Modelling of a calcium-looping fluidized bed reactor system ...

International Journal of Low-Carbon Technologies 2021, 16, 691–703© The Author(s) 2021. Published by Oxford University Press.This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), whichpermits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.https://doi.org/10.1093/ijlct/ctaa102 Advance Access publication 15 January 2021 691

Modelling of a calcium-looping fluidized bedreactor system for carbon dioxide removalfrom flue gas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Tsitsi Maparanyanga* and David LokhatReactor Technology Research Group, School of Chemical Engineering, University ofKwaZulu-Natal, Mazisi Kunene Road, Glenwood, Durban, South Africa. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

AbstractCalcium-looping process was simulated by solution of one-dimensional mass and energy balance equationsfor both interconnected fluidized bed reactors. Kinetics for the carbonator and calciner were derived fromliterature sources and were revised to include the effects of sulphation. The degree of apparent carbonationwas compared to the actual level of carbon dioxide removal through a series of sensitivity analyses. It hasbeen found that carbonation decreases with an increase in temperature. Sulphation increases with an increasein temperature. The activity of calcium oxide decreases with an increase in carbonation–calcination cycles.Neglecting the effect of sulphation during the design of the calcium-looping system leads to overestimationof active calcium particles that will react with carbon dioxide.

Keywords: calcium looping; sulphation; carbonator; calciner; calcination

*Corresponding author:[email protected]

Received 4 August 2020; revised 15 December 2020; editorial decision 22 December 2020; accepted 22December 2020

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1. INTRODUCTIONThe commencement of industrialization saw the marked increaseof greenhouse gases in the atmosphere compared to pre-industrialization levels. Carbon dioxide, methane and oxides ofnitrogen levels have increased in the atmosphere [1]. Althoughnatural processes like respiration add carbon dioxide into theatmosphere, man’s activities are the ones that add a greaterfraction of carbon dioxide in the atmosphere [2]. According to theUnited Nation’s Sustainable Development Goal number 13 [3], allshould take urgent action to fight climate change and its impacts,which mainly include combating greenhouse gas emissions.

Carbon capture and storage is one of the ways that are used toreduce greenhouse gases emission into the atmosphere [4]. Thereare various methods of capturing greenhouse gases from theatmosphere, which include separation with sorbents or solvents[5–7], separation with membranes and separation by cryogenicdistillation.

In this paper, the modelling and simulation of a calcium-looping system for carbon dioxide removal from flue gases wereconsidered. The calcium-looping method was proposed in 1999[8] and it is a method for carbon dioxide capture from flue gasesusing two coupled fluidized bed reactors. A limestone sorbent,

calcium oxide, is used for carbon dioxide capture. Carbon dioxideis captured through a chemical reaction resulting in the formationof calcium carbonate. Carbon dioxide capture takes place in thecarbonator after which the carbonate is passed to the calcinerfor regenerating the sorbent and carbon dioxide separation. Theseparated carbon dioxide is then compressed and stored.

Most of the studies on calcium-looping reactor modelling haveconcentrated on the carbonator, which is the most innovativecomponent. Different models of the carbonator have been pro-posed in literature with the first models being the bubbling flu-idized bed reactors [9]. The carbonator models that have beensuggested by researchers considered the carbonator as a circulat-ing fluidized bed [10–12], which has two compartments: the bot-tom dense zone and the lean zone. Most of the models proposedin literature have concluded that the calcium particles that react inthe fast regime influence carbonator efficiency. The percentage ofthe calcium particles that react in the fast regime is defined by theamount of fresh sorbent being introduced into the system and thesolid circulation between the calciner and carbonator. It has beenproposed in literature to design a model that considers the actualactivity of the calcium particles in the system according to theircarrying capacity, regardless of their preceding history of partialor full carbonation–calcination cycles [13]. True results would be

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T. Maparanyanga and D. Lokhat

obtained about the carbonator and general plant performance. It isalso important to measure the effect of sulphation and the amountof non-active calcium particles that react with sulphur dioxide inthe calcium-looping system.

2. CALCIUM-LOOPING PROCESSCalcium looping is a method that can be used for carbon dioxidecapture in pre-combustion and post-combustion. Calcium loop-ing involves carbon dioxide capture in a reactor, carbonator, ina process called carbonation where carbon dioxide reacts withcalcium oxide to form calcium carbonate. The calcium carbonateis passed into the second reactor, calciner, where the calcinationprocess takes place. Calcination is an endothermic reaction wherecalcium carbonate is decomposed to carbon dioxide and cal-cium oxide. The main advantage of calcium-looping technologyis that the calcium-looping reactors have already been establishedcommercially in large scale [14].

