# Wettability and Capillary pressure

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Wettability and Capillary pressure
In this module you will learn about Wettability and Capillary pressure Press the button to start

Topic overview Capillary Pressure 1 Introduction 2 Interfacial Tension
6 Laboratory Measurments of capillar pressure 3 Rock Wettability 5 Capillary pressure 4 The contact angle and interfacial tension Øvre farge små bokser: 202,250,250 sigle 202,202,250 Neder farge små bokser: 0,255,255 Main circle: Gradegring Daggry, diagonalt oppover The water rises higher in a small pipe The water rises higher in a small pipe

Section 1: Introduction
In a petroleum reservoir, the porous rock is generally saturated with several fluids, e.g., gas, oil, and water. Molecular forces induce a complex system of mutual static interactions between the fluids and the pore walls. The fluid molecules have different attractions to each other and the rock material, and they may be ordered in a sequence according to the strength of the attractions, implying water-wet, oil-wet and gas-wet material. The mutual attraction forces between the three fluids and the rock leads to the surface tension acting between fluids and the solid. Capillary pressure is the pressure difference across a curved fluid interface between two fluid phases. If the fluids are enclosed in a pore channel, a contact angle is defined where the curved fluid interface meets the wall. The contact angle is an expression for the balancing of attraction forces between the fluids and the wall of the pore channel. Gas distribution This is the distribution of Water, Oil and Gas. As you can see from the other figures,water has an residual saturation throughout the whole column, and the oilzone has an residual saturation in the gas zone. Oil distribution Water distribution Click the image to see a bigger version Formation rock

More about fluid distribution in reservoir
The Free Water Level The column to the right shows the composite, actual saturation distribution with height. There is a water-oil contact, a gas-oil contact and a vertical consentration grading of the three fluids. This vertical saturation distribution is determined by the capillary pressure curve. There is a well-defined height, The Free Water Level, where the capillary pressure is zero between oil and water. The Free Water Level Back

Section 2: Interfacial Tension
The interfacial tension between two fluids is a measure of how much energy is needed to enlarge the surface by one unit area. That is, the dimension is J/m2, or N/m. If a droplet of oil is deformed in water by external forces, the surface area is increased, and energy is stored as potential energy which is released again if the external forces are removed. Depending upon the relative magnitude of the intra, and inter fluid cohesive forces ( intermolecular) attractions, the interfacial tension may have different "signs". A "positive" interfacial tension (  > 0) means that the molecules of each fluid are most strongly attracted to the molecules of their own kind. Whereby the two fluids are immiscible, and their contact surface is minimized A ”neutral” interfacial tension ( = 0) means that the molecules of each fluid are attracted equally to the molecules of their own kind as to those of the other kind, and the two fluids are ”truly” miscible. A ”negative” surface tension ( < 0) means that the molecules of one fluid are more strongly attracted to the molecules of the other fluid. This kind of miscibility is called dissolution, wich usually means a chemical reaction between the two fluids, leading to a stable new fluid. Alcohol i water is an example of dissolution. The natural petroleum reservoir belongs to the immiscible category. The following types of of interface between immiscible substances are relevant to resevoir engineering: Liquid-Gas (LG) Liquid-Liquid (LL) Solid-Liquid (SL) Solid-Gas (SG) Read more.... Topic link w3

Section 2: Interfacial tension
Because the cohesive force is stronger on the denser fluids side, there is a sharp change in the molecular pressure across the boundary. As a result, the boundary surface - much like the rubber surface of a baloon, is in a state of tangential tension. Called the interfacial tension denoted by (). The magnitude of the interfacial tension, represents the work or energy required to keep the two fluids apart in a pressure equilibrium state. The stronger the intermolecular attractions within a fluid phase, the greater the work needed to bring its molecules to the surface and the greater the interfacial tension. Typical values of the surface tension range from 10 to 80 mN/m The table shows some surface tensions of relevant liquids (Liquid-Water) (Liquid-Vapor) The molecules at the surface are more attracted to the intrafluid space, and to the neighbouring molecules. Because of these forces, the surface area are minimized, leading to a surface tension The first column shows the surface tension Between a liquid and its own vapor Go back to previous page...

