Comprehensive Overview of the Effective Thermal Conductivity for Hydride Materials: Experimental and Modeling Approaches
, Julián A. Puszkiel 2,3,*, Jan Warfsmann 2,3, Fahim Karimi 2, Elio Jannelli 1, Claudio Pistidda 2, Thomas Klassen 2,3 and Julian Jepsen 2,3
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThe paper is related to solid state hydrogen storage technologies . This review article presents a comprehensive overview of experimental and modelling approaches to characterise ETP in MGBs. Methods for measuring the ETC of metal hydride layers are described, and results and applications are shown. A comprehensive description of the models used to calculate the ETC of MHB under different conditions is developed. Furthermore, the influence of operating parameters such as P, T and composition on the ETC of the presented models is analysed.
1. the abstract needs to be redone. A lot of unnecessary information that is found in other scientific articles. Need to indicate its unique approach.
2. The authors do not provide control methods for hydrogen storage technologies. There is no information on the application of neural networks in the paper. Analysis of references related to the application of nanomaterials and hydrogen storage management systems should be given. 10.3390/polym14224992
3. All formulas in the article without specifying physical dimensionality.
4. There are no summarising tables.
5. It is not clear why the authors of the paper use table number 1. Moreover, they have formatted this table as a figure.
6. The conclusions are cumbersome without any clear concept.
Author Response
We thank reviewer one for the comments. Please find the answers below.
Reviewer 1
1. The abstract needs to be redone. A lot of unnecessary information that is found in other scientific articles. Need to indicate its unique approach.
We thank the reviewer for this comment. To make the abstract less general, we modified it, especially in the first part. Modifications are highlighted in the text, and the revised version of the abstract is reported here:
"In metal hydride beds (MHBs), reaction heat transfer often limits the dynamic performance. Heat transfer within the MHB usually involves the solid and gas phases. To account for both, an effective thermal conductivity (ETC) is defined. Measuring and predicting the ETC of metal hydride beds is of primary importance when designing hydride-based systems for high dynamics. This review paper presents an integral overview of the experimental and modeling approaches to characterize the ETC in MHBs. The most relevant methods for measuring the ETC of metal hydride beds are described, and the results and scopes are shown. A comprehensive description of the models applied to calculate the ETC of the MHBs under different conditions is developed. Moreover, the effects of operation parameters such as P, T, and composition on the ETC of the presented models are analyzed. Finally, a summary and conclusions about experimental techniques, a historical overview with a classification of the ETC models, a discussion about the needed parameters, and a comparison between ETC experimental and calculated results are provided."
2. The authors do not provide control methods for hydrogen storage technologies. There is no information on the application of neural networks in the paper. Analysis of references related to the application of nanomaterials and hydrogen storage management systems should be given. 10.3390/polym14224992
The introduction of A.I. to control the technological stages of hydrogen production and storage is for sure interesting, but we think it is out of the scope of the current research, aiming to analyze only the effective thermal conductivity of MHBs. In addition, it would need to add more sections to the paper since the inclusion of A.I. in this kind field, in general, requires extensive analysis, and as mentioned above, it is out of the scope of this work.
3. All formulas in the article without specifying physical dimensionality.
Parameters are meant to be expressed in the SI units. All the symbols appearing in the equations are first described in the text and then in the tables at the end of the manuscript (List of abbreviations, List of symbols, List of Greek symbols).
4. There are no summarising tables.
There are two summarizing tables in the ESI, Table S1 and Table S2. Table S1 collects the central equation, a brief description, the list of parameters, and the main advantages and disadvantages of each reviewed model. In Table S2, the values and parameters used to measure and model the ETC are collected, as reported in the reference papers. Inserting such tables in the manuscript would have made it less readable due to the length of these resuming tables.
5. It is not clear why the authors of the paper use table number 1. Moreover, they have formatted this table as a figure.
In Section 4, we analyzed how the ETC is affected by temperature, pressure, and hydrogen concentration. The comparison was made considering the LaNi5 as the alloy, as it is possible to find in the literature the value of all the parameters needed by each model, which is not easy for other materials. In Table 1, the values of the parameters which are common to all the models were reported.
Regarding the format, we verified that Table 1 is not formatted as a Figure in the file, which can be downloaded by the Editor's website (the name of the file is manuscript.v2.docx), but some issues may have arisen during the download.
6. The conclusions are cumbersome without any clear concept.
To clarify the concepts and the main aspects analyzed in the text, some new conclusions have been added to Section 5, which are highlighted in the text. Figure S1 and Tables S1 and S2, which can be considered an integrant part of this section, have been reported in the Supplementary Information due to readability.
On behalf of all authors.
