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A theoretical plate in many
separation process A separation process is a method that converts a mixture or a solution of chemical substances into two or more distinct product mixtures, a scientific process of separating two or more substance in order to obtain purity. At least one product mi ...
es is a hypothetical zone or stage in which two phases, such as the liquid and vapor phases of a substance, establish an equilibrium with each other. Such equilibrium stages may also be referred to as an equilibrium stage, ideal stage, or a theoretical tray. The performance of many separation processes depends on having series of equilibrium stages and is enhanced by providing more such stages. In other words, having more theoretical plates increases the efficiency of the separation process be it either a
distillation Distillation, or classical distillation, is the process of separating the components or substances from a liquid mixture by using selective boiling and condensation, usually inside an apparatus known as a still. Dry distillation is the heating ...
, absorption, chromatographic,
adsorption Adsorption is the adhesion of atoms, ions or molecules from a gas, liquid or dissolved solid to a surface. This process creates a film of the ''adsorbate'' on the surface of the ''adsorbent''. This process differs from absorption, in which a ...
or similar process.


Applications

The concept of theoretical plates and trays or equilibrium stages is used in the design of many different types of separation.


Distillation columns

The concept of theoretical plates in designing
distillation Distillation, or classical distillation, is the process of separating the components or substances from a liquid mixture by using selective boiling and condensation, usually inside an apparatus known as a still. Dry distillation is the heating ...
processes has been discussed in many reference texts. Any physical device that provides good contact between the vapor and liquid phases present in industrial-scale distillation columns or laboratory-scale glassware distillation columns constitutes a "plate" or "tray". Since an actual, physical plate can never be a 100% efficient equilibrium stage, the number of actual plates is more than the required theoretical plates. : N_a = \frac where N_a is the number of actual, physical plates or trays, N_t is the number of theoretical plates or trays and E is the plate or tray efficiency. So-called bubble-cap or valve-cap trays are examples of the vapor and liquid contact devices used in industrial distillation columns. Another example of vapor and liquid contact devices are the spikes in laboratory Vigreux fractionating columns. The trays or plates used in industrial distillation columns are fabricated of circular steel plates and usually installed inside the column at intervals of about 60 to 75 cm (24 to 30 inches) up the height of the column. That spacing is chosen primarily for ease of installation and ease of access for future repair or maintenance. An example of a very simple tray is a perforated tray. The desired contacting between vapor and liquid occurs as the vapor, flowing upwards through the perforations, comes into contact with the liquid flowing downwards through the perforations. In current modern practice, as shown in the adjacent diagram, better contacting is achieved by installing bubble-caps or valve caps at each perforation to promote the formation of vapor bubbles flowing through a thin layer of liquid maintained by a
weir A weir or low head dam is a barrier across the width of a river that alters the flow characteristics of water and usually results in a change in the height of the river level. Weirs are also used to control the flow of water for outlets of l ...
on each tray. To design a distillation unit or a similar chemical process, the number of theoretical trays or plates (that is, hypothetical equilibrium stages), , required in the process should be determined, taking into account a likely range of feedstock composition and the desired degree of separation of the components in the output fractions. In industrial continuous fractionating columns, is determined by starting at either the top or bottom of the column and calculating material balances, heat balances and equilibrium flash vaporizations for each of the succession of equilibrium stages until the desired end product composition is achieved. The calculation process requires the availability of a great deal of
vapor–liquid equilibrium In thermodynamics and chemical engineering, the vapor–liquid equilibrium (VLE) describes the distribution of a chemical species between the vapor phase and a liquid phase. The concentration of a vapor in contact with its liquid, especially at ...
data for the components present in the distillation feed, and the calculation procedure is very complex. In an industrial distillation column, the required to achieve a given separation also depends upon the amount of
reflux Reflux is a technique involving the condensation of vapors and the return of this condensate to the system from which it originated. It is used in industrial and laboratory distillations. It is also used in chemistry to supply energy to reactions ...
used. Using more reflux decreases the number of plates required and using less reflux increases the number of plates required. Hence, the calculation of is usually repeated at various reflux rates. is then divided by the tray efficiency, E, to determine the actual number of trays or physical plates, , needed in the separating column. The final design choice of the number of trays to be installed in an industrial distillation column is then selected based upon an economic balance between the cost of additional trays and the cost of using a higher reflux rate. There is a very important distinction between the theoretical plate terminology used in discussing conventional distillation trays and the theoretical plate terminology used in the discussions below of packed bed distillation or absorption or in chromatography or other applications. The theoretical plate in conventional distillation trays has no "height". It is simply a hypothetical equilibrium stage. However, the theoretical plate in packed beds, chromatography and other applications is defined as having a height. The
empirical formula In chemistry, the empirical formula of a chemical compound is the simplest whole number ratio of atoms present in a compound. A simple example of this concept is that the empirical formula of sulfur monoxide, or SO, would simply be SO, as is the ...
known as Van Winkle's Correlation can be used to predict the Murphree plate efficiency for distillation columns separating binary systems.


