MCD

1
MCD Short-Cut Methods

• Because of the non-trivial nature of
  multi-component distillation problems, short-cut
  methods and correlations have been developed.
• Commonly used in the past until the advent of
  numerical computer packages, these were the
  methods of choice to enable the estimation of
  distillation column design for multi-component
  systems.
• Even so, they are still used in numerical
  computer packages to provide initial first
  estimates for the design of multi-component
  distillation systems.
• The DSTWU distillation package in Aspen Plus uses
  the
• Winn-Underwood-Gilliland short-cut methods and
  correlation.

2
MCD Short-Cut Methods Limiting Conditions

• MCD short-cut methods are based upon the limiting
  conditions for a distillation column
• Reflux Ratio L/V L/D N
• Total (L/V)max 1 8 Nmin
• Actual L/V L/D N
• Minimum (L/V)min (L/D)min Nmax
  8
• The actual or operating reflux ratio will lie
  between the total and minimum reflux ratios
  (L/V)min lt L/V lt 1.
• The operating reflux ratio, L/D, is often
  specified as a multiple of the minimum reflux
  ratio, (L/D)min, e.g.,
• L/D 2 (L/D)min.

3
MCD Short-Cut Methods

• Fenske Equation (Winn) determines the minimum
  number of stages, Nmin, and the optimum feed
  location, NF, min, at total reflux.
• Underwood Equations determines the minimum the
  reflux ratio, (L/D)min.
• Gilliland Correlation determines the actual
  number of stages, N, and the optimum feed
  location, NF, at the actual L/D.

4
Fenske (Winn) Equation Nmin

• While at times we cannot obtain a rigorous
  solution for complex systems, one can often
  obtain rigorous solutions for complex systems at
  limiting conditions.
• One such limiting condition for multi-component
  systems is the solution for Nmin at total reflux.
  This solution is known as the Fenske equation or
  Fenske method.

5
Fenske (Winn) Equation Derivation
6
Fenske (Winn) Equation Derivation
7
Fenske (Winn) Equation Derivation
8
Fenske (Winn) Equation Derivation
9
Fenske (Winn) Equation Derivation
10
Fenske (Winn) Equation Derivation
11
MCD Fenske (Winn) Equation Nmin
12
MCD Fenske (Winn) Equation FRs and xis
13
MCD Fenske (Winn) Equation Optimal Feed, NF,min
14
Binary Fenske (Winn) Equation Nmin
15
MCD Relative Volatilities
16
Binary System Relative Volatilities
17
Fenske Equation Methodology

• The ease with which one can use the Fenske
  equation to determine Nmin depends upon what is
  defined in the problem.
• If two fractional recoveries are specified, one
  can solve Eq. (9-15) and all of the ancillary
  equations directly.
• If one is given two compositions, xi and xj, then
  one needs to make some assumptions

18
Fenske Equation Methodology Non-Distributing
Non-Keys
19
Fenske Equation Some Final Notes