CHEMICAL ENGINEERING TRANSACTIONS  
 

VOL. 76, 2019 

A publication of 

 

The Italian Association 
of Chemical Engineering 
Online at www.aidic.it/cet 

Guest Editors: Petar S. Varbanov, Timothy G. Walmsley, Jiří J. Klemeš, Panos Seferlis 
Copyright © 2019, AIDIC Servizi S.r.l. 

ISBN 978-88-95608-73-0; ISSN 2283-9216 

Study of a Drop−Tube Carbonator Reactor for CSP−Calcium 

Looping Based on a Heterogeneous Reaction Model 

Evgenios Karasavvas, Kyriakos D. Panopoulos*, Simira Papadopoulou, Spyros 

Voutetakis 

Chemical Process and Energy Resources Institute (CPERI), Centre for Research and Technology – Hellas (CERTH), 57001 

Thermi-Thessaloniki, Greece  

panopoulos@certh.gr 

Calcium-looping (CaL) is a competitive thermochemical energy storage (TCES) alternative allowing 

uninterrupted power production from solar heat. In this work, a model-based approach of the very fast 

carbonation reaction (CaO (s)+CO2 (g)→CaCO3 (s)) is employed to simulate a drop-tube as the carbonator 

reactor. A one-dimensional (1D) heterogeneous plug flow reactor (PFR) model for gas and solid phase is 

developed at steady state conditions. The model handles gas and solids as two distinct phases characterized 

by individual physical properties each. Model simulations export useful information about crucial process 

variables variation along the reactor. A case study of carbonator operation is examined through process 

simulation subjected to different CO2/CaO molar ratios at the inlet of the reactor. In this way, the capabilities of 

the model are demonstrated related to different operating conditions providing insights for preliminary designs 

of similar reactors. 

1. Introduction 

Renewable energy sources contribute to global sustainability by massively cutting greenhouse gases emissions 

and helping to mitigate climate changes. Among others, solar energy stands as a free and endless source of 

energy that can be converted into electricity by means of a concentrated solar power plant (CSP). Thermal 

energy storage (TES), phase change materials (PCM) and thermochemical energy storage (TCES) systems are 

established as the most interesting and applicable energy storage technologies for CSPs 

(Chacartegui et al., 2016). The calcium-looping process proved as a promising technology for high energy 

storage efficiency in concentrating solar power plants through thermochemical energy storage 

(Karasavvas et al., 2018). The high energy density of the reversible and high endothermic/exothermic 

calcination-carbonation reaction system (Eq(1)), as well the low price, nontoxicity and wide availability of natural 

CaO precursors have driven the interest towards this application. 

𝐶𝑎𝐶𝑂3 (𝑠)  ↔ 𝐶𝑎𝑂 (𝑠) + 𝐶𝑂2 (𝑔)      𝛥𝛨𝑟𝑥𝑛
0 ≅ 178 𝑘𝐽/𝑚𝑜𝑙 (1) 

In SOCRATCES project (SOCRATCES Project, 2019), a prototype plant is being designed and constructed to 

demonstrate the proof of concept of the CSP-CaL integration. In the prototype operation, solar energy is 

exploited in the calcination section where natural limestone (CaCO3) decomposes towards CaO and CO2 (Eq(1)) 

in the calciner reactor. Thus, the produced solids (CaO) react back with the gas CO2 in the carbonator to form 

CaCO3 through the exothermic carbonation reaction, which allows recovering great amount of thermal energy 

and produce electricity at the power block (Figure 1). Carbonator reactor can be a drop-tube, known for his wide 

range of applicability in fast gas-solid reaction systems like CO2 capture in cement industry (Plou et al., 2019). 

