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UNDERSTANDING LIME CALCINATION KINETICS FOR ENERGY COST REDUCTION
Wicky Moffat and M. R. W. Walmsley
Presented at the 59th Appita Conference, Auckland, New Zealand 16-19 May 2006
The calcination of calcium carbonate (limestone) is an important step in the regeneration of kraft pulping chemicals and in the production of industrial calcium oxide (quicklime). Better understanding of the kinetics can lead to improved lime kiln efficiencies in both production rate and specific energy use. For this reason a fundamental investigation into lime calcination kinetics for the purpose of improving kiln efficiency was undertaken.
Important kinetic equations that apply to calcium carbonate calcination are reviewed. The effect of particle size and kiln temperature on reaction rate and the mechanism that control reaction rate are explained. Dimensionless variables which delineate between mass transfer, heat transfer and reaction rate control are identified and used to construct a kinetic behaviour diagram. The diagram is used to explain ways of improving kiln energy efficiency. This premise was tested experimentally in a laboratory kiln, and then transferred to an industrial kiln, where a 13% increase in energy efficiency and production was recorded.
Key words: calcination, lime kiln, reaction kinetics, energy reduction
Calcination of calcium carbonate is a highly endothermic reaction, requiring 3.16GJ of heat input to produce a tonne of lime (CaO). The reaction only begins when the temperature is above the dissociation temperature of the carbonates in the limestone or lime mud. This typically is between 780oC and 1340oC (1, 2). Once the reaction starts the temperature must be maintained above the dissociation temperature, and carbon dioxide evolved in the reaction must be removed. Dissociation of the calcium carbonate proceeds gradually from the outer surface of the particle inward, and a porous layer of calcium oxide, the desired product, remains.
The industrial process of calcination is usually carried out in a Rotary Kiln, where heat energy from a burning flame is supplied for drying, heating, and decomposing the calcium carbonate stone or particles. Carbon dioxide from both the heat source and the calcination reaction is produced in large quantities and reducing greenhouse gas emissions through improved kiln energy efficiency is a growing necessity. Kiln energy efficiencies typically range from 30-60% and most of the energy is lost in the flue gases, through the kiln shells and as heat in the product (2). Improving the energy efficiency of a lime kiln, not only reduces greenhouse gas emissions, but also has significant impact on the cost of producing lime. Understanding lime calcination kinetics has the potential to aid identification of energy reduction and energy efficiency opportunities.
An energy audit, carried out at Perry Lime Ltd, established the distribution of energy use in a lime kiln process as illustrated in Figure 1. The process was a typical quarry limestone processing facility with a conventional Rotary Kiln. The results are indicative, and are applicable to other limestone processing facilities. The aim of the audit was to quantify the total amount of energy used in the process, and to quantifying and qualifying energy losses.
Figure 1: Energy Distribution in a Lime Kiln Process (2)
The highest energy losses were recorded in the flue gases (32%). Other losses included convection loss from the kiln shell (5.8%), heat content losses in the product (2%) and miscellaneous losses (3.6%). Only 56.8% of the heat supplied was used to decompose calcium carbonate or in other words 43.2% of the energy was either irreversibly lost to surroundings or not recovered for more useful application.
To reduce these energy losses, a study was undertaken to identify the rate determining step of the kiln at Perry Lime Ltd, and to use this knowledge to speeding up the critical step without further heat addition. Although the kinetics and reaction mechanism of the thermal decomposition of calcium carbonate has been the object of many studies there are many aspects that are still not applied well at a mill level. One reason is, there is not consensus about many fundamental aspects of the process. For example, there are conflicting reports about the applicability of the particle reaction model, the process step that is rate-limiting, the influence of the carbon dioxide partial pressure, the effect of total pressure, and the effect of heat transfer through the calcium oxide ash layer covering the reacting particle.
The shrinking core reaction model is the most obvious particle reaction model to examine and is considered to have applicability. The calcination reaction is assumed to initially take place at the outer surface of the particle, and as the reaction proceeds, the exterior surface of the particle is covered by the porous product layer, while an unreacted core remains in the interior region of the particle. The porous layer is assumed to stay intact, giving a particle of constant size with a shrinking unreacted core.
