DOI: 10.3303/CET2188031

Paper Received: 27 May 2021; Revised: 13 August 2021; Accepted: 6 October 2021
Please cite this article as: Dimoliani M., Papadopoulos A.I., Seferlis P., 2021, Modeling and Parametric Investigation of Rotating Packed Bed
Processes for CO2 Capture and Mineralisation, Chemical Engineering Transactions, 88, 187-192 DOI:10.3303/CET2188031

CHEMICAL ENGINEERING TRANSACTIONS

VOL. 88, 2021

A publication of

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

Guest Editors: Petar S. Varbanov, Yee Van Fan, Jiří J. Klemeš

ISBN 978-88-95608-86-0; ISSN 2283-9216

Modeling and Parametric Investigation of Rotating Packed
Bed Processes for CO2 Capture and Mineralisation

Marianthi Dimoliania, Athanasios I. Papadopoulosa,*, Panos Seferlisa,b
a Chemical Process & Energy Resources Institute (C.P.E.R.I.), Center for Research and Technology Hellas (CE.R.T.H.),

57001, Thermi-Thessaloniki, Greece
b Department of Mechanical Engineering, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece

spapadopoulos@certh.gr

Rotating Packed Beds (RPB) are receiving increased attention in CO2 capture, due to their considerably lower
volume compared to conventional packed-beds and their beneficial effects on process capital costs. As a result
of these advantages, RPB have also been considered as a CO2 mineralisation option for the production of
precipitated calcium carbonate (PCC). In the area of CO2 capture, the few model-based investigations employ
either the two-film or Higbie’s penetration theory to model the gas-liquid mass transfer as the main driving force
of the systems’ operation. In the area of PCC production, there is only one model type available that is based
on the two-film theory. While the latter includes the limiting assumption of linear and steady-state mass transfer
within the liquid film, Higbie’s theory is considerably closer to realistic operation due to the assumption of time-
dependent and non-linear, gas-to-liquid mass transfer. Considering this significant advantage, this work
proposes for the first time a model for RPB-based, PCC production using Higbie’s penetration theory. The model
is first developed and validated considering solvent-based CO2 capture with monoethanolamine (MEA) solvent,
taking advantage of the available experimental data in published literature. The model is then adapted to PCC
production to perform a parametric investigation based on various performance indicators. Results indicate that
the proposed model enables improved accuracy compared to the two film theory. Higher rotation speeds and
liquid flowrates enable improved mass transfer, whereas PCC production can be achieved at lower energy
consumption simultaneously with high CO2 capture efficiency.

1. Introduction

The abatement of industrial CO2 emissions is a key requirement in order to avert the detrimental environmental
impacts associated with global warming. Absorption-based CO2 capture (Bui et al., 2018) and subsequent
transformation of CO2 into carbonated minerals such as precipitated calcium carbonate (PCC) (Jimoh et al.,
2018) represent mature and promising technologies for short- to medium-term implementation. There are
currently several large-scale pilot plants and two commercial installations of solvent-based absorption processes
worldwide (Idem et al., 2015). PCC has a very broad range of applications in building materials, cement, plastics,
paper, pharmaceuticals, dyes and represents a very appealing CO2 utilisation option for carbon leakage
industries such as cement, lime, paper and steel (Sargheini et al., 2012). Despite these promising
developments, CO2 absorption is predominantly performed in conventional packed-bed columns (Bui et al.,
2018), whereas PCC is produced in continuous stirred-tank (CSTR) reactors, with detrimental effects in both
cases on reaction rates, equipment sizes, and, eventually, capital expenditures (Jimoh et al., 2018). Rotating
packed beds (Wang et al., 2011) represent a type of intensified equipment that can address all these
shortcomings and promises significant size and capital cost reduction (Wang et al., 2015), compared to packed-
bed columns and CSTRs. This is because RPBs enable significant enhancement of the mass−transfer rate
between the gas and liquid phases (Vlahostergios et al., 2020) as they are contacted in the presence of a high
centrifugal field, with beneficial effects on the gas-liquid contact area (Qammar et al., 2018).
Although existing research efforts are predominantly based on experimental works in both the CO2 capture and
PCC production through RPBs (Neumann et al., 2018), model-based approaches are also very useful for
process scaling-up. In the area of CO2 capture there are few published works that focus on the development of

