A TITO Control Strategy to Increase Productivity in Uncertain Exothermic Continuous Chemical Reactors
Round 1
Reviewer 1 Report
This is a manuscript dealing with a very interesting topic, as it is control of continuous chemical reactors during different scenarios that can take place in a exothermic reaction. The manuscript needs significant improvements before it could be accepted for publication, starting by a thorough revision of the English language. It is highly deficient in its current form and often impedes to follow the discussion made by the authors. There are many syntax and grammar mistakes, as well as mispelled words.
Next, the manuscript is messy and has not been carefully prepared as concerns a clear description of all the assumptions, methods and hypotheses. Given the vast amount and the degree of complexity of the nomenclature use, a notation/abbreviations list is definitely missing, with many symbols and letters that are confusing and not carefully explained. In addition, some paragraphs of the Results section belong to other sections.
But foremost, the most troublesome aspect of the study presented here is the lack of experimental validation against empirical data and the extent of the study, which is somewhat poor and could have analyzed more in depth the case study presented. There are many exothermic reactions in which temperature gradients are an issue. However, the authors have overlooked this critical aspect by assuming an isothermal condition regulated by an idealized refrigerating system. This can only be valid in limited occasions, and somehow limits the impact of the findings presented here. The same can be argued about the lack of study of other important factors, namely the effect of pressure or analyzing other possible reaction orders apart from first order. Which is a pity, because the study could be very useful for many process and chemical engineers, but not with this limited and oversimplified case study.
Further comments:
- The state-of-the-art in the topic must be enhanced to adequately present previous efforts in this research line. For instance, lines 36-39: the authors claim that several control strategies have been presented in the open literature, but they just provide lump citations, without clearly explaining what these different control strategies are. The same applies to lines 58-60. What are the different approaches considering the uncertainties for the optimization of chemical processes? What were the main findings/conclusions from those cited works?
The rationale of the work has not been clearly presented. What has led to the approach presented here? What are the main reasons for adopting such strategy and not others? What is the differential advantage of following such strategy in comparison to the previous approaches/strategies in the literature?
- Methods: a CSTR reactor was assumed. The authors did not clearly explain that the material balance assumes no accumulation of of material over time and probably reactor volume is constant. All hypotheses assumed should be clearly explained in the text for readers' convenience. The same applies to the energy balance, which has been oversimplified. In fact, the explanatory paragraph on lines 84-90 should appear first at the beginning of Section 2 to clarify more the description of the case study. In line with this, a schematic diagram of the chemical process installation studied including process symbols and exactly signalling where the positions of the control loops and other auxiliary equipment (e.g. cooling jackets, stirrer, etc.) would help the reader understand better the case study presented here.
- Eqs. 3-6, according to the authors involve the use of dimensionless variables, but the dimensional analysis of the equations is impossible because some of the parameters/symbols are not clearly explained. Therefore, it is impossible for any reader to completely understand how these magnitudes were made dimensionless. The authors must make more efforts to clarify all the terms and symbols. For instance, how is A, mass concentration of reactive A made dimensionless? Without a proper explanation anyone would assume that such magnitude has dimensions. And what do the different parameters on lines 96-97 represent?
The statements on lines 99-102 are debatable to say the least, considering that many of those industrial cases involve reactions with heat and mass transfer limitations and follow kinetics of reaction orders different to 1 in many cases (not to mention that the reactor configuration rarely is CSTR in some of those cited industrial cases). Unless a proper, precise real case is presented to readers that is truly representative of the case study analyzed in this work, this paragraph is not acceptable.
Lines 105-120 belong to the Introduction section and should be moved there. Lines 120-177 describe the methodology and do not actually show results, and therefore they should be moved to Section 2 Materials and methods. The same applies to lines 179-182
The authors should carefully explain how they defined reactors' productivity and how it was made dimensionless. Please, also check Fig. 1 caption: presumably it is Open-loop dynamic... and not Closed-loop, according to the discussion in the text.
Acronyms should be written in full form the first time they appear on the text. (e.g., line 190, whtat does IMC stand for?
Figure 3 has not been presented in the text nor has been discussed.
Figure 7: rather than portrait it should be renamed as diagram. Please revise thoroughly the English language.
Author Response
The authors are very grateful with the academic editors of the journal for the opportunity to submit again a corrected version of the corresponding manuscript, also with the anonymous reviewers for his/her valuable comments, which help substantially to improve the technical content and readability of our proposal. We try to reply adequately to all the comments made for the reviewers and the corrections are now included in the corrected version of the manuscript and are highlighted in yellow color.
