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Chemical Engineering Science 62 (2007) 2590 2607www.elsevier.com/locate/ces
Rotary Cement Kiln Simulator (RoCKS): Integrated modeling ofpre-heater, calciner, kiln and clinker cooler
Kaustubh S. Mujumdara ,b, K.V. Ganesha, Sarita B. Kulkarni a, Vivek V. Ranadea,
aIndustrial Flow Modeling Group, National Chemical Laboratory, Pune 411 008, IndiabDepartment of Chemical Engineering, Indian Institute of TechnologyBombay, Powai, Mumbai 400 076, India
Received 10 January 2007; accepted 26 January 2007
Available online 14 February 2007
Abstract
This paper presents an integrated reaction engineering based mathematical model for clinker formation in cement industry. Separate models
for pre-heater, calciner, rotary kiln and cooler were initially developed and coupled together to build an integrated simulator. Appropriate models
for simulating gassolid contact and heat transfer in pre-heaters were developed. Calciner was modeled by considering simultaneous combustion
of coal particles and calcination of raw meal. Complex heat transfer and reactions (solidsolid, gassolid and homogeneous reactions in gas
phase) in rotary kiln were modeled using three sub-models coupled to each other. Solidsolid reactions in the bed region of the kiln were
modeled using pseudo-homogeneous approximation. Melting of solids in the bed and formation of coating within the kiln were accounted.
Clinker cooler was simulated by developing a two-dimensional model to capture cross-flow heat transfer between air and hot clinkers. The
individual models were coupled with each other via mass and energy communication through common boundaries. The coupled model equations
were solved iteratively. The model predictions agree well with the observations and experience from cement industry. The model was used
to gain better understanding of influence of operating conditions on energy consumption in cement plant. Several ways for reducing energy
consumption were computationally investigated. The integrated model, the developed software RoCKS (for Rotary Cement Kiln Simulator)
and results presented here will be useful for enhancing our understanding and for enhancing the performance of clinker manufacturing. 2007 Elsevier Ltd. All rights reserved.
Keywords: Cement; Energy consumption; Reaction engineering model
1. Introduction
Cement making processes are extremely energy consuming.
Typically for producing one ton of cement, a well-equipped
plant consumes nearly 3 GJ. For each ton of clinker produced,
an equivalent amount of green house gases are emitted. The
manufacture of cement has been the focus of considerableattention worldwide because of the high energy usage and high
environmental impact of the process. Considering the recent
impetus on reduction in emission of green house gases and re-
duction in energy consumption, there is a renewed emphasis
on developing computational models for cement industry and
using this understanding for performance enhancement.
Corresponding author. Tel.: +9120 25902170; fax: +9120 25902621.
E-mail address:[email protected](V.V. Ranade).
0009-2509/$- see front matter 2007 Elsevier Ltd. All rights reserved.
doi:10.1016/j.ces.2007.01.063
A schematic of typical clinker making process is shown in
Fig. 1. The raw meal consisting of predetermined quantities
of CaCO3, SiO2, Al2O3 and Fe2O3 are passed sequentially
through pre-heater, calciner, kiln and cooler to form cement
clinkers. In a pre-heater section the raw meal is pre-heated to
calcination temperature via hot gases coming from calciner. In
a calciner, raw meal is partially calcined. The energy requiredfor endothermic calcination reaction is provided by combusting
a suitable fuel. In most cases, coal is used to provide the re-
quired energy, especially in India. The calciner is supplied with
tertiary air from the cooler and air coming out of kiln exhaust.
The former is to supply sufficient O2 for coal combustion and
later to utilize the heat of kiln gases to enhance calcination
reaction. The hot gases from calciner are sent to pre-heater as-
sembly for pre-heating the solids. The partially calcined solids
from the calciner are fed slowly to a rotary kiln. In the rotary
kiln, remaining calcination and other clinkerization reactions
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K.S. Mujumdar et al. / Chemical Engineering Science 62 (2007) 25902607 2591
Cooled clinker
Calcineous
Raw meal
Pre-heater
Assembly
Calciner
Kiln
Cooler
Tertiary Air
Secondary Air
Coal
Air to cooler
Kiln Exhaust
Hot gases
to pre-heater
Pre-heated
Raw meal
Exhaust to
atmosphere
Coal
Vent Air
Fig. 1. Schematic of cement clinker process.
occur (formation of C2S, C3A, C4AF). The energy required for
endothermic clinker reactions is provided by combusting coal
in the kiln. The pulverized coal along with the pre-heated air
(secondary air) is fed to the kiln in a counter current modewith respect to solids. Part of the solids melts in the kiln.
The melt formation causes an internal coating on kiln refrac-
tories. Counter current flow of gas entrains solid particles in
the free board region. Such entrainment enhances rates of ra-
diative heat transfer by increasing effective emissivity and con-
ductivity. The hot clinkers are discharged from kiln to clinker
cooler and hot gases from kiln exhaust are sent to the cal-
ciner. In a clinker cooler, a part of energy of solids is recov-
ered back by heat exchange with air. The pre-heated air from
the coolers is passed to kiln and calciner as secondary and
tertiary air, respectively. A small part of air may be vented if
required.This brief overview of clinker formation clearly demonstrates
the strong coupling among pre-heater, calciner, kiln and cooler.
It is therefore essential to develop an integrated model for pre-
heater, calciner, kiln and cooler in order to capture key char-
acteristics of clinker manufacturing and to enable the model to
be used as simulation or optimization tool. Such an attempt is
made in this work.
Recently some attempts have been made to develop
computational fluid dynamics (CFD) based models to simulate
either calciner (for example,Lu et al., 2004) or kiln (for exam-
ple, Mastorakos et al., 1999; Mujumdar and Ranade , 2003).
Though such CFD models show promise in simulating details
of combustion and burner designs, it is almost impossible to
build CFD models for simultaneous and coupled simulations
of pre-heaters, calciner, kiln and cooler. The CFD models are
thus not very useful to gain understanding of coupling and
exploring ways to reduce overall energy consumption per tonof clinker. Some attempts have also been made to develop
reactionengineering models for kiln (for example, Mujumdar
and Ranade, 2006; Spang, 1972). Such models have shown
promising capabilities in capturing the overall behavior and
providing useful clues for reducing energy consumption in
rotary cement kilns. The numerical experiments using the com-
putational model could also predict the influence of kiln oper-
ating parameters on net energy consumption (NEC) in kilns.
Such guidelines can provide useful hints to operating engineers
for kiln optimization. However, none of these models have in-
cluded coupling of pre-heater, calciner, kiln and clinker cooler.
This work was undertaken to fulfill this need. The motivationof the present work was to develop a framework of reaction
engineering based computational model for clinker formation
in cement industry and use this framework subsequently for
exploring possible performance enhancement. The paper is
organized as follows.
The key issues in modeling individual models are discussed
in Section 2. The computational model and the modeling strat-
egy are thereafter presented in Section 3. Section 4 reports
the results of computational simulations of model with respect
to key operating parameters. The use of the developed model
to explore possible ways of reducing energy consumption in
kiln is discussed in Section 5. Key findings of the study are
summarized at the end.
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However, all the attempts for prediction of residence time in
cyclones were based on lab scale cyclones and none of the
studies were extended or reported for industrial scale cyclones.
