Capillary pressure
Encyclopedia
In fluid statics
, capillary pressure is the difference in pressure
across the interface between two immiscible fluids, and thus defined as
In oil-water systems, water is typically the wetting
phase, while for gas-oil systems, oil is typically the wetting phase.
The Young–Laplace equation
states that this pressure difference is proportional to the surface tension
,
, and inversely proportional to the effective radius, 
, of the interface, it also depends on the wetting angle
,
, of the liquid on the surface of the capillary.
The equation for capillary pressure is only valid under capillary equilibrium, which means that there can not be any flowing phases.
However, the quantities
, 
and 
are averaged quantities that are obtained by averaging these quantities within the pore space of porous media in either statistical manner or using the volume averaging method .
The Brooks-Corey correlation for capillary pressure reads
where
is the entry capillary pressure, 
is the pore-size distribution index and 
is the normalized water saturation (see Relative permeability
)
Fluid statics
Fluid statics is the science of fluids at rest, and is a sub-field within fluid mechanics. The term usually refers to the mathematical treatment of the subject. It embraces the study of the conditions under which fluids are at rest in stable equilibrium...
, capillary pressure is the difference in pressure
Pressure
Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...
across the interface between two immiscible fluids, and thus defined as
In oil-water systems, water is typically the wetting
Wetting
Wetting is the ability of a liquid to maintain contact with a solid surface, resulting from intermolecular interactions when the two are brought together. The degree of wetting is determined by a force balance between adhesive and cohesive forces.Wetting is important in the bonding or adherence of...
phase, while for gas-oil systems, oil is typically the wetting phase.
The Young–Laplace equation
Young–Laplace equation
In physics, the Young–Laplace equation is a nonlinear partial differential equation that describes the capillary pressure difference sustained across the interface between two static fluids, such as water and air, due to the phenomenon of surface tension or wall tension, although usage on the...
states that this pressure difference is proportional to the surface tension
Surface tension
Surface tension is a property of the surface of a liquid that allows it to resist an external force. It is revealed, for example, in floating of some objects on the surface of water, even though they are denser than water, and in the ability of some insects to run on the water surface...
,
, and inversely proportional to the effective radius, , of the interface, it also depends on the wetting angleContact angle
The contact angle is the angle at which a liquid/vapor interface meets a solid surface. The contact angle is specific for any given system and is determined by the interactions across the three interfaces. Most often the concept is illustrated with a small liquid droplet resting on a flat...
,
, of the liquid on the surface of the capillary.The equation for capillary pressure is only valid under capillary equilibrium, which means that there can not be any flowing phases.
In porous media
In porous media, capillary pressure is the force necessary to squeeze a hydrocarbon droplet through a pore throat (works against the interfacial tension between oil and water phases) and is higher for smaller pore diameter. The expression for the capillary pressure remains as before, i.e.,However, the quantities
, and are averaged quantities that are obtained by averaging these quantities within the pore space of porous media in either statistical manner or using the volume averaging method .The Brooks-Corey correlation for capillary pressure reads
where
is the entry capillary pressure, is the pore-size distribution index and is the normalized water saturation (see Relative permeabilityRelative permeability
In multiphase flow in porous media, the relative permeability of a phase is a dimensionless measure of the effective permeability of that phase. It is the ratio of the effective permeability of that phase to the absolute permeability...
)
See also
- Capillary actionCapillary actionCapillary action, or capilarity, is the ability of a liquid to flow against gravity where liquid spontanously rise in a narrow space such as between the hair of a paint-brush, in a thin tube, or in porous material such as paper or in some non-porous material such as liquified carbon fiber, or in a...
- Capillary numberCapillary numberIn fluid dynamics, the capillary number represents the relative effect of viscous forces versus surface tension acting across an interface between a liquid and a gas, or between two immiscible liquids...
- Disjoining pressureDisjoining pressureDisjoining pressure , in surface chemistry, according to an IUPAC definition, arises from an attractive interaction between two surfaces...
- Leverett J-function
- Young–Laplace equationYoung–Laplace equationIn physics, the Young–Laplace equation is a nonlinear partial differential equation that describes the capillary pressure difference sustained across the interface between two static fluids, such as water and air, due to the phenomenon of surface tension or wall tension, although usage on the...
- Amott test
- Laplace pressureLaplace pressureThe Laplace pressure is the pressure difference between the inside and the outside of a bubble or droplet. The effect is caused by the surface tension of the interface between liquid and gas.The Laplace pressure is given as...