Shimizu et al. [8] first proposed calcium looping. It involvesthe carbon dioxide separation from flue gas making use of thereversible reaction of calcium oxide and carbon dioxide and thecalcination of calcium carbonate to regenerate calcium oxide.

Important steps have been taken in the past to demonstratethe viability of the calcium-looping technology. Experimentaltestwork to test the viability of using calcium oxide as carbondioxide absorber in a calcium-looping system has been carriedout. Carbon dioxide capture efficiencies ranging from 70 to 97%have been achieved in different test facilities at lab-scale from 10to 30 KWth [9,14,15].

Several approaches have been made towards the developmentof carbonator reactor models integrated into a calcium-loopingsystem. Shimizu et al. [8] and Abanades et al. [9] used the bubblingbed model proposed by Kunii and Levenspiel [16] to predict thecarbon dioxide captured in a bubbling bed absorber that consistedof calcium oxide particles. Circulating fluidized bed carbonatorsare the most common choice for large-scale systems when highvolumes of flue gases are expected to enter the carbonator on con-dition that it operates at atmospheric pressure. The first approachto modelling of a CFB reactor acting as carbonator was proposedby Hawthorne et al. [10] and Alonso et al. [11]. The modelsprojected that capture efficiencies above 80% can be achievedunder reasonable conditions.

The main components in the calcium-looping technology arethe carbonator and regenerator (calciner). Flue gas is fed into thecarbonator, which operates between 600 and 700◦C where carbondioxide reacts with calcium oxide to form calcium carbonate.Lime is carbonated and passes through the cyclone where thestream is separated into a carbon dioxide-depleted gas stream anda stream of solids that are passed to the calciner for regeneration ofthe sorbent at a temperature around 850 to 950◦C [14]. Limestonereleases the carbon dioxide at high temperature in the calciner.The products from the calciner pass through a cyclone, wherecarbon dioxide is separated from solids.

Figure 1. Calcium-looping process.

Calcination uses a great amount of energy, almost 50% ofenergy used in the calcium-looping system, because there is needof heating up the solids from carbonator and calcination is anendothermic reaction [17].

Figure 1 (above) is a simplified diagram of the calcium-loopingprocess, flue gas containing carbon dioxide and sulphur dioxide(Stream S-1) enters the carbonator (Unit E-1), which containscalcium oxide as the sorbent. In the carbonator, carbon dioxidereacts with calcium oxide as shown in equation 1 (below) formingcalcium carbonate. A side reaction called sulphation also occursin the carbonator as sulphur dioxide reacts with either calciumoxide or the formed carbonate, as shown in equations 8 and 9,forming calcium sulphate. The carbon dioxide- and sulphurdioxide-depleted gases exit the carbonator as stream S-2. Calciumcarbonate and calcium sulphate leave the carbonator into thecalciner (Unit E-2) as stream S-3. Stream S-3 will combinewith stream S-5, which makes up calcium carbon, to replacedeactivated calcium oxide from the carbonator. In the calciner,calcium oxide is regenerated from calcium carbonate as shown byequation 5. Reaction conditions in the calciner do not allow forregeneration of calcium sulphate to calcium oxide. This is becausegeneration of calcium oxide from calcium sulphate requirestemperatures high enough to cause sintering and deactivationof the calcium oxide. Calcium sulphate together with deactivatedcalcium oxide will be removed from the calciner as stream S-7 while the regenerated calcium oxide is taken back to thecarbonator as stream S-4. The concentrated carbon dioxidestream, ready for storage, exits the calciner as stream S-6. Sidereactions such as sulphation and sintering result in the sorbentbeing inactive. Fresh sorbent will have to be added to compensatefor the loss.

In the carbonator, the reaction below takes place:

CaO + CO2 ↔ CaCO3 �H = −178KJ/mol (1)

Calcium oxide also reacts with sulphur dioxide in flue gas.Calcination and sulphation reactions can limit the carbonatortemperature to a maximum of 700◦C, above which sulphation rate

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Modelling of a calcium-looping fluidized bed reactor system

increases and the calcium carbonate decomposes releasing carbondioxide [18].

The two stages involved in carbonation are the following: thefast carbonation stage where the carbon dioxide is bound on thesurface of the calcium oxide and the slow carbonation stage wherediffusion occurs and carbon dioxide is bound in the calcium oxideparticle.

