dynamics of adsorptive systems for heat transformation: optimization of adsorber, adsorbent

S P R I N G E R B R I E F S I N A P P L I E D S C I E N C E S A N D T E C H N O LO G Y

Alessio SapienzaAndrea FrazzicaAngelo FreniYuri Aristov

Dynamics of Adsorptive Systems for Heat Transformation Optimization of Adsorber, Adsorbent and Cycle

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Alessio Sapienza • Andrea FrazzicaAngelo Freni • Yuri Aristov

Dynamics of AdsorptiveSystems for HeatTransformationOptimization of Adsorber, Adsorbentand Cycle

123

Alessio SapienzaConsiglio Nazionale delle RicercheMessinaItaly

Andrea FrazzicaConsiglio Nazionale delle RicercheMessinaItaly

Angelo FreniConsiglio Nazionale delle RicercheMessinaItaly

Yuri AristovBoreskov Institute of CatalysisNovosibirskRussia

ISSN 2191-530X ISSN 2191-5318 (electronic)SpringerBriefs in Applied Sciences and TechnologyISBN 978-3-319-51285-3 ISBN 978-3-319-51287-7 (eBook)https://doi.org/10.1007/978-3-319-51287-7

Library of Congress Control Number: 2018933011

© The Author(s) 2018This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or partof the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations,recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmissionor information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilarmethodology now known or hereafter developed.The use of general descriptive names, registered names, trademarks, service marks, etc. in thispublication does not imply, even in the absence of a specific statement, that such names are exempt fromthe relevant protective laws and regulations and therefore free for general use.The publisher, the authors and the editors are safe to assume that the advice and information in thisbook are believed to be true and accurate at the date of publication. Neither the publisher nor theauthors or the editors give a warranty, express or implied, with respect to the material contained herein orfor any errors or omissions that may have been made. The publisher remains neutral with regard tojurisdictional claims in published maps and institutional affiliations.

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Acknowledgements

One of the authors (Prof. Yuri Aristov) thanks the Russian Science Foundationfor financial support of the study on the pressure-driven HeCol cycle (grantN 16-19-10259).

v

Contents

1 Adsorptive Heat Transformation and Storage: Thermodynamicand Kinetic Aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Thermodynamic Cycles for AHT . . . . . . . . . . . . . . . . . . . . . . . . 3

1.1.1 Temperature-Driven Cycles . . . . . . . . . . . . . . . . . . . . . . 41.1.2 Pressure-Driven Cycles . . . . . . . . . . . . . . . . . . . . . . . . . 51.1.3 Other Presentations of the AHT Cycles . . . . . . . . . . . . . . 7

1.2 The AHT Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81.2.1 The First Law Efficiency . . . . . . . . . . . . . . . . . . . . . . . . 81.2.2 The Second Law Efficiency . . . . . . . . . . . . . . . . . . . . . . 9

1.3 Dynamics of AHT Cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.4 Adsorbents Optimal for AHT . . . . . . . . . . . . . . . . . . . . . . . . . . 12

1.4.1 The First Law Efficiency . . . . . . . . . . . . . . . . . . . . . . . . 131.4.2 The Second Law Efficiency . . . . . . . . . . . . . . . . . . . . . . 131.4.3 Adsorbent Optimal from the Dynamic Point of View . . . . 14

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2 Measurement of Adsorption Dynamics: An Overview . . . . . . . . . . . 192.1 Differential Step (IDS) Method . . . . . . . . . . . . . . . . . . . . . . . . . 212.2 Large Pressure Jump (LPJ) Method . . . . . . . . . . . . . . . . . . . . . . 222.3 Large Temperature Jump (LTJ) Method . . . . . . . . . . . . . . . . . . . 24

2.3.1 Volumetric Large Temperature Jump Method (V-LTJ) . . . . 252.3.2 Gravimetric Large Temperature Jump Method (G-LTJ) . . . . 27

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3 Experimental Findings: Main Factors Affecting the AdsorptiveTemperature-Driven Cycle Dynamics . . . . . . . . . . . . . . . . . . . . . . . 313.1 Adsorbate and Adsorbent Nature . . . . . . . . . . . . . . . . . . . . . . . . 32

3.1.1 Water Sorption Dynamics . . . . . . . . . . . . . . . . . . . . . . . . 333.1.2 Methanol Sorption Dynamics . . . . . . . . . . . . . . . . . . . . . 34

3.2 Adsorbent Grain Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

vii

3.2.1 Water Sorption Dynamics . . . . . . . . . . . . . . . . . . . . . . . . 363.2.2 Methanol Sorption Dynamics . . . . . . . . . . . . . . . . . . . . . 413.2.3 Ethanol Sorption Dynamics . . . . . . . . . . . . . . . . . . . . . . 44

3.3 Geometry of the Adsorber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483.3.1 Water Sorption Dynamics . . . . . . . . . . . . . . . . . . . . . . . . 493.3.2 Methanol Sorption Dynamics . . . . . . . . . . . . . . . . . . . . . 493.3.3 Ethanol Sorption Dynamics . . . . . . . . . . . . . . . . . . . . . . 52

3.4 Cycle Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 573.4.1 Methanol Sorption Dynamics . . . . . . . . . . . . . . . . . . . . . 573.4.2 Ethanol Sorption Dynamics . . . . . . . . . . . . . . . . . . . . . . 60

3.5 Residual Gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 613.5.1 Water Sorption Dynamics . . . . . . . . . . . . . . . . . . . . . . . . 62

3.6 Flux of Cooling/Heating Heat Carrier Fluid . . . . . . . . . . . . . . . . 65References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

4 Optimization of an “Adsorbent/Heat Exchanger” Unit . . . . . . . . . . 694.1 Optimization of the “Adsorbent–Heat Exchanger” Unit . . . . . . . . 71

4.1.1 Adsorbent Grain Size . . . . . . . . . . . . . . . . . . . . . . . . . . . 714.1.2 The Ratio “Heat Transfer Surface”/“Adsorbent Mass” . . . . . 744.1.3 The Effect of the Flow Rate of External Heat Carrier . . . . 764.1.4 Comparison of the Model Configurations

with Full-Scale AHT Units . . . . . . . . . . . . . . . . . . . . . . . 784.2 Compact Layer Versus Loose Grains . . . . . . . . . . . . . . . . . . . . . 794.3 The Effect of Residual Gases . . . . . . . . . . . . . . . . . . . . . . . . . . . 814.4 Reallocation of Adsorption and Desorption Times

in the AHT Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

viii Contents

Chapter 1Adsorptive Heat Transformationand Storage: Thermodynamicand Kinetic Aspects

Nomenclature

A AdsorberAd-HEx Adsorbent–heat exchangerAHP Adsorption heat pumpAHT Adsorptive heat transformerC Condenser, thermal capacity J K−1

COP Coefficient of performanced Thickness, mΔF Adsorption potential, J mol−1

E EvaporatorLTJ Large Temperature Jump methodLPJ Large Pressure Jump methodh Convective heat transfer coefficient, W m−2 K−1

HEx Heat exchangerHMT Heat and mass transferm Dry adsorbent mass, kgP Pressure, PaPD Pressure drivenQ Thermal energy, JR Universal gas constant, J mol−1 K−1

S Solid, entropy J kg−1, heat transfer surface area, m2

SP Specific power, W kg−1

T Temperature, KTD Temperature drivenU Overall heat transfer coefficient, W m−2 K−1

V Vapourw Water uptake, g g-1W Work, J

© The Author(s) 2018A. Sapienza et al., Dynamics of Adsorptive Systems for Heat Transformation,SpringerBriefs in Applied Sciences and Technology,https://doi.org/10.1007/978-3-319-51287-7_1

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Greek Symbols

D Differential operatork Thermal conductivity, W m−1 K−1

Subscripts

0 Initial stage, saturation vapourads Adsorbent/adsorptionc Coolingcon Condensationdes Desorptionef Effectiveev Evaporationf Fluidh HeatingH HighL LowM Mediummet Metalus Usefulw Wall/solid side

At present, the majority of thermodynamic cycles of heat engines arehigh-temperature cycles that are realized by internal combustion engines, steam andgas turbines, etc. [1]. Traditional heat engine cycles are mainly based on burning oforganic fuel that may result in dramatic increase of CO2 emissions and globalwarming. The world community has realized the gravity of these problems andtaken initiatives to alleviate or reverse this situation. Fulfilment of these initiativesrequires, first of all, the replacement of fossil fuels with renewable energy sources(e.g. the sun, wind, ambient heat, natural water basins, soil, air). These new heatsources have significantly lower temperature potential than that achieved byburning of fossil fuels which opens a niche for applying adsorption technologies forheat transformation and storage [2].

A classical heat engine consumes heat Q1 from a heat source with high tem-perature TM, discharges heat Q2 to a heat sink with lower temperature TL andproduces the maximal work W = Q1 − Q2 = Q1 (1 − TL/TM) [3] (the left part ofFig. 1.1). The produced work can be used to drive a heat pumping cycle (the rightpart of Fig. 1.1). An adsorptive heat transformer (AHT) operates between threethermostats (TL, TM, TH) (Fig. 1.2) and consumes/produces only thermal energy. Inthis chapter, we shortly survey the fundamentals of the heat transformation viaadsorption processes:

2 1 Adsorptive Heat Transformation and Storage …

(a) various heat transformers and thermodynamic cycles;(b) their first and second law efficiencies;(c) dynamic peculiarities of the AHT cycles.

Finally, the question “What adsorbent is optimal for particular AHT cycle?” isanalysed to make appropriate practical recommendations.

1.1 Thermodynamic Cycles for AHT

An AHT exchanges heat fluxes between three thermostats (I, II and III) maintainedat high (TH), middle (TM) and low (TL) temperatures (Fig. 1.2). The AHT trans-forms heat at three modes: (1) cooling, (2) heating and (3) upgrading temperaturepotential (heat amplification). Such a three temperature (3T) AHT consists of anevaporator, E, at temperature TL, a condenser, C, at temperature, TM, and anadsorber, A, among which a vapour, V, of the working fluid is exchanged andwhich consumes/supplies heat from/to the appropriate thermostats (Fig. 1.2).

The interaction between a non-volatile solid S (adsorbent) and a volatile V(adsorptive) compound

TM

TH

Q4

Q3

T

T

Q4

Q3

TM

TL

Q1

Q2

T

TL

Q1

Q2

WORK PRODUCTION HEAT PUMPING

Fig. 1.1 Three temperature(3T) diagram of the heattransformation

TH

TM

TL

C

E

Fig. 1.2 Operation principleof an AHT: 1—cooling mode,2—heating mode, 3–temperature upgrading mode

1 Adsorptive Heat Transformation and Storage … 3

Vþ S,VS ð1:1Þ

leads to transition of the vapour V into an adsorbed state VS (adsorbate) withreleasing the heat of adsorption Qads (discharging or heat release stage). The inverseprocess of VS decomposition (or vapour desorption) requires supply of thermalenergy which is converted to chemical (charging or heat storage stage). Theevaporator, E, is a source of the vapour at the adsorption stage, which is concen-trated in the condenser, C, during the desorption stage.

Two types of the cycles suggested for AHT essentially differ by the way ofadsorbent regeneration:

• by adsorbent heating up to the temperature sufficient for the adsorbate removal;• by reducing the adsorptive pressure over adsorbent at constant temperature.

The first, temperature-driven (TD), cycles are very common and widely used torealize cooling and heating modes (1 and 2 on Fig. 1.2) [2, 4]. The second,pressure-driven (PD), cycles are much less spread and suggested mainly for thetemperature upgrading mode (3 on Fig. 1.2) [5, 6]. In this book, generally TDcycles are considered as the most prevalent. However, the examination of PDcycles, even if preliminary, is very important as this way of desorption initiation canbe different from the TD one [7].

1.1.1 Temperature-Driven Cycles

A typical cycle driven by jump of the adsorbent temperature consists of two iso-steres and two isobars as presented on the Clapeyron diagram ln(P) versus (−1/T)(Fig. 1.3). The heat supplied from external heat source at temperature TH is used forisosteric heating of adsorbent (stage 1–2) and removing adsorbed vapour (regen-eration stage 2–3) at constant vapour pressure PM. Commonly, the regenerationtemperature has to be at least 50–60°C [8]. The heat Qdes is supplied for desorption.During desorption process 2–3, the valve between the adsorber and condenser isopened, and the desorbed vapour is collected in the condenser where the heat ofcondensation Qcon is released. The regenerated adsorbent is cooled by a heat carrier(cooling fluid) at temperature TM. The cooling is first performed at constant uptakew1 (isostere 3–4) and then at constant pressure PL (isobar 4–1). During adsorptionprocess 4–1, the valve between the adsorber and the evaporator is opened. The heatof adsorption Qads transfers to the cooling fluid and can be supplied to a consumer.During isosteric stages, the valve between the adsorber and condenser/evaporator isclosed.

Five basic TD cycles, such as air conditioning, heat pumping (two cycles) anddeep freezing (two cycles), were selected as reference cycles in the key review [2].These basic cycles differ by the three boundary temperatures TL, TM and TH [2].Small changes of this cycle classification have been recently suggested in [9, 10].


There are many modifications of this basic cycle suggested to improve its perfor-mance, the most important of which are heat [11] and mass recovery [12], cascadedsorption refrigeration [13] and thermal wave [14] cycles. Recently, reallocation ofthe duration of the adsorption and desorption phases of AHT cycle has been sug-gested in order to further improve both the cycle COP and specific power [15, 16].This new approach will be considered in Chap. 4. Further cycle modification wassuggested for a three-bed adsorption chiller in order to make possible a combinationof the “time reallocation” concept with the “mass recovery” approach [17].

1.1.2 Pressure-Driven Cycles

A typical PD cycle consists of two isosteres and two isotherms (Fig. 1.4). Theregeneration of adsorbent is performed at constant temperature TM by dropping thevapour pressure over the adsorbent (stage 4–1). It is somewhat similar to thepressure swing adsorption process used for gas drying and separation [18].

The initial adsorbent state (point 1 on Fig. 1.4) corresponds to temperature TMand pressure of the adsorptive vapour PL = P0(TL), where P0(TL) is the saturationvapour pressure at temperature TL. The weak isostere is characterized by theequilibrium adsorbate content w1 = w(TM, PL). Then, the adsorbent is heated up totemperature TH (stage 1–2) at constant uptake w1. At point 2, the adsorber isconnected with the evaporator maintained at TM that is the temperature of theexternal heat source which temperature level to be upgraded. The evaporator

ln (P)

1

32

4

LGSL

1/Tc 1/T2 1/Tg

ln(Pc)

1/Te

+Qd-Qc

-Qa - 1/T

Fig. 1.3 P-T diagram of the TD adsorptive cycle

1.1 Thermodynamic Cycles for AHT 5

generates the constant pressure PM = P0(TM) of adsorptive. This pressure jump P2

! PM causes the vapour adsorption that leads to an increase in the equilibriumadsorbate content up to w2 = w (TH, PM) (point 3 on Fig. 1.4). The heat ofadsorbate evaporation Qev is absorbed in the evaporator at T = TM, and the usefuladsorption heat Qads is released at constant temperature TH (isotherm 2–3) in theheating circuit of a consumer. Then, the adsorber is disconnected from the evap-orator and cooled down to the intermediate temperature TM (isostere 3–4) at con-stant uptake w2. At point 4, the adsorber is connected with the condensermaintained at temperature TL and pressure PL = P0(TL). This pressure drop P4 !PL results in the adsorbate desorption to restore the initial uptake w1 = w(TM, PL)(point 1). The heat Qdes needed for adsorbate desorption is supplied to the adsorbentat temperature TM from the external heat source (isotherm 4–1). The excess ofadsorbate is collected in the condenser releasing the heat Qcon to the ambient, andthe cycle is closed. The work is required to pump the liquid adsorbate from the lowpressure level in the condenser to the high pressure level in the evaporator.

This cycle was considered in [5, 19] for upgrading industrial waste heat andsuggested in [6] for increasing the temperature potential of the ambient heat to thelevel sufficient for heating dwellings. The main feature of the latter cycle is thatregeneration of adsorbent is performed by dropping the vapour pressure and thisdrop is ensured by low ambient air temperature (e.g. TL = (−20)–(−60)oC). In thiscase, the adsorbent regeneration does not need supply of energy that has com-mercial value, and it is easier at colder ambient. Since the useful heat that gainscommercial value is obtained by means a low ambient temperature, the newapproach is called “Heat from Cold” (HeCol). It can be interesting for countrieswith cold climate, especially for the Arctic zone [6].

Fig. 1.4 P-T diagram of the PD adsorptive cycle


1.1.3 Other Presentations of the AHT Cycles

Both types of the AHT cycles can be presented in many different ways, e.g. plottedas P(T) [20], T(S) [21] and w(ΔF) [9, 22] diagrams, where S is the entropy change,which sometimes can be more convenient than the Clapeyron chart. For instance,both TD and PD cycles in the w(ΔF) presentation are very simple. If there is nohysteresis, they are just one line that describes both isobaric adsorption and des-orption stages (Fig. 1.5). In this case, only two parameters (ΔFmin and ΔFmax) arenecessary to describe the cycle; therefore, it is convenient to plot the cycle ΔF-windows as made in [9, 23, 24].

Point A in Fig. 1.5 represents the boundary conditions at the end of theadsorption stage (point 1 on Fig. 1.3). It corresponds to the adsorption potentialΔFmin = −RT1 ln[Pe/Po(T1)] that characterizes the minimal adsorbent affinity nec-essary to bind an adsorptive at temperature T1 = Tc and pressure P(Te). Point B inFig. 1.5 represents the boundary conditions at the end of the desorption stage (point3 in Fig. 1.3) and corresponds to the adsorption potential ΔFmax = −RT3 ln[Pc/Po(T3)] that is defined by the conditions of heat rejection P(Tc) and adsorbentregeneration (TH). Adsorbate molecules that are bound to the adsorbent with anaffinity lower than ΔFmax = −RTH ln[Pc/Po(TH)] can be desorbed during theregeneration stage 2–3. Those bound more strongly remain adsorbed and are notinvolved in the heat transformation cycle.

If the two boundary temperatures TL and TM are fixed, the minimal desorptiontemperature Tmin = T2 can be estimated by equating the ΔF-values for the rich andweak isosteres:

�RTMIn PL=Po TMð Þ½ � ¼ �RTminIn PM=Po Tminð Þ½ �: ð1:2Þ

Equation (1.2) can be solved graphically to get Tmin(TL, TM). Interestingly, thisvalue is equal to that calculated by simple Trouton’s rule [8, 25]:

w

∆F∆Fmin ∆Fmax

wmax

wmin

A

B

Fig. 1.5 w(ΔF) presentationof AHT cycle

1.1 Thermodynamic Cycles for AHT 7

Tmin ¼ TMð Þ2=TL ð1:3Þ

within an accuracy of ±1°C [26]. Evidently, if the temperature of the external heatsource TH is lower than Tmin, the cycle cannot be realized at all. Although both rightand left parts of Eq. (1.2) depend on the adsorbate nature, the minimal desorptiontemperature does not.

The w(ΔF)-presentation is very convenient because the ΔF-value can be used todefine the AHT cycle borders, on the one hand, and is a universal measure of theadsorbent affinity to the adsorptive, on the other hand [9, 27]. Fortunately, for themajority of adsorbents promising for AHT, this presentation can be correctlyapplied, because there is a one-to-one correspondence between the equilibriumuptake w and the ΔF-value [26].

Although this and other cycle presentations listed above can be very useful forparticular cases, in whole, they are much less spreading than the commonClapeyron diagram.

1.2 The AHT Efficiency

Here, the efficiency of AHT cycles is considered based on the first and second lawsof thermodynamics. This analysis made is invariant with the cycle type (TD or PD),and the efficiencies are determined only by the heats exchanged and the cycleboundary temperatures.

1.2.1 The First Law Efficiency

For an ideal 3T cycle (with zero thermal masses), the energy balance is given as

Qcon�Qev�Qdes þQads ¼ 0 ð1:4Þ

(see definition of the heats on Figs. 1.2 and 1.3). The first law efficiency of AHTunit or its coefficient of performance (COP) is then defined as

COPc ¼ Qev=Qdes ð1:5Þ

COPh ¼ Qcon þQadsð Þ=Qdes ¼ 1þCOPc ð1:6Þ

for cooling and heating, respectively. For real systems, heating of inert masses(adsorbent, metal, etc.) is also important, and the COP value depends on theadsorbate mass Δw exchanged in the cycle


COPc Dwð Þ ¼ QevDw= QdesDwþC TH�TMð Þ½ � ¼ COPc Dw= DwþBð Þ½ �; ð1:7Þ

where B = C(TH–TM)/Qdes which is the ratio of the sensible heat of all inert massesto the latent heat necessary for desorption. Equation (1.7) suggests that to increasethe first law efficiency, the exchanged mass Δw = w2–w1 must be maximized andthe contribution B of inert masses minimized (see more detailed analysis in [20] andin Sect. 1.4.1).