This parameter was therefore treated as an adjustable param-
eter in the model. In the present work, we have adjusted the
residence time so as to get desired degree of calcination as per
industrial observations. It was confirmed from our prior simula-tions(Warudkar et al., 2005) that varying residence time in the
calciner by 10% had relatively small effect (2.5%) on pre-
dictions of percentage calcination. It is also essential to obtain
relevant kinetics for calcination reaction in calciner. Thermal
decomposition of limestone calcination is a complex process.
A wide discrepancy is observed in the proposed rates for cal-
cination reaction. In our recent work (Mujumdar and Ranade,
2006) we have compared models proposed by 18 investigators
which showed wide scatter. Watkinson and Brimacombe (1982)
have reported experimental data on calcination of limestone in
experimental kiln. The experimental conditions of their exper-
iments were close to industrial operations (bed temperature
1000.
1300 K). Their data was therefore used to find calcination
kinetics in this work.
2.3. Rotary kiln
The partially calcined raw meal is passed slowly to the rotary
kiln where the clinkerization reactions occur. In the initial part
of the kiln the remaining calcination occurs. Other solidsolid
and solidliquid clinkerization reactions take place as the solid
bed moves towards the burner. Part of the solids melts in the
kiln. The melt formation causes an internal coating on kiln re-
fractories. Counter current flow of gas entrains solid particles
in the freeboard region. Such entrainment enhances rates of ra-diative heat transfer by increasing effective emissivity and con-
ductivity. In this section we discuss the key issues involved in
modeling the cement kilns very briefly. The main key issues for
modeling the rotary cement kilns are estimating the residence
time of solids in the kiln, cinkerization reaction in bed region,
coal combustion in freeboard region, heat transfer between bed
freeboard and walls, melting/coating formation around the kiln
walls. These issues are discussed in detail in our recent work
(Mujumdar et al., 2006)and therefore are not repeated here.
2.4. Clinker cooler
The hot solids from the kiln are discharged on the grate of
clinker cooler. As the grate moves with uniform speed along
the cooler length, solids lose their heat to cross-flow air. A part
of the air is generally sent to the kiln as secondary air, a part to
calciner as tertiary air and a part is vented to the surroundings
(vent air). The most important key issue in modeling grate cool-
ers is predicting the heat transfer coefficient between hot solids
and cross-flow air. There is no information on modeling of heat
transfer in such cases. In absence of any relevant information
we have used heat transfer correlation in packed bed reactors
to estimate the heat transfer. Nsofor and Adebiyi (2001) have
carried experimental measurements and presented correlation
for forced convection gas particle heat transfer coefficient for
wide range of temperatures (2001000 C). Since the temper-
atures in clinker cooler are in the same range this correlation
was used to model heat transfer coefficient between solids and
gas. The computational models for individual components and
the coupling strategy are discussed in the following section.
3. Computational models and solution methodology
3.1. Cyclone pre-heater model
A schematic of pre-heater unit considered for developing
computational model is shown in Fig. 3a. The present frame-
work of computational models was developed for dry process
of clinker formation since this process is widely used in ce-
ment industry. For the dry processes, the moisture content is
generally present in very small amount (typically 0.5%, see
for example Engin and Ari, 2005; Peray, 1984). The energy
requirements for removing the moisture from the feed being
small (less than 0.5% of the total energy consumption), the feed
was considered to be free of moisture in this work. However,
the developed framework is quite general and including evap-
oration of moisture from the feed is straightforward. The gas
phase and solids in a cyclone was assumed to be completely
back mixed. In Fig. 3a, Ms is the mass of solids entering the
cyclone.Mg is the mass of the air entering the cyclone. Mse is
the mass of solids entrained from a cyclone. Each cyclone was
assumed to be lined with refractory of thicknesstr .
Thus, for any i th cyclone in pre-heater assembly the follow-
ing inlet streams were considered:
1. Solids from the (i 1)th cyclone (Ms,i1 at temperature
Ti1).2. Solids that are entrained by gas from (i +1)th cyclone
(Mse,i+1 at temperature Ti+1).
3. Air from(i +1)th cyclone (Mg at temperature Ti+1).
The outlet streams for this cyclone are:
1. Solids going out of cyclone (Ms,i at temperature Ti ).
2. Solids that are entrained by gas (Mse,i at temperature Ti ).
3. Air going out (Mg at temperature Ti+1).
The steady state material balance equation for ith cyclone is
written as
Ms,i1+ Mse,i+1= Ms,i + Mse,i , (1)
Mse,i =(1m,p)Ms,i . (2)
In the above equationsm,p represents the particle capture ef-
ficiency of thei th cyclone.Mrepresents the mass of the solids
(in kg/s) and subscripts s andse represent solids and entrained
solids, respectively, as explained earlier.
The steady state energy balance for the i th cyclone was writ-
ten as
Ms,i1 Cp,s Tc,i1+ Mse,i+1 Cp,s Tc,i+1
+Mg Cp,g Tc,i+1
=Ms,i Cp,s Tc,i + Mse,i Cp,s Tc,i
+ Mg Cp,g Tc,i +hcyc Acyi (Tc,i Tiw,i ). (3a)
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i
Tiw,i
1. Refractory
2. Shell
Mg,Mse,i-1Ti-1
Mg,Mse,iTi
Ms,i,Ti
12
Tow,i
Radiation and convection
Losses
Hot clinker, Ts, in Cold clinker, Ts, out
Secondary air Tertiary air Vent air
Cooling Air, Ta
T=0
x
T=0
y
x
T=0
T=0
y
L
Loses
Air in
Gas out
Coal in
Partially calcined raw meal
Raw meal
Ms,i-1Ti-1
Fig. 3. (a) Schematic of (a) cement pre-heater, (b) cement calciner, and (c) grate cooler.
In the aboveCp,s and Cp,g represents the specific heat of solids
and air, respectively. Subscript g represents the air and Tc,irepresents the temperature of solids and air in the i th cyclone.
hcycrepresents the heat transfer coefficient for energy exchange
between particle laden gas and cyclone inner walls. hcyc was
evaluated from the following empirical correlation given by
Gupta and Nag (2000)for heat transfer in cyclones:
hcycdc
kg=702.818+9.02871014u0Re+11.1385
Pu20
+ 4.50398105P
u0
Re+Rc,
where
Rc = Fpw
T4iw T
4g
Tiw Tg
dc
kg. (3b)
The LHS of Eq. (3a) thus represents the total energy entering
the cyclone and RHS represents the energy leaving out of the
cyclone. At steady state the heat given to cyclone walls must
be same as heat conduction in through refractory and cyclone
walls, which is equal to loss from shell walls due to convection
and radiation. The energy balance for heat transfer in cyclone
cross-section is written as
hcyc Acyi [Tc,i Tiw,i ] =2Lkr [Tiw,i Tr,i]
ln(rr /ri ), (4)
2Lkr [Tiw,i Tr,i]
ln(rr /ri )
=2Lksh [Tr,iTow,i ]
ln(r0/rr )
,
(5)
2Lksh [Tr,i Tow,i ]
ln(r0/rr )
=hconv Acyo [Tow,i T0] + cy Acyo [T4
ow,i T4
0].
