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Aim: Creating the model of thermal decomposition of energetic material (tetryl). Data:4 results (data sets) of DSC experiment carried out in linear heating mode at different temperature ramps Models:Two competing single-stage models – of N-order reaction (1) and of generalized autocatalysis (2) (1) (2) will be examined Aim: Creating the model of thermal decomposition of energetic material (tetryl). Data:4 results (data sets) of DSC experiment carried out in linear heating mode at different temperature ramps Models:Two competing single-stage models – of N-order reaction (1) and of generalized autocatalysis (2) (1) (2) will be examined ForK Tutorial Exercise 3 Evaluating the kinetic model of thermal decomposition from DSC data Continue Run Scoring

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ForK Tutorial. Exercise 3 Evaluating kinetic model of thermal decomposition from DSC data Select Estimation mode

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Preparing the project: Adding 4 experimental data sets

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Viewing data on the Chart (using the Show plot command) View derivative responses (dQ/dt)

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Plan of evaluation procedure. 1. Getting rough estimates of kinetic parameters using data sets for temperature ramps 2 and 3 K/min for the competing models. 2. Validating the results by adding data sets for temperature ramps 0.5 and 1 K/min. 3. Selecting more appropriate model. 4. Running non-linear parameters estimation on the basis of 4 data sets. Plan of evaluation procedure. 1. Getting rough estimates of kinetic parameters using data sets for temperature ramps 2 and 3 K/min for the competing models. 2. Validating the results by adding data sets for temperature ramps 0.5 and 1 K/min. 3. Selecting more appropriate model. 4. Running non-linear parameters estimation on the basis of 4 data sets. Click here to continue

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1. Defining the 0 weight of data sets for 0.5 and 1 K/min (These data sets will me omitted when parameters estimation) 00 2. Defining the model

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1. Creating the single stage model of N-order type

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2. Estimating the initial guess on kinetic parameters (using the Arrhenius method)

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Comparison of experiment and simulation based on initial parameters guess

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Observation 1 Activation energy is too big for a reaction proceeding in the temperature interval 140 220 o C Next step is to check how the model predicts reaction course at smaller temperature ramps.

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1. Returning to the weight=1 for data sets for 0.5 and 1 K/min 00 2. Viewing how the N-order model predicts reaction course

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Observation 2 The N-order model doesnt allow proper prediction of the reaction course – the simulated peaks appear later than experimental ones. Next step is to examine the alternative model of generalized autocatalysis. As earlier data sets for 2 and 3 K/min will be used for the analysis

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1. Defining the 0 weight of data sets for 0.5 and 1 K/min 00 2. Defining the model

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Changing the model type

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Estimating the initial guess on kinetic parameters (using the Arrhenius method)

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Comparison of experiment and simulation based on initial parameters guess

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Observation 1 Activation energy matches the reactions temperature interval though the shape of peaks simulated is somewhat distorted in comparison with the experimental peaks Next step is to check how the model predicts reaction course at lower temperature ramps.

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1. Returning to the weight=1 for data sets for 0.5 and 1 K/min 00 2. Viewing how the autocatalytic model predicts reaction course

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Observation 2 The autocatalytic model with the rough parameters estimates evaluated by using the simplified (Arrhenius) method doesnt provide appropriate fit of peaks shape but predicts properly location of the peaks. Next step is to run non-linear parameters estimation and check whether the model is capable of fitting all the data available.

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Adjusting numerical methods for parameters estimation and run estimation 1. Defining precision of numerical integration 2. Defining numerical methods that will be used 0.0000001 3. Run nonlinear estimation

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Value of the objective function SS before estimation Run optimization (using the tensor method in mode 1)

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Resultant value of the objective function SS. Estimation has been stopped manually when no further progress had been observed Use the Plot for viewing the results on the Chart

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Comparison of experiment and simulation based on final parameters vector. Solid lines – simulation. 1. Integral responses.

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Comparison of experiment and simulation based on final parameters vector. Solid lines – simulation. 2. Derivatives. The resultant kinetic model provides good fit of all the existing data. Estimates of the kinetic parameters are very reasonable. Conclusion: The kinetics created is in satisfactory agreement with experimental data and can be accepted for further use.

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The last step is to save the kinetics evaluated into the data volume. Calling the Save as option

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The 3 rd Exercise is over. Press [Esc] to close presentation. If you have ForK installed we recommend to repeat this exercise by yourself using demo data

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