Reviewers Reply.
Reviewer 1.
Comment 1.- This is a manuscript dealing with a very interesting topic, as it is control of continuous chemical reactors during different scenarios that can take place in an exothermic reaction. The manuscript needs significant improvements before it could be accepted for publication, starting by a thorough revision of the English language. It is highly deficient in its current form and often impedes to follow the discussion made by the authors. There are many syntax and grammar mistakes, as well as misspelled words. Next, the manuscript is messy and has not been carefully prepared as concerns a clear description of all the assumptions, methods, and hypotheses.
Reply 1.- Thank you for your valuable comments. The manuscript was completely revised and corrected. A detailed description of the corresponding assumption, methods and other hypotheses are carefully considered in the new version of the manuscript.
Comment 2.- Given the vast amount and the degree of complexity of the nomenclature use, a notation/abbreviations list is missing, with many symbols and letters that are confusing and not carefully explained. In addition, some paragraphs of the Results section belong to other sections. But foremost, the most troublesome aspect of the study presented here is the lack of experimental validation against empirical data and the extent of the study, which is somewhat poor and could have analyzed more in depth the case study presented.
Reply 2.- We are very grateful for your important comment. A detailed notation is now included in the corrected version of the manuscript and the text was restructured to avoid confusion and provide an adequate understanding to our main ideas. Related with the experimental validation of our proposed control strategy, in this stage the main goal of our proposal is to demonstrate, theoretically, the correctness of our proposal under the framework of variational calculus for the optimal control design. As usual, the first steps on the new control designs procedures are related to demonstrate analytically the correctness of the proposed design under the most common assumptions considered for the system under study and via numerical simulations show the corresponding performance to analyze possible future implementation, so the real-time implementation will be considered as a future work.
Comment 3.-There are many exothermic reactions in which temperature gradients are an issue. However, the authors have overlooked this critical aspect by assuming an isothermal condition regulated by an idealized refrigerating system. This can only be valid in limited occasions, and somehow limits the impact of the findings presented here.
Reply 3.- Thank you for your comment. Effectively, exits several chemical processes with temperature and concentration gradients, which are generally performed in tubular reactors. However, in this proposal is considered a homogeneous chemical reactor named continuous stirred tank reactor (CSTR), where a perfect mixing (very common assumption) is considered in the chemical rector, avoiding temperature and concentration gradients. On the other hand, temperature regulation in CSTR has been analyzed previously in the open literature and the control strategy is generally the same; regulate the temperature of the reactor via the temperature of the cooling jacket, considering that the dynamic behavior of it is faster that the reactor´s dynamic and then, the cooling jacket process is assumed in steady state, which is a typical assumption for control purposes (see corresponding references in the text). Properly we not assuming isothermal condition, in the proposed closed-loop strategy, as a first stage, the reactor is regulated to operate in isothermal condition via a Proportional-Integral controller, where the selected temperature setpoint provide an increase of the chemical product concentration via thermal effect in the corresponding reaction rate. The isothermal closed-loop operation is one of the most common tasks in the process operation to assure for example process security, therefore it is a valid consideration for exothermic chemical reactors.
Comment 4.-The same can be argued about the lack of study of other important factors, namely the effect of pressure or analyzing other possible reaction orders apart from first order. Which is a pity, because the study could be very useful for many process and chemical engineers, but not with this limited and oversimplified case study.
Reply 4.- We are agreed with your comment and effectively exist a lot of physical and chemical phenomena in reacting systems, however the inclusion of them in a mathematical model is a very difficult task, from the above and considering the modeling purposes, a set of common assumptions are considered to develop mathematical processes models. The mathematical modeling for control theory purposes has considered generally ordinary differential equation for the chemical reactor representation, which is, as usual, adequate for CSTR.
Additionally, we change the application case, then a new model of an exothermic CSTR with a Van de Vusse kinetic model, where there exist parallel and series chemical reactions in the chemical network.
Further comments: - The state-of-the-art in the topic must be enhanced to adequately present previous efforts in this research line. For instance, lines 36-39: the authors claim that several control strategies have been presented in the open literature, but they just provide lump citations, without clearly explaining what these different control strategies are. The same applies to lines 58-60. What are the different approaches considering the uncertainties for the optimization of chemical processes? What were the main findings/conclusions from those cited works?
Reply 5.- We are agreed with your comment. The introduction and other sections were rewritten in accordance with this query.