Dr. J.A. Puszkiel
Deputy of Head of the System Design Department
Helmholtz-Zentrum Hereon
Institute of Hydrogen Technology
Geb. 59, Büro 209
T. +49 (0) 4152 87-2171
m. +49 (0) 0176 72599729
[email protected]
https://www.hereon.de/hydrogen/
Helmut-Schmidt-Universität
Universität der Bundeswehr Hamburg
Geb. H1, Büro 1221
T. +49 (0) 40 6541 3297
m. +49 (0) 0176 72599729
[email protected]
https://www.hsu-hh.de/awt/
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsThere are an extremely large number of reviews on the effective thermal conductivity of porous systems. The novelty and relevance of the manuscript presented lies in the fact that the authors provide an overview of recent research on effective thermal conductivities for hydride materials.
1) The authors correctly note in the abstract and introduction that "metal hydride beds (MHBs), reaction heat transfer often limits the dynamic performance." The main comment of the reviewer is related to the fact that the refinement of effective thermal conductivity models should primarily be related to the need to refine the simulations carried out to determine the parameters of metal hydride systems being developed and designed. A vast majority of numerical base papers use the additive model k_eff = k_s*(1-pore) + k_g*pore (according to reviewer's assessment, more than 90%) and also do not take into account Knudsen effects. This model with constant values for k_s, k_g and pore actually mean using a constant value for the effective thermal conductivity. Note that in those papers k_s does not represent the thermal conductivity of the hydride material itself but some effective value which gives the desired k_eff value. The authors do not discuss how the refinement of models for determining k_eff will affect the accuracy of calculations performed and for which set of operating parameters such refinement would significantly affect simulation results. Discussion of this issue in presented manuscript can be useful and some information can be found in recent literatures ([1] for example).
2) The parameters of the hydride material change significantly during operation. First, the metal hydride bed parameters undergo noticeable changes during the activation of the material. Secondly, there is a significant change in the parameters during the absorption and desorption cycles, and the main problem is controlling the bed properties after loading the material into the system. Changes in the bed characteristics depend even on the configuration of the system (i.e., whether the free volume above the bed is sufficient for deformation or whether the material occupied the fixed volume). The authors emphasize the importance of the number of input parameters when comparing different models to determine the effective thermal conductivity. Practical recommendations for how and when to measure the characteristics of an alloy in order to best predict the metal hydride bed's characteristics during cycling operations can be useful.
3) The authors did not indicate all approaches to determining the effective thermal conductivity of metal hydride systems. The well-known Bruggeman’s formula for the effective thermal conductivity at k_s >> k_g (k_s is metal hydride thermal conductivity as bulk material) gives a simple approximation for the effective thermal conductivity: k_eff = k_g/pore^3. This formula requires a minimum number of input parameters and was first used [2] to predict the operation of metal hydride hydrogen purification systems, since for these systems k_g should be understood as the thermal conductivity of the gas mixture k_mix, the composition of which changes during operation. Later, this simplified approach showed its efficiency for systems of this class.
4. Additives are often added to the bed to improve the properties of the alloy (expanded natural graphite as example). These additives can greatly affect the effective thermal conductivity. It would be worth at least briefly indicating the possibility of modernizing the presented recommendations for calculating the effective thermal conductivity for this practically important case.
References:
1. Minko, K. B., Lototskyy, M. V., Bessarabskaya, I. E., & Tarasov, B. P. (2024). CFD simulation of heat and mass transfer processes in a metal hydride hydrogen storage system, taking into account changes in the bed structure. International Journal of Hydrogen Energy.
2. Artemov, V. I., Lazarev, D. O., Yan’kov, G. G., Borzenko, V. I., Dunikov, D. O., & Malyshenko, S. P. (2004). The effect of non-absorbable gas impurities on heat and mass transfer in metal-hydride devices for storage and purification of hydrogen. High temperature, 42, 987-995.
Conclusion. The work presents a high-quality review. The main recommendation is to quantify the need for clarifying the calculation methods for estimation effective thermal conductivity. Motivational part of the paper should demonstrate that the costs of improving approaches to determining effective thermal conductivity could be justified by more accurate simulation of newly developed metal hydride systems. Specific examples should be provided. Due to the complexity of presented models and a large number of difficult-to-determine input parameters, the use of these methods in real system modeling may be limiting.
Author Response
RESPONSE TO REVIEWERS
We thank reviewer one for the comments. Please find the answers below.
Reviewer 2
1. The authors correctly note in the abstract and introduction that "metal hydride beds (MHBs), reaction heat transfer often limits the dynamic performance." The main comment of the reviewer is related to the fact that the refinement of effective thermal conductivity models should primarily be related to the need to refine the simulations carried out to determine the parameters of metal hydride systems being developed and designed. A vast majority of numerical base papers use the additive model k_eff = k_s*(1-pore) + k_g*pore (according to reviewer's assessment, more than 90%) and also do not take into account Knudsen effects. This model with constant values for k_s, k_g and pore actually mean using a constant value for the effective thermal conductivity. Note that in those papers k_s does not represent the thermal conductivity of the hydride material itself but some effective value which gives the desired k_eff value. The authors do not discuss how the refinement of models for determining k_eff will affect the accuracy of calculations performed and for which set of operating parameters such refinement would significantly affect simulation results. Discussion of this issue in presented manuscript can be useful and some information can be found in recent literatures ([1] for example).
