High-temperature thermochemical energy storage – heat transfer enhancements within reaction bed

Applied Thermal Engineering 163 (2019) 114407

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High-temperature thermochemical energy storage – heat transfer enhancements within reaction bed Qasim Ranjha, Nasser Vahedi, Alparslan Oztekin

T

⁎

P.C. Rossin College of Engineering and Applied Science, Lehigh University, Bethlehem, PA 18015, USA

HIGHLIGHTS

unsteady simulations of thermochemical energy storage using Ca(OH) /CaO. • 3D hydration and de-hydration processes for discharging and charging studied. • Both reactor configurations considered for complete cycle. • Different transfer improvement with finned wall circular cross section reactor studied. • Heat • Charging and discharging time are reduced significantly with fins. 2

ARTICLE INFO

ABSTRACT

Keywords: Thermochemical energy storage Heat transfer enhancements Ca(OH)2/CaO Hydration Dehydration

Ca(OH)2/CaO reversible reaction system has high potentials to be used for high-temperature thermal energy storage. Endothermic dehydration of Ca(OH)2 and exothermic hydration of CaO can be carried out at high temperatures compatible with most of the concentrated solar power applications. One of the challenges in using Ca(OH)2/CaO is the slow rate of heat transfer inside the solid reaction beds. Heat transfer enhancement techniques are introduced in a circular fixed bed heated indirectly through heat exchanger walls. Two reactor configurations are studied: one in which the heat transfer fluid (HTF) flows through an outer annular shell and another in which the HTF flows through a central pipe. Dehydration and rehydration processes are simulated with and without fins attached to the heat exchanger wall extending into the reaction bed. Heat and mass transport equations coupled with reaction kinetics are solved numerically. The designed heat transfer enhancements (HTE) within the reaction beds resulted in a significant decrease in overall conversion time during the energy storage and discharge. It is shown that the reactor with an outer annular shell as the HTF channel has better performance compared to the reactor with internal pipe flow configuration for HTF.

1. Introduction Thermochemical energy storage (TCES) offers clear advantages compared to the latent heat storage and the sensible heat storage for high-temperature applications. TCES materials have, in general, a higher energy density than phase change and sensible heat storage materials [1]. Most TCES materials can be stored for prolonged periods and transported over long distances without thermal losses. Moreover, in gas-solid reactions, the reaction temperature can be controlled by adjusting the pressure of reactant gas(es). It is, thus, possible to store or release the heat at a desired operating temperature range for a selected reaction system [2]. Several reactions have been investigated as potential candidates for thermal energy storage (TES) systems for applications ranging from ⁎

heat pumps to concentrated solar power technologies [1,3]. Critical factors in the selection of any reaction system for high-temperature storage are energy density of the storage materials, the temperature range for exothermic and endothermic reactions, the thermal conductivity of reaction materials, the reaction rate, the reversibility, the cyclic stability, and the cost [4]. Out of several potential candidate reactions for TCES, metal hydroxides (Ca(OH)2/CaO and Mg(OH)2/ MgO pairs) meet most of the criteria and have experimental feedback of over ten years [1]. Given the higher energy density, the heat of reaction, low cost, and the charging/discharging temperature, Ca(OH)2/ CaO reaction system is well suited for CSP applications [5,6]. However, a common drawback of metal oxides/hydroxide systems is the poor thermal conductivity of the reaction materials. This study is aimed at improving the heat transfer within the Ca(OH)2/CaO reaction bed. The

Corresponding author. E-mail address: [email protected] (A. Oztekin).

https://doi.org/10.1016/j.applthermaleng.2019.114407 Received 10 March 2018; Received in revised form 5 September 2019; Accepted 16 September 2019 Available online 17 September 2019 1359-4311/ © 2019 Elsevier Ltd. All rights reserved.

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Nomenclature

U V v X

Acronyms CSP THE HTF TES TCES

Concentrated Solar Power Heat transfer enhancements Heat Transfer Fluid Thermal Energy Storage Thermochemical energy storage

K

µ

pre-exponential factor, 1/s specific heat, J/(kg.K) diameter activation energy, J/mole height of reactor enthalpy of reaction, J/mol permeability characteristic length of HTF channel molar mass, kg/mol pressure, Pa radius gas constant, J/mol. K rate of reaction Reynolds number heat source/sink, W/m3 mass source/sink, kg/ (m3. S) temperature, K time, sec thickness velocity of the gaseous phase, m/s

CaO (s ) + H2 O (g )

H 109kJ / mol

,mol/m3

reaction rate constant, 1/sec porosity dynamic viscosity of steam, Pa-s dynamic viscosity of air, Pa-s thermal conductivity, W/m.K density, kg/m3

Subscripts b c D eff h H eq ini M Q r rs S st

reversible reaction involving the endothermic dehydration of Ca(OH)2 and the exothermic hydration of CaO is shown in Eq. (1).

