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Exact Calculation Procedures
for Multicomponent Distillation
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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
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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)
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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 goodguess for N and NF.
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(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
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Component Mass Balance in Matrix Form
Mass balance for any component i at stage j:
Equilibrium relationships:
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Liquid component flow rates:
New form of the mass balance:
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Initial guess for the flow rates:
Assume CMO
Feed quality:
Rectifying section:
Stripping section:
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Bubble point calculations
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θ-convergence Method
This method defines a quantity θ that forces the
equation below to be verified:
with
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Once θ is found, one can compute the following:
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Convergence Test:
Calculate new Tj
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Energy Balance in Matrix From
Using the following equations, one gets a matrix equation:
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New values for Lj and Vj
If not use new values in step (3) (i.e., mass balance matrix equations)
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