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ScienceDirect Energy Procedia 75 (2015) 2106 – 2112

The 7th International Conference on Applied Energy – ICAE2015

The impact of adsorbate density models on the simulation of water sorption on nanoporous materials for heat storage Thomas Nagela, *, Steffen Beckertb, Norbert Böttchera, Roger Gläserb, Olaf Kolditza,c a

Department of Environmental Informatics, Helmholtz Centre for Environmental Research – UFZ, Permoserstr. 15, 04318 Leipzig, Germany b Institute of Chemical Technology, Universität Leipzig, Linnéstr. 3, 04103 Leipzig, Germany c Applied Environmental Systems Analysis, Technische Universität Dresden, Germany

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 very 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 right up to the reactor level of the heat store. © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license

© 2015 The Authors. Published by Elsevier Ltd. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Selection and/or peer-review under responsibility of ICAE

Peer-review under responsibility of Applied Energy Innovation Institute

Keywords: Zeolite; Adsorption; Heat storage; OpenGeoSys; Adsorbate density; Dubinin

1. Introduction The current ambitions towards a transformation of the energy supply system to renewable resources have increased the need for technologies to decouple energy supply and demand as well as for means to increase energy efficiency. Building climatisation, hot water supply and industrial process heat generation consume a significant share of the primary energy supply and offer considerable potentials for efficiency improvements. Intense research effort is invested into numerous kinds of thermal energy storage systems in order to improve our technological capabilities in this regard [1]. Among the technologies considered * Corresponding author. E-mail address: [email protected].

1876-6102 © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of Applied Energy Innovation Institute doi:10.1016/j.egypro.2015.07.331

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Thomas Nagel et al. / Energy Procedia 75 (2015) 2106 – 2112

for heat storage applications are various chemical reaction systems as well as ad- and absorption processes [2]. Nomenclature Sorb

adsorbent

Ads

adsorbate

‫ܣ‬

adsorption potential

J molିଵ

ߙ୅ୢୱ

thermal expansion coefficient of the adsorbate

K ିଵ

ܾ

van-der-Waals covolume

cmଷ molെ1

‫ܥ‬

loading (adsorbate mass per adsorbent mass)

g g ିଵ

‫ܪ‬୬

molar adsorption enthalpy

J molିଵ

‫ܪ‬୬஝

molar enthalpy of evaporation

J molିଵ

݄

specific adsorption enthalpy

J g ିଵ

‫݌‬

partial pressure of the vapour phase

Pa

‫݌‬ୱ

saturation pressure

Pa

ߩ୅ୢୱ

adsorbate density

g cmିଷ

ܴ

universal gas constant

J molିଵ K ିଵ

ܵ୬

molar adsorption entropy

J molିଵ K ିଵ

ܶ

absolute temperature

K

ܹ

adsorbed volume per unit mass of adsorbent

cmଷ g ିଵ

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. Water vapour adsorption in microporous solids such as zeolites is one of the considered options for the thermochemical heat storage [2]. The potential-theory of micropore volume filling pioneered by Polanyi and Dubinin (Dubinin-Polanyi theory) is a useful method for the description of adsorption equilibria [3]. Based on one single characteristic curve, the adsorption working pair (combination of an adsorbent with an adsorptive) can be extensively characterised. The corresponding isotherms, isobars, isosteres, enthalpies, etc. can all be derived from this single curve. One of the key parameters needed in Dubinin’s theory is a functional description for the temperature dependence of the adsorbate density. However, this density function is not uniquely defined. One of the most important characteristics of an adsorption working pair for energy storage applications is the adsorption enthalpy. As will be shown, the calculation of this enthalpy is especially sensitive to the choice of the density model. Several density formulations for adsorbed water exist in the literature [4-10] but no comparative analysis of the different models has been published, yet. It is the objective of the

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present study to present such a comparison as a prelude to later simulations right up to the reactor level. 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 store. 2. Adsorbate density models Adsorption equilibria can be described by a plane in the ‫ܥ‬-‫݌‬-ܶ space: ‫ܥ(ܨ‬, ‫݌‬, ܶ) = 0

(1)

By 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 adsorption potential ‫ܣ‬ can be found [3, 6]: ‫ ܴܶ = ܣ‬ln

‫݌‬ୱ ‫݌‬

(2)

