Performances and modelling of a circular moving bed thermochemical reactor for seasonal storage

Applied Energy 230 (2018) 803–815

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Applied Energy journal homepage: www.elsevier.com/locate/apenergy

Performances and modelling of a circular moving bed thermochemical reactor for seasonal storage

T

⁎

Joël Wyttenbacha, , Jacques Bougardb,c, Gilbert Descyc, Oleksandr Skrylnykb, Emilie Courbonb, Marc Frèreb, Fabien Bruyata a

Univ. Grenoble Alpes, CEA, LITEN, INES, F-38000 Grenoble, France Université de Mons, Service de Thermodynamique et de Physique Mathématique, 31 Boulevard Dolez, B-7000 Mons, Belgium c BESOL, rue de la Griotte, 2a, 5580 Rochefort, Belgium b

H I GH L IG H T S

novel solid/gas thermochemical reactor with a 0.35 m circular vibrating sieve is designed, manufactured and tested. • AAverage power is 356 W with a +6.0 K temperature rise, energy density is 200.4 W h/kg of 9% hydrated composite. • A reactorheating model is developed and compared to experimental results with a deviation below 0.73 K. • Kinetic equation accuracy is refined with a new term involving derived air flow humidity gradient through the reactor. • 2

A R T I C LE I N FO

A B S T R A C T

Keywords: Thermochemical reactor Circular vibrating bed Performance test Thermodynamic model Seasonal storage Space heating

A novel thermochemical reactor was designed, built, and tested at Besol’s and CEA-INES’ labs. Its circular shape and its vibrating bed allow to move the solid hydrate constantly, therefore increasing turbulence in the moist air heat and mass transfer region. A reactor model was developed and identified in order to calculate its performances over a wide range of operating conditions and to understand what are the key factors leading to increased performances, especially regarding the specific behavior of the composite material made of calcium chloride incorporated in a silica gel matrix. New kinetic equations were developed while combining sorption and porous medium physical phenomena. The model was further refined with a 10 layers solid bed spatial discretization. However vibrations actually mix those layers, which would require a more detailed approach. Nevertheless, outlet parameters were predicted in both modes with a deviation lower than 0.72 K equivalent. Test results in realistic conditions showed an average 356 W heating power with an air temperature elevation of +6.0 K, while desorption cooling power was 278 W with an average 4.5 K temperature decrease. The usable energy density with this 0.163 m3 uninsulated reactor was 200.4 W h per kg of 9% hydrated solid composite, which is adapted to seasonal storage since it is close to the 207.8 W h per kg theoretical target. Electrical consumption for air circulation is only about 10 W, but vibration accounts for almost 70 W, which still needs to be reduced. Detailed results showed that a continuous solid flow and a counter current configuration would lead to further increase average outlet temperature.

1. Introduction Seasonal storage is a technology that aims to heat buildings with the largest possible solar energy fraction [1], in order to reduce the use of fossil fuels, nuclear power and other non-renewable energy sources. For example, buildings’ share accounted for 20% of EU28 greenhouse gases emissions in 2015 [2], especially because they used only 18.7% of renewable energy for heating and cooling purpose [3].

⁎

As current major energy resources show quantitative and ecological limitations, it was shown in several countries (China [4], Denmark [5], world [6]) that renewable energy sources do have the potential to offset the energy footprint growth due to an increasing world population with an increasing affluence [7]. Since a significant part of world population lives in cold winter climatic regions, building space heating represents a large part of global energy consumption, which is why its primary energy footprint reduction is a major issue in order to decrease our

Corresponding author at: Univ. Grenoble Alpes, CEA, LITEN, INES, F-38000 Grenoble, France E-mail address: [email protected] (J. Wyttenbach).

https://doi.org/10.1016/j.apenergy.2018.09.008 Received 15 June 2018; Received in revised form 13 August 2018; Accepted 2 September 2018 0306-2619/ © 2018 Elsevier Ltd. All rights reserved.

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Nomenclature Ti To Ta Ts Ts,0 wi wo

ws∗ ps∗ ṁ da ṁ w

ṁ w,0 Xs Xs,0 Kloss k ki kj η cr cps cpw cpda cpwg Δhr Ms,0

inlet air temperature, °C outlet air temperature, °C ambient temperature, °C composite temperature, °C initial composite temperature, °C inlet air specific humidity (relative to a mass unit of dry air), kg/kgda outlet air specific humidity (relative to a mass unit of dry air), kg/kgda equilibrium air specific humidity around composite (relative to a mass unit of dry air), kg/kgda equilibrium water vapor partial pressure around composite, Pa dry air mass flow rate, kg/s water vapor flow rate, kg/s

Q̇ a

initial water vapor flow rate, kg/s composite hydration level, kg/kg initial composite hydration level, kg/kg reactor thermal losses coefficient, W/K kinetic proportional coefficient, s−1 kinetic integral coefficient, – porous solid permeability, s−1 reactor heat exchange efficiency, – specific heat times mass of reactor unit, J/K solid composite specific heat, J·(kg·K) water specific heat, J·(kg·K) dry air specific heat, J·(kg·K) water vapour specific heat, J·(kg·K) reaction enthalpy, J/kg solid composite mass, dehydrated (relative to a mass unit of dry air), kg/kgda reactor heat power measured on the air flow, W