The carbonation reaction may be represented by the followingempirical correlation modelled by Ylätalo [19]:

rcarb = msSave (Wmax − W) kcarb(CCO2 − CCO2e

)(2)

where ms is mass of solid, Save is the reaction surface area, Wmax−W represents the active fraction of the solid material, kcarb repre-sents the kinetic constant for the carbonation reaction and CCO2is carbon dioxide concentration in the flue gas.

The active fraction of the solid material is given by

Wmax − W = fa = 1 − e−t∗τ (3)

where t∗ is the characteristic time at which the reaction ratebecomes zero and τ is average residence time in the carbonator.The reaction surface area is given by Alonso et al. [11] as

Save = XaveρCaO

PMCao

emaxρCaCO3

PMCaCO3

(4)

where ρCaO and ρCaCO3 are densities of calcium oxide and calciumcarbonate, Xave is the average conversion of solids, PMCao andPMCaCO3 are molecular weights of calcium oxide and calciumcarbonate and emax is maximum thickness of the layer of calciumcarbonate on the pore wall.

The average value of the carbonation rate constant was calcu-lated by Bhatia and Permutter for temperatures ranging from 550to 725◦C [20] as 5.95 × 10−10 m4(mol s)−1.

In the regenerator, limestone is calcined releasing carbon diox-ide:

CaCO3 ↔ CaO + CO2 �H = 178KJ/mol (5)

Because calcination reaction is endothermic, heat must be sup-plied. Calcination is carried out at higher temperature than car-bonation. Due to sintering and sulphation reactions, and thesorbent deactivation caused by these reactions, the maximum rec-ommended temperature for calcination is 900◦C [18]. Calcinationprocess normally takes 0 to 15 minutes to complete. If the sorbentis exposed to high temperatures for a longer period, it will end updeviating from the required process (calcination) and is sintered.

Calcination is mainly affected by surrounding temperature andcarbon dioxide partial pressure at the calcium oxide/calcium/-carbonate/carbon dioxide interface. Calcination rate depends onthe properties of the limestone used and the relation of carbon

dioxide partial pressure, PCO2 to equilibrium partial pressure [21].Calcination is modelled by Ylätalo et al. [19] as given below:

rcalc = msWSaveMCaCO3

ρCaCO3

kcalc

(1 − PCO2

PCO2e

)(6)

where Save represents the reaction surface area, ρCaCO3 repre-sents the density of calcium carbonate, MCaCO3 represents themolar mass of calcium carbonate and kcalc represents the kineticparameter for the calcination reaction of the selected limestone.

The kinetic parameter for calcination was modelled by Silcoxet al. [22] as given below:

kcalc = 1.22 exp (−4026/T) (7)

(mol.m−2.s−1.atm−1)The evaluation of the kinetics of calcination can be complicated

by the following:• The concentration of carbon dioxide, which hinder the reac-

tion• Particle size which may cause mass transfer limitations• Catalysis or inhibition by impurities. Vanadium pentoxide

and fly ash are commonly known to inhibit calcination whilelithium carbonate accelerates it.

When a fuel with a sulphur content burns, sulphur dioxide isformed, which competes with carbon dioxide on reaction withcalcium oxide. Sulphur dioxide reacts with calcium oxide in twopossible ways:

CaO + SO2 + 12

O2 → CaSO4�H = −502KJ/mol (8)

CaCO3 + SO2 + 12

O2 → CaSO4 + CO2 �H = −324KJ/mol(9)

These reactions take over the formation of calcium carbonatedue to the differences in heat of reaction. The significance of theirinfluence depends on the sulphur dioxide content of the flue gas.Sulphation reaction can also take place in the calciner if heat issupplied using oxy-fuel combustion.

Heating solid particles at high temperatures but below theirmelting point will cause them to start to merge. Porous materialslike calcium oxide will shrink and the pores close as al the grainsthat initially formed the sorbent will fuse together to form largergrains. This is known as sintering and is more evident at hightemperatures and long periods of reaction. It will cause a drop inthe reactivity of the sorbent.

If temperatures become too high (above 900◦C for calciumoxide), sintering occurs at a high rate. This means the make-upflow will have to be increased too. Conditions in fluidized bedallow for sintering to occur. Sintering reduces the porosity andsurface area of the sorbent. Sintering is accelerated by presence ofcarbon dioxide and water [23].

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3. CALCIUM-LOOPING MODELLINGMost of the information from this section was adapted fromYlätalo et al. [19].

Two solids, calcium oxide and calcium carbonate, form themost part of carbonator and calciner. The required lime mass flowrate is calculated depending on the carbon dioxide mass flow rateand the absorption efficiency.

