Apps

Distillation Column

Apps.DistillationColumn History

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December 21, 2011, at 11:50 PM by 69.169.188.228 -
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[[Main/PythonApp | See Example Problems for Distillation Column PID and NLC control comparison]]
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* %list list-blogroll% [[Main/PythonApp | Download Example Problems for Distillation Column]]
December 21, 2011, at 11:09 PM by 69.169.188.228 -
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Attach:download.jpg [[Attach:python_distill_v0.5.5.zip | Distillation Column PID and NLC control comparison]]
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[[Main/PythonApp | See Example Problems for Distillation Column PID and NLC control comparison]]
December 05, 2011, at 11:13 PM by 69.169.188.228 -
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This distillation column is a separation of cyclohexane and n-heptane.  The two components are separated over 30 theoretical trays.  In general, distillation column models are generally good test cases for nonlinear model reduction and identification.  The concentrations at each stage or tray are highly correlated.  The dynamics of the distillation process can be described by a relatively few number of underlying dynamic states.  This model was published in:
to:
This distillation column is a separation of cyclohexane and n-heptane.  The two components are separated over 30 theoretical trays.  In general, distillation column models are generally good test cases for nonlinear model reduction and identification.  The concentrations at each stage or tray are highly correlated.  The dynamics of the distillation process can be described by a relatively few number of underlying dynamic states.

Attach:download.jpg [[Attach:python_distill_v0.5.5.zip | Distillation Column PID and NLC control comparison]]

This model was published in:
May 26, 2010, at 06:01 AM by 158.35.225.240 -
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* %list list-page% [[/online/view_pass.php?f=distill.apm|Solve model online]]
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* %list list-page% (:html:)<a href="/online/view_pass.php?f=distill.apm">Solve Model Online Through a Web-based Interface</a>(:htmlend:)
May 26, 2010, at 05:58 AM by 158.35.225.240 -
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* %list list-page% [[http://apmonitor.ath.cx/online/view_pass.php?f=distill.apm|Solve model online]]
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* %list list-page% [[/online/view_pass.php?f=distill.apm|Solve model online]]
March 06, 2010, at 02:39 AM by 206.180.155.75 -
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(:html:)<font size=1><pre>
to:
(:html:)<font size=2><pre>
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! Hahn, J. and T.F. Edgar, An improved method for nonlinear model reduction using balancing of
!  empirical gramians, Computers and Chemical
Engineering, 26, pp. 1379-1397, (2002)
to:
! Hahn, J. and T.F. Edgar, An improved method for
!  nonlinear model reduction using balancing of
!  empirical gramians, Computers and Chemical
Engineering, 26, pp. 1379-1397, (2002)
February 22, 2010, at 07:27 PM by 206.180.155.75 -
Changed lines 9-10 from:
* %list list-page% [http://apmonitor.ath.cx/online/view_pass.php?f=distill.apm| Solve model online]
to:
* %list list-page% [[http://apmonitor.ath.cx/online/view_pass.php?f=distill.apm|Solve model online]]
February 22, 2010, at 07:25 PM by 206.180.155.75 -
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* %list list-page% [http://apmonitor.ath.cx/online/view_pass.php?f=distill.apm| Solve model online]
April 23, 2009, at 10:29 AM by 158.35.225.231 -
Added lines 26-128:
! APMonitor Modeling Language
! http://www.apmonitor.com

! Binary Distillation Column from
!
! Hahn, J. and T.F. Edgar, An improved method for nonlinear model reduction using balancing of
!  empirical gramians, Computers and Chemical Engineering, 26, pp. 1379-1397, (2002)
!
! Liquid mole fraction of component A
!  at reflux ratio = 2
!
! Condenser  0.93541941614016
! Tray 1    0.90052553715795
! Tray 2    0.86229645132283
!  .        0.82169940277993
!  .        0.77999079584355
!  .        0.73857168629759
!  .        0.69880490932694
!  .        0.66184253445732
!  .        0.62850777645505
!  .        0.59925269993058
!  .        0.57418567956453
!  .        0.55314422743545
!  .        0.53578454439850
!  .        0.52166550959767
!  .        0.51031495114413
!  .        0.50127509227528
!  .        0.49412891686784
!  .        0.48544992019184
!  .        0.47420248108803
!  .        0.45980349896163
!  .        0.44164297270225
!  .        0.41919109776836
!  .        0.39205549194059
!  .        0.36024592617390
!  .        0.32407993023343
!  .        0.28467681591738
!  .        0.24320921343484
!  .        0.20181568276528
!  .        0.16177269003094
! Tray 29    0.12514970961746
! Tray 30    0.09245832612765
! Reboiler  0.06458317697321

Model binary
  Parameters
    ! reflux ratio
    rr = 0.7

    ! Feed Flowrate (mol/min)
    Feed =  2.0 ! 24.0/60.0
    ! Mole Fraction of Feed
    x_Feed = 0.5
    ! Relative Volatility = (yA/xA)/(yB/xB) = KA/KB = alpha(A,B)
    vol=1.6
    ! Total Molar Holdup in the Condenser
    atray=0.25
    ! Total Molar Holdup on each Tray
    acond=0.5
    ! Total Molar Holdup in the Reboiler
    areb=0.1
  End Parameters

  Variables
    ! mole fraction of component A
    x[1:32] = 0.3
  End Variables

  Intermediates
    ! Distillate Flowrate (mol/min)
    D=0.5*Feed
    ! Flowrate of the Liquid in the Rectification Section (mol/min)
    L=rr*D
    ! Vapor Flowrate in the Column (mol/min)
    V=L+D
    ! Flowrate of the Liquid in the Stripping Section (mol/min)
    FL=Feed+L