reactor circuits that are currently investigated to ensure water vapor transport from or to the solid material [24]. In closed reactor layout, pure water vapor reacts with the solid material. Water vapor transport is performed through an evaporation/condensation process just below available heat source’s temperature; the reactor usually works at low pressure [25]. Heat is transferred to or from the solid material thanks to an internal heat exchanger, which may be connected to the solar collectors or to the building heat distribution system. Closed reactor configurations are likely to result in technical difficulties such as the development of a large vessel able to maintain sub-atmospheric pressure over a long period of time [26,27]. Besides, they often exhibit significant drop in energy density at the reactor level because the low heat transfer coefficient between solid reactant and heat exchanger body requires to increase contact area, leading to a larger non-reactive volume portion [28]. In addition, the need of water vapor transport channels presents similar consequences. In open reactor configuration, moist air at atmospheric pressure acts as a mass and heat carrier fluid. It thus performs two tasks: the first one is to bring/extract the gaseous reactant to/from the solid material, and the second one is to carry heat between the reacting solid and the heat source/load [11]. As a result, current reactor designs usually present a porous solid hydrate bed through which the moist air flows [29]. An external heat exchanger allows to transfer heat from the solar collectors or to the building heat distribution system [30]. By considering that a volume of solid hydrate reacts with a much larger volume of moist air for a given reaction (this volume ratio may reach 40,000), one major issue resulting from such volume disparity is the pressure drop across the solid bed and the solid permeability [31]. This requires a careful design with a relatively high cross section and a small bed thickness. Reactor and storage can be either integrated or separated. With the integrated reactor, a parallel distribution brings moist air flow to the storage tank where the reaction takes place, while in a separated (also called external) reactor solid hydrate is circulated from its storage tank to a distinct vessel where it reacts with moist air [32]. In this paper, a composite material (CaCl2 trapped in the pores of a Silica Gel), which was deeply investigated and identified to have successfully passed all the necessary steps of characterization at the lab scale to be considered as a good storage medium, was used for testing a new technology of reactor separated from storage vessels and working in an open loop configuration. A solid transport system allows the reactor to be fed by the solid material prior to reaction. During reaction, the reactor works in a batch mode while the solid is kept in internal movement using a vibrating sieve. The reactor size is in between lab scale and real scale (considering application in a low energy dwelling). It was tested using a range of boundary conditions that are close to

reliance to greenhouse fossil fuels. Solar thermal technology allows to heat buildings efficiently, but an important limitation is the seasonal mismatch between solar resource availability and heating needs [8]. However, connecting solar to a seasonal storage improves significantly its usable fraction, thus reducing energy consumption and greenhouse gases emissions [9]. Thermochemical storage presents the highest theoretical energy density compared to sensible and latent technologies [10], and is nearly lossless over a long period of time [11]. This process takes advantage of reaction heat to store energy in chemical [12,13] bonds. Indeed, solid reactant hydration and dehydration are respectively exo- and endothermic [11]. While being promising, further multi-level R&D actions are needed for bringing seasonal thermochemical storage technology to the market [14]. These actions should address in an integrated way the questions of the solid material to be used as a storage medium, the design and sizing of the reactor and its integration in the whole energy system [15]. Several authors have presented material screenings to identify the best suited solid candidates in the frame of building space heating with solar summer desorption, using either purely chemical [16] or physical [17] reactions. On one hand, chemical candidates generate mono-variant reactions, where the heat of sorption is either entirely released or absorbed depending on equilibrium position, temperature and water vapor pressure. On the other hand, physical sorption candidates show a progressive behavior, where total reaction heat depends on the range of environmental conditions. The chemical sorbents have higher energy storage densities than physical ones, but their instability issues (deliquescence, agglomeration, crust formation, etc.) make difficult their use in a storage reactor. That is why several authors have been trying to develop composite materials based on a chemical candidate microencapsulated or impregnated in a porous matrix [18] to stabilize the salt while keeping high energy storage density [19,20]. Although composites for heat storage applications have been widely studied in terms of synthesis methods [21], macroscopic properties and structural characteristics, few of such materials were tested in near-to-real-size heat storage prototypes [22,23]. In Scapino et al. review [15], most of the large scale prototypes tests described were run with zeolites or silica gel, the composites materials were only tested in lab-scale prototypes. Thermochemical reactors are devices that allow solid material reactions to take place under favorable conditions that maximize the energy density while producing a given and stable thermal power. Water is one of the common gaseous reactant used with a solid hydrate in thermochemical energy storage applications; reactions are hydration and dehydration processes. Due to its thermodynamic properties, water evaporates below atmospheric pressure at typical outdoor temperature, for example 1228 Pa at 10 °C. There are two main types of 804

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reality in terms of air flowrate, inlet air temperature and water content. The paper aims at providing first performance data related to the proposed solid material reactor system. A second important feature is to propose a simple but reliable kinetics model for simulating the sorption process. The proposed model is described and used for representing the experimental data. In future works, the results will be used for simulating a whole system (solar collectors, reactor, heat distribution, and building) in different climate conditions in order to evaluate the energy and comfort performances of the related technologies (solid material and reactors). Such a circular vibrating bed reactor is a novel design in the context of thermochemical heat storage. It is expected to increase reaction kinetics especially because of its very specific solid particles movement. To assess its performance, this paper presents a first experimental and modelling approach.

through with a minimal pressure drop. A special attention was paid to select the right material regarding corrosion aspects [35]. Since the vibration tends to empty the central area and to overfill the outer circle, a recirculation ramp is set up in order to tackle this unwanted effect by constantly feeding the central area with solid particles taken from the outer circle. The vibration motors are assembled to the reactor at a specific angle, so that reactor vibrations are asymmetric and allow moving solid hydrate even against gravity as it is the case in the recirculation ramp. A controller driven loading and unloading mechanism allows performing fully automated batch tests. The air velocity is adjusted so that no fluidization occurs in the reactor. Indeed, a separation unit is required when the bed gets fluidized [36], which increases the size and the pressure drop of the reactor.

2. Experimental section: materials and methods

2.2. Material selection

2.1. Prototype presentation

The material selection is highly linked to the foreseen thermal application of the sorption reaction. The circular moving bed reactor presented in this study was developed to be the core of a seasonal solar heat storage for residential buildings. Consequently, the material was selected for its following properties:

A semi-continuous separate reactor with a vibrating sieve (Figs. 1 and 2) was developed and tested during this study, in the context of EUfunded SoTherCo project (www.sotherco.eu) (see Tables 1 and 2). The vibration is used to even the thickness of the solid hydrate bed and to increase the reaction kinetics [33,34] by moving and mixing the solid particles. Besides, vibrations ensure that a maximum amount of particles actually react with moist air. An even thickness leads to an even air flow distribution, which is of a major importance for reaction power and energy density. Although particles seem to describe circles in the reactor, it is not yet possible to ensure that each particle follow a single and predefined path in the reactor. Layers of particles get actually mixed together and may turn around more than once during their reaction time. For these reasons, the reactor is not fed continuously but works with batches of solid hydrate. The vibration bed is rather slightly conical than perfectly flat, its center being slightly higher than the rim. The sieve is made of metallic fabric and supported by 8 radial beams. Its opening size is selected to keep the solid hydrate on the upper side while letting the air flow

– – – –

Dehydration possible under 90 °C Hydration possible with absolute humidity above 4 g/kgda Hydration temperature compatible with space heating systems A maximal water exchange rate per mass of anhydrous material

