High Temperature Thermochemical Energy Storage

Proceedings of the ASME 2016 International Mechanical Engineering Congress and Exposition IMECE2016 November 11-17, 2016, Phoenix, Arizona, USA

IMECE2016-65912

HIGH TEMPERATURE THERMOCHEMICAL ENERGY STORAGE USING PACKED BEDS

Qasim A. Ranjha, Nasser Vahedi, Alparslan Oztekin* P.C. Rossin College of Engineering and Applied Science Department of Mechanical Engineering and Mechanics Lehigh University, Bethlehem, PA 18015 * Corresponding author ([email protected])

ABSTRACT Thermal energy storage units are vital for development of the efficient solar power generation systems due to fluctuating nature of daily and seasonal solar radiations. Two available efficient and practical options to store and release solar energy at high temperatures are latent heat storage and thermochemical storage. Latent heat storage can operate only at single phase change temperature. This problem can be avoided by some of the thermochemical storage systems in which solar energy can be stored and released over a range of high temperature by endothermic and exothermic reactions. One such reaction system is reversible reaction involving dehydration of Ca(OH) 2 and hydration of CaO. This system is considered in the present study to model a circular fixed bed reactor for storage and release of heat at high temperatures. Air is used as heat transfer fluid (HTF) flowing in an annular shell outside the bed for charging and discharging the bed. The bed is filled with CaO/Ca(OH)2 powders with particles diameter of the order 5μm. Three dimensional transient model has been developed and simulations are performed using finite elements based COMSOL Multiphysics. Conservation of mass and energy equations, coupled with reaction kinetics equations, are solved in the three dimensional porous bed and the heat transfer fluid channel. Parametric study is performed by varying HTF parameters, bed dimensions and process conditions. The results are verified through a qualitative comparison with experimental and simulation results in the literature for similar geometric configurations.

application of CSP systems. Thermal energy storage is one of the viable approach to resolve this mismatch between the solar energy supply and power demand. Based on the energy storage mechanism, thermal energy storage systems are classified to sensible, latent and thermochemical energy storage. Sensible heat storage requires large storage volumes due to low energy density of the storage media. Latent heat storage system can be used to store thermal energy at high temperature but they operate only at single temperature of phase change. Thermochemical energy storage systems have higher energy density and more chemical stability at high temperatures and thus are more suitable for CSP applications. [1-5] In TCES system, the thermal energy is absorbed via reversible endothermic reaction and produces a new product which can be stored in ambient condition for long time with a little energy degradation. The stored energy can be released through the reverse exothermic reaction whenever is needed. These unique features have made TCES as a potential candidate for thermal energy storage especially for CSP and for seasonal thermal energy storage [6]. There are several reversible chemical reactions available which has the potential to be used for TCES systems such as salt hydrates [7], metal hydroxide [8], metal carbonates [9] and many more. Due to higher cost, toxic products, less cyclic and storage stability, lower energy density, the salt hydrates and metal carbonates are less competitive than metal hydroxides for TCES applications. In metal hydroxide, the charging phase is carried out by heating the metal hydroxides at high temperatures available in CSP plants and discharging is done by bringing together the products under suitable conditions. The most widely known metal hydroxide with unique characteristics suitable for TCES is

INTRODUCTION Fluctuation in the rate of supply of solar radiation has imposed a noticeable restriction to the rapid growth and

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Copyright © 2016 by ASME

Calcium Hydroxide [10]. Due to lower cost, non-toxicity, high chemical stability for long terms storage and charge/discharge cycles, high enthalpy of reaction and wide range of discharge temperature calcium hydroxide has been studied more extensively compared to other possible TCES systems. The reaction equation is given as 𝐶𝑎(𝑂𝐻)2 (𝑠) + ∆𝐻 ↔ 𝐶𝑎𝑂(𝑠) + 𝐻2 𝑂(𝑔)

Hydration and dehydration processes are simulated with conditions mimicking typical CSP operations. Parametric study is performed by varying bed size, operating conditions and HTF parameters within the laminar flow regime. NOMENCLATURE Acronyms CSP Concentrating Solar Power HTF Heat Transfer Fluid TCES Thermochemical energy storage

(1)