SHRINKING CORE MODEL
In the shrinking core model there are four important steps which control the rate of decomposition of calcium carbonate: the conduction of heat through the reacted layer (ash layer) to the reacting core, the chemical reaction itself at the core, the diffusion of carbon dioxide away from the core through the porous ash layer, and the diffusion of carbon dioxide away from the particle through the gas film surrounding the particle.
Film Diffusion Resistance: This refers to the diffusion through the gas film surrounding the reacting particle which could create a concentration gradient across the film. In most reactions the resistance to diffusion through the ash layer is usually far greater than resistance to diffusion through the gas film. The gas film resistance is therefore assumed to be negligible. Researchers have generally agreed that film diffusion effects are an insignificant factor in the decomposition of limestone. Film diffusion will therefore be ignored in this project.
Chemical Reaction Control: This is when the actual reaction at the reacting surface is the rate determining step.
The rate expression is:
Solving the equation gives:
The concentration of solid, CB is equal to its molecular density, ρB
(3 and 4)
Ash Diffusion Resistance: This is resistance to the flow of gas across the reacted product and largely depends on the porosity of the product layer. By pseudo steady-state assumption, the material balance of the reacting component between the centre and the reaction surface can be written as:
By differentiating and making the rate of reaction equal to the rate of diffusion:
Expressing this equation in terms of the reacting fraction of solids:
This could be expressed as:
(8 and 9)
Particle Internal Heat Transfer Resistance: An alternative to mass transfer resistance by diffusion is heat transfer resistance by conduction. The ash layer that forms on the outer region of the particle may act to restrict heat transfer to the reacting core such that the supply of heat controls the rate of reaction. We have therefore developed an expression which defines the reaction path when heat transfer is the rate controlling step. This was done by considering the heat conducted through the ash layer, Qc and the heat absorbed in the reaction, Qr.
Heat of Reaction (Qr):
The rate of decomposition can be written as:
This can be written as:
By substituting for the surface area, S for a spherical particle the rate can be written as:
The heat flux, or the differential heat flow at the reaction interface can be calculated from the heat of reaction:
Substituting the rate expression gives:
The heat of reaction, Qr for a spherical particle can be obtained by integrating this expression from radius R to the reaction interface, rc:
Heat Conduction (Qc):
Similarly, the heat conducted through the ash layer, Qc can be calculated.
Qc = κs SΔT
The heat conducted from the particle surface to the reaction interface is:
Qc = κs S(Ts −Tc )
For a spherical particle, this becomes:
Under steady state conditions, the heat that is conducted through the ash layer becomes equal to the heat of reaction. This is the case when heat transfer is the rate determining step. This means no excess heat is conducted through the ash layer and Qc = Qr
But the rate, rA can be expressed in terms of reactant or product:
For the solid product B, the concentration CB is equal to the molecular density ρB
Substituting the rate expression and rearranging gives:
In developing this model we have assumed that all the heat conducted through the ash layer is used up in the reaction. This is based on the assumption that the temperature of the unreacted core homogenises at the reaction temperature, therefore no heating up of the unreacted core will occur while the reaction progresses. In reality however, Silva et al  found that the temperature of the unreacted core in heat transfer dependent gas-solid reactions homogenises just below the reaction temperature. However in the case of limestone, the unreacted core has a very high thermal conductivity, which means the temperature difference between the unreacted core and the reaction interface is very small. Therefore only a small amount of heat escapes through the reaction interface to warm up the unreacted core to the reaction temperature, and we have assumed this to be negligible. The amount of error introduced by this assumption is therefore very minimal.
The heat conduction controlled model is similar to the ash diffusion controlled model in that the total reaction time τ is predicted to be proportional to R2 and to decrease with temperature. Although investigators generally agree that temperature increases the rate of decomposition, there is general disagreement on the conditions under which heat transfer is the rate determining step. The temperature dependency of a reaction is a function of different parameters: activation energy, pre-exponential factor, the thermal conductivity of the particle and the temperature dependency of the diffusion coefficient. All these temperature dependent parameters need to be explored to establish the true temperature dependency of the reaction. What is presented here is only part of a more detailed study.
