Dynamic Analysis of the Temperature and the Concentration Profiles of an Industrial Rotary Kiln Used in Clinker Production

Cement is one of the most used building materials in the world. The process of cement production involves numerous and complex reactions that occur under different temperatures. Thus, there is great interest in the optimization of cement manufacturing. Clinker production is one of the main steps of cement production and it occurs inside the kiln. In this paper, the dry process of clinker production is analysed in a rotary kiln that operates in counter flow. The main phenomena involved in clinker production is as follows: free residual water evaporation of raw material, decomposition of magnesium carbonate, decarbonation, formation of C3A and C4AF, formation of dicalcium silicate, and formation of tricalcium silicate. The main objective of this study was to propose a mathematical model that realistically describes the temperature profile and the concentration of clinker components in a real rotary kiln. In addition, the influence of different speeds of inlet gas and solids in the system was analysed. The mathematical model is composed of partial differential equations. The model was implemented in Mathcad (available at CCA/UFES) and solved using industrial input data. The proposal model is satisfactory to describe the temperature and concentration profiles of a real rotary kiln.


INTRODUCTION
Some of the challenges facing the cement industries are the high energy demand of production, the continuous increase in fuel prices, process complexity and environmental impact (Atmaca and Yumruta 2014, Tsamatsoulis 2014, Kaddatz et al. 2013, Gartner and Macphee 2011, Schneider et al. 2011, Mujumdara et al. 2007).To address these challenges, there is great interest in optimising the cement production process (Copertaro et al. 2015, Utlu et al. 2006).
The best-known type of cement is called Portland cement, which is defined as a hydraulic cluster that is basically obtained by grinding a mixture of clinker and gypsum (Copertaro et DIULIA C.Q. RODRIGUES et al. al. 2015).Thus, one of the main steps of the process for obtaining cement is the synthesis of the clinker (Atsonios et al. 2015, Saidur et al. 2011).Synthesis occurs inside the rotary kiln and involves complex physical (phase changes) and chemical (endothermic and exothermic reactions) processes (Lourenço et al. 2013, Saidur 2011, Silva 2007, Boateng and Barr 1996).The main clinker components are C 3 S (3CaO.SiO 2 ), C 2 S (2CaO.SiO 2 ), C 3 A (3CaO.AlO 3 ) and C 4 AF (4CaO.Al 2 O 3 .Fe 2 O 3 ).The intermediate reactions for obtaining the clinker and their respective heats of reaction are shown in Table I, and the temperature ranges of the formation of chemicals are shown in Table II.
Clinker production can be performed in a dry or wet process (Paula 2009).On one hand, in the dry process, the mixture of agglomerates and aggregates are completely dried and ground to feed the kiln in powder form.On the other hand, in the wet process, the mixture is a mud that is fed into the kiln with approximately 30-40% of moisture (Saidur et al. 2011, Del Coz Díaz et al. 2002).This paper considers the dry clinker production, which is the most used process in Brazilian production of cement (Kihara and Visedo 2014).
A rotary kiln in a dry cement production can be divided into five zones (Stadler et al. 2011): heating zone, calcining zone, transition zone, firing zone and cooling zone.The position of the zones along the kiln depends on the temperature and the chemical reactions being performed in the solid (Spang 1972).The temperature profile along the rotary kiln is generally not directly measured due to the scarcity of sensors that supports its  In the originally proposed model (Spang 1972) the variation of gas temperature over time was not considered.To improve the description of the process, an adjustment was made in the gas energy balance (Equation 13 of the Appendix), which consisted of adding a term of gas temperature variation into the equation.In this way, Equation 13 was substituted by Equation 30.
The flame model originally described (Spang 1972) (Equations 17, 18 and 19 of the Appendix) was replaced by an amount of energy supplied to the kiln by the fuel combustion.These changes enable the industrial professional to use the model more directly.In this paper, the quantity of energy proposed for the fuel combustion is constant and equal to 326.7 kW/m (3.9×105 BTU/ft.h).This amount, adjusted by trial and error, approaches the values commonly used in industry.Thus, the new proposed model is composed of Equations 1-12, 14-16 and 20-30 as listed in the Appendix.
After adaptations, realistic values of the operational properties of the clinker production as reported by a Brazilian industrial plant were employed in the model.The composition of the raw material used in the industrial production of the clinker is shown in Table III.The values were normalized in relation to CaO (kg/kg).Other internal operating conditions.Thus, estimating the temperature profile along the kiln is an important object of study.
In a previous work (Spang 1972), a dynamic model was developed.The model was composed of partial differential equations describing the mass balance and the system power (Spang 1972).The model is capable of predicting the concentration and temperature profiles along a rotary kiln operating in counterflow (Spang 1972).A flame model was also developed to quantify the amount of energy supplied to the system (Spang 1972).The equations that comprise this model (Equations 1 to 29) are presented in the Appendix.The results qualitatively describe the behavior of kilns, but the steady state was not reached.
In the present paper, an adaptation of the previous model is implemented to make it more realistic (Spang 1972).Using realistic values of the operational properties provided by a Brazilian company, the concentration and temperature profiles of a real rotary kiln used in the industrial production of the clinker is obtained.

