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PROCEEDINGS OF ECOS 2019 - THE 32ND INTERNATIONAL CONFERENCE ON
EFFICIENCY, COST, OPTIMIZATION, SIMULATION AND ENVIRONMENTAL IMPACT OF ENERGY SYSTEMS
June 23-28, 2019, WROCLAW, POLAND
Effect of radiant properties and heat transfer
mechanisms on the thermal performance of a
Calcium Looping carbonator reactor
Pau Giméneza, Carlos Ortizb, Ricardo Chacarteguia and José Manuel Valverdeb
aEscuela Técnica Superior de Ingeniería, Universidad de Sevilla, Seville, Spain, pgimenez7@us.es (CA)
bFacultad de Física, Universidad de Sevilla, Seville, Spain, cortiz7@us.es
cEscuela Técnica Superior de Ingeniería, Universidad de Sevilla, Seville, Spain, ricardoch@us.es
dFacultad de Física, Universidad de Sevilla, Seville, Spain, jmillan@us.es
Abstract:
The promising Calcium-Looping technology can be integrated for thermochemical
energy storage (TCES) in Concentrating Solar Power plants, having the potential to
compete with the molten salt thermal storage system, the most cost-effective solution
nowadays. In the Calcium-Looping process, stored solar energy by the endothermic
calcination of limestone is released in the carbonator reactor, which is a key component
of the system. The complexity of this gas-solid reactor requires the use of simulation
tools to achieve a better understanding of the main parameters affecting its thermal
performance. Heat transfer inside a gas-solid reactor depends on complex mechanisms
that require a careful analysis. The present manuscript aims at modelling heat transfer in
the carbonator, which is considered as a downer reactor. One dimensional carbonator
reactor model is described and implemented, which allows assessing the effect of the
evolution of size dependent radiant properties of the particle-CO2 stream. The variation
of particle size over time due to either agglomeration or attrition is considered and its
impact on the performance of the system is addressed. The model considers carbonation
reaction kinetics as well as gas-particle wall convection and radiation heat transfer in
the downer reactor. The carbonator thermal performance is assessed under different load
scenarios. The ability to operate efficiently under partial-load conditions its fundamental
for releasing the stored energy coupling the demand requirements.
Keywords:
Energy Storage, Calcium looping process, Carbonator Downer reactor, 1-D modelling,
scale-up, particle radiant properties evolution
1. Introduction
Concentrated solar power (CSP) is an effective technology to convert solar energy into electricity.
However, the intermittency of large-scale solar energy supply to the electric grid poses significant
technical challenges because of the variability of the primary energy source. To provide
dispatchable electricity the development of cost-effective high capacity energy storage is a
fundamental issue to be addressed.
Current CSP technologies present energy-storage capability at the grid-scale, mainly based on
molten salt systems [1]. As an alternative, Thermochemical Energy Storage (TCES) is gaining
attention in the last years. TCES systems are based on reversible chemical reactions that store and
release energy in endothermic and exothermic steps, respectively. Among TCES, the Calcium-
Looping (CaL) process [2] is an attractive option mainly because of: i) its high energy storage
density; ii) its high energy release temperature; iii) the low cost, wide availability and non-toxicity
of natural raw materials used and iv) the large number of experimental works reported suggesting
its feasibility [3]–[5].
The CaL process as TCES system consists of the decomposition of CaCO3 by using solar energy to
produce CaO and CO2 by means of the endothermic calcination reaction. The products are stored
separately. When energy production is demanded, CaO and CO2 are sent to a carbonator reactor
wherein energy release occurs through the exothermic carbonation reaction (Eq. (1)).
CaO (s) + CO2 (g) →CaCO3 (s)
(1)
Several carbonator models have been already proposed in the literature [6]. Most of them consider
Fluidized Bed (FB) reactors as originally proposed for the CaL process for its application to capture
CO2 [7]. FB is a widely used technology in the industry, which allows reducing the risk that faces
implementing the CaL process. In the case of fine particles, with an important industrial interest
(i.e. cement and lime industry), fluidization is however difficult to achieve. As an alternative
downer reactors are presented as potential candidates [8].
Due the complexity of analysing the highly exothermic carbonation, accurate models are needed to
assess the potential of the technology before the development of pilot-scale prototypes. The present
work focuses on modelling the heat transfer mechanism inside of a CaL downer carbonator reactor.
A 1-D carbonator model which includes a rigorous heat transfer and kinetics analysis has been
developed to evaluate the carbonator behaviour under relevant operation conditions at pilot scale.
The model results will be used within the SOCRATCES H2020 project [9] to provide relevant data
for a kW-size prototype currently under development.
This paper is structured as follows: the modelled design is described in section 2. This section
includes the main assumptions; the heat transfer mechanisms (conduction, convection and
radiation); the carbonation kinetics and the implementation of the model. Section 3 contains the
main results and section 4 summarizes the conclusions of the analysis.
