A Critical Review and Future Trend on Relative Permeability Hysteresis - OnePetro
Capillary pressure and saturation relations for supercritical CO2 and brine in sand: measurements. Drainage and imbibition processes were measured on quartz sand with few investigations to date have directly measured these ba-. relationship between capillary pressure, relative perme-. ability and oil/water . to ﬁrst drainage and spontaneous imbibition capillary. pressure. Estimation of two-phase relative permeability relationships for organic liquid contaminants Publication Date: relative permeabilities, drainage and imbibition relative permeabilities were measured for several organic liquid-water systems.
Another important phenomenon associated with fluid flow through porous media is the concept of residual saturations. As when one immiscible fluid is displacing another, it is impossible to reduce the saturation of the displaced fluid to zero. At some small saturation, which is presumed to be the saturation at which the displaced phase ceases to be continuous, flow of the displaced phase will cease. This saturation is often referred to as the residual saturation.
This is an important concept as it determines the maximum recovery from the reservoir. Conversely, a fluid must develop a certain minimum saturation before the phase will begin to flow. The saturation at which a fluid will just begin to flow is called the critical saturation. Theoretically, the critical saturation and the residual saturation should be exactly equal for any fluid; however, often they are not identical.
Critical saturation is measured in the direction of increasing saturation, while irreducible saturation is measured in the direction of reducing saturation. Thus, the saturation histories of the two measurements are different. According to the figure, the non-wetting phase begins to flow at the relatively low saturation of the non-wetting phase.
Relative permeability -
The saturation of the oil at this point point A is called critical oil saturation Soc. This is the result of capillary pressure. The capillary pressure force the wetting phase to occupy the smallest pores at low saturation that have an ignorable contribution to the flow.
The following example uses capillary tubes and the HP equation to illustrate the effective reduction in permeability caused by introduction of second phase. Total flow rate through these capillary tubes because of applying a pressure difference could be calculated, using the HP equation: Now assume fluid number 2 with the same viscosity occupied the largest capillary tube, the same as the non-wetting phase occupied the largest pores at first. It is possible to express the conductive capacity when the two fluids are saturating the system to the conductive capacity when only one fluid saturates the system.
And the ratio of conductive capacities is: In this example the relative permeability values for the two fluids sum up to one. This behavior is not true in actual porous media.
Relative Permeability Curves | Fundamentals of Fluid Flow in Porous Media
In real porous medium, there is a minute film of wetting phase that wet the surface. If consider this film in this example, it would decrease the diameter of the larger tube available for fluid number 2 to flow, thus reduces the flow capacity for the second fluid, and yet the film itself would contribute no flow capacity to the wetting phase.
Thus the total fluid capacity of the tubes would be decreased. The structure of the porous material The wettabilities with respect to the various phases The previous saturation history of the phases The extent of the displacement process the number of pore volumes injected The endpoint saturation also can depend on IFTs when they are very low, and on the rate of displacement when it is very high.
Results reported by Chatzis et al. These results suggest two general conclusions: This wide range of wetting possibilities is an obstacle to interpreting or predicting the effect of wettability on endpoint saturations. Indeed, conflicting results for different porous media are likely. For example, Jadhunandan and Morrow  report that residual oil saturation displays a minimum value for mixed-wet media as wettability shifts from water-wet to oil-wet—counter to the results of Bethel and Calhoun,  who reported a maximum for media of uniform wettability.
Critical gas condensate saturation Interest in the mobility of condensates in retrograde gas reservoirs developed in the s, as it was observed that condensates could hamper gas production severely in some reservoirs, particularly those with low permeability. The trend of increasing critical condensate saturations with decreasing permeability, as summarized by Barnum et al.
The relationship of Fig. For example, in a gas reservoir, encroachment of the aquifer will lead to trapping of some portion of the gas. Several correlations and summaries for residual gas saturation are found in the literature: Katz and Lee  provide a summary of residual gas saturations in a graphical form that is useful for estimates. According to the model presented by Naar and Henderson  for multiphase flow through rock, the trapped or residual gas saturation is one-half of its initial saturation; this Naar-Henderson rule is the simplest correlation for residual gas.
Agarwal  correlated a large collection of residual gas saturations for consolidated and unconsolidated sandstones, for unconsolidated sands, and for limestones.
The ranges of parameters in the correlations are summarized in Table 2. The correlations may be erroneous outside of these ranges. Three of the Agarwal correlations are listed below: Permeability k is in millidarcies. Table 2 Land  suggested the following form for estimating trapped-gas saturation Sgr as a function of initial gas saturation Sgi: 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.
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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.
Relative Permeability Curves
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.
- Relative permeability
- Drainage imbibition relative permeability relationships dating
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.