Ca (OH )2 (s ) + H

rs

Mrs

Greek Symbols

Full Scripts A C D E H H K l M P r R R Re SQ Sm T t tw U

velocity of air molar density of solid reactant(s), volume of reaction bed, m3 conversion

reaction bed channel dehydration effective hydraulic hydration equilibrium initial mass heat reactor reactant solid solid phase/reaction bed steam

internal pipe as an HTF channel for heat pump applications. More recently, researchers used both direct and indirect modes of heat transfer in the Ca(OH)2/CaO reactor for thermal energy storage compatible with CSP applications. F. Schaube et al. [12,13] studied heat storage and release using Ca(OH)2/CaO in a circular reaction bed. HTF, along with the reaction gas, was forced through the porous bed for direct contact between HTF and the reaction material to enhance the heat transfer. In another study, fluidized bed using a direct heat transfer mode was studied by Pardo et al. [14] for Ca(OH)2/CaO powders. However, pumping power needed to force the HTF through the bed due to high-pressure drops prohibits scaling up the reactors with a direct heat transfer. Schmidt et al. [15] built the first pilot-scale reactor with multiple rectangular beds and HTF channels separated by heat exchanger walls. The reaction beds were packed with Ca(OH)2/CaO powders and heated indirectly through heat exchanger walls by the air while the reaction gas entered and left the beds from the top. Charging and discharging steps were carried out for ~2 bar steam pressure. Numerical studies in two-dimensional reactors were performed for the same system in a separate study [16] assuming highly porous bed and co/counter-current flow of the steam and the HTF. This rectangular reactor configuration with an indirect heat transfer mode was studied numerically in detailed three-dimensional simulation [17], and effects of the bed porosity and other parameters on the heat and mass transfer within the bed were investigated. Similar numerical analyses were performed for a circular fixed bed heated by HTF flowing through an outer annular shell [18]. While an indirect heat transfer through heat exchanger walls does not suffer from pressure drops or additional pumping power requirements, it results in slow conversion rates due to the poor thermal conductivity of the Ca(OH)2/CaO beds. This study is aimed at improving the heat transfer within a circular bed heated by air as HTF

(1)

Heat transfer to/from the reaction bed is a critical issue in the selection and design of any TES system. Various reactor configurations for the reaction system in Eq. (1) have been studied experimentally and numerically at laboratory and pilot scale utilizing various heat exchange methods between the HTF and the bed. A. Kanzawa and Y. Arai [7] first proposed the addition of copper plates within the Ca(OH)2 powdered bed in a decomposition reaction at high temperature for an energy storage step. The authors used additional copper plates inserted into the rectangular bed parallel to the bed walls, and they demonstrated that the heat transport within the bed was greatly improved. Fuji et al. [8] performed experiments on heat storage using the Ca (OH)2/CaO reversible reaction. Solidified cylindrical energy storage elements made of Ca(OH)2 were used instead of powders to enhance the physical parameters: the thermal conductivity, specific heat, and density of the reaction bed. The elements were packed in spiral fins with a pitch of 3–5 mm and were heated by air in the heat storage reaction. H. Ogura et al. [9] studied the effect of using vertical copper blades within a cylindrical CaO bed for a heat transfer enhancement during an energy release step. H. Ogura et al. [9] documented that the total conversion time is significantly lower in a reactor with copper blades. H. Ogura et al. [10] investigated the effect of heat exchange conditions on the performance of a heat pump dryer using the Ca(OH)2/CaO reaction. The reactor consisted of a cylindrical reaction bed filled with 0.7–1.0 mm size particles with an outer annular shell for the HTF (air). The annular shell was packed with a stainless mesh to enhance the heat transfer from air to the bed. These authors also studied [11] numerically and experimentally a cylindrical Ca(OH)2/CaO bed with an 2

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flowing either in an outer annular shell or a central pipe. Enhancement of heat transfer within the bed is achieved by attaching fins to the heat exchanger wall extending into the porous reaction bed. An attempt is made to combine the HTE techniques previously used for an indirectly heated/cooled Ca(OH)2/CaO bed for a single bed reactor which can be used to design a full-scale reactor with finned walls. Compared to the previous HTE techniques [7–11], the designed fin configurations neither sacrifice reaction bed volume nor do they restrict the flow of the reaction gas or the HTF. Also, the fin configurations are easier to incorporate with the reaction bed walls with less effort and cost. Moreover, detailed modeling of momentum and heat transport within the HTF channel would help design a reactor according to a particular temperature requirement. Internal pipe and outer annular shell are selected as HTF channels to minimize the computational cost as the focus here is on improving the heat transfer within the bed. However, the approach and the model can be extended to more than one reaction beds with proposed finned walls and HTF flowing perpendicular to the beds' axes.