Several thermochemical and composite systems were studied in the frame of the SoTherCo project. As a result, a specific composite was developed from a silica gel matrix impregnated with around 43 wt% of Calcium Chloride (CaCl2). The average grain size is 239 μm and the external porosity (between individual grains) is 40%. The synthesis method and the characterization tests were described by Courbon et al. [37,38] for different patented composites [39]. The water vapor sorption isotherms of the silica gel/CaCl2 43 wt% composite are presented in Fig. 3. The mechanism of water sorption was described in [37] and includes first the formation of the dihydrate CaCl2 from the anhydrous

MATher Air supply test chamber Air return Upper hopper Solid vacuum transport system

Air/water heat exchanger Water inlet Water outlet

Hydronic module

Vibrating reactor Vibration motor

Air inlet

Fig. 1. Circular vibrating thermochemical reactor assembled with an air/water heat exchanger. 805

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Solid hydrate inlet Homogenization ramp

Solid hydrate outlet Vibrating sieve Actuated brush

Fig. 2. Inside the vibrating reactor, without solid hydrate.

humidification cooling effect with a renewable low temperature heat source, while maintaining a higher temperature at the reactor inlet and a humidity rate adapted to the sorption reaction. System simulations were run under four European climates (Vienna, Stockholm Barcelona and Brussels) in order to define test operating conditions in adsorption phase from most frequent winter cases, while desorption conditions were computed from climatic conditions only. Solid composite material was prepared before performance tests so that the initial hydration level can be reached at the end of a realistic desorption reaction and conversely. The initial mass of each batch test was set so that the dehydrated portion of solid composite load remains 0.03 kg . constant at 2+ −0

Table 1 Reactor features. Reactor type Bed type Reactor inner diameter Reactor volume (vibrating vessel only) Sieve opening Sieve wire diameter Sieve material Batch load mass, 10% hydrated Vibration motor angle (reference horizontal plane) Vibration frequency Air velocity

m m3 μm μm

Moist air reactor, separated, working with solid batches Vibrating bed, not fluidized 0.669 0.163

kg °

53 35 Nickel 2.2 60°

Hz m·s−1

42 ≈0.15

2.4. Test setup and instrumentation The circular moving bed reactor was measured using the MATher test equipment located at CEA-INES facility. Test setup is described in Fig. 4. Air flow rate and humidity were measured at both inlet and outlet of the reactor, temperatures were measured by 15 calibrated thermocouples located on 5 different planes perpendicular to the air flow direction. Sensor types and measurement devices are described in Table 3. The thermochemical reactor was tested according to the process described in Fig. 5. Specific humidity was calculated from two measurements: relative humidity (capacitive sensors) and temperature (calibrated thermocouples or PT100). This technique implies higher specific humidity uncertainty for higher temperature, which is a problem for desorption tests. Thanks to a specific test equipment capability, it was possible to measure air inlet specific humidity correctly, but outlet humidity uncertainty was not guaranteed when air temperature exceeded 40 °C. To solve this metrological issue, we corrected this value on the basis of the

salt, followed by the formation of the tetrahydrate CaCl2, this tetrahydrate dissolves in the adsorbed water to form a salt solution in the pores of the silica gel. At higher humidities, the water sorption is due to absorption in the CaCl2 solution trapped in the silica gel pores.

2.3. Test operating conditions The thermochemical reactor described in this paper was designed to store solar heat and to restitute it for building space heating on a seasonal timeframe. For this reason, tests were conducted under realistic conditions that match real life application cases regarding climate, building type and system architecture. Since the reactor requires a humidity rate that is not always available in the winter atmosphere, a specific closed loop system architecture was developed during the SoTherCo project, with four major components: the reactor, a space heating exchanger, a recovery heat exchanger and a humidifier with built-in heat exchanger [40]. This allowed to compensate the Table 2 Reactor test operating conditions. Case Adsorption Adsorption Adsorption Adsorption

1 2 3 4

Desorption 1 Desorption 2

Climate

Ti [°C]

wi [kg/kgda]

ṁ da [kg/h]

Xs,0 [–]

Minit [kg]

Vienna Stockholm Barcelona Brussels

23.9 23.8 22.5 23.8

0.0069

220 200.4 210.9 218.4

9.0% ± 0.75

2.2

Combination of 4 climates

49.9 59.2

0.004 0.007

221.8 220.1

40.2% ± 0.13

2.8

806

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Fig. 3. Water vapor sorption isotherms of composite Silica gel/CaCl2 43 wt%. Adsorption isotherms are represented by continuous lines whereas desorption isotherms are represented by discontinuous lines.

total water mass transferred during a batch test. Indeed, this mass transfer was measured by two methods using either specific humidity gradient integration or differential solid composite weighing, the second one being the reference. As a result, outlet humidity was corrected to even the mass differences for each desorption test presented in this document. Hydration levels were measured with a moisture analyzer set at 150 °C, using samples of initial and final solid composite batch load.

Table 3 Sensor types and measurement devices. Measurand

Sensor type/measurement device

Air flow rate

Höntzsch VA Vortex air speed measurement, corrected with duct air speed profile measured onsite Thermocouples type T calibrated with their measurement line Rotronic HC2 relative humidity capacitive sensors Mettler Toledo HX204 moisture analyzer set at 150 °C until mass variation falls below 1 mg/300 s Ohaus Defender weighing scale, accuracy 20 g

Temperature Humidity Solid composite hydration level Solid composite mass

3. Thermochemical reactor model 3.1. Model presentation

can be written as:

It is well known that solid hydrates have the capability to take up water vapor and to rearrange into a more hydrated solid form while releasing heat. This describes an exothermic sorption reaction, which is reversible into an endothermic dehydration reaction. The general form

A(s) + x . H2 O(g ) ↔ (A. x . H2 O )(s) + x . Δhr

With purely chemical reactions, x is a stoichiometric reaction coefficient that is usually available in the literature and the behavior of

Air flowmeter Humidity sensor (capacitive)

Ambient air at 20°C

MATher test equipment

2 temperature sensors To = average of 5 temperature sensors 4 lateral temperature sensors

Solid hydrate vibrating bed

2 lateral temperature For desorption only, sensors Ti = average of 5 Ti = average of 3 temperature sensors temperature sensors MATher Humidity sensor (capacitive) test Air flowmeter equipment

Reactor enclosure (uninsulated)

(1)

