I am analyzing themogravimetric data (TGA) to determine kinetic parameters of thermal reaction of oil using Coats and Redfern method.
A plot of either ln{[(1-(1-a)1-n]/[T2(1-n)]} against 1/T or for n= 1, In{-ln(1-a)]/T2} against 1/T should yield a straight line with a slope ( -E/R) for the correct value of n.
Where a = fraction of the reactant decomposed at time t. Therefore, (1-a) = the remaining weight percent of the reactant.
The value of E obtained graphically is then used to calculate the pre-exponential factor.
I am validating my calculation using the data extracted from the work of Kamal N. Jha and Bela Verkoczy (The attached file "The Role of Thermal Analysis Techniques in the In-Situ Combustion Process"). In the attached calculation file (.xls), the calculated slopes are from 765 to 1074 for the temperature range of 140~360 oC. By multiplying the slopes to R (8.314 J/mol.K), the activation energy are from 6360~8930 J/mol. The results are much smaller than the values in the study of Jha and Verkoczy. Please refer to the excel file for your review.
I would like to hear your opinions and suggestions about this topic.
You fit over 140 - 360 oC. The reference fits over 50 - 260 oC and 260 - 400 oC. Why are you using one temperature range that is different from the reference?
Thank you for your answer, Dr. Jeffrey J. Weimer
As in my calculation sheet, the data was for Oil A in Helium (extracted from Fig. 4, pp. 332). The calculation results was then compared to that in Table 2 (pp. 334). The temperature range in my calculation (140 - 360 oC) match to the reference range (150 - 360 oC).
Could you let me know where did you get the reference temperature range?
Was I misunderstood somewhere? Please help me to figure out the errors.
I still do not understand why do we have to fit the data to the temperature ranges in Table 4 while the estimated kinetic parameters were reported in different temperature ranges Table 2.
Could you please explain more details about this reason?
I do not know. I only guessed.
I see one other possible mistake. The alpha parameter is not weight percent of compound. It is the relative weight loss.
For anything after this, you are best to contact the authors of the paper.
Thank you for your answer, Dr. Jeffrey J Weimer
I have updated the calculation sheet with alpha.
The alpha (a) is defined by:
a=(wi-wt)/wi-wf)
where wi, wt, and wf are the weight of sample at the initial, at time t, and final time, respectively.
In my calculation, the alpha was defined as:
a=(100-%TGt)/(100-%TGf)
The updated results show a slightly change compared to the previous results when alpha was not applied. The estimated activation energies are still very small compared to that reported by Kamal N. Jha and Bela Verkoczy.
I am going to contact the authors of the paper to ask for this matter.
Please check the following paper 10.1031@j15062a003 for Freeman paper
Thank you for your answer, Dr. Revathy Rajagopal
I cannot find the paper of Freeman with your suggested ID. Could you please give me the name of the paper?
Thank you very much.
Thank you for your suggested paper, Dr. Revathy Rajagopal
The method used in Freeman's paper is quite complicated. The method used in another paper "Kinetic Parameters from Thermogravimetric Data" by Coats and Redfern is an improved version compared to Freeman's method.
I have also applied Coats and Redfern's method on another dataset extracted from another study of Bela and Jha. The results show less difference between the calculated activation energy and that reported by Bela and Jha (28 kJ/mol compared to 32 kJ/mol).
Please give me your opinions and suggestions.
the value of alpha always lies between 0 to 1 in this kind of calculations. it starts from 0 and end up at 1. There is no other possibility. The updates file you shared later in comments with addition of a coulmn ( title alpha) doesn,t start with 0 value of alpha . its the calculation mistake, otherwise the formula for alpha calculation u mentioned is absolutly correct.
Alpha= (W0- Wt)/(W0-Wf)
where W0 is the initial weight
Wt is the weight at time t
Wf is the final weight at end of reaction.
Therefore fractional conversion should start from 0 when there is no change in weight.This will raise from zero with passage of reaction and end up at one. Its also dimension less.
Furthermore , i guess that you didn,t take the correct formulation of model ( g(alpha) for n=1 or when n is not equal to one. kindly recheck. whole calculation depends on correct inserting of data in correct formula. Attachement is your updated file . i am attaching it with corrected value of Alpha.
Nita Dragoe , Would you kindly let me know, what do you mean by overlapped processes? Is that about multi reaction( dehydration, devolatization, gragmentation or depolymerization , repolymerization etc) with in process OR its a term used in errors related with Data procesing?
Regards
what i want know how you can fixed the order of any reaction at XLX i can see all have take n=1;1/2/13... it is possible to know this value from equation de activited réaction
- Badges
- Science topic
- Similar topics
- Engineering
- Materials Engineering
- Coating