2. Design Model
A conceptual scheme of the CaL process integration in a CSP plant as TCES system is shown in
Figure 1. The process starts with the decomposition of CaCO3 to produce CaO and CO2 in an
endothermic calcination reaction. After heat recovery, CaO and CO2 streams are stored and ready to
be used on demand. In the power production mode, the reactants are sent to the carbonator reactor,
where the stored energy is released through the carbonation (the reverse reaction).
Figure 1. CCP-CaL conceptual scheme
The present work focuses on a downer carbonator reactor which consists of two concentric pipes
divided in two sections for a small-scale prototype. In the carbonator calcium oxide (CaO) particles
react with CO2 according to Equation (1). The heat released in the carbonation reaction is used to
preheat the inlet CO2 stream coming from the storage tank (in the first carbonation section) and to
run a thermal engine (in the second section) for power production. In the upper section a stream of
CaO
storage
CSP
Thermal
Power Input
CALCINER
CaCO3(s) →CaO (s) +CO2(g)
∆Hr0= +178 kJ/mol
CARBONATOR
CaO (s) +CO2(g) →CaCO3(s)
∆Hr0=-178 kJ/mol
Thermal Engine
Electric Power Output
CO2
storage
CO2 flows bottom-up while it is preheated from 25ºC. The external wall (3) is maintained at
constant temperature (880ºC) to ensure an adequate reaction extent. The preheated CO2 enters the
inner tube (the reactor) at the top. At this point the CO2 stream is mixed with the preheated CaO
particles, which temperature is calculated to achieve constant temperature (800ºC) of the mixture.
The stream of CO2 and solids flows through the carbonator reactor from top to bottom while the
carbonation reaction takes place.
In the lower section of the reactor, CO2 coming from the thermal engine within a closed-loop enters
at the bottom of the annulus space at 500ºC and flows bottom-up while absorbs heat from the
CO2/solids stream. The model considers the carbonation kinetics in the context of a 1-D reactor
model and yields the reaction rate and heat released.
Table 1. Carbonator reactor design parameters
Parameter
Value
Units
Internal carbonator diameter
D1
0.16
m
External carbonator diameter
D2
0.17
m
Internal annulus outer tube diameter
D3
0.19
m
Reactor length
L
4 (2 +2)
m
Carbonator thermal conductivity
k
16
W/(m K)
Emissivity of the reactor walls
εw
0.8
Reactor wall temperature in the preheating section
Tw3
880
ºC
Tin CO2+CaO to the carbonator
800
ºC
Tin CO2 from storage to preheating
25
ºC
Tin CO2 from thermal engine
500
ºC
Design pressure
P
1
bar
Median particle size, Dv (50)
ϕp
60
µm
2.1. Hypothesis and assumptions
In order to model the heat transfer mechanisms involved inside the carbonator reactor the following
assumptions have been made:
▪ The gas-particle domain is an entrained downer-flow where both species move at the same
speed. This is assumed because of the low gas velocity considered in this work to provide
enough residence time for the particles to react.
▪ The heat transfer through convection between the solids and the gas is neglected.
▪ The amount of CO2 captured in the carbonator by carbonation is not considered for the fluid
dynamics analysis. This is justified since the CO2 entering the reactor is well-above the
stoichiometric amount and therefore a relatively small difference exists between the inlet and
outlet mass flows.
▪ Heat transfer (radiation and convection) takes place in the radial direction between the
solids/gas mixture and the wall tube. This implies that the radiation between the reactor wall
at one section and the adjacent sections is not considered, neither between the solids/gas
mixture at one section and adjacent volumes.
▪ A one-dimensional model is considered with constant and uniform temperature as well as
constant and uniform particle concentration and distribution in each control volume.
▪ Axial heat conduction in the fluid is negligible
2.1. Conduction and convection
Conduction heat transfer occurs through the reactor wall. The resistance to thermal conduction of a
steel cylinder is considered with the dimensions and thermal conductivity specified in Table 1.
The model considers heat transfer by convection between the external annulus space and the CO2
stream in the preheating and the thermal engine sections, and between the reactor wall and the
CO2/solids stream.
Modeled Design
From thermal engine
(500ºC)
To thermal engine
CO2 preheating (25ºC)
CO2+CaO particles
(800ºC)
There are two walls at the concentric annular duct (wall 2 and 3) and both are involved in heat
transfer to the CO2 flowing across the annulus space. Two fundamental thermal boundary
conditions can be used to define the boundary conditions present in the prototype [10]. The thermal
boundary condition for the upper section (preheating of CO2) consists of a uniform temperature at
both walls. A fully developed laminar flow in a circular tube annulus with one surface insulated and
the other at constant temperature is the most suitable condition for both walls (2 and 3) of the upper
section [11]. The hydraulic diameter Dh (4 times the cross-sectional area of the flow divided by the
wetted perimeter of the cross-section) is calculated for the annulus space as the characteristic length
for the external (3) and internal (2) Nusselt number. The internal (2) and external (3) wall Nusselt
number are linearly extrapolated between the reported values at D2/D3=0.895.