Limestone (CaCO3) particles were reacted in a preheated oven at seven different temperatures (850 -1200oC). Five different particle sizes were used (4.75 - 25mm). The tests were done by heating a 20g sample of each particle size in a preheated oven at the required temperature. The particles were spread out to minimize inter-particle heat and mass transfer effects. The mass loss overtime was recorded. The time zero on the reaction curves represents the time at which the actual reaction started and mass loss started to occur. The experiment was stopped when no further mass loss was recorded. The Tekumi limestone, which was used in this experiment, has a purity of 98%. It is a shell material, with a trigonal crystal structure, and a rhombohedral formation. Impurities include magnesium carbonate, alumna, silica and iron.
All the experimental data were combined into one reaction curve which was then compared to the ideal chemical reaction control model and the ash diffusion control model in Figure 2.
Figure 2: Reaction Rate compared to Different Reaction Models
The reaction fitted more closely to the ash diffusion control model. This means either heat diffusion or carbon dioxide diffusion controls the rate of reaction in the temperature and particle size range studied.
Effect of Particle Size:
The effect of particle size on the rate of reaction was assessed (Figure 3). The results confirm that the larger particles require a longer conversion time than the small particles. The plots also show that the total conversion time is proportional to R2 and this confirms that ash diffusion control is predominant in the temperature and particle size range studied. The rate of reaction increased tremendously with decreasing particle sizes, as the effects of ash diffusion were minimized.
Figure 3: Variation of Reaction Rate with Particle Size
SHRINKING CORE MODEL WITH HEAT TRANSFER CONTROL
Experimental results support an ash diffusion controlled reaction model in the particle size and temperature ranges studied. However, to identify the type of diffusion controlling, it was necessary to test the ash layer heat conduction model in more detail. The ash heat conduction equation predicts that if heat conduction was rate controlling a plot of τ versus R2/(Ts – Tc) should yield a straight line.
Figure 4. The effect of limestone particle radius on total reaction time at temperature Ts = 850oC and assuming Tc = 780oC
The gradient in the plot
can be used to calculate the thermal conductivity Ķs.
Thermal conductivity, Ķs values of 0.2 to 2.8W/mK were obtained at temperatures of 850-1150oC. These values are comparable to literature values of 1.6W/mK at 900oC (Silva et al, 2000), supporting the assumption that heat transfer is the rate determining step in the particle size and temperature ranges studied.
An Arrenius relationship:
exists for the change in thermal conductivity with temperature, and a log plot of κs versus 1/Ts gives a straight line (Figure 5). This would confirm that heat conduction through the ash layer is rate controlling in the temperature and particle size range studied.
Figure 5. Dependence of thermal conductivity on kiln temperature.
The activation energy was found to be 121.766kJ/mol, compared to literature values of 110 – 200kj/mol. The results confirm that the conduction of heat to the reacting surface is rate controlling at the particle size and temperature ranges studied.
KINETIC BEHAVIOUR OF LIME DECOMPOSITION
Three dimensionless numbers were used to evaluate the rate controlling step in each particle size and temperature range to develop a kinetic behaviour diagram.
The Lewis number expresses the ratio of heat transfer to mass transfer, and enables the determination of the dominant characteristic. It is an indication of the relative magnitude of thermal and mass diffusivities.
A Lewis number <1 indicates that mass transfer is greater than heat transfer. This means heat transfer is the rate determining step. When the Lewis Number >1, heat transfer is greater than mass transfer and the system becomes mass transfer dependent.
The Damkohler number expresses the ratio of chemical reaction kinetics to the rate of mass transfer. It is the ratio of chemical reaction diffusivity to mass diffusivity.
A Damkohler number <1 indicates that mass transfer is greater than the rate of chemical reaction. This means chemical reaction kinetics are the rate determining step. When the Damkohler Number >1, the rate of chemical reaction is greater than the rate of mass transfer. The system becomes mass transfer dependent.
Chemical-Heat Transfer Number:
In a similar way, a dimensionless number relating thermal diffusivity to chemical diffusivity has been proposed. It is the ratio of thermal diffusivity to chemical diffusivity, and was obtained by calculating the ratio of the Lewis Number to the Damkohler Number.
A NCH number >1 indicates that heat transfer is greater than the rate of chemical reaction, which means chemical kinetics are rate controlling. When the NCH Number <1, the rate of chemical reaction is greater than the rate of heat transfer, making the system heat transfer dependent.
