The relationship of porosity, uncorrected air permeability, and various parameters derived from mercury injection-capillary pressure curves was established. Capillary Pressure Petrophysical Reservoir Model. .. ways: · To identify, with precision, the level of free water, even if the well has not penetrated this level. estimate permeability from porosity/water saturation relationships. It is crucial to express the relationship between capillary pressure and relative permeability and saturation to obtain typical capillary pressure.
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.
Al-Garni and Al-Anazi [ 15 ] correlated the wettability, capillary pressure, and initial fluids saturation for Saudi Arabia crude oil.
- Relative permeability and capillary pressure
- PEH:Relative Permeability and Capillary Pressure
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.
In their study, they modelled a dual network for dual porosity rocks which satisfactorily reproduced the capillary pressure curve, the porosity, and the permeability determined experimentally on a double porosity rock. They found that the contrast between primary and secondary pore space characteristics has a major effect on both the capillary pressure and the relative permeabilities. Li and Firoozabadi [ 20 ] showed that if the wettability of porous media can be altered from preferential liquid wetting to preferential gas-wetting, then gas well deliverability in gas condensate reservoirs can be increased.
Hui and Blunt [ 21 ] studied the effects of rock wettability on the flow of oil, water, and gas in hydrocarbon reservoirs.
They described the three-phase fluid configurations and displacement processes in a pore of polygonal cross section. Methodology The present work relies on laboratory experimental results obtained from routine and special core analysis. In conducting the routine core analysis, properties such as porosity, permeability, and the percentage saturation of the tested sample were determined, while only the capillary pressure data of the tested samples were determined during the special core analysis.
In this section, we describe the experimental procedures that were used in determining the above rock properties. Routine Core Analysis 4.
The testing procedure used in determining the grain volume and pore volume is as follows. Grain Volume Determination i The samples were dried and weighted after which they were loaded one after the other inside a diameter matrix cup.
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.
Relative permeability and capillary pressure -
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 following example shows just how small capillary numbers can be. 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.
Having defined the capillary number, the relationship between residual oil saturation and capillary number will be discussed next. 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. Residual Irreducible 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. The connate water saturation will also affect initial oil or gas relative permeability and, hence, the economic viability of 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.
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. The high-mobility phase is prone to bypass or "finger" through the low-mobility phase.
With "viscous fingering," the displacement must be 2D or 3D rather than 1D. One-dimensional displacements are preferred for measurement of relative permeabilities.
Relative Permeability Models Brooks-Corey and Related Models InCorey  combined predictions of a tube-bundle model with his empirical expression for capillary pressure to obtain expressions for gas and oil relative permeabilities.
These equations do not allow for nonzero critical gas saturation. The following "power-law" relationships are often used to describe oil, water, and gas relative permeabilities, respectively: The maximum relative permeabilities, kro max, krw,max, and krg,max, are between 0 and 1. These expressions are often referred to as modified Brooks-Corey relations, reflecting their similarity to the Brooks-Corey expression for oil relative permeability. They considered flow parallel and flow perpendicular to N laminations.
Journal of Petroleum Engineering
For flow perpendicular to laminations, The results of the averaging processes of upscaling are insensitive to the quality of measurements on small samples. The need for upscaling should diminish as increases in computer power permit higher-resolution models.
To obtain accurate measurements of capillary pressure and relative permeabilities, tests with representative samples at representative conditions are critical. Much of the available data in our industry do not pass this standard. Capillary end effects and viscous fingering have corrupted a significant portion of relative permeability data.
If capillary pressure and relative permeabilities are available, the extent of this corruption for a sample can be assessed and sometimes corrected. Such interpretations are particularly susceptible to error caused by the heterogeneity of the sample used for measurements. This susceptibility was conceded in the original literature on wettability interpretation, but it is not widely acknowledged.