective permeability of a fluid at a fixed saturation to the intrinsic permeability. Relative permeability varies from zero to 1 and can be represented as a function of saturation (Figure 5.8). Neither water nor oil is effectively mobile until the ST is in the range of 20 to 30% or 5 to 10%, respectively, and, even then, the relative permeability of the lesser component is approximately 2%. Oil accumulation below this range is for all practical purposes immobile (and thus not recoverable). Where the curves cross (i.e., at an Sm of 56% and 1 - Sm of 44%), the relative permeability is the same for both fluids. With increasing saturation, water flows more easily relative to oil. As 1 - SI0 approaches 10%, the oil becomes immobile, allowing only water to flow. 

Relative permeability is defined as the ratio between the permeability for a phase at a given saturation level to the total (or single-phase) permeability of the studied material. This parameter is important when the two-phase flow inside a diffusion layer is investigated. Darcy s law (Equation 4.4) can be extended to two-phase flow in porous media [213] ... 

Productive wells in vapour-dominated systems discharge steam only. Characteristically, wells in liquid-dominated systems discharge a mixture of water and steam. The steam forms essentially by depressurization boiling of the reservoir water. It is, however, not uncommon that some wells drilled into liquid-dominated systems discharge dry steam or possess a higher steam to water ratio than can be accounted for by depressurization boiling. The reason for this is partial or complete immobilization of the water in the aquifer due to the effects of capillary pressure and relative permeability. 

Once steady state is achieved, the flux of each phase is calculated. Steady state is considered attained when the saturation and flow rates of both phases do not change any more. The corresponding absolute flux is calculated by modifying the two-phase LB model, where a body force is applied to one phase and the density of the other phase is rendered zero at all locations. Finally, the ratio of flux of each phase from the two-phase calculation to the one obtained from the singlephase calculation gives the relative permeability related to the saturation level. 

The dimensionless partition coefficient K = cp/cl = Sr, also known as a relative solubility coefficient, is defined as the ratio of the concentration of a substance in the polymer cP to that in the liquid (food) cLat equilibrium. While D is practically independent of the liquid phase in contact with the polymer in these measurements, the K values are determined by the nature of the polymer and liquid contact phases. From the definition Sr = K, a relative peremeability coefficient can be calculated, Pr = Sr D, with the dimension D. Here, accordingly to Eq. (9-2) and the solubility constant in the polymer and in the liquid phases expressed as SP = cP/p and Sl = C Jp, respectively, the following relationship results between the absolute and relative permeability coefficients ... 

Basically, all of these closely related problems occur because gas-flood injection fluids have very small viscosities at the temperatures and pressures at which they are used. For example, the viscosity of CO2 at 13.8 MPa (2,000 psi) and 38°C (100°F) is about 0.066 cp, whereas the viscosities of reservoir oils are at least an order of magnitude greater (16). This produces a ratio of the mobility of the CO2 to the mobility of the oil that is much greater than one. (The mobility of a fluid is defined as its relative permeability divided by its viscosity for the definition of relative permeability, see equations below.)... 

Either the asphaltene precipitation or the multiple phase behavior of the process under "miscible" conditions appears to cause a certain extent of reduction of the mobility of the carbon dioxide, as compared to the mobility which would be calculated from the relative permeability of the carbon dioxide divided its viscosity (14-16). However, it is usually considered that this is not sufficient to resultinafavorable mobility ratio (a ratio of carbon dioxide mobility to crude oil mobility less than one). 

To measure the separation efficiency of a membrane reactor involving multiple reaction components, the extent of separation, briefly introduced in Chapter 7, was used to replace the more commonly used separation factor by Mohan and Govind [1988a]. This alternative index of separation performance is based on the flow quantities of the process streams involved while the separation factor is calculated from the compositions instead. The goals of a high conversion and a high separation sometimes contradict each other. The choice or, more often than not, compromise of the two goals depends, on one hand, on the downstream separation costs and, on the other, on the process parameters such as the ratio of the reactant permeation to reaction rate and the relative permeabilities of the reaction components. 

Table 4. Glassy polymer permeability ratios for H2 relative to CH4 and CO at 30 °C...

Note in particular that the ratio of the Ks as represented above is not the selectivity as would be defined by the permeability ratios—that is, by oii j = PilPj- Furthermore, the selectivity as used here is different from the concept of relative volatility, which is the ratio of the. Si-values, one to another. Furthermore, the ratio of the Si s so determined will be lower than would be suspected from the ratio of the permeabilities. The implication is that the ensuing permeability separations will be much less sharp than would be suspected from the permeability ratios or selectivities. 

Furthermore, the relatively larger the value of V", the more likely that the Si-ratio as designated above will approximate the permeability ratio. The relatively smaller the value of V" the more likely that the Si-ratio will approach unity. Last, however, the Si-ratio must be greater than unity for a separation to occur. 

This developed miscibility process results in a miscible fluid, that is capable of displacing all the oil which it contacts in the reservoir... The efficiency of this displacement is controlled by the mobility (ratio of relative permeability to viscosity) of each fluid. If the displacing fluid (i.e. carbon dioxide) is more mobile than that being displaced (i.e. crude oil) then the displacement will be relatively inefficient. Some of the residual oil saturation will never come into contact with carbon dioxide. Both laboratory and field tests have indicated, that even under favourable condition, injection of 0.15-0.6 10 m of carbon dioxide is required for recovery of an additional barrel (0.16 m ) of oil". Here our goal is to obtain a mass ratio of CO2 to incremental oil of 1 to 4, on the basis of the Bonder s data. 

Wang et al. tried to define a viscosity ratio as a criterion for the mobility control requirement. However, we have to point ont that the viscosity ratio J, / J,o required for the mobility control should depend on relative permeabilities and fluid saturations. 

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