Comment 6.- The rationale of the work has not been clearly presented. What has led to the approach presented here? What are the main reasons for adopting such strategy and not others? What is the differential advantage of following such strategy in comparison to the previous approaches/strategies in the literature?
Reply 6.- Thank you for your observation. We try to include in the corrected version of the manuscript a better description and explanation of our work.
Comment 7.- Methods: a CSTR reactor was assumed. The authors did not clearly explain that the material balance assumes no accumulation of material over time and probably reactor volume is constant. All hypotheses assumed should be clearly explained in the text for readers' convenience. The same applies to the energy balance, which has been oversimplified. In fact, the explanatory paragraph on lines 84-90 should appear first at the beginning of Section 2 to clarify more the description of the case study.
Reply 7.- Effectively, a CSTR reactors is assumed as process under study. We present a dynamic model of the chemical reactor, so the time derivatives, related with the accumulation terms, are always considered in our analysis. The corrected manuscript contains a detailed assumption for the new considered CSTR model, for example, we consider that the input and output volumetric flows are equal, and the reactor volume is constant, note that this are common assumption in simplified CSTR models for control purposes.
Comment 8.- In line with this, a schematic diagram of the chemical process installation studied including process symbols and exactly signaling where the positions of the loops and other auxiliary equipment (e.g. cooling jackets, stirrer, etc.) would help the reader understand better the case study presented here.
Reply 8.- This comment is considered in the new version of the manuscript (see Figure 1).
Comment 9.- Eqs. 3-6, according to the authors involve the use of dimensionless variables, but the dimensional analysis of the equations is impossible because some of the parameters/symbols are not clearly explained. Therefore, it is impossible for any reader to completely understand how these magnitudes were made dimensionless. The authors must make more efforts to clarify all the terms and symbols. For instance, how is A, mass concentration of reactive A made dimensionless? Without a proper explanation anyone would assume that such magnitude has dimensions. And what do the different parameters on lines 96-97 represent?
Reply 9.- We consider your comment. A new application example is now considered, this new model is presented in original variables.
Comment 10.- The statements on lines 99-102 are debatable to say the least, considering that many of those industrial cases involve reactions with heat and mass transfer limitations and follow kinetics of reaction orders different to 1 in many cases (not to mention that the reactor configuration rarely is CSTR in some of those cited industrial cases). Unless a proper, precise real case is presented to readers that is truly representative of the case study analyzed in this work, this paragraph is not acceptable.
Reply 10.- You are right. Considering the new application example, the paragraph was deleted.
Comment 11.- Lines 105-120 belong to the Introduction section and should be moved there.
Reply 11.- Thank you for the comment, it is now considered.
Comment 12.- Lines 120-177 describe the methodology and do not actually show results, and therefore they should be moved to Section 2 Materials and methods. The same applies to lines 179-182 The authors should carefully explain how they defined reactors' productivity and how it was made dimensionless.
Reply 12.- That you for the comment, it is now considered. The reactor´s productivity is calculated by the product of the corresponding output flow and the outlet B concentration.
Comment 13.- Please, also check Fig. 1 caption: presumably, it is Open-loop dynamic... and not Closed-loop, according to the discussion in the text.
Reply 13.- Thank you, it was checked.
Comment 14.- Acronyms should be written in full form the first time they appear on the text. (e.g., line 190, what does IMC stand for?
Reply 14.- Thank you, it was checked. Internal Model control IMC.
Comment 15.- Figure 3 has not been presented in the text nor has been discussed.
Reply 15.- That you for the comment, a new set of figures is now considered.
Comment 16.- Figure 7: rather than portrait it should be renamed as diagram. Please revise thoroughly the English language.
Reply 16.- Ok, a new set of figures is now considered. The language was revised.
We are grateful with yours comments.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
corrections to minor methodological errors and text editing
Author Response
The authors are very grateful with the academic editors of the journal for the opportunity to submit again a corrected version of the corresponding manuscript, also with the anonymous reviewers for his/her valuable comments, which help substantially to improve the technical content and readability of our proposal. We try to reply adequately to all the comments made for the reviewers and the corrections are now included in the corrected version of the manuscript and are highlighted in yellow color.
Reviewers Reply.
Reviewer 2.
Comment .- Corrections to minor methodological errors and text editing
Reply.- Thank you for your comment. The manuscript was completely revised and corrected. A detailed description of the corresponding assumption, methods and other hypotheses are carefully considered in the new version of the manuscript.
