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Relative Permeability
In multiphase flow in porous media, the relative permeability of a Phase (matter), phase is a dimensionless measure of the effective Permeability (Earth sciences), permeability of that phase. It is the ratio of the effective permeability of that phase to the absolute permeability. It can be viewed as an adaptation of Darcy's law to multiphase flow. Formulation For two-phase flow in porous media given steady-state conditions, we can write :q_i = -\frac \nabla P_i \qquad \text \quad i=1,2 where q_i is the Mass flux, flux, \nabla P_i is the pressure drop, \mu_i is the viscosity. The subscript i indicates that the parameters are for phase i. k_i is here the phase permeability (i.e., the effective permeability of phase i), as observed through the equation above. Relative permeability, k_, for phase i is then defined from k_i = k_k, as :k_ = k_i / k where k is the permeability of the porous medium in single-phase flow, i.e., the absolute permeability. Relative permeability must b ...
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Multiphase Flow
In fluid mechanics, multiphase flow is the simultaneous Fluid dynamics, flow of materials with two or more thermodynamic Phase (matter), phases. Virtually all processing technologies from Cavitation, cavitating pumps and turbines to paper-making and the construction of plastics involve some form of multiphase flow. It is also prevalent in many List of natural phenomena, natural phenomena. These phases may consist of one chemical component (e.g. flow of water and water vapour), or several different chemical components (e.g. flow of oil and water). A phase is classified as ''continuous'' if it occupies a continually connected region of space (as opposed to ''disperse'' if the phase occupies disconnected regions of space). The continuous phase may be either gaseous or a liquid. The disperse phase can consist of a solid, liquid or gas. Two general topologies can be identified: ''disperse'' flows and ''separated'' flows.'' ''The former consists of finite particles, drops or bubbles di ...
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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, ' ...
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Fluid Dynamics
In physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids – liquids and gases. It has several subdisciplines, including (the study of air and other gases in motion) and (the study of water and other liquids in motion). Fluid dynamics has a wide range of applications, including calculating forces and moment (physics), moments on aircraft, determining the mass flow rate of petroleum through pipeline transport, pipelines, weather forecasting, predicting weather patterns, understanding nebulae in interstellar space, understanding large scale Geophysical fluid dynamics, geophysical flows involving oceans/atmosphere and Nuclear weapon design, modelling fission weapon detonation. Fluid dynamics offers a systematic structure—which underlies these practical disciplines—that embraces empirical and semi-empirical laws derived from flow measurement and used to solve practical problems. The solution to a fl ...
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Buckley–Leverett Equation
In fluid dynamics, the Buckley–Leverett equation is a conservation equation used to model two-phase flow in porous media. The Buckley–Leverett equation or the Buckley–Leverett ''displacement'' describes an immiscible displacement process, such as the displacement of oil by water, in a one-dimensional or quasi-one-dimensional reservoir. This equation can be derived from the mass conservation equations of two-phase flow, under the assumptions listed below. Equation In a quasi-1D domain, the Buckley–Leverett equation is given by: : \frac + \frac\left( \frac f_w(S_w) \right) = 0, where S_w(x,t) is the wetting-phase (water) saturation, Q is the total flow rate, \phi is the rock porosity, A is the area of the cross-section in the sample volume, and f_w(S_w) is the fractional flow function of the wetting phase. Typically, f_w(S_w) is an S-shaped, nonlinear function of the saturation S_w, which characterizes the relative mobilities of the two phases: : f_w(S_w) = \frac = \fra ...
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Drainage
Drainage is the natural or artificial removal of a surface's water and sub-surface water from an area with excess water. The internal drainage of most agricultural soils can prevent severe waterlogging (anaerobic conditions that harm root growth), but many soils need artificial drainage to improve production or to manage water supplies. History Early history The Indus Valley Civilization had sewerage and drainage systems. All houses in the major cities of Harappa and Mohenjo-daro had access to water and drainage facilities. Waste water was directed to covered gravity sewers, which lined the major streets. 18th and 19th century The invention of hollow-pipe drainage is credited to Sir Hugh Dalrymple, who died in 1753. Current practices Simple infrastructure such as open drains, pipes, and berms are still common. In modern times, more complex structures involving substantial earthworks and new technologies have been common as well. Geotextiles New storm water drainag ...