Table 2. Nusselt number for a fully developed laminar flow in a circular tube annulus with: one
surface insulated and the other at constant temperature (on the left); uniform heat flux maintained
at both surfaces (on the right) [11].
D2/D3
Nu2
Nu3
D2/D3
Nuii
Nuoo
θ2*
θ3*
0.5
5.74
4.43
0.8
5.58
5.24
0.401
0.299
0.895
5.045
4.77
0.895
5.49
5.31
0.375
0.321
1
4.86
4.86
1
5.385
5.385
0.346
0.346
A fully developed laminar flow in a circular tube annulus with uniform heat flux kept at both
surfaces (wall 2 and 3) is used as the thermal boundary condition for the thermal engine section
(bottom section of the reactor) based on the work by Incropera and DeWitt [11]. If uniform heat
flux conditions exist at both surfaces, the Nusselt number may be computed from [11]:
(2)
Where hwi is the heat transfer convection coefficient between the wall ‘i’ and the fluid, and k is the
thermal conductivity of the fluid. The Nusselt number of the CO2/solids stream flowing through the
carbonator reactor has been calculated by considering a fully developed laminar flow within the
tubes assuming a negligible effect of the particles. The most reasonable conditions for the upper
section of the carbonator are a fully developed laminar flow and a constant surface temperature. The
Nusselt number for this case is equal to 3.66 independently of the Reynolds number, Prandtl
number, and axial location [11].
The lower section of the reactor (thermal engine section) is characterized by uniform surface heat
flux and laminar fully developed conditions. In this case the Nusselt number is constant (and equal
to 4.36), also independently of the Reynolds number, Prandtl number, and axial location [11].
Even though the selected correlations are valid only when both the velocity and temperature profiles
are fully developed and this might not be the case for the analysed reactor due to its length, the
calculated values for the convective heat transfer coefficient are underestimated, which means that
the performance of the system can be expected to be higher when the effect of the entry region on
the heat transfer convection coefficient is considered.
2.2. Radiation
In order to model the thermal radiation exchanged between the CO2/solids cloud and the reactor
wall, the CO2/solids emission and absorption coefficients must be determined (εg+p and αg+p,
respectively). High CaO particle loading leads to high thermal emissivity and absorptivity of the
mixture.
2.2.1. CO2 emissivity
The total radiant energy emitted by the CO2 can be calculated if the spectral emissivity ελ is known,
which has to be integrated over the wavelength λ [12]. The total emissivity εg depends on the
temperature, the thickness of the layer and partial pressure of the gas. For the simulated reactor the
partial pressure is equal to the total pressure and equal to 1 atm.
The total emissivity of CO2 can be determined using the “weighted sum of gray gases model’’.
Leckner (1972) [13] reports empirical correlations for the total emissivity derived from calculations
summing narrow band behaviour over the spectrum for CO2. In Leckner’s correlations and
equations, p is in bar, and lmb is in centimetres [14]. The parameter lmb is the mean beam length of
radiation within the relevant geometry calculated based on Equation 3, where V is the gas volume
and A is the heat transfer area for the gas volume. The correlation equation is:
(3)
where
and the different coefficients are tabulated [14]. The
emissivity depends solely on the equivalent layer thickness and the state of the gas (
CO2 temperature and pressure). The absorptance depends additionally on the
wall temperature, where the correction factor is used in this
case.
(4)
The emissivity and absorptivity of the CO2 stream, required to evaluate the emissivity and
absorptivity of the CO2-CaO mixture, is represented in Figure 2 as a function of the wall
temperature (1) for different gas temperatures. The emissivity of the CO2 stream presents a
maximum for a temperature ~1000 K. Nevertheless the variation of the emissivity is low for the
studied temperature range.
Figure 2. Emissivity (ε) and absorptivity (Av) of CO2 as a function wall temperature (Twall) for three
different gas temperature.
2.2.2. CO2 and CaO particles stream emissivity
The emissivity of a cloud of limestone suspended in a CO2 stream is calculated based on VDI Heat
Atlas, Part K [12]. The heat flux from the gas-particle mixture to the wall, , is calculated
from:
(5)
The expression is valid if the temperature, density, and concentration of the gas and particles are
constant in space, and its application requires knowledge of the gas emissivity and absorptance. ‘σ’
is the Stefan–Boltzmann constant. The total emissivity of a gas-particle mixture can be described
as:
(6)
Where
700 850 1000 1150 1300
0.08
0.10
0.12
0.14
0.16
Wall Temperature Twall [K]
e and Av [-]
e Tg= 700 K
AvTw
e Tg=1000 K
AvTw
e Tg=1300 K
AvTw
In a similar manner the absorptivity can be calculated:
(7)
Where . Here Lp is the particle loading, in kg/m3 and A is the
specific projected surface area of the particles, in m2/kg. Particle absorption (Qabs) and scattering
(Qbsc) coefficients for limestone have been extracted from the graphical information reported in
[12].