Author Response File: Author Response.pdf
Reviewer 3 Report
Authors Aguilar-López et al. have composed a very interested manuscript titled: "A TITO Control Strategy to Increase Productivity in Uncertain
Exothermic Continuous Chemical Reactors". The manuscript deals with the optimal control of an exothermic reactor, taking into account reactor productivity as the main optimization criteria. The manuscript can be of high interest to readers but it requires significant changes before publishing. These changes should include:
1) English language is nowhere near the satisfactory level required for publishing. Many sentences (especially in Introduction) are very hard to understand and even have wrong meaning. This is totally unacceptable and perhaps the authors should find a native English speaker to go through the whole manuscript.
2) Introduction seems too short and hastily done. Apart from unsatisfactory English language in it, it lacks important references from the optimal control, lifting of a nonlinear system, by adding additional dynamic equations etc. Most of all, Introduction should give in the end a reason why the manuscript is done in the first place, hint at the novelty, which seems to be completely missing also in the Conclusions.
3) The model equations shown in the second part of the manuscript should be done in a more transparent way. Equations 1 and 2 should be written in the same form as Equations 3, 4 and 5, and nondimensional variables should be defined in mathematical form so that all readers can see how Eq. 3, 4 and 5 transpire from Eq. 1 and 2. Also, while defining all constants it would be good to have some units so that the results themselves could have some physical meaning behind them.
4) Same as in 3, without any units, what time are we talking about? Is time in Figure 1-5, in seconds, minutes, hours, or something else? The two most important criteria for any process control are: time, and stability. Productivity is completely irrelevant if the process is not stable (or very close to instability zone) or if the control is too slow. The authors have given very little attention to these most important process control criteria. They should analyze this by showing additional graphs (maybe in Laplace domain) or doing a parallel optimization in which they would also prioritize control time.
5) The authors should also significantly improve the Conclusions and make it clear how their research is different than other papers found in academia and what the novelty is.
Author Response
The authors are very grateful with the academic editors of the journal for the opportunity to submit again a corrected version of the corresponding manuscript, also with the anonymous reviewers for his/her valuable comments, which help substantially to improve the technical content and readability of our proposal. We try to reply adequately to all the comments made for the reviewers and the corrections are now included in the corrected version of the manuscript and are highlighted in yellow color.
Reviewers Reply.
Reviewer 3.
1) English language is nowhere near the satisfactory level required for publishing. Many sentences (especially in Introduction) are very hard to understand and even have wrong meaning. This is totally unacceptable and perhaps the authors should find a native English speaker to go through the whole manuscript.
Reply 1.- We are very sorry for these mistakes; the corrected version of the manuscript is now revised.
2) Introduction seems too short and hastily done. Apart from unsatisfactory English language in it, it lacks important references from the optimal control, lifting of a nonlinear system, by adding additional dynamic equations etc. Most of all, Introduction should give in the end a reason why the manuscript is done in the first place, hint at the novelty, which seems to be completely missing also in the Conclusions.
Reply 2.- Thank you for your valuable comment. A practically new Introduction section is proposed to include a more detailed information.
3) The model equations shown in the second part of the manuscript should be done in a more transparent way. Equations 1 and 2 should be written in the same form as Equations 3, 4 and 5, and nondimensional variables should be defined in mathematical form so that all readers can see how Eq. 3, 4 and 5 transpire from Eq. 1 and 2. Also, while defining all constants it would be good to have some units so that the results themselves could have some physical meaning behind them.
Reply 3.- Thank you for your observation. A new mathematical model of the rector considered as application case is now included, it is presented in the original phenomenological variables.
4) Same as in 3, without any units, what time are we talking about? Is time in Figure 1-5, in seconds, minutes, hours, or something else? The two most important criteria for any process control are: time, and stability. Productivity is completely irrelevant if the process is not stable (or very close to instability zone) or if the control is too slow. The authors have given very little attention to these most important process control criteria. They should analyze this by showing additional graphs (maybe in Laplace domain) or doing a parallel optimization in which they would also prioritize control time.
Reply 4.- We are agreed with your comments. Some paragraphs with stability of the zero dynamic of the reactor are now included.
5) The authors should also significantly improve the Conclusions and make it clear how their research is different than other papers found in academia and what the novelty is.
Reply 5.- The conclusion section was improved to clarify the contribution of the proposed work.
