Conventional core porosity and permeability data were used to determine FZI for Confidence levels in distribution of initial water saturation and residual oil. curves and predict the saturation-relative permeability curves with a degree of accuracy comparable to the van. Genuchten  relationships.  Vapor-water . Here one would expect the permeability to either fluid to be lower than that for the single fluid saturated with 80% oil, and there is an irreducible water saturation of 20% due to the water wet nature of this .. and using the relationship;.
Water-Wet Relative Permeability Curves Oil and Water A schematic of oil-water relative permeability curves in a water-wet reservoir is shown below. In water-wet rock, a water layer wets the rock surface and acts like a lubricant for the oil located in the central parts of the pores. Swc is the connate or irreducible water saturation. This is the water saturation below which water is not mobile because of capillary forces. The relative permeability of water at water saturations below Swc is zero.
Sorw is the residual oil saturation or critical oil saturation. This is the oil saturation below which the oil is immobile, that is, its relative permeability is zero.
Oil-Wet Relative Permeability Curves Oil and Water The figure below displays a schematic of water-oil relative permeability curves in an oil-wet reservoir rock. In oil-wet rock, oil wets the pore surfaces and water occupies the central regions of the pores. Typically, the irreducible water saturation in oil-wet reservoir rock is lower than that in water-wet rock.
Gas-Oil Relative Permeability Curves The schematic below displays a set of gas-oil relative permeability curves. In this case, the wetting phase, the oil phase, impedes the flow of gas. The water saturation in the reservoir rock is taken to not exceed its irreducible value. This means that the water is not mobile, but exists in the pore space and simply reduces the available pore space that the gas and oil can occupy.
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Sgc is the critical gas saturation. This is the minimum saturation for gas to become mobile. Sorg is the residual oil saturation to gas.
Residual oil relationships Residual oil saturations after waterflooding or gasflooding are clearly significant for oil recovery. Here, the dependence of residual oil saturation on initial oil saturation and capillary number for a waterflood will be considered. The relationship between initial and residual oil saturation is termed the oil-trapping relationship. For strongly water-wet rocks, the oil-trapping relationship should be identical to the gas-trapping relationship.
Indeed, because of this analogy and because it is easier to measure gas-trapping relationships, few oil-trapping relationships have been measured. A set of oil-trapping relationships reported by Pickell et al. Oil-trapping relationships are important for estimating reserves in transition zones.
In conventional reservoir engineering, residual oil saturation refers to the remaining oil saturation after a displacement that starts near the maximum initial oil saturation, which generally equals one minus the initial water saturation. This topic has received much more attention in the literature than oil-trapping functions. The capillary number is the ratio of viscous forces to capillary forces. It is represented quantitatively with various expressions, as summarized by Lake.
A popular definition of the capillary number is as follows: The capillary number is small less than 0. The example below shows just how small capillary numbers can be. As the capillary number for an oil-displacing process increases, residual oil saturation decreases in the manner sketched in Fig. Above the "critical capillary number," the rate of decrease of Sor is particularly rapid.
The critical capillary number is 10—5 to 10—4 for porous media with fairly uniform pore sizes. With increasing distribution of pore sizes, the critical capillary number decreases, the Sor at low Nc increases, and the domain for decreasing S or becomes broader. Extensive discussion of these relationships is available elsewhere. Example 1 Use the following quantities to estimate a capillary number for a waterflood with Eq.
Capillary forces do indeed dominate flow processes for waterfloods. Even in high-velocity regions, such as the vicinity of a well that is producing oil and water, the capillary number will remain very small. Residual water saturation Residual, or irreducible, water saturation Swi is the lowest water saturation that can be achieved by a displacement process, and it varies with the nature of the process—gas displacement or oil displacement.
Also, Swi varies with the extent of the displacement, as measured by pore volumes of oil or gas injected or by time allowed for drainage. To be more specific, the results of Chatzis et al.
Furthermore, Swi should increase slightly with increasing breadth of grain-size distribution. Significant variations in Swi should occur when small clusters of consolidated media of one grain size are surrounded by media of another grain size: If the grains of the clusters are smaller than those of the surrounding media, Swi increases. If the grains of the clusters are larger than those of the surrounding media, Swi decreases.
The saturation of water in an oil or gas reservoir at discovery is called the connate water saturation, or Swc. The connate water saturation and the irreducible water saturation can differ. If the reservoir processes that produced the connate water saturation can be replicated, then the Swi for the replicated processes should be the same as Swc.
Swc is significant for its connection to initial oil or gas saturation in a reservoir. Bulnes and Fitting  concluded that low-permeability limestone reservoirs are more viable than sandstone reservoirs of the same permeability because the connate water saturation is lower in the limestones than in the sandstones; as a result, the relative permeabilities to oil are higher in the limestones than in the sandstones.
Salathiel  observed that the connate water saturations in carefully retrieved rock samples from some oil reservoirs are substantially lower than can be achieved when the rock is waterflooded and then oilflooded. He attributed this effect to the mixed-wettability condition. When the reservoir was first invaded by oil, the rock was water-wet, and low water saturations were obtained. However, the wettability of the rock surfaces that were now in contact with oil changed from water-wet to oil-wet as portions of the hydrocarbons adsorbed onto the solid surfaces.
Relative permeability -
So, when such a rock is waterflooded and then oilflooded, the connate water saturation is not obtained because the water in the oil-wet portions of the rock becomes trapped.
Temperature The effects of temperature on relative permeability have been studied primarily for applications to steamflooding and in-situ combustion.
Mechanistically speaking, temperature can affect relative permeability by altering the IFT between flowing phases or by altering the wettability of the porous material. IFT between water and oil should decrease with increasing temperature, but to substantially influence relative permeability, the IFT would need to decrease to 0.
Such reductions would be possible only at very high temperatures with light oils. Therefore, temperature-related IFT reductions could influence relative permeabilities for in-situ combustion processes, but they would not be important for typical steamflooding.
The influence of temperature on wettability and, hence, on relative permeability is more likely to be important for most applications. With increasing temperature, the wettability could shift either to more water-wet or more oil-wet conditions, depending on the reservoir fluids and the chemical composition of the porous medium.
Some of the studies concluded that these relative permeabilities were unaffected by temperature changes, while other studies concluded the opposite.
In the light of the previous paragraph, these contradictory observations in the literature are not surprising. However, Akin et al. The changing stability of the displacement estimated with the expression of Peters and Flock  causes the apparent relative permeabilities to change with temperature.
Nevertheless, it is possible that relative permeabilities do change with temperature for some systems. As Akin et al.