187

RPB process models and on the effects that different operating parameters have on separation efficiency,
carbon capture level and so forth (Borhani and Wang, 2019). Qian et al. (2009) developed a model of the
absorption of CO2 by aqueous N-methyldiethanolamine (MDEA), focusing on modeling the diffusion reaction
process by Higbie’s penetration theory. The same authors presented a follow-up study on the selective
absorption of hydrogen sulfide and CO2 by MDEA, using the same modelling approach. Sun et al. (2009)
presented a model for absorption of CO2 and ammonia into water in an RPB, based on the two-film theory for
reactive gas absorption. A similar modelling approach has been used by Yi et al. (2009) who studied the
absorption of CO2 into a Benfield solution (hot potassium carbonate promoted by diethanolamine) with limited
however information about the physical properties utilised in the study. Recently, Borhani et al. (2019) developed
a rate-based model using the two-film theory to represent the absorption process of CO2 in a concentrated
monoethanolamine (MEA) solution in an RPB. On the other hand, there is only one report that pertains to
modeling of an RPB for PCC (Pan et al., 2015), where the two-film theory was used to investigate the impact of
process parameters to conversion efficiency and energetic requirements. The focus was only on the gas-side
coefficient, despite the enormous importance of the liquid phase on process performance.
Clearly, Higbie’s penetration theory needs to be investigated in PCC production for various reasons. It is closer
to operating reality, since it assumes that the mass transfer of the gas into the liquid takes place at unsteady-
state conditions (Morsi and Basha, 2015). In the two-film theory, the liquid-side mass transfer coefficient is based
on the assumption that the concentration profile is linear and at steady-state within the liquid film, whereas it is
non-linear and time-dependent in reality. In Higbie’s theory the liquid-side mass transfer coefficient is expressed
within a non-linear function of the contact time and of the molecular diffusivity of the gas into the liquid.
This work proposes for the first time a model for PCC production in an RPB, based on Higbie’s penetration
theory. The Qian et al. (2009) implementation of Higbie’s theory on solvent-based CO2 capture is adopted,
whereby an analytical expression is used to model the concentration distribution of CO2 as a function of time
and penetration depth in the liquid film. The proposed implementation also requires knowledge of only the
reaction kinetic expressions to calculate the necessary mass transfer coefficient. This is very advantageous
compared to the implementation of Pan et al. (2015) of the two-film theory, where multiple, often difficult to track
down, properties are necessary to calculate the Reynolds, Scmidt, Grashof, Weber and Froude numbers. The
proposed model is first developed and validated for solvent-based CO2 capture using MEA, due to the ample
data available in published literature. It is subsequently used to model PCC production, where it is employed to
investigate the process operating performance based on different indicators.

2. Modeling of PCC production using Higbie’s penetration theory

2.1 PCC and main reactions

PCC is composed of either fine or very fine nanoparticles that are synthesised either by a carbonation or a
solution process after the calcination and hydration reaction of a carbonate rock. The absorption of CO2 in an
aqueous solution of Ca(OH)2 is primarily achieved by a series of equilibrium reactions that occur in the solution
and by the protonation of Ca(OH)2 expressed as follows:
Overall Chemical Reaction

𝐶𝑎(𝑂𝐻)2(𝑠) + 𝐶𝑂2(𝑔) ↔
𝐾1

𝐶𝑎𝐶𝑂3(s) + 𝐻2𝑂(𝑙)
(1)

𝐶𝑎𝐶𝑂3(s) + 2𝐻
+ ↔

𝐾2
𝐶𝑎2+ + 𝐻2𝑂(𝑙) + 𝐶𝑂2(𝑔)

(2)

Carbonic Species and Water Equilibria

𝐶𝑂2(g) + 𝐻2𝑂(𝑙) ↔
𝐾3

𝐻𝐶𝑂3
− + 𝐻+ (3)

𝐻𝐶𝑂3
− ↔

𝐾4
𝐻+ + 𝐶𝑂3

2− (4)

𝐶𝑂2(g) + 𝑂𝐻
− ↔

𝐾5
𝐻𝐶𝑂3

− (5)

𝐻2𝑂(𝑙) ↔
𝐾6

𝐻+ + 𝑂𝐻− (6)

Ionic-pair equilibria

𝐶𝑂3
2− + 𝐶𝑎2+ ↔

𝐾7
𝐶𝑎𝐶𝑂3(𝑠)

(7)

Solid-liquid Phase Equilibrium

𝐶𝑎(𝑂𝐻)2(𝑠) + 𝐶𝑂2(𝑔) ↔
𝐾8

𝐶𝑎2+ + 2𝑂𝐻− (8)

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The hydration of carbon dioxide is detailed in reactions (3)-(6). Reaction (5) is a rapid, reversible reaction taking
place in parallel with the fast, pseudo-first-order reversible reaction (1).

