The concept of theoretical plates and trays or equilibrium stages is used in the design of many different types of separation. 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{N_t}{E} 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 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 data for the components present in the distillation feed, and the calculation procedure is very complex.
Distillation and absorption packed beds Distillation and
absorption separation processes using
packed beds 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{H}\mathrm{HETP} 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 occurs.
Chromatographic processes The theoretical plate concept was also adapted for
chromatographic processes by
Martin and
Synge. The
IUPAC's
Gold Book provides a definition of the number of theoretical plates in a chromatography column. The same equation applies in chromatography processes as for the packed bed processes, namely: : N_t = \frac{H}\mathrm{HETP} In packed column chromatography, the HETP may also be calculated with the
Van Deemter equation. In capillary column chromatography HETP is given by the Golay equation.
Other applications The concept of theoretical plates or trays applies to other processes as well, such as
capillary electrophoresis and some types of
adsorption. ==See also==