Change in mass = total mass flows in-total mass flowsout + amount of material regenerated

The solid mass balance is given by

dms

dt=

∑ms,in −

∑ms,out +

∑rs (10)

where ms is the total mass in the reactor, ms,in is mass of solidsentering the reactor, ms,out is mass of solids exiting the reactor andrs represents solid mass change due to chemical reaction.

The gas mass derivative is much smaller than the solid massderivative and for this reason, the mass of the gas in the domaincan be assumed constant and therefore the change in gas mass tothe element is neglected.

dmg,i

dt=

∑mg,in,i − mg,out,j + rg,i (11)

There is no gas deposition into the control volume:

mg,out,i =∑

mg,in, i + rg,i (12)

∑mg,in,i = mg,i−1 (13)

where mg,i is the total gas mass in the domain, mg,in,i is gas flowinto the element, mg,out,j is gas flows out of the element and rg,iis the combined effect of chemical reactions such as calcination,carbonation, sulphation, combustion of char and volatiles.

The exiting gas either enters the succeeding control volume orleaves the reactor if the control volume was located at the exitof the reactor. The one-dimensional gas balance for a single gascomponent a is given by

dma,i

dt=

∑ma,in,i − ma,out,i +

∑ra,i =

∑ma,in,i − wa,ima,out,i +

∑ra,i (14)

where ma,i is the mass of the gas component, ma,in,i representsgas component entering a control volume, ma,out represents thegas component exiting the control volume and ra,i is the term forchemical reaction term for the gas component.

dwi

dt= 1

mgi

(mi,in − mi,out + ri

)(15)

The energy present in a control volume equals the energyassociated with total convective flows in solids and gases and total

energy by dispersion, total heat transfer and chemical reactions.

dEi

dt=

∑qconv,s +

∑qconv,g +

∑qdisp +

∑qht +

∑qchem

(16)where Ei is energy present in the control volume, qconv,s is energyassociated with convective flows in solids, qconv,g is energy asso-ciated with convective flows in gases, qdisp is energy associatedwith dispersion between elements, qht is heat transfer and qchemis energy associated with chemical reactions.

The left-hand side of equation 16 can be further expanded asfollows:

dEi

dt= dUs,i

dt+ dUg,i

dt= d

(ms,ius,i

)dt

+ d(mg,iug,i

)dt

= d(ms,i

(hs,i − pivi

))dt

+ d(mg,i

(hg,i − pivi

))dt

= d(ms,icp,sTi

)dt

+(mg,ihg,i

)dt

= dms,i

dtcp,sTi + dTi

dtms,icp,s

+ dmg,i

dthg,i + dhg,i

dtmg,i (17)

Assuming that gas mass is very small,

dmg,i

dthg,i = 0

where Us,i is the internal energy of the solid, Ug,i is the internalenergy of the gas, us,i is specific internal energy of solid phase, ug,iis the specific internal solid and gas phase enthalpies energy of gasphase, hs,i and hg,i are solid and gas phase enthalpies, pivi is workdone by phase and cp,s is specific heat capacity of the solids.

Solving the temperature derivative from equation 14 results in

dTi

dt=

∑qconv,s+g + ∑

qdisp + ∑qht + ∑

qchem − dms,idt cp,sTi − dhg,i

dt mg,i

ms,icp,s(18)

From the mass balance, the convective flow of solids can bewritten as

∑qconv,s =

∑qconv,s,in −

∑qconv,s,out

=∑

ms,in,icp,s(Ts,in−TNTP

)−∑ms,outcp,s

(Ti−TNTP

)(19)

where qconv,s,in represents the convective flows of energy in controlvolume, qconv,s,out represents the convective flows of energy out ofthe control volume, Ts,in represents temperature of the incomingmass flows and TNTP is reference temperature of the system.

Substituting equation 18 into equation 16 gives

∑qconv,s − dms,i

dtcp,sTi = cp,s

(∑ms,in,iTs,in −

∑ms,out,iTi − dms,i

dtTi

)(20)


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For solids with different heat capacities, equation 20 can bewritten as

∑qconv,s− dms,i

dtcp,sTi =

∑cp,sms,in,i

(Ts,in − TNTP

)−∑cp,sms,in,i (Ti − TNTP) (21)

The convective flows of the gas can be written as shown below:

∑qconv,g =

∑qconv,g,in −

∑qconv,g,out =

∑mg,in,ihg,in −

∑mg,out,ihg,i (22)

where qconv,g,in is convective energy flows of gases into the controlvolume and qconv,g,out is convective energy flows of gases out ofthe control volume.