Heat is absorbed and steam is released during charging process whereas steam is absorbed and heat is released during discharging process. Enthalpy of the reaction ∆𝐻, the difference between enthalpies of formation of the products and reactants, is calculated using the data from the Thermochemical Tables [22,23]. From thermo-physical data given in these tables, value of ∆𝐻 for this reaction varies from 95 kJ/mol to 109 kJ/mol for the range of temperatures between 250C and 7250C. CaO/Ca(OH)2 thermochemical storage system can be configured in a direct or an indirect heat transfer with HTF based on the types of the HTF passage in the reactor. For direct heating method, the HTF is forced to pass through the reactor and has direct physical contact with reactants/products which results in high pressure drop and less efficiency especially for large scale reactors [11,12]. For indirect heating, the HTF is passed through the channel adjacent to the reactor without a direct physical contact with reactants/products and heat is transferred to the bed from HTF through the reactor walls. In indirect heating the heat is transferred inside the reactor by means of conduction. Several experimental and numerical investigations have been conducted [13-15] to study these processes. The main concern is to find the optimum reactor design to reduce the effect of heat resistance within the reactor. Current researches have focused on reactors consisting of rectangular bed with HTF passing through the channels at both sides. Extensive studies have been documented to design cylindrical shaped reactor using heat pumps. Investigations reported in Ref [18-21] considered circular bed configuration with indirect heat transfer in the reactor. These systems are for low temperature heat pump applications with larger particle sizes (710-1000µm). Heat transfer fluid flows through a central concentric pipe in Ref [17]. Most recent studies on circular packed bed reactors used direct heat transfer approach where nitrogen (as HTF) and steam (reaction gas) were introduced to porous bed simultaneously [11,12]. The authors reported that such scheme resulted in high pressure losses. Current study is aimed at developing large scale TCES suitable for typical CSP applications using cylindrical reactor with HTF flowing in an external annulus. This geometry offers great advantage in terms of conduction within the bed and heat transfer from the bed. To exploit this feature of circular geometry fully, preliminary simulations for a single bed with heat transfer flowing in outer annulus parallel to bed axis are carried out. Transient simulations are conducted to study heat and mass transports inside the three dimensional porous bed. Equations governing conservation of mass, momentum and energy for various components are solved with coupled rate of reaction equation using finite element method embedded in COMSOL.

Full Scripts ΔH Enthalpy of reaction, J/mol C Specific heat, J/(kg.K)

d

Diameter, m

k K M n P ṠQ Ṡm T t h u X R Ṙ θ

Reaction rate constant, 1/sec Permeability, m2 Molar mass, kg/mol Total number of mesh elements Pressure, Pa Heat source/sink, W/m3 Mass source/sink, kg/(m3.s) Temperature, K Time, sec Overall heat transfer coefficient, W/m2.K Velocity of gaseous phase, m/s Conversion [-] Radius, mm Rate of reaction Dimensionless temperature, 𝑇𝑠 − 𝑇𝑒𝑞 𝑇𝑒𝑞 ρ Molar density of solid reactant(s), rs ,

Vrs

𝑀𝑟𝑠

mol/m3 Greek Symbols ϵ Porosity η Dynamic viscosity, Pa-s λ Thermal conductivity, W/m.K ρ Density, kg/m3 Subscripts b c D eq eff H HTF m p Q rs s s1

2

Bed Channel Dehydration Equilibrium Effective Hydration Heat transfer fluid Mass Particle Heat Reactant solid Solid phase (bed) CaO


s2 st ini

Ca(OH)2 Steam Initial

properties as a functions of the porosity, temperature and the conversion. These equations are given below:

GOVERNING EQUATIONS The reaction rate of hydration/dehydration process is governed by equations (2) and (3). Equations governing the conservation of mass and the heat transport are used to determine the temperature distribution and pressure variations in the bed. Temperature and pressure distribution within the bed are derived by solving the coupled nonlinear partial differential equations (2)-(7) simultaneously. The rate at which the reactants are converted into products is governed by dX dt

= (1 − X)k H/D θ

(2)

where Vrs is the molar density of the solid reactants. The equation governing the conservation of mass for the steam is + ∇. (ρst ust ) ± Ṡm = 0

(ρC)HTF

(4)

where ε is the porosity of the bed, ρst and ust are the density and the velocity of the steam, and Ṡm is the mass source/sink that is related to the rate of reaction and the porosity. For the steam pressure distribution and the steam flow motion in the bed, Darcy’s law and Kozeny-Carman equation [16] are used. The equations governing the steam flow motions yield: ust = − K=