Figure 3. Absorption and Backscattering coefficients for limestone as a function of mean particle
diameter (on the left). Purple triangles are the values for 60μm size limestone particles (left). γ and
β parameters as a function of mean particle diameter required to calculate the emissivity and
absorptivity of the gas and particles (εg+p and αg+p) (on the right). Extracted from VDI heat atlas
[12]
The absorption and scattering coefficients Kabs,g and Kemi,g can be determined as
and
2.3. Carbonation kinetics
The energy released in the exothermic carbonation reaction is transferred to the CO2-particles
stream and then to the carbonator reactor wall. Due the required residence time of the CaO particles,
a low CO2 velocity inside the carbonator is imposed. Consequently, the convective heat transfer
coefficient is also small and therefore heat transfer is clearly dominated by radiation.
The carbonation energy released in the upper part of the carbonator is used to preheat the CO2
stream while the energy released at the bottom section is used to heat up a CO2 stream used to run a
thermal engine for power production. Depending of the residence time of the CaO particles and
temperature of the streams the heat from carbonation can be totally released in the first section of
the carbonator, along the whole reactor or not totally released if the particles residence time is not
high enough for the reaction to be fully achieved.
The carbonation kinetics model used is based on a Prout-Tompkins model functionmodified by
introducing a conversion limit [15]. The conversion at the end of the fast reaction-controlled
stage mainly depends on the number of cycles, the calcination and carbonation conditions and the
CaO precursor considered [16]. Under the specific conditions considered in this paper (calcination
and carbonation under full CO2 atmosphere at 950ºC and 800ºC respectively), most of the
carbonation occurs in the fast reaction-controlled stage while the contribution from the diffusion-
controlled stage is negligible [16]. A conservative residual conversion value of =0.15 is
considered for the simulations [17]. In the case of fine particles (of size below ~50 m), for which
carbonation in the fast reaction-controlled phase is not limited by pore plugging, this residual value
could be as high as ~0.5 [16].
The temperature dependence of the reaction rate and consequently the extent of the reaction are
considered. The pre-exponential factor (=74666 s-1) has been inferred from experimental
tests.
0
0,2
0,4
0,6
0,8
1
1,2
1,4
0 100 200 300
Qabs & Qbsc [-]
dp·[10-6] m
Qabs (Limestone)
Qbsc (Limestone)
0,0
0,5
1,0
1,5
2,0
2,5
3,0
3,5
4,0
0 100 200 300
βand γ
dp·[10-6] m
β
γ
(8)
The model assumes a linear evolution of the carbonation degree up to X=0.5·Xk which slope is
determined by 0.5·Xk/ t0 , with t0=2 / r(T,P). From this point X evolves with Equation 8. The CO2
partial pressure at equilibrium and values of enthalpy-entropy changes in the chemical
decomposition and desorption stage, and activation energies have been extracted from Ortiz el al.
[15] with the equilibrium pressure
[18].
2.4. Heat transfer model
The energy balance is calculated in each control volume: “ge” (external flow), “gi” (internal flow),
as well as in the external and internal surfaces of the reactor wall. The external wall temperature is
kept at a constant value in the preheating section, which is calculated by the model in order to
achieve the desired CO2 temperature at the reactor inlet (800ºC in the base case). For j=1 to nwall
(number of sections of the reactor tube) the energy balance at the annulus space can be written as:
(9)
Where the different heat flows (
is convection from the wall ‘i’ to the CO2 flow,
is the
net radiation leaving the wall “i”) in the equation are calculated from:
(10)
The temperature of each control volume is the average between the inlet and outlet
temperatures
. K23 is the radiant constant between two concentric cylinders
with emissivity εw for the internal surface of the external cylinder (3) and the external (2) surface of
the carbonator tube. The required power to maintain the wall at constant temperature is calculated
by
. The energy balance at the external (2) and internal (1) wall surface can
be written as:
;
;
(11)
where RCD is the thermal conduction resistance of a steel cylinder. The energy balance at the reactor
control volume is given by:
(12)
Which considers the enthalpy of the CaO particles and CO2. Kinetic and potential energy variations
considered in the Equation 20 can be neglected compared to the enthalpy changes taking place in
each control volume. Figure 4, on the left, shows the control volumes where the energy balance is
calculated for the preheating section (upper section of the carbonator) and the thermal engine
section (lower section of the carbonator). The diagram on the right shows the effect of the different
variables on the heat transfer mechanism considered in the model.
Figure 4. Control volumes for the energy balance in each carbonator section. Model design and
structure: gn: reaction enthalpy released; w: wall; i: interior; e: exterior; g: gas (left). Model
interdependences (right).
