### MODELAND SIMULATION OFHEAT TRANSFER, MAGNETITE OXIDATION

AND NOx FORMATIONINA GRATEKILN TACONITE PELLETINDURATION FURNACE

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# • • • • MODEL AND SIMULATION OF HEAT TRANSFER, MAGNETITE OXIDATION

AND NOx FORMATION IN A GRATEKILN TACONITE PELLETINDURATION FURNACE

Richard A. Davis Department ofChemical Engineering University ofMinnesota Duluth 207 Engineering Building 10 University Drive Duluth, Minnesota 55812 internet: rdavis@d.umn.edu

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# • • • Model and Simulation of Heat Transfer, Magnetite Oxidation and NOx Formation in a Grate-Kiln Taconite Pellet Induration Furnace Richard A. Davis Department of Chemical Engineering University of Minnesota Duluth 207 Engineering Building 10 University Drive Duluth, Minnesota 55812 internet: rdavis@d.umn.edu 

# Abstract University of Minnesota 57th Mining Symposium Duluth, Minnesota April 25, 1996



### A numerical model was developed to simulate the combined effects of heat transfer, \ 

### magnetite oxidation, and NOx formation in 

### a grate-kiln furnace for taconite pellet induration. Heat transfer from the flame in the kiln was described by the net radiation method. The shrinking core model was used to account for magnetite oxidation on the grate. A novel approach to simulate oxidation oftumbling pellets in a kiln was derived
. The Zeldovich mechanism was used to predict thermal NO generation. Temperature fluctuations in the gas streams were estimated with a clipped Gaussian probability density function. The thermal energy balances and mass balances resulted in coupled systems of first-order differential equations, which were solved numerically. The model is capable of predicting NO production and magnetite oxidation in agreement with observation ofplant performance
.

1

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### ~ 

# .. .. .. .. .. .. .. .. .. • • • • 

# • • • • 

# .. .. 5 1. Introduction
In this work, a model was developed and used to simulate the synergistic effects of heat transfer and magnetite oxidation on the formation ofoxides ofnitrogen (NOx) in the gratekiln system. Previous models of the grate-kiln system have not included the combined effects ofheat transfer with NOx reaction inthe kiln (Thurlby, 1988; Young, et al., 1979). The simulation was applied toa grate-kiln system at the USS MinnTac taconite pelletizing plantin Mountain Iron, Minnesota, and tuned with NOx plant data collected in a study by Zahl, et al. (1995). The grate-kiln taconite pellet induration system involves several stages ofheat and oxygen transfer to a traveling bed ofspherical taconite pellets shown in Figure 1. At the heart of the process is the rotary kiln where pellets are heated to tempbratures in excess of 1600 K with a high temperature flame. The remaining steps in the process were designed to efficiently recover thermal energy from the pelletbed and supply oxygen (02) from the air to oxidize the magnetite in the pellets to hematite. In the overall grate-kiln system, wateris initiallyremoved from the pelletsby thermal action in a two stage dryer (not shown). The temperature ofthe bed ofpellets is gradually increased further in a preheatfurnace. The pelletbed reaches its final temperature in the rotary kiln, fired with a single burner. Inthis model, the burneris fueled with natural gas mixed with substoichiometric primary air. The pellets exiting the kiln are cooled by an updraught of ambient air through the pellet bed traveling along a grate in a revolving two stage cooler. Hot air from the first stage ofthe cooler is passed to the kiln as secondary air where it flows above the pellet bed countercurrent to the flow ofpellets through the kiln. The secondary air is required for complete combustion ofthe burner gases and oxidation ofthe magnetite in the pellets. The
warm air from the second stage of the cooler is used in the first stage of the dryer. The gases (secondary air and combustion products) from the kiln are used to preheatthe pellet



### 2bed on a traveling grate before the pellets are fed to the kiln. Finally, the gas from the preheaterisused in the second stage ofthe dryer orvented as waste gas along with the air exiting from the dryer. Although the design ofthe grate-kiln system is for efficientheat and mass transfer, itmay notbe the optimal design for minimizing the formation of

### NOx. Whennatural gas is used to fuel the kiln burner in the presence of excess air the principal mechanism of 

### NOx formation 

### is the thermally inducedcombination ofoxygen and nitrogen in the airin the post combustion zone after the burner. Fuel 

### NOx, derived from nitrogen sources in the burner fuel, and prompt 

### NOx, formed from the reactions ofcombustion hydrocarbon free radicals with air, are less significant in fuel lean flame mixtures burning natural gas (Miller and Bowman, 1989). The effects of any efforts to reduce**th~rmal** 

### NOx formation on the complex heat transfer to the pellet bed cannot be ignored because the heat transfer mechanisms and 

### NOx formation are coupled through temperature. 

# 2. Thermal 

# NOx Formation
The formation of

### NO from Oz and Nz in air at high temperatures was assumed to follow the well known Zeldovich mechanism (Miller and Bowman, 1989; Zeldovich, et al., 1947): k, 

### O+N 2 

### <=>N+NO

k, (1)
k, 

### N + 0 2 

### <=>0+ NO k, (2)
k, 

### N+OH<=>NO+H k, (3)
The reaction step in eq 1 is generally considered rate limiting due to the high activation energy required to break the Nz bond (Monnot, 1985; Palmer, 1974; Wark and Warner,

... 1981). Reaction 3 is considered negligible under conditions offuel lean flames where the


### 3

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# • 

# .. .. partial pressure of OH and H from combustion reactions is small relative to the partial pressure of02 and atomic 0 (Monnot, etal., 1985; Wark and Warner, 1981): (4) (5) 

### Taconitekilns typically operate underconditions ofapproximately 500% excess air overall Itis commonto treat the faster combustion reactionsas instantaneous and irreversible, as first proposed by Zeldovich (Chigier, 1981; Zeldovich, et al., 1985). This assumption decouples the combustion reactions from the NO reactions inthe model. Application ofthe steady-state approximation to atomic nitrogen ineqs 1-2 gives thefollowing expression for the rate ofNO generation perunit volume. 

