Transcript E-Modul - University of Stavanger

In this module you will learn about
Wettability and
Capillary pressure
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Title page
Topic overview
1 Introduction
Topic overview
2 Interfacial tension
3 Rock Wettability
1 Introduction
4 The wetting angle and
interphase tension
Capillary
Pressure
5 Capillar pressure
2 Interfacial
Tension
6 Laboratory
Measurments
Of capillary
Pressure
6 Laboratory
Measurments
of capillar
pressure
3 Rock
Wettability
4 The contact angle
and interfacial
tension
water
The water rises higherThe
in a small
pipe
rises higher in a small pipe
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References
Helpful Facts
5 Capillary
pressure
Title page
Topic overview
1 Introduction
Section 1: Introduction
2 Interfacial tension
3 Rock Wettability
4 The wetting angle and
interphase tension
5 Capillar pressure
6 Laboratory
Measurments
Of capillary
Pressure
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
Oil distribution
Water distribution
Formation rock
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Click the image to see
a bigger version
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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.
Title page
Topic overview
More about fluid distribution in reservoir
1 Introduction
2 Interfacial tension
3 Rock Wettability
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
5 Capillar pressure
capillary pressure curve. There is a well-defined height, The Free Water Level, where
6 Laboratory
the capillary pressure is zero between oil and water.
Measurments
4 The wetting angle and
interphase tension
Of capillary
Pressure
The Free Water Level
The Free Water
Level
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References
Helpful Facts
Title page
Topic overview
1 Introduction
2 Interfacial tension
3 Rock Wettability
4 The wetting angle and
interphase tension
5 Capillar pressure
6 Laboratory
Measurments
Of capillary
Pressure
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.
Topic link w3
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....
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References
Helpful Facts
Title page
Topic overview
1 Introduction
2 Interfacial tension
3 Rock Wettability
4 The wetting angle and
interphase tension
5 Capillar pressure
6 Laboratory
Measurments
Of capillary
Pressure
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-Vapor)
(Liquid-Water)
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
Go back to previous page...
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The first column shows the surface tension
Between a liquid and its own vapor
Helpful Facts
Title page
Topic overview
1 Introduction
2 Interfacial tension
3 Rock Wettability
4 The wetting angle and
interphase tension
5 Capillar pressure
6 Laboratory
Measurments
Of capillary
Pressure
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.
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References
Helpful Facts
Title page
Topic overview
1 Introduction
2 Interfacial tension
3 Rock Wettability
4 The wetting angle and
interphase tension
5 Capillar pressure
6 Laboratory
Measurments
Of capillary
Pressure
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...
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References
Helpful Facts
Title page
Topic overview
1 Introduction
2 Interfacial tension
3 Rock Wettability
4 The wetting angle and
interphase tension
5 Capillar pressure
6 Laboratory
Measurments
Of capillary
Pressure
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:  os ,  ws ,  wo . 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:
 ws dAws  ( osdAos )   owdAow  0
Here dA denotes an infinitesimal change in area. Since dAws = - dAos and
dAow = dAws cos, we get the the Young-Dupre equation:
 os   ws
 cos
 ow
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
Developers
References
Helpful Facts
Title page
Topic overview
1 Introduction
2 Interfacial tension
3 Rock Wettability
4 The wetting angle and
interphase tension
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
1
1 
pc  po  pw   ow   
 R1 R2 
5 Capillar pressure
6 Laboratory
Measurments
Of capillary
Pressure
If the two radii are equal the equation can be reduced to
pc 
2 cos c
rc
As you can see here the contact angle determines the capillary pressure
Have a look on a
popular animation
Click to
Watch movie
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Topic link w3
References
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Capillar pressure
in reservoir
The animation will have a speed slow enough
so you can read the text
The Free Water Level
Back
Title page
Topic overview
Water rise in a sugar lump
1 Introduction
2 Interfacial tension
3 Rock Wettability
The movie shows a sugar lump immersed in coffe-water
to illustrate the effect of surface tensions
4 The wetting angle and
interphase tension
5 Capillar pressure
6 Laboratory
Measurments
Of capillary
Pressure
Click image to start movie
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References
Helpful Facts
Title page
Topic overview
1 Introduction
2 Interfacial tension
3 Rock Wettability
Section 6: Laboratory measurments of capillary pressure
Laboratory measurements of capillary pressure generally employ the principal
relationship:
pc 
4 The wetting angle and
interphase tension
5 Capillar pressure
6 Laboratory
Measurments
Of capillary
Pressure
 cos 
r
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:
pc1
pc2

cos 1 cos 2
Wich leads to the spesific relationship (for reservoir-lab):
pc,res  pc,lab
 cos res
cos lab
Instrument for measurement of
capillary pressure in lab.
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References
Helpful Facts
Title page
Topic overview
1 Introduction
2 Interfacial tension
3 Rock Wettability
4 The wetting angle and
interphase tension
5 Capillar pressure
6 Laboratory
Measurments
Of capillary
Pressure
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Module made by
Student
Odd Egil Overskeid
Petroleum Technology Dept.
Stavanger University College
Norway
Topic author and coordinator
Professor
Svein M. Skjæveland
Petroleum Technology Dept.
Stavanger University College
Norway
http://www.ux.his.no/~s-skj/
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References
Helpful Facts
Title page
Topic overview
1 Introduction
2 Interfacial tension
3 Rock Wettability
References
A.B.Zolotukhin and J.-R.Ursin
Education course in Reservoirtechnique 1
4 The wetting angle and
interphase tension
5 Capillar pressure
6 Laboratory
Measurments
Of capillary
Pressure
Developers
References
Helpful Facts
Title page
Topic overview
1 Introduction
2 Interfacial tension
3 Rock Wettability
4 The wetting angle and
interphase tension
5 Capillar pressure
6 Laboratory
Measurments
Of capillary
Pressure
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.
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