Section 3: Rock Wettability
Wettability is a relative concept, expressing the tendency of one fluid to be preferred over the other fluid by the rock walls. If a water-wet rock sample containing mostly oil is submerged in a beaker of water, water will be sucked into the sample, expelling oil, to be seen at the water surface in the beaker. This effect is very important in evaluation of a waterflood. If a fractured reservoir is oil-wet, the injected water wil just be recyled throught the fractures at high pumping costs. The wettablility of a reservoir rock, can be estimated quantitativley by measuring the contact angle between the liquid-liquid, or liquid-gas interface and the solids surface. This angle called the wetting angle () reflects an equilibrium between the interfacial tension of the two fluid phases and their individual adhesive attraction to the solid. By convention the angle is measured on the denser fluid side. If the measured angle is less than 90, the denser fluid is the wetting phase. Opposite if  is greater than 90, the lighter fluid is considered the wetting phase The table shows some values of the wetting angle and interfacial tension for some typical pairs of fluids relevant to a reservoir engineer Topic link On the picture you can see a core plug, saturated with oil being immersed into water. Because the consolidated, sedimentary plug is water-wet, the water is attracted into the core and oil is expelled when the plug is immersed in the water. Since oil is lighter than water, oil droplets is seen on the water surface. If the plug had been oil-wet, nothing would have happened.

Section 4: The contact angle and interfacial tension
The water drop on the rock surface, submerged in oil, will find an equilibrium shape determined by the principle of minimum energy: The sum of the surface tensions (energies) of rock-water, rock-oil, water-oil has to be at a minimum. The tangent to the oil-water surface at the tripple-point defines the contact angle . The cosine of this angle is measure of the wettability. For 100% water-wet material,  = 0, for 100% Oil-wet material,  = 180, and for indifferent wettability  = 90. Standard symbol for interfacial tension is the greek letter sigma, . Read more...

Section 4: The contact angle and interfacial tension
For a reservoir system of two immiscible fluids such as oil and water, there are three types of interfacial tensions to be considered: The three interfacial tensions are not independent. In order to reveal their relationship a simle experiment can be performed on the droplet below. Pulling this droplet slightly out of equilibrium, we set up an equation expressing the change in energy due to the change in area: Here dA denotes an infinitesimal change in area. Since dAws = - dAos and dAow = dAws cos, we get the the Young-Dupre equation: Go back.. The Young-Dupre equation shows that the wetting angle reflects the equilibrium among the three interfacial tensions involved. This is a most usefull fact, when it comes to measure the capillary pressure Pulling the droplet a little "delta" out of its equilibrium position, and expressing the change in surface energies, gives the equilibrium equation above that leads to the Young-Dupre equation Topic link

Section 5: Capillar pressure
Capillary pressure is the pressure diffrence between to fluid phases, caused by the surface tensions. The Laplace equation shows the relationship between the curvature of the meniscus and the capillary pressure If the two radii are equal the equation can be reduced to As you can see here the contact angle determines the capillary pressure Click to Watch movie Have a look on a popular animation Topic link w3

Capillar pressure in reservoir
The animation will have a speed slow enough so you can read the text The Free Water Level Back

Water rise in a sugar lump
The movie shows a sugar lump immersed in coffe-water to illustrate the effect of surface tensions Click image to start movie Back

Section 6: Laboratory measurments of capillary pressure
Laboratory measurements of capillary pressure generally employ the principal relationship: With r taken to be the median or modal value of the rock´s pore-size distribution: however, fluids other than the reservoir fluids are normally used for shear convenience. For a particular porous medium and two diffrent pairs of fluids, the following general relationship is valid: Wich leads to the spesific relationship (for reservoir-lab): Instrument for measurement of capillary pressure in lab.

Developers Module made by Student Odd Egil Overskeid
Petroleum Technology Dept. Stavanger University College Norway Topic author and coordinator Professor Svein M. Skjæveland

References A.B.Zolotukhin and J.-R.Ursin
Education course in Reservoirtechnique 1

Helpful facts Capillary pressure is a phenomenon occuring in ALL porous systems, when two phases are present. You will encounter in the litterature that sometimes the pressure difference between to phases are referred to as “molecular” pressure difference, or in the case of a droplet wetting a surface, just “pressure difference”. And in the case of a capillary pipe: Capillar pressure. They all talk about the same thing: Capillary pressure. In more serious texts, the author usually defines capillary pressure as a general reference to the pressure leap between to phases when their interphase is curved. The surface forces between a liquid and a solid is usually referred to as adhesion forces. And the forces between to fluids as surface tensions The interphase forces acting on a dual fluid system in an porous rock are ALL surface tensions. So we are again talking about the same thing: tensions due to energy difference between the phases. Of course the solid can not "bend" but it´s still surface tension.