3. Results
3.1. Base case
As a base case the model is applied to the study of a 4.5 kWt downer carbonation reactor. This base
case considers a mass flow of the different streams as indicated in Table 3 (100% flow) where the
mass flow of CO2 (20 kg/h) is the stoichiometric mass flow required to achieve a complete reaction
of the CaO (25.48 kg/h). However, if we consider that the residual CaO conversion is X=0.15 and
thus a maximum amount of 15% of CaO reacts, the amount of CO2 entering the reactor is 6.67
times higher than the stoichiometric amount required to reach this residual conversion. Under these
conditions the power required to preheat the CO2 stream and to achieve a carbonation of the CaO
particles up to their residual conversion has been calculated. The mass flow rate of the heat transfer
fluid (HTF, CO2) sent to thermal engine is the sum of the previous two (45.48 kg/h).
Figure 5 shows the temperature profile along the carbonator reactor and annulus space. The CO2
stream enters at the bottom of the preheating section (reactor height 2 m) at 25ºC and it is heated up
to achieve 869ºC at the outlet, just before entering the carbonator at the top. CaO particles at 730ºC
are mixed with the CO2 stream. The mixture enters the carbonator at 800ºC. High solids storage
temperature is considered in this model as in previous works [17] and the storage temperature is
calculated based on the CO2 preheating section outlet temperature. Note that assuming that the CO2
enters the reactor at ambient temperature is the most conservative situation, which will occur at the
starting-up or if CO2 comes directly from storage. After the process starts, the CO2 exiting the
carbonator at high temperature (since it is in excess over the stoichiometric value) will be
recirculated (after solids separation) and mixed with the CO2 coming from the storage, which leads
to a much higher CO2 inlet temperature [2]. The CO2 and CaO particles are mixed up at the top of
the carbonator and flow in the same stream along the downer reactor. As shown in Figure 5, the
reactor is cooled down by HTF (CO2) preheating.
The gas and solids residence time (~7 s) depends on the CO2 mass flow rate and its temperature,
which affects its density. As pointed out from the assumptions made, it is assumed that the solids
and gas are moving at the same velocity through the downer reactor.
The extent of carbonation X as a function of reactor length is plotted also in Figure 5. As may be
seen, CaO particles leave the first 2 m of the reactor with a carbonation degree X~ 0.072 indicating
w3(i) w2(i) w1(i)
ge(2i-1)
ge(2i)
P(i) gn(i)
ge(2i+1)
gi(2i-1)
gi(2i)
gi(2i+1)
ge(2i-1)
ge(2i) gn(i)
ge(2i+1)
gi(2i-1)
gi(2i)
gi(2i+1)
QCVw3
QRDw3
QCVw2
QRDw2
QCVw1
QRDw1
QCVw3 QCVw2 QCVw1
QRDw3 QRDw2 QRDw1
w3(i) w2(i) w1(i)
QCD21
QCD21
Øp
QRD
QREAC
QCD
Lp
QCV
CO2
s
Tg
Tw
lmb εg
Av
εw
αg+p
εg+p
v
Di
hCV
r
Tg
X
Tg
Tw
Energy
Balance
that carbonation up to half of the residual value (X=0.15) takes place in the preheating section. This
means that CaO particles exits the first 2 m of reactor after having already reached half of their
maximum conversion in the fast reaction-controlled phase. Table 4 shows the results for the
simulated base case.
Figure 5. Carbonator reactor temperature profile (ge: external gas; gi internal gas; w3: external
wall).The carbonation degree is also represented as a function of the reactor height.
The slope of the extent of carbonation X is reduced as the CO2 and CaO particles reach a
temperature close to the equilibrium temperature (~896ºC) where the reaction is low. At this point
the extent of carbonation X speeds up as heat is removed from the CO2 and CaO particles stream.
For this reason the slope of X increases as the CO2 and CaO particles reach the coldest section of
the preheated CO2.
3.2. Effect of CO2 and CaO mass flow rate
In this section the effect of the CO2 and CaO mass flow rate is evaluated. The CO2 and CaO mass
flow from the base case are multiplied by 0.875, 1.5 and 2 respectively (Table 3).
Table 3. Simulation cases to evaluate the effect of mass flow rate on the performance of the system.
87.5%
100% base case
150%
200%
Mass flow CO2 [kg/h]
17.5
20
30
40
Mass flow CaO [kg/h]
22.30
25.48
38.22
50.96
Mass flow HTF thermal engine [kg/h]
39.8
45.48
68.22
90.96
When the mass flow of the CO2 is increased the velocity of the gases increases and the residence
time in each section is reduced. The CO2 outlet temperature of the preheating section is reduced,
which means that the CaO particles must be fed at higher temperature to achieve the desired
temperature of the mixture at the carbonator inlet (800ºC). Figure 6 shows the carbonation degree as
a function of the reactor height for the four cases analyzed.
Figure 6. Carbonation degree as a function of the reactor height for different mass flow rate
simulated.