Table 1 Geometric and physical parameters. Parameter

Symbol

Value

Solid density of CaO [12,13,19,20] Solid density of Ca(OH)2 [12,13,19,20] Porosity [13] Solid particle size [16]

ρs1 ρs2 ε dp

1,666 [g/cm3] 2,200 [g/cm3] 0.5 and 0.8 5 [μm]

Pre-exponential factor for hydration [19] Pre-exponential factor for dehydration [19] Activation energy for hydration [19] Activation energy for dehydration [19] Effective thermal conductivity [13] Height of the reactor

AH AD EH EH λeff hr

53 × 103[1/s] 715 × 107 [1/s] 83 × 103 [J/mol] 187 × 103[J/mol] 0.4 and 0.1 [W/(m.K)] 200 [mm]

pipe as HTF channel. Counterflow scheme between the HTF (air) and the reaction gas (steam) is used where steam enters the reaction bed from the top, and HTF enters from the bottom. The height of the reactor in each configuration is kept the same at hr = 200 mm . For comparison of two reactor configurations, the volume of the reaction bed is held constant. Size of the HTF channel in both reactors is determined for the fixed value of Reynolds number, Re , and the inlet air velocity. ( U) D Re = µ air h , where is the density of air, U is the average air velocity, air µ is the dynamic viscosity of the air, and Dh is the hydraulic diameter of the HTF channel. Reynolds number of 1,500 and HTF inlet velocity of 25 m/s are used in each case to determine the size of the HTF channel. Geometric and physical parameters employed are listed in Table 1. The wall between the HTF channel and the bed is augmented with fins of the same thickness to enhance the heat transfer within the reaction bed. The fins extend into the bed to a depth of 0.75 × rb in the

2. Reactor concept 2.1. Reactor geometry Fixed circular reaction bed packed with fine particles of Ca(OH)2/ CaO is considered with two HTF channel configurations. Numerical simulations of the dehydration (charge) and the hydration (discharge) reaction are carried out. Fig. 1 shows the proposed reaction bed and the HTF channel configurations. Configuration ‘a’ uses an outer annular shell for the flow of HTF, whereas the configuration ‘b’ uses internal

Fig. 1. Reaction bed configurations with (a) an outer annular and (b) an internal pipe as HTF channels. Dimensions of each reactor are displayed. 3

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reactor ‘a’ and rc + 0.75 × (rb rc tw) in the reactor ‘b’. Dimensions of each reactor are depicted in Fig. 1, and the reactors with the finned wall are shown in Fig. 2. Presence of fins breaks the symmetry and leads to a non-axisymmetric velocity and temperature field. The lower bed porosity of 0.5 causes stronger axial variations in the temperature and velocity field compared to high bed porosity of 0.8. As a result, both flow and temperature field are expected to display stronger three-dimensional structures in the 0.5 porosity bed than in the 0.8 porosity bed. It was documented in our earlier study [17] that the bed porosity ε ≤ 0.6 leads to three-dimensional transports within the bed due to the slower flow of the reaction gas (steam).

ust =

dp2 . 3

equation (K = 180 . (1 )2 . With particle size of dp = 5 µm , the permeability is 7 × 10−14 m2 for = 0.5 and 1.7 × 10−12 m2 for = 0.8. Conservation of energy is used for generation and transport of heat of the reaction within the porous reaction bed.

( C)eff

ln

105

=

SQ = (1

st )

t

+

.( st ust ) ± Sm = 0

R = Vrs

eq

)RMst

TBed +

.(

eff

TBed) ± SQ = 0

(6)

(7)

)R H

dX dt

(8)

where Vrs is the molar density or the molar concentration of the reactant solid. The fraction of solid reactants converted into products during the reaction, X, is given by

(2)

dX = dt

(1

X) K (T)(

TBed Teq

1)

(9)

The reaction rate constant, K , is a function of the bed temperature and is defined by

(3)

K (T) = Ae

Eq. (3) governs the transport of the steam within the porous bed. , ρst and ust are bed porosity, steam density and, steam velocity, respectively. Sm is the steam generation/consumption during the dehydration/hydration process.

Sm = (1

st C st u st .

H is the enthalpy of the reaction. The terms with subscript ‘eff’ represent the effective properties of the porous bed comprising steam and the solid reactant, whereas the subscript ‘Bed’ stands for the solid reaction bed. Specific heat, C , of the materials involved is taken as a linear function of the temperature from thermochemical data [21]. The rate of reaction, R , in Eq. (7) is the rate at which reactants are converted into products.

A detailed mathematical model for this system was given in an earlier study [17]. Eqs. (3) through (12) are used for the energy and mass transport within the reactor along with the reaction kinetics.

(

(TBed) + t

where , C, and are density, specific heat, and thermal conductivity, respectively. SQ is a heat source (exothermic reaction) or a heat sink (endothermic reaction).

• The porous bed is treated as a continuum. • Reaction bed porosity remains constant. • Copper is used for the heat exchanger wall. • The effective thermal conductivity of the bed is constant. • Heat transfer between gaseous and solid reactants/products is neglected. • The density of the solid bed changes with reaction. • Specific heats of the solids change with temperature. • Following relation between the equilibrium pressure, P , and tem12, 845 + 16.508 Teq

(5)

where ust is steam velocity, Pst is steam pressure, st is the viscosity of the steam. K is the bed permeability determined by the Carman-Kozeny

Following assumptions are applied to the model:

Peq

Pst

st

2.2. Governing equations

perature, Teq , of steam is used [19].

