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Exact Calculation Procedures

for Multicomponent Distillation

1Binous - Exact Distillation Calculation

Stage-by-stage calculations require good first guess of

compositions at some point in the column

Method using matrix methods will be described: not

restricted to cases where a good guess of composition is

available

We will describe a simple matrix method using:

θ−convergence method

2Binous - Exact Distillation Calculation

MESH equations are the same (physical operation is unchanged)

We will rearrange the equations to enhance convergence

especially when one good first guess is available

Solve equation by type instead of stage-by-stage

All mass balance equations for component i are grouped and

solve simultaneously (equations are written in matrix form)

3Binous - Exact Distillation Calculation

Specify F, zi, TF, N, NF, P, Treflux, L/D and D

Simulation problem with D specified

Design problem:

Run a series of simulation problems with good guess for N and NF.

4Binous - Exact Distillation Calculation

5Binous - Exact Distillation Calculation

(1) Guess vapor and liquid flow rates: Lj and Vj for each stage j

(can use CMO) / Guess Tj for each stage j

(2) Calculate K values

(3) Solve component mass balance equations

(4) Use θ-convergence and bubble-point calculations to get T

If θ ≠ 1 go to step (2) with new Tj

(5) Solve energy balance to get Lj and Vj for each stage j

Convergence check not satisfied

then go to step (3) with new Lj and Vj 6Binous - Exact Distillation Calculation

7Binous - Exact Distillation Calculation

8Binous - Exact Distillation Calculation

Component Mass Balance in Matrix Form

Mass balance for any component i at stage j:

Equilibrium relationships:

9Binous - Exact Distillation Calculation

Liquid component flow rates:

New form of the mass balance:

10Binous - Exact Distillation Calculation

11Binous - Exact Distillation Calculation

12Binous - Exact Distillation Calculation

Initial guess for the flow rates:

Assume CMO

Feed quality:

Rectifying section:

Stripping section:

13Binous - Exact Distillation Calculation

Bubble point calculations

14Binous - Exact Distillation Calculation

θ-convergence Method

This method defines a quantity θ that forces the

equation below to be verified:

with

15Binous - Exact Distillation Calculation

16Binous - Exact Distillation Calculation

Once θ is found, one can compute the following:

17Binous - Exact Distillation Calculation

Convergence Test:

Calculate new Tj

18Binous - Exact Distillation Calculation

Energy Balance in Matrix From

Using the following equations, one gets a matrix equation:

19Binous - Exact Distillation Calculation

20Binous - Exact Distillation Calculation

New values for Lj and Vj

If not use new values in step (3) (i.e., mass balance matrix equations)

21Binous - Exact Distillation Calculation

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