1.2.2 The Second Law Efficiency

For an ideal TD system, the energy balance (the first law) of Eq. (1.4) should besupplemented with the entropy balance and given as

�Qcon=TM þQev=TL þQdes=TM � Qads=TH ¼ DS� 0: ð1:8Þ

If all the processes are completely reversible, the entropy generation is equal tozero (DS = 0). Figure 1.1 can be used for better physical interpretation of thesecond law analysis. It illustrates that a 3T AHT cycle can be conditionally dividedinto two Carnot cycles, namely the bottom cycle between temperatures TL and TMand the top cycle between temperatures TM and TH. For instance, for the heatamplification (mode 3 on Fig. 1.2), the bottom cycle works as a heat engine cycleand the top one as a heat pump cycle. Both the cycles are coupled and runsimultaneously. The bottom cycle produces the work W = Q1(1 − TL/TM) which isused to upgrade the heat Q3 to higher temperature level TH in the top cycle(Fig. 1.1). The Carnot efficiency of the heat engine working at very unusual con-ditions is shown in Fig. 1.6 left: the heat is consumed at TM = 2°C = 275 K andrejected at TL between 275 and 100 K. The thermostat at 2°C can be a naturalnon-freezing water reservoir, such as ocean, sea, river, lake, underground water. If

(a) (b)

Fig. 1.6 The second law efficiency for two (a) and three (b) temperature cycles as a function ofthe ambient air temperature TL (left—TM = constant = 275 K; right—the TM values are indicatednear appropriate curves (in K) and (TH−TM) = 30 K) [6])

1.2 The AHT Efficiency 9

the other natural thermostat, e.g. the ambient air, has temperature TL = −30°C(243 K) and −50°C (223 K), the efficiency of the Carnot heat engine equals 0.116and 0.189, respectively (Fig. 1.6a). It seems quite encouraging, especially if keep inmind that the heat at TM is consumed for free. Afterwards, this work can be used toupgrade the temperature of heat taken from the water basin up to a higher level (TH)sufficient for heating, thus gaining commercial value [6].

The Carnot efficiency of the whole 3T heat transformer was calculated forcooling, heating and temperature upgrading modes in [28, 29]:

COPCc ¼ 1=TM�1=THð Þ= 1=TL�1=TMð Þ; ð1:9Þ

COPCh ¼ 1=TL�1=THð Þ= 1=TL�1=TMð Þ; ð1:10Þ

COPCT ¼ 1=TL�1=TMð Þ= 1=TL� 1=THð Þ: ð1:11Þ

The function COPTC(TL) is calculated from Eq. (1.11) for various TM and the

constant temperature lift (TH − TM) = 30 K (Fig. 1.6b). At ambient temperatureTL = −40°C, the Carnot efficiency is higher than 0.6 and further increases if morewarm natural water is available (e.g. underground water at TM = 30°C).

Equations (1.5) and (1.6) express the first law AHT efficiency through theenthalpies of evaporation and desorption which are characteristics of the adsorbent–adsorbate pair. The second law efficiency in Eqs. (1.9)–(1.11) depends only on thethree temperatures that determine the AHT cycle, but not on properties of theworking pair in an explicit form. The link between these two COP definitions wasconsidered in [29] (see also Sect. 1.4.2).

1.3 Dynamics of AHT Cycles

Another important figure of merit that is used to characterize the AHT performanceis the specific power (SP) which can be defined as

SP ¼ Qus=ðmadstÞ; ð1:12Þ

where Qus is the useful heat (e.g. Qev for cooling cycles), mads is the dry adsorbentmass, and t is the cycle time. The power can also be related to a unit volume of theadsorbent or the whole AHT device. This parameter defines the quantity ofadsorbent or the size of AHT unit necessary to obtain a given power.

The target to develop compact and efficient AHT units asks for a high rate ofadsorption/desorption process at the isobaric stages of AHT cycle (Fig. 1.3). Theinteraction of vapour molecules with a solid surface is itself very fast, and theoverall rate is usually determined by the intensity of heat and mass transfer(HMT) in the unit “adsorbent–heat exchanger” (Ad-HEx). Namely, poor HMT isconsidered to be a crucial factor for heat transformers based on solid sorption


technology [30] and its improvement is a key point. The heat transfer is deemed tolimit the sorption processes if the adsorbent bed is composed of loose grains. Themass transfer is crucial for compact adsorbent beds/layers consolidated with abinder.

The heat transfer in AHT systems is characterized by the overall heat transfercoefficient U given by the well-known relation:

1USf

¼ 1hf Sf

þ 1hwSef

þ defkef Sef

; ð1:13Þ

where Sf and Sef are the heat transfer surfaces on the fluid and solid sides, hf and hware the heat transfer coefficients on these sides, and def and kef are the effectivethickness and thermal conductivity of the adsorbent bed.

It is convenient to use Eq. (1.13) for analysing the main heat transfer resistances(Fig. 1.7):

• The first term in the right side describes the heat transfer between the heat carrierfluid and the HEx fin; the heat transfer coefficient hf is high (> 500−1,000 W/(m2 K)) except for the special case of thermal wave process for which a laminarflow is required [14]. The heat transfer surface Sf has to be maximized; there-fore, advanced HEx modules are highly desirable as discussed in Chap. 4;

• Slow heat transfer in AHT units is deemed to be due to the high thermal contactresistance between the adsorbent bed and the HEx wall (the second term inEq. (1.13)) and the low effective thermal conductivity of the bed (the thirdterm). This is especially crucial for AHT utilizing loosed adsorbent grains. Thehigh wall contact resistance is mainly due to (a) increasing porosity of theadsorbent bed adjacent to the HEx wall and (b) the absence of gas convection inthe voids near the wall. In the majority of mathematical models, the heat transfer

Fig. 1.7 Schematics of various heat transfer resistances in the Ad-HEx unit

1.3 Dynamics of AHT Cycles 11

coefficient hw on the solid side is taken as 15–50 W/(m2 K) [31, 32]. It can beenhanced by (a) increasing the bed density near the wall due to grain gluing(binding) [33] or by the bed filling with multi-sized grains [34]. The “wall–bed”heat transfer can also be enhanced by simply extending the heat transfer surfaceSef as typical for well-designed Ad-HExes [35]. In this case, the term (hw Sef)can reach high values even if hw is small, provided Sef be high enough [30];

• High heat transfer resistance is caused by the low effective conductivity kef ofthe granular bed itself (about 0.1 W/(m K) for zeolite and 0.2–0.3 W/(m K)active carbon). This conductivity can be increased by developing either con-solidated adsorbent beds or coated HEx surfaces [30, 33, 36] with advanced kef -values. However, in consolidated beds/coatings the mass transfer problems canarise. The extensive, yet efficient, trick is reduction of the bed thickness that isreadily reached in modern HExs with extended surface area (see Chap. 4). Asshown in [35], for the loose grains configuration, practically interesting SPvalues can be obtained only for thick enough beds of 2–4 mm.

It is worthy to mention that the above-discussed low values of the bed heattransfer parameters (hf and keff) were measured under quasi-equilibrium conditions,means, at small deviation of the system from the equilibrium. Typical examples arethe IDS method (see [37] and Sect. 2.1) suggested for measuring the gas diffusivityunder isothermal and isobaric conditions, or a hot wire method [38] widely appliedfor determination of the thermal conductivity by analysing the system response aftera small deviation from adsorption or thermal equilibrium. For real AHT units, theessential temperature difference (20–40°C) between the HEx fin and the adsorbentbed is typical. This may result in significant intensification of heat and mass transfer(see [7, 39] and Chap. 4).

1.4 Adsorbents Optimal for AHT

Future progress in the AHT field is essentially related to the development ofinnovative adsorbents suitable of efficient AHT performance. Two complementarystrategies are used [40]: (a) systematic testing for AHT aims various adsorbentsinitially developed for other targets (gas drying, separation, etc.) and (b) tailoring ofnew specific adsorbents adapted to variety of AHT cycles under different climaticand boundary conditions. The first step of both strategies is the formulation ofrequirements to an adsorbent which is, in theory, optimal for the particular AHTcycle [40]. The requirements evidently depend on what criterion is used to evaluatethe optimal performance: the first or second law efficiency. More difficult is theassessment of the dynamic optimality, which depends less on adsorbent inherentproperties and more on a number of external factors, such as design of heatexchanger, configuration of adsorbent bed, efficiency of heat supply/rejection,pressure and temperature levels. [7, 9, 39]. The requirements to adsorbents optimal


for common TD cycles are discussed below. Those for PD cycles have recentlybeen formulated elsewhere [41, 42].

1.4.1 The First Law Efficiency

According to Eqs. (1.5) and (1.6), the ideal cooling and heating COP approaches to1 and 2, respectively, when Qev ! Qdes. For instance, this COP for silica gels islarger than for zeolites as less heat is used for regeneration (45–55 kJ/mol vs. 60–80 kJ/mol). If carefully account for the inert masses M (Eq. (1.7)), the COP cansignificantly decrease, when these masses are 2–3 times larger than the mass ofadsorbent mads [20]. This is more pronounced for the “Fuji silica RD—water”system than for “Mitsubishi AQSOA Z02—water” one, because for the lattersystem the exchanged mass Δw is 3–4 times larger, which accords with Eq. (1.7).

For well-designed AHT units (mmet/mads � 1), the COP approaches its maximumvalue (Qev/Qdes) already at Δw � (0.1–0.15) and (0.2–0.3) g/g for water andmethanol/ammonia, respectively. Hence, to achieve the maximum first law effi-ciency it is sufficient to use an adsorbent that exchanges the mentioned amount of aworking fluid (or more) between the rich and weak isosteres. Such an adsorbentmay be considered as harmonized with the particular cycle. Well-enough adsor-bents of water, methanol and ammonia adequately satisfy this condition for airconditioning and heat pumping cycles.

It is important to highlight that:

(a) searching for adsorbents with very large Δw values (> 0.5 g/g), such as SWSs[43], MOFs [44], is the ultimate priority for heat storage rather than for cooling/heating applications;

(b) the maximum COPc (0.7–0.9) for real AHT cycles is significantly lower thanpredicted (Eq. (1.9)) for a reversible Carnot cycle with the same boundarytemperatures [45, 46]. Very special case when the first and second law effi-ciencies are equal is considered right below;

(c) the question “What is the well-designed Ad-HEx unit?” is considered inSect. 1.4.

1.4.2 The Second Law Efficiency

As stated just above, the experimental COP of typical adsorptive and absorptivechillers is significantly lower than predicted by Eq. (1.9) [46]. This difference isonly slightly compensated by various modifications of the basic 3T cycle, e.g. byusing “double-effect” cycles in which waste heat from an upper cycle is used todrive a lower cycle [13, 25]. The main reason of this huge distinction is the thermalentropy production caused by the external thermal coupling ΔT = TH – TM [45].

1.4 Adsorbents Optimal for AHT 13

Indeed, the process of heat transfer during the adsorber heating (stages 1–2 and 2–3) and cooling (3–4 and 4–1) is highly irreversible; therefore, to enhance the AHTefficiency the thermal coupling should be minimized.

The most of entropy is produced during isobaric adsorption (4–1) and desorption(2–3) stages. If the heat for regeneration is supplied directly at the minimal des-orption temperature (TH = Tmin = T2), there is no thermal coupling at stage 2–3;therefore, no entropy is generated during desorption process. As a result, the COPvalues calculated from the first and second laws are equal, so that the maximum(Carnot) efficiency is reached as shown in [29].

This imposes appropriate requirements on the shape of the sorption isobar for anadsorbent optimal for TD AHT cycles: The rich and weak isosteres must coincide,so that the cycle becomes degenerated, and the isobaric adsorption 4–1 and des-orption 2–3 (Fig. 1.3) occur immediately and completely at temperatures TM andTH (Fig. 1.8a), respectively [26]. The degenerated cycle can be realized only withan adsorbent characterized by a mono-variant equilibrium. The optimal adsorbenthas to sorb a large amount of adsorbate in a stepwise manner directly at TM and PL

and completely desorb it at TH and PM (Fig. 1.8b). Hence, in theory, the adsorbentoptimum for AHT should have a stepwise adsorption isobar [26, 47]. Real adsor-bents, however, exhibit S-shaped adsorption isobars (Fig. 1.8c) instead of strictlystepwise ones. Such adsorption equilibrium corresponds to isotherms of types Vand VI in the IUPAC classification [48]. The second law harmonization of theadsorbent and the cycle means that the position of the step must coincide with theboundary temperatures TM = T4 at P = PL and T2 = TH at P = PM as shown inFig. 1.8b. If the adsorbent is not optimal so that the adsorbate is removed atTH > Tmin, the efficiency becomes lower than the Carnot one.

Hence, a high second law efficiency may be attained by a proper choice ofadsorbent without using efficient, but sophisticated methods of heat recovery inmulti-bed [49] and thermal wave [14] systems, or “multi-effect” cycles [13, 25].

1.4.3 Adsorbent Optimal from the Dynamic Point of View

As mentioned above, it is more difficult to formulate the dynamic requirements tothe optimal adsorbent because the whole unit “adsorbent + heat exchanger” has tobe considered [7, 9, 39]. A simplified dynamic analysis can be performed for thecommon case when the adsorption rate, at least, initial, is controlled by the heattransfer between the adsorbent and heat exchanger (HEx) fin [50].

This analysis reveals that for the process intensification and reduction of thecycle time the most profitable is to supply the majority of heat to or reject it fromthe adsorbent bed at maximal possible temperature difference between the HEx andthe adsorbent. At desorption stage, the position of the isobar step should be close tothe minimum desorption temperature T2, while the regeneration temperature THshould be higher to create sufficient driving force to supply heat for desorption. Atadsorption stage, the step should be positioned at temperature Tads that is higher


than the temperature TM of cooling fluid to create sufficient driving force forrejecting heat of adsorption. It is worthy to mention that this dynamic requirementto maximize the temperature difference DT = TH – Tdes (or Tads – TM) is in a dis-tinct contradiction with the thermodynamic requirements which suggest to mini-mize DT to reduce the entropy generation. Thus, proper choice of the isobar step

Fig. 1.8 Degenerated AHTcycle characterized by asingle adsorption/desorptionisostere (a); correspondingstep-like (b, d) and S-shaped(c) isobars of adsorption (atP = PL) and desorption (atP = PM) optimum from thethermodynamic (b, c) anddynamic (d) points of view[9]

1.4 Adsorbents Optimal for AHT 15

position greatly depends on which output parameter is to be maximized—theefficiency or the power. If both parameters are important, a reasonable compromisemust be reached by intelligent design of the “adsorbent—heat exchanger”(Ad-HEx) unit (see Chap. 2). This situation is very typical since the highest COP isalways obtained at low power [30], means, at slow dynamics. In any case, the mostadvantageous adsorption isobar is step-like with the largest acceptable ΔT betweenthe step temperature and the HEx fin temperature (Fig. 1.8d).

The two types of adsorptive cycles for heat transformation, namely temperatureand pressure driven, dictate two different methodologies for studying the cycledynamics. A Large Temperature Jump (LTJ) method [51] imitates non-isothermalconditions of the isobaric stages of TD AHT cycles (2–3 and 4–1 on Fig. 1.3).A Large Pressure Jump (LPJ) method can be used to simulate isothermaladsorption/desorption dynamics caused by the vapour pressure jump/drop atappropriate stages of PD AHT cycles (2–3 and 4–1 on Fig. 1.4) [52]. The lattermethod is known since many years [53]; however, until recently, it has been used ina way that the pressure jump/drop was not linked with the particular AHP cycle (seee.g. [54]) as discussed in [7]. Both these methods are comprehensively introducedin Chap. 2, and appropriate results obtained are considered in Chap. 4.

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33. J. Bauer, R. Herrmann, W. Mittelbach, W. Schwieger, Zeolite/aluminum compositeadsorbents for application in adsorption refrigeration. Int. J. Energy Res. 33, 1233–1249(2009)

References 17

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Chapter 2Measurement of Adsorption Dynamics:An Overview

Nomenclature

Ad-HEx Adsorbent–heat exchangerCOP Coefficient of performanceLTJ Large Temperature Jump methodV-LTJ Volumetric version of the Large Temperature Jump methodG-LTJ Gravimetric version of the Large Temperature Jump methodLPJ Large Pressure Jump methodHEx Heat exchangerIDS Isothermal Differential StepP Pressure, PaPD Pressure drivenSCP Specific cooling power, W kg−1

T Temperature, KTD Temperature driven

Subscripts

ads Adsorbent/adsorptionc Condensatione EvaporationH High

Analysis of the Ad-HEx dynamic behaviour is of pivotal importance in develop-ment of advanced adsorber concepts, enabling reduction of weight and volume ofthe real adsorption heat pump/chiller unit, as well as its energy density enhance-ment. In general, the experimental methodologies for adsorber performance eval-uation can be distinguished considering different scales of the tested adsorber:

(1) Investigation of adsorption kinetics of the adsorbent itself, allowing to obtaindetailed experimental data, that are useful for estimating the heat and masstransfer characteristics.


19




In case of water as adsorbate kinetics of adsorption in common porous media(zeolite, silica gel, etc.) was a subject of numerous studies [1], demonstrating thatthe adsorption kinetics is dictated by heat transfer and water transport throughadsorbent pores. In the following paragraph, we treat an Isothermal DifferentialStep (IDS) method that is considered today the most adequate method to measurethe water adsorption kinetics on adsorbents.

(2) Study of adsorption dynamics of the adsorbent (Ad) and heat exchanger(HEx) as an integrated unit (Ad-HEx).

This is an important aspect, as the overall adsorption rate depends on both heatand mass transfer properties of the combination of the adsorbent itself and the heatexchanger unit. Another important requirement is to study the adsorption dynamicsunder operating conditions that are as close as possible to the real operating con-ditions of an adsorption heat pump. To fit these requirements, two main differentapproaches are used [2]:

(a) a Large Pressure Jump (LPJ) method, where adsorption is initiated by a pres-sure jump imposed to the sample, continuously cooled by an external source. Inthis method, the heat transfer properties of the samples still have major influ-ence in the experiments due to the heat released during adsorption. The LPJmethod is adequate for pressure-driven AHT cycles (see Chap. 1, Fig. 1.4)

(b) a Large Temperature Jump (LTJ) method, where adsorption is enabled by atemperature swing of a heat exchanger wall that is in thermal contact with theadsorbent under an almost isobaric ad/desorption stage. The LTJ method ispractically implemented in two ways, depending on the measurement techniquefor monitoring the temporal evolution of the adsorbed mass: indirect (volu-metric) and direct (gravimetric). These LTJ methods are suitable for commontemperature-driven AHT cycles (see Chap. 1, Fig. 1.3)

In the following paragraph, the fundamentals and main apparatuses realized forthe LPJ and LTJ tests are introduced.

(3) Study of the dynamic behaviour of full-scale adsorbers, allowing to evaluate thecoefficient of performance (COP) and the Specific Cooling Power (SCP), thatare important figures of merit for adsorption heat pumping/cooling processes.

Normally, such experimental studies are carried out by dedicated test-rigs thatare designed to test the entire adsorber under realistic boundary conditions [3]. Thisspecific testing methodology will not be a subject of this book.

20 2 Measurement of Adsorption Dynamics: An Overview

2.1 Differential Step (IDS) Method

The Isothermal Differential Step (IDS) method is considered the simplest and mosteffective method to investigate the adsorption kinetics of the adsorbent, allowing toobtain important kinetic parameters like the diffusion constant, vapour diffusivityand heat transfer parameters [1]. The uptake rate is determined by the analyticalsolution of the differential mass balance equation. Normally, measurement ofkinetic curves is coupled with water adsorption equilibrium measurement, as theknowledge of adsorption equilibrium parameters is required for the data analysis.

IDS method involves the following typical test procedure:

(i) setting of initial equilibrium between the adsorbent and adsorbate vapour atgiven pressure P0 and temperature T0;

(ii) stepwise change of pressure by a small value ΔP (typically a few mbars)under isothermal conditions;

(iii) direct measurement of the adsorbent weight evolution due to water sorption(i.e. measurement of the kinetic curves).

Many papers on the IDS method are available in literature. Here, as an example,we report application of the IDS method for studying the kinetics of wateradsorption on silica Fuji Davison RD and the composite sorbent SWS-1L “calciumchloride in silica gel” [4, 5]. In such works, the IDS method was applied by using aCAHN 2000 thermo-balance, which is a force-to-current converter (balance reso-lution: 0.1 mg, reproducibility ± 0.2 mg, accuracy ± 0.1%). Figure 2.1 shows theoverall schematic of the closed-volume thermo-gravimetric system. The essentialcomponents are the measuring cell (glass version) where the sample and balance arecontained, a vacuum pump for initial degassing operations, a thermostated waterreservoir, which acts as vapour dosing system, a thermal regulator that allows thesample temperature control with accuracy ± 0.1 K.

