Main

## Main.KineticModeling History

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!!!! Case Study on Dynamic Parameter Estimation
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!!!! Dynamic Parameter Estimation

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May 11, 2015, at 01:19 PM by 45.56.3.184 -
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April 11, 2013, at 05:51 AM by 69.169.188.188 -
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April 11, 2013, at 05:49 AM by 69.169.188.188 -

Nonlinear confidence intervals can also be visualized as a function of 2 parameters. In this case, both parameters are simultaneously varied to find the confidence region. The confidence interval is determined with an F-test that specifies an upper limit to the deviation from the optimal solution

-> Attach:f-test_equation.gif

with p=2 (number of parameters), n=number of measurements, theta=[parameter 1, parameter 2] (parameters), theta'^*^' as the optimal parameters, SSE as the sum of squared errors, and the F statistic that has 3 arguments (alpha=confidence level, degrees of freedom 1, and degrees of freedom 2). For many problems, this creates a multi-dimensional nonlinear confidence region. In the case of 2 parameters, the nonlinear confidence region is a 2-dimensional space. Below is an example that shows the confidence region for the dye fading experiment confidence region for forward and reverse activation energies.

-> Attach:dye_2d_confidence_region.png

The optimal parameter values are in the 95% confidence region. This plot demonstrates that the 2D confidence region is not necessarily symmetric.
March 12, 2013, at 07:43 AM by 66.178.116.12 -
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* [[Attach:dye_fading_multiple.zip | Confidence Intervals with Multiple Dynamic Data Sets in Python (zip)]]
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* [[Attach:dye_fading_multiple_conf_int.zip | Confidence Intervals with Multiple Dynamic Data Sets in Python (zip)]]
March 12, 2013, at 07:17 AM by 66.178.116.12 -
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* [[Attach:dye_fading_multiple.zip | Fitting Multiple Dynamic Data Sets in Python (zip)]]
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!!!! Nonlinear Confidence Intervals

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!!!! Multiple Data Sets

* [[Attach:dye_fading_multiple.zip | Fitting Multiple Dynamic Data Sets in Python (zip)]]
* [[Attach:dye_fading_multiple.zip | Confidence Intervals with Multiple Dynamic Data Sets in Python (zip)]]
March 10, 2013, at 03:26 AM by 206.104.4.34 -
March 10, 2013, at 03:22 AM by 206.104.4.34 -
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* [[Attach:dye_fading_conf_int.zip | Nonlinear Confidence Intervals in MATLAB and Python (zip)]]
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* [[Attach:dye_fading_conf_int.zip | Nonlinear Confidence Intervals in Excel, MATLAB, and Python (zip)]]
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March 08, 2013, at 08:41 PM by 66.178.116.12 -
* [[Attach:dye_fading_multiple.zip | Fitting Multiple Dynamic Data Sets in Python (zip)]]
March 05, 2013, at 01:00 AM by 128.187.97.21 -
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* [[Attach:dye_fading_conf_int.zip | Nonlinear Confidence Intervals (zip)]]
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* [[Attach:dye_fading_conf_int.zip | Nonlinear Confidence Intervals in MATLAB and Python (zip)]]
March 01, 2013, at 12:39 AM by 128.187.97.21 -
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* [[Attach:dye_fading_experiment.zip | Dye Fading Experiment Files in MATLAB and Python (zip)]]
February 01, 2013, at 03:16 AM by 128.187.97.21 -
* [[Attach:dye_fading_conf_int.zip | Nonlinear Confidence Intervals (zip)]]
January 11, 2013, at 02:22 PM by 69.169.188.188 -
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December 22, 2012, at 01:10 PM by 69.169.188.188 -
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December 22, 2012, at 12:07 AM by 69.169.188.188 -
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An engineer collected time-varying data for a non-isothermal run and needs you to estimate the kinetic parameters. The temperature ranged from  about 60 - 140 degF. In order to appropriately size the reactor vessel, they need the kinetic parameters with the associated 95% confidence intervals.
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An engineer collected time-varying data for a non-isothermal run and needs you to estimate the kinetic parameters. The temperature ranged from  about 60 - 140 degF. In order to appropriately size the reactor vessel, engineers need the kinetic parameters with the associated 95% confidence intervals.
December 22, 2012, at 12:00 AM by 69.169.188.188 -
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December 21, 2012, at 11:59 PM by 69.169.188.188 -
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Reaction 1 is very fast and can be assumed to be instantaneous when the phenolphthalein (Ph) is added to a hydroxide solution. We are considering using phenolphthalein as an indicator to determine the residence time of several large CSTR reactors in a pilot plant. Please determine the kinetic parameters for reaction 2 with respect to phenolphthalein associated with the fading of phenolphthalein in sodium hydroxide solutions (reaction order, k, and Ea).

An engineer collected time-varying data for a non-isothermal run and needs you to estimate the kinetic parameters. The temperature ranged from  about 60 - 140 degF. In order to appropriately size the reactor vessel, they need the heat of reaction within a 95% confidence level.
to:
Reaction 1 is very fast and can be assumed to be instantaneous when the phenolphthalein (Ph) is added to a hydroxide solution. We are considering using phenolphthalein as an indicator to determine the residence time of several large CSTR reactors in a pilot plant. Please determine the kinetic parameters for reaction 2 with respect to phenolphthalein associated with the fading of phenolphthalein in sodium hydroxide solutions (reaction orders, A1, A2, Ea1, and Ea2).

An engineer collected time-varying data for a non-isothermal run and needs you to estimate the kinetic parameters. The temperature ranged from  about 60 - 140 degF. In order to appropriately size the reactor vessel, they need the kinetic parameters with the associated 95% confidence intervals.
December 21, 2012, at 11:56 PM by 69.169.188.188 -
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December 21, 2012, at 11:54 PM by 69.169.188.188 -
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December 21, 2012, at 11:52 PM by 69.169.188.188 -
(:title Estimate Kinetic Parameters from Dynamic Data:)
(:keywords nonlinear, optimization, engineering optimization, dynamic estimation, interior point, active set, differential, algebraic, modeling language, university course:)
(:description Case study on dynamic reconciliation for kinetic modeling using optimization techniques in engineering:)

!!!! Case Study on Dynamic Parameter Estimation

The reaction of phenolphthalein with a base solution follows the 2 reaction sequence given below.

* Reaction 1:
** Irreversible reaction, fast reaction dynamics
** Ph + 2 OH- => Ph(2-) + 2 H2O
* Reaction 2:
** Reversible, slow reaction dynamics
** Ph(2-) + OH- <=> PhOH(3-)

Reaction 1 is very fast and can be assumed to be instantaneous when the phenolphthalein (Ph) is added to a hydroxide solution. We are considering using phenolphthalein as an indicator to determine the residence time of several large CSTR reactors in a pilot plant. Please determine the kinetic parameters for reaction 2 with respect to phenolphthalein associated with the fading of phenolphthalein in sodium hydroxide solutions (reaction order, k, and Ea).

An engineer collected time-varying data for a non-isothermal run and needs you to estimate the kinetic parameters. The temperature ranged from  about 60 - 140 degF. In order to appropriately size the reactor vessel, they need the heat of reaction within a 95% confidence level.