### 2[O](k,Ts[OJ[N 2 ]- 

### k,k 4 [

### N0] 2 ) 

### s 

## =

NO 

### k,[N0]+q0 2 ] (6)


### where the concentrations of the gas phase species were calculated assuming ideal gas behavior. The rates of generation per unit volume of 02 and N2 are both -0.5sNo· The Arrhenius temperature dependent reaction rate constants recommended by Hanson and Salimian (1984) were used in the simulation. Application of the rate law in eq 6 requires an assumption that the oxygen dissociation reaction approaches equilibrium much faster than the NO formation reaction (Wark and Warner, 1981; Clarke and Williams, 1991). The composition of atomic oxygen is found from the superequilibrium relationship ofWarnatz (1984). At lower temperatures, NO "freezes", and essentially all the NO is irreversibly oxidized further to NOz according to the following stoichiometricequation (Palmer, 1974; Wark and Warner, 1981):



### 4Thethermal NO reaction rate becomes important in 

### air attemperatures inexcess of 1800 K, increasing exponentially with temperature. Inturbulentflow with combustion, locally high temperatures in the gas phase envelope around the flame contribute significantly to thetotal thermal NOformation (Khalil, 1982). Theeffect offluctuating temperatures inthe kiln on the NO reaction rate was modeled by assuming a truncated Gaussian probability density function (PDF) for the temperature distribution inthe flame or secondary 

### air streams about the average gas stream temperatures. The standard deviation from the mean gas temperature was approximated by the following function of the difference between the
meanflame and secondary air temperatures. (8)
The denominator in eq 8 is based on the characteristic of the PDF that 99.74% of the temperature distribution occurs within ±3aofthe mean temperature. The expected value of the reaction rate was calculated by integrating the rate law in eq 6 about the PDF between thelimits ±3a:
3" s [ (T- T ) 2 } 

### Sa=I NO 

### exp m T

N 

### a..fiii 2a2 -3<1 (9)

where Tm is the mean gas stream temperature (flame or secondary air stream). A similar approach was used by Bilger (1980) and Carvalho, etal. (1990) to account for temperature effects oncombustion ofhydrocarbons intheirmodels ofturbulent reacting flows. 

## 3. Magnetite Oxidation
The pellets were assumed to be spherical with magnetite evenly distributed throughoutthe; pellet. Theoverallreaction ofoxygenwith magnetite to form hematite is


### 5

# • t. t. 

# • • • • • • • • 

# • • • • 

# • • • 

# .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ' (10)
The magnetite oxidation reaction was assumed irreversible. The shrinking core model provides an adequate description ofmagnetite oxidation in the preheat furnace and cooler where air is drawn through the pelletbed traveling along the grate (Nateson and Philbrook, 1969). The oxidation of magnetite in the kiln pellet bed is difficult to model due to the complicated mixing ofthe secondary airwith the tumbling pelletbed as the kiln rotates. A simple, novel approach to modeling magnetite oxidation in a rotary kiln was developed here based on a mathematical description ofthe periodic cascading ofthe pellet bed, exposing the internal pellets to the secondary 

### air
. 

### 3.1 Shrinking Core Model The shrinking core model applied to taconite pellets assumes

### ~ retreating reaction interface between an outer ash layer ofhematite and an unreacted magnetite core, as illustrated in Figure 2. Experimental evidence suggests that the shrinking core interface is sharp, and that the oxidation reaction is controlled by the diffusion of02through the outer ash layer (Pape, et al., 1976; Papanastassiou and Bitsanes, 1973). Hence, the rate of reaction is equal to the rate ofdiffusion of

### 02 to the core/ash layer interface. The differential change in the pelletcore radius with position along the grate is proportional to the 02concentration

· gradientevaluated atthecore radius: (11)

where Ub is the superficial velocity ofthe pelletbed, Pc is the molar density ofmagnetite in theunoxidized core, and De is the effective diffusivity in the porous pellet: (12)



### 6where ep is the porosity ofthe pellet and 'tp is poretortuosity. The diffusivity of

### 02, Do2, waspredicted from thekinetic theory ofgases (Reid, et al., 1987). Assuming uniform, porous, spherical pellets, the quasi-steady state approximation to the diffusion reaction equation in the ash layeris (Fogler, 1992): (13)
subject to the boundary conditions (14) (15)
The surface concentration of

### 02is found from the massbalance for 

### 02 atthe pellet surface: 

## D,

# d~**]** =k{[OJ 8 

## -[OJP} at 

## r=r" (16)



## ,, where k is the mass transfer coefficient for flow through a bed of spheres taken from Incropera and DeWitt (1990). Uponintegration ofthe diffusion equation and substitution ofthe boundary conditions, the 

### 02 concentration gradient at the core radius is (17)

where the concentration atthe pellet surface was determined from eq 16: 

## [02], (18)

7This result, substituted into eq 17, gives the differential changein the core radius with axial position along the grate based on the oxidation reaction stoichiometry ofeq 10: (19)

Atz = 0, rc = rp. and the derivative 

### is indeterminate. Application ofL'Hopital's rule to this expression gives the initial derivative atthe start ofthe grate: 

# drcl = 

### dz z=O 4k[02 ] 

## •• (20)

Theheat generated by the oxidation ofmagnetite is also proportional to the derivative ofthe
core radius: (21)

where Mfris the exothermic heat ofreaction, eq 10, and Ab is the cross sectional area of the bed. The pellet surface area perunit bed volume ofa porous bed ofspheres is (22)
where Eb is the pelletbed porosity. 

### 3.2 Oxidation in the Rotary Kiln Thetransport and reaction of (h inthe cascading pellet bed in the kiln is complicated bythe intermittent tumbling action of the pellets induced by the rotating action of the kiln. A simple, novel approach was used here thatprovided satisfactory results, while avoiding the difficult, rigorous approach ofprevious modeling efforts (Young, et al., 1979). This approach is based on the mathematical description ofa cascading bed in a rotary kiln : developedby Saeman (1951). The number ofcascades perkiln revolution is 

### 8

### c, = . 

# _,(wb) sm - 2R 

### (23)

where R is the radial position ofthe pelletin the bed, and Wb is the width ofthe top ofthe bed, as shown in Figure 3: Wb 

## =2R,sin1/> (24)


### The axial velocity ofa pellet at kiln

### radius R is 

# uP =nwb(8+

# ~cos!/>)[ rc ] sm'"
. -1

# wb 'Y 

# sm - 2R 

### (25)

where n is the kiln rotational·speed, 9 is the kiln angle ofinclination, <)> 

### is the bed angle of repose, and \jl 

### is the angle from the kiln centerline to the top of the bed, as illustrated in Figure 3. The average number ofcascades perunitbed length is (26)



### The pellets do not necessarily travel along an arc ofradius R as suggested by eqs 23 and 25. However, the average number ofcascades is independent ofradial position in thebed. This model assumes that all 

### ofthe 02in the porous bed at any position is consumed by the unreacted magnetite in the core of the pellets. With each cascade, the depleted 02 is replaced with 02from the secondary air above the bed when the covered pellets become exposed. The concentration of02percascade inthe bed was calculated assuming ideal gas behavior at the bed temperature and secondary air partial pressure above the bed. The moles of 02 used by the bed was calculated as the product of the bed volume with the , number oftimes the bed turns over and the average concentration inthe bed. This gives the average moles of02reacted percascade: 