Measurements are carried out using a small amount of sample (typically 10 mg)in order to reduce thermal effects [1]. For further reduction of these effects, theadsorbent grains are dispersed on the surface of aluminium pan and mixed withsmall pieces of copper wire in order to increase the heat capacity of the measuringcell and keep the sample as close as possible to the ideal isothermal condition.

Typical experimental run to obtain direct experimental data for the kinetics of wateradsorption is as follows: the sample under test is initially degassed at high temperaturefor several hours and then cooled down to the required test temperature under vacuumconditions (P = 1e−4 kPa). Afterwards, the measuring cell is connected to the ther-mostated evaporator in order to establish fixed pressure and temperature conditionsuntil reaching equilibrium conditions over the sample. Subsequently, the connectionbetween evaporator and measurement chamber is closed and the temperature ofevaporator is slightly increased in order to obtain a correspondent water vapour pres-sure increase (typically 2–3 mbar). Finally, the gate valve connecting the evaporatorand measurement chamber is suddenly opened, allowing a quasi-instantaneous pressure

2.1 Differential Step (IDS) Method 21

increase over the sample. Correspondingly, the sample weight starts to increase due towater adsorption, and the kinetic curve is measured as a function of time.

Measurements of kinetics of water adsorption are presented in [4, 5] in a tem-perature range of 30–80°C, water vapour pressure p = 10–80 mbar, for variousgrain sizes ranging between 0.3 and 1.2 mm. The data obtained are usually treatedto extract the diffusion constant, the apparent diffusivity and pore diffusivity ofwater. However, IDS method cannot be used to study AHT cycles, due to essen-tially different testing conditions of the adsorbent.

2.2 Large Pressure Jump (LPJ) Method

The LPJ method for kinetic characterization of adsorbents was firstly applied byDawoud et al. in [6] (2003). According to the proposed technique, the driving forcefor water adsorption is a large jump of the pressure over the adsorbent that isstrongly non-isothermal. The schematic of the LPJ kinetic test-rig used in [6] isdepicted in Fig. 2.2. The set-up consists of two main chambers. The first chamber isthe measuring cell, in which the sample is placed (normally about 3 grams ofadsorbent as loose pellets). The temperature of the holding surface, on which thesample is located, is adjusted and controlled using an oil circuit coupled to the

Fig. 2.1 Schematic of the closed-volume thermo-gravimetric system for measurement of IDSkinetic curves [4, 5]


circulating thermal bath 2. The second chamber is a constant volume vapour vessel.A water circuit coupled to the circulating thermal bath 1 allows the management ofthe temperature of this vessel. The typical test procedure is the following: regen-eration of the adsorbent material by heating up at high temperature keeping themeasuring cell under continuous evacuation for 2 h. Subsequently, the adsorptiontemperature inside the measuring cell is established and the water vapour is chargedinside the vapour vessel, by means of the vapour generator. Once reached the initialconditions, the connection between the vapour vessel and the measuring chamber isopened and the adsorption phase starts, followed by the pressure decreasing insidethe system. Since the volumes of the chambers are known and both vapour pressureand temperature are measured, the decrease of pressure can be used to indirectlydetermine the amount of vapour adsorbed. The uncertainty associated with thedetermination of the remaining water loading amounts to ±0.003 g/g.

The set-up was used to experimentally study the kinetics of water vapouradsorption on microporous and mesoporous silica gels, alumina and compositesorbents [6]. The LPJ method can be used to test various adsorbents stacked inmonolayer or multiple layers.

Additionally, mathematical models of coupled heat and mass transfer were devel-oped in [7, 8], in order to simulate the dynamics of water adsorption caused by theconstant volume adsorption large temperature process as well as to estimate the dif-fusion coefficients and the heat transfer coefficients in adsorbent layers and grains.

Fig. 2.2 Test-rig for measuring the adsorption kinetics of according to the LPJ procedure [6]

2.2 Large Pressure Jump (LPJ) Method 23

Van Heyden et al. developed a similar experimental approach in [9], with theuseful addition of a heat flux metre to measure the released heat of adsorption aswell as the sample surface temperature during the adsorption process. The exper-imental apparatus was conceived for characterizing samples with an adsorbent massranging from 0.5 to 5 g.

The kinetic test facility above described was used to study the adsorption kineticcurves of consolidated layers of AlPO-18 zeolite and polyvinyl alcohol as a binderon aluminium supports investigated in [9]. The same set-up was used to determinethe rate of adsorption of zeolite (13X, 4A, Y-type) coatings directly crystallized onmetal surfaces by using the substrate heating method [10, 11].

In conclusion, when applying the LPJ method, it is necessary to consider thefollowing issues:

(1) the initial and final pressures of as well as the support temperature should not bearbitrary selected, but must be equal to appropriate values of the AHT cyclestudied (simulated) (see Chap. 1, Fig. 1.4). If so, the LPJ method gives fullyadequate information about the dynamics of appropriate PD AHT cycle. Thefirst attempt of such application has been made in [12];

(2) a large water vapour reservoir is required in order to test relevant amount ofadsorbent.

2.3 Large Temperature Jump (LTJ) Method

Aristov et al. [13] firstly developed a new measurement method able to reproducethe isobaric ad/desorption step typical of an adsorption heat pump/chiller operationdriven by a temperature jump/drop (TD cycles). This method, based on an indirectvolumetric measurement (V-LTJ) of the uptake evolution versus time, was furtherdeveloped by Sapienza et al. [14] adding a weighing sensor to directly measure thesample mass during isobaric adsorption and desorption stages.

In this chapter, this method will be described highlighting its potentiality and thetwo different version of this method developed:

• the volumetric Large Temperature Jump method (V-LTJ method) [13];• the gravimetric Large Temperature Jump method (G-LTJ method) [14].

Both experimental set-ups are based on the monitoring of the uptake during areal isobaric step of an adsorptive cooling cycle. Figure 2.3 depicts a hypotheticalthermodynamic cycle (A–B–C–D) working under the following operating condi-tions: evaporation temperature Te, condensation temperature Tc, desorption tem-perature TH. Numerical values of Tc, Te and TH depend on the equilibriumproperties of the tested working pair. In order to study the adsorption kinetics,


firstly, the sample is heated up to TH and evacuated by the use of a vacuum pumpfor the initial out-gassing phase making the sample almost completely dry(p < 0.1 mbar). Subsequently, the dry adsorbent is cooled down to the startingtemperature of the isobaric adsorption phase Tstart-ads that is uniquely determined bythe boundary conditions of the simulated cycle and from the equilibrium data of thetested working pair [14].

2.3.1 Volumetric Large Temperature Jump Method (V-LTJ)

The Large Temperature Jump (LTJ) technique, in its volumetric version, wasdeveloped by Aristov et al. [13]. In this case, the driving force for water desorptionis a large jump/drop of the temperature over the adsorbent under almost isobaricconditions, which allows to closely replicate the desorption/adsorption phase of areal adsorption machine. The V-LTJ kinetic set-up, depicted in Fig. 2.4, can beconsidered as a direct modification of the LPJ set-up. The main difference is theintroduction of a heat source/sink in the oil loop connected to the measuringchamber, which allows to fix the final temperature for enabling the ad/desorptionphases.

Typical adsorption LTJ run consists of the following phases. The dry adsorbentsample is heated to the starting temperature of the isobaric adsorption stage andevacuated using a vacuum pump. Afterwards, the vapour vessel and the measuringcell are connected to the evaporator and the starting pressure of the adsorption

Temperature

P c

P e

T c

Pressure

B C

D

T e T h

T start_adsT end_ads

A

Fig. 2.3 Testing procedure detailed on the isosteric adsorption chart for a generic adsorbent pair[14]

2.3 Large Temperature Jump (LTJ) Method 25

process is fixed. The sample is equilibrated with water vapour for a few hours. Onceadsorption equilibrium is established, a sudden drop in temperature is applied to theadsorber by the external hydraulic loop. The adsorption process driven by thesample cooling starts which results in reducing the vapour pressure inside thesystem with time. This decrease typically does not exceed 2 to 3 mbar, which isquite typical for adsorption heat pumps. To simulate the desorption run, the reversetemperature leap is performed. The pressure variation is used to calculate theamount of vapour adsorbed on the adsorbent.

The LTJ set-up offers the additional possibility to introduce a known amount ofinert gas inside the measuring cell, which allowed the interesting opportunity tostudy the effect of residual non-adsorbable gases on water adsorption dynamicsunder typical conditions of an adsorption machine [16]. The V-LTJ apparatus wasfurther applied to study effects of adsorbent nature, its grain size, heating rate, etc.,on the uptake evolution and AHT-specific power. This approach was used also totest different adsorbents of water, ammonia, ethanol and methanol. Exhaustivedetails on the various experimentation results will be provided in the followingchapters.

Very recently, another kinetic test facility based on the V-LTJ method wasrealized at Fraunhofer ISE and used to study a monolayer of loose microporoussilica gel grains, as presented in [17], which also reports an interesting comparisonamong the kinetics set-ups available at ISE, CNR ITAE and BIC.

However, the V-LTJ method still presents some limitations, namely, the pos-sibility of testing only flat-plate adsorber configurations and the reduced quantity of

Fig. 2.4 Schematic of the test-rig for measuring the kinetics of small-scale adsorbers, accordingto the volumetric LTJ procedure, as reported in [15]


adsorbent that can be loaded inside the measuring cell, in order to keep the pressuredecreasing within the acceptable range, allowing to consider the test almostisobaric.

2.3.2 Gravimetric Large Temperature Jump Method(G-LTJ)

Recently, a new version of the LTJ approach has been developed by Sapienza et al.[14] in order to overcome the limits showed by the V-LTJ version. In this case, theevolutions of the adsorption/desorption phases are directly followed by measuringthe weight of the adsorber by the use of a load cell on which the adsorber is located.This is why it is referred as the gravimetric Large Temperature Jump; indeed, it canbe employed to test more complex small-scale adsorber concepts with a remarkablerange of masses (5–600 g) and a wide kind of configurations (e.g. grains, coatingintegrated in flat-plate or finned tubes heat exchangers).

Figure 2.5 shows the schematic of the new experimental set-up, whose maincomponents are the weighing unit connected to the adsorber to be tested and a

Ad-HEx

Fig. 2.5 Schematic of the test-rig for measuring the kinetics of small-scale adsorbers, accordingto the gravimetric LTJ procedure, as reported in [14]

2.3 Large Temperature Jump (LTJ) Method 27

hydraulic heating/cooling loop. The core of the system is the weighing unit basedon load cells able to monitor the time evolution of the uptake during the ad/desorption stages with an accuracy of ± 0.1 g and the time response faster than0.1 s. Further components are the measuring chamber 1, where the weighing unitand the adsorber are placed, and the vacuum chamber 2 working as evaporator/condenser during the isobaric adsorption/desorption phases. The two chambers areconnected by an electro-pneumatic valve.

Typical testing procedure consists of the following phases: firstly, the sample isheated up and evacuated by the use of a vacuum pump for the initial out-gassingphase. This stage is carried out until reaching a constant sample mass.Subsequently, the dry adsorbent is cooled down to the starting temperature of theisobaric adsorption phase. At the same time, the evaporator is kept at constanttemperature. Afterwards, the chamber 1 is fed with water vapour allowing theadsorbent to adsorb water vapour. After reaching the adsorption equilibrium, a fastcooling of the sample promotes the water vapour adsorption on the material, as in areal adsorption heat pump, until reaching the final temperature. Consequently, thesample weight increasing is measured, that directly corresponds to the wateradsorbed. The test is considered completed when the new equilibrium point isachieved and the weight remains constant. The G-LTJ set-up allows to test differentAd-HEx configuration such as loose grains placed on flat-plate with a monolayer ormultilayer configuration (Fig. 2.6a [14]) or small but representative peace of realAd-HEx (Fig. 2.6b, [18]).

Moreover, the G-LTJ set-up above described can be also used to verify the effectof residual gas (e.g. air, hydrogen) on dynamics of isobaric adsorption stage of anadsorptive chiller [19].

References

1. J. Karger, D.M. Ruthven, Diffusion In Zeolites and Other Microporous Solids (Wiley,London, 1992)

2. Y.I. Aristov, Adsorption dynamics in adsorptive heat transformers: review of new trends.Heat Transf. Eng. 35(11–12), 1014–1027 (2014)

3. A. Freni, F. Russo, S. Vasta, M. Tokarev, Y.I. Aristov, G. Restuccia, An advanced solidsorption chiller using SWS-1L. Appl. Therm. Eng. 27, 2200–2204 (2007)

Fig. 2.6 Views of the flat-plate and finned flat-tubes adsorbers tested in [14, 18] by G-LTJ set-up


4. Y.I. Aristov, I.S. Glaznev, A. Freni, G. Restuccia, Kinetics of water sorption on SWS-1L(calcium chloride confined to mesoporous silica gel): influence of grain size and temperature.Chem. Eng. Sci. 61(5), 1453–1458 (2006)

5. Y.I. Aristov, M. Tokarev, A. Freni, I.S. Glaznev, G. Restuccia, Kinetics of water adsorptionon silica Fuji Davison RD. Microporous Mesoporous Mater. 96(1–3), 65–71 (2006)

6. B. Dawoud, Y.I. Aristov, Experimental study on the kinetics of water vapor sorption onselective water sorbents, silica gel and alumina under typical operating conditions of sorptionheat pumps. Int. J. Heat Mass Transf. 46, 273–281 (2003)

7. B. Dawoud, U. Vedder, E.-H. Amer, S. Dunne, Non-isothermal adsorption kinetics of watervapour into a consolidated zeolite layer. Int. J. Heat Mass Transf. 50, 2190–2199 (2007)

8. B.N. Okunev, A.P. Gromov, L.I. Heifets, Y.I. Aristov, Dynamics of water sorption on a singleadsorbent grain caused by a large pressure jump: modelling of coupled heat and mass transfer.Int. J. Heat Mass Transf. 51, 5872–5876 (2008)

9. H. van Heyden, G. Munz, L. Schnabel, F. Schmidt, S. Mintova, Kinetics of water adsorptionin microporous aluminophosphate layers for regenerative heat exchangers. Appl. Therm. Eng.29, 1514–1522 (2009)

10. L. Schnabel, M. Tatlier, F. Schmidt, A. Erdem-Senatalar, Adsorption kinetics of zeolitecoatings directly crystallized on metal supports for heat pump applications (adsorptionkinetics of zeolite coatings). Appl. Therm. Eng. 30, 1409–1416 (2010)

11. M. Tatlier, G. Munz, G. Fueldner, S.K. Henninger, Effect of zeolite A coating thickness onadsorption kinetics for heat pump applications. Microporous Mesoporous Mater. 193, 115–121 (2014)

12. Y.I. Aristov, Adsorptive transformation of ambient heat: a new cycle. Appl. Therm. Eng. 124,521–524 (2017)

13. Y.I. Aristov, B. Dawoud, I.S. Glaznev, A. Elyas, A new methodology of studying thedynamics of water sorption/desorption under real operating conditions of adsorption heatpumps: experiment. Int. J. Heat Mass Transf. 51, 4966–4972 (2008)

14. A. Sapienza, S. Santamaria, A. Frazzica, A. Freni, Y.I. Aristov, Dynamic study of adsorbersby a new gravimetric version of the Large Temperature Jump method. Appl. Energy 113,1244–1251 (2014)

15. I.S. Glaznev, Y.I. Aristov, Kinetics of water adsorption on loose grains of SWS-1L underisobaric stages of adsorption heat pumps: The effect of residual air. Int. J. Heat Mass Transf.51, 5823–5827 (2008)

16. I.S. Glaznev, D.S. Ovoshchnikov, Y.I. Aristov, Effect of residual gas on water adsorptiondynamics under typical conditions of an adsorption chiller. Heat Transfer Eng. 31(11), 924–930 (2011)

17. A Sapienza, A Velte, I Girnik, A Frazzica, G Füldner, L Schnabel, Y Aristov, “Water-SilicaSiogel” working pair for adsorption chillers: adsorption equilibrium and dynamics. Renew.Energy (2017 in press). https://doi.org/10.1016/j.renene.2016.09.065

18. S. Santamaria, A. Sapienza, A. Frazzica, A. Freni, I.S. Girnik, Y.I. Aristov, Water adsorptiondynamics on representative pieces of real adsorbers for adsorptive chillers. Appl. Energy 134,11–19 (2014)

19. A. Sapienza, A. Frazzica, A. Freni, Y.I. Aristov, Dramatic effect of residual gas on dynamicsof isobaric adsorption stage of an adsorptive chiller. Appl. Therm. Eng. 96, 385–390 (2016)

References 29

http://dx.doi.org/10.1016/j.renene.2016.09.065

Chapter 3Experimental Findings: Main FactorsAffecting the AdsorptiveTemperature-Driven Cycle Dynamics

Abbreviation

Nomenclature

AC Air conditioningAd-HEx Adsorbent heat exchangerAHT Adsorptive heat transformerd Grains diameter, mmD Diffusivity, m2 s−1

ΔF Adsorption potential, J mol−1

FAB Flat adsorbent bedG Grain size, mmLTJ Large Temperature Jump methodG-LTJ Gravimetric version of Large Temperature Jump methodV-LTJ Volumetric version of Large Temperature Jump methodHEx Heat exchangerIM Ice makingJ Heat flux, Wm Dry adsorbent mass, kgM Molecular mass, g mol−1

P Pressure, Paq Dimensionless conversionR Adsorption rate, g/s; particle radius/grain size, mmS HEx heat transfer surface area, m2

T Temperature, °C, HEx thickness, mmt Time, sU Overall heat transfer coefficient, W m−2 K−1

V Flow rate, dm3 min−1

w Water uptake, g g−1

W Specific cooling power, W/gHEx width, mm


31




Greek Symbols

D Differential operatorη Dynamic viscosity, kg m−1 s−1

s Characteristic time, s

Subscripts

0 Initial stage, vapour saturation∞ Infinityads Adsorbent/adsorptionair Airdes DesorptionEnd Endingfin HEx fing Grainh HydrogenH HighH2O Waterht Heat transferin InitialL LowM Mediummax Maximummt Mass transfertr Transport pores

In Chap. 2, the two main methods to study the sorption dynamics for AHT cycleswere widely described: (i) the Large Pressure Jump (LPJ) method, in whichadsorption is initiated by a jump of pressure over the sample, is the most adequatefor pressure-driven AHT cycles; (ii) the Large Temperature Jump (LTJ) method, inwhich adsorption is enabled by a temperature swing of a heat exchanger wall that isin contact with the adsorbent under an almost isobaric ad/desorption stage, is theproper choice for temperature-driven AHT cycles (see Chaps. 1 and 2).

In this chapter, the main factors affecting the sorption dynamics will be high-lighted for temperature-driven AHT cycles by the analysis of results achieved bythe two versions (namely V-LTJ and G-LTJ) of the LTJ method.

3.1 Adsorbate and Adsorbent Nature

In the present paragraph, the influence of adsorbate and adsorbent nature on thesorption dynamics will be highlighted for the most common working pairs.

32 3 Experimental Findings: Main Factors Affecting …

3.1.1 Water Sorption Dynamics

Many studies have been carried out at the Boreskov Institute of Catalysis(Novosibirsk, Russia) by the V-LTJ set-up aiming at comparative evaluation of thewater sorption kinetic properties of various adsorbents promising for AHT. Part ofthe results is reported and discussed in [1, 2].

In [1], three water adsorbents were considered (i.e. Fuji RD silica gel, compositeSWS-1L and Mitsubishi AQSOA™-FAM-Z02) in shape of loose grains of 0.8–0.9 mm size. The evolution of the water uptake in time is presented in Fig. 3.1under typical conditions of isobaric adsorption stage. It takes 101, 307 and 453 s toreach 80% of the equilibrium uptake for silica gel, SWS-1L and FAM-Z02,respectively, as seen from the dimensionless curves (Fig. 3.1a). It looks as if thesilica gel ensures the fastest water adsorption, however that is a superficial con-clusion. The shortest time for setting the adsorption equilibrium on the silica is dueto its smaller equilibrium uptake that is 0.12 g/g as compared with 0.22 g/g forSWS-1L and FAM-Z02. At short adsorption time (t < 30 s), all the studiedadsorbents possess almost the same absolute adsorption rate (Fig. 3.1b) roughlyequal to 0.002 g/s. Moreover, the absolute rate of water adsorption on the silica isequal to or smaller than on FAM-Z02 at any time. The initial cooling power for thethree adsorbents is nearly the same and can reach 2.5 kW/kg because the highinitial adsorption rate is almost equal for the three adsorbents.

