Rigorous computer methods for solving multicomponent distillation problems are available, but the approximate, or "shortcut", methods described here are common for preliminary design, examining the relationships between design parameters, process synthesis, etc.
As we did with binary columns, we'll work with ideal stages which can be converted to real stages using an efficiency factor. The limiting cases of total and infinite reflux apply to multicomponent columns just as they do to binary systems.
The overall approach to solving multicomponent problems is the same we use for all equilibrium stage systems -- use the equilibrium relationships and the operating relationships. The equilibrium relationships are more complex for multicomponent systems; in particular, the identity of the most volatile component may change with temperature in the system.
You may wish to review multicomponent bubble and dew point calculations. These were likely covered in your thermodynamics and material balance classes.
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For a multicomponent flash distillation, the operating equation
Because a flash is a single equilibrium stage, equilibrium fixes another relationship between y and x. If this is represented by an equation, using distribution coefficients for instance, the two equations (equilibrium and operating) can be combined and rearranged
The first step in setting up multicomponent distillation problems is to select two components to serve as the heavy key and the light key. Key components must be present in both the overhead and the bottoms, so that by specifying the recovery of the keys, you specify the extent of the split.
Product specifications for these calculations are generally in the form of recovery specifications -- for example, of the butane in the feed, 75% exits in the overhead -- rather than mole fractions, since to calculate mole fractions requires prior knowledge of how all the components distribute between the products.
Non-key components (everything but the keys) are classed as distributed if they occur in both products, or non-distributed if they appear in only one product. Remember, keys must be distributed. Non-keys may be distributed when they have volatilities very close to the keys or between the keys, and when the desired separation is sloppy.
The Shiras equation can be used to predict component distribution at minimum reflux:
The Fenske equation can be used to determine the minimum number of stages theoretically necessary to make a given separation at total reflux. The equation can be written for any two components. Typically, you will initially apply the equation to the key components and solve for the number of stages:
Once Nmin has been established, you can use the same equation to determine the splits of the other components in the mixture.
Minimum reflux calculations are based on invariant zones around the feed where the compositions stop changing. These are similar to the pinch point idea used for binary columns.
One way to determine an approximate minimum reflux ratio is to represent a multicomponent mixture as a pseudobinary system. This is done by creating a hypothetical feed made up of the two key components only. A McCabe-Thiele construction can then be used to determine the pinch and minimum reflux. The accuracy of the approximation depends heavily on how large a portion of the material is made up of the keys. Considering this limitation, and the amount of work required to recast the calculations, other methods are usually preferred.
Often, minimum reflux is estimated using the Underwood method. This assumes equimolar overflow and defines relative volatilities for each component relative to some reference component, usually the heavy key:
The approach is fairly straightforward as long as the keys are the only distributed components. If, however, there are distributed non-keys, the second equation must be written for each viable value of . These are then solved simultaneously for xDi and Rmin.
It should also be noted that the Rmin determined by this approach is the "internal" or "effective" reflux, not necessarily the "external" or "returned" reflux. The latter must be obtained by enthalpy balance. Fortunately, the difference is sigificant mainly if the mixture is "wide boiling".
The Underwood method assumes constant molar overflow and relatively constant relative volatilities. If these do not apply, caution is necessary when applying the results.
Gilliland plots can be used to find the actual stages required for a given reflux rate or vice versa. The plots relate two variables:
The Eduljee equation is a numerical fit of the charts:
Erbar and Maddox have also prepared plots for determining the number of stages. These show curves of on axes of vs. .
The Kirkbride equation allows you to predict the optimal feed stage, by determining the relative number of trays in the rectifying and stripping sections:
Mathcad Example -- Multicomponent Distillation Calculations (NonDistributed NonKeys) (Mathcad 8 file)
Mathcad Example -- Multicomponent Distillation Calculations (Distributed NonKeys) (Mathcad 8 file)
References:
R.M. Price
Original: 3/6/97
Revised: 4/24/98, 3/3/99, 2/27/2003
Copyright 1997, 1998, 1999, 2003 by R.M. Price -- All Rights Reserved