The Dubinin-Polanyi theory now reduces the two-dimensional description in Eq. (1) to a so-called characteristic curve ‫ )ܹ(ܣ‬that is temperature-independent for a given adsorption working pair and expresses the relationship between the differential molar work and the adsorbed specific volume ܹ [3, 7]. The maximum value of the adsorbed specific volume is referred to as ܹ଴ and represents the maximum uptake defined by the pore space available for the adsorptive. For zeolites, it can be calculated from their crystal structure [4]. The temperature dependent adsorbate density is now defined such that it maps the temperature-dependent maximum loading into this temperature independent available volume: ߩ୅ୢୱ (ܶ) =

‫ܥ‬଴ (ܶ) ܹ଴

(3)

The exact functional relationship of ߩ୅ୢୱ (ܶ) is unknown. Its determination is complicated by the fact that ‫ܥ‬଴ is difficult to determine, i.e. due to the influence of capillary condensation at higher loadings [4]. Several approaches to describe ߩ୅ୢୱ (ܶ) are proposed in the literature (supercritical phenomena will not be considered here): The work by Núñez [6] estimates the adsorbate density by the density of the free liquid, both below and above the boiling point, whereas in references [8, 9], the density of the free liquid is only used below the boiling temperature. Nikolaev and Dubinin [8] linearly interpolate between the density at the boiling point and the van-der-Waals co-volume ܾ at the critical temperature. In contrast, Cook and Basmadjian [9] extrapolate linearly above the boiling point requiring that the transition between the two regions be continuous. It was later found experimentally that the adsorbate density as well as its temperature dependence is different from that of the free liquid [10]. This is likely due to steric factors and a compressibility that increases with temperature, which determine the density evolution under the action of pressures caused by the adsorption field. These pressures can be on the order of 100 MPa according to reference [10]. Specifically, for water adsorbed onto a zeolite NaA, the temperature dependence of the adsorbate density was linear and values were always higher than those of the free liquid over a temperature range of 260 K to 470 K [10]. Recently, two additional models have been proposed addressing the use of microporous adsorbents for heat storage applications: Hauer [4] used a linear relationship over the considered temperature range, while Mugele [5] employed the equation listed

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in Table 1 (see Appendix A). This table also lists the mathematical formulation of the other models discussed previously. In Fig. 1(a), the described models are compared. Additionally, the density of water at a pressure of 100 MPa was calculated using the IAPWS 1997 formulation [12] and plotted for comparison. This corresponds to the density of free water under a pressure comparable to that assumed to act on the adsorbate in micropores [10].

3. Consequences for the adsorption enthalpy and reactor level simulations A macroscopic model for the description of reactive mass and heat transport in thermochemical heat stores [13] has been extended to describe sorption systems. The implementation is realised in the scientific software package OpenGeoSys [14]. The governing equations describe a water vapour-nitrogen mixture permeating a fixed particle bed and are summarised in [13]. Dubinin’s theory is used to determine two quantities in the macroscopic transport equations: Firstly, a density production term which is describing the amount of vapour adsorbed or desorbed. It depends on the local distance of the current thermophysical state from the sorption equilibrium which is described based on the characteristic curve of the simulated material pair. Secondly, the specific enthalpy ȟ݄ characterising the amount of heat released or required during adsorption or desorption, respectively. The corresponding molar enthalpy of adsorption is calculated as the sum of the enthalpy of evaporation, the adsorption potential and an entropic term [4]: ȟ‫ܪ‬୬ = ȟ‫ܪ‬୬୴ + ‫ ܣ‬െ ܶȟܵ୬

(4)

The change in entropy is related to the slope of the characteristic curve [4]: ȟܵ୬ = ߙ୅ୢୱ ܹ

߲‫ܣ‬ ฬ ߲ܹ ்

(5)

An insufficient accuracy of ‫ ܣ‬will reflect more severely in the accuracy of the partial derivative in Eq. (5). Hence, a mathematical description of the characteristic curve has to sufficiently represent the experimental data to allow a correct calculation of the adsorption enthalpy [4]. In Eq. (5) the choice of the density model will have the most significant impact in the applications of Dubinin’s theory for the simulation of heat storage devices.