Fig. 3.1 Dimensionless(a) and absolute(b) adsorption uptake curvesfor loose grains of 0.8–0.9 mm size, initiated by atemperature drop 60°C ! 35 °C: (1)—Fuji RD,(2)—SWS-1L, (3)—FAM-Z02.PH2O = 10.3 mbar [1]

3.1 Adsorbate and Adsorbent Nature 33

For most of the adsorption step (80–90%), the process can be satisfactorilydescribed by the exponential equation Eq. (3.1):

Dm tð Þ=Dm1 ¼ 1� exp �t=sð Þ ð3:1Þ

where s is the characteristic adsorption time. These results demonstrate that thesorption dynamics can formally be described by a modified LDF model by using asingle characteristic time per fixed configuration. An important difference from thecommon LDF model [3] is that this characteristic time does not depend on thetemperature which is variable during the adsorption run [4].

3.1.2 Methanol Sorption Dynamics

The sorption dynamics of two adsorbent materials has been tested and reported inthe literature for methanol adsorption, namely a composite sorbent based on LiCland silica gel as hosting matrix [5] and an activated carbon, ACM-35.4 [6]. In orderto investigate the effect of the adsorbent material on the sorption dynamics for thecomposite LiCl/silica, the kinetic tests were performed by varying the salt contentinside the silica gel matrix [5]. For the composite, the main contribution to theoverall adsorption capacity is represented by the reaction between methanol and thesalt confined inside the pores. Two salt contents, namely 21 and 13 wt%, weretested. The ad/desorption kinetic curves are represented in Fig. 3.2. These testswere performed for a monolayer configuration of the adsorbent bed for which theinter-granular diffusional resistance can be neglected. Although the initial rates areagain equal regardless of the salt content, the characteristic times to reach equi-librium are 70 and 44 s for adsorption as well as 32 and 15 s for desorption runs.This difference can be justified by the larger mass of exchanged methanol for LiCl(21 wt%)/SiO2 (0.50 g/g) as compared to LiCl (13 wt%)/SiO2 (0.32 g/g). It allowsthe conclusion to be made that the parameter affecting the sorption rate is the heatand mass transfer rather than the interaction between methanol and salt. It can alsobe stated that the decrease in the characteristic time is due to reducing the saltcontent and, accordingly, to the lower amount of methanol ad/desorbed, whichallows the sorption equilibrium to be reached more rapidly.

A direct comparison between the sorption kinetics on the composite sorbent andthe activated carbon tested in [6] is not possible, because the applied boundaryconditions are slightly different. Concerning the activated carbon ACM 35.4, themain conclusion that can be drawn is that the vapour transport inside the carbonpores is fast, so that the kinetics is almost completely affected by the heat transferrather than by vapour transportation inside the grains up to 4.0 mm of grain size.


3.2 Adsorbent Grain Size

The adsorbent grain size represents one of the key parameters to be experimentallyinvestigated for optimizing the achievable dynamic performance of adsorbers.

Indeed, both heat and mass transfers inside the adsorber are influenced by thesize of the adsorbent grains. Particularly, the mass transfer is affected by theintra-granular resistance offered towards the diffusion of the refrigerant inside thegrain itself as well as by the inter-granular resistance through adsorbent layers. Onthe other hand, the overall heat transfer is affected by the convective/conductiveresistance due to the contact between the heat exchanger surface and the adsorbentgrain, the grain thermal conductivity itself and the convective contribution due tothe refrigerant vapour flux.

All these contributions are regulated by specific physical laws and are related tothe grain size, but they are strictly coupled and only a devoted experimental activitycan efficiently describe the phenomenon. As follows, the experimental studies onthe effect of the grain size on the sorption dynamics will be summarized below forthe different working pairs.

Fig. 3.2 Kinetic curves ofmethanol adsorption (a) anddesorption (b) for LiCl(21wt%)/SiO2 (1) and LiCl(13wt%)/SiO2 (2) composites [5]

3.2 Adsorbent Grain Size 35


The influence of the sorbent grain size on the water sorption kinetics was widelystudied in [7, 8]. In particular, in [8], the study was carried out by the V-LTJmethod for a monolayer of loose AQSOA™-FAM-Z02 grains employed in a FAB.Figure 3.3 shows the dimensionless adsorption and desorption uptake curves forloose grains with five grain sizes (i.e. 0.2–0.25 mm (■), 0.4–0.5 mm (●), 0.8–0.9 mm (▲), 1.0–1.2 mm (▼) and 1.9–2.1 mm (►) measured for an adsorptionstep performed at T drop from 60 to 35 °C p0H20 ¼ const = 12:3mbarð Þ and Tjump from 46 to 90 °C p0H20 ¼ 42:4mbarð Þ.

An initial part of the experimental uptake and release curves can be satisfactorilydescribed by the exponential equation (Eq. 3.1). This approximation is excellent forlarge grains and describes well the experimental curves up to the dimensionlessconversion of at least 0.70 with a single s value.

Both adsorption and desorption processes become slower for larger adsorbentgrains that is reasonable. The dependence ln(t) versus ln(2R) is a straight line withthe slope a equal to 1.33 and 1.20 for adsorption and desorption, respectively(Fig. 3.4). Hence, the characteristic sorption time can be written as s * Ra [10].

The maximal specific power Wmax [W/gadsorbent] generated during ad/desorptionin evaporator/condenser was calculated in [8] and here is shown in Table 3.1.

For monolayer configuration of the flat adsorbent bed, the “grain size sensitive”regime is revealed, because the maximal specific power Wmax * 1/s * R−a

reduces for larger grains. Moreover, the Wmax value is not a linear function of the(S/m) ratio any more.

These two findings present an important difference between mono- and multi-layer FAM-Z02 configurations. In equation s * Ra, the exponent a is constant forgrains of 0.20–2.1 mm size. This may be an indication that, for the T-initiation, heatand mass transfer processes cannot be distinguished by a mere variation of the

Fig. 3.3 Dimensionless uptake/release curves for water adsorption (a) and desorption (b) as wellas evolution of the metal support temperature (♦). Grain size—0.2–0.25 mm (■), 0.4–0.5 mm(●), 0.8–0.9 mm (▲), 1.0–1.2 mm (▼) and 1.9–2.1 mm (►). Solid lines present exponentialapproximation [8]


adsorbent grain size, as it takes place for isothermal gas adsorption initiated by ajump of gas pressure over the grain (P-initiation). Indeed, in the latter case, theadsorption rate in large adsorbent grains is controlled by intra-granular gas diffusionand the characteristic adsorption time s * R2 [9]. For small grains, the process rateis controlled by heat rejection from the grain external surface and s * R1 [9]. Ifthese transfer mechanisms are independent, a crossover from a = 1 to a = 2 shouldtake place at increasing grain size.

Thus, an important difference of the T-initiation is that heat and mass transferprocesses may be inseparably coupled.

The influence of grains’ dimension was further investigated in [10] by the G-LTJmethod for a FAB composed of grains of a FAM-Z02 placed on a flat type alu-minium HEx, under operating conditions reproducing an AHT cycle (TH = 90 °C,TL = 10 °C, TM = 30 °C) both for the monolayer and multilayer configuration.

Table 3.1 Characteristic ad/desorption times s, s 0.5, s 0.8, s 0.9, specific powers Wmax and W0.8

and overall heat transfer coefficient U for various grain sizes [8]

Grainsize, mm

Run s, s s 0.5, s s 0.8, s s 0.9, s Wmax,kW/kg

W0.8,kW/kg

U, W/(m2 K)

S/m,m2/kg

0.2–0.25 Ads 17 12 38 74 25.3 11.5 100 7.0

Des 15 10 29 57 26.7 15.1 87

0.4–0.5 Ads 30 22 54 88 14.7 8.1 118 3.5

Des 32 21 49 79 14.5 8.9 94

0.8–0.9 Ads 102 72 161 220 4.5 2.7 72 1.75

Des 68 50 106 150 7.7 4.1 100

1.0–1.2 Ads 125 87 201 288 3.2 2.2 66 1.35

Des 95 66 153 219 5.1 2.9 86

1.9–2.1 Ads 275 190 443 634 1.7 1.0 60 0.77

Des 210 146 338 484 2.5 1.3 74

Fig. 3.4 Dependence s(2R)in double logarithmiccoordinates—red, adsorption,black, desorption [8]


The tested grain size was ranged from 0.35 to 2.5 mm, while the performedtemperature drop was from 66 to 30 °C, in accordance with the isosteric chart of thetested working pair.

For the monolayer configuration, the influence of the grain size on theadsorption dynamics is shown in Fig. 3.5 where the adsorption kinetic curves arepresented as the water dimensionless uptake w(t)/w∞ versus time, where w(t) is theinstantaneous uptake and w∞ is the equilibrium uptake. For a monolayer config-uration, the adsorption kinetics became faster for smaller grains as the heat andmass transfer is favoured by the lower overall resistances.

At least 80% of the water sorption was satisfactorily described by an exponentialequation with the characteristic times reported in Table 3.2 as well as the specificcooling powers W80 % and Wmax calculated for all the tests carried out. These datademonstrated that the specific configuration is able to produce the maximumspecific cooling power ranging between 1.1 and 8.8 W/g. In particular, for the

Fig. 3.5 Water dimensionless uptake, the plate and adsorbent temperatures versus time for thetested grain sizes at TH = 90 °C, TL = 10 °C, TM = 30 °C [10]

Table 3.2 Characteristic times and specific cooling powers for the monolayer configuration [10]

T drop(°C) d(mm) s (s) s0.8 (s) W80%(W/g) Wmax(W/g)

66 ! 30 0.350–0.425 62 91 4.40 8.80

0.710–0.850 124 195 2.10 4.20

1.000–1.180 162 242 1.65 3.30

1.180–1.600 189 287 1.58 3.15

1.600–2.000 288 449 0.87 1.75

2.000–2.400 383 563 0.69 1.4

2.400–2.500 449 660 0.56 1.1


smallest grain size (0.350–0.425 mm) at TM = 30 °C, W80 % = 4.40 W/g andWmax = 8.80 W/g were obtained.

The study of the multilayer configuration was performed [10] for four grainsizes (0.350–0.425 mm, 0.71–0.85 mm, 1.0–1.18 mm and 1.6–2.0 mm). For all thesizes, the S/m ratio was kept constant (S/m = 1.23 m2/kg) that means the dry massof adsorbent was constant. Obviously, the reduction in the grain size leads to theincrease in the number of layers. In particular, for the four tested grain sizes thenumber of layers was respectively 8, 4, 2 and 1.

Figure 3.6 displays the adsorption kinetic curves as the water dimensionlessuptake versus time. The plot shows that, at the constant S/m, the adsorption kineticsdoes not depend on the grain size. This indicates the existence of a “grain sizeinsensitive mode”. At this mode, the grains of different size result in the samedynamic performance if the ratio (S/m) is constant. This confirmed the existence ofthe “grain size insensitive” regime earlier revealed by the V-LTJ for Fuji silica RD[11] and FAM-Z02 [12].

The effect of the grain size on the water sorption dynamic was further studied in[13] for a more complex Ad-HEx configuration consisting in a small but repre-sentative piece of a finned tube HEx adsorber filled with loose grains of theMitsubishi AQSOA™-FAM-Z02 sorbent [14].

Figure 3.7 shows the Ad-HExs tested in [13] charged with AQSOA™-FAM-Z02 grains of four sizes, ranging between 0.15 and 1.18 mm, while the S/mratio was nearly constant, 2.6 ± 0.3 m2 kg−1.

All the experimental ad/desorption curves (Fig. 3.8) follow an exponentialbehaviour described by Eq. 3.1 or Eq. 3.2 and begin with the same slope (i.e. allsamples have the same initial ad/desorption rate).

Dm tð Þ=Dm1 ¼ exp �t=sð Þ ð3:2Þ

This is probably due to the heat transfer between the metal fins and the adsorbentthat is the dominant resistance at short times. Except for the largest AQSOA Z02grains, no effect of the grain size on desorption dynamics is found.

Fig. 3.6 Waterdimensionless uptake w(t)/wmax versus time for thetested grain sizes atTH = 90 °C, TL = 10 °C,TM = 30 °C [10]


This confirms the “grain size insensitive” or “lumped” regime already observedfor a FAB configuration. Despite the highest (S/m) ratio (3.2 m2 kg−1), the Ad-HExcharged with the AQSOA Z02 grains of 1.00–1.18 mm size shows a desorption ratethat is slower by a factor of 1.8. Indeed, increasing the particles size slows down themass transport inside the grains and the process becomes “grain size sensitive”. Theintra-granular mass transfer resistance is likely a reason of the adsorption ratereduction for the AQSOA Z02 grains of 1.00–1.18 mm size (Fig. 3.9).

For adsorption, the “lumped” regime is found for the narrower range of the grainsize, c.a. 0.30–0.71 mm. For smaller grains, a dramatic rate slowdown (by a factorof 1.55) is detected. That may be due to the reduced bed permeability and theconsequent inter-grain mass transfer resistance along the narrow triangular channels

Fig. 3.7 View of tested representative piece of real adsorbers [13]

Fig. 3.8 Grain size (in mm) effect on the adsorption/desorption dynamics for a representativepiece of a real adsorber Ad-HEx 1 [13]


between the secondary fins. This resistance is absent in the FAB configuration. Insum, when the sorption rate is controlled by the heat transfer between the adsorbentand the metal support no effect of the grain size is observed. The “grain sizeinsensitive” mode, similar to that first revealed for a flat-plate configuration, takesplace also for more complicated configurations. Under this mode, it is not necessaryto precisely select the adsorbent grain size: the grains should just be sufficientlysmall to assure the “lumped” mode. On the other hand, using too small grains is notrecommended, as the inter-grain diffusional resistance may become a rate-limitingprocess [13].


The effect of grain size on the dynamics of methanol sorption on the LiCl/silicacomposite was deeply investigated in [5]. Experimental tests were conducted onmonolayers of the adsorbent grains with three grain sizes, namely 0.4–0.5 mm,0.8–0.9 mm and 1.6–1.8 mm, and two different salt contents. As reported inFig. 3.10, only the smallest grains show an exponential ad/desorption evolution ofthe kinetics. Differently, a clear deviation from the exponential evolution washighlighted for larger grains. In particular, a dramatic increase of time to reach 90%of total conversion (3920 s) was achieved by the largest grains (1.6–1.8 mm).Furthermore, as can be highlighted in Table 3.3, the total uptake variation for the

Fig. 3.9 Grain size effect forAd-HEx 1 on the adsorption/desorption dynamics with themain resistances depicted(namely inter-particlediffusion, heat transfer metal/adsorbent, intra-particlediffusion). Blue—adsorption,red—desorption [13]

Table 3.3 Effect of the grainsize on dynamics of methanolad/desorption on/from themonolayer of LiCl(21 wt%)/SiO2 composite [5]

Dgr, mm Δw, g/g Adsorption Desorption

s, s s0.9, s s, s s0.9, s

0.4–0.5 0.50 107 251 – 650

0.8–0.9 0.36 196 520 – 920

1.6–1.8 0.30 – 3920 – 4550


0.8–0.9 mm and 1.6–1.8 mm grains appeared to be lower than the one obtained forthe 0.4–0.5 mm grains. This behaviour has been justified by analysing the sorptionreaction and the silica gel matrix pore volume. Indeed, the sorption starts from thepores adjacent to the external surface, creating a solution, which occupies the silicagel pores close to the external surface of the grain. This causes a reduction of themethanol diffusion through the solution layer, which limits the interaction betweenthe methanol vapour and the salt embedded in the inner part of the silica gel grains,which leads to the lower adsorption. In order to reduce this negative effect, asufficient residual empty volume inside the pores should be guaranteed, in order toleave enough space for the vapour to diffuse inside the pores. Accordingly, asreported in Fig. 3.10, the largest grains (i.e. 1.6–1.8 mm) were tested with twodifferent salt contents, namely 21 and 15 wt%, confirming that the latter compositewas characterized by faster and almost-exponential kinetics. Furthermore, theobtained uptake variation, 0.32 g/g, was in agreement with the equilibrium data.This can be related to the fact that passing from 21 to 15 wt% of the salt content, theempty volume, available for methanol diffusion, raised from 0.07 to 0.22 cm3/g. Itcan be stated that for composite “salt in host matrix” it is necessary to design a

Fig. 3.10 Kinetic curves formethanol adsorption (a) anddesorption (b) on LiCl(21wt%)/SiO2 (1–3) and LiCl(15wt%)/SiO2 (4) grains of varioussize Dgr = 0.4–0.5 (1), 0.8–0.9 (2) and 1.6–1.8 (3, 4) mm.Lines—exponential fits [5]


smart composite in order to have a correct balance between the salt content and porevolume guarantying sufficient empty space for sorptive diffusion. In this context, arecommendation is to have at least 20–25% of the matrix pores empty at themaximal sorption uptake wmax.

Similarly, in [6], the grain size effect was investigated on the activated carbonACM-35.4. Differently from the composite sorbent, in this case also the largestgrain size reached the complete adsorption capacity under the given testing con-ditions. The curves reported in Fig. 3.11 for the monolayer configuration confirmedthat there is a clear deceleration of the kinetics with increasing the grain size. Thiscan be related both to the intra-granular diffusion resistance and to heat transferefficiency.

Fig. 3.11 Kinetic curves ofmethanol adsorption on(a) and desorption from (b) amonolayer of looseACM-35.4 grains withDgr = 0.8 – 0.9 (1),1.0 – 1.25 (2), 1.6 – 1.8 (3),2.5 – 2.8 (4) and 4.0 – 4.1(5) mm [6]


3.2.3 Ethanol Sorption Dynamics

The effect of adsorbent grain size with ethanol as refrigerant has been experi-mentally investigated both on a sorbent composite [15] and on one of the mostpromising activated carbons available on the market [16]. In both cases, the FABconfiguration has been investigated by means of the V-LTJ apparatus available atthe Boreskov Institute of Catalysis, whose working principle and main featureshave been previously reported.

In [15], the composite sorbent (19 wt% LiBr)/silica was investigated as ethanolsorbent, by testing four different grain sizes, namely 0.2–0.4, 0.4–0.6, 0.6–0.7 and0.9–1.0 mm. Two operating conditions were simulated: the first one representing atypical ice making (IM) cycle, while the second one representing a typical airconditioning (AC) cycle. Taking into account the experimental findings thatshowed the influence of the S/m ratio on the achievable dynamics of differentworking pairs [11, 17], the analysis was performed keeping this ratio nearly con-stant: S/m = 3.4 ± 0.4 m2 kg−1. For ethanol adsorption experiments, as reported inFig. 3.12, the dimensionless conversion q(t) can be satisfactorily represented by anexponential evolution Eq. (3.1), for the grain size between 0.2 and 0.7 mm (cor-relation factor R2 = 0.97 – 0.99). This allows the determination of characteristictimes that are able to take into account the whole heat and mass transfer resistancesin the FAB. For the grain size in the range 0.9–1.0 mm, the sorption kineticevolution is far from the exponential one. For this reason, also the s0.8, whichrepresents the time needed to reach the 80% of overall conversion, was used todescribe the sorption dynamics.

As reported in [15, 16], for the investigated FAB configuration, the sorptiondynamics is strongly influenced by the grain size. Indeed, both the characteristictime, s, and the time for 80% of the total conversion, t0.8, increase when the grainsize is increased from 0.2–0.4 to 0.9–1.0 mm. This evolution is observed both

Fig. 3.12 Adsorption kinetic curves for the investigated LiBr/silica—ethanol working pair, forFAB configuration. Solid lines represent the experimental outcomes; dashed lines represent theexponential fits. Investigated working conditions: a IM, b AC [15]


under IM and AC cycles. This behaviour was defined as “grain size sensitiveregime” in [11]. Since in the FAB configuration the inter-granular diffusion is fastenough to be neglected, the sorption rate variation can be clearly related to theintra-granular diffusion resistance and to the heat transfer between the flat-plate heatexchanger and the adsorbent grains. Nevertheless, the previous studies [6, 11]demonstrated that the dynamics of thin layers of activated carbon [6] and silica gel[11] with different working fluids, having S/m > 0.8 m2 kg−1 and 2.0 m2 kg−1,

respectively, were invariant with respect to the S/m ratio. Accordingly, since in [15]the S/m ratio was always equal to 3.4 ± 0.4 m2 kg−1, it was possible to assume thatthe heat flux between the heat transfer surface and sorbent was similar for eachinvestigated grain size. This allowed to the conclusion to be made that the exper-imentally highlighted slowdown of the sorption dynamics on larger grains wasdirectly related to the intra-particle diffusion mechanism.

Different behaviour was obtained for ethanol desorption experiments. FromFig. 3.13, it is possible to highlight that the evolution can be well represented by theexponential law in Eq. (3.2) at least for q > 0.2 − 0.4. Above these values, adeceleration has been highlighted under both IM and AC conditions, which causesa deviation from the exponential evolution. As summarized in Table 3.4, the des-orption runs are always faster than the adsorption ones. Differently from theadsorption runs, there is a clear transition from the “lumped regime”, in which thedynamics is insensitive to the grain size, for q < 0.6 mm, to the “grain sensitiveregime”, for q > 0.6 mm.