2.2 Main theory aspects and model development

Higbie’s penetration theory investigates the diffusion of gas into an element of the fluid, as the latter slides over
their common interface. As implied by its definition, the basis of this theory lies in the fact that, in unsteady-state
mass transfer, the depth of penetration into the exposed boundary is dependent on the time of contact; deeper
penetration is achieved in longer contact times (Morsi and Basha, 2015). In the case of an RPB, the intense
centrifugal forces result in a sharp change of the concentration of the dissolvable gas into the liquid film, which
has a short lifetime on the packing surface due to its continuous renewal. This shorter mean lifetime of the liquid
film results in a higher mass transfer coefficient. Considering the above, an RPB model is developed where it is
assumed that the concentration of every component changes only in the radial direction, as the circumferential
motion can be considered insignificant due to little circumferential diffusion of the liquid (Burns and Ramshaw,
1996). It is assumed that the liquid motion in the RPB does not involve back-mixing, hence the liquid radial flow
can be approximated by plug flow (Qian et al., 2009). The liquid flow rate is assumed to be constant due to
insignificant increase of the liquid mass as the liquid moves outwards. The pressure drop in the RPB is assumed
to be negligible because it is minor compared to the overall system pressure (Yi et al., 2009). Although the
absorption reaction of CO2 is exothermic, the variation on temperatures of both gas and liquid can be neglected.
This assumption has been verified experimentally by observing that the temperature difference between the
inlet gas and outlet liquid streams is very small (Yi et al., 2009). Ιnvestigations focus on steady-state RPB
operation, where the gas phase resistance is assumed to be negligible, countercurrent contact between liquid
and gas is implemented, laminar film flow is assumed on the packing surfaces and all the reactions occur in the
liquid film (Yi et al., 2009). The motion of liquid and gas particles is described by Fick’s law of diffusion:

𝑁𝐶𝑂2 = 𝐷𝐶𝑂2
𝑑𝐶𝐶𝑂2

𝑑𝑥
|𝑥=0 = √𝑘𝜊𝜈 𝐷𝐶𝑂2 (𝑐𝑐𝑜2,0 − 𝑐𝑐𝑜2,𝑒𝑞 ) (9)

where 𝑁𝐶𝑂2 is the mass transfer rate at the gas-liquid interface (kmol/m
2s), 𝐷𝐶𝑂2 is the diffusivity of CO2 (m

2/s),
𝑘𝜊𝜈 is the overall reaction rate constant (1/s), 𝑐𝑐𝑜2,0 is the concentration of CO2 at the gas-liquid interface (mol/L)
and 𝑐𝑐𝑜2,𝑒𝑞 is the equilibrium concentration of CO2 for the reaction (mol/L). Subsequently, a differential mass
balance for the gas phase of CO2 can be introduced, as follows:

𝑘𝑦 𝑎(𝑦 −
𝐻

𝑃

𝐾2𝐾3

(𝑐𝐶𝑎(𝑂𝐻)2,𝑡𝑜𝑡 − 𝑐𝐶𝑎(𝑂𝐻)2 )𝑐𝐻𝐶𝑂3−

𝑐𝐶𝑎(𝑂𝐻)2
)2𝜋ℎ𝑅𝑑𝑅 = 𝐺𝑁2 𝑑(

𝑦

1 − 𝑦
) (10)

where 𝑦 is the mole fraction of CO2 in the gas (-), 𝑘𝑦 = 0.082𝑇𝑘𝐿 (𝑃)/(𝐻), 𝑎 is the specific area (m2/m3), 𝐻 is
Henry’s constant for absorption of CO2 into Ca(OH)2 (-), 𝑃 is the total pressure of the system (kPa), 𝐾2, 𝐾3 are
the equilibrium constants of reactions (2) and (3) (-), 𝑐𝐶𝑎(𝑂𝐻)2,𝑡𝑜𝑡 is the bulk concentration of total Ca(OH)2 at the
liquid outlet (mol/L), 𝐺𝑁2 is the flow rate of N2 (m

3/s), ℎ is the packing height (m) and 𝑅 is the geometrical radius
(m). Based on the reaction stoichiometry, differential mass balances for HCO3

- and Ca(OH)2 are also needed:

𝑘𝐿 𝑎
𝑃

𝐻
(𝑦 −

𝐻

𝑃

𝐾2𝐾3

(𝑐𝐶𝑎(𝑂𝐻)2,𝑡𝑜𝑡 − 𝑐𝐶𝑎(𝑂𝐻)2 )𝑐𝐻𝐶𝑂3−

𝑐𝐶𝑎(𝑂𝐻)2
)2𝜋ℎ𝑅𝑑𝑅 = 𝑄𝐿 𝑑(𝑐𝐻𝐶𝑂3− ) (11)

