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The McCabe–Thiele method is a technique that is commonly employed in the field of
chemical engineering Chemical engineering is an engineering field which deals with the study of the operation and design of chemical plants as well as methods of improving production. Chemical engineers develop economical commercial processes to convert raw materials ...
to model the separation of two substances by a distillation column. It uses the fact that the composition at each theoretical tray is completely determined by the
mole fraction In chemistry, the mole fraction or molar fraction, also called mole proportion or molar proportion, is a quantity defined as the ratio between the amount of a constituent substance, ''ni'' (expressed in unit of moles, symbol mol), and the to ...
of one of the two components. This method is based on the assumptions that the distillation column is isobaric—i.e the pressure remains constant—and that the flow rates of liquid and vapor do not change throughout the column (i.e., constant molar overflow). The assumption of constant molar overflow requires that: * The heat needed to vaporize a certain amount of liquid of the feed components are equal, * For every mole of liquid vaporized, a mole of vapor is condensed, and * Heat effects such as heat needed to dissolve the substance(s) are negligible. The method was first published by Warren L. McCabe and Ernest Thiele in 1925, both of whom were working at the
Massachusetts Institute of Technology The Massachusetts Institute of Technology (MIT) is a Private university, private research university in Cambridge, Massachusetts, United States. Established in 1861, MIT has played a significant role in the development of many areas of moder ...
(MIT) at the time.


Construction and use

A McCabe–Thiele diagram for the distillation of a binary (two-component) feed is constructed using the vapor-liquid equilibrium (VLE) data—which is how vapor is concentrated when in contact with its liquid form—for the component with the lower boiling point. On a planar graph, both axes represent the mole fractions of the lighter (lower boiling) component; the horizontal (x) and vertical (y) axes represents the liquid and vapor phase compositions, respectively. The x = y line (see Figure 1) represents the scenarios where the compositions of liquid and vapor are the same. The vapor-liquid equilibrium line (the curved line from (0,0) to (1,1) in Figure 1) represents the vapor phase composition for a given liquid phase composition at equilibrium. Vertical lines drawn from the horizontal axis up to the x = y line indicate the composition of the inlet feed stream, the composition of the top (distillate) product stream, and the composition of the bottoms product (shown in red in Figure 1). The rectifying section operating line for the section above the inlet feed stream of the distillation column (shown in green in Figure 1) starts at the intersection of the distillate composition line and the x = y line and continues at a downward slope of L / (D + L), where L is the molar flow rate of reflux and D is the molar flow rate of the distillate product, until it intersects the q-line. The stripping section operating line for the section below the feed inlet (shown in magenta in Figure 1) starts at the intersection of the red bottoms composition line and the x = y line and continues up to the point where the blue q-line intersects the green rectifying section operating line. The q-line (depicted in blue in Figure 1) intersects the point of intersection of the feed composition line and the x = y line and has a slope of q / (q - 1), where the parameter q denotes mole fraction of liquid in the feed. For example, if the feed is a saturated liquid, q = 1 and the slope of the q-line is infinite (drawn as a vertical line). As another example, if the feed is saturated vapor, q = 0 and the slope of the q-line is 0 (a horizontal line). The typical McCabe–Thiele diagram in Figure 1 uses a q-line representing a partially vaporized feed. Example q-line slopes are presented in Figure 2. The number of steps between the operating lines and the equilibrium line represents the number of
theoretical plate A theoretical plate in many separation processes 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 ...
s (or equilibrium stages) required for the distillation. For the binary distillation depicted in Figure 1, the required number of theoretical plates is 6. Constructing a McCabe–Thiele diagram is not always straightforward. In
continuous distillation Continuous distillation, a form of distillation, is an ongoing separation in which a mixture is continuously (without interruption) fed into the process and separated fractions are removed continuously as output streams. Distillation is the se ...
with a varying reflux ratio, the mole fraction of the lighter component in the top part of the distillation column will decrease as the reflux ratio decreases. Each new reflux ratio will alter the gradient of the rectifying section curve. When the assumption of constant molar overflow is not valid, the operating lines will not be straight. Using mass and enthalpy balances in addition to vapor-liquid equilibrium data and enthalpy-concentration data, operating lines can be constructed using the Ponchon–Savarit method. If the mixture can form an
azeotrope An azeotrope () or a constant heating point mixture is a mixture of two or more liquids whose proportions cannot be changed by simple distillation.Moore, Walter J. ''Physical Chemistry'', 3rd e Prentice-Hall 1962, pp. 140–142 This happens beca ...
, its vapor-liquid equilibrium line will cross the x = y line, preventing further separation no matter the number of theoretical plates.


See also

*
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 ...
*
Azeotropic distillation In chemistry, azeotropic distillation is any of a range of techniques used to break an azeotrope in distillation. In chemical engineering, ''azeotropic distillation'' usually refers to the specific technique of adding another component to genera ...
* Batch distillation


References


External links


More detailed information on how to draw a McCabe–Thiele DiagramDetailed discussion of McCabe–Thiele method
by Tore Haug-Warberg, Norwegian University of Science and Technology, Norway
Interactive McCabe–Thiele Diagram
{{DEFAULTSORT:McCabe-Thiele method Distillation