Air flow Fig. 4. Instrumentation of the sorption reactor. 807

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Solid composite is prepared to the requested hydration level

Solid composite mass and hydration levels are measured

Air flow starts, measurements start

Reactor is filled with solid composite, vibration starts

Reaction

Reactor is emptied when hydration level counter reaches its target

Air flow stops, vibration stops, measurements stop

Solid composite mass and hydration levels are measured

Fig. 5. Reactor test process.

the system is mono-variant. However, in the present case, the selected material is a composite where a chemical hydrate (Calcium Chloride, CaCl2) is included in the pores of a matrix of silica gel. The system becomes bi-variant. For each temperature, the partial vapor pressure at equilibrium is a complex function of the solid reactant hydration level, including various sorption phenomena [26,37,41]. Therefore, it is more convenient to express the heat of reaction Δhr as a function of water mass rather than solid mass. The reaction heat power depends on water mass transfer rate from the gas phase to the solid hydrate:

ṁ w =

The water transfer from surrounding air to the solid hydrate is classically defined by a pressure gradient method. If the pressure of the water contained in the air is greater than the equilibrium water pressure of the solid at its temperature and hydration level, then the water is transferred from the air to the solid. Respectively, if the equilibrium water vapor pressure of the solid is the greatest, then the water is transferred from the solid to the air. Mass transfers and air circulation are illustrated in Fig. 7. Several authors define the kinetic coefficient with a proportional equation between pressure gradient and water flowrate [43]. Assuming that vapor partial pressure gradient is approximately proportional to absolute humidity gradient in moist air, we have:

Therefore, the solid/gas water mass transfer kinetic has to be quantified in order to calculate reaction heat power. To do this, we need first to describe the reactor model (see Fig. 6). During adsorption phase, the heat resulting from the hydration reaction of the solid is mainly transferred to the air, with some thermal losses to the ambience. Dynamically, solid hydrate and reactor are inertial masses that have to be taken into account especially because batch tests are short, making transient behaviors important. Therefore, we can write following energy conservation equation [42]:

Qth = ṁ w . Δhr = ṁ ma . cpma . (To−Ti ) + (Ms,0. (cps + Xs . cpw ) + Cr ). + Kloss . (Ts−Ta)

ṁ w = k . Ms,0. (wi−ws∗)

(To−Ti ) (Ts−Ti )

dTs dt (3)

To, wo Ambiant air Ta Reactor enclosure Cr Solid hydrate vibrating bed Ms,0, c ps, Xs, Ts,

Thermal losses Kloss

(4)

As stated by Marias et al. [11], outlet air temperature is usually very close to solid temperature, which means that the efficiency is close to 1. Water mass is transferred from the gaseous phase contained in moist air to the solid hydrate. We define therefore the solid hydration level with following equation:

Ms = Ms,0 (1 + Xs )

(7)

The various physical and chemical coupled phenomena occurring inside the pores of the composite are not precisely known. However, it may be assumed that the specific humidity, ws∗, of the gaseous layer around the grain (see Fig. 7) is well thermodynamically connected to the vapor pressure measured in equilibrium conditions (Fig. 3). The proportional kinetic equation can also be presented from the solid hydrate point of view. In this case, vapor flow rate is proportional to the difference between the actual solid hydration level and the equilibrium hydration level at surrounding pressure and temperature [27]. This proportional equation describes quite accurately the steady state reactor behavior. However, the tested reactor works with batches of solid composite, which means that filling and emptying procedures induce major disturbances. Consequently, the kinetic has to be defined with a term that delays and/or softens water vapor mass flow rate variations. Authors describing vapor diffusion in porous materials [44] usually solve Fick’s law by discretizing the volume into constant pressure steps.

The thermal losses from the reactor enclosure to ambient air, Kloss. (Ts − Ta), uses the temperature of the solid as reference. However, the temperature of the enclosure is not uniform, increasing from the bottom to the top, and moreover is time varying. The exact calculation of the global heat transfer appears then to be very complex. The global coefficient Kloss has thus to be considered as a useful average in the scope of a simplified simulation. The sensible temperature elevation should relate to moist air flow. However, inlet and outlet humidity content are different, so the minimal amount of humidity should be considered. This would link the sensible term to output conditions and would introduce a difference between desorption and adsorption reactions. Since humidity has a limited impact on global moist air specific heat, it was decided to ease calculation process by considering dry air flow only. The air is heated by the solid and we can consider that this heat transfer is characterized by an efficiency η defined in following equation:

η=

(6)

3.2. Water mass transfer kinetics

(2)

Qth = ṁ w . Δhr

dMs dX = Ms,0 s dt dt

‫כ‬

Air flow rate Ti, wi

(5)

Fig. 6. Thermochemical reactor model.

The mass transfer is therefore: 808

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Ms,0. ki Ms,0. k d (ṁ w ) . . (wi−ws∗) + (1−Ms,0. kj ). mda 1−Ms,0. kj dt

ṁ w = Incoming moist air Specific humidity

Dry air flowrate Water vapor flowrate

Specific humidity

Air at the solid composite equilibrium specific humidity Solid composite grain

3.3. Composite state equation, spatial discretization The state equation of the solid hydrate defines the link between its hydration level, temperature and equilibrium pressure. Since the material used here is a composite, its equation is specific and has to be defined through isotherm measurements, where the adsorbed water mass is measured under several water vapor pressures. The equation of state f is therefore:

‫כ‬

Hydration level

Fig. 7. Water mass transfer from moist air to solid hydrate.

Then, water vapor flux is proportional to pressure or concentration variation across two steps. Integrating those equations leads to a progressive material mass variation, meaning that vapor storage is taken into account. The solid composite bed considered in this study shows similarities with porous materials. For this reason, a non-exclusive modelling option is to combine their respective kinetic terms usually found in the literature. To do this, the composite bed is considered as a single layer of porous material, where the water pressure gradient is replaced by the almost proportional air specific humidity gradient. Sorption and diffusion kinetic equations can be combined in a single expression:

ṁ w = k .