Several studies related to mathematical model development of drop-tube reactors implemented in different 

applications have been published before. Gasification of biomass (Kasule et al., 2012), cooper oxidation 

(Schöß et al., 2016), or calcium oxide carbonation in CO2 capture processes (Spinelli et al., 2018) are some 

indicative examples. This work encompasses the development of a one-dimensional (1D) steady-state 

mathematical model for the carbonation reaction, focused on CSP-CaL applications. The model is used as a 

 
 
 
 
 
 
 
 
 
 
                                                                                                                                                                 DOI: 10.3303/CET1976147 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Paper Received: 25/04/2019; Revised: 28/05/2019; Accepted: 29/05/2019 
Please cite this article as: Karasavvas E., Panopoulos K.D., Papadopoulou S., Voutetakis S., 2019, Study of a Drop−Tube Carbonator Reactor 
for CSP−Calcium Looping Based on a Heterogeneous Reaction Model, Chemical Engineering Transactions, 76, 877-882  
DOI:10.3303/CET1976147 
  

877



tool for the reactor simulation, where useful results are extracted for design purposes under the framework of 

SOCRATCES prototype erection. The model generally describes carbonator operation as a drop-tube, by 

calculating energy, mass, and momentum balances under several operating conditions and regimes.  

 

 

Figure 1: Basic block diagram of SOCRATCES prototype. 

2. SOCRATCES reactor description 

The proposed carbonator reactor resembles a drop tube. It is divided into two sections of two meters length 

each (Figure 2). The inner diameter of the reactor (~0.16 m), and the total length (~4 m) was set in order to 

achieve high solids residence times.  

 

 

Figure 2: Conceptual carbonator layout for the down-flow of CaO solids. 

Gas (CO2) and solids (CaO) enter from the top of reactor, while the product as well the unconverted reactants 

are discharged in an extension vessel at the bottom (Figure 2). Before the injection, the calcined solids are 

stored in a heated tank (200-600 oC) on top of the reactor (Figure 2). CO2 is provided by pressurized 

bottles, while CaO particles enter the reactor via a dosing screw feeder located between the top vessel and the 

Storage Section Calcination SectionCarbonation Section

CaCO3

CaO

CO2

POWER 

BLOCK
POWER

C

A

R

B

O

N

A

T

O

R

C

A

L

C

I

N

E

R

Solar 

Energy

CaCO3/CaO

CO2

CaO

Air

CO2

To Power 

Block

878



inlet of the reactor. For cooling purposes, the reactor is encircled by a set of helical gas coils that work as a heat 

exchanger and remove the produced heat released by the exothermic reaction. Fresh air is the heat transfer 

fluid passing through the cooling coils, as it performs a cheap and abundant source of heat sink. The produced 

hot air is later used to provide heat to the power block (Figure 2). The entire reactor segments are surrounded 

by two furnaces blocks, that ensure the preheating of the overall system at temperatures at which carbonation 

reaction is triggered (~600-850 oC).  

3. Drop-tube reactor mathematical model description 

The mathematical model of the carbonator was developed to describe the physical and chemical processes 

taking place inside the reactor. The model is one-dimensional (1D) at steady state conditions that simulates a 

single-stage carbonator reactor as an industrial drop-tube. A Euler-Euler approach is implemented to describe 

the gas-solid system, which means that each phase (gas & solid phase) is treated separately and owns a finite 

volume-fraction at the reactor. Also, the plug flow assumption has been considered for both phases as 

experimentally proved for a spiral-shaped entrained flow carbonator reactor (Plou et al., 2019), as well for the 

carbonation of fine CaO particels in a drop-tube. (Turrado et al., 2018). In this model, mass, momentum and 

energy balance equations for solid and gas phase are considered separately. The mass balance of a component 

under the plug flow assumption is given by the generic equation below (Eq(2)), where, C, denotes the 

component concentration, u, the velocity of the flowing ingredient, D, the diffusivity coefficient, �̇�, the rate of 

mass consumption or generation, and ▽ is the differential operator in Cartesian coordinates.  