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Imbibition
Imbibition is a special type of diffusion that takes place when liquid is absorbed by solids-Colloid, colloids causing an increase in volume. Water surface potential movement takes place along a concentration gradient; some dry materials absorb water. A gradient between the absorbent and the liquid is essential for imbibition. For a substance to imbibe a liquid, there must first be some attraction between them. Imbibition occurs when a wetting fluid displaces a non-wetting fluid, the opposite of drainage in which a non-wetting phase displaces the wetting fluid. The two processes are governed by different mechanisms. Imbibition is also a type of diffusion since water movement is along the concentration gradient. Seeds and other such materials have almost no water hence they absorb water easily. Water potential gradient between the absorbent and liquid imbibed is essential for imbibition. Examples One example of Imbibition in nature is the absorption (chemistry), absorption of w ...
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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.F ...
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Permeability (earth Sciences)
In fluid mechanics, materials science and Earth sciences, the permeability of porous media (often, a rock or soil) is a measure of the ability for fluids (gas or liquid) to flow through the media; it is commonly symbolized as ''k''. Fluids can more easily flow through a material with high permeability than one with low permeability. The permeability of a medium is related to the '' porosity'', but also to the shapes of the pores in the medium and their level of connectedness. Fluid flows can also be influenced in different lithological settings by brittle deformation of rocks in fault zones; the mechanisms by which this occurs are the subject of fault zone hydrogeology. Permeability is also affected by the pressure inside a material. The SI unit for permeability is the square metre (m2). A practical unit for permeability is the '' darcy'' (d), or more commonly the ''millidarcy'' (md) The name honors the French Engineer Henry Darcy who first described the flow of wat ...
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TEM-function
In petroleum engineering, TEM (true effective mobility), also called TEM-function 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 analyzing capillary pressure In fluid statics, capillary pressure () is the pressure between two immiscible fluids in ...
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Morris Muskat
Morris Muskat (21 April 1906 – 20 June 1998) was an American petroleum engineer. Muskat refined Darcy's equation for single phase flow, and this change made it suitable for the petroleum industry. Based on experimental results worked out by his colleagues, Muskat and Milan W. Meres also generalized Darcy's law to cover multiphase flow of water, oil and gas in the porous medium of a petroleum reservoir. The generalized flow equation provides the analytical foundation for reservoir engineering that exists to this day. Early life and career Muskat was born in Riga, Russian Empire. He came to the United States with his family in 1911, and became an American citizen in 1914. Muskat attended Marietta College and Ohio State University, then taught physics at Bowling Green University. He earned his doctorate in physics from the California Institute of Technology in 1929. After graduating from Caltech, Muskat joined Gulf Research & Development Company where he started as a Research ...
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LET Model For Relative Permeability
Let or LET may refer to: Sports * Let serve, when the served object in certain racket sports hits the net and lands in the correct service court, such as; ** Let (badminton) ** Let (pickleball) ** Let (tennis) * Ladies European Tour, the ladies professional golf tour of Europe Terminology * -let as an English diminutive suffix * Let expression, a name binding construct in computer programming languages * Let statement, a statement used in word problems requiring algebraic equations * Letting, a system of payment for the temporary use of something owned by someone else, also known as "rental" People, titles, characters * Licensed engineering technologist * Let, a fictional character from the anime series '' Rave Master'' Places, locations * County Leitrim, Ireland, Chapman code LET * Let, West Virginia * Leț, a village in Boroșneu Mare Commune, Covasna County, Romania * Alfredo Vásquez Cobo International Airport (IATA code LET), Leticia, Colombia * Lei Tung station (stati ...
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Corey Model
Corey is a masculine given name and a surname. It is a masculine version of name Cora, which has Greek origins and is the maiden name of the goddess Persephone. The name also can have origins from the Gaelic word ''coire'', which means "in a cauldron" or "in a hollow". As a surname, it has a number of possible derivations, including an Old Norse personal name '' Kori'' of uncertain meaning, which is found in Scandinavia and England, often meaning curly haired. As an Irish surname it comes from Ó Comhraidhe (descendant of Comhraidheh). Notable people or fictional characters named Corey include: First name A *Corey Adam (born 1981), American stand-up comedian * Corey Adams (born 1962), Australian rugby player * Corey Adamson (born 1992), Australian baseball and Australian rules football player *Corey Allan (born 1998), Australian rugby player *Corey Allen (1934–2010), American film and television director * Corey Anderson (other), multiple people *Corey Arnold (born ...
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