Distillation and absorption packed beds

Distillation and absorption separation processes using
packed bed In chemical processing, a packed bed is a hollow tube, pipe, or other vessel that is filled with a packing material. The packing can be randomly filled with small objects like Raschig rings or else it can be a specifically designed structur ...
s for vapor and liquid contacting have an equivalent concept referred to as the plate height or the height equivalent to a theoretical plate (HETP). HETP arises from the same concept of equilibrium stages as does the theoretical plate and is numerically equal to the absorption bed length divided by the number of theoretical plates in the absorption bed (and in practice is measured in this way). : N_t = \frac\mathrm where N_t is the number of theoretical plates (also called the "plate count"), is the total bed height and is the height equivalent to a theoretical plate. The material in packed beds can either be random dumped packing (1-3" wide) such as Raschig rings or structured sheet metal. Liquids tend to wet the surface of the packing and the vapors contact the wetted surface, where
mass transfer Mass transfer is the net movement of mass from one location (usually meaning stream, phase, fraction or component) to another. Mass transfer occurs in many processes, such as absorption, evaporation, drying, precipitation, membrane filtration ...
occurs.


Chromatographic processes

The theoretical plate concept was also adapted for chromatographic processes by
Martin Martin may refer to: Places * Martin City (disambiguation) * Martin County (disambiguation) * Martin Township (disambiguation) Antarctica * Martin Peninsula, Marie Byrd Land * Port Martin, Adelie Land * Point Martin, South Orkney Islands Au ...
and Synge. The
IUPAC The International Union of Pure and Applied Chemistry (IUPAC ) is an international federation of National Adhering Organizations working for the advancement of the chemical sciences, especially by developing nomenclature and terminology. It is ...
's
Gold Book The International Union of Pure and Applied Chemistry publishes many books which contain its complete list of definitions. The definitions are divided into seven "colour books": Gold, Green, Blue, Purple, Orange, White, and Red. There is also an e ...
provides a definition of the number of theoretical plates in a chromatography column.Definition of the number of plates (in chromatography)
IUPAC Gold Book
The same equation applies in chromatography processes as for the packed bed processes, namely: : N_t = \frac\mathrm In chromatography, the HETP may also be calculated with the
Van Deemter equation The van Deemter equation in chromatography, named for Jan van Deemter, relates the variance per unit length of a separation column to the linear mobile phase velocity by considering physical, kinetic, and thermodynamic properties of a separation. ...
.


Other applications

The concept of theoretical plates or trays applies to other processes as well, such as
capillary electrophoresis Capillary electrophoresis (CE) is a family of electrokinetic separation methods performed in submillimeter diameter capillaries and in micro- and nanofluidic channels. Very often, CE refers to capillary zone electrophoresis (CZE), but other elect ...
and some types of
adsorption Adsorption is the adhesion of atoms, ions or molecules from a gas, liquid or dissolved solid to a surface. This process creates a film of the ''adsorbate'' on the surface of the ''adsorbent''. This process differs from absorption, in which a ...
.


See also

*
Batch distillation Batch distillation refers to the use of distillation in batches, meaning that a mixture is distilled to separate it into its component fractions before the distillation still is again charged with more mixture and the process is repeated. This is in ...
* Continuous distillation *
Extractive distillation Extractive distillation is defined as distillation in the presence of a miscible, high-boiling, relatively non-volatile component, the solvent, that forms no azeotrope with the other components in the mixture. The method is used for mixtures hav ...
*
Fenske equation The Fenske equation in continuous fractional distillation is an equation used for calculating the minimum number of theoretical plates required for the separation of a binary feed stream by a fractionation column that is being operated at total ...
*
Fractional distillation Fractional distillation is the separation of a mixture into its component parts, or fractions. Chemical compounds are separated by heating them to a temperature at which one or more fractions of the mixture will vaporize. It uses distillation to ...
* McCabe–Thiele method


References


External links


Distillation, An Introduction
by Ming Tham, Newcastle University, UK
Distillation Theory
by Ivar J. Halvorsen and Sigurd Skogestad, Norwegian University of Science and Technology, Norway {{Chemical equilibria Separation processes Unit operations Chemical engineering Chromatography Distillation