K ηst

∇Pst

3 d2 p .ε

180(1−ε)2

∂(Ts ) ∂t

(9)

(ρC)eff = (1 − ϵ)(ρC)s + ϵ(ρC)st

(10)

(λ)eff = (1 − ϵ)λs + ϵλst

(11)

(ρC)s = (1 − X)(ρC)s1 + X(ρC)s2

(12)

∂THTF ∂t

+ (ρC)HTF uHTF . ∇THTF + ∇. (−λHTF ∇THTF ) = 0 (13)

where, THTF is the temperature of the HTF and CHTF, ρHTF, λHTF are the specific heat, density and the thermal conductivity of the HTF, respectively. The differential vector operator and the Laplace operator written for the polar coordinate system is given below. The vector operator is applied to various flow parameters in conservations laws as a divergence and a gradient operator.

(5)

∇= 𝑖̂𝑟

𝜕 𝜕𝑟

+ 𝑖̂𝜃

1 𝜕 𝑟 𝜕𝜃

+ 𝑖̂𝑧

𝜕

(14)

𝜕𝑧

(6) ∇2 =

where P is the pressure of the steam, K is the permeability and ηst is the viscosity of the steam, and dp is the diameter of the solid particles. The equation governing the temperature distribution within the bed is obtained from the conservation of energy (ρC)eff

ṠQ = (1 − ϵ)Ṙ∆H

Continuity condition is applied at the interface between the bed and the HTF channels. The equations governing the fluid motion of the HTF are the Navier-Stokes equations. They are solved by applying the no-slip and no-penetration conditions on the wall of the heat transfer fluid channels. The flow regime of the HTF is laminar for all the cases considered in this study. Accordingly, the effect of various parameters on the HTF outlet temperature is investigated. The energy equation for HTF is

dt

∂t

(8)

where Mst is the molecular weight of the steam and ∆H is the enthalpy of reaction. Cs, ρs, and λs are the mass-averaged specific heat, density and the thermal conductivity of the bed. Cs1, ρs1, λs1 and Cs2, ρs2, λs2 are the specific heat, density and the thermal conductivity of the CaO and Ca(OH)2, respectively.

where X is the conversion, kH/D is the rate constant for hydration/dehydration process, θ = (Ts – Teq)/Teq, Teq is the normalizaed equilibrium temperature and T s is the solid phase (bed) temperature. The rate of reaction, Ṙ is given by dX Ṙ = Vrs . (3)

∂(ϵ.ρst )

Ṡ𝐦 = (1 − ϵ)ṘMst

𝜕2 𝜕𝑟 2

+

1 𝜕 𝑟 𝜕𝑟

+

1 𝜕2 𝑟 2 𝜕𝜃 2

+

𝜕2 𝜕𝑧 2

(15)

Simple regression models from the data [22,23] are used to determine temperature dependent enthalpy, specific heat and solid density for the temperature range of interest (3000C6000C). The values of different parameters [10-12] used in this study are listed in the Table 1.

+ ρst Cst ust . ∇Ts + ∇. (−λeff ∇Ts ) ± ṠQ = 0 (7)

where Ceff, ρeff, and λeff are the effective specific heat, density and the thermal conductivity of the bed respectively. Cst is the specific heat of the steam and ṠQ is the heat source/sink due to the reaction. Several supplementary equations are used to determine the mass and heat source terms included in the conservation laws. Auxiliary equations are also used to determine the physical

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Table 1 Physical parameters used

ρs1[kg/m3] ρs2 [kg/m3] ε [-] dp [μm] KH [1/s] KD [1/s] λeff [W/(m.K)]

1666 2200 0.5-0.8 5 -0.05 -0.05(0.1) 0.1

Following assumptions are applied: - The porous bed is assumed as continuum. - Constant values of the reaction rate constants for hydration and dehydration process are used. - Effective thermal conductivity of the bed is assumed to be constant for a fixed value of bed porosity. - The steam is considered as an ideal gas. - Interface condition is used at the wall between HTF and the bed. - Heat transfer between the solid bed and the steam is neglected. - Specific heat, solid density and reaction enthalpy change with the temperature during the reaction. - Steam is assumed to be saturated. Equilibrium temperature changes with the steam pressure. The relation between the equilibrium pressure and temperature is given by [13] P

11375 + eq [K]

st ln ([bar] )=T

14.574

Figure 1: Geometry of the model (left), and axisymmetric model (right) showing location of the two points for temperature and conversion recording.