K

(

E ) RTBed

(10)

where A is the pre-exponential factor, E is activation energy, and R is the gas constant. Conservation of mass, momentum and energy equations for HTF yield.

(4)

( C) HTF

where R is the rate of reaction and Mst is the molar mass of the steam. Darcy’s law is used to relate the velocity and the pressure field of the steam inside the reactor bed.

THTF + ( C)HTF uHTF . t

THTF +

.(

HTF

THTF) = 0

(11)

Conservation of energy for the wall separating HTF from the reaction bed is given by

Fig. 2. Reactors shown in Fig. 1 with fins attached to the wall between the bed and the HTF channel. 4

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( C) Wall

TWall + t

.(

TWall) = 0

Wall

in Fig. 3. The points are marked along with the height of the bed at 0.01 × hr , 0.5 × hr and 0.95 × hr . The same probe points are used for the reactors without fins for proper comparison.

(12)

The subscripts ‘HTF ’ and ‘Wall ’ are for the heat transfer fluid and the wall between the reaction bed and HTF channel. Initial and boundary conditions for the Eqs. (3)–(12) are given in Table 2.

3.1. Dehydration – charging -(reactor ‘a’) Time evolution of temperature at various locations and the average conversion during the dehydration (charging) process in the reactor ‘a’ with rb = 10 mm are shown in Fig. 4. Size of the HTF channel in all the configurations is determined by keeping the inlet velocity at 25 m/s and Reynolds number constant at 1,500. The temperature at points in the middle of the bed (points 2,5,8) and along the bed axis (points 1,4,7) and the average conversion of the reactants into the products are shown as a function of time. At the start of dehydration (charging), the whole reactor is set in the thermal equilibrium at 450 °C and, the bed pressure is set equal to the equilibrium pressure corresponding to this temperature according to Eq. (2). The inlet temperature of the HTF is set at 550 °C for t > 0 to allow the heat transfer from the HTF to the bed. Dehydration reaction initiates as soon as the bed temperature rises above the equilibrium temperature within the bed. Reaction equilibrium temperature within the bed also changes with the bed pressure due to steam generation. In order to avoid the re-hydration reaction, the bed temperature should be higher than the equilibrium temperature of dehydration. At the end of the dehydration process, the whole reactor comes in thermal equilibrium at the HTF inlet temperature. The temperature at the locations (4,7,8) away from the HTF inlet drops below the initial temperature due to the slow rate of heat transfer

3. Results and Discussion Coupled set of Eqs. (2)–(12) along with other auxiliary equations is solved numerically using finite elements with COMSOL Multiphysics. Quadratic tetrahedral elements are used for conversion, steam transport within the bed, and heat transfer within the wall. First-order tetrahedral elements are used for heat transfer within the bed, whereas first-order tetrahedral and prism elements are used within the HTF domain. Mesh is refined in all domains until temperature and conversion profiles are independent of mesh density. Temporal convergence is achieved using adaptive time steps. An absolute tolerance value of 5 × 10−5 and a relative tolerance value of 0.01 are set for all variables. Results of the mathematical model were validated in previous studies [17,18] against the experimental results [15] for rectangular and circular reaction beds. The validity of the model and the numerical settings were established in these studies and is, therefore, not repeated in this work. Instantaneous temperature is recorded on a vertical plane through the bed axis in the middle of the two fins in both reactors in cases of the finned wall. The cut planes and the radial location of points are shown Table 2 Initial and Boundary Conditions. Eqns

Boundary/initial condition

6,11,12

At t = 0

TBed = THTF = TWall = Tini/H = 350°C

At t = 0

TBed = THTF = TWall = Tini/D = 450°C

6,11,12 6,11,12 6,11,12 11 11

K T}

Insulated walls of the reactor ‘a’

At h = 0, hr At r = r b

n. q = 0 {q = n. q = 0

K T}

Insulated walls of the reactor ‘b’

No-slip (reactor ‘b’)

At r = (rc + tw),r b uHTF = 0 At

{

(rc + tw) < r0

At

0 < r < rc THTF/H = 350°C, h=0 t>0

At

At At

{t0 =< 0r < r

b

THTF/D = 550°C,

650°C,

HTF inlet Temperature (reactor ‘a’)

HTF inlet Temperature (reactor ‘b’)

Initial pressure and steam pressure at the top inlet; hydration

P = 3, 000 pa

h = hr P = 200, 000 pa 0 < r < rb

{t0 =< 0r < r

b

Initial pressure and steam pressure at the top outlet; dehydration

P = 13, 300 pa

h = hr P = 13, 300 pa 0 < r < rb

{ {

At At

HTF inlet velocity (reactor ‘b’)

0 < r < rc m uHTF = 25 s h=0

At

At

Inlet velocity of HTF (reactor ’a’)

(rc + tw) < r
At

3

No-slip (reactor ‘a’)

At r = (rc + tw),r b uHTF = 0

At

3

Initial reactor Temperature (dehydration)

n. q = 0 {q = n. q = 0

11

3

Initial reactor Temperature (hydration)

At h = 0, hr At r = r b

At

3

Description

{

h=0 0 < r < rb r = rb 0 < h < hr

No mass flux; hydration and dehydration (reactor ‘a’)

n. ust = 0 n. ust = 0

h=0 (rc + tw) < r
n. u st = 0

r = rb 0 < h < hr

n. u st = 0

No mass flux; hydration and dehydration (reactor ‘b’)

5

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Fig. 3. Locations where time evolution of temperature is displayed.