0 0.5 1 1.5 2 2.5 3 3.5 4
0
100
200
300
400
500
600
700
800
900
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
Reactor Height [m]
Tempeature [ºC]
Twe
X
XX
Tge
Tge
Tgi
Tgi
CO2 preheating
HTF (CO2) to thermal engine
0
0,03
0,06
0,09
0,12
0,15
01234
X
Reactor Height [m]
X (0.875m)
X (1m BASE CASE)
X (1.5m)
X (2m)
As may be seen in Figure 6, by increasing the mass flow rates of all components 1.5 times, the
particles residence time is not high enough to complete the reaction, and therefore a part of energy
is not released. The mass flow rates should be optimized to ensure a complete reaction, for instance,
reducing the CO2 mass flow to CaO mass flow ratio, which in the simulated case is clearly over the
stochiometric value taking into account the maximum CaO conversion (X=0.15). In other words,
the optimum mass flow of CO2 entering the carbonator has to be higher than the stochiometric
amount and with a maximum value that ensure an enough residence time of the particles to achieve
the maximum carbonation achievable. Table 4 summarizes the simulations results by varying the
total mass flow rates.
Table 4. Summary of the results: base case vs. different CO2 and CaO mass flow rate and base case
with different particle size.
Mass flow rate of CO2 and CaO
87.5%
100%
150%
200%
100%
100%
CaO particle size
μm
60
60
60
60
30
120
1
Reaction power release
W
2936
3339
4773
5812
3341
3336
2
Reaction power release in the
upper section
W
1495
1613
2051
2421
1624
1583
3
Electrical power supply in the
CO2 preheating section
W
4104
4749
7019
8641
4732
4793
4
Maximum electrical power supply
in the CO2 preheating section per
meter
W/m
4983
5004
5013
5112
4983
5061
5
Preheating power absorbed by the
CO2 flow
W
4584
5208
7360
8809
5207
5210
6
Power supplied to the thermal
engine
W
4140
4541
5762
6559
4574
4436
7
Sensible heat transferred from the
CaO flow
W
846.7
833.9
665.1
456.3
858
761
8
X at carbonator L=2m
0.076
0.072
0.061
0.054
0.072
0.070
9
X at carbonator L=0m
0.149
0.149
0.142
0.129
0.149
0.149
10
Maximum temperature at the CO2
and CaO particles stream
ºC
887.1
886
882.1
881.2
885.8
886.4
11
Minimum temperature at the CO2
and CaO particles stream
ºC
658.9
678.4
735.4
766.8
674.9
689.1
12
Residence time in the upper
section
s
3.9
3.4
2.3
1.7
3.4
3.4
13
Residence time at the carbonator
s
8.0
7.0
4.6
3.5
7.0
7.0
14
Maximum global heat transfer
coefficient (Umax) at the thermal
engine section referred to the
internal wall surface Aw1
W/(m2
ºC)
38.3
38.0
36.8
35.8
39.1
35.0
15
Minimum global heat transfer
coefficient (Umin) at the thermal
engine section referred to the
internal wall surface Aw1
W/(m2
ºC)
24.6
25.1
26.6
27.32
25.7
23.3
16
Outlet temperature to the thermal
engine
ºC
809.2
797.2
752.8
716.8
799.3
790.5
17
Outlet temperature at the
carbonator
ºC
658.9
678.4
735.4
766.8
674.9
689.1
18
Inlet CaO particle temperature
ºC
725.1
729.7
773.7
847.2
729.8
729.4
19
Average εg+p
0.32
0.32
0.32
0.32
0.34
0.27
20
Average αg+p
0.32
0.32
0.32
0.32
0.34
0.27
As can be seen in Table 4, the HTF temperature exiting the carbonator varies in the range 809.2-
716.8ºC when the CO2 and CaO mass flow increases. The case with lower mass flow rates
(87.5%) leads to the higher carbonator degree X at carbonator L=2 m. As the mass flow rate
increases the power required to preheat the CO2 stream increases at a faster rate than the power
supplied to the thermal engine. This confirms that to increase the electric power production of the
system the CO2/CaO mass flow ratio must be optimized instead just increased.
3.3. Effect of CaO particle size
The CaO particle size is a critical parameter because it influences the reactivity and the carbonation
conversion as well as the radiation heat transfer mechanism consequently the effect of the particle
size on the performance of the system is addressed in this section.
The reactivity of CaO due to the conditions of high CO2 concentration and high temperature
potentiate the blocking of pores of the CaO particles. This mechanism limits the reactivity of the
particles if their size is greater than approximately 50 μm, so by using fine particles the CaO
conversion (and therefore the system efficiency) can be highly enhanced [16]. This is an important
advantage for using downer reactors (which allows operate with fine particles) instead FB reactors.
In the case of fine particles, the attrition is not very relevant. However, the agglomeration can be an
important effect to consider because the intensity of the Van de Wall forces is greater than the
weight of the particles when the size is reduced below ~ 50 μm. The ratio between both forces
(VdW/Weight) increases proportionally to the inverse of the size of the particles raised to the cube
[19].