(6)
In the above equations,Tiw,i is the internal wall temperature of
thei th cyclone,Tr,iis the temperature of interface of refractory
and shell, Tow,i is the temperature of external wall of the ith
cyclone andT0is the ambient temperature.L is the total height
the cyclone, kr is the thermal conductivity of the refractory
and ksh is the thermal conductivity of cyclone walls. r0 is the
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The individual species balances for limestone and calcium
oxide are given as
dmCaCO3,L
d = rc, (18)
dmCaO,L
d =rc MwCaO
Mw CaCO3. (19)
The energy balance for the raw meal particle is given as
d(mp,LCp,s TL)
d =hc,L
LAp (Tg TL)
+ LLAp (T
4g T
4L )
+ Cp,s TLdmp,L
d , (20)
where TL is the temperature of raw meal particle, L is the
emissivity of solid particle, LAp is the area of the raw meal
particle (which was calculated based on conversion i.e., mass ofraw meal particle reacted) and is residence time of raw meal
particle in the calciner.hc,L was estimated by using Eq. (11).
3.2.2. Continuous phase
The over all gas mass balance is given as
dmg
dt=mgin mgout+ [mp,cin mp,cout]
c Np
+ [mp,Lin mp,Lout ]LNp, (21)
where mg is the mass of the air in the calciner, cNp is the
number of particles of coal coming in per unit time and L
Npis the number of particles of raw meal coming in per unit time.
The individual species mass balance for rate of change of mass
of oxygen, carbon-dioxide, volatile matters and water can be
written as
dyO2dt
=1
mg
mg,in yO2in mg,out yO2out
[mp,c yc,cin mp,c yc,cout ]
c Np MwO2
Mw char
rcombg
Mw vol Vreact MwO2 ZO2 yO2 dmg
dt ,
(22)
dyCO2dt
=1
mg
mgin yCO2in mgout yCO2out
+[mp,c yc,cin mp,c yc,cout]
c Np M wCO2
Mwchar
+ [mp,Lin mp,Lout ]LNp
+
rcombg
Mw vol
Vreact M wCO2 ZCO2
yCO2
dmg
dt , (23)
dyv
dt=
1
mg
mg,in yv,in mg,out yv,out
+ [mp,cin yv mp,cout yv] c Np
rcombg
Mwvol Vreact M wvol Zvolyvol
dmg
dt
, (24)
dyw
dt=
1
mg
mgin ywin mgout ywout
+
rcombg
Mw vol
Vreact Mww ZH2O yw
dmg
dt
,
(25)
where yO2, yCO2, yv, yw are the respective mass fractions of
oxygen, carbon-dioxide, volatile matters and water. Mw O2,Mw CO2 , Mwvol and Mww are their respective molecular
weights.Vreact is the volume of reactor. Subscripts in and outrepresent the inlet and outlet conditions and Z is the stoichio-
metric coefficient.
The energy balance equation for the gas phase is given as
dmgCp,g Tg
dt=mgin Cp,g Tg,in mgout Cp,g Tg
+Sgcomb+ Sccomb+ Scalc
hcyc Acyi (Tg Tiw ), (26)
where
Sgcomb= rcombg Hcombg Vreact, (26a)
Sccomb=
0
hc Ap (Tg Tcl)+c Ap (T
4gT
4cl)
+ Cp,c Tcldmp,c
d
(1fc)Hcomb rcomb
d, (26b)
Scalc=
0
hc,L
LAp (Tg TL)+LLAp (T
4g T
4L )
+ Cp,s TLdmp,L
d +rc Hcalc d. (26c)
In the above equations, Sgcomb, Sccombare the heat source term
for gas-phase from volatile combustion and char combustion,
respectively. Scalcis the heat sink term from calcination. Hcombg,
Hcalcare the enthalpies of volatile combustion and calcination.
hc,Lis the convective heat transfer coefficient between raw meal
particles and air. The steady state equations across the cyclone
walls were written same as that of pre-heaters explained in
the previous section to obtain temperature of calciner internal
walls, refractory and outer walls.
The calciner model equations were solved using an iterative
method. The model equations for gas phase were solved as-
suming steady state. For the first iteration, source terms from
discrete phase were assumed to be zero. The temperature and
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mass of species obtained by solving continuous phase were used
in discrete phase equations to get the new source terms from
the discrete phase. The sources from the discrete phases were
passed to continuous phase to get the new mass and temperature
terms for discrete phase. This procedure was continued till the
subsequent changes in temperature of gas phase were within
0.1%. Suitable under-relaxation parameters were defined toaccelerate convergence. Typically about 20 iterations were re-
quired to achieve convergence. The differential equations for
discrete phase were solved by modified Gears method imple-
mented in ODEPACK (Hindmarsh, 1983). The algebraic equa-
tions for continuous phase were solved using NewtonRaphson
method.
3.3. Kiln model
A comprehensive one-dimensional model was developed to
simulate complex processes occurring in rotary cement kilns.
A modeling strategy comprising three sub-models viz. model
for simulating variation of bed height in the kiln, model for
simulating clinkerization reactions and heat transfer in the bed
region and model for simulating coal combustion and heat trans-
fer in the freeboard region was developed. The Kramers model
(Kramers and Croockewit, 1952)which relates volumetric flow
rate of solids,v, with kiln tilt (, radian), angle of repose (,
radian), radius of kiln(R,m), rotational speed of kiln (n) and
height of solids (h) was used to model bed height variation in
the kiln. The clinkerization reactions in solid bed were modeled
assuming solids as pseudo fluids. Melting of solids in bed re-
gion and formation of coating within the kiln were accounted.
Combustion of coal in the freeboard region was modeled by
accounting devolatilization, finite rate gas phase combustionand char reaction. Knowing the bed and freeboard gas temper-
atures, the temperatures of kiln inner wall, refractory and shell
were obtained by solving steady state energy balance across
the kiln walls. The details of the models and model equation
are discussed in detail in our recent publication (Mujumdar
et al., 2006) and are not repeated here for the sake of brevity.
3.4. Cooler model
The mathematical model of cooler was based on a schematic
shown inFig. 3c. Solids of uniform particle size and constant
porosity were assumed to move in a plug flow with constantgrate speed. Air was assumed to enter in a cross-flow mode
with respect to solids in y direction. The amount of air fed to
the cooler was distributed as secondary air (to kiln) from the
front section of cooler, followed by the tertiary air (to calciner)
and finally the vent air (Locher, 2002) as shown in Fig. 3c.
The amount of secondary, tertiary and vent air (in kg/s) go-
ing to kiln, calciner and exhaust, respectively, were assumed
to be proportional to the fraction of length of each section in
the cooler. The fractional length of each section was user in-
put to the model. To get the temperature profiles of solid bed
and air, the clinker cooler was divided into n segments along
the length of the cooler and m segments along the height of
the cooler. Mass and energy balances were solved for these
segments. Conductive heat transfer was considered for solids in
both horizontal and vertical directions. Convective heat transfer
coefficient between air and solids was calculated from empiri-
cal correlation assuming solids as packed bed as discussed pre-
viously. The boundary conditions used in the model are shown
inFig. 3b. The model equations are presented in the following.
Mass balance for solids can be written asdms(i,j)
dx=0. (27)
Assuming steady state operation, the energy balance equation
can be written as
(s (1)us,x Cp,s Ts )
x+
(s (1)us,y Cp,s Ts )
y
={(1)ksTs /x}
x+
{(1)ksTs /y}
y
a hc,c (Ts Tg). (28)
In this equations
is the cement clinker density,Cp,s is clinker
heat capacity, us is grate speed, and Ts is clinker temperature
of solid at any point,ks is clinker thermal conductivity,a is the
surface area per unit volume, hc,c is convective heat transfer
coefficient between solid clinker and air in the cooler, is
the porosity, Tg is air temperature at any point in the cooler.
In Eq. (28) the first and second terms of the right-hand side
represents the conductive heat transfer. The last term in right-
hand side represents convective heat transfer between the air
and solids.