The different behaviour obtained between adsorption and desorption runs can bejustified by analysing the absolute ethanol vapour pressure inside the system.Indeed, there is a difference of about 7.0 kPa passing from adsorption to desorption,and thus, the higher pressure gradient inside the adsorber promotes faster diffusion,limiting the influence of the intra-granular diffusion.

Similarly, in [16], the influence of grain size on the sorption dynamics of acommercial activated carbon (SRD 1352/3) with ethanol as working fluid was

Fig. 3.13 Desorption kinetic curves for the investigated LiBr/silica—ethanol working pair, forFAB configuration. Solid lines represent the experimental outcomes; dashed lines represent theexponential fits. Investigated working conditions: a IM, b AC [15]


investigated. Four different grain sizes, namely 0.21–0.43, 0.43–0.60, 0.71–0.85and 1.00–1.18 mm, were prepared and tested in the FAB configuration. Both IMand AC conditions were investigated, employing three different S/m ratios, namely1.3, 2.53 and 4.98 m2 kg−1.

Figure 3.14 reports the kinetic adsorption and desorption curves measured overthe FAB configuration at two S/m ratios, 1.3 and 4.98 m2 kg−1. It is evident that

Table 3.4 80% conversiontimes and characteristic timesfor ethanol adsorption anddesorption on LiBr/silica forthe FAB configuration [15]

Grain size, mm t0.8, s s, s t0.8, s s, s

IM cycle AC cycle

Adsorption

0.2–0.4 70 37 55 31

0.4–0.6 120 57 80 43

0.6–0.7 145 76 105 50

0.9–1.0 455 – 250 –

Desorption

0.2–0.4 44 25 57 25

0.4–0.6 42 24 52 26

0.6–0.7 50 31 54 30

0.9–1.0 63 35 80 40

Fig. 3.14 Kinetic curves (symbols) and exponential fittings (lines) of ethanol adsorption/desorption on activated carbon SRD 1352/3 for FAB configuration with S/m = 1.3 m2 kg−1 (a, b)and S/m = 4.98 m2 kg−1 (c, d) [16]


generally the dynamics fits quite well with the exponential laws reported byEqs. (3.1) and (3.2). The obtained characteristic times are summarized in Table 3.5.A slight deviation from the exponential evolution was observed for the thickestlayers (having the lowest ratio S/m = 1.3 m2 kg−1) at high conversion degree. Thefirst experimental evidence is that the measured kinetic curves on FAB with dif-ferent grain sizes but equal S/m ratio almost coincide. In order to analyse a tran-sition from the “lumped” to “grain size sensitive” regime, the initial adsorption(desorption) rate, R0, was analysed for each investigated configuration:

R0 ¼ dw=dt jt!0 ¼ Dwt!1=s ð3:3Þ

As reported in Fig. 3.15, for thin layers (S/m � 2.53 m2 kg−1) with the grainsize � 0.71 − 0.85 mm, the calculated initial adsorption rate is insensitive to the

Table 3.5 Characteristic times for ethanol adsorption and desorption on activated carbon SRD1352/3 for the FAB configuration [16]

Grainsize, mm

IM cycle AC cycle

s [s] s [s]

S/m[m2 kg−1]1.30

S/m[m2 kg−1]2.53

S/m[m2 kg−1]4.98

S/m[m2 kg−1]1.30

S/m[m2 kg−1]2.53

S/m[m2 kg−1]4.98

Adsorption

0.21–0.43 90 44 22 78 28 15

0.43–0.60 – – 22 – – 15

0.71–0.85 89 43 22 76 33 16

1.00–1.18 96 43 – 80 32 –

Desorption

0.21–0.43 78 26 15 81 31 15

0.43–0.60 – – 15 – – 16

0.71–0.85 70 30 15 – 32 17

1.00–1.18 77 33 – 86 39 –

Fig. 3.15 Initial adsorption (a, b) and desorption (c) rate for the grain sizes 0.21–0.43 (■, □),0.43–0.60 (●, ○), 0.71–0.85 (▲, Δ) and 1.0–1.18 (▼, ▽) mm, for AC (a, c) and IM (b, c) cycles[16]


grain size and linearly increases with the S/m ratio, both under the IM and ACconditions. Accordingly, under these conditions, the only parameter affecting thesorption dynamics is the S/m ratio, thus confirming the prominence of the heattransfer between heat exchanger and adsorbent grains over the mass transport as themain phenomena affecting the overall achievable dynamics. It clearly confirms thatthe “grain size insensitive” or “lumped” regime is established. Differently, for thegrains larger than 1.0 mm and the beds at S/m < 2.53 m2 kg−1, a deviation of theR0 from the linear fit is highlighted, confirming that under these configurations, theintra-particle diffusion resistance plays a crucial role, thus bringing the system to the“grain sensitive regime”. Similar conclusions can be drawn for the desorption runs.

According to these outcomes, the main reported recommendation for thisworking pair is to make use of high S/m (>2.5 m2 kg−1) and small adsorbent grainsizes (� 0.85 mm).

3.3 Geometry of the Adsorber

Experimental testing of adsorption dynamics on more realistic adsorber configu-rations (e.g. small-scale real finned tubes HExs, multilayers of adsorbent grains)allows investigating how the geometry of the HEx, in terms of thickness of thesorbent layer or channel length, can contemporarily affect the inter-granular masstransfer resistance (e.g. along the channels’ length of the HEx/thickness of theadsorber) and the intra-granular mass transfer resistance (inside each grain) as wellas the heat transfer (between HEx and adsorbent material) and consequently theoverall performance.

For instance, Fig. 3.16 summarizes the heat and mass transfer phenomenaaffecting the sorption dynamics inside an adsorbent bed. These analyses are ofprimary importance in order to assess the optimal adsorbent bed configuration, ableto reach the right compromise between sorption dynamics (i.e. specific power) andefficiency (i.e. coefficient of performance).

Fig. 3.16 Schematic of heatand mass transfer phenomenaoccurring in a real adsorbentbed configuration: arrows(1) inter-particle diffusion;arrows (2) intra-particlediffusion; arrows (3) heattransfer between primary heattransfer surface and adsorbentgrains; arrows (4) heattransfer between secondaryheat transfer surface (fins) andadsorbent grains [15]



The effect of the adsorber’s channel length was studied in [13] for small butrepresentative pieces of a finned flat-tube HEx obtained by filling these small HExswith loose grains of AQSOA™-FAM-Z02. Specifically, the dynamic analysis wascarried out for three HEx fragments with different geometry aspects W/T = Width/Thickness with almost constant volume and ratio between the heat transfer surfaceS and the dry adsorbent mass m (S/m = 2.75 ± 0.35 m2 kg−1). The AQSOA Z02grain size was varied between 0.150 and 1.180 mm. Results in terms of the char-acteristic time are reported in Fig. 3.17 for both desorption and adsorption steps.

For all desorption runs, the characteristic time is found to be quite similar,sdes = (85 ± 12) s despite the grain size and the HEx geometry aspect. Thisunambiguously confirms that the desorption dynamics is invariant with respect tothe ratio (S/m). A tendency to increasing this time is observed for Ad-HEx1 and 2,filled with the smallest grains, as well as for Ad-HEx3 with the longest channels.This tendency is more pronounced for adsorption runs. The invariance is observedonly for Ad-HEx1 filled by the grains of 0.30–0.35 mm and 0.60–0.71 mm andAd-HEx2 with the grains of 0.60–0.71 mm. The corresponding adsorption time is(110 ± 5) s. For smaller grains of 0.150–0.212 mm loaded into Ad-HEx1 and of0.15–0.35 mm inside Ad-HEx2, the adsorption becomes slower. This may becaused by increasing the inter-grain mass transfer resistance along the narrowquasi-triangular channels between the secondary and primary fins [13].


The effect of the thickness of the adsorbent layer on methanol sorption dynamicswas investigated in [5] for the multilayer FAB configuration of the compositesorbent LiCl/silica gel. In Fig. 3.18, both adsorption and desorption runs are

Fig. 3.17 Influence of theadsorber’s channel length onthe water sorptioncharacteristic time [13]

3.3 Geometry of the Adsorber 49

compared for one, two and four sorbent grain layers. As expected, a deceleration ofkinetics was highlighted for thicker bed. The adsorption curves resultedalmost-exponential, while the desorption ones were far from the exponential evo-lution. The exponential characteristic time, s, and the time needed to reach 90% ofmethanol exchange, t0.9, were calculated for each configuration and reported as afunction of the number of layers, which is inversely proportional to the heat transfersurface, since the tested sorbent mass was constant (Fig. 3.19). Interestingly, theevolution was linear for both adsorption and desorption runs. Particularly, both sand t0.9 for desorption runs approach zero when 1/S tends to zero. This means that,during desorption, the heat transfer is the main mechanisms affecting the kineticperformance. Differently, the adsorption runs were always slower than the des-orption ones, confirming that the mass transfer resistance can play an important roleduring this phase.

The same approach was followed in [6] to investigate the influence of thenumber of layers on the adsorption and desorption dynamics for activated carbonACM-35.4. As already found for the composite sorbent, also in this case thekinetics is slower when the number of layers increases, as depicted in Fig. 3.20. In[6], different grain sizes were tested employing the same ratio of the heat transferarea to the adsorbent mass, S/m, varying the bed thickness. As displayed inFig. 3.21, under the same testing conditions, the kinetics for both adsorption anddesorption are overlapped each other regardless of the grain size, when the S/m iskept constant. This means that one layer of 1.6–1.8 mm grains performs as two

Fig. 3.18 Kinetic curves ofmethanol ad- (a) anddesorption (b) at variouslayer’ numbers. N = 1 (1), 2(2) and 4 (3) and theirexponential fits (lines) [5]


Fig. 3.19 Adsorption anddesorption characteristic timesas a function of number oflayer (or 1/S) [5]

Fig. 3.20 Kinetic curves ofmethanol adsorption (a) anddesorption (b) at N = 1 (1), 2(2), and 4 (3).Dgr = 1.6 − 1.8 mm [6]


layers of 0.8–0.9 mm grains, since both are characterized by the same S/m ration(i.e. 1.56 m2 kg−1). This was found also for other working pairs and defined as“grain size insensitive” regime, meaning that, although the heat and mass transfersare strongly coupled, under these conditions the vapour transport through theadsorbent grains is sufficiently fast and the main factor affecting the sorptionkinetics is the heat transfer. Interestingly, no transition was observed to the “grainsensitive” regime for this working pair. Accordingly, for the investigated workingpair, it is possible to characterize the adsorption/desorption kinetics by constant heattransfer coefficients, independent from the grain size and the layer number, makingthe designing of the adsorber easier. Nevertheless, these results should be verifiedunder more complex heat exchanger geometries, like the one whose schematic isreported in Fig. 3.16.


As already reported for the grain size, also the effect of the adsorber’s channellength, with ethanol as refrigerant, has been experimentally investigated on both asorbent composite [15] and one of the most promising activated carbons available

Fig. 3.21 Kinetic curves formethanol adsorption (a) anddesorption (b) at (S/m) = 1.56(1), 1.24 (2), 0.78 (3) and 0.62(4) m2/kg and the grain size0.8–0.9 (○), 1.0–1.25 (△),1.6–1.8 (■), 2.5–2.8 mm (▼)and 4.0–4.1 mm (◇) [6]


on the market [16]. The G-LTJ apparatus was employed for such a kind of analysis.Particularly, the two finned tube aluminium HExs (i.e. HEx 1 and Hex 2), reportedin Fig. 3.7, were tested.

In [15], the experimental analysis was performed on a composite sorbent LiBr/silica. Since the aim was to compare the experimental data with the ones obtainedfor the FAB configuration, a similar S/m ratio (3.4 ± 0.4 m2 kg−1) for eachinvestigated grain size was prepared, as reported in Table 3.6.

The experimental tests were performed applying the same working boundaryconditions, namely air conditioning (AC) and ice making (IM) as for the FABconfiguration, both for adsorption and desorption runs. In Fig. 3.22, for instance,the dynamic evolutions of the specific Ad-HEx (i.e. HEx 1 with grain size 0.8–0.9 mm) both for adsorption and for desorption runs under the AC and IM con-ditions are reported. Interestingly, also for more complicated Ad-HEx configura-tions, the kinetic curves can be satisfactorily represented by exponential curves atleast up to 80% of conversion. Accordingly, a characteristic time, sads, was againcalculated for each test and summarized in Table 3.7.

As expected, comparing the data reported in Tables 3.4 and 3.7, it is evident thatthe adsorption rate of FAB is always higher than the one measured for the Ad-HExconfigurations. Due to the highly coupled heat and mass transfer phenomena inside

Table 3.6 Investigated Ad-HEx configurations [15]

Grain size, mm S/m, m2 kg−1 (Ad-HEx 1) S/m, m2 kg−1 (Ad-HEx 2)

0.2–0.4 3.03 3.32

0.4–0.6 3.61 3.24

0.6–0.7 3.11 3.31

0.9–1.0 3.44 3.75

Fig. 3.22 Kinetic curves of ethanol adsorption (a) and desorption (b) for the composite LiBr/silica under AC (1) and IM (2) conditions, for HEx 1 and grain size 0.8–0.9 mm [15]


the adsorbent bed, different features of the HEx can cause this behaviour. Some ofthe possible causes are:

• The lower heat transfer efficiency of the fins (secondary heat transfer surface)compared to the primary heat transfer surface (in direct contact with the heattransfer fluid);

• The presence of inter-particle diffusion resistance, due to the thin channelsbetween the fins;

• The mass transfer resistance added by the metallic net employed to keep theadsorbent material inside the HEX.

Furthermore, also other issues like the non-sufficient evaporator/condenserpower and the presence of residual air inside the testing chamber can affect theachievable dynamics.

In order to highlight the effect of the inter-granular diffusion resistance, it ispossible to compare the results obtained for the two Ad-HExs tested. Indeed, thelength of the channels for HEx 2 is double than the one for HEx-1. Since the heattransfer surface is the same, the observed deceleration of the adsorption runs forAd-HEx 2 compared to the ones measured for Ad-HEx 1 can be directly correlatedto the increased inter-granular diffusion resistance due to the longer mass transferpath faced by the vapour along the channels of Hex 2. Analysing the data reportedin Table 3.7, it can be verified that the characteristic times for Ad-HEx 2 can bedoubled or even triplicate compared to the Ad-HEx 1, depending on the grain size.Actually, the effect of the grain size on the dynamics of the two small-scale con-figurations is not monotonous, as pointed out by Fig. 3.23. The increase in grainsize from 0.2–0.4 mm up to 0.4–0.6 mm for IM adsorption runs and up to 0.6–0.7 mm for AC adsorption runs results in a reduction of the characteristic time,which means an acceleration of the dynamics. This behaviour is typically related tothe highly coupled inter-granular and intra-granular diffusion resistances as well asto the heat transfer resistance. Accordingly, looking at Table 3.7, it can be stated

Table 3.7 Characteristictimes for ethanol adsorptionand desorption on LiBr/silicafor the Ad-HEx 1 andAd-HEx 2 configurations [15]

Grain size,mm

Ad-HEx 1, sads, s Ad-HEx 2, sads, s

IMcycle

ACcycle

IMcycle

ACcycle

Adsorption

0.2–0.4 218 193 480 385

0.4–0.6 170 157 490 359

0.6–0.7 215 216 350 307

0.9–1.0 320 213 520 437

Desorption

0.2–0.4 43 36 38 37

0.4–0.6 38 43 40 47

0.6–0.7 45 53 42 55

0.9–1.0 56 58 53 58


that, for grains larger than 0.4–0.6 mm and 0.6–0.7 mm for Ad-HEx 1 and Ad-HEx2, respectively, the intra-granular diffusional resistance exceeds the inter-granularone. Accordingly, the smaller the grain size, the faster the adsorption. This wasalready highlighted in Fig. 3.14, where only intra-granular diffusional resistanceaffected the adsorption dynamics of the FAB configuration. Differently, for grainssmaller than 0.4–0.6 mm and 0.6–0.7 mm for Ad-HEx 1 and Ad-HEx 2, respec-tively, the inter-particle diffusional resistance becomes more relevant, thus affectingthe overall sorption dynamics. As reported in [15], the inter-granular diffusion in thelarge pores between the adsorbent grains at high ethanol pressure can be modelledlike a laminar flow with the Poiseuille diffusivity according to Eq. 3.4 [1].

Dtr ¼ DPois ¼ DP8g

� dtr2

� �2

; ð3:4Þ

where η represents the dynamic viscosity of ethanol vapour and dtr the size of thetransport pores. Accordingly, the grain size reduction causes a diffusivity reduction,which means slower adsorption dynamics.

In order to better investigate the effect of the inter-granular diffusion resistance,the ratio r = sads(Ad-HEx 2)/sads(FAB) between the characteristic adsorption timesof Ad-HEx 2 and FAB configurations was introduced. In Fig. 3.24, the ratio r isreported as a function of the grain size. It is evident that the ratio is higher forsmaller grains, which confirms the higher contribution of the inter-particle diffu-sional resistance in the low grain size range (i.e. <0.7 mm).

Differently from the adsorption runs, the desorption runs only slightly affectedby the channel length. Indeed, passing from the FAB configuration to real Ad-HExconfigurations, only a slight increase of the characteristic desorption times isobtained. Particularly, the characteristic times are slightly higher for the grainsizes >0.4–0.6 mm, which confirms that the intra-granular diffusion resistance

Fig. 3.23 Characteristic times of ethanol sorption and desorption for Ad-HEx1 (■) and Ad-HEx2(○) under conditions of the IM (a) and AC (b) cycles [15]


plays a role during the desorption phase. On the contrary, comparing the charac-teristic times reported in Table 3.7 for Ad-HEx 1 and Ad-HEx 2, there is no evidentdifference, which further confirms that the desorption runs are not affected by theinter-granular diffusion resistance for these configurations. This can be justified bythe higher absolute vapour pressure during desorption runs (ranging between 77and 100 mbar for IM and AC cycles, respectively) which pushes the mass transportamong the grains.

Finally, looking at the ratio r, reported in Fig. 3.24, it is evident that the growthof characteristic desorption times for Ad-HEx 2, compared to the FAB configura-tion, ranges between 1.4 and 1.8. This can be justified by lower heat transferefficiency due to the presence of secondary heat transfer surfaces (fins).

Similar investigations have been performed also for the working pair “activatedcarbon/ethanol”, as reported in [16]. In order to investigate the effect of theinter-granular resistance, in this case, three different HExs were selected, having thesame heat transfer surface area, but different length of the channels along the fins.HEx 1 and HEx 2 are the ones previously discussed, while HEx 3 is characterizedby a thickness, H, three times higher than HEx 1. As already specified for otherworking pairs, the comparison of adsorption/desorption dynamics was carried outby keeping the same S/m ratio as the one tested for the FAB configuration. In thiscase, the tests were conducted only on the selected grain size 0.43–0.60 mm, withan S/m in the range 4.8–5.0 m2 kg−1. As reported in Fig. 3.25 also for activatedcarbons, the adsorption runs are more influenced by the inter-particle diffusionresistance than the desorption runs. Indeed, while the characteristic adsorptiontimes, for the AC cycle, rise from 32 s for Ad-HEx 1 to 94 s for Ad-HEx 2 and750 s for Ad-HEx 3, the desorption times are almost the same for Ad-HEx 1 andAd-HEx 2 (i.e. 25 s) with only a slight increase, up to 40 s, for Ad-HEx 3.

Fig. 3.24 Ratio r for ethanoladsorption (■, □) anddesorption (●, ○) under IM(■, ●) and AC (□, ○) cycleconditions [15]


Comparing these results to the characteristic adsorption times, obtained for thesame S/m ratio, in the FAB configuration, a reduction of the dynamics is high-lighted for the real Ad-HEx configurations. This behaviour can be again caused by alower heat transfer efficiency, as well as the inter-granular diffusion resistance andmass transfer resistance added by the metallic net.

3.4 Cycle Boundary Conditions


In order to investigate the effect of the boundary conditions on methanol adsorptiondynamics employing the composite LiCl/SiO2 as sorbent, the adsorption/desorptionruns were performed by varying the ending ad/desorption temperature [5].Particularly, the adsorption runs were performed keeping fixed the initial temper-ature, Tin_ads = 50 °C, and varying the ending adsorption temperatureTend_ads = 30, 35 and 40 °C, while the desorption runs were performed startingfrom Tin_des = 60 °C and varying the ending desorption temperature Tend_des = 70,75, 80, 85 and 90 °C.

All the experimental adsorption kinetic curves were well represented by theexponential evolution, as reported in Fig. 3.26. In Fig. 3.27, the initial coolingpower against the driving temperature difference ΔTads = Tin_ads − Tend_ads isreported. This graph allows guessing that the initial sorption rate is mainly deter-mined by the heat transfer efficiency between sorbent and metal support; indeed, theachievable cooling power is a linear function of the temperature difference betweenthe HEx and the grains. A similar conclusion was drawn for methanol/activatedcarbon ACM-35.4 [6]. Furthermore, it is evident that, for chemical reactions, anadditional driving force is needed to start the sorption process. In the present case,for the gas–solid reaction LiCl + 3CH3OH = LiCl∙3CH3OH, a supercooling tem-perature of about 8 °C is necessary, as highlighted in Fig. 3.27.