Charging (Dehydration) Process: At the early stage of the discharging process, the temperature of the bed and the heat transfer fluid is nearly the same. Initial pressure of the bed is set at 0.2bar which is the equilibrium pressure corresponding to the initial temperature. Equilibrium temperature changes with the pressure of the steam, according to equation 16. The pressure of the steam varies as the decomposition reaction proceeds. The rate of conversion, X, is directly related to the difference between the bed temperature and the reaction equilibrium temperature. In order to keep the difference sufficiently high, the inlet temperature of the HTF is set at 5900C. Pressure at the steam outlet is maintained at 0.2bar during the charging process. Under this condition the steam leaving the bed is condensed under the ambient conditions. Discharging (Hydration) Process: Steam and CaO are brought together in an exothermic reaction to release the stored heat. Similar to the charging process, the bed and the heat transfer fluid are in thermal equilibrium at temperature equal to equilibrium temperature (3500C) corresponding to the initial pressure (0.03bar). At the steam inlet, a constant pressure of 2bar is applied. As the steam enters the bed, the reaction starts and heat is generated. Pressure inside the bed increases and so does the equilibrium temperature and absolute value of θ. In case of highly porous bed (ε=0.8), the steam reaches all sections of the bed quickly despite its consumption due to the reaction. The conversion then proceeds with the removal of heat from the bed.

(16)

MODEL DESCRIPTION The geometry of the circular porous bed with the outer annular shell is shown in Figure 1. The bed is filled with CaO/Ca(OH)2 powder during discharging and charging process and HTF flows in the annular shell. Steam is introduced from the top of the bed while HTF flows outside in the annular shell either in the same direction of steam flow (co-current flow) or in the opposite direction to it (counter-current flow). Charging and discharging process are set according to equation 16. These conditions are determined from the available high temperature source during dehydration process and from the required outlet temperature during hydration process. The heat exchange range of a typical CSP system ranges from 400 0C to well above 700 0C. A dehydration reaction should, therefore, be carried out in this range of temperature. The hydration process temperature, on the other hand, depends on the steam pressure and initial conditions. Hence, steam pressure can be varied to determine the reaction equilibrium temperature according to equation 16. These initial and boundary values are discussed separately for charging and discharging processes below.

RESULTS AND DISCUSSION Finite element based standard COMSOL modules are used to solve the governing equations. Normal mesh size is selected for the porous medium and the heat transfer fluid flow domains. Element size and mesh density is different in these domains due to different physics. Spatial convergence analyses were performed by varying the mesh density in the porous domain. For temporal convergence, an adaptive time step is used. Figure

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the bed (points 1 and 2). Compared to the dehydration process, profiles for hydration process have quite different characteristics. 625

1.0

Temperature [0C]

600

0.8

575 550

T1

525

T2

500

0.6 0.4

X1

475

X2

450

0.2

Conversion, X [-]

2(a) shows the temperature profile at location 1 (a point on axis of the reactor as shown in Figure 1) and Figure 2(b) shows average conversion in the reactor over time for mesh size of 149923, 322207, 523649 and 703471. Reactor temperature and conversion times predicted using different mesh densities are very similar; indicating that spatial convergence is attained. Results presented in this paper is obtained using mesh density of 523649.

425

0.0 4000 6000 8000 10000 Time [s] Figure 3: Bed temperature and conversion recorded as a function of time at locations 1 and 2, which are shown in Figure 1. Temperature T and conversion X are shown during charging process (dehydration) for ε = 0.8, Re = 1500 and Rb 0

Figure 2: (a) Temperature at location 1 and (b) average conversion in bed during dehydration for different mesh densities. The letter n denotes the total number of elements in the mesh.

