Elsevier

Applied Energy

Volume 185, Part 2, 1 January 2017, Pages 1965-1970
Applied Energy

Assessment of adsorbate density models for numerical simulations of zeolite-based heat storage applications

https://doi.org/10.1016/j.apenergy.2015.10.126Get rights and content

Highlights

  • Characteristic curves fit for binderless Zeolite 13XBFK.

  • Detailed comparison of adsorbate density models for Dubinin’s adsorption theory.

  • Predicted heat storage densities robust against choice of density model.

  • Use of simple linear density models sufficient.

Abstract

The study of water sorption in microporous materials is of increasing interest, particularly in the context of heat storage applications. The potential-theory of micropore volume filling pioneered by Polanyi and Dubinin is a useful tool for the description of adsorption equilibria. Based on one single characteristic curve, the system can be extensively characterised in terms of isotherms, isobars, isosteres, enthalpies etc. However, the mathematical description of the adsorbate density’s temperature dependence has a significant impact especially on the estimation of the energetically relevant adsorption enthalpies. Here, we evaluate and compare different models existing in the literature and elucidate those leading to realistic predictions of adsorption enthalpies. This is an important prerequisite for accurate simulations of heat and mass transport ranging from the laboratory scale to the reactor level of the heat store.

Introduction

Mitigation of climate change has become an important goal of many countries’ policies. In order to limit global warming, greenhouse gas emissions have to be reduced drastically. The two main measures to achieve this goal are the decrease of primary energy consumption and the transformation of the energy supply system towards renewable resources. Therefore, intense research effort is invested to increase the energy efficiency of, e.g., building cooling, heating, hot water supply [1], [2], waste heat recovery [3] and cogeneration/trigeneration [4].

Increasing the share of renewable energy sources in energy production requires a stronger decoupling of supply and demand. Hence, there are many new developments in energy storage systems—one of the most promising means to cope with the intermittent nature of renewables [5]. Suitable systems include compressed air energy storage, flywheel energy storage, battery energy storage, capacitors and several kinds of heat storage systems, amongst others. Besides using sensible or latent heat for heat storage applications, it is also possible to employ reversible chemical reactions or sorption processes for heat storage [6], [7], [8]. This study focuses on the latter, specifically on water vapour adsorption to microporous solids. The working principle of sorption heat storage is the following: During the discharge of the storage the adsorptive (e.g. water) is adsorbed to the solid surface of the adsorbent, mainly in its micro- and mesoporosity. This exothermic process is accompanied by the release of the adsorption enthalpy as heat. For charging the storage, the loaded adsorbent is heated up causing the adsorbate to be desorbed. The main features of sorption storage are its high storage density, its suitability for long-term storage—if one separates the reaction/sorption working pair no reaction will take place so that the storage will not discharge—and its cyclability. One application benefitting from these properties is the domestic storage of solar heat. In this setting, charging the storage with heat from a simple solar collector takes place at a temperature between 110 °C and 180 °C, and discharge typically at a temperature between 40 °C and 90 °C. An overview of the current state of sorption heat storage can be found, e.g. in the review articles by N’Tsoukpoe et al. [9] and Yu et al. [10]. Comparisons of different energy storage technologies have been performed, e.g. by Luo et al. [5] and Xu et al. [11].

Computational models can be used to design and simulate heat storage devices based on an experimental physical–chemical characterisation of the storage material. One practical benefit of such an approach lies in the ability to simulate on a larger scale the behaviour and performance of a heat storage device based on standard laboratory scale material tests without having to run expensive experiments on the application scale. Only the most promising materials will then have to be tested in full scale experiments.

There are several approaches for the description of adsorption equilibria of porous solids, e.g., Langmuir- and BET-isotherms or Dubinin–Polanyi theory [12]. The latter, however, is outstanding as “[n]o other adsorption model allows the extrapolation of one measured isotherm to other [sic] with different temperatures” [13]. This feature makes it a good candidate for use in numerical simulations. Based on one single so-called “characteristic curve” the adsorption working pair can be extensively characterised, i.e. all isotherms, isobars, isosteres, etc. can be derived from it. Above all, Dubinin’s theory also allows to calculate the enthalpy of adsorption—a very important characteristic of an adsorptive/adsorbent combination regarding heat storage.

One of the key parameters needed in Dubinin’s theory is a functional description for the temperature dependence of the adsorbate density. This density function, however, is hard to determine from measurements [14]. Yet, the calculation of the adsorption enthalpy is especially sensitive to it. Several density formulations for adsorbed water exist in the literature [14], [15], [16], [17], [18], [19], [20] but no comparative analysis of the different models has been published, yet. It is therefore unclear to what extent the choice of a particular density model will impact the results obtained in computational simulations and hence their predictive capabilities concerning the performance of the heat storage system. It is the objective of the present study to present such a comparison as a prelude to later simulations right up to the reactor level. An additional intention of this study is to determine the significance of this impact and whether a particular density model can be considered more suitable than others. The results may serve as a practical guide for modellers in the field of adsorption energy storage.

Section snippets

Adsorbate density models

Adsorption equilibria can be described by a plane in the p-T-C space:F(p,T,C)=0By evaluating the change in the molar free enthalpy (i.e. the chemical potential) induced by an isothermal transition of a fluid from the free liquid state to the adsorbed state, the specific adsorption potential Am can be found [16], [21]:Am=RMAdsTlnpspThe Dubinin–Polanyi theory now reduces the two-dimensional description in Eq. (1) to a so-called characteristic curve Am(W) that expresses the relationship between

Characteristic curve and isotherms

A widely used relationship for fitting to an experimentally obtained characteristic curve is the Dubinin–Astakhov equation [12]. However, it is not able to fit the experimental data we used sufficiently well, thus leading to inaccuracies in the adsorption enthalpies. Hence, we employed a rational polynomial as suggested by Núñez [16] for fitting, see Fig. 2a. The measured isotherms and those derived from the characteristic curve using the density model by Hauer [14] are compared in Fig. 2b.

This

Discussion

The effective use of zeolites and other microporous adsorbents for heat storage applications depends both on the practically achievable adsorption capacity and the enthalpy of adsorption. An accurate quantification of the latter is crucial for the adequate simulation of adsorption heat storage. As already mentioned, Dubinin’s approach requires the description of the temperature-dependent adsorbate density. The choice of the density model has a significant impact especially on the estimation of

Conclusion

Although the predicted enthalpies for the individual density models differ considerably, the storage densities obtained from the simulation do not exhibit an equally wide spread. Due to the region to which temperature, vapour partial pressure and adsorbate loading are confined in practical applications and due to the way they are linked based on Eq. (1), those parts of the enthalpy curves where deviations amongst the models are greatest (e.g. high loading at high temperature) do not have a big

Acknowledgements

We express our thanks to Dr.-Ing. H. Kerskes, Universität Stuttgart, Germany, for his kind permission to use the adsorption isotherm data. Funding was provided by the Helmholtz Initiating and Networking Fund through the NUMTHECHSTORE project.

References (29)

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This paper was presented at the 7th International Conference on Applied Energy (ICAE2015), March 28–31, 2015, Abu Dhabi, UAE (Original paper title: “The impact of adsorbate density models on the simulation of water sorption on nanoporous materials for heat storage” and Paper No.: 300).

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