### 9

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# • 

# - - - 'tfiJ**--~-----**

(27)
The differential form ofeq 27, with substitution from eq 26 gives the moles of Oz reacted per unit kiln length: dN o, _ [02

### ]bebL,Ab sin1/1 

# dz- Wb(O+ 

### lp"coslf>) Inthis case, the heatofthe magnetite oxidation reaction per unit length is

The total moles ofmagnetite oxidized is 4No2:

The total moles ofmagnetite oxidizedperpelletis: (28)

(29)

(30)

(31)
The change in the unreacted core radius is calculated from the total moles of magnetite

. oxidized:

- 3 p ( 3N ) 113 

### rc - rd- 4;r;pc (32)
whererei is the average pellet core radius feeding the kiln. The assumption ofcomplete Oz consumption with each cascade was verified here with the shrinking core model for each cascade atvarious temperatures and Ozcompositions typically found during kiln operation (Potts, 1991)
.

10

## 4. Heat Transfer
The primary mechanism ofheat transfer in the preheat furnace and cooler is convection between the secondary air andpelletbed. The principleheat transfermechanism in the kiln is radiation from the flame, followed by conduction from the kiln wall, and convection from the secondary air. 

### 4.1 Rotary Kiln Thermalenergy is liberated during the combustion ofnatural gas inthe burner zone ofthe kiln. illthis study, natural gas is assumed to be pure methane. Approximately 10% ofthe stoichiometric air required for complete combustion ispremixed with the fuel inthe burner (Zahl, et al., 1995). The rest ofthe oxygen required for coi:pplete combustion is supplied as secondary air. The combustion rate and flame shape are governed by the flux ofair to the flame stream from the secondary air. The flame and secondary air streams were modeled as perfectly mixed plug flows, withno inter stream mixing, except for a constant flux of entrained gas from the secondary air stream to the flame stream. Thematerial balances for the gas streams follow. 

### dF

- 1 =PN



### dz t 8 

### dF

- 8 =-P N



### dz t 8 (33) (34)
where Ng is the molar flux of gas from the secondary air entrained by the flame and Ptis theperimeter ofthe flame: (35) where

### Rtis the local flame radius.

11**··~**



# ... 

# .,**~** 

# '

.. Ill 

# • •**~**

### ~**~ ~** **~** 

## I I 

# ' 

# 'This approach is similar to that of Jenkins and Moles (1981), Gorog, et al. (1983), and Silcox and Pershing (1990), exceptthese authors calculated the flame dimensions a priori. The first two sets of authors combined the flame and air streams into a single plug flow stream upon complete combustion. Silcox and Pershing (1990) treated the flame stream as a constant radius plug flow surrounded by a secondary air stream in plug flow. Here, the flame and secondary air streams were also allowed to extend along the entire length ofthe kiln, but the cross sectional area of the flame was permitted to vary as a function ofthe flame and secondary air stream volumetric flow rates and temperatures. Assuming ideal gasbehavior and uniform pressure, the cross sectional area ofthe flame is (36)
where

### Atis the total cross seCtional area ofthekiln above the'pellet bed: 

## A• = 

## R?[n--0.5(2¢

## -sin2¢)] (37)
The radius ofthe flame is: (38)
As the flame stream entrains the secondary air, the radius grows, increasing the rate of

. entrainment Inthe limit ofz**~** 0, this modelreduces to the semi-empirical expression for

gas entrainment rate by ajetin a moving fluid derived by Ricou and Spalding (1961): (39)
where 

### A. is a constant which includes the flux term and the kiln cross sectional area. The superficial axial velocity ofthe pellet bed is defined in terms ofthe mass flow rate of the bed and the cross sectional area ofthekiln thatis occupied by the bed:

12(40)

where Pp isthepellet density. The cross sectional area ofthe bedis: (41)
where Rr is the inside radius to thekiln refractory lining. Saemon's (1951) predicted the velocity ofthe pelletbased on angle ofrepose and inclination:



### u 

## = (

# ~~

# )[8

### +arctan(R,

# c~scf> )coscf>

# }1- cohp)'12



### • 0.5R;(2cf>-sin2cf>)sincf> (42)

where 9 is the kiln angle of inclination. The values for thebed angle of repose and the 

### ' superficialvelocity are found by solvingthe nonlinear eqs 40-42 simultaneously for cj> and



### Flame Steam Inthe case ofcomplete combustion, the reaction stoichiometry is equimolar: CH 4 

### +20 2 -7 C0 2 

### +2H,O (43)

· The change in composition of each individual species in the flame and secondary air

streams is governed by the NOformation and combustion reactions. A differential material balance for each ofthe combustionreactants and products intheflame streamis: 

### dF 

## -'=v,y 0 P 1N, 

### dz ' (44)

where 'lli is the combustion reaction coefficient for species i in terms of 

### 02. A stoichiometric amount offuel is assumed to becompletely com busted with the air entrained by the flame. During combustion, the coefficients ofthe various species are: CI4 = -112;



### 13

# .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. • • 'tit 'tit 

# = Oz

## =0; COz = 1/2; HzO 

## = 1. The postcombustion coefficients are: 

### CI4

## =0; Oz

## = 1; 

### C02 =0; HzO 

### = 0 . The differential species balances for the non-combustion speciesinthe flame steam are: dF; PN A- -=y. f 

### + ,s. dz ' 8 ' (45)
whereSi is the rate ofgeneration ofspecies i inequation 9 based onthe stoichiometry ofthe overall NOreaction: N 2 +0 2**~2NO** (46)
A differentialenergybalancefor the flame stream includes the flux ofenthalpy from the gas stream: 

### (47)

where q' rfis the net rate ofthermal radiation to the flame perunitlength. The enthalpy of species i in the flame stream is defined as 

### r, Hfi = H[

### +

# J cP,dT (48) r•

· where 

### HO is the enthalpy offormation at a reference temperature, T0 • The initial flame

temperaturewas assumed to bethe adiabatic flame temperature for complete combustion of the primary air
. 