    ! Vapor Mole Fractions of Component A
    ! From the equilibrium assumption and mole balances
    ! 1) vol = (yA/xA) / (yB/xB)
    ! 2) xA + xB = 1
    ! 3) yA + yB = 1
    y[1:32] = x[1:32]*vol/(1+(vol-1)*x[1:32])
  End Intermediates

  Equations
    ! condenser
    acond * $x[1] = V*(y[2]-x[1])

    ! 15 column stages
    atray * $x[2:16]  = L*(x[1:15]-x[2:16]) - V*(y[2:16]-y[3:17])

    ! feed tray
    atray * $x[17] = Feed*x_Feed + L*x[16] - FL*x[17] - V*(y[17]-y[18])

    ! 14 column stages
    atray * $x[18:31] = FL*(x[17:30]-x[18:31]) - V*(y[18:31]-y[19:32])

    ! reboiler
    areb  * $x[32] = FL*x[31] - (Feed-D)*x[32] - V*y[32]
  End Equations
End Model
April 23, 2009, at 10:29 AM by 158.35.225.231 -
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Attach:reflux_step.gif
to:
Attach:reflux_step.gif

----

(:html:)<font size=1><pre>

</pre></font>
(:htmlend:)
November 04, 2008, at 03:44 PM by 158.35.225.231 -
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* %list list-page% [[Attach:distill.apm| Distillation column model - 5 components, 7 stages]]
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* %list list-page% [[Attach:distill.apm| Distillation column model - 5 components, 8 stages]]
November 04, 2008, at 03:44 PM by 158.35.225.231 -
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This distillation column is a separation of cyclohexane and n-heptane.  The two components are separated over 30 theoretical trays.  In general, distillation column models are generally good test cases for nonlinear model reduction and identification.  The concentrations at each stage or tray are highly correlated.  The dynamics of the distillation process can be described by a relatively few number of underlying dynamic states.  This model was published in 
to:
This distillation column is a separation of cyclohexane and n-heptane.  The two components are separated over 30 theoretical trays.  In general, distillation column models are generally good test cases for nonlinear model reduction and identification.  The concentrations at each stage or tray are highly correlated.  The dynamics of the distillation process can be described by a relatively few number of underlying dynamic states.  This model was published in:
November 04, 2008, at 03:44 PM by 158.35.225.231 -
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!!! Multi-component Distillation Column
Changed lines 11-14 from:

Binary Distillation Column with 30 trays (cyclohexane n-heptane)

Distillation column models are generally good test cases for nonlinear model reduction and identification.  The concentrations at each stage or tray are highly correlated.  The dynamics of the distillation process can be described by a relatively few number of underlying dynamic states.  A couple papers have been published with this model as an example application
One in particular is:
to:
!!! Binary Distillation Column

This distillation column is a separation of cyclohexane and
n-heptane.  The two components are separated over 30 theoretical trays.  In general, distillation column models are generally good test cases for nonlinear model reduction and identification.  The concentrations at each stage or tray are highly correlated.  The dynamics of the distillation process can be described by a relatively few number of underlying dynamic statesThis model was published in
November 04, 2008, at 03:35 PM by 158.35.225.231 -
Added lines 4-5:
The distillation column in this example is built from a number of pre-existing model objects.  The model objects used in this example include the distillation stage, feed, flash, mixer, splitter, stream lag, and vessel.  These basic models are connected to form the multicomponent distillation tower.
Added lines 10-15:
Binary Distillation Column with 30 trays (cyclohexane n-heptane)

Distillation column models are generally good test cases for nonlinear model reduction and identification.  The concentrations at each stage or tray are highly correlated.  The dynamics of the distillation process can be described by a relatively few number of underlying dynamic states.  A couple papers have been published with this model as an example application.  One in particular is:

Hahn, J. and T.F. Edgar, An improved method for nonlinear model reduction using balancing of empirical gramians, Computers and Chemical Engineering, 26, pp. 1379-1397, (2002)

Added lines 17-18:

The figure below displays the system response after a step change in the reflux ratio from 3.0 to 1.5.  Each trajectory represents the mole fraction of cyclohexane at each tray.  The top reflux material becomes less pure (more n-heptane) due to the increased draw from the top of the column.
November 04, 2008, at 03:28 PM by 158.35.225.231 -
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!! Distillation Column

* %list list
-page% [[Attach:distill.apm| Distillation column model - 5 component, 7 stages]]

* %list list-page% [[Attach:binary.apm| Binary distillation column model - 30 stages]]
to:
!! Distillation Columns

----
*
%list list-page% [[Attach:distill.apm| Distillation column model - 5 components, 7 stages]]

----

*
%list list-page% [[Attach:binary.apm| Binary distillation column model - 30 stages]]

Attach:reflux_step.gif
November 04, 2008, at 03:27 PM by 158.35.225.231 -
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* %list list-page% [[Attach:distill.apm| Binary distillation column model - 30 stages]]
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* %list list-page% [[Attach:binary.apm| Binary distillation column model - 30 stages]]
November 04, 2008, at 03:26 PM by 158.35.225.231 -
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* %list list-page% [[Attach:distill.apm| Distillation column model]]
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* %list list-page% [[Attach:distill.apm| Distillation column model - 5 component, 7 stages]]

* %list list-page% [[Attach:distill.apm| Binary distillation column model - 30 stages
]]
November 04, 2008, at 02:46 PM by 158.35.225.231 -
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[[Attach:distill.apm| Distillation column model]]
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* %list list-page% [[Attach:distill.apm| Distillation column model]]
November 04, 2008, at 02:45 PM by 158.35.225.231 -
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!! Distillation Column

[[Attach:distill.apm| Distillation column model]]