2000

Temperature [0C]

575 550 525 500 475 450 425 400 375 350 325 0

1.0 0.9 T1 0.8 T 2 0.7 0.6 X 1 0.5 X 2 0.4 0.3 0.2 0.1 0.0 1000 2000 3000 4000 5000 6000 Time [s]

Conversion, X [-]

=20mm

Results presented in the current study are obtained using counter-current flow configuration where heat transfer fluid flows outer to the bed in opposite direction to the flow of steam inside the bed. Figure 3 displays bed temperatures and conversions at two locations, which are indicated in Figure1, during the dehydration process. Points 1 and 2 are located at the axis of the bed and close to bed wall, respectively. T 1, T 2, X 1 and X 2 are the temperatures and conversions at points 1 and 2, respectively. These results correspond to a constant porosity of 0.8 and Reynolds number of 1500. Reynolds number of the heat transfer fluid flow is calculated as Re = Uavdh/ν, where Uav is the average velocity of the HTF in the channel, d h is the hydraulic diameter of the HTF channel and ν is the kinematic viscosity of the HTF. Bed temperatures and conversions are determined at points 1 and 2 as shown in the schematic (see Figure 1). The temperature close to wall rises sharply at the early stage of the hydration until the reaction commences and the heat sink is activated. The heat absorbed during the reaction is removed by the steam being generated and leaving the bed. Due to constant value of high porosity considered, the steam leaves the bed rapidly with a very small pressure rise in the bed. This results in a small increase in the reaction equilibrium temperature from the initial temperature (4500C) and a high value of θ is maintained throughout the bed at all times during conversion, as shown in Figure 2. The conversion closer to the wall is completed much sooner than the conversion near the center, as expected.

Figure 4: Bed temperature and conversion recorded as a function of time at locations 1 and 2, which are shown in Figure 1. Temperature T and conversion X are shown during discharging process (hydration) for ε = 0.8, Re = 1500, Pst=2bar and Rb =20mm

The rate of temperature increase and the rate of conversion are greater for hydration process than the rate of temperature decrease and the rate of conversion for dehydration process, as shown in Figures 3 and 4. This is due to the slower reaction rate for the dehydration kinetics. The reaction rate constant for dehydration is lower than that for hydration due to different sequence of heat and mass transfer. In dehydration process heat transfer occurs first followed by mass transfer whereas hydration process commences with mass transfer and heat transfer follows. Also the rate of heat transfer is different in these processes because of the difference in temperature gradients across the bed

Hydration process is simulated for the same value of the bed porosity and Reynolds number of heat transfer fluid as dehydration process. Initial and boundary conditions, however, were chosen to match the high temperature range typical of a CSP plant. Figure 4 shows the bed temperature and conversions as a function of time at points at the center and near the wall of

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at various stages of these processes. Hydration and dehydration temperature and conversion profiles are verified by comparing against the experimental and numerical results documented in the literature [11,13,14,17]. An exact comparison against experimental observations may not be suitable for now due to either different geometry or different mode of heat transfer employed in studies mentioned above. The geometry, process parameters and sequence of steam and HTF flow used here have not been employed so far. Our predictions for both hydration and dehydration process agrees qualitatively with results reported. Further study is needed to validate complex physical models and numerical methods employed here. Points 1 and 2 are selected to record the conversion and temperature in time. Two points selected are: one is at the center and the other one is close to the wall. Temporal characteristics of the temperature and the conversion will be expected to be very different at these two locations. Heat is transferred primarily in the radial direction and that results in propagation of reaction front radially inward. Figure 4 shows the temperature and conversion contours at 500s and 2500s into the process during the hydration reaction. Temperature contours (top) also include the HTF channel whereas the conversion contours include only the reactor bed. Red color denotes the maximum value of temperature/conversion and blue denotes the minimum value.

difference between the bed and the inlet steam pressure is higher. That results in acceleration of the steam flow inside the bed. This, combined with the greater temperature difference between HTF and the bed, enhances the conversion.

Conversion, X [-]

1.2 1.0 0.8 T_ini=325

0.6 0.4

T_ini=394

0.2

T_ini=450

0.0 0

2000

4000 6000 Time [s]

8000

10000

Figure 6: Average conversion for different initial bed and HTF temperatures during hydration process for ε = 0.8, Re = 1500, Pst=2bar and Rb =20mm

In addition to initial temperature and pressure, we have studied the effects of geometric parameters as part of the parametric study conducted here. In order to increase the energy density of the bed, either porosity of the bed can be decreased or the size of the bed can be increased. Decreasing the porosity or increasing the size of the bed will have the similar impact on the total conversion time. It is expected that the conversion time increases as the porosity decreases or the size of the bed increases. Porosity value, however, cannot be decreased beyond a certain value because it will restrict the transport of reaction gas within the bed. Also, to have an optimum value of bed permeability for better conversion we need to have a compromise between the porosity and the particle size, as indicated by the Kozeny-Carman relation (equation 6). The porosity or particle size variation is, therefore, not discussed here. The effect of bed dimensions on the conversion time is shown in Figure 6. With highly porous beds like the one considered here (ε=0.8), conversion varies almost linearly with the volume of the bed. A lower value of porosity may give different results with combined effect of size and porosity variation.