CALCULATION PROCEDURES
Initially, a modification of the original model (Spang 1972) was performed to obtain a more realistic description of the temperature and concentration profiles of the clinker components along the rotary kiln.industrial operating properties employed in the model are shown in Table IV.The inner radius of the kiln was estimated to be 1.84 m (6.05 ft), the initial solid temperature, 562 ºR (312 K), and the initial temperature of the kiln wall, 662 ºR (367 K).These estimates were performed based on previous data (Spang 1972) and industrial realities.
The model was solved for different inlet speeds of gas and solid until the final composition of the clinker obtained in the simulation was similar to the actual values obtained in the cement industry ( V).The best values for the gas and the solid inlet speeds were 274.32 m/s (-900 ft/hr) and 5.4864 m/s (18 ft/hr), respectively.Next, the temperature and concentration profiles obtained for the rotary kiln were analyzed considering these values.
For further analysis, the established inlet speed of gas and solid were varied as -20%, -10%, +10% and +20% to characterize the differences between the systems profiles.Subsequently, the obtained profiles were analyzed.
The model was solved using the discretization method for finite differences.Forty points of discretization were defined along the length of the rotary kiln.Discretization of the points was implemented according to the incoming stream of gas and solids into the kiln (Figure 1).For the discretization of the equations related to the solids, backward differentiation was used because they are fed into the beginning of the kiln (z = 0), and forward differentiation was used in the equations related to the gas because it is fed into the end of the kiln (z = L).The ordinary differential equations, functions of time, resulted from the discretization that were resolved by the numerical integrating method of Runge-Kutta with a variable step for error control, with an established tolerance of 10 -7 .The model was implemented in Mathcad.