(a)

(b)

Fig. 1: (a) Adsorbate density versus temperature for the different models. Significant deviations can be observed both in magnitude and trend (slope), especially above the boiling point of 100 °C. (b) Isotherms for water vapour adsorption onto zeolite 13XBF. Solid lines connect experimental values, while the dashed lines are the corresponding isotherms derived from the characteristic curve ‫ )ܹ(ܣ‬based on the density model used in reference [4].

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The thermal expansion coefficient of the adsorbate directly follows from the temperature dependence of the density, namely the slope in the ߩ- ܶ-diagramme, as ߙ୅ୢୱ = െ

1 ߲ߩ୅ୢୱ ߩ୅ୢୱ ߲ܶ

(6)

4. Experimental data Experimental water adsorption isotherms of binderless granulated 13X zeolite spheres (KÖSTROLITH® 13XBF by CWK Bad Köstritz, Germany) with a mean diameter of 2.0 mm were analysed using the theory outlined above. The measurements were performed in a sorption analyser IGA002 (company Hiden Isochema) [15]. The characteristic curve was calculated from the experimental data set and fitted using a rational polynomial following the procedure given in reference [6]. The measured isotherms and those derived from the characteristic curve using the density model by Hauer [4] are compared in Fig. 1(b). Next, each density model described above has been used in the establishment of the characteristic curve from which the adsorption enthalpy was derived subsequently (see Fig. 2(a)). As expected from Eq. (4), the entropic contribution increases with temperature. Equation (5) further shows that increased thermal expansion coefficients lead to an increase in the entropies. This is confirmed in Fig. 2(b) where two of the more extreme cases are compared: The model with the lowest thermal expansion coefficient (Mugele [5], compare Fig. 1(a)) and the model using the density of the free liquid (Núñez [6]). The latter leads to a significant overestimation of the entropic contribution at higher temperatures. Its applicability has not been shown for microporous adsorbents over a wide temperature range but only for water sorption at 30 °C on calcium chloride confined to mesoporous silica gel in reference [6]. 5. 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 very useful 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 the energetically relevant adsorption enthalpies. Models with an effectively linear behaviour over the considered temperature range performed well in capturing the typical shape of the adsorption enthalpy curve with its two steps, as it was observed experimentally in references [4, 5, 6, 15]. The entropic contribution remained small even for higher temperatures (Fig. 2(a)). The linear development of the adsorbate density has also been supported experimentally [10]. The other density models [6, 9] translate into high values for the thermal expansion coefficient leading to high entropic contributions and thus unrealistic shapes of the enthalpy curves for the data set and temperature range considered here (compare Fig. 2(b)). The mentioned two-stepped shape is a direct consequence of the characteristic curve (not shown). To capture this, a sufficiently accurate fit of the experimental data is required. If a general formulation for the characteristic curve, e.g. the DubininAstakhov formulation used in [15], is used, it may often not be possible to capture such characteristics (see Fig. 2 in [15]).


(a)

(b)

Fig. 2: Exemplary adsorption enthalpies (solid curves) and entropic contributions (dashed curves; specific entropies ȟs are used) for water adsorption on zeolite 13XBF. The curves in (a) are based on the density model used by Mugele [5] and the ones in (b) are based on the density of the free liquid that was used in reference [6].

Therefore, our recommendations for energy storage applications are to use (i) a sufficiently general mathematical expression for an accurate fit of the experimentally determined characteristic curve instead of a generic (albeit physically motivated) model and (ii) a (quasi) linear density model as applied in [4, 5]. Acknowledgements We express our thanks to Dr.-Ing. H. Kerskes 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 [1] K. Kaygusuz. The viability of thermal energy storage. Energy Sources, 21(8):745–755, 1999. [2] N. Yu, R.Z. Wang, and L.W. Wang. Sorption thermal storage for solar energy. Progress in Energy and Combustion Science, 39(5):489–514, 2013. [3] M.M. Dubinin. Theory of the physical adsorption of gases and vapors and adsorption properties of adsorbents of various natures and porous structures. Bulletin of the Academy of Sciences of the USSR, Division of Chemical Science, 9(7):1072–1078, 1960. [4] A. Hauer. Beurteilung fester Adsorbentien in offenen Sorptionssystemen für energetische Anwendungen. PhD thesis, Fakultät III - Prozesswissenschaften, Technische Universität Berlin, 2002. [5] J. Mugele. Optimierung von Speichermaterialien für den Einsatz in geschlossenen thermochemischen Wärmespeichern für gebäudetechnische Anwendungen. VDI Verlag, 2005. [6] T. Núñez. Charakterisierung und Bewertung von Adsorbentien für Wärmetransformationsanwendungen. PhD thesis, Universitätsbibliothek Freiburg, 2002. [7] M.M. Dubinin. Contemporary status of the theory of the volume filling of the micropores of carbonaceous adsorbents. Bulletin of the Academy of Sciences of the USSR, Division of Chemical Science, 40(1):1–19, 1991.