Fig. 4. Temperature at the points within the bed (without fins) shown in Fig. 3(a) and average conversion during the dehydration process (rb = 10 mm ) for ε = 0.5.

to these regions within the bed. At the early stage of the dehydration, the reaction starts in the regions close to HTF inlet (points 1,2,5) and the heat sink is activated which causes the temperature to drop slightly in the upper and the middle parts since the rate of heat transfer from HTF is not fast enough. Such a temperature drop does not occur in the reactor with the finned wall, as shown in Fig. 5. Time evolution of temperature at three points (1,4,7) located along the axis is plotted for the reactor ‘a’ with and without fins for comparison. Fig. 5 shows the evolution of the temperature and conversion in the reactor without and with fins. The average conversion time in a reactor with and without fins is about 8,000 s and 11,000 s, respectively. The conversion in the finned reactor is about 27% faster compared to that in the reactor without fins.Fig. 6.

the bed. Heat is generated from the exothermic reaction with a sudden rise in the bed temperature. Also, the reaction equilibrium temperature rises with an increase in the steam pressure according to Eq. (2). The bed temperature needs to be kept below the equilibrium temperature of dehydration to avoid the reverse reaction. Fig. 7 depicts the time evolution of temperature at various points and the conversion during the hydration process in the reactor ‘a’ with and without fins. The temperature at three points (1,4,7) along the bed axis and the average conversion are compared. Average conversion time in the finned wall reactor is 1400 s whereas it is 4,000 s in the reactor without fins. The conversion time is reduced by about 65% in the reactor with fins compared to that in the reactor without fins. The heat transfer enhancement with fins is more significant in the hydration (~65%) than in the dehydration process (~27%). The temperature gradient across the bed wall and the nature of the process dictate the conversion time. During the hydration process, the reaction is faster, and heat is generated spontaneously creating a temperature difference of around 200 °C across the heat exchanger wall. During the dehydration reaction, however, the difference between the initial thermal equilibrium temperature and the HTF inlet temperature is set at 100 °C. Another reason for the pronounced difference in the conversion times between the hydration and dehydration phase is the way these processes are executed. During the dehydration process, the air inlet temperature is set at a higher value than the initial bed

3.2. Hydration – discharge - (reactor ‘a’) The hydration (discharge) process is initiated by setting the whole reactor in the thermal equilibrium at 350 °C, and the bed pressure equals the equilibrium pressure determined from the initial equilibrium temperature using Eq. (2). HTF inlet temperature is also set at the same temperature (350 °C) for t > 0 to allow the heat transfer from the bed to the HTF after the onset of the exothermic reaction within the bed. Steam inlet pressure is set at 2 bar for which the equilibrium temperature is 550 °C. The reaction initiates with steam transport within 6

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Fig. 5. Average conversion and temperature along the bed axis of the reactor 'a' without fins (a) and with fins (b) during the dehydration (charging) process for ε = 0.5(rb=10 mm) .

Fig. 6. Temperature at the points within the bed (without fins) shown in Fig. 3(a) and average conversion during the hydration process for ε = 0.5(rb = 10 mm ).

temperature to drive the endothermic reaction. The thermal energy provided by the HTF is used to supply the endothermic heat of reaction. The endothermic reaction starts with heat transfer from HTF to the bed with release of reaction gas (steam). Hence, the temperature gradient across the wall, along with the kinetics parameters, determine the reaction rate and conversion time. In contrast, the hydration process is driven by the steam flow; as a result, at the beginning of the process, the reaction material experiences a large temperature jump. The heat released by the reaction is transferred to HTF that contributes to the acceleration of the reaction. In order to isolate the effect of the temperature difference between HTF inlet and bed on the conversion time, dehydration process is simulated with HTF inlet temperature of 650 °C, thus creating the same temperature difference of 200 °C across the bed wall as the hydration

process. The average conversion time in the reactor with and without fins are 5,500 s and 4,200 s, respectively, for ε = 0.5 as listed in Table 3 and depicted in Fig. S1. The conversion in the finned reactor is about 24% faster compared to that in the reactor without fins. Increasing HTF inlet temperature to 650 °C has profoundly improved the storage duration (the conversion time is reduced from 11,000 s to 5,500 s) compared with the inlet temperature of 550 °C, but the fin effectiveness has not been changed considerably. Table 3 also compares the effect of temperature difference across the bed wall on the conversion time during the dehydration process. The total conversion time for dehydration is still significantly greater than for the hydration with the same temperature gradient across the bed wall. During the hydration process, transport of the reaction gas into the bed is faster because of the set pressure at the inlet. 7

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Fig. 7. Average conversion and temperature along the bed axis of the reactor ‘a’ without fins (a) and with fins (b) during the hydration process for ε = 0.5 (rb = 10 mm ).