Ms,0. (wi−ws∗)

+ kj. Ms,0. (wi−wo)

f (Ts, Xs,ws∗) = 0

d (wi−wo) ṁ w = Ms,0. ⎛k . (wi−ws∗) + ki. + kj. (wi−wo)⎞ dt ⎝ ⎠

(12)

As it was measured by Courbon et al. [37], the equation of state is not linear and different for adsorption and desorption. Therefore, each curve was modeled with differentiated mathematical expressions over 3 material hydration level ranges. These curves provide a relation between Ts , Xs , and ps∗, where water vapor partial pressure ps∗ can be easily replaced by air specific humidity ws∗ using Eq. (13).

ws∗ =

0.62198 101325 −1 ps∗

(13)

The identification process lead to define equations of state as described in Tables 4 and 5. With additional equations:

(8)

The first term k . Ms,0. (wi−ws∗) reflects Eq. (7) proportional sorption approach and the second term kj. Ms,0. (wi−wo) comes from porous material Fick’s law. This second term refines model accuracy, but cannot match the progressive start of the reaction following reactor loading. To do this, a derived term has to be added as follows:

⎛22.595 −

ps∗ = e⎝

5166.8 ⎞ ⎛1 273.15 + Ts ⎠ ∗ ⎜

⎝ 0.362

1000 1.14 ⎞⎤ −⎡−(Xs −0.14) ⎛ + 0.1878∗e−0.059 ∗ Ts ∗210 ⎠ ⎦ ⎝ 210 ⎣

⎞⎟ ⎠

(18)

(9)

ps∗ = a +

Unlike sorption vapor source or sink, water vapor diffusion kinetic depends on the specific humidity gradient through the reactor, its link to solid material hydration level is indirect. Diffusion can be seen as the ability to move water vapor through the porous medium along a decreasing water pressure gradient, either to the solid reactant, or to the surrounding air ducts. Now, the diffusion term involving the air specific humidity gradient is used a second time in a derived form. It was introduced because the shape of the modeled outlet humidity curve did not match experimental results. Adequate dynamic water transfer models were not found in the literature, which is why our approach was to analyze the measured curve in order to find the missing mathematical term in the equation, considering temperature or even electrical analogy. Although this point is not detailed here, the physical process inducing this derived behavior would have to be further investigated in a complementary article. A similar approach could be applied to the source or sink term, which depends on solid material equilibrium specific humidity. However, this equilibrium is a non-linear expression matching experimental data and its differentiation induces divergent numerical results. Again, dissociating partly the processes into physical and chemical sorption may help to minimize non-linearity problems by describing two specific kinetic behaviors. However, results show that the current model represents reactor behavior with an adequate accuracy in the context of a global approach. The moist air reactor works with an air flow rate generated by an external fan. As a result, we can link the water flow with the humidity gradient as follows:

ṁ wi−wo = w ṁ da

(11)

Outlet moist air

1 ⎛ 21000 21000 ⎞ ∗ ⎛−a− ∗ 1− 2 ⎝ a∗ (1878∗ b+ 1.14) ⎠ ⎜ (1878∗ b+ 1.14) ⎝ ⎜

⎟

2

+

21000 X −0.14 ⎞ ⎛ +a⎞ −4∗a∗ S (1878 ∗ b + 1.14) 0.001878 ∗b ⎟ ⎠ ⎝ ⎠ ⎜

⎟

where

a=e

(22.595 −

5166,8 ) 273.15 + Ts

(19)

b = e−0.059 ∗ Ts

At a given time and with a time step duration short enough to approximate correctly the continuous sorption reaction, Eqs. (3)–(6) and (11)–(12) define a system of 6 variables that can be solved either analytically or with a numeric method. Reactor composite bed’s height was discretized so that diffusion can be correctly calculated. To do this, we considered the solid bed as a number of identical cylinders placed on top of each other. They feature reactor’s diameter and their added height equals bed’s height. Specific humidity and hydration level variables wi , wo and Xs have to be understood as series wi, i , wo, i and Xs, i , corresponding to layer “i” as described in Fig. 8. A hybrid resolution method was selected: temperature and humidity differential equations were solved analytically at each time step, Table 4 Solid material equations of state for adsorption. ps∗ Xs ⩽ 0.14 0.14 < Xs ⩽ 0.32

(10)

Xs > 0.32

When identifying Eqs. (9) and (10), we see that the water vapor flow is given by following differential equation: 809

(

⎛1− 1− Xs 0.14 ⎝

)

0.406

5699.6

⎞ ∗e24.315 − 273.15 + Ts ⎠

⎛0.4375 + 0.5625∗ ⎝

(

5699.6 Xs − 0.14 0.286 ⎞ ∗e25.142 − 273.15 + Ts 0.18 ⎠

Xs − 0.14 25.142 − 5699.6 273.15 + Ts ∗e 0.18

)

(14) (15) (16)

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Table 5 Solid material equations of state for desorption.

XS ⩽ 0.14

⎛ 0.14 < XS ⩽ ⎜0.14 + ⎜ ⎝ ⎛ XS > ⎜0.14 + ⎜ ⎝

0.21 1.14 1+ 1878 ∗ e−0.059 ∗ Ts

0.21 1.14 1+ 1878 ∗ e−0.059 ∗ Ts

⎞ ⎟ ⎟ ⎠

⎞ ⎟ ⎟ ⎠

Table 6 Constant parameters.

ps∗

Parameter

Unit

Value

Description

Eq. (18) Eq. (19)

Minit

kg

2,2|2,8

Ta cr Kloss η cps cpw Δhr Δt N

°C J/K W/K – J·(kg·K) J·(kg·K) J/kg s –

20,0 3500 7 0,95 600 4180 2,700,000 10 10

Initial solid composite mass. Adsorption|Desorption Ambient temperature Specific heat times mass of reactor unit Reactor thermal losses coefficient Reactor heat exchange efficiency Solid composite specific heat Water specific heat Reaction enthalpy Resolution time step Discretized bed: number of layers

XS − 0.14 0, 001878 ∗ e−0.059 ∗ Ts

(17)

considering all other parameters constant. Then, the resulting values were transferred to following time step. Under similar conditions, this method gives slightly better results compared to a strictly numerical calculation.

stands for the different case studies and function E calculates the statistical expected value.

3.4. Method of comparison between experimental and simulation results

Cc = Ej (0.5∗

3.4.1. Convergence criteria The two variables to be compared between test and simulations are: – Outlet temperature To – Outlet specific humidity wo

n

⎯⎯⎯⎯⎯⎯→

∑kj=1 ( grad (T )j,k)2

+ 0.5∗

⎝

da

2

⎯⎯⎯⎯⎯⎯→ grad (w )j, k ⎟⎞ ) ⎠ (21)

3.4.2. Model parameter tuning The comparison between calculated and measured performance curves allows tuning the kinetic parameters in order to minimize the convergence criteria. This identification is done separately for adsorption and desorption models Parameters given in Table 6 are constant for all tests. Parameters to be initialized are summed up in Table 7. We note that composite temperature is not initialized at ambient temperature. Before introducing the composite in the reactor, the air flow is already flowing through the reactor, which means that the reactor itself is close to air inlet temperature. Therefore, initial solid temperature was set from a combination of inlet and ambient temperatures, which provides the model with a better accuracy.