The mass balance for air can be written as
dma(i,j)
dy=0. (29)
Energy balance for air can be written as
(gug,x Cp,g Tg)
x+
(gug,y Cp,g Tg)
y
={kgTg/x}
x+
{kgTg/y}
y+a hc,c (Ts Tg).
(30)
In this equation g is the density of the air,ug,y is inlet speed
of cooling air, and Tg is air temperature at any point, k is air
thermal conductivity,Ts is solid temperature at any point in the
cooler. In Eq. (30) the left-hand side terms represents the net
energy input by the air. First two terms in the right-hand side
represent the conduction between the air layers and the final
term is due to the convection between solids and air.
In Eq. (30) hc,c is convective heat transfer coefficient be-
tween solid clinkers and air. Developing accurate models for
convective heat transfer coefficient between solids and air is
important in capturing heat transfer in the cooler. In this work
the convective heat transfer coefficient was calculated based on
empirical expression given by Nsofor and Adebiyi (2001). The
empirical expression is given as
Nu=8.74+9.34 [6(1)]0.2 Re0.2 Pr0.33
(30
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It is important to note that the Reynolds numbers for commer-
cial clinker cooler are significantly higher (Re 1000.2000)
as compared to the experimental conditions of Nsofor and
Adebiyi (2001). However, as discussed earlier, there are no
other systematic experimental studies reported to predict con-
vective heat transfer coefficients in clinker coolers. The empiri-
cal correlation (Eq. (31)) was developed for particle sizes closeto those found in industrial clinker coolers and for wide range
of temperature conditions as observed in clinker coolers. Fortu-
nately, the empirical correlation seems to be weekly dependent
on Reynolds number (Reynolds number is to power 0.2). There-
fore possible errors associated with Eq. (31) are not expected
to change the simulation results significantly (predicted Nus-
selt number is 50.60). Hence Eq. (31) was used to predict
gas solid heat transfer in clinker coolers in the present model.
All the physical properties for determining heat transfer coef-
ficient were calculated at an average temperature of solids and
air as Tf =(Ts +Tg)/2. The system of algebraic linear equa-
tions formulated for above model equations was solved using
tri-diagonal matrix algorithm (TDMA).
3.5. Integrated model and solution strategy
The individual models for pre-heater, calciner, kiln and
cooler described in the previous section were coupled with
each other to develop a simulator for the entire system. The
schematic of the simulator is shown inFig. 4.The required in-
puts to the simulator are flow rates and composition of (a) raw
meal entering the pre-heater, (b) air entering the cooler, (c) coal
entering the calciner and the kiln, and (d) the material prop-
erties and operating parameters of the individual equipments
(for example, kiln RPM, grate speed of cooler). However, tosolve the integrated simulator, it is necessary to know the in-
let conditions for the calciner (flow rate, mass fractions and
temperature of solids and air from pre-heater, kiln and cooler),
pre-heater (flow rate and temperature of air from calciner), kiln
(flow rate, mass fractions and temperature of secondary air
from cooler and partially calcined raw meal from the calciner)
and cooler (flow rate and temperature of solids from kiln).
To generate these inputs a pre-processor was developed. The
function of pre-processor was two-fold. The pre-processor was
used to develop good initial guess for the simulator and also to
check for any inconsistency of input data. The pre-processor
generated the initial guess (for mass flow-rates, composition
and temperatures of raw meal and air) for the individual mod-els based on overall material and energy balances. Following
parameters were provided to the pre-processor to achieve this:
1. Percentage calcination occurring in the calciner(P ).
2. Temperature of secondary air (Tg,S)and tertiary air (Tg,T)
leaving the cooler.
3. Temperature of air leaving the kiln (Tg,K ).
4. Temperature of air exiting the pre-heater to the atmosphere
(Tg,P).
5. Temperature of solids exiting the cooler (Ts,R ).
6. Heat losses (HLoss,K ) and heat of clinkerization reaction in
the kiln (HR,K ).
These values are usually known or can be easily available for
any cement plant and can therefore be used to generate good ini-
tial guess for faster convergence of solution. The pre-processor
solves mass and energy balance equations as discussed in the
following. Based on the percentage calcination in the calciner,
the mass of CO2 produced in calciner was calculated as
mCO2,C = mCaCO3,i P MwCO2
Mw CaCO3, (32)
where mCaCO3,i is the total amount of CaCO3 in the inlet raw
meal. The mass flow rate of solids entering the kiln was calcu-
lated as
Ms,C =Ms,P mCO2,C , (33)
where Ms,C is the mass flow rate of raw meal leaving the
calciner or entering the kiln, Ms,Pis the mass flow rate of the
solids entering the pre-heater. The corresponding mass fraction
of solids species leaving the calciner or entering kiln were
calculated as
xCaCO3,C =mCaCO3,i mCaCO3,i P
Ms,C,
xCaO,C =(mCO2,C )(M wCaO)
(Ms,C )(MwCO2 ),
xSiO2,C =mSiO2,i
Ms,C, xAl2O3,C =
mAl2O3,i
Ms,C,
xFe2O3,C =mFe2O3,i
Ms,C, (34)
wherex is the mass fraction of the component in the raw meal.The amount of clinker leaving the kiln or entering the cooler
Ms,K was calculated as
Ms,K =Ms,C (Ms,C )xCaCO3,C
MWCaCO3MwCO2 . (35)
Based on overall material balance on kiln, the amount of air
leaving the kiln was calculated as
Mg,K =Mg,S+Ms,C xCaCO3,C Mw CO2
Mw CaCO3
+ Mc,K
yc,K
MwCO2
MwCaCO3, (36)
where Mg,Sis the mass of secondary air entering the kiln, Mg,Kis the air leaving the kiln or entering the calciner, Mc,K is the
amount of coal entering the kiln and yc,K is the mass fraction
of char entering the kiln. The amount of air leaving the pre-
heater assembly was calculated as
Mg,P =Mg,K +Mg,T +mCO2,C
+ Mc,C yc,c Mw CO2
Mw CaCO3, (37)
where Mg,P is the mass of air entering the pre-heater, Mg,T
is the mass tertiary air entering the calciner, mCO2,C is the
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Call PreprocessorConsistence Checks
&
Generate initial guess
Call Sub-models
Update variables
Converged
YN
No
Yes
Post Processing
User Input
Dimensions, MOC,
Mass Flow Rate,
Mass Fractions,
Temperature
Fig. 4. Solution methodology of the simulator.