Author Response File: Author Response.pdf
Reviewer 4 Report
The paper presents an optimal control and compares its performance with a traditional one. The motivation of the paper is clearly stated and the problem is solved correctly. However, in my opinion, the model used is too simplified, which limits the contribution of the research. The main point here is that a power-law type reaction rate is used. The paragraph after equation 6 says that such rates are valid for Fisher-Tropsch, pyrolysis and combustion of sulphur species. I can tell that those systems follow complex mechanisms. For example, the water-gas shift reaction (Fisher-Tropsch) follows a highly complex reaction rate that can be found here https://doi.org/10.1016/j.cej.2020.124181. Pyrolysis involves hundreds of simultaneous reactions (https://doi.org/10.1016/j.wasman.2016.10.024), but none of them is useful for process control when considered individually. I can tell also that the contact process (sulphur oxidation) also follows a highly complex reaction rate and is thermodynamically limited by equilibrium. The three examples mentioned present large thermal effects, hence, constant properties should not be used. I believe that the paper is still a contribution, but the applicability of the results must be stated more carefully, otherwise, will drive further readers to a wrong conclusion.
As the authors should know, the control will perform well if the model is reliable. So, what would be more interesting would be to use a realistic reaction rate to estimate the response of the system, but a simplified one (power-law) to compute the action of the controller. That would be a much better contribution since it reflects a "real world" situation. Otherwise, the limitations of the research must be more clearly stated in the manuscript
Other minor observations:
1. A nomenclature table would be very useful. The value/meaning of several symbols is missing or hard to find
2. The mathematical expressions for the non-denationalization of the variables should be added to the manuscript
3. The font size of the figures is too small. Please make it larger.
Author Response
The authors are very grateful with the academic editors of the journal for the opportunity to submit again a corrected version of the corresponding manuscript, also with the anonymous reviewers for his/her valuable comments, which help substantially to improve the technical content and readability of our proposal. We try to reply adequately to all the comments made for the reviewers and the corrections are now included in the corrected version of the manuscript and are highlighted in yellow color.
Reviewers Reply.
Reviewer 4.
Comment 1.- The paper presents an optimal control and compares its performance with a traditional one. The motivation of the paper is clearly stated, and the problem is solved correctly. However, in my opinion, the model used is too simplified, which limits the contribution of the research. The main point here is that a power-law type reaction rate is used.
Reply 1.- Thank you for this important comment, we change the application case and a CSTR model which consider a Van de Vuss reaction is now considered, so the results and discussions are completely new.
Comment 2.- The paragraph after equation 6 says that such rates are valid for FisherTropsch, pyrolysis and combustion of sulphur species. I can tell that those systems follow complex mechanisms. For example, the water-gas shift reaction (FisherTropsch) follows a highly complex reaction rate that can be found here https://doi.org/10.1016/j.cej.2020.124181. Pyrolysis involves hundreds of simultaneous reactions (https://doi.org/10.1016/j.wasman.2016.10.024), but none of them is useful for process control when considered individually. I can tell also that the contact process (sulphur oxidation) also follows a highly complex reaction rate and is thermodynamically limited by equilibrium. The three examples mentioned present large thermal effects; hence, constant properties should not be used.
Reply 2.- Thank you again for your comment, considering the new proposed model as the application case, the corresponding paragraph is not relevant, so it was deleted.
Comment 3.- I believe that the paper is still a contribution, but the applicability of the results must be stated more carefully, otherwise, will drive further readers to a wrong conclusion. As the authors should know, the control will perform well if the model is reliable. So, what would be more interesting would be to use a realistic reaction rate to estimate the response of the system, but a simplified one (power-law) to compute the action of the controller. That would be a much better contribution since it reflects a "real world" situation. Otherwise, the limitations of the research must be more clearly stated in the manuscript.
Reply 3.- Ok, as mentioned above, a new reactor´s model is now considered, we believe that this model is more realistic and the corresponding results in our proposal can be better.
Comment 4.- Other minor observations: 1. A nomenclature table would be very useful. The value/meaning of several symbols is missing or hard to find 2. The mathematical expressions for the non-denationalization of the variables should be added to the manuscript 3. The font size of the figures is too small. Please make it larger.
Reply 4.- we are grateful with yours comments. The corrected version of the manuscript contains a detailed nomenclature of the used variables and its numerical values. As well ass, a new set of figures is included.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
The authors have made significant efforts to give adequate responses to the different issues raised in the previous round of revisions. The changes made to the manuscript have enhanced it. I think the manuscript can be accepted for publication once that the English language has been polished. There are various statements starting with the term 'Now' and some long statements including various commas could be split into different sentences for better reading. Furthermore, some minor grammar mistakes were found (e.g. lines 277-278), as well as some typos (line 298 and line 302 'positives') and some not-so-appropriate expressions (line 279: 'Remember that...'). The whole revision of the English language by a native speaker or an English teacher is advised.