Fig. 3.25 Comparison of adsorption and desorption runs for AC (a) and IM (b) cycles among thethree Ad-HExs tested [16]


As summarized in Table 3.8, the sorption kinetics in the monolayer becomesclearly slower when the driving temperature difference is limited, e.g. 10 °C,reaching a characteristic time of 365 s. On the contrary, the initial sorption process,

Fig. 3.26 Dynamics ofmethanol ad- (a) anddesorption (b) at variousboundary temperatures Tdes

and Tads. LiCl(21 wt%)/SiO2-Gr646. Dgr = 0.4 − 0.5 mm.Tin_des = 60 °C,Tin_ads = 50 °C. Lines—exponential fits [5]

10

5

00 5 10 15 20 25

15

Wm

ax, k

W/k

g

Δ T, 0CΔ

Fig. 3.27 Initial coolingpower Wmax versus thedriving temperature differencefor the methanol sorption onthe LiCl/silica composite [17]


up to a dimensionless sorption of 0.15, is in line with the ones obtained for higherdriving temperature difference. Accordingly, it is possible to conclude that about 15wt% of the salt confined inside the mesopores of the silica gel matrix reacts veryfast with methanol, making the heat transfer as the main mechanism for the sorptionkinetic determination. After a dimensionless sorption uptake of 0.15 is reached, aprocess deceleration is observed. The mechanism causing this deceleration isprobably the reaction between methanol and salt. Indeed, the reaction is driven bythe difference between the current adsorption potential DF(P, T) and the adsorptionpotential of the ending state DFend(Pend, Tend). Looking at the equilibrium curvereported in Fig. 3.28, the adsorption potential at 40 °C and 59 mbar is about4.62 kJ mol−1, while the most active salt reacts with methanol at the adsorptionpotential 4.9 kJ mol−1 and the least active salt at 4.6 kJ mol−1. Hence, the drivingadsorption potential difference is 0.3 kJ mol−1 and almost 0 kJ mol−1 for the “fast”and “slow” salt, respectively, while, for instance, when the Tads_end = 35 °C theadsorption potential difference is 1.0 kJ mol−1 and almost 0.7 kJ mol−1 for the

Table 3.8 Characteristic times and uptake variation for methanol sorption on a monolayer of LiCl(21 wt%)/SiO2 grains with Dgr = 0.4 − 0.5 mm, P = 60 mbar and Tin_ads = 50 °C [5]

Tend_ads [°C] s [s] s0.9 [s] Dw [g/g]

30 53 140 0.63

35 70 165 0.50

40 365 860 0.44

Fig. 3.28 Dubinin fitting for methanol adsorption on LiCl(21 wt%)/SiO2 with the highlightedtested ending conditions, i.e. 30, 35 and 40 °C [5]

3.4 Cycle Boundary Conditions 59

most and least active salt, respectively. Accordingly, it can be stated that the limitedadsorption potential difference for DTads = 10 °C causes the slowdown of theadsorption kinetics. It can be concluded that the overall sorption kinetics dependson two driving forces, namely the driving force for the chemical reaction (i.e. theadsorption potential difference) and the driving force for heat transfer (i.e. thedifference between initial and ending adsorption temperatures).

For the desorption runs, the effect of the ending desorption temperature on thedynamics was not monotonous, as can be highlighted by Fig. 3.26 and Table 3.9.Actually, at the minimum ending desorption temperature, 70 °C, the kinetics wasexponential with a short characteristic time of 15 s. This is caused by the lowuptake variation obtained under these working conditions, 0.21 g/g, which is due tothe methanol removal from the LiCl–methanol solution, which does not form solidsalt under these conditions. Indeed, the adsorption potential for T = 70 °C andP = 274 mbar is 4.29 kJ mol−1 which is lower than the equilibrium potential atwhich the LiCl solid formation occurs, i.e. 4.6–4.9 kJ mol−1. At Tads_end = 75 °C,the adsorption potential is 4.90 kJ mol−1 that is barely sufficient for the salt for-mation. This causes a clear methanol uptake exchange increasing up to 0.54 g/g,but a strong reduction of the kinetics, due to very limited adsorption potentialdifference driving force. This reduction is also reflected in the deviation from theexponential evolution. Further increasing of the ending desorption temperature, upto 90 °C, increases the adsorption potential difference, thus making the desorptionprocess faster, obtaining once more the typical exponential evolution.

It can be concluded that the ad/desorption kinetics for working pairs employingadsorbents with chemical reaction is strongly dependent on the driving forceapplied for the chemical reaction itself, i.e. the difference in adsorption potentialbetween the initial and ending state. Therefore, the boundary conditions must becarefully selected since they affect the available driving force for the ad/desorptionmethanol/salt reaction.


The effect of boundary conditions on the adsorption dynamics of working pairsemploying ethanol as refrigerant is well elucidated in [15, 16] by comparing the

Table 3.9 Characteristic times and uptake variation for methanol desorption from a monolayer ofLiCl(21 wt%)/SiO2 grains with Dgr = 0.4 − 0.5 mm, P = 274 mbar and Tin_des = 60 °C [5]

Tend_des [°C] s [s] s0.9 [s] Dw [g/g]

90 30 110 0.61

85 32 120 0.60

80 – 307 0.58

75 – 410 0.54

70 15 55 0.21


kinetics under typical IM and AC working boundary conditions. The tests wereperformed by exactly replicating the real isobaric temperature drop/jump duringadsorption/desorption runs. In Table 3.10, the experimental conditions employedfor simulating the IM and AC cycles by means of LTJ kinetic apparatuses aresummarized for two adsorbents: LiBr–silica gel composite and AC SRD 1352/3.Once the three cycle temperatures, namely adsorption/condensation, evaporationand desorption, are fixed, the initial temperature for isobaric adsorption/desorptionruns vary according to the slope of the isosteres of the given adsorbent.

Interestingly, looking at the characteristic adsorption times reported for LiBr–silica gel composite and AC SRD 1352/3 in Tables 3.3 and 3.7, under the FABconfigurations, the kinetics measured for AC cycle is always faster than the oneobtained for IM cycle. This behaviour can be justified taking into account two mainphysical parameters affecting the sorption dynamics, namely the absolute ethanolpressure and the driving temperature difference for adsorption run (i.e.ΔTads = Tin_ads − Tend_ads). Looking at the experimental conditions, it is evidentthat the absolute pressure for AC cycle (i.e. 31 mbar) is higher than for IM cycle(i.e. 12.6 mbar) for both samples. On the contrary, the driving temperature differ-ence is higher for AC cycle than for IM cycle for the LiBr/silica composite, while,conversely, for SRD 1352/3 it is higher for IM cycle than for AC cycle.Accordingly, it can be stated that the most influencing working boundary conditionaffecting the adsorption dynamics is represented by the absolute pressure inside thereactor during the adsorption runs.

As already pointed out, the desorption runs look unaffected by the boundarycondition. This can be again related to the high absolute vapour pressure as well asthe high mean temperature at which the desorption runs occur, which reduce theeffect of inter-granular and intra-granular diffusion resistance.

3.5 Residual Gases

It is common opinion and experience that residual gases can drastically affect theperformance of adsorption heat transformers. In practice, gases can be present insideevacuated equipment for different reasons: air due to minor leaks, hydrogen due to

Table 3.10 Working boundary conditions for ice making (IM) and air conditioning (AC) for bothLiBr/SG and SRD 1352/3 adsorbents [16]

Adsorbent Cycle Tev

[K]Pev[mbar]

Tcond

[K]Pcond[mbar]

Tin_des

[K]Tend_des

[K]Tin_ads

[K]Tend_ads

[K]ΔTads

[K]

LiBr/SG IM 270 12.6 298 78.4 330 363 328 298 30

AC 283 31.0 303 104.1 333 363 340 303 37

AC SRD1352/3

IM 270 12.6 298 78.4 330 368 327 298 29

AC 283 31.0 303 104.1 338 368 325 303 22

3.4 Cycle Boundary Conditions 61

corrosion, etc. Therefore, extremely careful degassing of adsorbers and evaporator/condenser is mandatory to start operating and periodically during running.

Residual gases affect the sorption kinetics by the effective gas sweeping to thesurface where it accumulates as a gas-rich layer [18, 19]. The transfer of vapour tothe surface may then become controlled by the process of diffusion through thislayer. This process is relatively slow compared with adsorption process controlledby inter- and/or intra-granular heat and mass transfer resistances typical foradsorption of pure vapour in an adsorbent bed [1].


Experimental studies of the effect of non-adsorbables on dynamics of the watervapour adsorption were performed for ideal adsorber configurations based on loosegrains placed on metal plate which imitates a HEx fin [20–22] as well as forrepresentative fragments of real adsorbers suggested and tested for various AHT[23]. Studies on this issue were performed applying the LTJ method that allowsreproduction of real operating conditions of typical AC cycle, both in the volu-metric (V-LTJ) and in gravimetric (G-LTJ) versions.

In particular, the effect of residual gases was studied in [23] for an Ad-HExconfiguration realized by embedding loose grains of aluminophosphate AQSOA™-FAM-Z02 [14] inside two finned flat-tube HExs made of aluminium and having thesame finned pack type. These HExs (Fig. 3.7) were manufactured to have similarvolume and different thicknesses (22 and 40 mm) to evaluate the effect of theinter-granular resistance as reported in [23] where detailed description of theAd-HExs is given. The paper reports the study of the effect of residual air as well ashydrogen.

The effect of the residual air on the sorption kinetics was evaluated for the airpressure ranging between 0.06 and 2.1 mbar for HEx 1 and 0.04 and 1.06 mbar forHex 2.

The dimensionless uptake curves for HEx 1 at different air pressure [Fig. 3.29left] show that the adsorption process becomes slower due the presence of residual

0

0,2

0,4

0,6

0,8

1

0 500 1000 1500 2000 2500 3000

w(t

)/w∞

Time [s]

no air0.06 mbar0.1 mbar0.19 mbar0.23 mbar0.46 mbar0.8 mbar2.1 mbar

1 2 3 4 5 6 7 8

1

2

3

4

5

67

8

y = e-0,002322x

R² = 0,949284

0,0

0,2

0,4

0,6

0,8

1,0

0 200 400 600 800 1000 1200

1-w

(t)/w

∞

Time [s]

Fig. 3.29 Dimensionless uptake curves in the presence of air for HEx1 (left) and exponentialapproximation of the kinetic curve at pair = 0.46 mbar (right) [23]


air. Furthermore, at any content of air, the uptake curves w(t)/w∞ are exponential asshown in Fig. 3.29 right where the fitting curve for pair = 0.46 mbar is reported.

The dependence of the adsorption time on the air partial pressure as well as itslinear approximation is reported for both HExs in Fig. 3.30.

It is worth to notice that the slowing down becomes relevant already at the Pair aslow as 0.04–0.06 mbar where the characteristic time rises by a factor of 1.5–2 for bothHExs tested. Therefore, the first important finding is that even very small amounts ofair in the components of an AC unit can significantly worsen the dynamics of isobaricadsorption stage and, hence, reduce the cooling power of the unit.

Therefore in [23], a first recommendation, recommendation 1, is given and saysas follows: extra-careful degassing of both adsorbers and evaporator/condenser isstrictly necessary before starting AHT operation to reach a low level of residual air.Moreover, due to possible minor leaks and very slow desorption of air from theadsorber, periodical degassing of AHT unit may be necessary during its long-termexploitation.

Figure 3.30 shows also that the characteristic adsorption time is a function of theresidual air pressure. At pair > 0.05 − 0.10 mbar, the characteristic time increasingcan be described by a linear function:

s ¼ s0 þBpair ð3:5Þ

where the constants s0 and B depend on the HEx geometry as shown in Fig. 3.30.Both these constants are approximately twice larger for HEx 2 that shows much

higher sensitivity to residual air. This indicates that air mainly affects the vapourtransfer rather than the heat transfer in the adsorber. Indeed, the surface areas activein heat transfer (Sht) for HEx 1 and HEx 2 are very similar, while those active inmass transfer (Smt) are different. Since Smt(HEx 1)/Smt(HEx 2) = 2, therefore, onemay guess that s * (1/Smt). Hence, air is concentrated near the external (or themass transfer) surface of the HEx, covered by the metal net, and blocks a directaccess of water vapour to the adsorbent, so that the vapour molecules have to

y = 586,74x + 164,81

y = 1132,2x + 308,92

0

200

400

600

800

1000

1200

1400

1600

0 0,25 0,5 0,75 1 1,25 1,5 1,75 2 2,25

Cha

ract

eris

tic ti

me

[s]

Air partial pressure [mbar]

1

2

Fig. 3.30 Dependence of theadsorption time on the airpartial pressure for Hex 1 andHex 2 [23]

3.5 Residual Gases 63

diffuse through a thin air layer to reach the adsorbent grains. In fact, the smaller thesurface area of mass transfer, the easier to block it. Thereby in [23], a secondrecommendation, recommendation 2, is given and concerns the Ad-HEx design: itis profitable to maximize the area of mass transfer surface, thus minimizing thepossibility of its blocking by residual gas.

In [23] also the effect of presence of hydrogen on the sorption kinetics wasevaluated for the H2 pressure ranging between 0.27 and 3.0 mbar for Hex-1. Asshown in Fig. 3.31, at any H2 pressure, the uptake curves are exponential and thepresence of hydrogen also slows down the adsorption process.

A comparison of the effect of residual air and hydrogen on the sorption kineticsas function of the gas content is reported in Fig. 3.32 where the linear approxi-mation is also plotted.

The influence of residual hydrogen is less strong as compared with air, and forHEx 1, the slope B(H2) is equal to (155 ± 20) s/mbar (Fig. 3.32). The experimentalratio B(air)/B(H2) = 3.77 is close to the ratio of effective diffusivities (cm2/s) in thebinary mixture “air–vapour”

Da ¼ 292= p H2Oð Þþ pair½ � ð3:6Þ

and “hydrogen–vapour”

0,0

0,2

0,4

0,6

0,8

1,0

0 500 1000 1500 2000

w(t

)/w∞

Time [s]

no hydrogen0.27 mbar0.53 mbar1.61 mbar1.65 mbar

1 2 3 54

12345

y = e-0,005646x

R² = 0,960599

0,0

0,2

0,4

0,6

0,8

1,0

0 50 100 150 200 250 300 350 400 450

1-w

(t)/w

∞

Time [s]

Fig. 3.31 Dimensionless curves of water adsorption in the presence of hydrogen for HEx1 (left)and exponential approximation of the uptake curve at PH2 = 1.61 mbar (right) [23]

y = 586,74x + 164,81

y = 153,11x + 69,999

0

200

400

600

800

1000

1200

1400

1600

0 0,25 0,5 0,75 1 1,25 1,5 1,75 2 2,25 2,5 2,75 3

Cha

ract

eris

tic ti

me

[s]

Gas partial pressure [mbar]

1

2

Fig. 3.32 Adsorption timeversus partial pressure ofresidual gas as well as itslinear approximation: 1—air,2—hydrogen. Hex [23]


Dh ¼ 1136= p H2Oð Þþ ph½ � ð3:7Þ

(the vapour, air and hydrogen partial pressures are in mbar), equals to Dh/Dair = 3.89 � (Mair/Mh)

1/2, where Mair and Mh are the molecular masses of air andhydrogen.

This less dramatic effect of hydrogen can be attributed to its higher diffusivity ascompared to air. It leads to faster H2 motion away from the HEx mass transfersurface that promotes destroying of the gas-rich layer.

Results achieved in [23] by the G-LTJ method are in good agreement with thoseobtained for loose grains of various adsorbents (Fuji silica RD, SWS-1L,AQSOA-Z02) and reported in [20–22]. Several features of the gas influence inthese papers are similar:

• an abrupt increase in the adsorption time at very low gas pressurepair < 0.1 mbar;

• a linear dependence of the adsorption time on the gas pressure at higher pgas;• the effect of hydrogen is less strong as compared with air.

This surprising likeness probably comes from the fact that the mechanism offormation of the gas-rich layer in both cases is the same and originates from theStephan flux of vapour molecules incipient as a result of water adsorption on thesurface [18, 19].

It is also worth to notice that, as reported in [23], the rate of desorption is onlyslightly affected by the residual gas (air or hydrogen) because the gas-rich layerdoes not form in this case. The desorption rate was limited by the intra-particlevapour diffusion or the dissipation of adsorption heat from the grain external sur-face. Some little reduction of the desorption rate (not presented) can be attributed tosmaller rate of vapour condensation in the presence of air. Indeed, the total pressurein the condenser somewhat increases due to the effective air sweeping to thecondensation surface.

3.6 Flux of Cooling/Heating Heat Carrier Fluid

The flow rate V of the external heat carrier (commonly water) flowing into theadsorber can affect the sorption dynamics. In [13], this effect was studied for thedesorption dynamics for an adsorber based on an aluminium radiator filled withAQSOA in shape of grains of 0.30–0.35 mm size (namely Hex1 described inprevious paragraphs). The experimental activity carried out by the G-LTJ methodwas performed comparing the characteristic time obtained for different Reynoldsnumbers/flow rates (from 10 to 290) as reported in Table 3.11.

Results showed no effect of the flow rate at V > 2.4 dm3 min−1, while at lowerrate a worsening of the desorption dynamics was observed probably due to insuf-ficient heat transfer from the heat carrier to the adsorber. Obviously, this minimal

3.5 Residual Gases 65

flux characterizes the particular tested Ad-HEx and cycle conditions, while, toextend these considerations to other HExs, the results were analysed in terms of theheat flux J(t) between the HEx fins and the adsorber. For desorption run, it can bewritten as

J tð Þ ¼ U � S � Tfin � Tads tð Þ½ � ¼ U � S=mð Þ �m � Tfin � Tads tð Þ½ � ð3:8Þ

where U is the heat transfer coefficient [W m−2 K−1], Tfin [°C] is the HEx’s fintemperature, and Tads [°C] is the temperature of adsorbent layer adjacent to the fin.Each multiplier in Eq. (3.8) affects the minimal sufficient flow rate. For instance, forAd-HEx, that has the same (S/m) ratio, but is larger than Ad-HEx tested in [11] by afactor of N, the flux increases by a factor of N due to larger adsorbent mass, m.Therefore, for the flow rate upscaling, the minimal sufficient rate (2.4 dm3 min−1)should be related to the adsorbent mass, thus obtaining c.a. 30 dm3 min−1 kg−1.This flux is deemed to guarantee sufficient heat supply/release to/from any enlargedfinned flat-tube Ad-HEx with the same adsorbent (the same [Tfin − Tads(t)]) andHEx geometry (the same (S/m) ratio). Similarly, the flux increases for HExs withlarger ratio (S/m) and higher heat transfer coefficient.

The optimal flow rate estimated in [13] by a kinetic measurement can becompared with the normalized fluxes calculated from the literature data for otherfinned flat-tube HExs employed in larger-scale adsorption chiller set-ups, namely68 dm3 min−1 kg−1 [24], 71 dm3 min−1 kg−1 [25] and 54 dm3 min−1 kg−1 [26]. Inall those tests, the flow rate was c.a. 2 times larger than the minimal flux estimatedby the kinetic measurements. This may be partly due to lower (S/m) value or to thenon-optimal operating conditions management.