Lime Kinetic Behaviour Diagram
The three dimensionless numbers can be used to construct a "Lime Kinetic Behaviour Diagram". This was done by evaluating the particle sizes and temperatures at which each of the dimensionless numbers is equal to one. Figure 6 shows the particle size and temperatures at which the decomposition of limestone would be chemical reaction, heat or mass transfer controlled. It is therefore a useful design, troubleshooting and process improvement tool.
Figure 6: The Effects of Temperature on the Rate of Reaction
The results show that for >6mm particles, the decomposition of limestone is heat transfer dependent at temperatures below 1100oC. At these low temperatures, the lower thermal conductivities and the small internal temperature gradients within the particle would cause the reaction to be heat transfer dependent. Few authors have reported this kinetic phase. Hills  used thermogravimetric experiments and found the reaction to be heat transfer dependent, but the results have been discredited by many authors because of the large samples used in their experiments.
At temperatures above 1100oC the reaction shifts to a mass transfer dependent system. Under these conditions, the temperature gradient between the surface of the particle and the reacting core is very high. This, coupled with the higher thermal conductivities, would cause faster heat transfer through the ash layer. On the other hand, the diffusivity of carbon dioxide through the ash layer is less temperature sensitive. This means mass transfer begins to take place at a slower rate than heat transfer. Feng and Lombardo  identified an expansion and shrinking phenomena during calcination. They found that at 900-1100oC CaO expands by 0.2%. This expansion is far less than the tabulated coefficient of thermal expansion for CaO because sintering and expansion are competing phenomena. Above 1100oC the particle begins to shrink because sintering becomes predominant compared to thermal expansion. They reported that intra-particle porosity, number of pores, total surface area, pore diameter and total porosity all tend to decrease at high temperatures. These micro-structural changes could be causing a shift from a heat transfer dependent system to a mass transfer dependent system. Trikkel and Kuusik , also reported pore-blockage above 1100oC, as opposed to high porosity at lower temperatures. The diffusion of carbon dioxide through the ash layer should become more difficult at high temperatures, and the reaction becomes mass transfer limited. Adanez, et al , also reported that the specific surface area of calcined limestone is reduced at high temperatures due to a sintering effect.
The results also showed that the decomposition of lime is chemical reaction controlled for particles smaller than 4mm. This seems to suggest that a reduction in particle size leads to a reduction in heat and mass transfer effects within the particle. Work done by Ar and Dogu  fitted the chemical reaction controlled shrinking core model. They used particles as small as 1.015mm in their gravimetric experiments. Hu and Scaroni  also reported that chemical kinetics were rate controlling for particles smaller than 10μm. Borgwardt, , found the decomposition to be 'reaction rate controlled' for very small particles (1-90μm). However the results obtained by Acke and Panas  could not fit this model, even though they used the same particle size range. This difference could be attributed to the bigger sample weights used in their experiments. Inter-particle heat and mass transfer could have affected their results.
For 4-6mm particles, the results show that the reaction shifts between chemical kinetics and heat and mass transfer kinetics. These intermediate particles are large enough to experience some heat or mass transfer effects, but small enough to be chemical kinetics dependent. Garcia-Labiano et al , reported that the reaction shifts between chemical kinetics and mass transfer for 90μm-6mm particles. Thermogravimetric analysis work done by Khinast et al,  suggested that the rate determining step shifts between chemical kinetics and mass transfer, depending on particle size and CO2 partial pressure. Hu and Scaroni  did some scanning electron microscopic analysis work and concluded that chemical kinetics, heat transfer and mass transfer all offered resistance to the calcination process. They ranked these effects in the order:
Heat > Mass > Chemical kinetics for particles larger than 20μm.
APPLICATION OF THE KINETIC BEHAVIOUR DIAGRAM
The study has demonstrated that the kinetics of the decomposition of lime are variable, depending on particle size and temperature. Lime mud kilns in the pulp and paper industry operate mostly in the chemical kinetics zone due to the small particle sizes. However they often move into the chemical/heat/mass shift region due to pelletization of the mud particles . Horizontal raw limestone Rotary Kilns use 6–25mm particles and are mostly heat transfer dependent. Vertical shaft kilns normally use very large particles (25-50mm). Higher kiln temperatures are required to minimize residence times for these large particles and this moves shaft kilns into the mass transfer dependent region. The lime kinetic behavior diagram was used to determine where a raw limestone kiln was operating, thereby simplifying process improvement decisions.