Higher bed pressure results in higher equilibrium temperature causing the temperature gradient across the bed wall to increase. In contrast, the steam generation within the bed during dehydration reaction causes the equilibrium temperature to rise resulting in reduced temperature gradient across the bed wall. The relation between pressure and reaction equilibrium temperature during hydration and dehydration processes influences the temperature gradient differently across the wall, and thus, affects the bed heat transfer and conversion contrarily.

velocity of 25 m/s. Despite the similar dimensions as in the reactor ‘a’ and the same operating conditions, the heat transfer enhancement with fins is not as profound as in the reactor ‘a’. For reactor ‘b’, the total conversion time for the hydration process is ~5400 s without fins and ~4000 s with the fins. These total conversion times are determined from the actual data as the elapsed time when the conversion reaches unity. Average conversion time is reduced by ~26% in the reactor ‘b’ whereas it is ~65% in the reactor ‘a’ with the same reaction bed size and initial/boundary conditions. This difference can be attributed to the fact that there is a smaller contact area between the reaction bed and HTF within the reactor ‘b’. The contact area is 0.02611 m2 in the reactor ‘a’ and 0.01229 m2 in the reactor ‘b’. The difference in percentage decrease in the average conversion (40.4%) is nearly equal to the percentage decrease in the contact area (~47%) of the wall and the reaction bed. The difference in the effect of fins between the reactor ‘a’ and the reactor ‘b’ is also visible in Figs. 9 and 10. The instantaneous isotherms during the hydration process with and without fins in the reactor ‘a’ and

3.3. HTE comparison of the reactors ‘a’ and ‘b’ We next investigate the influence of fins in the reactor ‘b’ (internal pipe configuration) for the hydration process. Time evolution of temperatures and the averaged conversion within the reactor are depicted in Fig. 8 for both with and without fins cases. The volume of the reaction bed is the same as in the reactor ‘a’. Size of the HTF channel in the reactor ‘b’ is determined in the same way as in the reactor ‘a’ with fixed Reynolds number of 1500 and HTF inlet

Table 3 Conversion time for various bed sizes of the reactor ‘a’ with and without fins (ε = 0.5). r b (mm)

10 10 10 15 20 25

vb (m3)

2.372e-4 2.372e-4 2.372e-4 5.432e-4 9.757e-4 1.534e-3

Process

Dehydration Dehydration Hydration Hydration Hydration Hydration

Temperature difference across the bed wall (THTF − TBed)

100 °C 200 °C 200 °C 200 °C 200 °C 200 °C

8

Conversion time (s) without HTE

With HTE

11,000 5,500 4,000 7,500 13,000 20,500

8,300 4,200 1,400 2,000 3,000 4,250

% decrease with HTE

27% 24% 65% 73% 77% 80%

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Fig. 8. Average conversion and temperature at points 2, 4 and 6 in the reaction bed of the reactor 'b' without fins (a) and with fins (b) during the hydration process for ε = 0.5.

‘b’ are depicted in Figs. 9 and 10. Fig. 9 shows temperature contours at t = 1500 s for the reactor ‘a’ with and without fins. It reveals that the reaction bed with fins has almost reached initial thermal equilibrium conditions with the removal of the heat. At the same instant, the minimum temperature in the reaction bed without fins on the right is above the initial thermal equilibrium temperature (350 °C) whereas the center of the bed is still close to the maximum reaction equilibrium temperature (550 °C) corresponding to the inlet steam pressure of 2 bar. Fig. 10 shows temperature contours of the bed in the reactor ‘b’ at

2,500 s during the hydration process. The temperature at the locations between the fins and away from the HTF channel is still close to the 500 °C whereas most of the reaction bed without fins is at a temperature close to the equilibrium temperature (550 °C) corresponding to the inlet steam pressure. Given the effect of fins in the reactor ‘a’ is far more significant than in the reactor ‘b’, further simulations were carried out for the different reaction bed sizes of the reactor ‘a’ for energy release step (hydration) only. The reaction bed sizes of rb = 15 mm , rb = 20 mm and rb = 25 mm are considered.

Fig. 9. Temperature (0C) contours of the reaction bed in the reactor ‘a’ with fins (left) and without fins (right) at t = 1500 s during the hydration process for ε = 0.5. 9

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Fig. 10. Temperature contours of the reaction bed in the reactor ‘b’ with fins (left) and without fins (right) at t = 2500 s during the hydration process for ε = 0.5.

