Distillation

To reduce load times, this material is divided into seven files, corresponding to the numbered points below. The present file (distill5.html) contains point 5 only.
  1. Distillation Principles
  2. Distillation Modeling
  3. Distillation Operating Equations
  4. Distillation Calculations
  5. Distillation Enthalpy Balances
  6. Enthalpy-Concentration Method
  7. Equipment & Column Sizing

Distillation V: Enthalpy Balances

Some equations in this document are being displayed using MINSE, a browser independent approach to displaying equations on the web. If the equations are not properly formatted by your brower, you need to RENDER EQUATIONS (select this link) by invoking Ping's MINSE polymediator. This will run a special program that should cause them to be formatted for viewing by your browser.

Variations in internal vapor and liquid flows inside a distillation column depend on the enthalpies of the mixtures. Equimolal overflow assumes the rates are independent of the energy balance. To remove the assumption we must consider the enthalpy balances explicitly.

The overall enthalpy balance on a distillation column with NT trays is:

'deriv(M;B*h;B+M;D*h;D+'Sum(M;n*h;n,i,1,NT),t)=F*h;F-D*h;D-B*h;B
where the Q terms are the condenser and reboiler loads. This equation reduces at steady-state to:
F*h;F +Q;R = D*h;D + B*h;B +Q;C

For a given feed and products, only one of QC and QR may be independently set. Normally, QC is chosen to get the desired operating pressure, product and reflux rates, and QR found by balance. In operation, however, the reboiler duty is usually varied to control an inventory or product composition.

Rectifying Section

Balances on the rectifying section are:

'deriv(M;D*h;D+'Sum(M;n*h;n,i,1,NF),t)=V;(n+1)*H;(n+1)-D*h;D-L;n*h;n - Q;C
0=V;(n+1)*H;(n+1)-D*h;D-L;n*h;n
These can be combined with the steady state balance on the accumulator:
0 = V;1*H;1 - R*h;D - D*h;D - Q;C
to eliminate the condenser duty:
0 = V;(n+1)*H;(n+1) - D*h;D - L;n*h;n - (V;1*H;1 - R*h;D - D*h;D)
0 = V;(n+1)*H;(n+1) - L;n*h;n - V;1*H;1 + R*h;D
V;(n+1) = 'quot(L;n*h;n+V;1*H;1-R*h;D ,H;(n+1))
In cases where constant molar overflow is not valid, this equation may be used to calculate vapor flowrates.

Stripping Section

The balance for the stripping section:

'deriv(M;B*h;B+'Sum(M;n*h;n,i,NF,NT),t)=L;(n-1)*h;(n-1)-V;n*H;n+Q;R-B*h;B
is combined with the steady state balance on the reboiler:
0 = L;1*h;1 - V;B*H;B - B*h;B +Q;R
in order to obtain:
0 = L;(n-1)*h;(n-1) - V;n*H;n - L;1*h;1 + V;B*H;B

Calculations

In order to solve problems when constant molar overflow does not apply, one must simultaneously solve the set of equations consisting of:

These equations are linked with enough complications, that an iterative solution is typically required.

An alternative to iterative solution is to solve the system graphically using an Enthalpy Concentration method.

R.M. Price
Original: 2/27/97
Revised: 3/5/97, 1/27/98, 2/14/2003

Copyright 1997, 1998, 2003 by R.M. Price -- All Rights Reserved