These two variables provide distinct information about how the model understands the actual reaction. While temperature drives the usable heat transfer to space heating system, specific humidity reflects reaction power at solid composite level, without being disturbed by heat losses and inertia. The problem is to give a similar weight to these two variables in the convergence criteria calculation. Since we have here constant air inlet conditions, outlet temporal variations are equivalent to gradients temporal variations. Then, we consider that sorption heat power can be calculated either by a temperature gradient times heat capacity or by a specific humidity gradient times reaction heat. In this specific context of sorption solid/air reaction, we can calculate a coefficient that converts humidity gradient into temperature gradient under ideal conditions (no thermal losses, no inertia).

4. Results and discussion 4.1. Experimental test results

⎯⎯⎯⎯⎯⎯→ Δhr ⎯⎯⎯⎯⎯⎯→ grad (T ) ≈ . grad (w ) cpda

(20)

Inlet and outlet temperatures presented in Table 8 and Figs. 9–11 were averaged from 3 to 5 measurements, as shown in Fig. 4. Because desorption inlet temperature is the highest one to be measured in this experimentation, it was particularly influenced by thermal losses around the uninsulated reactor. Therefore, the average inlet temperature was calculated with two additional sensors located closer to the sieve in order to take into account these losses, and only desorption cases with inlet temperature below 60 °C were selected. At reactor

Eq. (20) is an approximation since water vapor is not considered in the air specific heat. Because of mass transfers, the water vapor flowrate heated or cooled with dry air depends on reaction conditions. In our cases, dry air flowrate is by far the major contributor to moist air flowrate. Consequently, specific humidity gradient was multiplied by Δhr and cpda

the convergence criteria Cc was calculated according to Eq. (21) where j

Outlet moist air Solid hydration level

Δh

n

∑kj=1 ⎜⎛ cp r .

Dry air flowrate

Air specific humidity

Incoming moist air Dry air flowrate Fig. 8. Reactor’s solid bed discretization scheme. 810

Reactor diameter

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gradients were 1.52–1.80 g/kgda, with peaks at 2.95–3.24 g/kgda. Energy density calculated with specific humidity and reaction heat was 132 W h per kilogram of solid composite at its initial hydration level (40.5%). This is lower than the expected 167 W h/kg since desorption reactions were stopped too early and did not reach the 9% hydration level target. Thermal losses were quite important because of higher temperatures in desorption phase and also because of the large size of the reactor compared to its heat power.

Table 7 Initialized parameters. Parameter

Unit

Description

Method

Ti

°C

Inlet air temperature

wi

kg/kgda

ṁ w,0

kg/s

Ts,0

°C

Inlet air specific humidity Initial water vapor flow rate Initial composite temperature

Constant equal to average measured value Constant equal to average measured value Always 0

Xs,0

kg/kg

Initial composite hydration level

Adsorption: Equal to Ti Desorption: Equal to 0.88 * Ti + 0.12 * Ta Equal to measured value with moisture analyzer

4.4. Electrical consumption For both adsorption and desorption, electrical power consumption was below 80 W. While air flow circulation accounts for approximately 10 W, we see that the vibration costs too much electrical power in the context of energy efficient generators. The current 2.8 adsorption coefficient of performance [45] need to be clearly improved.

outlet, spatial standard deviation is 0.3 K for adsorption and 1.0 K for desorption, while at reactor inlet, it is respectively 0.04 K and 4.9 K. This latter value is higher because it is calculated with the 2 additional sensors located in a different section plane. Inlet and outlet air specific humidity was calculated from temperature and relative humidity using NF X15-110 standard equations.

4.5. Comparison between model and experimental results 4.5.1. Results and analysis of adsorption reaction model Adsorption kinetic parameters were identified with a fitting procedure that minimizes the convergence criteria between experimental and model outputs. They are reported in Table 9. Thermal losses were also identified through the Kloss coefficient, although it is also possible to perform a calculation with conduction and convection coefficients from literature. A comparison of experimental and numerical results is presented in Fig. 9. With the optimized set of kinetic parameters, the standard deviation averaged on the four case studies is 0.731 K, with the above defined transposition of humidity results in Kelvin. While this result is good enough for the purpose of dimensioning a reactor or predicting its behavior under different inlet conditions, qualitative analysis gives some leads for a better understanding of the processes involved. The model curves presented in Fig. 9 show more variations than the actual measurements. Model’s first peak is higher than measurements for both temperature and humidity absolute gradients. Later on, model gradients decrease quickly and become lower than the measured ones. Then and until reaction end, gradient variations are slow and monotonic. Model gradients decrease slower, which is why they finally exceed measured ones. Reducing the model temporal variations cannot be done with current model: a higher derived coefficient would not fit reaction start as accurately. When looking at the composite equilibrium curve shown in Fig. 10, we see that it shows a high variation rate right after the first humidity gradient peak. This knee shape is due to the thermochemical reaction, which increases the sorption reaction’s intensity when composite hydration level is low, at the beginning of the test. Inherently, equilibrium curves do not reflect kinetic effects, as they were measured after stabilization by means of a thermogravimetric analysis. However, they identify different sorption processes that can be linked to the composite hydration level as described by Courbon et al. [37]. Therefore it would be possible