𝑑𝐶

𝑑𝑡
+▽ (𝑢𝐶) = 𝐷 ▽2 𝐶 + �̇�        (2) 

Pressure along the reactor, voidage of gas phase, velocity and temperature profiles of each phase as well as 

conversion of reactants, are the state variables derived from the mass, energy and momentum equations. Drag, 

buoyancy and friction forces (i.e., friction forces between gas-wall and solids-wall) are calculated for both 

phases, while momentum losses are computed due to mass transfer rate from one phase to another. The CO2 

is modelled as a compressible gas obeying the low of ideal gases. The model takes also into account the 

modifications of particles characteristics as the carbonation reaction proceeds. The solid phase density 

continuously varies between the density of pure CaO and CaCO3 linearly with CaO conversion. Moreover, each 

phase encompasses their own physiochemical properties which may vary as reaction occurs.  

The gas-solid heterogeneous reaction rate has been previously inferred within the framework of SOCRATCES 

project and the kinetics were calculated using the Prout-Tompkins model (Eq(3)) to fit experimental data 

(Ortiz et al., 2018). X, denotes the mass conversion of CaO and r, the carbonation reaction rate depending on 

the temperature of particles surface and pressure of gas phase. The kinetic data deduced for particle sizes of 

around 45-75 μm and refers to SOCRATCES prototype operating conditions (i.e. 1-1.7 bar & ~800-900 oC).  

𝑑𝑋

𝑑𝑡
= 𝑓(𝑋)𝑟(𝑇, 𝑃)        (3) 

The heat produced due to the exothermic reaction is initially transferred from solids surface to the gas phase 

and then to the wall. For that purpose, the relative heat transfer terms and heat transfer coefficients have been 

computed separately (VDI Heat Atlas, 2010). In this way, the surplus heat which hinders reaction rate is removed 

out of the system. No a priori wall temperature profile is assumed in this model, but a constant wall temperature 

is considered. Theoretically, the actual wall temperature profile can be introduced into the model once 

experimental information is acquired from real plant operation, while parameters tuning will enhance model 

predictive capabilities towards the scale-up of the process. 

3.1 Model assumptions  

The one-dimensional (1D) mathematical model of carbonator reactor is at steady state and simulates gas and 

solids as two separate phases. Consequently, the radial dispersions of mass, energy and momentum are 

neglected at the present study. Mass, energy, and momentum transport terms are developed for gas and solid 

phase. The entrained-flow system is assumed to be very dilute in the solid phase such that the particle-wall and 

particle-particle interactions may be neglected. Subsequently, the conductive heat transfer between single 

particles and particles to wall is neglected too. Solids are assumed to be spherical with a uniform size, while no 

temperature variations are considered within the bulk of the particle. Also, kinetic energy and work forces of the 

system are considered unimportant in comparison to the thermal energy due to the high temperature of the 

reactor.  

The mathematical problem is a DAE (Differential and algebraic equations) system which consists of 11 first-order 

differential and 38 algebraic equations integrated simultaneously by a first-order backward finite difference 

879



method. In this work the mathematical model is numerically computed by a solver for stiff differential equations 

with a multistep integration option. The developed system of DAE is treated as an initial value problem. Initial 

values are set for each differential variable initiating integration process.  

4. Results and discussion 

In this section, the carbonator reactor is simulated via the model presented before under different inlet 

conditions. The base case input data implemented to the model are presented here after (Table 1).  

Table 1: Base case input data for carbonator simulation. 

Carbonator variable/parameter Value 

Inlet reactants temperature (oC)  600 

Reactor pressure (kPa) 

Initial CaO flow rate (kg/h) 

Initial CO2 flow rate (kg/h) 

Reactor diameter (m)  

Reactor length (m)  

Solids average diameter (m) 

Reactor wall temperature (oC) 

Maximum sorbent conversion (-)  

101.32 

12.70 

10.00 

0.16 

4.0 

75∙10-6 

500 

15 % and 70 % 

 

The dimensions of the reactor are pre-determined due to a priori reactor design. The operating conditions are 

pre-defined in accordance with the scheduled carbonator operation for 10 kWth thermal energy released due to 

the exothermic carbonation reaction. The same conditions are implemented both for a “low” maximum sorbent 

conversion (i.e., sintered CaO after multiple cycles, XCaO,max~15 %) and for a “high” maximum sorbent 

conversion (i.e., fresh CaO, XCaO,max~70 %). The capabilities of the model are demonstrated in terms of several 

process variables profiles along the reactor length (Figure 3 and Figure 4). 