−𝑘𝐿 𝑎
𝑃

𝐻
(𝑦 −

𝐻

𝑃

𝐾2𝐾3

(𝑐𝐶𝑎(𝑂𝐻)2,𝑡𝑜𝑡 − 𝑐𝐶𝑎(𝑂𝐻)2 )𝑐𝐻𝐶𝑂3−

𝑐𝐶𝑎(𝑂𝐻)2
)2𝜋ℎ𝑅𝑑𝑅 = 𝑄𝐿 𝑑(𝑐𝐶𝑎(𝑂𝐻)2 ) (12)

where 𝑐𝐻𝐶𝑂3− , 𝑐𝐶𝑎(𝑂𝐻)2 are the bulk concentrations of HCO3
-
and Ca(OH)2 in the liquid phase and 𝑄𝐿 is the

volumetric flow rate of the liquid (m3/s). The analytical expression of the liquid-side mass transfer coefficient
𝑘𝐿 used here is independent of the characteristics of the flow, but is affected by the mean lifetime of the liquid
film, the reaction rate constant and the liquid diffusivity of CO2 (Qian et al., 2009):

𝑘𝐿 =
√𝑘𝜊𝜈 𝐷𝐶𝑂2

𝑡̅
[𝑡̅𝑒𝑟𝑓(√𝑘𝜊𝜈 𝑡̅) + √

𝑡̅

𝜋𝑘𝜊𝜈
𝑒 −𝑘𝜊𝜈𝑡

̅
+

2𝑘𝜊𝜈
𝑒𝑟𝑓(√𝑘𝜊𝜈 𝑡̅)] (13)

where 𝑡̅ is the mean lifetime of the liquid film (s) and 𝑒𝑟𝑓 is an excess error function. The implementation of Qian
et al. (2009) on amine-based CO2 capture is used a) to validate the model based on the MEA solvent and b) to
adapt the model on the PCC production process. By applying the calculated liquid-side mass transfer coefficient
𝑘𝐿 , the problem solution is addressed as an initial value problem with ordinary differential equations (ODE-IVP).

189

3. Results and Discussion

3.1 Validation for CO2 capture using MEA

The proposed model is validated considering CO2 absorption in MEA (Liu et al., 2016), due to the availability of
modeling and experimental results in published literature. Works that pertain to experimental and model-based
assessment of CO2 absorption in Ca(OH)2 for the production of PCC focus exclusively on the gas-side mass
transfer coefficient, which is not considered in the current implementation of Higbie’s penetration theory. The
proposed model is validated in Figure 1 against results using the two-film theory (Borhani et al., 2019) and in
Table 1 against experimental results (Jassim et al., 2007).

(a) (b)

Figure 1: Comparison of a) the CO2 mole fraction in the gas phase (𝑦𝐶𝑂2 ) with respect to the RPB radius,

and b) the CO2 capture level in the RPB with respect to the rotation speed (𝜔), for MEA between Higbie’s
penetration theory and the two film theory (Borhani et al., 2019)

As depicted in Figure 1a, the outer radius where flue gas enters the RPB is the point where the highest amount
of CO2 in the flue gas appears. The effect of rotor speed is presented in Figure 1b for the penetration and the
two-film theory. The increase of the rotor speed increases the CO2 Capture Level (CCL). This is due to the
improved mas transfer rate that results from increasing the rotor speed. As shown in Figure 1b, the agreement
between the two modeling theories is better at higher rotor speeds. In order to gain better insight into the model
predictions, error analysis is utilised in this study. The CCL is employed to compare the predicted values from
the developed model of this work (penetration theory) with experimental data (Jassim et al., 2007) and predicted
values from the two film theory (Borhani et al., 2019). Consequently, the relation of absolute relative deviation
(ARD %) is shown in Table 1. ARD % reflects the comparison of the experimental and predicted CCL % values,
with the latter calculated based on the outlet 𝑦𝐶𝑂2

𝑜𝑢𝑡 and inlet 𝑦𝐶𝑂2
𝑖𝑛 mole fractions of CO2 in the gas phase.

Table 1: Model prediction results compared to experimental values. CCL %=(𝑦𝐶𝑂2
𝑖𝑛 − 𝑦𝐶𝑂2

𝑜𝑢𝑡 )/𝑦𝐶𝑂2
𝑖𝑛 and ARD % =

|(𝐶𝐶𝐿𝐸𝑥𝑝 − 𝐶𝐶𝐿𝑃𝑟 𝑒 )/𝐶𝐶𝐿𝐸𝑥𝑝 |.