Please also provide references for the numerical values considered in Table 1 or explanations on how those values were selected.
Author Response
The authors are again very grateful with the academic editors of the journal for the opportunity to submit again a corrected version of the corresponding manuscript, also with the anonymous reviewers for his/her valuable comments, which help substantially to improve our proposal. We have done our best to write the manuscript so that it is readable. In this sense, the manuscript was revised by native English-speaking editors.
We are very grateful with the reviewer 1 for his/her valuable comments and the positive comments.
The corrections are now included in the corrected version of the manuscript and are highlighted in yellow color.
Reviewers Reply.
Reviewer 1.
Comment 1. The authors have made significant efforts to give adequate responses to the different issues raised in the previous round of revisions. The changes made to the manuscript have enhanced it. I think the manuscript can be accepted for publication once that the English language has been polished. There are various statements starting with the term 'Now' and some long statements including various commas could be split into different sentences for better reading. Furthermore, some minor grammar mistakes were found (e.g. lines 277-278), as well as some typos (line 298 and line 302 'positives') and some not-so-appropriate expressions (line 279: 'Remember that...'). The whole revision of the English language by a native speaker or an English teacher is advised.
Reply 1.- Thank you again for your comment, we take in account your suggestions. The manuscript has undergone English language editing by MDPI (see the English Editing Certificate in attached files).
Comment 2.- Please, also provide references for the numerical values considered in Table 1 or explanations on how those values were selected.
Reply 2.- The corresponding references are now included.
Author Response File: Author Response.pdf
Reviewer 3 Report
Significant changes have been made but English language is still beyond any level required for publishing. The first sentence of the Conclusions goes: "In this work is presented a Two-Input Two Output (TITO) control strategy, selecting as the control pairs the reactor’s temperature-jacket-temperature and the productivity-input mass flow." Unfortunately, the whole manuscript is hastily done and there are many mistakes like these. Let me remind you, this is the after the major revision.
The most problematic are mistakes in the newly added research part. Equation 2 is incorrect. The last term should be "-2*k3*CA2". The authors can refer to Chemical Reaction Engineering by Octave Levenspiel for more details. Accordingly, all other simulations and optimizations need to be repeated.
I suggest to readers to submit a new manuscript and next time, don't submit a draft version and then a completely other one in a few days, but submit something worthy of publishing. This is nowhere near a publish-ready material.
Author Response
Please see the attachment
Author Response File: Author Response.pdf
Reviewer 4 Report
My comments were addressed I have no further comments. Congratulations to the authors.
Author Response
We deeply thank the reviewer 4 for his congratulations to our manuscript.
Reviewers Reply.
Comment: My comments were addressed I have no further comments. Congratulations to the authors.
Reply: Thank you, is very nice your comment.
Round 3
Reviewer 3 Report
Dear authors, you still have not fixed a very major error in your equations. You need to fix your model and do the simulations and optimizations again.
Let me remind you that if your reaction follow stoichiometry (a, b, c, d) then the reaction rate, r, will as follows (Levenspiel, Chemical Reaction Engineering):
aA + bB ---> cC + dD
r=-rA/a = -rB/b = rC/c = rD/d = k * cAa * cBb
From here, reaction rates for components will be:
rA = -a*r = - a * k * cAa * cBb
rC = c*r = c * k * cAa * cBb
etc. In order words, from two moles of A you get c moles of C and d moles of D. When the reaction follows stoichiometry, product D is produced d/a times faster than reactant A is spent.
In your example, in Eq. 5, you would have -2*k3*cA^2 instead of -k3*cA^2. In Eq. 8 you already put +k3*cA^2. Or, in other words, because you get from 2 moles of A, 1 mole of D, the reaction rate at which the reactant is decomposed is two times higher than the reaction rate at which product D is formed. This is basic chemical engineering, which you can find in:
Chemical Reaction Engineering, by Octave Levenspiel, New York: Wiley
IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "Rate of reaction".
Laidler, K.J.; Meiser, J.H. (1982). Physical Chemistry. Benjamin/Cummings.
Laidler, K.J. (1987). Chemical Kinetics (3rd ed.). Harper & Row.
and many others.
This change will greatly change your results. Also, energy balance might be affected if you change component reaction rates accordingly.
If you leave it like this, it is simply wrong and would tarnish all the hard work you put into this research.
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