Laboratory Testing on a Limestone Kiln
The 'lime kinetic behaviour' diagram shows that heat transfer is the most important step in the calcination of raw limestone (6-25mm particles). Laboratory tests were carried out to assess different methods of enhancing heat transfer inside the kiln. The energy audit has also shown that most of the energy losses (32%) are through the exhaust gases. Two ways of trapping that energy inside the kiln were proposed: a trefoil system or a lifter system.
Figure 7: Drying Curves for a Trefoil and a Lifter Kiln
These were tested in a laboratory kiln, 1.0m long and 0.1m diameter. Limestone samples were dried at 110oC and the drying curves were plotted.
The trefoil increased the rate of reaction by almost 50%, as opposed to the 25% achieved by fitting a set of lifters in the kiln. Although both systems increased the mixing and turbulence in the kiln, the trefoil increased the heat transfer surface area by 180%, hence the additional energy efficiency improvement. This is despite the fact that the trefoil acts as an airflow shield, thereby increasing both carbon dioxide concentration and furnace pressure.
Industrial Application of the Trefoil
The results were transferred to an industrial kiln. A 4m long trefoil section was placed just before the beginning of the calcination zone. The positioning of the trefoil extended the calcination zone and increased heat transfer.
Figure 8: A Trefoil Inside the Kiln
An energy audit was carried out and a new distribution curve was established.
Figure 9: Energy Distribution in a Trefoil Kiln Compared to a Conventional Kiln
The new energy distribution showed a 13% increase in the amount of energy used for calcinations, coupled with a 11.1% reduction in energy losses through waste gases. Thus, energy efficiency increased from 56.5% to 69.5%. This was despite a 20% reduction in airflow through the kiln, a 5% increase in carbon dioxide concentration and a 0.5kpa increase in total furnace pressure. However increased heat transfer overcame these setbacks to give a 13% increase in production. This clearly demonstrates that heat transfer is the rate controlling step in the calcination of limestone.
The study has demonstrated that the kinetics of the decomposition of lime are variable, depending on particle size and temperature. The lime kinetic behaviour diagram can be used to determine where a kiln is operating, thereby simplifying process improvement decisions. For raw limestone kilns the conduction of heat through the ash layer to the reacting surface is the most critical step in the process. The reaction temperature has a direct effect on the conductivity of the ash layer, and hence on the rate of reaction. The reaction rate can be enhanced through improved heat transfer systems.
b molar ratio of the reactant, Dimensionless
CA concentration of gaseous product, mol/m3
CB concentration of the solid product, mol/m3
De diffusion coefficient of the gaseous phase, m2/s
Dc chemical reaction diffusion coefficient, m2/s
α thermal diffusion coefficient, m2/s
Cp specific heat capacity, W/m2K
Kr reaction rate constant, mol/m3s
NA number of particles of solid A in the sample
NCH chemical-heat transfer number, Dimensionless
Da Damkohler Number, Dimensionless
Le Damkohler Number, Dimensionless
R particle radius, m
rA reaction rate, mol/s
rc radius at the reacting core, m
S particle surface area, m2
t time of reaction, s
Tc temperature of the reacting particle core, K
Ts kiln temperature or surface temperature of the particle, K
κs thermal conductivity through the ash layer, W/(m2K)
ΔΗr heat of reaction, J /mol
ρB molecular density of the product layer, mol/m3
τ total reaction time (conversion time), s
χB extent of conversion to CaO, %
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Financial and technical assistance from Perry Lime Ltd Department of Materials and Process Engineering at the University of Waikato, and the New Zealand Foundation for Research, Science and Technology (UOWX0302) is gratefully acknowledged. We also acknowledge the technical support from the CHH Kinleith Mill.
Wicky Moffat1, M.R.W. Walmsley2
1 Carter Holt Harvey, Kinleth Pulp and Paper Mill, Tokoroa, NZ
2 Department of Materials and Process Engineering, University of Waikato, Hamilton ,NZ