References

1. I.Y. Aristov, Optimal adsorbent for adsorptive heat transformers: dynamic considerations. Int.J. Refrig 32, 675–686 (2009)

2. I.Y. Aristov, Experimental and numerical study of adsorptive chiller dynamics: loose grainsconfiguration. Appl. Thermal Eng. 61, 841–847 (2013)

3. E. Glueckauf, Part 10. Formulae for diffusion into spheres and their application tochromatography. Trans. Faraday Soc. 51, 1540–1551 (1955)

Table 3.11 Study of effectof flow rate on the desorptiondynamics [13]

Flow rate, [dm3

min−1]<0.1 1.0 1.4 2.4 2.8

Manifold inletvelocity, [m/s]

0.02 0.21 0.3 0.50 0.59

Reynolds tube inlet 10 103 145 250 290

sdes 80% [s] 142 105 87 80 82


4. Y.I. Aristov, B. Dawoud, I.S. Glaznev, A. Elyas, A new methodology of studying thedynamics of water sorption/desorption under real operating conditions of adsorption heatpumps: experiment. Int. J. Heat Mass Transf. 51, 4966–4972 (2008)

5. Larisa G. Gordeeva, Yuriy I. Aristov, Composite sorbent of methanol “LiCl in mesoporoussilica gel” for adsorption cooling: dynamic optimization. Energy 36, 1273–1279 (2011)

6. L.G. Gordeeva, Y. Aristov, Dynamic study of methanol adsorption on activated carbonACM-35.4 for enhancing the specific cooling power of adsorptive chillers. Appl. Energy 117,127–133 (2014)

7. Y. Aristov, I.S. Glaznev, I.S. Girnik, Optimization of adsorption dynamics in adsorptivechillers: loose grains configuration. Energy 46, 484–492 (2012)

8. I.S. Girnik, Y. Aristov, Dynamics of water vapour adsorption by a monolayer of looseAQSOA™-FAM-Z02 grains: Indication of inseparably coupled heat and mass transfer.Energy 114, 767–773 (2016)

9. D.M. Ruthven, Principles of Adsorption and Adsorption Processes (Wiley, New York, 1984)10. A. Sapienza, S. Santamaria, A. Frazzica, A. Freni, Y. Aristov, Dynamic study of adsorbers by

a new gravimetric version of the Large Temperature Jump method. Appl. Energy 113, 1244–1251 (2014)

11. Yuriy I. Aristov, Ivan S. Glaznev, Ilya S. Girnik, Optimization of adsorption dynamics inadsorptive chillers: loose grains configuration. Energy 46(1), 484–492 (2012)

12. I.S. Girnik, Y. Aristov, Dynamic optimization of adsorptive chillers: The “AQSOA™-FAM-Z02—Water” working pair. Energy 106, 13–22 (2016)

13. S. Santamaria, A. Sapienza, A. Frazzica, A. Freni, I.S. Girnik, Y. Aristov, Water adsorptiondynamics on representative pieces of real adsorbers for adsorptive chillers. Appl. Energy 134,11–19 (2014)

14. H. Kakiuchi, M. Iwade, S. Shimooka, K. Ooshima, M. Yamazaki, T. Takewaki, Water Va-poradsorbent FAM-Z02 and its applicability to adsorption heat pump. Kagaku KogakuRonbunshu 31, 273–277 (2005)

15. L. Gordeeva, A. Frazzica, A. Sapienza, Y. Aristov, A. Freni, Adsorption cooling utilizing the“LiBr/silica—ethanol” working pair: dynamic optimization of the adsorber/heat exchangerunit. Energy 75, 390–399 (2014)

16. Vincenza Brancato, Larisa Gordeeva, Alessio Sapienza, Angelo Freni, Andrea Frazzica,Dynamics study of ethanol adsorption on microporous activated carbon for adsorptive coolingapplications. Appl. Thermal Eng. 105, 28–38 (2016)

17. Larisa Gordeeva, Y. Aristov, Dynamic study of methanol adsorption on activated carbonACM-35.4 for enhancing the specific cooling power of adsorptive chillers. Appl. Energy 117(15), 127–133 (2014)

18. W. Nusselt, Surface condensation of water vapour. Z. Ver. Deut. Ing. 60, 541–546 (1916)19. D.A. Frank-Kamenetskiy, Diffusion and heat transfer in chemical kinetics (Nauka, Mos-cow,

1967)20. I.S. Glaznev, Y. Aristov, Kinetics of water adsorption on loose grains of SWS-1L under

isobaric stages of adsorption heat pumps: the effect of residual air. Int. J. Heat Mass Transf. 51(25–26), 5823–5827 (2008)

21. B.N. Okunev, A.P. Gromov, V.L. Zelenko, I.S. Glaznev, D.S. Ovoshchnikov, L.I. Heifets, Y.Aristov, Effect of residual gas on the dynamics of water adsorption under isobaric stages ofadsorption heat pumps: mathematical modelling. Int. J. Heat Mass Transf. 53, 1283–1289(2010)

22. I.S. Glaznev, D.S. Ovoshchnikov, Y. Aristov, Effect of residual gas on water adsorptiondynamics under typical conditions of an adsorptive chiller. Heat Transf. Eng. J. 31(11), 924–930 (2010)

23. A. Sapienza, A. Frazzica, A. Freni, Y. Aristov, Dramatic effect of residual gas on dynamics ofisobaric adsorption stage of an adsorptive chiller. Appl. Thermal Eng. 96, 385–390 (2016)

References 67

24. W.S. Chang, C.C. Wang, C.C. Shieh, Experimental study of a solid adsorption cooling systemusing flat-tube heat exchanger as adsorption bed. Appl. Thermal Eng. 27, 2195–2199 (2007)

25. Y. Aristov, A. Sapienza, A. Freni, D.S. Ovoschnikov, G. Restuccia, Reallocation ofadsorption and desorption times for optimizing the cooling cycle parameters. Int. J. Refrig 35,525–531 (2012)

26. A. Sapienza, S. Santamaria, A. Frazzica, A. Freni, Influence of the management strategy andoperating conditions on the performance of an adsorption chiller. Energy Int. J. 36, 5532–5538 (2011)


Chapter 4Optimization of an “Adsorbent/HeatExchanger” Unit

Abbreviation

Nomenclature

AC Adsorptive ChillerAd-HEx Adsorbent Heat ExchangerAHT Adsorptive Heat TransformerC Gas/vapour molar density, mol m−3

COP Coefficient of Performanced Grain’s diameter, mmD Diffusivity, m2 s−1

LTJ Large Temperature Jump methodV-LTJ Volumetric Version of Large Temperature Jump methodHEx Heat ExchangerJ Heat flux, WL Adsorbent layer thickness, mm; HEx length, mm Dry adsorbent mass, kgM HEx’s mass, kgN Moles of air moleculesP Pressure, PaR Grain radius, mm; adsorption-to-desorption time ratio, s/s; universal gas

constant, J mol−1 KS HEx heat transfer surface area, m2

SCP Specific Cooling Power, W kg−1

SP Specific PowerT Temperature, KTD Temperature Drivent Time, s; cycle time, sU Overall heat transfer coefficient, W m−2 K−1

v Velocity of the convective flux, m s−1


69




V HEx’s volume, dm3; volumetric flow rate, dm3 min−1

VCP Volumetric Cooling Power, W/dm3

w Water uptake, g g−1; HEx’s widthW Specific cooling power, W kg−1

z Coordinate in the direction perpendicular to the flat adsorbent bed, m

Greek Symbols

q Adsorbent layer density, kg m−3

s Characteristic time, s

Subscripts

0 Initial stagea Airads Adsorbent/adsorptionCon Condensationconv Convectivedes Desorptiondif Diffusionalev Evaporationf FinH HighL LowM Mediummin Minimalmt Mass transferreg Regenerationv Vapour

Despite significant progress, the AHT technology as yet remains unfinished andexpensive, so that there is still a big room for its improvement [1, 2]. This concerns,first of all, enhancement of the AHT dynamics, like the ad/desorption rate andfinally the specific power that is the main figure of merit of the AHT dynamicperformance. Therefore, further R&D activity is necessary to realize the potentialeconomic and ecological advantages of the AHT technology [3]. The optimizationof the AHT dynamic performance is a multi-purpose task that includes, first of all,the improvement of the “adsorbent–heat exchanger” unit.

Two basic configurations of the Ad-HEx were tested at laboratory and com-mercial scales [4–6], namely (a) a bed of loose adsorbent grains that contact withthe HEx surface and (b) a consolidated adsorbent layer attached/glued to the HExsurface. We focus here on the first configuration, because:

70 4 Optimization of an “Adsorbent/Heat Exchanger” Unit

• it is simple in realization and ensures good inter-grain vapour transport. It ischeap, free of binder and does not need sophisticated maintenance due topossible release of non-condensable gases by the binder during operation;

• numerous experimental results obtained for a flatbed of loose grains of manypromising adsorbents clearly demonstrated that this configuration can provide aspecific cycle (corresponding to 70% conversion) power of 2–5 kW/kg, whereasthe initial power can exceed 10 kW/kg [7] (see Chap. 3). These values are verypromising for designing compact and efficient AHT units;

• direct comparison of the two mentioned configurations made in [8] clearlydemonstrated that both the COP and SCP related to the HEx total volume weresignificantly larger for the loose grains configuration than for the coated one:COP = 0.4 and 0.24 respectively; SCP = 212 and 93 kW/m3 respectively.

Therefore, we consider heat and mass transfer on the solid (loose grains bed)side, assuming that heat transfer on the liquid side is fast enough. The minimal flowrate of the heat carrier fluid, which ensures this fast transfer, is only shortly analysedin 4.1.3 [9]. We also suppose that the evaporator/condenser power fits the power ofadsorption/desorption processes. The effect of residual air that can be veryimportant for real AHT machines is briefly discussed in 4.3 [10]. Towards the end,a better organization of AHT cycles by proper reallocation of the durations of AHTadsorption and desorption stages is considered in 4.4 [11].

4.1 Optimization of the “Adsorbent—Heat Exchanger”Unit

The main progress in enhancing the AHT dynamic performance is expected toresult from an intelligent optimization of the “adsorbent–heat exchanger” unit. Theadsorbent is an important part of any AHT unit; therefore, it has to be in harmonywith all other components, the cycle boundary conditions and the cycle manage-ment strategy [12]. Here we consider the optimization of the loose grains config-uration and tried to answer the following practical questions:

What is the optimum size of adsorbent grains?What is the optimum adsorbent mass per m2 of heat transfer surface area?

4.1.1 Adsorbent Grain Size

It is well known that adsorption dynamics on a single porous grain strongly dependon the grain size [13]. For gas adsorption initiated by a jump of gas pressure overthe grain, the adsorption rate in large adsorbent grains is controlled by intra-particlegas diffusion and the characteristic adsorption time s * R2. For small grains, theprocess rate is controlled by heat rejection from the grain external surface and

4 Optimization of an “Adsorbent/Heat Exchanger” Unit 71

s * R1. A gradual crossover between these limits is observed at increasing grainsize, and this allows distinguishing the contributions of heat and mass transfers.

Surprisingly, for the flatbed of loose grains, a “grain size insensitive” (or“lumped”) regime was experimentally found for water and methanol ad/desorptiondriven by a temperature jump: first, in [14] and then in many other papers, e.g. [7,15]. It was also predicted by mathematical modelling of the TD water adsorption onzeolite 13X [16] and SWS-1L [17]. Under this regime, the bed adsorption dynamicsdoes not depend on the adsorbent grain size if the ratio (S/m) is constant for variousbeds (Fig. 4.1).

For instance, for water adsorption on Fuji silica gel, this regime was observedfor grains smaller than d < 0.8 mm and (S/m) > 1.0 − 1.5 m2/kg [14], and onMitsubishi AQSOA™-FAM-Z02—at d = 0.2–0.9 mm and 0.44 m2/kg � (S/m) �1.75 m2/kg [15]. For methanol adsorption on carbon AC-35.4, the “lumped” modewas observed over the whole experimental range: 0.3 m2/kg � (S/m) � 3.1 m2/kgand d = 0.8–4.0 mm [18]. Probably, in this case, the ad/desorption dynamics iscontrolled by the heat transfer between the metal and the adsorbent, while the ad/desorption itself is fast enough to readily adapt to variations in the heat transfer. The“grain size sensitive” regime is realized for silica grains larger than 0.8 mm for whichthe adsorption rate is not sufficiently fast to follow the heat flux changes that lead tothe reduction of the total rate. Therefore, the size of the loose adsorbent grains has tobe selected in such a way to realize the “grain size insensitive”mode. In so doing, it isnot necessary to precisely select the adsorbent grain size within the mentioned range.

The “grain size insensitive” mode is also found in more complex Ad-HExesfilled with loose AQSOA Z02 grains [9]. Except for the largest grains (1.00–1.18 mm), no effect of the grain size on desorption dynamics is found. For the1.00–1.18 mm grains, the desorption rate was slower by a factor of 1.8 probablydue to slow vapour transport inside the grains. The intra-grain mass transferresistance is likely a reason of the adsorption rate reduction for the AQSOA Z02grains of the same size (see Fig. 9 in [9]). For adsorption, the “lumped” regime wasfound for narrower range of the grain size, c.a. 0.30–0.71 mm. For smaller grains, adramatic rate slowdown (by a factor of 1.55) is detected. That may be due to thereduced bed permeability and the consequent inter-grain mass transfer resistance

Fig. 4.1 Schematic presentation of flatbeds having the same (S/m) ratio and different size d ofadsorbent grains


along the narrow triangular channels between the secondary fins (see also paragraph4.1.4 and Figs. 4.2, 4.3). This resistance is absent at the flat-plate Ad-HExconfiguration.

In sum, when the sorption rate is controlled by the heat transfer between theadsorbent and the metal support, no effect of the grain size is observed, and the“grain size insensitive” mode takes place. In this case, it is not necessary to pre-cisely select the adsorbent grain size: the grains should just be sufficiently small toassure the “lumped” mode. On the other hand, using too small grains is not rec-ommended as the inter-grain diffusional resistance may become a rate-limitingprocess. For Ad-HEx1 [9] and consequently for similar larger-scale commercialAd-HExs, the grain size of 0.3–0.6 mm represents a good compromise choice.Similar grain size is optimal for Fuji silica RD as well [14].

Fig. 4.2 View of the analysed Ad-HExs taken from [11] (a), [20] (b), [22] (c) and [23] (d)

4.1 Optimization of the “Adsorbent—Heat Exchanger” Unit 73

4.1.2 The Ratio “Heat Transfer Surface”/“Adsorbent Mass”

The dynamic study of water, methanol and ammonia adsorption on loose grains ofvarious adsorbents revealed that, under “grain size insensitive” mode, the sorptionrate is proportional to the ratio (S/m) of the area of heat transfer surface, S, betweenthe adsorbent bed and the HEx fins to the adsorbent mass, m, that was first revealedin [14] (see Chap. 3 for details). The invariance of the methanol adsorptiondynamics on this ratio has recently been found also for “HeCol” cycle driven by apressure jump [19]. Therefore, it is convenient to use this ratio to assess the degreeof a dynamic perfection of an Ad-HEx unit: the larger is this ratio, the higher powerper unit adsorbent mass can be obtained. To characterize a heat exchanger itself, theratios S/V [m2/dm3] and S/M [m2/kg] can be used where V and M are the HEx’svolume and mass. Evidently, for making a compact Ad-HEx, both ratios have to bemaximized. The values of (S/m) and (S/V) were assessed for the selectedlaboratory-scale AHT prototypes of four different types for which the data areavailable in literature (Table 4.1) [14]:

(a) a compact heat exchanger of a finned flat-tube type tested at ITAE-CNR(Messina, Italy) with the distance between the flat tubes of 10 mm and betweenthe fins of approximately 2 mm [11]. Grains of water adsorbent are contactedmainly with fins that are secondary heat transfer elements (Fig. 4.2a). The heattransfer distance is only 0.5–1 mm, while the vapour has to penetrate in thenarrow slits (1 � 10 � 27 mm3) through the maximal distance of 13.5 mm.

Fig. 4.3 Tested Ad-HEx configurations: flat beds of loose adsorbent grains (schematics—a, view—b); finned flat-tube HEx tested (schematics—c, view—d) [31]. Arrows demonstrate inter-grain(1) and intra-grain (2) diffusion, heat transfer between cooling/heating fluid and adsorbent grains(3), and between HEx fins and adsorbent grains (4)


This well-designed heat exchanger has (S/m) � 4 m2/kg, (S/M) = 2.6 m2/kg,(S/V) = 1.51 m2/dm3 and the ratio (adsorbent mass/HEx mass) > 0.5;

(b) a finned tube heat exchanger: each tube is 1230 mm length with the spacebetween fins of 2.5 mm. Each fin is 0.3 mm thick and 23 mm high (Fig. 4.2b).The composite adsorbent of water with the particle diameter from 0.5 mm to1 mm is filled between the fins. The density of the adsorbent is about 600 kg/m3 and the mass is 22 kg. The heat transfer area in each finned tube is 35.4 m2

[20];(c) a plate heat exchanger is made of a nickel-brazed stainless steel and designed as

29 layers of active carbon each 4 mm thick (Fig. 4.2c). The loose adsorbentgrains are directly contacted with flat-tube plate that is a primary heat transferelement, and no secondary elements, like fins, are installed. The heat con-duction path length through the adsorbent is approximately. 2 mm that togetherwith a larger heat conductivity of carboneous adsorbent enables rapid tem-perature cycling [21, 22]. Although the mass transfer occurs through the narrow

Table 4.1 Parameters of the selected Ad-HEx units taken from literature [14]

Reference [11] [20] [21, 22] [23]

HEx type Finned flat tube Finned tube,loose grains

Plate Finnedtube,compactlayer

Dimensions [mm] 257 � 170 � 27 See text 150 � 150 � 150 See text

Metal mass, M [kg] 0.636 – 9 6.08

Overall volume, V [dm3] 1.1 33.3a 3.37 8.6

Typical adsorbent mass, m[kg]

0.4 22 0.75 1.75

Mass metal/massadsorbent, M/m

1.81 – 12 3.5

Heat transfer surface,S [m2]

1.66 35.4 1.35 1.7

Ratio S/V [m2/dm3] 1.51 1.06 0.40 0.20

Ratio S/m [m2/kg] *4 1.61 1.80 0.97

Prototype specific powerWp, [kW/kg]

0.4 0.25 0.6 1.2c

1.3–2.6b 0.3d

0.12e

Estimated power W0:8,[kW/kg]

2.5 1.0 1.1 0.6

Ratio Wexp=W0:8 0.15 0.25 0.5 0.2avolume available for adsorbentbmaximal power [23]cinstantaneous power in the condenser [23]dinstantaneous power in the evaporator [23]eaverage cycle power [23]


slits (4 � 150 � 150 mm3) over the maximal distance of 75 mm, it does notlimit the process rate because of high NH3 pressure (1–10 bar);

(d) Figure 4.2d shows the Ad-HEx that consists of a finned tubes heat exchangerwith the space between fins filled by a compact layer of SWS-1L (CaCl2confined to the pores of silica KSK) containing 25 wt% of bentonite clay as abinder. Each tube is 560 mm length with the space between fins of 2 mm. Massof the adsorbent is 1.75 kg. The total heat transfer area is 1.7 m2 [23]. Duringthe adsorption phase, the instantaneous useful effect was 0.3 kW/kg of (ad-sorbent + binder), while the instantaneous power supplied during desorptionwas about 1.2 kW/kg. The specific cooling power calculated considering thetotal cycle time (that is similar to W0:8) was 0.12 kW/kg.

Unfortunately, we could not make this analysis for commercial AC units havingadsorbent layer consolidated with HEx fins that have recently appeared in themarket [24]. To the best of our knowledge, the input data that are necessary for suchstudy are not available in literature.

For the analysed Ad-Hex units, the ratio S/m is typically of 1–4 m2/kg. Indeed,for a single fin with the surface Sf that is covered from both sides with an adsorbentlayer of the thickness L, the ratio S/m = 2Sf /(2Sf L q) = 1/(q L), where q is the layerdensity. As q = 500 − 800 kg/m3 for loose grains, one can expect S/m � 5 m2/kgat L = 0.3 mm and S/m � 1 m2/kg at L = 1 mm for loose grains. For compactlayer, q = 1000 − 1600 kg/m3; hence, this ratio properly decreases.

This comparison of various Ad-HExs was performed at similar boundary con-ditions typical for AHT cycles; however, these conditions were not equal.Nevertheless, it is a useful and reasonable estimation, because the earlier datarevealed that the cycle boundary conditions do not strongly affect the wateradsorption dynamics [25].

4.1.3 The Effect of the Flow Rate of External Heat Carrier

The heat transfer on the liquid side has to be ensured fast enough in order to neglectits influence on the adsorption dynamics. It is always held in the conditions of theV-LTJ experiments. For representative pieces of real Ad-HExes, the minimal flowrate of the heat carrier fluid, which guarantees the fast transfer, was experimentallymeasured in [9]. It was made for Ad-HEx2 with AQSOA Z02 grains of 0.30–0.35 mm size. Table 4.2 shows the main hydrodynamic parameters at the HEx

Table 4.2 Flow rate effect on the desorption dynamics

Flow rate, dm3 min−1 <0.1 1.0 1.4 2.4 2.8

Manifold inlet velocity, m/s 0.02 0.21 0.3 0.50 0.59

Reynolds tubes inlet 10 103 145 250 290

sdes 80%, s 142 105 87 80 82


manifold inlet and at each its single-finned tube inlet having assumed uniforminternal distribution of the heat carrier fluid.

No effect of the flow rate is found at V � 2.4 dm3 min−1. At lower rates, thedesorption time gradually increases that is probably due to insufficient heat transferfrom the heat carrier to the adsorbent bed. In order to avoid this limitation, all othertests in this study have been performed at V = 2.8 dm3 min−1. It is evident that thisminimal flux characterizes the particular Ad-HEx and cycle conditions. For itscorrect upscaling to larger HExs, it is helpful to consider the heat flux J(t) betweenthe HEx fins and the adsorbent bed. For desorption run, it can be written as

JðtÞ ¼ U � S � ½Tfin � TadsðtÞ� ¼ U � ðS=mÞ � m � ½Tfin � TadsðtÞ� ð4:1Þ

Here U is the heat transfer coefficient, Tfin is the fin temperature and Tads is thetemperature of adsorbent layer adjacent to the fin. Each multiplier in Eq. (4.1)affects the minimal sufficient flow rate. For instance, for Ad-HExs that have thesame (S/m) ratio, but larger than Ad-HEx2 by a factor of N, the flux increases by afactor of N due to larger adsorbent mass, m. Therefore, for the flow rate upscaling,the minimal sufficient rate (2.4 dm3 min−1) should be related to the adsorbent mass,thus obtaining c.a. 30 dm3 min−1 kg−1 . This flux is deemed to guarantee sufficientheat supply/release to/from any enlarged finned flat-tube Ad-HEx with the sameadsorbent (the same [Tfin − Tads(t)]) and HEx geometry (the same (S/m) ratio).