CO2produced in calciner due to calcination reaction andMc,Cis the amount of coal entering the calciner and yc,c is the mass
fraction of char entering the calciner. The temperature of solids
leaving the kiln was calculated as
Ts,K =(Ms,R Cp,s Ts,R + Mg,T Cp,g Tg,T +Mg,S Cp,g Tg,S)(Mg,in Cp,g Tg,in)
(Ms,K Cp,s ). (38)
In the above equation, Mg,in and Tg,in are the mass flow rate
and temperature of air entering the cooler and Ts,R is the tem-
perature of solids exiting the cooler. The temperature of solids
entering the kiln or exiting calciner (Ts,C ) is calculated as
Ts,C =(Ms,K Cp,s Ts,K +Mg,K Cp,g Tg,K +HR,K +HLoss,K Mg,S Cp,g Tg,SHc,K )
(Ms,C Cp,s ). (39)
In the above equation, Hc,K is the heat released due to coal
combustion in kiln,HR,K is heat required for clinker reactions
andHLoss,K is the loss from the kiln. The temperature of solids
entering the kiln is essentially same as temperature of gases
leaving the calciner (Tg,C ). Finally, the temperature of solids
entering the calciner or leaving the pre-heater assembly (Ts,P)
was calculated as
Ts,P =(Ms,C Cp,s Ts,C +Mg,C Cp,g Tg,C + Hcalc Mg,K Cp,g Tg,K Mg,T Cp,g Tg,T Hc,C )
(Ms,P Cp,s ). (40)
In the above equation, Hc,Cis the heat released due to coal com-
bustion in the calciner and Hcalc is the heat required by calci-
nation reaction. This was easily calculated based on percentage
calcination occurring in the calciner. The heat losses in calciner
are negligible as compared to total heat supplied to the calciner
(< 5% of total energy input) and therefore was not considered
in pre-processor calculations. In this way the input conditions
(mass, mass fractions and temperature) for pre-heater, calciner,
kiln and cooler were calculated using pre-processor. The values
calculated by pre-processor were passed as input conditions to
the individual models. The individual models were then solved
iteratively as shown inFig. 4.The iterations were continued till
the temperature of solids and gases at exit of individual com-
ponents were within error of 1%. Suitable under-relaxation
parameters were used. Typically 1020 iterations were required
for solution to converge. We have also carried out several test
simulations of limiting cases to verify that implemented nu-
merical techniques and computer programs are correctly solv-
ing the model equations. For example, the calciner and kiln
were solved by switching off the calcination and clinkeriza-
tion reactions in the calciner and kiln, respectively. For these
simulations the material and energy balances converged to an
error of 1% giving verification that numerical calculations
are correctly solving the model equations. It was also verified
that the converged solution is not a function of initial guess or
under-relaxation parameters. An easy to use, graphical user
interface (GUI) based software called RoCKS (Rotary Cement
Kiln Simulator) was developed based on the integrated modules
of pre-heater, calciner, kiln and cooler.
4. Results and discussion
The integrated model (RoCKS) presented in the previous
section was used to simulate performances of pre-heater, cal-
ciner, rotary kiln and cooler in clinker manufacturing. Based on
the available data on rotary kilns (Mujumdar et al., 2006) and
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available information from some of the cement industries, a
typical clinker manufacturing configuration was selected as a
base case. Some assumptions were made to fill in the gaps in the
available data. The details of selected configuration are given in
Tables 2ac. Though the developed mathematical framework is
general enough to accommodate temperature dependent phys-
ical properties like heat capacity, at this stage, these propertieswere treated as constants. The physical properties of solids and
air used in this work are specified in Table 3a. Our prior simu-
lations of kiln and calciner (Mujumdar et al., 2006; Warudkar
et al., 2005) indicated that the errors in overall energy
consumption associated with the assumption of temperature
independent values of specific heat were within 1%. The oper-
ation of the base case (described inTables 24)was computa-
tionally studied to understand the various processes occurring
in individual units in clinker formation. On obtaining satisfac-
tory results from the base case, several numerical experiments
were performed using the model for understanding interac-
tions among different processes and for possible optimization
of clinker manufacturing process.
4.1. Base case simulation
The predicted results from the simulation of the base case
are summarized in Table 4. The mass fractions and tempera-
tures of solids and air in pre-heaters, calciner, kiln and cooler
obtained from the simulation are plotted inFigs. 5 and 6, re-
spectively. It is important to note that the flow of air is counter
current with respect to the flow of solids in the system. The ab-
scissas ofFigs. 5 and 6denote particular equipment in clinker
formation as discussed below. Abscissas 14 corresponds to
Table 2
The dimensions of (a) pre-heater unit, (b) kiln and (c) cooler
S/No. Description Units Values
(a)
1 No. of pre-heaters 4
2 Height of cylindrical section m 5
3 Height of conical section m 3
4 Diameter of cyclone m 3
5 Diameter of cone tip m 1
6 Refractory thickness m 0.13
7 Shell thickness m 0.03
8 Inlet duct height m 1
9 Inlet duct width m 1
10 Diameter of outlet pipe m 1
(b)
1 Length m 50
2 Inner diameter m 3.4
3 Coating thickness m 0.136
4 Refractory thickness m 0.2
5 Shell thickness m 0.025
(c)
1 Length m 11
2 Width m 1
Table 3
(a) The physical properties of solids and air, (b) particle size and composition
of coal and (c) particle size and composition of raw meal
Description Air Raw meal Coal
(a)
Thermal conductivity, W/m K 0.116 0.5 0.5
Emmisivity 0.4 0.9 0.8Heat capacity, J/kg K 1000 1000 1000
Viscoscity, kg/m s 1e05
Density, kg/m3 1.3 1500 1000
Char calorific value, kcal/kg 5600
Volatile calorific value, kcal/kg 11 900
(b)
Coal particle size, 50 m
Volatile (CH4)a, 27%
Char, 58%
Ash, 15%
(c)
Raw meal particle size, 50 m
CaCO3, 80%
CaO, 0%
SiO2, 14%
Fe2O3, 3%
AL2O3, 3%
a Mujumdar et al. (2006).
pre-heater assembly. Abscissas 4 and 5 denote the calciner in
the system. Abscissas 515 denote the rotary kiln and 1518
denote the cooler section. Fig. 5 shows a plot of mass frac-
tions in pre-heater, calciner, kiln and cooler (only CaO, C2S
and CO2 mass fractions are plotted for the sake of brevity).Since there is no reaction occurring in pre-heater section, the
composition of CaO and CO2in this section do not vary. How-
ever, in the pre-heater section the raw meal gets heated from
300 to 1069 K and hot gases from calciner get cooled (from
1224 to 539 K) as can be seen fromFig. 6.As the raw meal
passes through the calciner, it gets partially calcined. There-
fore, CaO concentration increases in the calciner section as
can be seen from Fig. 5. Similarly since CO2 is formed due
to calcination and coal combustion, the mass fraction of CO2increases in the calciner. Coal combustion in the calciner ac-
counts for rise in temperature of both solids and gas in the
calciner (seeFig. 6). Remaining clinkerization reactions occurin kiln. The mass fraction and temperature profiles obtained in
kiln (as shown inFigs. 5 and 6) are similar to previously pub-
lished results(Mujumdar and Ranade, 2006; Mastorakos et al.,
1999). Since there is no reaction occurring in the cooler, mass
fraction of solids in the clinker cooler do not vary. However,
air entering the cooler gets pre-heated (from 300 to 1200 K)
and solids get cooled (from 1632 to 476 K) in the cooler sec-
tion. The predicted energy requirements of individual processes
like clinkerization reactions, losses, melting predicted by the
model are listed inTable 4. The obtained results are qualita-
tively similar to previously published results (Engin and Ari,
2005). The performance of the overall system was characterized
in terms of NEC per unit weight of product (clinker coming out
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K.S. Mujumdar et al. / Chemical Engineering Science 62 (2007) 25902607 2601
Table 4
Complete energy balance of the system
S/No. Description Pre-heater Calciner Kiln Cooler
1 Solid inlet temperature, K 300 1069.2 1214.8 1622.4
2 Mass flow rate, kg/s 50 50 37.74 32.3
3 Air inlet temperature, K 1214.8 1114.5 1229.9 300
4 Air flow rate, kg/s 60.8 46.7 16.2 455 Coal flow rate, kg/s 2.15 0.9
6 Coal inlet temperature, K 350 350
7 Heat with solids in, kJ/kg clinker 463.0 1650.2 1415.3 1622.4
8 Heat with air in, kJ/kg clinker 2297.9 1603.6 615.0 416.7
9 Heat with coal in, kJ/kg clinker 23.2 9.7
10 Combustion of coal, kJ/kg clinker 1876.7 747.1
11 Heat of reaction, kJ/kg clinker 1384.5 219.0
12 Heat of melting, kJ/kg clinker 44.2
13 Heat of solids leaving, kJ/kg clinker 1650.2 1415.3 1622.4 463.0
14 Heat of air leaving, kJ/kg clinker 1014.4 2297.9 1603.6 1415.3
15 Heat of vent air in cooler, kJ/kg clinker 109.4
16 Heat with ash, kJ/kg clinker 3.22 2.24
17 Loses, kJ/kg clinker 98.9 43.5 140.7
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Divisions across the cement clinker process
Massfraction
CaO -Solid mass fraction
C2S-Solid mass fraction
CO2-Gas mass fraction
Pre-Heaters
Calciner
Kiln
Cooler
Fig. 5. Solid and gas mass fractions in pre-heaters, calciner, kiln and cooler
in a cement clinker process.