The variation of particle size over time due to either agglomeration or attrition is considered and its
impact on the performance of the system is assessed. Two main cases are analysed: a lower particle
size (ϕp=30 μm) produced by attrition or when smaller particles are used; and larger particles
(ϕp=120 μm) to consider the effect of agglomeration of CaO fine particles over time. Figure 7
(right) shows the effect of CaO particle size on the emissivity of the CO2-particle stream for
different gas temperatures for the base case conditions. The lower the particle size the higher
emissivity of the mixture and this favours the radiation mechanism over convection. Figure 7 (left)
shows the temperature dependence emissivity and absortivity of the CO2-CaO mixture for the base
case.
Figure 7. Emissivity and absorptivity of the CO2-CaO mixture vs Twall for different gas-particle
temperature. (ϕp=60 μm) (left). Effect of CaO particle size on the emissivity of the CO2-particle
stream for different gas temperatures (right).
The effect of the particle size over the reaction extent is shown in Figure 8. As may be seen, the
effect of the particle size in the reactor is not too relevant. This is important since, on one hand, it
makes possible use a wide range of particles size and on the other hand reduces the potential
negative effects of agglomeration and attrition phenomena.
700 800 900 1000 1100 1200 1300
0.20
0.24
0.28
0.32
0.36
0.40
Wall Temperature Twall [K]
agspa, egspa
agspa (Tg=700 K)
egspa 700 K
agspa (Tg=1300 K)
egspa 1300 K
agspa (Tg 1000 K)
egspa 1000 K
700 800 900 1000 1100 1200 1300
0.22
0.26
0.30
0.34
0.38
Temperature [K]
egspa
egspa Fp = 30 mm
egspa Fp = 60 mm
egspa Fp =120 mm
500
600
700
800
900
0 0,5 1 1,5 2
Temperature [ºC]
Reactor Height [m]
Tgi (30 μm)
Tge (30 μm)
Tgi (120 μm)
Tge (120 μm)
20
25
30
35
40
0 0,5 1 1,5 2
Global heat transfer
coefficient U [W/(m2ºC)]
Reactor Height [m]
30 μm
60 μm
120 μm
Figure 8. Carbonator reactor temperature profile for the external (ge) and internal (gi) flow as a
function of the reactor height in the thermal engine section. Base case with particle size of ϕp=30
μm (attrition) and ϕp=120 μm (agglomeration (left). Effect of the particle size on the global heat
transfer coefficient U [W/ (m2·ºC)] in the thermal engine section of the carbonator as a function of
the reactor height (right).
Despite there is a small change in the overall process extent with the particles size variation, the
global heat transfer coefficient (U) at the thermal engine carbonator section present appreciable
differences. As shown in Figure 8 (right), the higher the average particle diameter the lower U
value. This is a consequence of the lower emissivity of larger particle size (Figure 7).
Table 4 summarizes the main simulations results by varying the average particle size. As previously
discussed, small differences exist in these cases. For a fixed value of HTF mass flow entering the
carbonator, the stream temperature at the reactor exit varies between 799 and 790ºC, and therefore it
would produce almost the same power in the thermal engine for all cases. In the same line, in all
cases occurs a similar overall reaction extent. Remarkably, the model assumes that CO2 and CaO
particles evolve along the reactor at the same velocity. In a real case, the particles velocity will
present certain independence of the gas velocity and therefore the particle size will condition the
particles residence time and therefore the overall carbonating extent and the thermal power released.
4. Conclusions
A novel model has been developed to assess the effect of different design and operation parameters
on the heat released in a carbonator reactor which was previously stored, for example, by
calcination using concentrated solar power. The effects of reactor size, operating conditions (P, T)
or even changes in CaO precursors can be analysed from this model. The present work analyses the
influence of changes in CaO particle size due to either agglomeration or attrition on the energy
released to the thermal engine for power production. Mass flow rates effects are also studied.
The results obtained suggest that the scale-up of the process is feasible keeping in mind the
assumptions and simplifications made. Simulation results confirmed that successful operation of a
large-scale Calcium Looping unit requires an optimum heat transfer design including a detailed
characterisation of each heat transfer mechanism.
For the conditions considered it is inferred that changes in CaO particle size have a moderated
impact on the global heat transfer coefficient in the thermal engine section, which determines the
power supplied to the thermal engine. The effect of particle size on the reaction extent is negligible
for the proposed downer reactor. However, the reduction in the particle size might mitigate the
adverse effect of pore blockages, which is extremely important in the carbonation conditions for
particle diameter higher than 50 μm. It might allow the system to reach a higher carbonation
conversion residual value and therefore notably higher overall process efficiency.
As an energy storage system, the CaL process allows a variable power production to match the
electricity demand requirements. Results suggest that increasing the mass flow of the streams in the
same ratio does not necessarily conduct to a higher power production. From an on-design operation,
to increase the power production due an eventual increase in the demand, the mass flow rates of
CaO, CO2 and HTF (sent for the thermal engine) must be optimised independently. Further research
is needed to analyse several operation conditions and to verify up to which extent the assumptions
made for implementing model are valid.
