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Leverett J-function
In petroleum engineering, the Leverett ''J''-function is a dimensionless function of water saturation describing the capillary pressure, :J(S_w) = \frac where S_w is the water saturation measured as a fraction, p_c is the capillary pressure (in pascal), k is the permeability (measured in m²), \phi is the porosity (0-1), \gamma is the surface tension (in N/m) and \theta is the contact angle. The function is important in that it is constant for a given saturation within a reservoir, thus relating reservoir properties for neighboring beds. The Leverett ''J''-function is an attempt at extrapolating capillary pressure data for a given rock to rocks that are similar but with differing permeability, porosity and wetting properties. It assumes that the porous rock can be modelled as a bundle of non-connecting capillary tubes, where the factor \sqrt is a characteristic length of the capillaries' radii. This function is also widely used in modeling two-phase flow of proton-excha ...
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Water Saturation
Water content or moisture content is the quantity of water contained in a material, such as soil (called soil moisture), rock, ceramics, crops, or wood. Water content is used in a wide range of scientific and technical areas, and is expressed as a ratio, which can range from 0 (completely dry) to the value of the materials' porosity at saturation. It can be given on a volumetric or mass (gravimetric) basis. Definitions Volumetric water content, θ, is defined mathematically as: :\theta = \frac where V_w is the volume of water and V_\text = V_s + V_w + V_a is equal to the total volume of the wet material, i.e. of the sum of the volume of solid host material (e.g., soil particles, vegetation tissue) V_s, of water V_w, and of air V_a. Gravimetric water content is expressed by mass (weight) as follows: :u = \frac where m_w is the mass of water and m_s is the mass of the solids. For materials that change in volume with water content, such as coal, the gravimetric water content, ''u' ...
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Capillary Pressure
In fluid statics, capillary pressure () is the pressure between two immiscible fluids in a thin tube (see capillary action), resulting from the interactions of forces between the fluids and solid walls of the tube. Capillary pressure can serve as both an opposing or driving force for fluid transport and is a significant property for research and industrial purposes (namely microfluidic design and oil extraction from porous rock). It is also observed in natural phenomena. Definition Capillary pressure is defined as: :p_c=p_-p_ where: :p_is the capillary pressure :p_ is the pressure of the non-wetting phase :p_ is the pressure of the wetting phase The wetting phase is identified by its ability to preferentially diffuse across the capillary walls before the non-wetting phase. The "wettability" of a fluid depends on its surface tension, the forces that drive a fluid's tendency to take up the minimal amount of space possible, and it is determined by the contact angle of the fluid.Fan ...
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Pascal (unit)
The pascal (symbol: Pa) is the unit of pressure in the International System of Units (SI), and is also used to quantify internal pressure, stress, Young's modulus, and ultimate tensile strength. The unit, named after Blaise Pascal, is defined as one newton per square metre and is equivalent to 10 barye (Ba) in the CGS system. The unit of measurement called standard atmosphere (atm) is defined as 101,325 Pa. Common multiple units of the pascal are the hectopascal (1 hPa = 100 Pa), which is equal to one millibar, and the kilopascal (1 kPa = 1000 Pa), which is equal to one centibar. Meteorological observations typically report atmospheric pressure in hectopascals per the recommendation of the World Meteorological Organization, thus a standard atmosphere (atm) or typical sea-level air pressure is about 1013 hPa. Reports in the United States typically use inches of mercury or millibars (hectopascals). In Canada these reports are given in kilopascal ...
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Square Metre
The square metre ( international spelling as used by the International Bureau of Weights and Measures) or square meter (American spelling) is the unit of area in the International System of Units (SI) with symbol m2. It is the area of a square with sides one metre in length. Adding and subtracting SI prefixes creates multiples and submultiples; however, as the unit is exponentiated, the quantities grow exponentially by the corresponding power of 10. For example, 1 kilometre is 103 (one thousand) times the length of 1 metre, but 1 square kilometre is (103)2 (106, one million) times the area of 1 square metre, and 1 cubic kilometre is (103)3 (109, one billion) cubic metres. SI prefixes applied The square metre may be used with all SI prefixes used with the metre. Unicode characters Unicode has several characters used to represent metric area units, but these are for compatibility with East Asian character encodings and are meant to be used in new documents. * * * * ...