### Secondary Air Stream
The secondary air stream differential species balances are dF, PN A- -=-y. f 

### + 

# ,s. dz ' 8 '

14 (49)A differential thermal energy balance in the secondary air stream results in the following first-order differential equation. (50)
where q' gc is the convective heat transfer rate perunitlength between 

### tbe secondary air and the surrounding kiln wall and pellet bed. The heat transfer coefficients of Tscheng and Watkinson (1979) were used to predictthe convective heattransfer rates between the gas, and the pelletbed and kiln wall. The secondary air stream enthalpies 

### are defined similarly to eq 48. 

### Pellet Bed Thethermal energy balance around the pelletbed involves heat transfer between the bed and the kiln wall, secondary air, flame stream, and the heatreleased from the exothermic reaction ofmagnetite oxidation : (51)
where mb is the mass flow rate ofthepelletbed, q' gb is the convective heat transfer rate per unit length from the gas to the bed, q' wb is the non-radiative heat transfer rate per unit lengthfrom the wall to the bed, q'rb is the netradiation perunitlengthto thebed, and q' ox is the heat generated perunitlength bythe magnetite oxidation reaction inthe bed. The pelletbed was modeled as an inner core ofpellets surrounded by an outer mantle of pellets, as suggested by Thornton and Batterham (1982). The heat transfer between the bed mantle and coreis assumed to obey a simple first-order mixing rule: (52)

15

# • It 

# • It It 

# • • It 

# • • • It 

# • 

# • • 

# • • 

# • • • • • 

# • • • • 

# • • • 

# • • 

# • • • • • 

# • • • 

# • • 

# • • • 

# • t where Tm is the mean bed temperature and 'tm is the first-order mixing time constant, which must be determined from experiments
. 

### Wall Temperature The wall temperature was calculated from the inside wall surface energy balance, assuming ' no axial heatconduction and steady-state operation: (53)

where q'bw , q' gw, and q' rw 

### are the heat transferrates perunit length between the bed and the wall, the gas and the wall, and the net radiation to the wall, respectively. The sum of resistances to heat transferthrough the wall normal to the axis is
(54)


### where R8 

### is the inside radius ofthe kiln shell, 

### Ro is the outside shellradius, and Ki 

### are the thermal conductivities of the different wall materials, 

### i. To avoid solving the non-linear wall temperature equation at each step in the integration, eq 53 was transformed into an ordinary first-order differential equation:
(55) Eq 53 was solved once for the initial inside wall surface temperature condition. A heat transfercoefficientcorrelation for free convection from arotating cylinderrecommended by ·Barr, et al. (1989) was used in the simulation. Tscheng and Watkinson (1979) also recommend a heat transfer coefficient for the combined effects of conduction and convection between the bed and the wall.


### 16

### Radiation The three body radiation model comprised ofthe kiln wall, pelletbed, and flame is based
onthe netradiation approximation method ofThornton andBatterham (1982). A weakness ofthis model is that radiation exchange between surfaces at different axial positions along the kiln is ignored. However, Thurlby (1988) reported success using this model for a grate-kiln system. Gorog, et al. (1981) also considered kiln heat transfer by the more rigorous zoning method and concluded that >86% of the net radiative heat flux occurs within ±0.3kiln diameters along the kiln axis. The net radiation heat transfer rate per unit length from the wall to the pellet bed was calculated using the simple two-body formula for concentric cylinders: 

## 2¢R,a(r:**-T~)** 1 1 

### -+--1 £b £w (56)

The air between the three bodies was assumed to be transparent to thermal radiation. Itwas also assumed that no radiation transmits through the three bodies. Thethermal radiation emission rate from each surface i is (57)
Ofthe net energy arriving at a surface, G, pG is reflected, and (1-p)G is absorbed. The total rate ofenergy per unitlength leaving surface i is (58) Considering all the surfaces, the total incidentradiation perunit length on any one surface is



### 17----- ----- -- ----**---------------~~--**

(59) 

### where Fji are the view factors, which have been calculated for a cylindrical flame over a flat bed in a rotary kiln by Thornton and Batterham (1982). These equations are solved simultaneously for Gi. The net radiation absorbed bya body (surface) perunit area is 

# q;, =(1-p1

## )G1 -E, (60) 

### where 

### Pt and Pt, 

### are the perimeters ofthe flame and bed. Pw is the exposed wall perimeter, calculated as follows. (61) 

### The kiln model results in a simultaneous system of 17 coupled first-order ordinary ' 

### differential equations. Eleven equations for the species balances inthe flame and secondary air streams, two equations for the bed temperatures, two equations for the air and flame temperatures, one equation for the kiln wall temperature, and one equation for the pellet oxidation. 

## 4.2 Preheat Furnace
In the preheat furnace, the flow ofgases above the pellet bed was modeled as a perfectly stirred tank. 

### The energy balance under steady state operationbecomes: T;" 

### F.,, 

# f c

pa,,dT

## =UA(T • ., - T

### ~) (62) T•• 

### where T**~** 

### is the outside ambient air temperature. The overall heat transfer coefficient for heat loss through the wall is defined in terms of a sum ofconvective and conductive heat transfer resistances:

18UA= 

### A,. 

### + A, ( 1 Lir Liw 1 ) ( 1 Lir Liw 1 )



### -+-+-+- -+-+-+- hi l(r 1(w how hi 1(r 1Cw hot (63)

where Aw and At are the heat transfer areas of the wall and top roof of the preheater, respectively, M is the preheaterrefractory thickness, /';.w is the preheaterwall thickness, hi is the internal heat transfer coefficient, 

### how is the externalwallfree convectionheattransfer coefficient, hot is the external top free convection heat transfer coefficient and K is the wall
orrefractorythermal conductivity. Theoutside surface temperature was calculated from an energybalance across the boundary layer outside the furnace: (64)
Theinside surface temperature wascalculated in a similarmanner: (65)
The results in a system ofnon-linear algebraic equations in Tg, Tsi and T80 which mustbe solved simultaneously by a trial and error technique such as Newton's method. The bed ofpellets traveling along the grate was treated as 

### 5 discrete layers of uniform thickness, similarto the approach ofThurlby (1988) and Thurlby et al. (1979). The pellets within a layer were assumed to be perfectly mixed. The gas was assumed to move, unmixed in cross flow through the bed layer, as illustrated in Figure 

### 4. Using an average heat capacity and heattransfer coefficient, the differential ternperature change across a layer is: (66)

19

# r

. 

# • 

# .. • ' 

# • 

# • • ,' . 

# ._ 

# - • • 

# • • • • 

# .. 

# - • 

# • • 

# •

... 