Figure 5 Contours of instantaneous temperature (Top) and conversion (bottom) at two different instants (t = 500s and t = 2500s) during hydration process for ε = 0.8, Re = 1500, Pst=2bar and Rb =20mm

Since the conversion is directly affected by the heat transfer from the bed during hydration, effect of varying the initial conditions was also studied while keeping the bed porosity and Reynolds number constant. Figure 5 shows conversion profiles for three initial temperature conditions. Initial pressures for the three cases were also varied accordingly using equation 16. It can be seen that the conversion time decreases as the difference between maximum equilibrium temperature (corresponding to the steam inlet pressure) and the initial bed temperature increases. Since the initial pressure of the bed is lower the

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450 Avg. Outlet Temperature [0C]

Conversion, X [-]

1.2 1.0 0.8 0.6

r-10mm

0.4

r-20mm

0.2

r-30mm

0.0 0

2000

4000 6000 Time [s]

8000

10000

Re=500

425

Re=300 400

Re=100

375

350 0

3000 4000 5000 6000 Time [s] Figure 9 Average heat transfer fluid outlet temperature for various values of Reynolds number of heat transfer fluid during hydration process, ε = 0.8, Tini = 350, Pst=2bar.

Figure 7: Average conversion for various radii of the bed during hydration process for ε = 0.8, Re = 1500, Tini = 350 and Pst= 2bar.

Conversion is directly affected by the difference in the bed temperature and the reaction equilibrium temperature. To maintain this difference, heat transfer to and from the bed during dehydration and hydration process is important. With the assumption of constant effective thermal conductivity of the bed, the effect of heat transfer fluid flow characteristics is studied. Figure 7 shows the influence of varying Reynolds number on the conversion and on the average heat transfer outlet temperature during hydration process. The values of Reynolds number were chosen within the laminar flow regime (Re=100,300,500). As was expected there is no noticeable difference in average conversion profiles for the three values of Reynolds number. The temperature profiles in Figure 8, on the other hand, show considerable difference in maximum heat transfer fluid outlet temperature. There is also a noticeable difference for most of the reaction time: outlet temperature varies only slightly after 500s for Re=500 and Re=300 whereas the temperature continually changes in time during the reaction for Re=100. This is important in regard to selection of Reynolds number which matches the output temperature requirements for a particular application.

Avg. Conversion, X [-]

1.0 0.8 Re=100 Re=300

0.4

Re=500

0.2 0.0 0

1000

2000

CONCLUSION A three dimensional circular bed filled with CaO/Ca(OH)2 powder is modeled as thermochemical energy storage for high temperature applications. Previously, circular reactor beds with indirect heat transfer were considered with either central pipe or coil type heat exchangers [17,18] for heating and cooling of the bed. This study considers an outer annular shell for the flow of HTF to study the heat transfer within the bed. The present concept can easily be extended further for cross flow situation in large scale three dimensional model. Charging and discharging processes are simulated with initial and boundary conditions representing typical CSP applications. The effects of bed dimensions, process conditions and heat transfer fluid parameters were considered. Circular geometry with this particular flow scheme of reaction gas and HTF with the given initial and boundary conditions has not been analyzed numerically or experimentally yet. Therefore the model is validated only qualitatively against earlier experimental and numerical studies with similar operating conditions for different bed and heat exchanger configurations [13-15]. The model and the results obtained therewith constitute a preliminary study for high temperature thermochemical energy storage system. Circular geometry has certain advantages over its rectangular counterpart in terms of heat transfer which can be properly exploited by considering reaction gas and heat transfer flow in cross flow situation and the turbulent flow of heat transfer fluid. Future studies on this system will include a complete three dimensional model with cross flow scheme and relaxation of some of the assumptions made in the model. Heat transfer enhancement techniques to overcome the problem of inherently low thermal conductivity of the solid materials is also proposed.

1.2

0.6

1000

2000

3000 4000 5000 6000 Time [s] Figure 8 Average conversion for various values of Reynolds number of heat transfer fluid during hydration process, ε = 0.8, Tini = 350, Pst=2bar.

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