4.2. Adsorption Heat power was measured between 328 and 386 W on the air flow. Because of thermal losses, this is 6.7% lower than power calculated with specific humidity and reaction heat (2630 kJ/kgwater). Temperature gradients reached a maximum value shortly after batch test started. While averaged values were 5.3–6.5 K, they peaked at 7.6–8.6 K. In the same way, averaged specific humidity gradients were −2.25 to −3.21 g/kgda, with peaks at −3.24 to −3.65 g/kgda. Energy density calculated from air flow heat power was between 186 and 212 W h per kilogram of solid composite at its initial hydration level (9%), while the target density is 207.8 W h/kg for a reaction between 9% and 40% hydration level. This is a fairly high value in the context of seasonal storage and compared to other sensible or phase change technologies. Temperature lifts were also adapted to the application, but a constant output power would be more relevant. A continuous solid flow would lead to such a result, and a counter current configuration would lead to a maximal outlet temperature. 4.3. Desorption Heat power was measured between 173 and 213 W with specific humidity and reaction enthalpy (2675 kJ/kgwater). Because of thermal losses, this is 67% lower than power calculated on the air flow. It is also lower than adsorption heat power, because of relatively low desorption temperatures that reduced the average difference with composite equilibrium temperature. Temperature gradients reached a minimum value shortly after batch test started. While averaged values were −3.8 to −5.2 K, they peaked at −10.4 to −15.7 K. In the same way, averaged specific humidity

Table 8 Reactor test results presented for a single batch load. The subscripts refer to a batch test duration: “min” for minimum, “max” for maximum, “avg” for average and “final” for final state. Climate

Ti [°C]

wi [kg/kgda]

ṁ da [kg/h]

To,max [°C]

(To-Ti)avg [°C]

wo,min [kg/kgda]

(wo-wi)avg [kg/kgda]

Xs,final [–]

Q̇ a,avg [W]

Adsorption: Xs,0 [–] = 9.0% ± 0.75; Minit [kg] = 2.2 1. Vienna 23.9 0.0069 220 2. Stockholm 23.8 200.4 3. Barcelona 22.5 210.9 4. Brussels 23.8 218.4

31.5 32.32 31.04 31.95

5.31 6.24 6.48 5.96

3.44 3.15 3.43 3.48

−2.25 −3.21 −2.95 −2.43

0.393 0.421 0.399 0.407

328 346 386 365

Desorption: Xs,0 [–] = 40.2% ± 0.13; Minit [kg] = 2.8 1. Combined 49.9 0.004 221.8 2. Combined 59.2 0.007 220.1

39.5 43.5

−3.82 −5.18

7.16 10.58

1.52 1.8

15 15.6

−236.5 −318.7

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7

1,4

6

1,2 ws* L1 [kg/kg]

5

1

4

ws* L2 to L9

0,8

3

ws* L10 [kg/kg] Xs L1 [kg/kg]

0,6

2

Xs L2 to L9

0,4

Xs L10 [kg/kg] 1

0,2

0

0 0

1000

2000

3000

4000

5000

Fig. 10. Batch test: Equilibrium specific humidity and hydration level for a 10 layers composite bed.

6

50

5 4

45

3 2

40

1 35 0

1000

2000

3000

To, measure [°C] wo, model [g/kg_da]

4000

5000

Time [s]

6000

7000

0 8000

To, model [°C] wo, measure [g/kg_da]

12

60

Temperature [°C]

11 10

55

9 8

50

7 6

45

5 40 0

1000

2000

To, measure [°C] wo, model [g/kg_da]

3000

4000

Time [s]

5000

6000

Specific humidity [g/kg_da]

Temperature [°C]

7

Specific humidity [g/kg_da]

8

55

4 7000

To, model [°C] wo, measure [g/kg_da]

Fig. 11. Desorption batch tests: experimental results compared to thermodynamic model. Table 9 Adsorption kinetic parameters. Parameter k ki kj

Fig. 9. Adsorption batch tests: experimental results compared to thermodynamic model.

Unit −1

s – s−1

Value

Description

0.025 −2.7 0.3

Kinetic proportional coefficient Kinetic integral coefficient Porous solid permeability

discretization of the composite bed: we assumed that layers are arranged on top of each other and that individual composite grains remain at a constant altitude. In fact, vibrations direction displays a vertical element, which is why grains do not stay in their initial horizontal layer and a certain amount of mixing happens between layers. Whether this spatial discretization improves model accuracy or not is questionable. We figured that curve fitting is slightly better with spatial discretization at the beginning of the test, but the one layer approach is

to differentiate kinetic coefficients by type of ongoing sorption process. As we noted that model’s humidity gradient peak is bigger than measured one, affecting a slower kinetic coefficient only to thermochemical reaction would dilute its intensity over time, which would increase model’s accuracy. Another improvement possibility lies in the spatial 812

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Reaction duration is quite short with separated reactors, because the solid material load is relatively small (2.2 kg in this study). Since the literature mainly deals with slower and longer reactions, a new kinetic model had to be developed. Indeed, models described in previous studies tend to overestimate heat power during the first period of the reaction. They calculate the water transfer rate without delay, even though air specific humidity changes suddenly when the fan starts. While this discontinuity may not affect temperature prediction for high thermal inertia systems, modeling needs to be refined for separated reactors. As a result, a new kinetic expression was presented in this paper, based on a novel derived term of air flow humidity gradient through the reactor. The mathematical expression suggests that the mass transfer rate rises gradually between air and solid material, even when air specific humidity changes suddenly. The improved model accuracy regarding experimental results is of a major interest for mass transfer understanding, while also raising questions for further researches. Indeed, this behavior has to be physically explained, and there is a discussion whether the progressive delay effect should apply to diffusion only or to both diffusion and sorption processes. In future works, modelling accuracy could also be improved by dissociating kinetics into two coefficients related to the physical and chemical reactions involved, as we see that the reaction’s start (chemical) should be slowed down and that the reaction’s end (physical) should be accelerated. Finally, adding a certain amount of particle mixing should be investigated in order to make the bed’s spatial discretization more realistic. There are also reactor design improvements to be investigated in further studies. To reduce electrical consumption, performance should be measured using smaller vibrating actuators or alternative kinetic enhancers as ultrasounds. To improve outlet temperature levels, a proper thermal insulation should be setup and a counter current configuration should be tested, for example with several reacting beds placed on top of each other.

