However, by providing a capillary pressure correlation, we are able to extract relative permeabilities and to show good consistency between rock property. It is crucial to express the relationship between capillary pressure and relative permeability and saturation to obtain typical capillary pressure. The difference in pressure () is called capillary pressure. is interfacial tension between the two fluids and and are principle radii of curvature.
For connected pathways of oil and water then both indices can be greater than zero. Capillary pressure diagram used to characterize wettability.
This index is based on the ratio of the two areas representing forced imbibition in Figure 2: The range is from for a completely water-wet material to for a completely oil-wet material. In general this index is not used very much. In this work, the wettability of the tested samples was not determined. Most common aquifer materials such as quartz, carbonates, and sulfates are strongly water-wet and since the tested samples are quartz and carbonates materials, it was therefore assumed that they are water-wet.
When two immiscible fluids are in contact in the interstices of a porous medium, a discontinuity in pressure exists across the interface separating them.
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The difference in pressure is called capillary pressure. The capillary pressure is dependent on the interfacial tension, pore size, and wetting angle. Capillary pressure curves directly determine the irreducible water saturation, residual oil saturation, and rock wettability and can be used to determine water oil contact point and approximate oil recovery. Figure 2 is a capillary pressure diagram showing how it can be used to characterize wettability and the capillary pressure is the difference in pressure as exemplified by Figure 3 where the porous medium can be described by a capillary tube where a clear interface exists between the immiscible fluids.
Water flood performance is also significantly affected by the capillary pressure of the rock [ 9 ].
Relative permeability and capillary pressure -
Fluid interface in a tapered capillary tube. By definition, the capillary pressure is the nonwetting fluid pressure minus the wetting fluid pressure: The capillary pressure can be calculated by the Laplace equation: The capillary pressure equation can be expressed in terms of the surface and interfacial tension by where is interfacial tension between the two fluids and and are principle radii of curvature and is the contact angle. Capillary pressure data are not only important for obtaining reservoir rock properties such as pore size distribution, permeability, and water saturation profile within the oil reservoir but also provide important information for water flooding designs and reservoir simulation studies.
Capillary pressure is typically measured in the laboratory by mercury injection, porous plate, or centrifugation techniques.
- Comparison Between Capillary Pressure and Relative Permeability
- Relative permeability and capillary pressure
- Journal of Petroleum Engineering
The porous plate method PP has been used for years in acquiring reliable capillary pressure data representative of reservoir rock fluid properties.
In recent years, the method is also found to be reliable and subject to less experimental errors and analysis when used for electrical resistivity RI measurements as well. A major problem has been the long time scales required for achieving reliable data.Hydrostatic Pressure and Permeability
The mercury injection technique is fast and can reach very high capillary pressure but the test uses nonrepresentative fluid, mercury and it is destructive, whereas the centrifugation technique [ 10 ] uses reservoir fluids and decreases the equilibrium time by using high centrifugal forces. In this study, the porous plate method was used in acquiring the capillary pressure data of the tested samples.
The term relative permeability refers to the phase permeability relative to the absolute permeability: Several mathematical models have been proposed to infer relative permeability from capillary pressure data. InDerahman and Zahoor demonstrated a method of calculating the permeability using capillary pressure curves measured by mercury injection [ 7 ].
A tortuosity factor in the model was earlier introduced and the method was modified by representing capillary pressure curve as a power law function of the wetting phase saturation [ 11 — 13 ].
As mentioned previously, capillary pressure and relative permeability are both measured in the laboratory; however, it is time consuming and expensive to both in many cases. For the purpose of this study, the empirical Brooks-Corey-Burdine formulae [ 11 — 13 ] are used: Justification for This Study Several studies have been conducted on wettability reversal effects on oil recovery using different surfactants to deliberately improve oil recovery; however, the literature is sparse on wettability alteration that results from contact with the components of corrosion inhibitors or paints; the focus of this study.
Moreover, no study of such has been reported on the Niger Delta formations. Brief Literature Cited Sayari and Blunt [ 14 ] performed benchmark experiments on multiphase flow in which they investigated the effect of wettability on relative permeability, capillary pressure, electrical resistivity, and nuclear magnetic resonance NMR.
In that study, they compared the results obtained from a suite of experimental measurements on well characterized systems that studies relevant properties such as capillary pressure, relative permeability, NMR response, and resistivity index with numerical predictions using pore-scale modeling where the pore space was imaged with micro-CT scanning.
Relative Permeability From Capillary Pressure - OnePetro
Al-Garni and Al-Anazi [ 15 ] correlated the wettability, capillary pressure, and initial fluids saturation for Saudi Arabia crude oil. In their study, they correlated irreducible oil saturation and capillary pressures using rock centrifuge measurements for Berea rock Sandstone samples on Saudi crude oils during drainage and imbibition cycles by varying each time the wettability of the tested samples using different Saudi oils heavy, medium, and light.
He used the Hassler and Brunner equation at each radial position in the rock to calculate the capillary pressure, which together with saturation measured with MRI at each position directly produces a capillary pressure curve with as few as single centrifuge equilibrium [ 10 ].
The findings of that study were that cationic surfactant dodecylamine alters the wettability of glass slide surface while anionic surfactant; stearic acid alters the wettability of marble surface. They were able to correlate the proposed NMR wettability indices water index, oil index, or combined index with the traditional Amott-Harvey indices, suggesting that quantitative information about rock wettability can be gained from NMR measurements.
That new model was based on extension of Leverett scaling theory. Some writers use "absolute permeability" or "intrinsic permeability" in place of permeability. For multiple-phase flow, the following expressions define relative permeabilities, specifically written for oil and water flow without gravitational effects in the x direction: Relative permeabilities are dimensionless functions that usually range between 0 and 1.
The difference in pressure between the two phases is the capillary pressure: Capillary pressure is often defined as the pressure of the less-dense phase minus the pressure of the more-dense phase.
Effective permeability In some discussions, the products of permeability and relative permeability e. Effective permeability of oil at irreducible water saturation, or ko Swiis sometimes used to normalize relative permeabilities in place of absolute permeability.
With this normalization, kro Swi equals 1. It is possible for water relative permeability to exceed 1 when ko Swi is the normalizing factor. One must be very careful when using data to note whether absolute permeability or an effective permeability is used for normalizing.
The need for accurate measurement of capillary pressure and relative permeability functions increases with the resolution of reservoir models.
With low-resolution models, there is a need for algorithms to "upscale" permeabilities, relative permeabilities, and capillary pressures from the scale of measurement on a small sample of rock to the relatively huge size of blocks in reservoir models.