Substituting equation 18 to equation 22 gives

∑qconv,g−dhg,i

dtmg,i =

∑mg,in,ihg,in−

∑mg,out,ihg,i−dhg,i

dtmg,i

(23)where hg,in is the enthalpy of the incoming flows.

The enthalpy change in time can be written as

dhg,i

dtmg,i = mg,i

∑ dwi

dtha,i (24)

where ha,i is the gas component enthalpy.Chemical reactions that can be considered include evaporation,

carbonation, sulphation and the combustion of char and volatiles.

∑qchem =

∑rc,iQi (25)

where rc,i is the rate of reaction and Qi is the general reactionenthalpy.

Applying Fick’s law of diffusion to the modelling approach, thefollowing equation for dispersion is obtained [24]:

∑qdisp = Dscp,sAbρ

−ave

dT−i

dz+ Dscp,sAtρ

+ave

dT+i

dz(26)

where Ds is the dispersion coefficient, Ab/t is the cross section ofthe bottom/top element boundary and ρ

+/−ave is the average density

between calculation element and siding element.Heat transfer to the surfaces is given by the expression

∑qht = αtotAx (Ti − Tx) (27)

where αtot is the total heat transfer coefficient

αtot = 5.0ρ0.391s T0.408

i (28)

Table 1. Laboratory simulation input variables.

Variable Value

Flue gas mass flow (kg/s) 0.403Flue gas temperature (◦C) 25CO2 in flue gas (w-%) 14.4–43.2O2 in flue gas (w-%) 5.00N2 in flue gas (w-%) 51.76–80.56SO2 in flue gas (w-%) 0.04–0.08Solid mass in reactor (kg) 1.83

Substituting equations 21, 23, 25 and 26 into equation 18 givedTi

dtms,icp,s =

∑cp,sms,in,i

(Ts,in − TNTP

)

−∑

cp,sms,in,i (Ti − TNTP) +∑

mg,in,ihg,in

−∑

mg,out,ihg,i − mg,i∑ dwi

dthj,i

+ Dscp,sAbρ−ave

dT−i

dz+ Dscp,sAtρ

+ave

dT+i

dz

+ 5.0ρ0.391s T0.408

i Ax (Ti − Tx) +∑

rc,iQi (29)

Each reactor was divided into one-dimensional control vol-umes. Time-dependent mass and energy balances were solvednumerically using appropriate ODE tools in MATLAB. Figure 2,below, shows the calculation procedure for the reactor model.

The output variables (mass fraction of exit gases, mass of exit-ing solids and energy adsorbed or released by the system) wereextracted from the MATLAB solution of the time-dependent massand energy balances. These values were then transferred to anexcel spreadsheet for plotting and analysing. Mass flow rate ofsorbent, carbon dioxide partial pressure at the calcium oxide-calcium carbonate interface, temperature of incoming solid flowsand concentration of carbon dioxide and sulphur dioxide in theflue gas stream were varied based on literature data, using valuesabove and below those stipulated by different researchers. Whileone variable was being varied, all the other variables were beingkept constant. The following assumptions were made:

• Instant and complete mixing of solids in both reactors• Plug-flow of the gas phase in the carbonator• Calcination goes to completion instantaneously in the calciner

The input conditions for the laboratory simulation are shownin Table 1 below.

Table 2, below, shows the input parameters for the differentsimulations done.

4. RESULTS AND DISCUSSION4.1. Effect of temperatureFigure 3a shows the effect of temperature on carbonation,between 600 and 700◦C. As the temperature increases, the mass


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Table 2. Input variables for the different simulations done.

Simulationnumber

Sorbentflowrate(kg/s)

Inputsorbenttempera-ture (◦C)(carbona-tor)

Inputsolid tem-perature(◦C)(calciner)

Carbondioxide con-centration influe gas(mol/m3)

Carbondioxidepartialpressure(kPa)

Flue gas composition (w-%)

SO2 CO2 O2

1 100.000 610–690 900–990 1.320–3.961 2.026–9.119 0.04–0.08 10.0–30.0 5.02 1.743 610–690 900–990 1.320–3.961 2.026–9.119 0.04–0.08 10.0–30.0 5.03 1.743 500–590 900–990 1.320–3.961 2.026–9.119 0.04–0.08 10.0–30.0 5.04 0.116 610–690 900–990 1.320–3.961 2.026–9.119 0.04–0.08 10.0–30.0 5.05 0.011 610–690 900–990 1.320–3.961 2.026–9.119 0.04–0.08 10.0–30.0 5.06 1.743 610–690 900–990 1.320–3.961 2.026–9.119 0 10.0–30.0 5.0

Figure 2. Calculation procedure for reactor model.

