Main.EthylAcetate History

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April 12, 2013, at 08:11 AM by 128.187.97.24 -
Added lines 47-64:

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!!!! Nonlinear Confidence Intervals

* [[Attach:ethyl_acetate_conf_int.zip | Nonlinear Confidence Intervals in MATLAB]]

The above script produces 1-dimensional confidence intervals for all of the reaction parameters. In this example, the reversibility of the reaction is tested by including the reverse reaction rate in the data fit. The optimizer decides whether to assign a sufficiently large reverse reaction rate to optimally fit the model to the dynamic data.

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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. See the [[Main/KineticModeling | Dye Fading Experiment]] for an example of a 2D nonlinear confidence region.
March 25, 2013, at 09:39 AM by 69.169.188.188 -
Changed line 12 from:
Determine the kinetic parameters for the Ethyl-Acetate/Sodium Hydroxide reaction including the pre-exponential factor (''A''), reaction orders (''α'' and ''β''), and activation energy (''E'_a_''') for the reaction.
to:
Determine the kinetic parameters for the Ethyl-Acetate/Sodium Hydroxide reaction including the frequency factor (''A''), reaction orders (''α'' and ''β''), and activation energy (''E'_a_''') for the reaction.
March 25, 2013, at 09:39 AM by 69.169.188.188 -
Changed lines 34-35 from:
The concentration of hydroxide ion is related to the pH and pKw.
to:
Once the pH is measured, it must be translated into a hydroxide concentration for use in these calculations. The concentration of hydroxide ion is related to the pH as measured by the probe and pKw which is temperature dependent.
Changed lines 42-43 from:
The self ionization of water as indicated by pKw is dependent on the temperature'^2,3^'
to:
More information is contained in the experimental data when the temperature is varied throughout the one hour run. The variable temperature also causes the pKw to change. The self ionization of water as indicated by pKw is dependent on the temperature'^2,3^'
Deleted line 46:
March 25, 2013, at 09:33 AM by 69.169.188.188 -
Changed lines 28-34 from:
The measured amount of Ethyl Acetate is added to the Sodium Hydroxide solution. The temperature and pH are measured over the course of an hour to record the data for analysis. The concentration of hydroxide ion is related to the pH and pKw.
to:
The measured amount of Ethyl Acetate is added to the Sodium Hydroxide solution. The temperature and pH are measured over the course of an hour to record the data for analysis. Download the sample scripts and model files below for a starting point for the dynamic simulation and parameter estimation.

Attach:download.jpg [[Attach:ethyl_acetate.zip | Download APM Python and MATLAB Files]]

-> Attach:ethyl_acetate_results.png

The concentration of hydroxide ion is related to the pH and pKw.
March 25, 2013, at 09:27 AM by 69.169.188.188 -
Changed lines 51-70 from:
-> [3] Wikipedia, [[http://en.wikipedia.org/wiki/Self-ionization_of_water|Self-ionization of water]], URL: http://en.wikipedia.org/wiki/Self-ionization_of_water.
to:
-> [3] Wikipedia, [[http://en.wikipedia.org/wiki/Self-ionization_of_water|Self-ionization of water]], URL: http://en.wikipedia.org/wiki/Self-ionization_of_water.

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March 25, 2013, at 09:24 AM by 69.169.188.188 -
Changed lines 30-31 from:
-> -log(C'_OH'^-^'_')= pKw - pH
to:
-> -log'_10_'(C'_OH'^-^'_')= pKw - pH
Added lines 39-40:

-> Attach:pKw_temperature_dependence.png
March 25, 2013, at 09:23 AM by 69.169.188.188 -
Changed lines 28-29 from:
The measured amount of Ethyl Acetate is added to the Sodium Hydroxide solution. The temperature and pH are measured over the course of an hour to record the data for analysis. The concentration of hydroxide ion is related to the pH by the following correlations that accounts for the temperature dependency of pKw'^2^'.
to:
The measured amount of Ethyl Acetate is added to the Sodium Hydroxide solution. The temperature and pH are measured over the course of an hour to record the data for analysis. The concentration of hydroxide ion is related to the pH and pKw.
Changed lines 31-32 from:
-> pKw = 4470.99 / T - 6.0875 + 0.01706 T
to:
Added lines 36-40:
The self ionization of water as indicated by pKw is dependent on the temperature'^2,3^'

-> pKw = 4470.99 / T(K) - 6.0875 + 0.01706 T(K)

Changed lines 47-49 from:
-> [2] Whitfield, M. (1975). Chemical Oceanography. In J. P. Riley, & E. Skirrows, Vol. 2 2nd Ed. (pp. 44-171). Academic, New York.
to:
-> [2] Whitfield, M. (1975). Chemical Oceanography. In J. P. Riley, & E. Skirrows, Vol. 2 2nd Ed. (pp. 44-171). Academic, New York.

-> [3] Wikipedia, [[http://en.wikipedia.org/wiki/Self-ionization_of_water|Self-ionization of water]], URL: http://en.wikipedia.org/wiki/Self-ionization_of_water
.
March 25, 2013, at 09:07 AM by 69.169.188.188 -
Added lines 17-20:
This reaction has been studied previously and literature values provide starting values for the parameter estimation'^1^'.