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Porosity
Porosity or void fraction is a measure of the void (i.e. "empty") spaces in a material, and is a fraction of the volume of voids over the total volume, between 0 and 1, or as a percentage between 0% and 100%. Strictly speaking, some tests measure the "accessible void", the total amount of void space accessible from the surface (cf. closed-cell foam). There are many ways to test porosity in a substance or part, such as industrial CT scanning. The term porosity is used in multiple fields including pharmaceutics, ceramics, metallurgy, materials, manufacturing, petrophysics, hydrology, earth sciences, soil mechanics, and engineering. Void fraction in two-phase flow In gas-liquid two-phase flow, the void fraction is defined as the fraction of the flow-channel volume that is occupied by the gas phase or, alternatively, as the fraction of the cross-sectional area of the channel that is occupied by the gas phase. Void fraction usually varies from location to location in the flow ch ...
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Surface Tension
Surface tension is the tendency of liquid surfaces at rest to shrink into the minimum surface area possible. Surface tension is what allows objects with a higher density than water such as razor blades and insects (e.g. water striders) to float on a water surface without becoming even partly submerged. At liquid–air interfaces, surface tension results from the greater attraction of liquid molecules to each other (due to cohesion) than to the molecules in the air (due to adhesion). There are two primary mechanisms in play. One is an inward force on the surface molecules causing the liquid to contract. Second is a tangential force parallel to the surface of the liquid. This ''tangential'' force is generally referred to as the surface tension. The net effect is the liquid behaves as if its surface were covered with a stretched elastic membrane. But this analogy must not be taken too far as the tension in an elastic membrane is dependent on the amount of deformation of the m ...
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Contact Angle
The contact angle is the angle, conventionally measured through the liquid, where a liquid–vapor interface meets a solid surface. It quantifies the wettability of a solid surface by a liquid via the Young equation. A given system of solid, liquid, and vapor at a given temperature and pressure has a unique equilibrium contact angle. However, in practice a dynamic phenomenon of contact angle hysteresis is often observed, ranging from the advancing (maximal) contact angle to the receding (minimal) contact angle. The equilibrium contact is within those values, and can be calculated from them. The equilibrium contact angle reflects the relative strength of the liquid, solid, and vapour molecular interaction. The contact angle depends upon the medium above the free surface of the liquid, and the nature of the liquid and solid in contact. It is independent of the inclination of solid to the liquid surface. It changes with surface tension and hence with the temperature and purity of t ...
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Proton Exchange Membrane Fuel Cell
A proton is a stable subatomic particle, symbol , H+, or 1H+ with a positive electric charge of +1 ''e'' elementary charge. Its mass is slightly less than that of a neutron and 1,836 times the mass of an electron (the proton–electron mass ratio). Protons and neutrons, each with masses of approximately one atomic mass unit, are jointly referred to as "nucleons" (particles present in atomic nuclei). One or more protons are present in the Atomic nucleus, nucleus of every atom. They provide the attractive electrostatic central force which binds the atomic electrons. The number of protons in the nucleus is the defining property of an element, and is referred to as the atomic number (represented by the symbol ''Z''). Since each chemical element, element has a unique number of protons, each element has its own unique atomic number, which determines the number of atomic electrons and consequently the chemical characteristics of the element. The word ''proton'' is Greek language, G ...
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TEM-function
In petroleum engineering, TEM (true effective mobility), also called TEM-function developed by Abouzar Mirzaei-Paiaman, is a criterion to characterize dynamic two-phase flow characteristics of rocks (or dynamic rock quality). TEM is a function of relative permeability, porosity, absolute permeability and fluid viscosity, and can be determined for each fluid phase separately. TEM-function has been derived from Darcy's law for multiphase flow. :\mathit = \frac in which k is the absolute permeability, k_\mathit is the relative permeability, φ is the porosity, and μ is the fluid viscosity. Rocks with better fluid dynamics (i.e., experiencing a lower pressure drop in conducting a fluid phase) have higher TEM versus saturation curves. Rocks with lower TEM versus saturation curves resemble low quality systems. TEM-function in analyzing relative permeability data is analogous with Leverett J-function In petroleum engineering, the Leverett ''J''-function is a dimensionless function ...
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Amott Test
The Amott test is one of the most widely used empirical wettability measurements for reservoir cores in petroleum engineering. The method combines two spontaneous imbibition measurements and two forced displacement measurements. This test defines two different indices: the Amott water index (I_w) and the Amott oil index (I_o). Amott–Harvey index The two Amott indices are often combined to give the Amott–Harvey index. It is a number between −1 and 1 describing wettability of a rock in drainage processes. It is defined as: :AI=I_w-I_o These two indices are obtained from special core analysis (SCAL) experiments ( porous plate or centrifuge) by plotting the capillary pressure curve as a function of the water saturation as shown on figure 1: :I_w=\frac with S_ is the water saturation for a zero capillary pressure during the imbibition process, S_ is the irreducible water saturation and S_ is the residual oil saturation after imbibition. :I_o=\frac with S_ is the oil saturation f ...
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