of carbonate formed or rate of carbonation decreases. Figure 3bshows the mass of solid formed at different temperatures, froma lower temperature of 500◦C. For temperatures below 600◦C,the decrease in amount of carbonate formed (carbonation) is lessthan it is after 600◦C. The optimal temperature for carbonationwould be approximately 600◦C for it is high enough to drivethe carbonation reaction and not too high to accelerate thesulphation reaction. Figure 3c shows the mass of solid formed atdifferent temperatures from 600 to 900◦C. Carbonation decreasesas temperature increases and carbonation falls to zero after 790◦C.Carbonation and sulphation reactions can limit the carbonatortemperature to a maximum of 700◦C, above which sulphationrate increases and the calcium carbonate decomposes releasingcarbon dioxide.

Figure 4 shows the changes exit mass fractions of carbon diox-ide, oxygen and sulphur dioxide with increase in carbonationtemperature. In the exit stream, mass fractions of carbon dioxideincrease and mass fraction of sulphur dioxide (defined as the massof gas element in the exit stream divided by the total amount of gasin the exit stream) decrease as temperature increase. Accordingto Le Chatelier, if a constraint (such as a change in pressure, tem-perature or concentration of a reactant) is applied on a system inequilibrium, the equilibrium will move so as to tend to counter theeffect of the constraint [25]. Carbonation is an exothermic reac-tion therefore increasing the temperature will favour the reversereaction thus lowering the rate of carbonation. According to Luet al. [26], there is an increase in carbonation as temperaturedecreases but temperatures below 500◦C are too low to drive thecarbonation reaction.

The rate of sulphation increases as temperature increases.Unfortunately, increase in temperature accelerates sulphationbecause of the higher activation energy needed for the sulphationreaction [27]. With low amounts of sulphur dioxide in the fluegas, sulphation goes to completion and no sulphur dioxide will befound in the exit stream.

Figure 5a shows the change in mass fraction of carbon diox-ide in the calciner exit stream as temperature increases whileFigure 5b shows the variation in carbon dioxide mass fraction inthe calciner exit gas as a function of temperature and sorbent to


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Figure 3. Mass of solid formed versus temperature at constant flue gas composition for first carbonation–calcination cycle: (a) for temperatures above 500◦C, (b)from 500◦C and (c) for temperatures up to 900◦C.

carbon dioxide flow ratio in the carbonator. It can be seen thatas sorbent to carbon dioxide flow ratio increases, carbon dioxidemass fraction in the calciner exit stream increases. An increase inthe sorbent to carbon dioxide ratio in the carbonator means moreactive calcium oxide for carbon dioxide absorption, hence morebound carbon dioxide being carried over to the calciner.

Figure 6 shows that as temperature increases, carbon dioxidemass fraction in the calciner also increases. This shows that calci-nation rate will be also increasing thus more carbon dioxide beingformed. Calcination is an endothermic reaction, therefore increas-ing the temperature will favour the forward reaction, which if isformation of products (carbon dioxide and calcium oxide).

It can be seen from Figure 5b that as amount of sorbentincreases, the calciner exit stream will be containing more carbon

dioxide. This is because more carbon dioxide would have beenabsorbed by the sorbent.

It is therefore recommended to use high sorbent to carbondioxide flow rates (above 10 000) so that a more concentratedstream of carbon dioxide will be produced and collected forstorage.

4.2. Bed mass versus number ofcarbonation–calcination cyclesFrom Figure 6a, the amount of active calcium oxide decreasesas number of carbonation–calcination cycles increase. Figure 6bshows the changes in bed mass composition versus carbonation–calcination cycles, up to 100 cycles. There is a sharp decrease


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Figure 4. Exit gases mass fraction versus temperature at constant flue gascomposition for first carbonation–calcination cycle.

in active calcium oxide in the first 10 cycles and after about100 cycles, the active calcium particles remain constant. This iscaused by the decay in activity of calcium oxide as the number ofcarbonation–calcination cycles increases [28].

The amount of calcium oxide not reacted (inactive) increasesas number of carbonation–calcination cycles increases becauseof the decay in activity of calcium oxide with an increase innumber of carbonation–calcination cycles. Calcium carbonaterecycled into the system also decreases with increasing numberof carbonation–calcination cycles.

The optimum number of carbonation–calcination cycles fromFigure 6a and b is less than 20 after which the most part (morethan 75%) of the sorbent will be inactive.