MEA
wt. (%)

𝜔 (rpm) Experimental CCL %
(Jassim et al., 2007)

Predicted CCL %
(Two film theory)

Predicted CCL %
(Penetration

theory)

ARD %
(Two-film theory)

ARD %
(Penetration

theory)
56 600 94.9 91.0 93.51 4.11 1.46
56 1,000 95.4 97.6 97.30 2.31 1.99
75.1 1,000 91.2 97.05 93.5 6.41 2.52
77 600 84.2 90.06 82.9 6.97 1.54

The proposed model based on Higbie’s penetration theory is validated successfully against experimental data.
The lower ARD % indicates that the penetration theory is more accurate compared to the two-film theory. The
proposed model does not require calculations pertaining to flow characteristics (e.g., Reynolds, Schmidt,
Grashof numbers) and to properties such as interfacial area and effective area, that are demanding to determine
and there is often a lack of the necessary data.

3.2 Effect of key operating factors on PCC production

The effect of key operating parameters such as the rotation speed (ω) and liquid flow rate (𝑄𝐿 ) on 𝑘𝐿 are shown
in Figures 2a and 2b for the production of PCC. The 𝑘𝐿 values are enhanced with increasing ω (i.e., up to 800–

190

2,200 rpm) and 𝑄𝐿 (i.e., up to 5.5– 8.5 lt/min), indicating that the mass transfer resistance is reduced in the
investigated ranges. The simultaneous implementation of high ω and 𝑄𝐿 is desired to attain high 𝑘𝐿 .

(a) (b)

Figure 2: Effect of a) rotation speed (𝜔), and b) liquid flow rate (𝑄𝐿 ) on 𝑘𝐿 for PCC production at T=313.15 K

Figure 3a shows the influence of different specific surface areas of packing materials on the CO2 capture level
for different rotation gravity levels (rotation speeds). It appears that a higher specific surface area enables
improved capture of CO2 by the Ca(OH)2. Figure 3b shows the CO2 capture level with respect to the RPB radius,
for different dissipation energy (𝜖) values. The latter are associated with energy consumption and influence the
mixing. Two interesting trade-offs appear here. Lower dissipation energy (slower mixing) enables higher CO2
capture along the RPB radius, but the dissipation energy is higher (faster mixing) toward the outer radius of the
RPB, where the CO2 capture level is higher. The fast-mixing case (𝜖=0.1 MW/kg) enhances the CCL and
reaches the maximum value (98 %) at the outer radius of the RPB. Dissipation energy values of 0.1 MW/kg and
0.01 MW/kg result in a similar performance, especially at the outer RPB end. This means that the same capture
level may eventually be achieved with 10 times lower energy consumption. On the other hand, higher capture
efficiency may be maintained along the RPB radius at a considerably lower energy rate, if the initially high
efficiency within the first few meters is sacrificed.

(a) (b)

Figure 3: CO2 capture level against a) gravity level (rotation speed) for different packing specific surface areas

(𝑎), and b) RPB radius for different dissipation energies (𝜖) at 𝜔 =1000 rpm. The results are for 𝑄𝐿=5.5 lt/min
and the gravity level range corresponds to 𝜔 between 400-1,200 rpm

4. Conclusions

The proposed model was validated successfully against experimental data and Higbie’s penetration theory was
shown to enable improved predictions compared to the two-film theory. The obtained results indicated that the
optimum, liquid-side mass transfer coefficient can be reached as the rotation speed and liquid flow rate increase
simultaneously. Higher specific surface areas of the packing material enable improved carbon capture
efficiency. The latter can also be attained by lower energy consumption, which further enables efficient capture
along the RPB radius. The proposed model is reliable in predictions performed for CO2 absorption in both MEA
solvent and Ca(OH)2. It requires less input data compared to models developed previously based on the two-

191

film theory, as the calculation of complex flow numbers and properties is avoided. The presented model was
implemented only for the liquid phase of the process. It would be worthwhile extending the model toward the
gas phase. Although such an extension would enable predictions for all the investigated phenomena, the
advantages of the proposed model reported in the manuscript (e.g., the avoidance of the need for gas side
transfer coefficients or the need to calculate multiple flow-related numbers) would be abolished. Although
isothermal operation was assumed, the attained results were very satisfactory, based on the performed
validation.

Acknowledgements

This research has been co‐financed by the European Union and Greek national funds through the Operational
Program Competitiveness, Entrepreneurship and Innovation, under the call RESEARCH – CREATE –
INNOVATE (project code: T1EDK-02472)

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