3.4. Reaction bed size variations (reactor ‘a’)

Fig. 12 shows the average temperature profiles for various reaction bed sizes during hydration reaction for reactor ‘a’. It is obvious that the rate at which heat is removed increases with the proposed HTE. For the reactor ‘a’ withrb = 15 mm , the HTE reduce the time to reach initial thermal equilibrium by ~41%. In the same way, the removal of heat from the bed for rb = 20 mm and rb = 25 mm is completed in ~75% and 77% less time, respectively.

The poor thermal conductivity of the solid reaction materials imposes limitations on the diameter of the circular reaction bed, whereas the rate of steam transport poses limitations on the height of the bed. The designed HTE significantly overcomes the first limitation provided the bed is heated through outer wall owing to the larger contact area with HTF. The effect of the finned wall is, thus, further investigated by varying the size of the reaction bed with other parameters held unchanged. Fig. 11 shows the average conversion during the hydration process for various reaction bed diameters of the reactor ‘a’ with and without the HTE. The average conversion time is reduced by 73% with HTE for the bed size rb = 15 mm . As the radius of the reaction bed increases the finned wall becomes increasingly more effective. Average conversion time with HTE is reduced by 77% in the case of rb = 20 mm and by 80% in case ofrb = 25 mm . Table 3 summarizes the HTE effects in the reactor ‘a’ for the cases discussed above. The designed fin configuration can effectively overcome the problem of the slower heat transfer rate when the bed size is increased. Heat transfer during the charging and discharging process is vital in every TES system. It is particularly more important in TCES as slow rate of heat transport can reverse the reaction in some regions as was reported in our earlier study [17] on the same reaction system with a rectangular bed.

3.5. Porosity variation (reactor ‘a’) The value of the reaction bed porosity considered in this study is = 0.5. Under practical conditions, a higher value of the bed porosity is preferable as it will increase the bed permeability and consequently enhance the transport of the reaction gas within the bed. For comparison, a case with higher bed porosity = 0.8 considered for hydration reaction in the reactor ‘a’. The bed porosity variation affects both the bed permeability and the effective thermal conductivity of the reaction bed [13]. The bed permeability corresponding to porosity value = 0.8 would be 1.7 × 10−12, and the effective thermal conductivity would be 0.1 W/(m.K). Increasing the bed porosity will affect the transport of the reaction gas directly as depicted in Figs. 13 and 14 for dehydration and hydration, respectively. The reaction gas pressure in both figures is measured at the bottom of the reactor ‘a’ along its axis (point 1). This point is most remotely located from the reaction gas inlet/exit where

Fig. 11. Average conversion for rb = 15 mm, rb = 20 mm and rb = 25 mm without fins (solid lines) and with fins (dotted lines) in the reactor ‘a’ during the hydration process for ε = 0.5. 10

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Fig. 12. Average bed temperature without fins (a) and with fins (b) during the hydration process for various bed sizes of the reactor ‘a’ for ε = 0.5. (rb = 15 mm , rb = 20 mm and.rb=25 mm)

the effect of the porosity change on the gas pressure is maximum. The difference in the pressure due to the porosity change decreases as the steam exit is approached at the top of the bed. The effect of porosity change on steam pressure during dehydration (Fig. 13) is more significant than in hydration. This is because a constant high pressure applied at the inlet during hydration (Fig. 14) that drives the reaction gas into the bed. During dehydration, the pressure within the bed increases because of steam generation during the reaction, which then flows towards the exit at the top of the bed (Fig. 13). The bed porosity has a strong influence on the HTF outlet temperature. During the hydration, the bed with the lower bed porosity releases more heat; increasing the average outlet temperature of the HTF, as shown in Fig. 15. The effect is reversed for the dehydration reaction (see Fig. 16) where the bed with a lower porosity needs more heat to be transferred during the endothermic reaction, and thus the

HTF average outlet temperature is lowered for ε = 0.5 compared to ε = 0.8. Next, the effect of the HTE in the highly porous bed (ε = 0.8) is compared with the lower porosity bed discussed in earlier sections. A comparison is made for the hydration process in the reactor ‘a’ with and without HTE. Fig. 17 shows the temperature profiles at points 1, 4 and 7 along the bed axis of the reactor ‘a’, and the average conversion during the hydration process for ε = 0.8. The average conversion time without HTE is 1,850 that is reduced to around 850 s after using HTE. The percentage reduction in the overall conversion time is 54%. In the case of ε = 0.5, the percentage reduction in overall conversion time was 65% with HTE. Although the effective thermal conductivity is also reduced in case of higher porosity, the heat transport is enhanced because of unrestricted transport of the reaction gas within the bed resulting in the higher conversion rates and hence faster heat generation and

Fig. 13. Steam pressure at point 1 in the reactor 'a' during the dehydration process for = 0.5 and 11