# - • 

# • • • 

# • • • 

# - 

# - • • • • • • 

# • • • • 

# • • 

# • 

# - • • • where y is positive in the vertical down direction. Eq 66 was integrated overt'ly to give the following function ofthe gas temperature leaving bed layerj . (67)
The total bed volume is divided by 5, the number ofpellet bed layers, VtJS = t'lyWb. The non-linear gas temperature equations for each layer were transformed into ordinary firstorder differential equations to avoid iterating on each equation at each step in the model solution. The procedure is similar to the oneused for the kiln wall:


### dT 

## -"-=

dz ( djgj dTgj-l 

### + djgj dTbj) 

# lJTgj-t dz ()Tbj dz djgjjJTgj (68)
The initial conditions are found from the solution to eq 67 at z = 0 . The differential energy balance for the pelletbed layeri is

arbi 

### q,c 

### +qox



### dZ mbcp (69)
Thebedlayertemperature was assumed to beuniform such thatthe convective heat transfer rate from the gas maybe described interms ofthelog-mean temperature difference: (70) where (71)

The heat ofthe magnetite oxidation reaction is proportional to the rate ofoxidation given in eq 21. 

### 20

### Thepreheatermodel results in a system of 15 simultaneous first-order ordinary differential equations. Five equations each for the pellet oxidation, gas temperature and pellet bed temperature in the discretized bed layers. The heat transfer coefficients were evaluated from standard correlations for flow past flat surfaces, flow through packed beds of spheres, and natural convection from vertical and horizontal surfaces (Incropera and De Witt, 1990). 

### 4.3 Cooler The heat transfer model in the cooler is similar to the preheater model, except the gases flow up through the bed, as illustrated in Figure 5. The cooler is designed as a grate revolving on a circular path, but the average traveling length ofthe pelletbed was taken as the average inside arc length. The temperature of the gases leaving the cooler was calculated from the solution to the steady-state energy balance around the gas stream leaving the pellet bed. 

# 5. Model Solution Procedure
The value for the gas flux to the flame was determined from correlation of experimental data for NO formation and temperatures of the pellet bed and gases in the kiln. The solution to the model equations is necessarily iterative due to the counter current flow of gas and pellets through the kiln. The three models are coupled through the gas and pellet temperatures between the preheat furnace and kiln, and between the kiln and cooler, as illustrated in Figure 1. The steps in the solution procedure are outlined in Figure 6. 

### 1. Solve eqs 40-42 for <)l 

### and u in the kiln by Newton's method, with a variable step partial derivative approximations (NEWTONVS, Hanna and Sandall, 1995). 

### 2. Guess values for the gas temperatures, 

### 02, from the kiln to the preheater, and 

### 03, from the coolerto thekiln.
21

# ..

.. .. .. • 

# • 

# .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ... 

# .. ... ... 

# .. • 

# .. .. .. • 

# .. .. .. .. • • • 3. Solve for the pellet bed temperature feeding the kiln, P2, and the gas temperature exiting the preheatfurnace, G1, with thepreheatmodel equations. The temperature of the gas above the bedwas calculated from the solution to the non-linear energy balance around the gases with NEWTONVS. Theinitial gas temperatures were calculated from the solution to the system ofnon-linear equations by the delta-square iterative method (Hanna and Sandall, 1995). The system of partial differential equations was solved numerically by an improved Euler's method with extrapolation and variable steps, adjusting the integration step size to control error(IEXVS, Hanna and Sandall, 1995)
. 4. Solve for the preheatfeed gas temperature, G2, and thekiln exitpellet bed temperature, P3, with the kiln model, guessing P3 until the kiln solution for P2 agrees with the preheat solution. The guess for P3 was automatically upgraded by the secantmethod
. The initial flame and wall energy balances were also solved numerically for the initial flame and wall temperatures using NEWTONVS. The system offirst order ordinary differential equations was also solved numerically by the IEXVS method. Theintegral in eq 9 was evaluated numerically using Simpson's rule with 200 intervals between the integration limits
. 5. Solve for the gas temperature exiting the cooler, G3, with the cooler model, based on the exiting pellet bed temperature, P3, from the kiln solution in step 4. The model equations were solved using the same numerical techniques as step 3 . 6. Replace the gas temperatures between the kiln and the preheater and cooler, G2 and G3, with the upgraded values for these temperatures from steps 3 and 4 . 7. Repeat steps 3-6 until satisfactory convergence inG2 and G3 is achieved
. Atmost 15 iterations on steps 3 through 6 were required to reach a converged solution
.

22 '(, '

# 6. Simulation Results
The USS MinnTacplant operation parameters used in the model calibration and simulation
are listed in Table I. Initially, the rotary kiln model was calibrated by adjusting the gas entrainment flux in eq 33 and the mixing time constant in eq 52 for reasonable model prediction agreement with the measured bed temperatures and N02 production rates reported by Zabl, eta!. (1995) and Potts (1991). The gas entrainmentflux was found to be 4 molfm2·s. The pellet bed mixing time constant was 1xJ03 

### s. The adjusted parameters were used in the grate-kiln model to simulate the pellet bed temperature, magnetite oxidation, flame shape, combustion, gas temperatures, and NO formation profiles in the preheatfurnace, rotary kiln, and cooler. The shrinking magnetite core radius profile is plotted with the pelletbed temperature profile in Figure 7. Most ofthe oxidation occurs in the preheat bed where 74% ofthe magnetite
was gradually converted to hematite. Only 3.8% ofthe oxidation was estimated to occur in 'the kiln where the secondary air is poorly mixed with the pelletbed. Potts (1991) reported
a maximum of5% oxidation ofmagnetite in the kiln. Therest ofthe magnetite is oxidized quickly inthepresence oflarge 02concentrations and high temperatures inthe cooler. The heatreleased by the final oxidation causes the bed temperature to slightly increase before the pellets coolto their fmal temperature in thefirst stage ofthe cooler.

,The temperature proftles of the pelletbed, kiln wall surface, and flame stream are shown together in Figure 8. Thepeakflame temperature of2114 K occurred at approximately 16
m into thekiln where thefuel iscompletely com busted. Thepelletbed reached a maximum temperature of 1652 K in the cooler where the final magnetite oxidation heats the pellet ' further. Zahl, et al. (1995) estimated the visible natural gas flame length at7.5 to 12m. At

the pointofpellet discharge from thekiln, the simulation shows the flame stream and wall temperatures lower than the bed, due to convective cooling from outside the kiln. The
23**~---- ---~~** 