more accurate after the knee shape. As a result, a better and more complex model would use layers with a certain amount of particles mixing. 4.5.2. Results and analysis of desorption reaction model Desorption kinetic parameters were identified like adsorption ones. They are reported in Table 10. Desorption tests and model fitting (Fig. 11) show that the kinetic parameters are different from adsorption ones. This difference is not surprising for reversible reactions as it has already been studied [32], but we also note that the specific humidity gradient between air inlet and solid composite equilibrium is clearly greater for desorption than for adsorption. The proportional kinetic coefficient links this gradient to the water vapor mass transfer rate. It is likely that a limiting effect prevents the reaction from very high transfer rates, meaning that a more realistic coefficient would be defined as a decreasing function of the above mentioned gradient. Compared to measured values, parameters shown in Table 10 provide the numerical model with a 0.596 K standard deviation averaged on the two case studies. 4.6. Comparison with similar studies Experimental results found in previous studies were measured on various vessel types and under many different operating conditions. A comparison is presented in Table 11, which has to be considered with some limitations: – Zondag et al. [12] and Michel et al. [42] reactors work with pure thermochemical materials, which tend to solubilize when highly hydrated. In the present paper, the encapsulation in a silica gel matrix solves this problem, but also decreases energy density. – In some cases, a higher dehydration temperature increases energy density: MgCl2 (2–6 H2O) material involves two chemical reactions that occur at different temperatures, while silica gel water content is linked to temperature and humidity. – The surface heat power is calculated from heat power and air flow cross section surface, it allows to compare heat power of various size reactors. Zondag et al. [12] present a quite high surface power because the equilibrium temperature is up to 45 K higher than inlet temperature, while this temperature difference is only 17.7 K for Michel et al. [42] and up to 26 K in this study.

5. Conclusion Because of seasonal mismatch between heating needs and solar resource, a long term heat storage needs to be developed in order to increase free solar thermal energy use in buildings. To do this, a novel thermochemical reactor was designed, built, and tested at Besol’s and CEA-INES’ labs. Thermochemical technology was selected for its high energy density and because it doesn’t present long term losses. The reactor is separated from the storage tanks, it works with moist air flow at atmospheric pressure and presents a vibrating sieve. The solid material moves constantly, thus increasing its mass transfers with air flow vapor content. Adsorption and desorption are respectively exo- and endothermic reactions, which allows to store and to restitute heat. The solid material was specially developed prior to this study as a composite made of calcium chloride incorporated in a silica gel matrix, so that its mechanical transport properties remain relatively constant over a wide range of solid hydration levels. This introduced a process where monovariant chemisorption and bi-variant physisorption reactions take place simultaneously. The thermochemical reactor was tested according to temperature and humidity conditions calculated for a specific heat storage system integration under four different climates. Test results showed that the average adsorption heat power was 356 W with an average air

This comparison shows that the separated vibrating reactor is a very interesting technology for providing a high surface heat power when equilibrium temperature is not much higher than air inlet temperature. Therefore, the temperature gap between charge and discharge can be greatly reduced as we see that one of the charging tests was conducted at only 50 °C. A lower charging temperature increases the efficiency of a full solar thermochemical storage system as solar thermal panels have a better efficiency and overall thermal losses are reduced. The kinetic models found in the literature define water vapor transfer rate as follows: – For Mette et al. [27], it is proportional to water vapor gradient between air inlet and solid material equilibrium. – For Piot [44], it is proportional to water vapor gradient between air inlet and outlet, as a consequence of Fick’s law. – For Marias [32], it is proportional to a power function of reaction advancement corrected with logarithmic vapor pressure ratio of solid material equilibrium over air inlet. – For Michel [13], it is proportional to reaction advancement corrected with a function of solid equilibrium and air inlet vapor pressure ratio. – For Lu et al. [46], it is proportional to reaction advancement and to a temperature gradient between sorption material equilibrium and local temperature.

Table 10 Desorption kinetic parameters.

813

Parameter

Unit

Value

Description

k ki kj

s−1 – s−1

0.0117 −9 −0.3

Kinetic proportional coefficient Kinetic integral coefficient Porous solid permeability

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Table 11 Reactor experimental results comparison with similar studies. Author

Reactor type

Solid reactant

Zondag et al. [12]

Integrated

MgCl2 (2–6 H2O)

Michel et al. [42]

Multi-layer, integrated

SrBr2 (1–6 H2O)

This study

Separated, vibrating

60% SG + 40% CaCl2 (15–40% H2O)

Inlet air test conditions

51 °C 7.5 g/kgda 33 kg/h 25 °C 6.2 g/kgda 283 kg/h 22.6 °C 6.9 g/kgda 211 kg/h

Peak values

Energy density|dehydration temperature

Air temperature elevation

Heat power

Surface Heat power

14 K

130 W

1940 W/m2

541 W h/kg|130 °C

7.2 K

575 W

140 W/m2

314 W h/kg|80 °C

8.5 K

504 W

1433 W/m2

160 W h/kg|60 °C, 200 W h/ kg|85 °C

temperature elevation of +6.0 K and peaks at +8.2 K, while desorption cooling power was 278 W with an average 4.5 K temperature decrease. The surface heat power was up to 1433 W/m2 with a relatively close equilibrium temperature, which would allow to design an efficient storage system thanks to a reduced charge/discharge temperature gap. The usable energy density was 200.4 W h per kg of 9% hydrated solid composite, which is fairly high compared to other sensible or phase change technologies for seasonal storage, especially for an uninsulated reactor. Electrical consumption dedicated to air flow circulation accounted for about 10 W, which is fully adapted to the application, but vibration accounted for almost 70 W, which still needs to be reduced. Using available isotherm curves, a reactor model was developed and identified in order to understand the thermodynamics involved and to build a sizing tool. This lead to a major finding with the introduction of a new dynamic term in the kinetic model, while combining sorption and porous medium equations. Indeed, the water vapor mass transfer rate equation included a derived term of air flow humidity gradient through the reactor, in addition to sorption and diffusion terms. The smooth rise of the water transfer rate allowed to better fit the startup phase of each test, especially regarding the air outlet humidity prediction. Using a 10 layers solid bed spatial discretization also refined model’s accuracy during startup phase, but reaction vibrations actually mixed those layers, which slightly decreased model’s accuracy at the end of the reaction. Nevertheless, this 10 layers model was selected for its overall better results. Outlet temperature and humidity were compared between model and actual tests. When considering contextual effects of humidity on temperature, model’s average deviation was 0.73 K over 4 adsorption cases and 0.60 K over 2 desorption cases, while identified kinetic coefficients were not similar in both modes. To further improve this fairly good model accuracy, the main leads would be to consider dissociated chemical/physical sorption kinetics and to implement a certain amount of particle mixing between layers. Temperature and heat power results show that the reactor design is well adapted to long-term heat storage for space heating. In addition, outlet temperature levels could be even further optimized with an adapted insulation and a counter-current configuration, while downsizing vibrating actuators or using alternative kinetic enhancers as ultrasounds would reduce electrical consumption.

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