Acknowledgement
The research leading to these results has received funding from the European Union’s Horizon 2020
research and innovation programme under grant agreement No 727348, project SOCRATCES. The
Spanish Government Agency Ministerio de Economia y Competitividad (MINECO-FEDER funds),
has supported the participants through contracts CTQ2017-83602-C2 (-1-R and -2-R). The
University of Seville has supported the corresponding author through a PSI contract at the Energy
Engineering Department.
References
[1] National Renewable Energy Laboratory (NREL), “Concentrating solar power projects.
National Renewable Energy Laboratory (NREL),” 2016. [Online]. Available:
http://www.nrel.gov/csp/solarpaces/power_tower.cfm. [Accessed: 12-Jan-2016].
[2] R. Chacartegui, A. Alovisio, C. Ortiz, J. M. Valverde, V. Verda, and J. A. Becerra,
“Thermochemical energy storage of concentrated solar power by integration of the calcium
looping process and a CO2 power cycle,” Appl. Energy, vol. 173, pp. 589–605, 2016.
[3] J. M. Valverde and S. Medina, “Limestone calcination under calcium-looping conditions for
CO2 capture and thermochemical energy storage in the presence of H2O: An in situ XRD
analysis,” Phys. Chem. Chem. Phys., vol. 19, no. 11, pp. 7587–7596, 2017.
[4] B. Sarrión, A. Perejón, P. E. Sánchez-Jiménez, L. A. Pérez-Maqueda, and J. M. Valverde,
“Role of calcium looping conditions on the performance of natural and synthetic Ca-based
materials for energy storage,” J. CO2 Util., vol. 28, no. June, pp. 374–384, 2018.
[5] M. Benitez-Guerrero, J. M. Valverde, P. E. Sanchez-Jimenez, A. Perejon, and L. A. Perez-
Maqueda, “Multicycle activity of natural CaCO3 minerals for thermochemical energy
storage in Concentrated Solar Power plants,” Sol. Energy, vol. 153, pp. 188–199, 2017.
[6] I. Martínez, G. Grasa, J. Parkkinen, T. Tynjälä, T. Hyppänen, R. Murillo, and M. C. Romano,
“Review and research needs of Ca-Looping systems modelling for post-combustion CO2
capture applications,” Int. J. Greenh. Gas Control, vol. 50, pp. 271–304, 2016.
[7] T. Shimizu, T. Hirama, H. Hosoda, K. Kitano, M. Inagaki, and K. Tejima, “A twin fluid-bed
reactor for removal of CO2 from combustion processes,” Chem. Eng. Res. Des., vol. 77, no.
1, pp. 62–68, 1999.
[8] M. Spinelli, I. Martínez, and M. C. Romano, “One-dimensional model of entrained-flow
carbonator for CO2capture in cement kilns by Calcium looping process,” Chem. Eng. Sci.,
vol. 191, pp. 100–114, 2018.
[9] “Socratces Project | Energy Storage Technologies Viable & Sustainable.” [Online].
Available: https://socratces.eu/. [Accessed: 27-Feb-2019].
[10] W. M. Rohsenow, J. R. Hartnett, and Y. I. Cho, Hand Book of Heat Transfer. 1998.
[11] F. P. Incropera, D. D. P., T. Bergman, and A. Lavine, Fundamentals of Heat and Mass
Transfer, 5th ed. New York, 2007.
[12] VDI Heat Atlas. Düsseldorf Germany: Springer, 2010.
[13] B. Leckner, “Spectral and total emissivity of water vapor and carbon dioxide,” Combust.
Flame, vol. 19, no. 1, pp. 33–48, 1972.
[14] R. Siegel, Thermal Radiation Heat Transfer, Fourth Edition. Taylor & Francis, 2001.
[15] C. Ortiz, J. M. Valverde, R. Chacartegui, and L. A. Perez-Maqueda, “Carbonation of
Limestone Derived CaO for Thermochemical Energy Storage: From Kinetics to Process
Integration in Concentrating Solar Plants,” ACS Sustain. Chem. Eng., vol. 6, no. 5, pp. 6404–
6417, 2018.
[16] M. Benitez-Guerrero, B. Sarrion, A. Perejon, P. E. Sanchez-Jimenez, L. A. Perez-Maqueda,
and J. Manuel Valverde, “Large-scale high-temperature solar energy storage using natural
minerals,” Sol. Energy Mater. Sol. Cells, vol. 168, no. November 2016, pp. 14–21, 2017.
[17] C. Ortiz, M. C. Romano, J. M. Valverde, M. Binotti, and R. Chacartegui, “Process
integration of Calcium-Looping thermochemical energy storage system in concentrating
solar power plants,” Energy, vol. 155, pp. 535–551, 2018.
[18] I. Barin, “Thermochemical data of pure substances VCH, Weinheim (1989),” 1989.
[19] A. Castellanos, J. M. Valverde, and M. A. S. Quintanilla, “Aggregation and sedimentation in
gas-fluidized beds of cohesive powders,” Phys. Rev. E - Stat. Physics, Plasmas, Fluids,
Relat. Interdiscip. Top., vol. 64, no. 4, p. 7, 2001.