# .-

• 

# .. • • 

# - .. - .. .. .. .. -**~** 

# .. - .. .. - .. 

# .. • 

# - - • 

# - • • 

# - 

# - • 

# .. • • • 

# • 

# • • • 

# • • • 

# • • 

# • 

# • 

# • • 

# • • temperature ofthe secondary air stream remained relatively constant at approximately 1450 K . The model prediction of the kiln flame stream geometry is illustrated in Figure 9. The results are drawn to scaleinthe bottom plot. Inthe burner-zone, the diameter ofthe flame ranges from 1 to 3m. This is in general agreement with the 1.5 to 4.5 m diameter of a visible natural gas flame observed by Zahl, et al. (1995). The NO profile in the kiln is shown in Figure 10 along with the flame steam temperature profile. These results show a marked increase in NO formation in the post combustion zone, consistent with observation (Chigier, 1981). The model predicts a gradual increase ofNO formation in the burner zone, followed by rapid production ofNO after the fuel is completely combusted and the hotcombustion products in the flame stream are mixed with 

### Oz from the secondary air stream. The NO production practically stops when the flame stream cools to temperatures below 1800 K. The final concentration ofNOz was 526 ppm. resulting in a production rate o 278 kg NOz/hr. Zahl, et al. (1995) measured the NOz composition and production rates at 528 ppm and 290 kg/hr, respectively. The agreement in N02 composition between the simulation and experiments was expected because the model was adjusted accordingly
. There are three variables controlling the formation ofNOx: the reacting gas temperature, the partial pressure of 

### Oz in the gas streams, and the residence time of the NO reactants near the peak flame temperature. Generally, the NO production rate is expected to increase with increasing gas temperature, residence time and 

### Oz partial pressure. The flow rate of the secondary air is an important parameter affecting all three factors. Increasing the secondary air flow rate lowers the gas temperature and residence time while increasing the 

### Oz availability. This also increases the percent of magnetite oxidation in the preheat furnace. Conversely, decreasing the secondary air flow rate increases the gas residence

24

# ! L time and temperature while lowering the 02 

### availability. In this case, a higher percent of the magnetite oxidation occurs inthe cooler. Simnlations were also performed with ±15% of the secondary air flow rate to the first cooler stage, as listed in Table II. When the secondary airflow rate was increased by 15%, the composition of N02 

### decreased to 470 ppm, but the production rate increased to 285 kg/hr. The fraction of magnetite oxidized in the preheat furnace also increased to 77%. When the secondary airflow rate was decreased by 15%, the model simulation predicted an increase inthe composition ofN02

### in the gas stream at 620 ppm, corresponding to an N02 

### production rate of 279 kg/hr. The fraction of magnetite oxidized in the preheat furnace decreased to 71%. Although lowering the secondary air flow rate caused the gas,temperature to increase, the partial pressure of02

### in the gas streams decreased because a relatively larger fraction was removed by the cooler bed oxidation and combustion in the flame. This resulted in an overall net decrease in the production rate ofN02. 

## 7. Conclusions
The objective ofthis work was to investigate the simnltaneous phenomena ofheat transfer, magnetite oxidation and NOx formation in a grate-kiln taconite induration furnace. In 

### the process, models were constructed to solve the material and energy balances that govern the temperature and composition profiles throughout the system. Three contributions of this work are the novel approach developed to account for magnetite oxidation in the rotary kiln, the Gaussian PDF temperature weighted average NO reaction rate to account for temperature fluctuations around the flame, and the model ofthe flame formed from the constant flux ofair

### from the secondary air. Also, accounting for NO formation provides an additional verification ofheattransfer modeling in thekiln.

25

# .. ,. ,. 

# .. .. .. • 

# ... 

# .. • • 

# .. .. • • 

# • • 

# .. • 

# • • 

# .. .. .. • 

# .. ... ... 4 

# ... ... ... ... ... ... ... 

# .. .. .. • • 

# .. .. .. .. • The significant heat transfer mechanism in the kiln is radiation to the bed followed by conduction from the wall. Process modifications aimed at decreasing NOx must not significantly lower the flame temperature below the level required to maintain the heat transfer rates needed to achieve the optimal pellet bed temperature. Also, fuel rich conditions at low temperatures are the conditions for carbon monoxide (CO) formation (Palmer, 1974). The reduction ofNOx requires smaller flame temperatures, shorter gas residence times, and lower Oz concentrations at the peak flame temperature. Based on a preliminary.study ofthe effects ofthe secondary airflow rate, it appears that the availability of

### Oz is the controlling factor for NOx formation
. Future modeling and simulation work is needed to include the effects ofthe endothermic calcination reactions and investigate process changes to decrease the residence times ofOz
nearthepeak flame and airtemperatures to reduce NOx
. 

# Acknowledgments
This work was sponsored by the Minnesota Department ofNatural Resources and the Iron 

### Ore Research Cooperative Program.


# Nomenclature A = cross sectional area a = pellet surface area perunit bed volume c = number ofcascades Cp = heat capacity Cr = number ofcascades per revolution D = gas diffusivity De = effective gas diffusivity E = emissive powerperuuitlength Ff = flame stream molarflow rate Fg = secondary air stream molar flow rate Fi = view factor for surface i G = radiation powerincident on a surface perunitlength 

### 26,j
' q H = 

### enthalpy Mlr = 

### heatofmagnetite oxidation reaction h = 

### heattransfercoefficient J = 

### total radiation emissive power perunitlength k = 

### mass transfer coefficient ki = 

### reaction rate constantfor reaction i L = 

### length m = 

### mass flow rate N = 

### moles Ng = 

### entrainmentflux n = 

### rotational velocity p = 

### perimeter q' 

### heat transferrate per unitlength = R = kiln

### radius r = 

### pelletradius s = 

### reactionrate 

### T = 

### temperature 

# u = 

### overallheat transfercoefficient u = 

### linearvelocity 

# w = 

### width y = 

### gas phase mole fraction z = 

### preheat, kiln, 

### cooler length coordinate Greek Symbols E = 

### porosity or emissivity «!> = 

### bed angle ofrepose, rad 1C = 

### thermal conductivity 

# e = kiln 

### angle ofinclination, rad p = 

### density (J = 

### standard deviation or StefanBoltzmann constant 't = 

### mixing time constant '\) = 

### reaction stoichiometric coefficient 

# "' = 

### bed angle from kiln

### centerline, rad Subscripts 

### b 

# = pelletbed c = 

### pellet core, cooler, or convection f = 

### flame**~** = 

### secondary air 1 = 

### species, stream, initial, inside k = kiln 

### lM = 

### log mean value M = 

### magnetite m = 

### mean value o 

### = outside surface 

### Ch = 

### oxygen ox = 

### magnetite oxidation p 

# = pellet ph = 

### preheater r = 

### radiation orrefractory 27

# ---- 

# .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. • 

# .. .. .. • 

# .. • 

# • 

# .. .. • • • • • 

# .. .. .. • • 

# • 

# • 

# .. .. .. .. .. t 

# = top w = kiln 

### wall oo = 

### outside conditions 

### Superscripts o reference value = 

### average reaction rate 

# Literature Cited 1. Barr, P.V.; Brimacombe, J.K.; Watkinson, A.P., "A heat transfer model for the rotary kiln: Part II. 