4.3. Effect of changing carbon dioxide concentration inthe flue gasRate of carbonation, which is directly proportional to rate offormation of calcium carbonate, increases as carbon dioxide con-centration in the feed stream increase. The increase in rate ofcarbonation is due to an increase in reactant available for reaction.There is a linear correlation between carbonation and amountof carbon dioxide in flue gas because the rate of carbonation isdirectly proportional to carbon dioxide concentration in the fluegas as proposed by Ylätalo et al. [19] in the equation 2.

4.4. Change in sorbent to carbon dioxide flow ratioIncrease in sorbent to carbon dioxide flow rate ratios leads tohigher reaction rate in the carbonator. The sulphation reaction

Figure 5. Carbon dioxide mass fraction in the exit gas versus temperature: (a)at constant carbon dioxide partial pressure (9119.25 Pa) and (b) as a function oftemperature and sorbent to carbon dioxide flow ratio to the carbonator.

also increases as shown by the decrease in mass fraction of sulphurdioxide leaving the reactor as sorbent to carbon dioxide flow ratiosincrease. As the amount of sorbent increases, there will more sor-bent available for reaction with the carbon dioxide as well as thesulphur dioxide hence an increase in rate of reaction. Figure 8b


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Figure 6. Bed mass versus number of carbonation–calcination cycles at constanttemperature (610oC) and flue gas composition: (a) for up to 500 cycles and (b)for up to 100 cycle.

shows that sulphur dioxide is depleted instantly as sorbent tocarbon dioxide flow rate ratios increase. This is because sulphurdioxide will be present in very small quantities in the feed gas andhence will be totally absorbed by the sorbent. As sorbent to carbondioxide flow rate ratio decreases to below 1, sulphur dioxidedepletion becomes slow and only goes up at elevated temperature

Figure 7. Mass of carbonate formed versus carbon dioxide concentration in fluegas at constant temperature (6000C).

(above 640◦C) because of the higher activation energy needed forthe sulphation reaction.

A higher sorbent to carbon dioxide flow rate ratio (Figure 8a)allows for higher absorption of carbon dioxide and sorbent tocarbon dioxide ratios above 20 are optimal. It can clearly beseen that at this ratio, the mass fraction of the gas in the exitgoes down rapidly. Lower sorbent to carbon dioxide flow rates(<20) result in high carbon dioxide mass fractions in the exit gasstream. The challenge of higher sorbent to carbon dioxide flowrate ratios is that they also allow for higher adsorption of sulphurdioxide.

4.5. Effect of change in carbon dioxide partial pressureFigure 9 shows the change in carbon dioxide mass fraction withpartial pressure at constant temperature. As carbon dioxide par-tial pressure (at the calcium oxide–calcium carbonate interface)increases in the calciner, the rate of calcination, which is directlyproportional to increase in carbon dioxide mass fraction in theexit gas stream, decreases. More calcium carbonate is recycled tocarbonator without conversion to calcium oxide. Maybe sorptioneffects at the calcium oxide/calcium carbonate/carbon dioxideinterface are the reason for the decay [29].

4.6. No sulphationSimulations were also performed for the case in which the effectof sulphation was ignored.


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Figure 8. Variation of mass fraction in the carbonator exit gas as a function of temperature and sorbent to carbon dioxide flow ratio (Fr/Fco2): (a) carbon dioxide,(b) sulphur dioxide and (c) oxygen.

Figures 10 and 11 show a comparison of carbonation reactiontaking place in the presence as well as in the absence of sulphurdioxide. When carbonation takes place in the absence of sulphurdioxide, more calcium oxide will be in the bed and available forreaction with carbon dioxide. When sulphur dioxide is taken intoaccount, more active calcium oxide is consumed by both reactions(carbonation and sulphation) but when sulphation is ignored, onereaction, carbonation, consumes the active calcium oxide thus abigger amount of calcium oxide will be in the bed.

Neglecting sulphation when designing calcium-looping reac-tors will therefore lead to over estimation of active calcium oxide

in the carbonator and therefore lower amount of carbon dioxideabsorbed than expected.

In Figure 11, there is a sharp decrease in active calcium oxidein the first 10 cycles and after about 100 cycles, the active calciumparticles remain constant. This is caused by the decay in activityof calcium oxide as the number of carbonation–calcination cyclesincreases [28]. Figure 6b also shows the same effect. There isno appreciable difference in the curves because sulphur dioxideconcentration in the flue gas is very low compared to that ofcarbon dioxide making the amount of active calcium oxide usedin the sulphation reaction small.


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Figure 9. Carbon dioxide mass fraction versus partial pressure at constanttemperature (900◦C).

Figure 10. Active calcium oxide in carbonator versus temperature at constantflue gas composition and sorbent flow rate.