of the kiln). The NEC is calculated as
NEC=(ERXN,C +ERXN,K +EMELT,K )+ ELOSS+(EG,OUT+ ES,OUT EG,IN ES,IN). (41)
In the above equation, ERXN denotes the energy required for
clinkertization reactions and subscripts C and K denotes the
calciner and the kiln, respectively. The term EMELT,K denotes
the energy required for melting in the kiln. ELOSS denotes the
summation of energy losses from pre-heater assembly, calciner
and kiln. The other terms denote energy flow rates (subscripts
IN or OUT) for the gas and solid streams (subscripts G or
S) which denote the energy required to raise the sensible heat
of the solids. Based on above calculations, the NEC predicted
by the integrated simulator, for these operating conditions was
2635 kJ/kg clinker (630 kcal/kg clinker) which seems to be
reasonable when compared with industrial observations. Over-
all the integrated simulator was able to predict the clinker man-
ufacturing process in cement industry reasonably well.
4.2. Influence of key design and operating parameters on NEC
On obtaining a reasonable agreement, the model was used to
explore space of design and operating parameters to understand
influence of these parameters on the performance of clinker
manufacturing. All these simulations were carried for a fixed
product composition (C3S mass fraction 0.48 in the product).This was achieved by altering coal flow rate either to calciner
or kiln. This analysis is presented in the section below.
4.2.1. Effect of number of pre-heaters
The effect of changing number of pre-heaters in pre-heater
assembly (from 3 to 5) on NEC was studied. For this simulation
the coal in the kiln was adjusted to get same product composi-
tion at the kiln exit. The results for this simulation are shown
in Fig. 7. It can be seen from Fig. 7 that as number of pre-
heaters in pre-heater assembly increases, solids get pre-heated
to a higher temperature before they enter the calciner (see sec-
ondary axis in Fig. 7). Therefore the coal requirement for a
fixed product composition decreases. Thus the NEC decreases
as number of pre-heaters increases. However, the overall cap-
ital cost increases by increasing number of pre-heaters in the
system. The developed model will be useful to carry out cost
to benefit analysis for introducing additional pre-heater in the
pre-heater assembly.
4.2.2. Effect of percentage calcination in the calciner
The pre-calcination of raw meal in calciner is an important
process in cement process. We have studied the effect of per-
centage calcination in calciner on NEC. To vary the percent-
age calcination in calciner the coal feed rate to the calciner
and kiln was altered for the same clinker composition. The
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0
500
1000
1500
2000
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Divisons accross the cement clinker process
Gastemperature,
K
0
500
1000
1500
2000
Solidtemperatu
re,
K
Solid temperature
Gas temperature
Pre-heaters
Cooler
Kiln
Calciner
Solids leaving 3rd preheater
Gases entering 3rd preheater
Fig. 6. Temperature profile across pre-heaters, calciner, kiln and cooler in a cement clinker process.
615
620
625
630
635
640
645
2 3 4 5 6
Number of pre-heaters
Energyc
onsumption,
kcal/kgclinker
1000
1020
1040
1060
1080
1100
Solidtemperatureenteringcalciner,K
Fig. 7. Effect of pre-heater number on overall energy consumption.
simulation results are shown in Fig. 8.As can be seen from
Fig. 8, the NEC was found to decrease till 70% calcination and
then it increases with further increase in percentage of calcina-tion. The secondary axis ofFig. 8shows that the kiln exit gas
temperature also shows a similar trend. Table 5shows a com-
plete comparison of heat of reaction occurring in kiln and cal-
ciner in this process. The heat of reaction in kiln decreases as
the percentage calcination increases in calciner. The total heat
of reaction in kiln is the summation of heat of calcination (en-
dothermic reaction) and the heat of clinker formation (exother-
mic reactions). When calcination occurs pre-dominantly in the
pre-calciner (> 70%), the energy requirements for reactions in
kiln reduce drastically. This causes increase in kiln flue gas
temperature and increase in losses from kiln shell. Therefore
the NEC and kiln flue gas temperature increases if more than
70% calcination occurs in the calciner. The model and the
626
631
636
641
646
651
656
661
666
40 50 60 70 80 90 100
% Calcination
EnergyCo
nsumption,
kcal/kgclinker
1000
1100
1200
1300
1400
1500
Kilnex
itgasTemperature,
K
Fig. 8. Effect of percentage calcination on overall energy consumption.
Table 5
Heat of reaction in calciner and kiln
S/No. Heat of reaction
1 Calcination, % 50 60 70 80 90
2 Heat of reaction
in calciner, kJ/kg
clinker
1038.5 1176.6 1384 1618.5 1802.5
3 Heat of reaction in
kiln, kJ/kg clinker
582.9 433.2 219 20.2 178.4
RoCKS software were thus able to provide valuable clues for
determining the optimum percentage calcinations desired for
minimizing NEC.
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615
620
625
630
635
640
0 0.5 1 1.5 2 2.5 3 3.5
Kiln tilt, Degree
Energy
consumption,
kcal/kg
clinker
400
800
1200
1600
2000
Residencetimeofsolids,s
615
620
625
630
635
640
2 3 54 6 7 8 9
Kiln Rpm
EnergyConsumption,
kc
al/kg
clinker
500
1000
1500
2000
2500
Residencetimeofsolid
sinkiln,s
Fig. 9. Effect of (a) kiln RPM and (b) kiln tilt on overall energy consumption.
4.2.3. Effect of kiln RPM, kiln tilt and grate speed of clinker
cooler
The effect of kiln rotational speed and kiln tilt on the overall
performance is shown inFig. 9a and b. For these simulations
the coal flow rate to the kiln was varied to maintain constant
product composition. It can be seen fromFig. 9a as kiln RPMdecreases, the NEC decreases. Changes in kiln RPM changes
the bed height and the residence time of solids in the kiln as
can be seen fromFig. 9a and b (2002.4 s for 3rpm; 1058.2 s for
5.5 rpm and 703.4 s for 8 rpm). Our simulation results indicate
that it seems to be beneficial to operate kilns at lower rpm as
long as adequate mixing of solids is occurring. FromFig. 9b it
can be seen that energy consumptions in kilns operated at lower
tilt is less as compared to kilns at higher tilt. The grate of clinker
cooler is the important parameter that controls the residence
time of solids and subsequently the heat exchange between hot
solids and counter current air in the cooler. We have studied the
influence of varying grate speed on overall energy consumption.