 

   

    

Figure 3: Process variables profiles under different CO2 excess at the inlet of carbonator for sintered CaO with 

respect to the: (a) CaO conversion, XCaO; (b) Gas phase temperature, Tg; (c) Thermal energy production rate 

due to reaction, Qrxn; (d) Solid phase velocity, vp. 

0 1 2 3 4
0.00

0.05

0.10

0.15

 

 

C
a
O

 c
o

n
v
e
rs

io
n

 (
-)

Length of reactor (m)

 CO2 excess 0%

 CO2 excess 50%

 CO2 excess 100%

 CO2 excess 150%

 CO2 excess 200%

0 1 2 3 4

600

650

700

750

800

850

900
 CO2 excess 0%

 CO2 excess 50%

 CO2 excess 100%

 CO2 excess 150%

 CO2 excess 200%

 

 

 Length of reactor (m)

G
a
s
 p

h
a
s
e
 t

e
m

p
e
ra

tu
re

 (
o
C

)

0 1 2 3 4

0

1

2

3

4
 CO2 excess 0%

 CO2 excess 50%

 CO2 excess 100%

 CO2 excess 150%

 CO2 excess 200%

 

 

 Length of reactor (m)

Length of reactor (m)

T
h

e
rm

a
l 
e

n
e

rg
y
 p

e
r 

le
n

g
th

 o
f 

re
a

c
to

r 

(k
W

/m
)

0 1 2 3 4
0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1
 CO2 excess 0%

 CO2 excess 50%

 CO2 excess 100%

 CO2 excess 150%

 CO2 excess 200%

 

 

 
Length of reactor (m)

S
o
li
d

 p
h

a
s
e
 v

e
lo

c
it
y
 (

m
/s

)

(d) 

(a) (b) 

(c) 

880



Among the most significant variables of the process constitute the sorbent conversion, XCaO, gas phase 

temperature, Tg, rate of produced thermal energy due to reaction, Qrxn and solid phase velocity, vp. The sorbent 

conversion designates the extent of reaction, while Qrxn indicates about the reaction rate and the zone of reactor 

where carbonation is accomplished. Reactor temperature is exhibited by the gas phase temperature (Tg), while 

solid phase velocity, vp, provides insights about the residence time of particles. Negligible deviation between 

solid and gas phase velocity and temperature is observed in these solids’ sizes order of magnitude (~30-75 μm), 

while a noteworthy difference is inferred for more coarse particles (>100 μm) (not shown in the graphs). 

Five different CO2 ratios at the inlet of the reactor are examined with respect to the variables mentioned before 

(Figure 3). As seen, in all cases, the maximum sorbent conversion (15 %) is achieved (Figure 3a). However, 

the greater the CO2 excess, the higher the solid phase velocity and thus the shorter the residence time in the 

reactor (Figure 3d). This has an important effect in the profile of CaO conversion, which induces a delay in the 

maximum conversion approach. Temperature of reactor increases as exothermic reaction occurs until a 

maximum value, and then drops as is completed (Figure 3b). Carbonation performs a very abrupt reaction rate 

leading to the completion within the first 2 meters of the reactor in all cases. As long as the CO2 excess 

increases, reaction rate performs a smoother profile (Figure 3c). 

In case of using fresh material (CaO) passing through the reactor, a different approach in carbonation reaction 

is observed. In particular, the equilibrium temperature (~890 oC) is reached almost at all CO2 ratios, hindering 

the reaction progress (Figure 4b). Once temperature of reactants approximates equilibrium temperature, 

reaction rate diminishes near to zero and then, further conversion depends on the cooling rate of the reactor. 