4.7. Energy balancesFigure 12 shows the relationship between amount of energyreleased during carbonation and number of carbonation–calcination cycles. As number of carbonation–calcination cyclesincreases, the amount of energy released decreases. This is

Figure 11. Active calcium oxide versus number of carbonation–calcinationcycles at constant temperature (610 ◦C) and flue gas composition.

Figure 12. Energy released in carbonator versus number of carbonation–calcination cycles.

because as the carbonation–calcination cycles increase the rateof carbonation decreases.

As the number of carbonation–calcination cycles increases, theamount of energy absorbed in the calciner decreases (Figure 13).The same reason as in carbonator applies; the rate of calcination


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Figure 13. Energy absorbed in the calciner versus number of carbonation–calcination cycle.

also decreases with increase in number of carbonation calcinationcycles. The decreases in reaction rates are caused by deactiva-tion of the sorbent (calcium oxide) as number of carbonation–calcination cycles increase.

5. CONCLUSIONIt has been observed from the analysis of the simulation datathat carbonation, sulphation as well as calcination reactions aresignificantly temperature dependent. As temperature increases,the rate of carbonation decreases while the rate of sulphationincreases. Carbonation is an exothermic reaction and increasingthe temperature of the system will favour the reverse reactionthus lowering the rate of carbonation. It is therefore necessary tohave a low temperature that allows little sulphation, as sulphationreduces the amount of active calcium carbonate for carbonation,and at the same time the temperature should not be too low tosuppress the carbonation reaction. Temperatures below 500◦C aretoo low to drive the carbonation reaction [26]. For temperaturesbelow 600◦C, the decrease in amount of carbonate formed (car-bonation) is less than it is after 600◦C. The optimal temperaturefor carbonation would be approximately 600◦C for it is highenough to drive the carbonation reaction and not too high toaccelerate the sulphation reaction.

Rate of carbonation increases as carbon dioxide concentra-tion in flue gas increases. This is because carbonation is directlyproportional to amount of carbon dioxide in the flue gas stream.

Increase in the sorbent to carbon dioxide flow ratio leads to anincrease in both carbonation and sulphation, as more reactant willbe available for reaction with the flue gas stream. High sorbentto carbon dioxide flow ratios also lead to a more concentratedstream of carbon dioxide being removed from the calciner as morecarbon dioxide would have been absorbed in the carbonator.

A temperature increase in the calciner leads to an increase inrate of calcination. If temperatures become too high (above 900◦Cfor calcium oxide), sintering occurs at an elevated pace [23].This means that although the rate of calcination increases withan increase in temperature, temperatures above 900◦C should beavoided.

Increase in carbon dioxide partial pressure in the calcinercauses a decrease in calcination reaction. A low carbon dioxidepartial pressure is recommended for an increase in calcination.

The amount of active calcium oxide particles decreases as thenumber of carbonation–calcination cycles increase. There is asharp decrease in the first 10 cycles and after about 100 cycles;the active calcium particles remain constant. It is recommendedthat the number of carbonation–calcination not exceed 20 afterwhich most (more than 75%) of the sorbent will be inactive.

Neglecting the effect of sulphation in the design of the coupledfluidized bed system leads to overestimation of the active fractionof calcium oxide particles that will react with carbon dioxide inthe flue gas. Lower amount of carbon dioxide will be absorbedthan estimated.

Energy adsorbed and released by calcination and carbonationrespectively decreases as the number of carbonation–calcinationcycles increases due to the decrease in carbonation and calcinationreactions as the number of cycles increases.

Symbols usedGreek symbolsρ [kg m−3] densityα heat transfer coefficientOther symbolsA [m2] cross sectional areaC concentrationc heat capacityD [m2.s] dispersion coefficientE [J] energye [m] thickness of calcium carbonate on the pore wallh enthalpykcarb [m4(mol. s)−1] kinetic constant for carbonationkcalc [mol.m−2.s−1.atm−1] kinetic constant for carbonationm [kg] massm [kg/s] mass flow ratep [Pa] partial pressurePM [kg] molecular weightQ [J] reaction enthalpyqdisp [J/s] energy associated with dispersion between elementsqchem [J/s] energy associated with chemical reactionqht [J/s] heat transferr [kg. s−1] rates [m2] surface area


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t [s] timeT [oC] temperatureTNTP [oC] reference temperature of the systemu specific internal enthalpyW [−] active fraction of calcium particlesX [−] conversion

Sub- and superscriptss solidg gasi, j control volumein into control volume/elementout out of control volume/elementcalc calcinationcarb carbonation

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