We thank the reviewer for this suggestion. The broadly used additive model was not included in this review as it is not representative of the complexity of the thermal conductivity of MHBs. In addition, we checked the results obtained by using this model and found highly overestimated values in most of the conditions.
That said, investigating how much the addition of complexity to the ETC model affects the accuracy of the calculations is an interesting analysis. In a certain way, it can be said that the base information for this kind of study is included in Section 4, where the comparison between the reviewed models is presented, and in Table S2, containing the comparison between experimental and simulated data for all the models. For this reason, we decided to add some comments on this topic in Section 5. In the following, it is reported the part that has been added, which is also highlighted in the text:
"In this regard, the simple additive equation keff=ks·(1-ε)+kg·ε is widely used to model the ETC of MHBs [169]. Despite its simplicity, it does not represent the complexity of the effective thermal conductivity of MHBs, limiting the evaluation of the effects of several parameters on the ETC and leading to overestimating the value of keff (quick calculations would give values around 5 W m-1·K-1). The comparison of data reported in Table S2 also gives information on how accurately the models predict the experimental values of the ETC, making it possible to analyze how the complexity of the models relates to their accuracy. Nevertheless, they must take into consideration the type of systems, in terms of materials, and the operative conditions, in terms of temperature and pressure, at which these evaluations have been performed."
2. The parameters of the hydride material change significantly during operation. First, the metal hydride bed parameters undergo noticeable changes during the activation of the material. Secondly, there is a significant change in the parameters during the absorption and desorption cycles, and the main problem is controlling the bed properties after loading the material into the system. Changes in the bed characteristics depend even on the configuration of the system (i.e., whether the free volume above the bed is sufficient for deformation or whether the material occupied the fixed volume). The authors emphasize the importance of the number of input parameters when comparing different models to determine the effective thermal conductivity. Practical recommendations for how and when to measure the characteristics of an alloy in order to best predict the metal hydride bed's characteristics during cycling operations can be useful.
This contribution is punctual and valuable. To take this into account, we considered adding the following periods to the manuscript in Section 1, which are also highlighted in the text:
"Most of the parameters regarding the solid phase undergo a relevant variation during operation, as the solid matrix is originally constituted and is first activated and then cycled. Being interested in the hydrogenation-dehydrogenation processes, the parameters should be evaluated after cycling once the material can be considered stable. In addition, how the parameters change during ABS/DES cycles, including the expansion/compression related to the process, should also be considered.."
3. The authors did not indicate all approaches to determining the effective thermal conductivity of metal hydride systems. The well-known Bruggeman's formula for the effective thermal conductivity at k_s >> k_g (k_s is metal hydride thermal conductivity as bulk material) gives a simple approximation for the effective thermal conductivity: k_eff = k_g/pore^3. This formula requires a minimum number of input parameters and was first used [2] to predict the operation of metal hydride hydrogen purification systems, since for these systems k_g should be understood as the thermal conductivity of the gas mixture k_mix, the composition of which changes during operation. Later, this simplified approach showed its efficiency for systems of this class.
From Bruggeman's formula, a very simple model for effective thermal conductivity is derived, which is very interesting and easily applicable. We decided not to include it in the analysis as, due to its simplicity, it also does not take into account some basic aspects which, in our opinion, significantly affect the ETC of MHBs. By excluding the solid thermal conductivity, it becomes impossible to evaluate the contribution of different solids to the effective thermal conductivity of a system, which, according to several experimental results (some of which have also been included in this research and were reported in Table S2), is relevant in determining the value of ETC.
4. Additives are often added to the bed to improve the properties of the alloy (expanded natural graphite as example). These additives can greatly affect the effective thermal conductivity. It would be worth at least briefly indicating the possibility of modernizing the presented recommendations for calculating the effective thermal conductivity for this practically important case.
This observation is very pertinent, and we are working on the introduction of high-thermal conductivity additives to metal hydride systems, both experimentally and numerically. To consider this aspect, it was introduced a brief consideration on this topic at the end of Section 5 here reported:
‘’It is a common practice [170] to add heat conductivity enhancers, like expanded natural graphite (ENG), copper, etc., as a mixture with the powder active material. Commonly, the ETC models consider the solid phase to be made only of the hydride-forming alloy. In the future, it would be of great interest to develop novel models in order to account for a multiphase solid material for the representation of the ETC through models that are as realistic as possible.’’
On behalf of all authors.
Dr. J.A. Puszkiel
Deputy of Head of the System Design Department
Helmholtz-Zentrum Hereon
Institute of Hydrogen Technology
Geb. 59, Büro 209
T. +49 (0) 4152 87-2171
m. +49 (0) 0176 72599729
[email protected]
https://www.hereon.de/hydrogen/
Helmut-Schmidt-Universität
Universität der Bundeswehr Hamburg
Geb. H1, Büro 1221
T. +49 (0) 40 6541 3297
m. +49 (0) 0176 72599729
[email protected]
https://www.hsu-hh.de/awt/
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsAccept in present form
