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. Lecture 17

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 ∞ Nmin Actual L/V L/D N Minimum (L/V)min (L/D)min Nmax = ∞ The actual or operating reflux ratio will lie between the total and minimum reflux ratios – (L/V)min < L/V < 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. Lecture 17

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. Lecture 17

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. Lecture 17

Fenske (Winn) Equation – Derivation Lecture 17

Fenske (Winn) Equation – Derivation Lecture 17

Fenske (Winn) Equation – Derivation Lecture 17

Fenske (Winn) Equation – Derivation Lecture 17

Fenske (Winn) Equation – Derivation Lecture 17

Fenske (Winn) Equation – Derivation Lecture 17

MCD Fenske (Winn) Equation – Nmin Lecture 17

MCD Fenske (Winn) Equation – FR’s and xi’s Lecture 17

MCD Fenske (Winn) Equation – Optimal Feed, NF,min Lecture 17

Binary Fenske (Winn) Equation – Nmin Lecture 17

MCD Relative Volatilities Lecture 17

Binary System Relative Volatilities Lecture 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… Lecture 17

Fenske Equation Methodology – Non-Distributing Non-Keys Lecture 17

Fenske Equation – Some Final Notes Lecture 17