The results for these simulations are shown inFig. 10.It can be
620
625
630
635
640
645
650
0.06 0.08 0.1 0.12 0.14 0.16 0.18
Grate speed, m/s
Energyconsumption,
kcal/kgofclinker
1050
1100
1150
1200
1250
1300
1350
Secondaryairte
mperature,
K
Fig. 10. Effect of cooler grate speed on overall energy consumption.
seen fromFig. 10that the NEC increases with increasing gratespeed. The increase in grate speed reduces residence time of
solids in the cooler. This results in less convective heat transfer
between solids and air as clearly indicated by temperature of
secondary air plotted in Fig. 10. Therefore the simulation results
indicate that it is better to operate grates in the cooler at lower
speed. The simulations presented here provide useful trends of
energy consumption as a function of key operating parameters
in cement clinker process. This result also gives us a scope to
understand the importance of design parameters (kiln tilt) on
plant performance and can be very useful to plant engineers.
4.2.4. Effect of solid loadingThe predicted results in the form of NEC and corresponding
overall losses for different solids flow rates are shown in Fig. 11.
It can be seen that the NEC per unit weight of product decreases
as solids flow rate increases. This is because the net energy loss
from the entire system decreases as the solid flow rate increases
(see Fig. 11). Thus, it is beneficial from the point of view
of energy consumption to operate the units with higher solids
flow rate. Other operational concerns like increase in dusting
and mixing, however, need to be considered while identifying
maximum solids flow rate specifically for cement kilns.
4.2.5. Effect of coal compositionThe effect of varying coal composition to the kiln on NEC
is shown in Fig. 12. From Fig. 12, it can be seen that the
overall energy consumption does not change significantly with
changing coal composition (ash content 9%, 15% and 40%).
For these simulations the coal flow rate to the kiln was ad-
justed so that the same amount of energy is supplied to the
kiln. Therefore the insignificant change in overall energy con-
sumption does not seem to be surprising. However, as the
coal composition changes, the flame characteristics in the kiln
vary. The predicted dimensionless flame length by the simu-
lator for varying coal composition is shown in Fig. 12. The
flame length was calculated by tracking the region in freeboard
where char and volatiles composition in coal go to zero. The
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600
610
620
630
640
650
44 45 46 47 48 49 50 51
Raw meal flow rate, kg/s
Energyconsumption
,kcal/kgclinker
250
270
290
310
330
350
Totallossesinclinkerpr
ocess,
kJ/kgclinker
Fig. 11. Effect of raw meal flow rate on overall energy consumption.
600
610
620
630
640
650
30 40 50 60 70
Char Percentage, %
Ene
rgycomsumption,
kcal/kgofclinker
0.4
0.44
0.48
0.52
0.56
Flamelength,
dimensionless
Fig. 12. Effect of coal composition on overall energy consumption.
dimensionless flame length was calculated as the ratio of pre-
dicted flame length to length of the kiln. It can be seen that
coal with higher ash content tends to have a longer flame as
compared to coal with lower ash content. The flame length is a
complicated function of amount of oxygen, amount of char and
temperature of gas and particle in the freeboard region. Coalswith higher ash content tends to consume oxygen at a slower
rate and therefore result in longer flames. Such simulations can
therefore provide useful information to kiln operators to pre-
dict the flame characteristics for wide variety of coal available
in the market.
4.2.6. Effect of secondary shell
Heat losses to the surrounding from the kiln shell by radia-
tion and convection are a significant source of energy loss in
cement kilns and therefore the overall process. These losses
can be reduced by using a secondary shell. The idea is to cover
the kiln shell with another metallic shell having low surface
590
592
594
596
598
600
15 20 25 30 35 40 45
Air flow rate through secondary shell, kg/s
Energycomsumption,kcal/kgofclinker
1090
1095
1100
1105
1110
1115
1120
Kilnfluegastemperature,
K
Fig. 13. Effect of secondary shell, on overall energy consumption.
emissivity and thermal conductivity (Engin and Ari, 2005).
However, merely covering kiln shell with metallic shell and
insulating it can lead to enormously high shell temperatures.
Hence a practical approach to use secondary shell would be to
feed air through the interstitial space of shell and secondary
shell to recover the energy and still operate kilns under realis-
tic conditions(Mujumdar et al., 2006). The developed RoCKS
frame work was used to explore the possibility of using such
a secondary shell. The losses in kiln reduced from 140 kJ/kg
of clinker to 1.4kJ/kg of clinker on applying a secondary
shell and insulation of dimensions and operating conditions
specified in Mujumdar et al. (2006). The NEC reduces from 2635kJ/kg clinker to 2493 kJ/kg clinker (i.e., 630 kcal/kg
clinker to 596 kcal/kg clinker) by using secondary shell and
passing air of about 30 kg/s through the interstitial space
(Fig. 13). If the air coming out of annular space at 496K
can be utilized within the cement plant (refrigeration, drying
of fly ash and so on), the use of secondary shell appears to
be promising for reducing NEC in the clinker manufacturing
process.
5. Conclusions
A comprehensive model was developed to simulate complexprocesses occurring in pre-heater, calciner, kiln and cooler for
clinker formation in cement industry. The models for pre-heater
and calciner were developed assuming solids and gas to be
completely back mixed. The computational model for the kiln
was developed assuming gas and solids as plug flow. The inte-
grated simulator was converted into simple to use GUI based
software for cement industry, named as RoCKS. RoCKS was
used to simulate performance of pre-heater, calciner, kiln and
cooler for clinker formation. Detailed validation was unfortu-
nately not possible since adequate industrial data could not be
obtained. However, the model predictions agreed reasonably
with industrial observations. RoCKS was used to understand
influence of various design and operating parameters on overall
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performance. Specific conclusions based on this computational
study are:
Including an additional pre-heater reduces NEC. The devel-
oped model can be used to evaluate relative benefits of en-
ergy savings by additional pre-heater and required additional
capital expenses. There is an optimum value for percentage of calcination car-
ried out in calciner with respect to overall energy consump-
tion in clinker manufacture. With the parameters selected in
this work, this optimum value of percentage calcination in
calciner is about 70.
The simulation results indicated that operating kiln with
higher solid loading, lower rpm, lower tilt and lower grate
speed reduces energy consumption per unit production. The
upper limit on solid loading (bed height) and lower limits on
rpm and tilt (mixing and heat transfer) need to be identified
based on other practical issues.
The use of secondary shell appears to be a promising method
to reduce overall energy consumption, if the hot air generates
in such secondary shell (200 C) can be utilized in some
other processes in cement plants.
The model was also able to predict kiln characteristics like
maximum flame temperature and overall flame length for coals
with different compositions. The models and results presented
here will help in developing a better understanding of clinker
manufacturing process and may provide clues for possible
optimization.
