The Influence of Variable CO₂ Emission Tax Rate on Flexible Chemical Process Synthesis

Round 1

Reviewer 1 Report

This paper demonstrates how the CO₂ tax affects the optimal results of synthesizing chemical processes using mixed-integer nonlinear programming (MINLP). The studied research is important and meaningful. However, there are many important points to be considered before any decisions. Therefore, my comments are given below:

1. The originality of the paper needs to be further clarified.
2. Literature review: an updated and complete literature review with strong relevance to the topic of the paper should be conducted. In particular, the authors should review more recent studies which reported the influence of CO₂ tax rate on process design.
3. In the Methods section, please explain in detail the mathematical model P1. Are there any references? Similar issues with other equations P1 – P6.
4. Was the process superstructure in Figure 1 cited from previous works?
5. What difference between the non-integrated process and the heat integrated process?
6. There are many grammatical errors throughout the manuscript.

Author Response

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Reviewer 2 Report

The approach to process synthesis under CO2 uncertain taxes via two-stage stochastic optimization, if computationally feasible, is the right way to approach it. In fact, it is in line with recently published work in this journal (e.g. https://doi.org/10.3390/pr9071203). Nonetheless, in this reviewer's opinion, this paper does not provide enough novel contributions nor interesting results:

• The theoretical background in Section 2 is well known in the PSE community and beyond. Moreover, the formulations are not clear, e.g., why retrofit is not considered in P5 and P6 while it is in P4? Binary variables y in P4 must be fixed to the values got in P2 according to the explanation in the text. P3 is just a particular case of P4, so the approach is the same.
• The conclusion after the presented results is what everybody already knew in advance: higher CO2 penalties force the use of better raw material and more efficient equipment, hence larger initial invesments. Moreover, the claim of that this paper demonstrates how the CO2 tax affects process synthesis via MINLP is just because the presented cases are (assumed, as no equations are provided) formulated nonlinear, but it would be the same in linear formulations.
• Moreover, the presented cases for demostrating what is already intuitive does not seem to be actual industrial cases in which the authors have proven the approaches to make a design in practice, but just taken from the literature, as no model equations are presented for them. In this regard, it is difficult for the reader to understand the presented economic results because of lack of justification, e.g.: Why the presented approaches and results might be different if one can formulate a particular problem as MILP instead of MINLP? Which optimization method has been used, local or global? If all streams in the HEN must reduce their temperature, why some are labelled as cold and others as hot? In fact, C1 owes a higher temperature than H1. Moreover, why is a hot utility needed in this case? If the overall HEN needs to dissipate heat! In principle, unless some restrictions on the heat exchanger sizes or location (not mentioned) there should be a solution in which there is no need of hot utility. In the multiperiod stochastic approach it is said that the period length is arbitrary, but this is not true because it directly influences the solution in the case studies as, for instance, the CO2 accounted cost from hot utilities increases with time whereas the cost accounted in the heat exchangers manufactured is fixed, i.e., does not depend on the period lengths. In the chemical process case, it is said that the first-stage variables are the choice of feed stream and reactor, but from same streams and reactor-type choices there are presented different invesment values. It is not clear if the size of the reactor is also a first-stage variable and, in general across the paper it is never clear which are the first-stage and second-stage decision variables. According to the given justification in the text before Figure 6, the invesment should be also higher for the value of 10€/t tax, because at this value the choice is Feed 2 acording to Table 2.

Overall, this paper lacks of many details and looks more like a technical report for a project than a research article. Even so, I realized that this paper is just a naive extension of a previously published one of the same authors in the ESCAPE conference (https://doi.org/10.1016/B978-0-12-823377-1.50160-9), that has not even being cited here. For all these reasons, I cannot recommend it for publication in Processes.

Author Response

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Round 2

Reviewer 2 Report

It turned out that many of my previous questions were due to various typos and errata in the manuscript. The authors have now fixed them, so at least the paper results look coherent with what is expected from the proposed approach.

However, a couple of my previous questions/request are not fixed/answered satisfactorily in my opinion:

• Regarding the previous paper from the authors, labelled as [32] in the revised version, only a sentence is added saying that the presented examples are extended versions of such work. The extra answer provided in the letter does not convince me in the sense that a low percentage of coincidence of the text between both papers does not prove that the content is extended enough. One can rewrite to say the same with different and many more words. What I request is explicitly saying up to what contribution was covered in the conference paper, and what's newly added here since that contribution: It can be theoretical, other case study, extra experimental data for test, comparison with more approaches, etc.
• The comment about the influence of period lenght in the muti-period stochastic approach (the authors keep that there is no influence) illustrated by me with the HEN example was not answered.

Also, just for the record, I want to comment further that, when I asked why the presented approaches and results might be different if one can formulate a particular problem as MILP instead of MINLP, I had clear that formulations in the process industry are usually nonlinear by nature and that linear approximations may lack accuracy in the solutions. What I wanted to highlight with that question was a claim (that seems to be removed in the revised version) mentioning that the obtained conclusions on how CO2 tax affect process synthesis where thanks to the nonlinear formulation, which is not true in many cases. Moreover such claim was not justified in this paper, as no comparison with linearized MILP approach is provided.

Author Response

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Author Response File: Author Response.docx