For that reason, sorbent final conversion is continuously boosted towards higher values as CO2 excess also 

increases, acting as a heat sink that cools the reactor. However, after a critical CO2 excess value (~150 %), the 

lower residence time of solids (Figure 4d) surpasses the privilege of the better cooling (due to higher CO2 

excess) and leads eventually to lower final conversions (Figure 4a). Also, the region of reactor that carbonation 

occurs, broads further as CO2 excess increases at the inlet (Figure 4c). 

 

    

    

Figure 4: Process variables profiles under different CO2 excess at the inlet of carbonator for fresh CaO with 

respect to the: (a) CaO conversion, XCaO; (b) Gas phase temperature, Tg; (c) Thermal energy production rate 

due to reaction, Qrxn; (d) Solid phase velocity, vp. 

0 1 2 3 4
0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7
 CO2 excess 0%

 CO2 excess 50%

 CO2 excess 100%

 CO2 excess 150%

 CO2 excess 200%

 

 

C
a
O

 c
o

n
v
e
rs

io
n

 (
-)

Length of reactor (m)
0 1 2 3 4

550

600

650

700

750

800

850

900

 CO2 excess 0%

 CO2 excess 50%

 CO2 excess 100%

 CO2 excess 150%

 CO2 excess 200%

 

 

 Length of reactor (m)

G
a

s
 p

h
a

s
e

 t
e

m
p

e
ra

tu
re

 (
o
C

)

0 1 2 3 4

0

2

4

6

8

10

 

 

 Length of reactor (m)

Length of reactor (m)

T
h

e
rm

a
l 
e

n
e

rg
y
 p

e
r 

le
n

g
th

 o
f 

re
a

c
to

r 

(k
W

/m
)

 CO2 excess 0%

 CO2 excess 50%

 CO2 excess 100%

 CO2 excess 150%

 CO2 excess 200%

0 1 2 3 4
0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8
 CO2 excess 0%

 CO2 excess 50%

 CO2 excess 100%

 CO2 excess 150%

 CO2 excess 200%

 

 

 
Length of reactor (m)

S
o
li
d

 p
h

a
s
e
 v

e
lo

c
it
y
 (

m
/s

)

(d) 

(a) (b) 

(c) 

881



5. Conclusions 

In this study, a one-dimensional drop-tube carbonator model for CSP-Calcium looping has been developed to 

simulate carbonation reaction. The model provides the main trends of reactor performance under sintered and 

fresh CaO material. CO2 excess at the inlet of the reactor was examined by means of the sorbent 

conversion, temperature profile of carbonator, rate of produced heat due to exothermic reaction and solid phase 

velocity profile along the reactor. Kinetics and operating conditions were determined previously due to 

SOCRATCES project requirements. For sintered CaO, the maximum sorbent conversion is obtained (~15 %), 

while for the fresh one, an adequate reaction performance within the actual length of reactor is observed (~52 

%). The CO2 excess seems to highly affect reaction rate and carbonation yield. In particular, it determines the 

residence time of solids inside the reactor and consequently the sorbent conversion profile (sintered CaO). Also, 

CO2 absorbs the surplus heat of reaction which hinders carbonation improvement (fresh CaO). This very first 

carbonator modeling approach stands as a tool for entrained-flow design studies and can be further used as a 

provision for scale-up via experimental validation and tuning of model parameters. 

Acknowledgments 

This research has received funding from the European Union HORIZON 2020 project SOCRATCES-SOlar 

Calcium-looping integRAtion for Thermo-Chemical Energy Storage, under Grand Agreement Number: 727348. 

We acknowledge professor Angeliki Lemonidou and her research team in the Aristotle University of Thessaloniki 

(AUTH) as part of SOCRATCES consortium for providing as with experimental data for carbonation kinetics.  

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