### Development ofthe cross section model," Metall. Trans. B, 20B, pp. 403-419, 1989
. 2. Bilger, R.W., ''Turbulent Reacting Flows" in Turbulent Flow with Non-Premixed Reactants (eds Libby & 

### Williams), Springer-Verlag, 1980
. 3. Carvalho, M.G.; Semiao, V.; Lockwood, F.C.; Papadopoulos, C. "Prediction of nitric oxide emissions from an industrial glass-melting furnace," J. 

### Inst. Energy, 63 (454), 1990, pp. 39-47, 4, Chigier, N., 

### Energy, Combustion, andEnvironment, McGraw-Hill, new York, pp. 328-329, 1981. 5. Fogler, H.S., 

### Elements ofChemical Reaction Engineering, 2nd ed., Prentice-Hall, Englewood Cliffs, NJ, pp. 582-587, 1992
. 6. Gorog, J.P.; Adams, T.N.; Brimacombe, J.K., "Heat Transfer from Flames in a Rotary Kiln," 

### Metall. Tans. B, 14B, pp.411-424, 1983
. 7. Gorog, J.P.; Brimacombe, J.K.; Adams, T.N., "Radiative Heat Transfer in Rotary Kilns," 

### Metall. Tans. B, 12B, pp.55-70, 1981. 8. Hanna, O.T.; Sandall, O.C., 

### Computational Methods in Chemical Engineering, Prentice-Hall, Engelwood Cliffs, NJ, 1995
. 9. Hanson, R.K.; Salimian, S., "Survey of Rate Constants in H/N/0 Systems," 

### Combustion Chemistry, Gardiner, W.C. Ed., p. 361, 1984 10. Incropera, F.P.; DeWitt, D.P., 

### Fundamentals of Heat andMass Transfer, 3rd ed., Wiley, New York, 1990
. 11. Jenkins, B.

### G.; Moles, F.D., "Modeling ofheat transfer from a large enclosed flame in a rotary kiln," 

### Trans. I. 

### Chern. E., 59, pp. 17-25, 1981. 12. Khalil, E.E., 

### Modeling of Furnace Combustors, Abacus Press, Kent, Great Britain, pp. 179-181, 1982
. 13. Miller, J.A. and Bowman, C.T., "Mechanism and Modeling ofNitrogen Chemistry in Combustion," 

### Prog. Energy Combust. Sci., 15, pp.287-338, 1989
.
28

### 14. Monnot, G., Principles of Turbulent FiredHeat, 

### GulfPublishing Co., Houston TX, pp. 204-207' 1985. 15. Nateson, K.; Philbrook, W.D., "Mathematical model for reaction rate and temperature profile during oxidation ofmagnetite pellets," Proceedings-Ironmaking Conference, 28, pp. 411-428, 1969. 16. Palmer, H.B. "Equilibria and Chemical Kinetics in Flames" in Combustion Technology, 

### Palmer, H.B. and Beer, J.M, eds, Academic Press, New York, pp. 19-20, 1974. 17. Papanastassiou, D.; Bitsanes, G., "Mechanisms and kinetics underlying the oxidation ofmagnetite in the induration ofiron ore pellets," MetalL Trans., 

### 4, pp. 487-496, 1973 18. Pape, P.O.; Frans, R.D.; Geiger, G.H., "Magnetite oxidation kinetics and thermal profiles in a magnetite pellet plantcooler," Ironmaking Steelmaking, 

### 3, pp. 138-145, 1976. 19. Potts, R.D., "Induration of Taconite Pellets Using a Grate-Kiln System," AIME/University ofMinnesota Mining Symposium, Duluth, MN, Jan. 8-9, 1991. 20. Reid, R.C.; Prausnitz, J.M.; Poling, B.E., The Properties of Gases andLiquids, 4th ed., 

### McGraw-Hill, New York, 1987. 21. Ricou, F.P.; Spalding, D.B., "Measurements of entrainment by axisymmetrical turbulentjets," 1. FluidMech., 

### 11, pp. 21-32, 1961. 72. Saeman, W.C., "Passage of Solids Through Rotary Kilns," Chern. Eng. Prog., 

### 47, pp. 508-514, 1951. 23. Shigeno, Y.; Sakakibara, T.; Omori, Y., "In 

### Situ Measurement of Effective Gas Diffusivity through Hematite Pellets during Stepwise Reductions," Metall. Trans. B, 

### 21B, pp. 677-686, 1990. 24. Silcox, G.D.; Pershing, D.W., "The effects ofrotary kiln operating conditions and design on burden heating rates as determined by a mathematical model ofrotary kiln 

### heat transfer," 1. Air Waste Manage., 

### 40 (3) pp. 337-344, 1990. 25. Thornton, G,J,; Batterham, R.J., "The Transfer of Heat in Kilns, "Chemeaca 82, Tenth Australian Chemical Engineering Conference, The Institute of Engineers, Australia, National publication no. 82/9, pp. 260-66, 1982. 26. Thurlby, J.A., 

### "A dynamic mathematical model ofthe complete grate/kiln iron-ore pelletinduration process," Metall. Trans. B, 

### 19B, pp. 103-112, 1988. 27. Thurlby, J.A.; Batterham, R.J.; Turner, R.E., "Development and Validation of a Mathematical Model for the Moving Grate Induration of Iron Ore Pellets," Int. 1. Minerals Proc., 

### 6, pp. 43-64, 1979. 28. Tscheng, S.H.; Watkinson, A.P., "Convective Heat Transfer in a Rotary Kiln," Can. J. Chern. Eng., 57, pp. 433-443, 1979.