= 0.8 with.rb = 10 mm

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Fig. 14. Steam pressure at point 1 in the reactor 'a' during the hydration process for ε 0.5 and ε = 0.8 with.rb = 10 mm

consumption during exothermic and endothermic reactions, respectively. Effectiveness of the fins for ε = 0.8 is less than for ε = 0.5 because there is less material in high porosity bed for the conversion compared to that in lower porosity bed. The dehydration process is simulated with 650 °C HTF inlet temperature for ε = 0.8, and the average conversion and temperature variation along the bed are depicted in Fig. S2. The charge (dehydration) conversion time in the module without and with fins are 3,900 s and 3,400 s, respectively. The fins reduce the conversion time by 13% for ε = 0.8 compared to 24% for ε = 0.5. Table 4 compares the conversion time of the dehydration and hydration for ε = 0.8 and 200 °C temperature difference between the HTF and bed. In Fig. S3, steam pressure at point 1 in low and high porosity bed is compared for the process with HTF inlet temperature of 650 °C. Comparison of Fig. S3 and Fig. 13 reveals that higher temperature difference helps to accelerate the endothermic reaction by creating higher pressure inside the bed. The average outlet temperature of HTF is shown in Fig. S4 for ε = 0.5 and 0.8 with HTF inlet temperature of 650 °C. The outlet temperature rises similarly as in case of HTF inlet temperature of 550 °C (see Fig. 16 and Fig. S4).

indirectly through heat exchanger walls. Heat exchanger wall with fins projecting into the solid reaction bed is considered. The vertical fins are arranged radially within the bed with two HTF channel configurations, one with HTF flowing in an outer annular channel (reactor ‘a’) and other with HTF flowing in a central pipe (reactor ‘b’). Charging and discharging processes are simulated in the reactor ‘a’ with and without HTE. The conversion time and the heat transfer in the reactor are influenced by the temperature gradient across the bed wall and how each process is executed. For the same temperature gradient across the bed wall, the total conversion time is reduced by ~24% and ~65% for the charging (dehydration) and discharging (hydration) process, respectively. Lesser effect of the HTE in charging process is attributed to the reaction initiation by heat transfer for the dehydration vs. the reaction initiation with steam transfer for hydration. This difference in the reaction initiation causes the temperature gradient across the bed wall to decrease during the dehydration reaction and increase during the hydration reaction. HTE is also applied to the reactor ‘b’ with the same reaction bed size, HTF inlet velocity, and Reynolds number. The reduction in the average conversion during the hydration is found to be 26%. Reduction in the average conversion times increased to 73%, 77% and 80% for the reaction bed radii of 15 mm, 20 mm, and 25 mm, respectively, within the reaction ‘a’. The reactor ‘a’ is then simulated using higher porosity of 0.8 and lower thermal conductivity of 0.1 W/ (m.K). For the same reaction bed size, the average conversion time is less with faster heat transfer than for the lower porosity of 0.5 during dehydration and hydration. Higher porosity facilitates the unrestricted transport of the reaction gas with higher rates of heat generation/ consumption during exothermic/endothermic reactions. However, in a reactor with higher porosity, the effectiveness of HTE is less for the

4. Conclusion Ca(OH)2/CaO system has great potentials to be used as TCES for CSPs owing to its higher energy density, storage and discharge temperature range, nontoxicity, availability, and cost. One of the major challenges faced by this system in its use as TCES is the poor thermal conductivity of the solid reactants/products. This study introduces HTE for a circular fixed reaction bed for Ca(OH)2/CaO system heated/cooled

Fig. 15. Average outlet temperature of HTF in the reactor 'a' during the hydration process for ε = 0.5 and ε = 0.8.(rb=10 mm) 12

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Fig. 16. Average outlet temperature of HTF in the reactor 'a' during dehydration process for ε = 0.5 and ε = 0.8.(rb=10 mm)

Fig. 17. Average conversion and temperature along the bed axis of the reactor 'a' without fins (a) and with fins (b) during the hydration process for ε = 0.8(rb=10 mm) .

Table 4 Conversion time for various bed sizes of the reactor ‘a’ with and without fins (ε = 0.8). r b (mm)

10 10

vb (m3)

2.372e-4 2.372e-4

Process

Dehydration Hydration

Temperature difference across the bed wall (THTF − TBed)

200 °C 200 °C

13

Conversion time (s) without HTE

(With HTE)

3,900 1,850

3,400 850

% decrease with HTE

13% 54%

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same bed size during both processes due to less material available for the conversion. The finned reactors introduced here significantly enhance the heat transport to overcome the limitation in the size of fixed Ca(OH)2/CaO reaction bed. It is concluded that in order to maximize the effect of the HTE the circular reaction bed must be heated from the outer wall. The design of the HTF channel, namely outer annular shell, used in this study, is chosen to minimize the computational costs. More efficient and practically feasible way of heating the circular reaction bed through the outer wall, however, is the crossflow configuration between the HTF and the steam flow. Future study will, therefore, consider this configuration with a single bed or multiple beds arranged in different arrays.

[8] [9]

[10] [11] [12]

Appendix A. Supplementary material

[13]

Supplementary data to this article can be found online at https:// doi.org/10.1016/j.applthermaleng.2019.114407.

[14]

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