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[8] K.M. Nikolaev and M.M. Dubinin. Concerning adsorptional properties of carbon adsorbents 3. A study of adsorption isotherms of gases and vapors on active carbons over a wide interval of temperatures, including the critical region. Bulletin of the Academy of Sciences of the USSR, Division of Chemical Science, 7(10):1124–1133, 1958. [9] W.H. Cook and D. Basmadjian. Correlation of adsorption equilibria of pure gases on activated carbon. The Canadian Journal of Chemical Engineering, 42(4):146–151, 1964. [10] I.I. Seliverstova, A.A. Fomkin, and V.V. Serpinskii. Adsorption of a liquid on a microporous adsorbent along the liquidvapor equilibrium line. communication 2. Average density of adsorbed substances in a microporous adsorbent. Bulletin of the Academy of Sciences of the USSR, Division of Chemical Science, 35(6):1116–1120, 1986. [11] A. Hauer. Thermal energy storage with zeolite for heating and cooling applications. In Proceedings of the International Sorption Heat Pump Conference, Shanghai, pages 24–27, 2002. [12] W. Wagner, J.R. Cooper, A. Dittmann, J. Kijima, H.-J. Kretzschmar, A. Kruse, R. Mares, K. Oguchi, H. Sato, I. Stocker, et al. The IAPWS industrial formulation 1997 for the thermodynamic properties of water and steam. Journal of Engineering for Gas Turbines and Power, 122(1):150–184, 2000. [13] T. Nagel, H. Shao, A.K. Singh, N. Watanabe, C. Roßkopf, M. Linder, A. Wörner, and O. Kolditz. Non-equilibrium thermochemical heat storage in porous media: Part 1 – Conceptual model. Energy, 60:254–270, 2013. [14] O. Kolditz, S. Bauer, L. Bilke, N. Böttcher, J.O. Delfs, T. Fischer, U.J. Görke, T. Kalbacher, G. Kosakowski, C.I. McDermott, et al. OpenGeoSys: an open-source initiative for numerical simulation of thermo-hydro-mechanical/chemical (THM/C) processes in porous media. Environmental Earth Sciences, 67(2):589–599, 2012. [15] B. Mette, H. Kerskes, H. Drück, and H. Müller-Steinhagen. Experimental and numerical investigations on the water vapor adsorption isotherms and kinetics of binderless zeolite 13X. International Journal of Heat and Mass Transfer, 71(0):555–561, 2014.

Appendix A. Table 1: List of the density models. The Index c denotes critical values. M is the molar mass, R the universal gas constant. Reference

Up to boiling point

Mugele [5]

ߩ୅ୢୱ (ܶ) =

Above boiling point ߩଶ଴ιେ 1 + ߙ୅ୢୱ,ଶ଴ιେ (ܶ െ 293.15K)

Hauer [4]

ߩ୅ୢୱ (ܶ) = ߩଵ଴ιେ ‫[ ڄ‬1 െ 3.781 ‫ ڄ‬10ିସ (ܶ െ 283.15K)]

Núñez [6]

Free liquid

Nikolaev and Dubinin [8]

Free liquid

Cook and Bamsmadjian [9]

Free liquid

ߩ(ܶ) = ߩଵ଴଴ιେ െ

‫ܯ‬ ܾ (ܶ െ 373.15K) ܶୡ െ 373.15K ߩଵ଴଴ιେ െ

ߩ୅ୢୱ (ܶ) = ߩଵ଴଴ιେ ‫[ ڄ‬1 െ ߙ୅ୢୱ,ଵ଴଴ιେ (ܶ െ 373.15K)]

Biography Dr. Thomas Nagel is work group leader at the Department of Environmental Informatics of the Helmholtz Centre for Environmental Research UFZ. He holds a master’s degree in Mechanical Engineering from Chemnitz University of Technology and a PhD in Bioengineering from Trinity College Dublin.