29**--------~~···-**



### 29. Wark, K.; Warner, C.F.,

### AirPollution: Its Origin and Control, 2nd ed., Harper and Row, New York, pp 371-387, 1981. 30. Young, R.W.; Cross, M.; Gibson, R.D., "Mathematical model of grate-kiln-cooler process used for induration ofiron ore pellets," 

### lronmnking Steelmnking, 1, pp. 1- 

### 13, 1979. 31. Zabl, R.K.; Haas, L.A.; Engesser, J., "Formation ofNOx in 

### Iron Oxide Pelletizing Furnaces," US Bureau ofMines, NRRI, Minnesota DNR final report, September 29, 1995. 32. Zeldovich, Y.B.; Barenblatt, G.I., Librovich, V.B.; Makhviladze, G.M., 

### The Mathemntical Theory ofCombustions and Explosions, Consultants Bureau, New York, pp. 30-36, 1985. 33. Zeldovich, Y.B.; Sadovnikov, P.Y.; Frank-Kamenetskii, D.A., 

### Oxidation of Nitrogen 

### in Combustion, Academy ofSciences ofthe USSR, Moscow, 1947.

30Preheater G2



# ... --- --- ,... Rotary Kiln 

## ,.. 

# -.,;;f.- I

- ... .., I To dryer u u u:u u u**~** ----------

# --- ... 

### A ' ' "' P2 From dryer - P3 

# ' G1 Cooler To Dryer 

# +P4 

# + I I I 

## G4 1ststage 

### Figure 1. Countercurrent flow of process gasses and pellet bed. Pl = 

### pellet bed temperature into the Preheater. G 1

## =Gas temperature exiting.the preheater. P2 

## =Pellet temperature between the kiln and the preheater. G2 = 

### Gas temperature exiting the kiln, entering the preheater. P3 

## =Pellet bed temperature exiting the kiln into the cooler. G3 

## = Gas temperature from the cooler to the kiln. P4 = 

### Pellet temperature leaving the cooler. G4 = 

### Gas temperature entering the cooler.

Pellet Surface [02] p



### Figure 2. Cross section of spherical pellet. 31

# ,...---- 

# • • • • 

# • • • 

# • 

# • • • • • • • • 

# • • • 

# • • • • • • 

# • • • • • • 

# • • • 

# • • • • • • • 

# • • 

# • • • (a)



## (b)

(c) 

# ......

# .......

# ... lll
......... T
............ 

### Bed ...

# .......

# ...

·----------------------------------------------

... 

## ........

# ...

# ....

# .. \If ""'""..,.., T
......... 

# e

.. """"'.. \II ::::::;. ;. . . . . . . . . . "'
............ .., ... T

# :{/fff{:::}/}}}}}}:}}\\:{::::::\3·~~**·:::::::::::::/7F:~::~::~:ff.f.:.~:.~f:~~:~:** . ································· ········································ 

## . ······················ ········································ 0 ••••••••••••••••••••••••••••••••••••••••••••••••••••••••• 

### . ············································· 

### . ··································· 

### ...........·.· ·::::.·:::::

### .

Figure 

### 3. (a) Inclined kiln angle ofinclination, 9, (b) angle ofbed surface from the centerline, 

### 'If, and (c) bed angle ofrepose, cjl•



### 32Layer 1
2 

### 3 4 

### 5

LayerS 

### 4 3 2 1 Tout


### tl.y

Figure 4. Preheatfurnace beddiscrete layers.

T



### air fl.y



### Figure 5. Cooler bed discrete layers and gas temperatures. 

### 33 .

# - 

# .-**~** 

# .-1 .-1**~ ~**  

# .. .. .. .. .. .. .. .. trll**~ ~** **~ ~**  

### till till till 

# .. Iii Iii**~** 

### Iii



# - - • 

# • •**~** 

# • c 4**~**

# ~ --------- --- ------ -- 

# • • 

# • • • Start 

# • 

# • • Guess 

# • Tg2,Tg3 

# • 

# • 

# • No 

# .. .. • • Preheat Model 

## Yes 

# • Calculate Tp2 Print 

# • • Conuerged Results 

# • 

# • • • 

# • • 

# .. • Kiln Model 

# .. Calculate Tg2 

# • • 

# • • • No 

## Yes Cooler Model 

# • Calculate Tg3 

# • • • • Figure 

### 6. Numerical simulation flow diagram 

# • • 

# • • 

# .. 34 

# .. ..7 

# i 1800 ! 6 

# I 1600 5 1400**~**

# --~ 1200 

### E 4 

### E 

# I/ """"-**~ ~**  

# % c:r 3 1000**~** ,_o 

# "'**.~** 2 

# I 800
1 Kiln Cooler 600 Preheat 0 400 0 20 40 60 80 100 120 

### z (m) Figure 7. Magnetite core radius and pelletbedtemperature inthe grate-kiln system. 2200 2000 1800 1600 

### T 

### (K) 1400 1200 1000 Post-Burner Zone Burner Zone

800 0 5 10 15 20 

### 25 30 35 40 

### z (m) Figure 8. Flame, wall and bed temperature profiles in the kiln.



### 35

### ,...---

..



# ' t 

# t 

# • • 

# • • t t 

# • t 

# • • • 

# • • • • • 

# • • 

# • • • • • • • 

# • • • • • 

# • • 

# • • • • 

# • 

# • • • • 

# • 

# • _..... 

### E**~**



## .... 0.:



## .... 0.:**~** 

### E a. a.**~**

0 

### z >- 3 2 1 0 -1 -2 -3

600 500 400 300 200 100 0 0

0 PostBurnerZone Burner Zone
Flame

·-- · -- · ·--····Centerline

Bed.
5 10 15 20 25 30

5 10 15 20 25 30 

### z (m) Figure 9. Kiln flame stream profile**-------~**

# ~~-\

Post-Burner Zone 

# I \ i \ 

# ! \**~** I ! 

## ! Burner Zone ! 

## i 35 40

35 40

2200
2000
1800 _-I**~** 

## 3 1600
1400
1200 0 5 10 15 20 25 30 35 40 

## z (m) Figure 10. NO composition and flame temperature inthekiln
. 

### 36Table 

### L Grate-kiln process simulation parameters. 

### Pellet Bed m 141 k 

### s 0.0062 m 0.4 

### Pc
Preheat Furnace 22m bed 

### volume 

### Vb 22m3 bed width 

## wh Sm 

### Kiln fuel feed rate 

### F· 100 molls (10% 

### stoich. air kiln len th L 

### 40m entrainment

### flux N 

### 4mollm2·s refracto inside radius 

## Rr 3m £b 

### 0.6 Ef 

### 0.8 Ew 

### 0.4 

## q, 0.69 rad kiln 

# e 0.052 rad t 

### 1000s 

### Cooler 3100 molls (air) 54m bed volume 

# v 309m3 bed width 

## w 7.5m

37

### TableIL N 2 ormation an secondary-mr ow rate simulation results Gas Flow Rate 

### -15% 0% 15%**F~**

### preheat (molls) 

### 2720 3190 3700**PeakT~** 

### (K) 

### 1510 1440 1360 PeakTr(K) 

### 2140 2110 2090 PeakTh (K) 

### 1680 1630 1600 rc preheater (mm) 

### 4.0 3.8 3.7 YNOz 

### (ppm) 

### 620 526 470 mNo2 

### (kg!hr) 

### 279 278 285