Exact Calculation Procedures for Multicomponent Distillation Methodآ  for Multicomponent Distillation

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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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