-> Attach:ethyl_acetate_lit_values.png

Changed lines 28-29 from:
The measured amount of Ethyl Acetate is added to the Sodium Hydroxide solution. The temperature and pH are measured over the course of an hour to record the data for analysis. The concentration of hydroxide ion is related to the pH by the following correlations that accounts for the temperature dependency of pKw'^1^'.
to:
The measured amount of Ethyl Acetate is added to the Sodium Hydroxide solution. The temperature and pH are measured over the course of an hour to record the data for analysis. The concentration of hydroxide ion is related to the pH by the following correlations that accounts for the temperature dependency of pKw'^2^'.
Changed lines 41-43 from:
-> [1] Whitfield, M. (1975). Chemical Oceanography. In J. P. Riley, & E. Skirrows, Vol. 2 2nd Ed. (pp. 44-171). Academic, New York.
to:
-> [1] Laidler, K. J.  and Chen, D. (1957). The influence of pressure on the kinetics of the alkaline hydrolysis of esters and amides. Trans. Faraday Soc., 1958,54, 1026-1033, DOI: 10.1039/TF9585401026 [[http://pubs.rsc.org/en/content/articlelanding/1958/TF/tf9585401026 | View Article]]

-> [2
] Whitfield, M. (1975). Chemical Oceanography. In J. P. Riley, & E. Skirrows, Vol. 2 2nd Ed. (pp. 44-171). Academic, New York.
March 25, 2013, at 08:55 AM by 69.169.188.188 -
Changed lines 12-13 from:
Determine the kinetic parameters for the Ethyl-Acetate/Sodium Hydroxide reaction including the rate constant, reaction order, and activation energy for the reaction.
to:
Determine the kinetic parameters for the Ethyl-Acetate/Sodium Hydroxide reaction including the pre-exponential factor (''A''), reaction orders (''α'' and ''β''), and activation energy (''E'_a_''') for the reaction.
Changed lines 15-37 from:
-> k = A exp(-E'_a_'/RT)
to:
-> k = A exp(-E'_a_'/RT)

The data is obtained by operating a glass reaction vessel with the following supplies:

* Fisher Scientific accumet XL60 pH meter and probe
* Benchtop heat exchanger
* 95.5 wt.% Ethyl Acetate
* Sodium Hydroxide solution

The measured amount of Ethyl Acetate is added to the Sodium Hydroxide solution. The temperature and pH are measured over the course of an hour to record the data for analysis. The concentration of hydroxide ion is related to the pH by the following correlations that accounts for the temperature dependency of pKw'^1^'.

-> -log(C'_OH'^-^'_')= pKw - pH
-> pKw = 4470.99 / T - 6.0875 + 0.01706 T

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References

-> [1] Whitfield, M. (1975). Chemical Oceanography. In J. P. Riley, & E. Skirrows, Vol. 2 2nd Ed. (pp. 44-171). Academic, New York.
March 25, 2013, at 08:40 AM by 69.169.188.188 -
Changed line 15 from:
->-> k = A exp(-E'_a_'/RT)
to:
-> k = A exp(-E'_a_'/RT)
March 25, 2013, at 08:40 AM by 69.169.188.188 -
Changed lines 14-15 from:
-> r = k C'_OH_''^α^' C'_Et-Ac_''^β^'  with k = A exp(-E'_a_'/RT)
to:
-> r = k C'_OH_''^α^' C'_Et-Ac_''^β^'
->-> k = A exp(-E'_a_'/RT)
March 25, 2013, at 08:40 AM by 69.169.188.188 -
Changed lines 14-15 from:
-> r = k C'_OH_''^α^' C'_Et-Ac_''^β^'
-> with k = A exp(-E'_a_'/RT)
to:
-> r = k C'_OH_''^α^' C'_Et-Ac_''^β^'  with k = A exp(-E'_a_'/RT)
March 25, 2013, at 08:39 AM by 69.169.188.188 -
Changed lines 14-15 from:
-> r = k C'_OH_''^α^' C'_Et-Ac_''^β^'
to:
-> r = k C'_OH_''^α^' C'_Et-Ac_''^β^'
-> with k = A exp(-E'_a_'/RT)
March 25, 2013, at 08:38 AM by 69.169.188.188 -
March 25, 2013, at 08:37 AM by 69.169.188.188 -
Added lines 13-14:

-> r = k C'_OH_''^α^' C'_Et-Ac_''^β^'
March 25, 2013, at 08:36 AM by 69.169.188.188 -
Changed line 10 from:
-> CH'_2_'COOCH'_2_'CH'_3_' + NaOH → CH'_2_'COO'^-^'  Na'^+^' CH'_3_'CH'_2_'OH
to:
-> CH'_2_'COOCH'_2_'CH'_3_' + NaOH → CH'_2_'COO'^-^'  Na'^+^' + CH'_3_'CH'_2_'OH
March 25, 2013, at 08:36 AM by 69.169.188.188 -
Added lines 1-12:
(:title Estimate Ethyl Acetate Kinetic Parameters from Dynamic Data:)
(:keywords nonlinear, optimization, engineering optimization, dynamic estimation, interior point, active set, differential, algebraic, modeling language, university course, Ethyl Acetate:)
(:description Case study on dynamic reconciliation for kinetic modeling using optimization techniques in engineering for Ethyl Acetate kinetics:)

!!!! Case Study on Dynamic Parameter Estimation


This assignment contains a kinetic analysis of several experiments using the reaction of Ethyl Acetate with Sodium Hydroxide to produce Ethanol and Sodium Acetate.

-> CH'_2_'COOCH'_2_'CH'_3_' + NaOH → CH'_2_'COO'^-^'  Na'^+^' CH'_3_'CH'_2_'OH

Determine the kinetic parameters for the Ethyl-Acetate/Sodium Hydroxide reaction including the rate constant, reaction order, and activation energy for the reaction.
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