RESULTS AND DISCUSSION
Successive integrations were made in the model equations until the variations between the results  were no longer observed, which indicates achievement of the steady state of the rotary kiln.
The temperature profiles of the gas, solid, and wall along the kiln's length in continuous operation are presented in Figure 2a.As expected, the kiln's temperature increases along its length to a maximum and then decays.
The CaCO 3 concentration profile along the length of the kiln is shown in Figure 2b.The profile follows the general pattern of a previous simulation (Spang 1972).Initially, there is a high concentration of CaCO 3 that decreases along the length of the kiln until it reaches zero.
The water concentration profile along the length of the kiln in steady state is shown in Figure 2c.The concentration of molecular water contained in the beginning of the feeding of solids decreases along the kiln until it becomes zero, as expected.Note that the final composition of the clinker widely varies from one industry to another and may vary even between operations of a same kiln because the composition of raw material is not constant, i.e., it may depend on the natural sources.In addition, changes in the operating conditions of a kiln produces variances in the final clinker concentration.An important aspect to highlight is that during the simulation of the actual system, it was not trivial to set values of inlet gas flow and solid flow that together satisfied the required values for the profiles of temperature and clinker concentration.
The profiles of temperature and clinker concentration obtained by varying the inlet gas speed by -20%, -10%, +10% and +20% are shown in Figures 3 and 4, respectively.The temperature profiles in Figure 3 are very similar, with only slight differences in the shapes of the temperature peaks noticed.In Figure 4, it is observed that C 3 A, C 4 AF and CaO have similar profiles in all of the proposed systems, whereas C 3 S and C 2 S have different profiles in each one of them.In general, the increase of the inlet gas speed from -20% to +10% increases the final concentration of C 3 S and decreases the final concentration of C 2 S.However, with +20% increase of inlet gas speed there is a decrease of the final concentration of C 3 S and an increase of C 2 S concentration.
As the quantity of energy proposed for the fuel combustion is constant, the increase of the inlet gas speed increases the energy transfer from the solid that is near the output of the kiln to the solid inside the equipment.The energy transfer is responsible for the increase of temperature inside the kiln, which is necessary for the chemical reactions to occur (Table II).The increase of the inlet gas speed from -20% to +10% increases the consumption of C 2 S and the production of C 3 S while CaO is available (Figure 4a, b and c).A +20% increase of the inlet gas speed strongly promotes the formation of C 2 S, produced in lower temperatures than C 3 S (Table II), and consequently reduces the availability of CaO in the system.Therefore, even with an increase of temperature, the production of C 3 S is limited (Figure 4d).
The temperature and clinker concentration profiles that were obtained by varying the inlet solid speed by -20%, -10%, +10% and +20% are shown in Figures 5 and 6, respectively.In Figure 5, it is observed that the temperature of the burning zones, which correspond to the highest peak, decrease with the increase of the inlet solid speed.There is also an enlargement of the transition zone that corresponds to the second highest peak.In Figure 6, the concentrations of C  II), a reduction of temperature in the system (Figure 5) does not significantly affect the production of these species, which is not true for C 3 S that are formed at higher temperatures (Table II).An increase of the inlet solid speed promotes a decrease of the temperature profile of the kiln and consequently reduces the formation of C 3 S from C 2 S, which occurs at temperature above 1260 o C (Figure 2).For this reason the profiles of C 3 S and C 2 S are modified.

CONCLUSIONS
A mathematical model able to describe the temperature and concentration profiles of the clinker components along a real rotary kiln, in continuous operation, was developed.The mathematical model proposed in this paper does not require advanced computing to be solved, and it is easily adaptable to new industrial realities.
Variations of the gas and solid inlet speeds by -20%, -10%, +10% and +20% were individuality analysed according to the resulting temperature and concentration profiles of the clinker.These results were obtained via the model in the simulation of the real process.These parameters of operation were chosen because they have a significant influence in the process of cement production, and they can be changed without much modification in the kiln.In addition, these parameters can be used to find new operating conditions for the equipment.

Figure 1 -
Figure 1 -Volume control used in the mathematical modelling of the rotary kiln (adapted from Spang 1972).
The concentration profiles of C 3 S, C 2 S, C 3 A, C 4 AF, and CaO along the length of the kiln in continuous operation are shown in Figure2d.A decreasing behavior in the concentration of reactants followed by the formation of the clinker components is observed, which is in agreement with the expected.

Figure 2 -
Figure 2 -Temperature profiles of the gas, the solid and the industrial rotary kiln's wall (a); concentration profiles of CaCO3 (b); concentration profiles of water (c) and concentration profiles of C3S, C2S, C3AF and CaO (d) in the industrial rotary kiln at steady state.
3 A, C 4 AF and CaO along the kiln have relatively similar profiles in all of the proposed systems, whereas C 3 S and C 2 S have different profiles in each one of them.The increase of the inlet solid speed promotes a later formation of C 3 S through the length of the kiln and decrease in the C 3 S final concentration.There is also an increase in the final concentration of C 2 S. As the formation of C 3 A and C 4 AF occurs before 1205 o C (Table Temperature profiles of the gas (Tg), the solid (Ts), and the wall (Tw) of the industrial rotary kiln at the steady state.(a) -20% of inlet gas speed; (b) -10% of inlet gas speed; (c) +10% of inlet gas speed; (d) +20% of inlet gas speed.DIULIA C.Q. RODRIGUES et al.

Figure 6 -
Figure 6 -Concentration profiles of C 3 S, C 2 S, C 3 A, C 4 AF and CaO in the industrial rotary kiln at steady state.(a) -20% of inlet gas speed; (b) -10% of inlet gas speed; (c) +10% of inlet gas speed; (d) +20% of inlet gas speed.