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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). [2] The typical McCabe–Thiele diagram in Figure 1 uses a q-line representing a partially vaporized feed.
Fractionation at total reflux. 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column that is being operated at total reflux (i.e., which means that no overhead product distillate is being withdrawn from the column).
These types of VLE diagrams are used in the McCabe–Thiele method to determine the number of equilibrium stages (or theoretical plates) needed to distill a given composition binary feed mixture into one distillate fraction and one bottoms fraction. Corrections can also be made to take into account the incomplete efficiency of each tray in a ...
The problem of generating a function whose graph passes through a given set of function values is called interpolation. This interpolation formula is named after the Danish mathematician Thorvald N. Thiele. It is expressed as a continued fraction, where ρ represents the reciprocal difference:
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. [2] [3] In an industrial distillation column, the N t required to achieve a given separation also depends upon the amount of reflux used. Using ...
This is a diagram exemplifying how the en:McCabe-Thiele method is used to determine the number of theoretical equilibrium stages required in a distillation unit. Licensing I, the copyright holder of this work, hereby publish it under the following license:
The Thiele Modulus was developed to describe the relationship between diffusion and reaction rates in porous catalyst pellets with no mass transfer limitations. This value is generally used to measure the effectiveness factor of pellets. The Thiele modulus is represented by different symbols in different texts, but is defined in Hill [2] as h T.
Given a simple, binary component feed, analytical methods such as the McCabe–Thiele method [5] [6] [7] or the Fenske equation [5] can be used to assist in the design. For a multi-component feed, computerized simulation models are used both for design and subsequently in operation of the column as well.