Similarly, the flux increases for HExs with larger ratio (S/m) and higher heattransfer coefficient (e.g. for adsorbent bed consolidated with fins). The effect of thetemperature difference [Tfin − Tads(t)] may depend on the shape of adsorption isobaras discussed in [7].

The flow rate estimated above can be compared with the normalized fluxescalculated from the literature data for other finned flat-tube HExs, namely 68 dm3

min−1 kg−1 [26], 71 dm3 min−1 kg−1 [11] and 54 dm3 min−1 kg−1 [27]. In all thosetests, the flow rate was c.a. 2 times larger than the minimal flux estimated in thispaper. This may be partly due to larger (S/m)-value for those HExs or to thenon-optimal operating conditions management.

Two HExs filled with AQSOA™-FAM-Z02 loose grains were tested foradsorptive air conditioning in [28]. They corresponded to (S/m) ratios of 1.15 and2.7 m2/kg; therefore, tentative cycle SPs of 0.7 and 1.8 kW/kg may be expected asestimated in [29]. The experimental values were much lower, probably because thenormalized fluxes of heat carrier (2.7 and 6.6 dm3/(min kg)) were non-sufficient forefficient cooling/heating of these HExs.

Working with the specific optimal flux previously identified allows gettingdiverse benefits in accordance with [30]. Firstly a reduced flux produces an NTUincrease (as NTU * 1/V), which means higher HEx effectiveness. In addition,considering a real adsorption cycle operation mode, one can expect larger COPvalues, thanks to the reduced heating power adopted. In addition, the share ofelectrical energy saved could be used in favour of the pumps supplying theevaporator/condenser. This expedient may contribute to the harmonization of allsystem components.


4.1.4 Comparison of the Model Configurationswith Full-Scale AHT Units

Numerous dynamic studies performed by the V-LTJ method for the simplest flatconfiguration of the bed of loose adsorbent grains (Fig. 4.3) unambiguouslydemonstrated that this bed geometry allows quite fast ad/desorption under typicalconditions of isobaric stages of AHT cycle. This configuration is somewhat idealwhen compared with those in real AHT units (Fig. 4.3) because there is no limi-tation of inter-grain mass transport and jump/drop of the metal plate temperature isvery fast [3, 7]. Because of this, the specific cooling power is rather high; forexample, for loose grains of AQSOA™-FAM-Z02, the maximal (initial) specificpower Wmax can reach 10–12 kW/kg and the average cycle power W0:8 corre-sponding to 80% conversion—3 kW/kg (Fig. 4.4).

These encouraging values imply that the adsorbent grain itself is “fast” enoughand capable of generating high SP, if heat and mass transfer to/inside the bed issufficient to reach this SP. The SP-values for the flat FAM-Z02 bed can be com-pared with those obtained for the same working pair and boundary conditions butfor more complex Ad-HEx configuration, namely small fragments of the com-mercial finned flat-tube HEx (Fig. 4.3c, d) [9]. Both uptake and release curvesrecorded for those Ad-HExs were found to be exponential; however, even for thefastest runs the exponential times were larger by a factor of 1.4–1.7 as comparedwith the appropriate flat configuration with the same (S/m) ratio equal to 2.8 m2/kg.The maximal cooling power is lower accordingly (Fig. 4.4a) that can be becausesecondary fins of the Ad-HEx fragment transfer heat worse than its primary fins.

S/m, m2/kgS/m, m2/kg S/m, m2/kgS/m, m2/kg

(a) (b)

Fig. 4.4 Maximal specific power Wmax (a) and average cycle power W0:8 (b) against the (S/m)ratio [15]. Grains of 0.2–0.25 mm (○), 0.30–0.35 mm (□), 0.4–0.5 mm (D), and 0.8–0.9 mm (∇).Data for the fragment of commercial Ad-HEx (*) [9] and the full-size laboratory-scale Ad-HEx(◊) [8] are presented for comparison [29]


Further comparison can be made with the data reported for the full-size AHTprototype used loose AQSOA™-FAM-Z02 grains as reported in [8]. The prototypewas based on a commercial finned flat-tube HEx (Valeo Thermiquem) withS/m = 3.6 m2/kg. Although precise comparison is hardly possible because severalparameters were different or not controlled, the general tendency is quite clear: thecycle specific power (0.35–0.50 kW/kg) reached in the prototype is significantlylower than measured for the flatbed configuration (2.9 kW/kg) and the HEx frag-ments (1.4 kW/kg). Similar reduction of SP for large-scale AHT prototypes wasrevealed in [28].

This further SP-reduction can be attributed to several imperfections and pitfallsof either AHT apparatuses or process organization rather than to poor adsorbentproperties. At least, the following factors can lead to lower process power [7, 14]:

• insufficient power of evaporator or/and condenser that does not fit the power ofadsorption/desorption process;

• insufficient flow rate or/and wrong distribution of cooling/heating liquid (see4.1.3);

• not optimal duration of AC cycle and its ad/desorption phases (see 4.4);• the presence of residual air (see 4.3).

Only the first issue is briefly discussed right here; the other factors are com-prehensively analysed elsewhere in this chapter. Since a “true” temporal evolutionof the sorption uptake/release should be nearly exponential [3, 7], the powerconsumed/released in the evaporator/condenser significantly changes over the AHTcycle: for example, the initial specific power is much higher than the average cyclepower (Fig. 4.4). Therefore, both evaporator and condenser have to be properlydesigned to support these wide variations.

Thus, despite significant progress achieved in adsorptive chillers for the lastdecades [24, 32], still there is big room for their further dynamical improvement, sothat much more efficient and compact AHT units can be designed on the base ofloose adsorbent grains.

4.2 Compact Layer Versus Loose Grains

Two basic configurations of the Ad-HEx are considered in the literature and testedin various AHT prototypes [4–6], namely the granulated and consolidated adsor-bent beds. In this chapter, we consider the first configuration, and this choice ismainly based on the results of the direct comparison of the two configurations madein [8]. Below we give more details of this important comparison.

In that work, the adsorbent coatings on aluminium surfaces were prepared by adip-coating method starting from a water suspension of silico-alumino-phosphate,SAPO-34 and a silane-based binder. Silane-zeolite coatings demonstrated goodinteraction between the metal support, binder and zeolite. The equilibrium of water


vapour adsorption on the coating is found to be the same as for the originalSAPO-34 material. Subsequently, the SAPO coating was applied on a finnedflat-tubes aluminium heat exchanger realizing a full-scale Ad-HEx with a uniformadsorbent coating of 0.1 mm thick and a metal/adsorbent mass ratio equal to 6(Fig. 4.5). The cooling capacity of the realized coated Ad-HEx was measured by alaboratory-scale adsorption chiller under realistic operating conditions for air con-ditioning applications (Tev/Tcon/Treg = 15/28/90 °C).

The coated adsorber delivered the high Mass Specific Cooling Power (675 W/kgads) related to the adsorbent mass, however, much lesser value VCP = 93 W/dm3

related to the HEx total volume. On the other hand, the granulated Ad-HEx, testedfor comparison, exhibited just a bit lower SCP (498 W/kgads), but a much higherVCP of 212 W/dm3. The larger mass of water exchanged for the granulatedAd-HEx permits to achieve also a much higher COP = 0.40 versus 0.24 for thecoated HEx. This difference is related with a bigger influence of metal mass for thecoated one as discussed in Chap. 1.

Fig. 4.5 Detailed view and main features of the blank, coated and granular HExes [8]


Results of testing demonstrated that the HEx filled with loose grains of SAPO-34allowed much larger volumetric SP and COP than the coated HEx. The coatedadsorber shows better Mass Specific Cooling Power that can be important if theadsorbent material is expensive as in the SAPO-34 case. An interesting approach isto combine a coated HEx with filling the residual space between the fins with loosegrains of the same or another (more cheap) adsorbent as reported in [33].

4.3 The Effect of Residual Gases

Only a few mentions can be found in the literature on the effect of non-adsorbablegases on the heat and mass transfer process in real adsorptive chillers. The firstexperimental study of the effect of non-adsorbables on dynamics of the watervapour adsorption on representative fragments of real adsorbers was reported in[10]. The tests are performed on two small, but representative, pieces of realadsorbers with similar heat transfer surface area and different mass transfer areasdue to different thicknesses. The adsorbers are filled with loose grains of a com-mercial adsorbent AQSOA-Z02 that is considered to be promising for adsorptionchillers. More experimental details can be found in [10] and Chap. 3.

Some important findings are:

(1) at any gas pressure Pgas, experimental uptake curves are exponential;(2) the adsorption rate is extremely sensitive to traces of residual air: even at Pgas

� 0.03 − 0.06 mbar the rate reduces by a factor of 1.5–2;(3) at Pgas � (0.06 − 0.2) mbar, the characteristic time increases as s = s0 + BPgas,

where s0 and B depend on the HEx geometry and the nature of residual gas(air or H2);

(4) the effect of hydrogen is less dramatic as compared with air; the ratio B(air)/B(H2) = 3.77 is close to the ratio of effective diffusivities in the binary mixture“gas–vapour”.

The slowing down of the adsorption process is caused by the effective gassweeping to the adsorber mass transfer surface where it accumulates as a gas-richlayer. The minimal amount Nmin of residual air necessary to form the blockingair-rich layer is evaluated by developing a one-dimensional stationary model of thevapour adsorption in the presence of gas. The adsorber can be considered as a flatsurface with the external area Smt through which the adsorbent exchanges vapourwith the gas phase. The latter contains water vapour with the molar density Cv0

[mol/m3] as a main component and residual air with the molar density Ca0, whilethe total molar density C0 = Cv0 + Ca0 is constant. As the adsorption results in thereduction of the number of moles of water vapour in the gas phase, it causes the gasflux perpendicular to the adsorbent bed surface. This flux J [moles m−2 s−1] hasdiffusional and convective constituents and can be written as

4.2 Compact Layer Versus Loose Grains 81

JP ¼ Jdif þ Jconv ¼ � Dv dCv=dzð ÞþDa dCa=dzð Þ½ � þ v Cv þCað Þ; ð4:2Þ

where Dv and Da [m2 s−1] are the diffusivities of vapour and air, v [m s−1] is the

velocity of convective flux, and z [m] is the coordinate in the direction perpen-dicular to the flat adsorbent bed. For ideal gases, C = P/(RT) (R is the universal gasconstant and T is the absolute gas temperature), and Eq. (4.2) can be rewritten as

JP ¼ � Dv=RTð Þ dPv=dzð Þ � Da=RTð Þ dPa=dzð Þþ v=RTð Þ Pv þPað Þ; ð4:3Þ

or singly for the water vapour flux

Jv ¼ � Dv=RTð Þ dPv=dzð Þþ v=RTð ÞPv: ð4:4Þ

At steady-state conditions, the latter flux is equal to the adsorption rate W perunit mass transfer surface; hence,

�Dv dPv=dzð Þ ¼ W RT � v Pv: ð4:5Þ

The velocity of convective flux can be obtained from Eq. (4.4) by taking intoconsideration that Jv = W and the following relations are valid for binary gasmixture (dPv/dz) = − (dPa/dz) and Dv = Da [34]:

v ¼ W RTð Þ= Pv0 þPa0ð Þ ¼ W RTð Þ=P0: ð4:6Þ

Substituting the v-value in Eq. (4.5), one can obtain

� dPv=dzð Þ ¼ W RTð Þ= Dv P0ð Þ P0 � Pvð Þ ¼ P0 � Pvð Þ=L0: ð4:7Þ

The combination L0 = (Dv P0)/(W RT) has the dimension of length [m] andrepresents a typical size of space near the external mass transfer surface where thevapour (air) pressure changes. We have estimated this length for the conditions ofour experiments in the presence of air. We have estimated the water vapour dif-fusivity Dv as 2.2�10−3 m2/s according to Eq. (2) of Ref. [10]. The initial adsorptionrate per a unit mass transfer surface for HEx1, W = W0/Smt, can be obtained fromthe experimental adsorption rate W0 = 0.18 (g H2O)/s measured at Pa = 0 and T �320 K: W = 9 g/(m2 s) = 0.5 mol/(m2 s). As a result, we have obtainedL0 = 2�10−3 m = 2 mm. When the adsorption flux W reduces, the characteristiclength increases and approaches to infinity at W ! 0 that corresponds to a uniformair distribution and a zero gradient of the vapour pressure.

The amount Nmin of air molecules (in moles) that are contained inside thistransient layer of thickness L0 can be briefly estimated from the ideal gas lawPavV = NminRT, where Pav is the average air pressure in the layer (Pav � P0/2) andV is the air volume (V � Smt L0):


Nmin � ðPavVÞ=ðRTÞ ¼ ðP0SmtL0Þ=ð2RTÞ ¼ P20S

2mtDv

� �= W0 R

2T2� �

: ð4:8Þ

This value can be considered as a minimal amount of air that is necessary toform the air-rich layer (at a fixed adsorption flux W). If the total amount Ntotal of airinside the HEx unit is much lower than the minimal one (Ntotal << Nmin), no air-richlayer can be developed and no slowing down of the adsorption process takes place.

Therefore, recommendation 1 is to maintain the total amount of air inside anAC unit lower than the minimal value defined by Eq. (4.8). This allows an esti-mation of the maximal rate A of air leakage/desorption (in mol/year) that isacceptable in order to guarantee efficient dynamic operation of an AC unit for thecertain time t [year]: A = Nmin/t or in terms of the maximal pressure incrementAp = A(RT)/Vunit [Pa/year], where Vunit is the volume of gas phase inside the ACunit. The latter volume includes the volumes of HEx, evaporator, connecting pipesand valves, and can be considered as a “dead” volume of the AC unit. This volumeis often considered as unwanted because it can limit the performance of adsorptionchillers due to reducing the amount of adsorbate exchanged [35].

Probably, the formation of the air-rich layer with the characteristic length L0corresponds to the sharp increase of the adsorption time at very low air pressure(see Chap. 3). For particular conditions of our experiments (Pav � 500 Pa, V � Smt

L0 = 4�10−5 m3, T � 320 K), the blocking amount of air is Nmin � 7�10−6 mol (or c.a. 4�1018 air molecules) for HEx1. The total volume of our experimental unit is c.a.15 dm3, and this amount of air corresponds to an air partial pressure of (1–2)Pa = (0.01 − 0.02) mbar. This correlates well with our observation that the increaseof the adsorption time becomes essential already at Pair as low as (0.03–0.06) mbar:in this pressure range, the s-value abruptly rises by a factor of 2 for HEx1.

As seen from Eq. (4.8), the blocking amount of air Nmin * P02 Smt

2 significantlyincreases at larger total pressure P0 and mass transfer surface Smt. The latter con-firms our above-mentioned conclusion that the smaller the surface area of masstransfer, the easier to block it. The revealed quadratic dependence on the totalpressure shows that residual gas makes significantly less effect in the case ofmethanol and ammonia as working fluids. Indeed, for a typical chilling cycle, apressure at the adsorption stage is 50–100 mbar for methanol and 500–700 mbarfor ammonia that is, respectively, one and two orders of magnitude larger than forwater. Hence, the blocking amount of air increases approximately by a factor of 102

for methanol CH3OH and 104 for ammonia.Hence, air is concentrated near the external (or the mass transfer) surface of the

HEx and blocks a direct access of water vapour to the adsorber so that the vapourmolecules have to diffuse through an air layer to reach the adsorbent grains. In fact,the smaller the surface area of mass transfer, the easier to block it. Thereby, rec-ommendation 2 concerns the HEx design: it is profitable to maximize the area ofmass transfer surface, thus minimizing the possibility of its blocking by residualgas.

Thus, extra-careful degassing of both adsorbent and evaporator/condenser isstrictly necessary before starting AC operation to reach a low level of residual air.

4.3 The Effect of Residual Gases 83

Moreover, due to possible minor leaks and very slow desorption of air from theadsorbent, periodical degassing of AC unit may be necessary during its long-termexploitation. In the latter case, a getter can be also used to remove traces of air fromthe evacuated space as it takes place in various high vacuum electronic devices. Thegetter helps to maintain the vacuum by a strong chemical bonding of air (N2 andO2) molecules.

4.4 Reallocation of Adsorption and Desorption Timesin the AHT Cycle

Numerous results obtained by the LTJ method have prompted that the duration ofdesorption phase of AHT cycle is commonly shorter than that of adsorption one [7,11, 12]. Therefore, the equal duration of adsorption and desorption phases is hardlyan optimal case, and proper reallocation is necessary to grant more time foradsorption at the expense of desorption shortening [11, 27, 36–38]. This reallo-cation mode was first experimentally realized in a single-bed adsorption chiller in[11]. These tests confirmed that the optimal desorption duration should indeed be1.5–2.5 times shorter than the adsorption one, and for the optimal ratio R = tdes/tads,both the COP and the cooling power may increase by 1.5–2 times as compared withthe common case tdes = tads.

The proposed reallocation of ad/desorption durations causes a subsequentchange in cooling cycle organization, because each adsorber now is connected withan evaporator longer than the half-cycle time. Let, for instance, the time tdes betwice as short than the time tads. In this case, one of the following cycle rear-rangements can be done:

For a two-bed configuration, the two modes are possible (Fig. 4.6a):

• one bed is connected with the evaporator where cold is produced. At the sametime, another bed is under regeneration and is connected with the condenserwhere heat is rejected;

ADSORPTION ADSORPTION DESORPTION

ADSORPTION DESORPTION ADSORPTION

1/3 tCYCLE 1/3 tCYCLE 1/3 tCYCLE

Ad-HEx 1

Ad-HEx 2

Ad-HEx 1

Ad-HEx 2

Ad-HEx 3

ADSORPTION ADSORPTION DESORPTION

ADSORPTION DESORPTION ADSORPTION

DESORPTION ADSORPTION ADSORPTION

1/3 tCYCLE 1/3 tCYCLE 1/3 tCYCLE(a) (b)

Fig. 4.6 Management of two-bed (a) and three-bed (b) adsorption cooling system withreallocated duration of adsorption/desorption steps


• both the beds are linked with the evaporator and generate a double chillingeffect.

Thus, cold is continuously generated so that each bed is linked with the evap-orator two thirds of the cycle time tcycle and with the condenser only one third. Inthis case, to smooth the cooling effect produced, the chiller could be equipped withan intermediate cold storage unit. To allow the use of a continuous driving heatinput, an intermediate heat store or a buffer may also be needed.

For a three adsorbers configuration, at any time, two beds are connected with theevaporator and generate a nearly constant cooling power while the third bed isreleasing heat to the condenser (Fig. 4.6b). No intermediate cold storage is nec-essary in this case.

On the basis of the above-mentioned results, a three-bed adsorptive chiller wasdeveloped at ITAE-CNR and comprehensively tested [33].

The cooling machine was designed to operate with a ratio between theadsorption and desorption phases’ duration equal to 2. The three adsorbers areconnected to single evaporator and condenser layout. Each adsorber was realizedemploying two different sorbent materials in two different configurations: (i) acoating of Mitsubishi AQSOA™-FAM-Z02 and (ii) grains of a commercialmicroporous Silica Gel. Water was selected as refrigerant while up to now themachine operates without any mass/heat recovery.

A first testing campaign was carried out at ITAE laboratories by a test benchspecifically developed for thermally driven chillers. At nominal boundary condi-tions (i.e. TH * 90 °C, TL * 18 °C and TM * 25 °C), the cooling machine wasable to deliver an Average Cooling Power of 4.4 kW, an overall VCP of 9.4 kW/m3, with a COP of 0.35 while the VCP referred to the volume of the adsorbers(VCPAd-HEx) was *275 kW/m3.

The achieved VCPAd-HEx for the full-scale three-bed chiller is in good agreementwith previous results obtained for a small-scale Ad-HEx with similar design asreported in [27] where the idea to reallocate the time management strategy wasverified at laboratory-scale level. In [27], a small-scale Ad-HEx, using FAM Z02 assorbent, showed an optimal adsorption-to-desorption time ratio of 2.5. Under thisoperation mode, it was able to deliver about 223 kW/m3 of cooling power atTL = 15 °C, TM = 35 °C, TH = 90 °C that is quite close to the results achieved forthe three-bed full-scale adsorption chiller and even higher than results achievedemploying a ratio R equal to 1 [27].

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