Notation
a surface area per unit volume, m2/m3
A0 devolatilization constant
Acyi internal surface area of cyclone, K
Acyo external surface area of cyclone, K
Ap surface area of coal particle, m2
LAp surface area of solid particle, m2
Cp,c specific heat capacity of coal particle, J/kg K
Cp,g specific heat capacity of air, J/kg K
Cp,s specific heat capacity of solids, J/kg K
dc inner diameter of cyclone, mdp radius of particle, m
E1 energy of activation for char combustion, J/mol
E2 energy of activation for calcination, J/mol
fc fraction of heat given to coal particle released
due to coal combustion
fv,0 initial mass fraction of volatiles in coal particle
Fpw view factor
hc heat transfer coefficient between coal particle
and gas, W/m2 K
hc,c heat transfer coefficient between clinker and gas,
W/m2 K
hc,L heat transfer coefficient between solid particle
and gas, W/m2 K
hcyc heat transfer coefficient between particle laden
gas and cyclone inner wall, W/m2 K
Hc,C heat of coal combustion in calciner, J/kg
Hc,K heat of coal combustion in kiln, J/kg
Hcalc heat of calcination reaction in calciner, J/kg
Hcomb heat of char combustion, J/kg
Hcombg heat of volatile gas phase combustion, J/kgHLoss,K heat losses in the kiln, J/kg
HR,K heat required for clinker reactions, J/kg
kg thermal conductivity of air/gas, W/m K
kr thermal conductivity of refractory, W/m K
ks thermal conductivity of clinker, W/m K
ksh thermal conductivity of shell, W/m K
ks,c rate constant of char combustion, kg/m2 skPa
r ks rate constant of calcination of calcium carbon-
ate, mol/m2 s1
r k
s rate constant of calcination of calcium carbon-
ate, mol/m2 s1
L total height of cyclone, m
ma mass of air in cooler, kg/s
mAl2O3,i mass of total aluminum oxide in solids in cal-
ciner, kg/s
mCO2,C mass of carbon-dioxide produced in calciner due
to calcination, kg/s
mCaCO3,i mass of total calcium carbonate in solids in cal-
ciner, kg/s
mFe2O3,i mass of total ferrous oxide in solids in cal-
ciner, kg/s
mSiO2,i mass of total silicon dioxide in solids in cal-
ciner, kg/s
mg mass of gas in calciner, kg
mgin mass of air entering in calciner,kg/smgout mass of air leaving calciner, kg/s
mg,K mass of air leaving the kiln calciner, kg
mp,c mass of coal particle, kg
mp,cin mass of coal particle entering calciner, kg
mp,cout mass of coal particle leaving calciner, kg
mpc,0 initial mass of coal particle, kg/s
mp,L mass of solid particle, kg
mp,Lin mass of solids entering calciner, kg
mp,Lout mass of solids leaving calciner, kg
ms mass of solids/clinker in cooler, kg
Mc,C mass of coal entering the calciner, kg/s
Mc,K mass of coal entering the kiln, kg/sMg mass of gas in cyclones, kg/s
Mg,K mass flow rate of secondary air entering the
kiln, kg/s
Mg,P mass flow rate of gas entering the pre-heater,
kg/s
Mg,S mass flow rate of secondary air entering the
kiln, kg/s
Mg,T mass flow rate of tertiary air entering the cal-
ciner, kg/s
Ms mass of solids in cyclones, kg/s
Mse mass of solids entrained by gas in cyclones, kg/s
Ms,C mass flow rate of solids leaving the calciner, kg/s
Ms,K mass flow rate of clinker leaving the kiln, kg/s
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Ms,P mass flow rate of solids entering the pre-heater,
kg/s
Mw CaCO3 molecular weight of calcium carbonate, kg/kmol
Mw CaO molecular weight of calcium oxide, kg/kmol
Mw char molecular weight of carbon, kg/kmol
Mw CO2 molecular weight of carbon-dioxide, kg/kmol
Mw O2 molecular weight of oxygen, kg/kmolMw vol molecular weight of volatile, kg/kmol
Mw w molecular weight of water, kg/kmol
Nu Nusselt numbercNp number of coal particles entering calciner per
secondLNp number of solid particles entering calciner per
second
pO2 partial pressure of oxygen in gas, kPa
pCO2 partial pressure of carbon-dioxide in gas, kPa
peq equilibrium partial pressure for carbon-dioxide
in gas, kPa
P the percentage calcination occurring inside the
calciner
P pressure drop across the cyclone, mm of H2O
Pr Prandtl number
rc rate of calcination, kg/s
rcomb rate of combustion of char particles, kg/s
rcombg rate of combustion of volatiles, kg/s
ri internal diameter of cyclone, m
r0 external diameter of cyclone, m
rp radius of solid particle, m
rr internal diameter of cyclone shell, m
R gas constant
Rc non-dimensional form of radiative heat transfer
coefficientRe Reynolds number
T0 ambient air temperature, K
Tc,i temperature of solids and gas in cyclone, K
Tcl temperature of coal particle, K
Tf average temperature of solids and air in
cooler, K
Tg temperature of gas, K
Tg,in temperature of gas entering calciner, K
Tg,out temperature of gas exiting calciner, K
Tg,K temperature of gas leaving the kiln, K
Tg,S temperature of secondary air, K
Tg,T
temperature of tertiary air, K
Tg,P temperature of gas leavingthe pre-heater, K
Tiw,i the internal wall temperature of the cyclone, K
Tow,i the external wall temperature of the cyclone, K
TL temperature of solid particle in calciner, K
Tr,i the temperature of interface of refractory and
shell in cyclone, K
Ts temperature of solids/clinker in cooler, K
Ts,C temperature of solids entering the kiln, K
Ts,R temperature of solids exiting the cooler, K
u0 inlet gas velocity in cyclone, m/s
us,x grate speed in x direction, m/s
us,y grate speed in y direction, m/s
ug,x air velocity inx direction, m/s
ug,y air velocity iny direction, m/s
Vreact volume of reactor, m3
xAl2O3,C mass fraction of aluminum oxide entering kiln
xCaCO3,C mass fraction of calcium carbonate entering kiln
xCaO,C mass fraction of calcium oxide entering kiln
xFe2O3,C mass fraction of ferrous oxide entering kiln
xSiO2,C mass fraction of silicon dioxide entering kilnyc,c mass fraction of char in coal particle in calciner
yc,cin mass fraction of char entering in coal particle
yc,cout mass fraction of char leaving in coal particle
yc,K mass fraction of char in coal particle entering
the calciner
yv,c mass fraction of volatiles in coal particle
yO2 mass fraction of oxygen in gas
yO2,in mass fraction of oxygen entering calciner in gas
yO2,out mass fraction of oxygen leaving calciner in gas
yCO2 mass fraction of carbon-dioxide in gas
yCO2,in mass fraction of carbon-dioxide entering cal-
ciner in gas
yCO2,out mass fraction of carbon-dioxide leaving calciner
in gas
yv mass fraction of volatiles in gas
yw mass fraction of water in gas
Z stoichiometric component
Greek letters
porosity of clinker bed in cooler
c emissivity of coal particle
cy emissivity of cyclone outer wall
L emissivity of solid particlem,p mass efficiency of the cyclone
residence time of coal particle in calciner, s
g density of air/gas, kg/m3
s density of solids, kg/m3
StephanBoltzmann constant(W/m2 K4)
residence time of raw meal particle in calciner, s
Chemical species
C2S (2CaOSiO2)
C3S (3CaOSiO2)C3A (3CaOAl2O3)
C4AF (4CaOAl2O3Fe2O3)
Acknowledgments
The authors wish to acknowledge financial support provided
by CSIR (under the NMITLI scheme) for this study. The au-
thors would also like to acknowledge many helpful discussions
with Professor Anurag Mehra during the course of this work.
One of the authors, K.S.M is grateful to Council of Scientific
and Industrial Research (CSIR), India for providing financial
support.
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K.S. Mujumdar et al. / Chemical Engineering Science 62 (2007) 25902607 2607
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