MODEL AND SIMULATION OF HEAT 

TRANSFER, MAGNETITE OXIDATION 

AND NOx FORMATION IN A GRATEKILN TACONITE PELLET INDURATION 

FURNACE 
~ ~ 

... 

• 

• 

• .. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

• 

• 

• 

• 

• 

• 

• 

• 

• 

• 

• 

• 

.. 

• 

• .. 

.. 

.. 

.. 

.. 

.. 

.. 

• 

• 

• 

• 

• 

• 

MODEL AND SIMULATION OF HEAT 

TRANSFER, MAGNETITE OXIDATION 

AND NOx FORMATION IN A GRATEKILN 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 
~ ~ 

~ 

~ 

~ 

~ 

... 

... 

... 

... 

... 

... 

... 

... 

... 

... 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

• 

• 

• 

• 

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 of tumbling 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 of plant 

performance . 

1 
,. 

~ ~ 

~ 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

• 

• 

• 

• 

• 

• 

• 

.. 

• 

.. 

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 of oxides of nitrogen (NOx) in the gratekiln system. Previous models of the grate-kiln system have not included the combined 

effects of heat transfer with NOx reaction in the kiln (Thurlby, 1988; Young, et al., 1979). 

The simulation was applied to a grate-kiln system at the USS MinnTac taconite pelletizing 

plant in 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 of heat and oxygen 

transfer to a traveling bed of spherical 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 pellet bed and supply oxygen (02) from the air 

to oxidize the magnetite in the pellets to hematite. In the overall grate-kiln system, water is 

initially removed from the pellets by thermal action in a two stage dryer (not shown). The 

temperature of the bed of pellets is gradually increased further in a preheat furnace. The 

pellet bed reaches its final temperature in the rotary kiln, fired with a single burner. In this 

model, the burner is 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 of the 

cooler is passed to the kiln as secondary air where it flows above the pellet bed 

countercurrent to the flow of pellets through the kiln. The secondary air is required for 

complete combustion of the burner gases and oxidation of the 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 preheat the pellet 

2 
bed on a traveling grate before the pellets are fed to the kiln. Finally, the gas from the 

preheater is used in the second stage of the dryer or vented as waste gas along with the air 

exiting from the dryer. 

Although the design of the grate-kiln system is for efficient heat and mass transfer, it may 

not be the optimal design for minimizing the formation of NOx. When natural gas is used 

to fuel the kiln burner in the presence of excess air the principal mechanism of NOx 

formation is the thermally induced combination of oxygen and nitrogen in the air in the post 

combustion zone after the burner. Fuel NOx, derived from nitrogen sources in the burner 

fuel, and prompt NOx, formed from the reactions of combustion 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+N2 <=>N+NO 

k, (1) 

k, 

N + 02 <=>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 of fuel lean flames where the 

3 
• • • • • • • .. 

.. 

.. 

.. 

• 

.. • 

.. 

partial pressure of OH and H from combustion reactions is small relative to the partial 

pressure of 02 and atomic 0 (Monnot, et al., 1985; Wark and Warner, 1981): 

(4) 

(5) 

Taconite kilns typically operate under conditions of approximately 500% excess air overall 

It is common to treat the faster combustion reactions as instantaneous and irreversible, as 

first proposed by Zeldovich (Chigier, 1981; Zeldovich, et al., 1985). This assumption 

decouples the combustion reactions from the NO reactions in the model. Application of the 

steady-state approximation to atomic nitrogen in eqs 1-2 gives the following expression for 

the rate of NO generation per unit volume. 

2[ O](k,Ts[ OJ[ N2 ]- k,k4 [ N0]2

) 

s = 

NO k,[N0]+q02 ] 

(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 super equilibrium relationship ofWarnatz (1984). 

At lower temperatures, NO "freezes", and essentially all the NO is irreversibly oxidized 

further to NOz according to the following stoichiometric equation (Palmer, 1974; Wark and 

Warner, 1981): 

4 
The thermal NO reaction rate becomes important in air at temperatures in excess of 1800 K, 

increasing exponentially with temperature. In turbulent flow with combustion, locally high 

temperatures in the gas phase envelope around the flame contribute significantly to the total 

thermal NO formation (Khalil, 1982). The effect of fluctuating temperatures in the kiln on 

the NO reaction rate was modeled by assuming a truncated Gaussian probability density 

function (PDF) for the temperature distribution in the 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 

mean flame 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 ±3a of the mean temperature. The expected value of 

the reaction rate was calculated by integrating the rate law in eq 6 about the PDF between 

the limits ±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, et al. (1990) to account for temperature 

effects on combustion of hydrocarbons in their models of turbulent reacting flows. 

3. Magnetite Oxidation 

The pellets were assumed to be spherical with magnetite evenly distributed throughout the; 

pellet. The overall reaction of oxygen with magnetite to form hematite is 

5 
• 

t. 

t. 

• 

• 

• 

• 

• 

• 

• 

• 

• 

• 

• 

• 

• 

• 

• 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. ' 

(10) 

The magnetite oxidation reaction was assumed irreversible. The shrinking core model 

provides an adequate description of magnetite oxidation in the preheat furnace and cooler 

where air is drawn through the pellet bed 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 of the secondary air with the tumbling pellet bed as the kiln rotates. A 

simple, novel approach to modeling magnetite oxidation in a rotary kiln was developed here 

based on a mathematical description of the periodic cascading of the 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 of hematite 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 of 02 through the outer ash layer 

(Pape, et al., 1976; Papanastassiou and Bitsanes, 1973). Hence, the rate of reaction is 

equal to the rate of diffusion of 02 to the core/ash layer interface. The differential change in 

the pellet core radius with position along the grate is proportional to the 02 concentration 

· gradient evaluated at the core radius: 

(11) 

where Ub is the superficial velocity of the pellet bed, Pc is the molar density of magnetite in 

the unoxidized core, and De is the effective diffusivity in the porous pellet: 

(12) 

6 
where ep is the porosity of the pellet and 'tp is pore tortuosity. The diffusivity of 02, Do2, 

was predicted from the kinetic theory of gases (Reid, et al., 1987). 

Assuming uniform, porous, spherical pellets, the quasi-steady state approximation to the 

diffusion reaction equation in the ash layer is (Fogler, 1992): 

(13) 

subject to the boundary conditions 

(14) 

(15) 

The surface concentration of 02 is found from the mass balance for 02 at the pellet surface: 

D, d~ ] =k{[OJ8 -[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). 

Upon integration of the diffusion equation and substitution of the boundary conditions, the 

02 concentration gradient at the core radius is 

(17) 

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

[02], (18) 

7 
This result, substituted into eq 17, gives the differential change in the core radius with axial 

position along the grate based on the oxidation reaction stoichiometry of eq 10: 

(19) 

At z = 0, rc = rp. and the derivative is indeterminate. Application of L'Hopital' s rule to this 

expression gives the initial derivative at the start of the grate: 

drcl = 

dz z=O 

4k[02 ] 

•• (20) 

The heat generated by the oxidation of magnetite is also proportional to the derivative of the 

core radius: 

(21) 

where Mfr is the exothermic heat of reaction, eq 10, and Ab is the cross sectional area of 

the bed. The pellet surface area per unit bed volume of a porous bed of spheres is 

(22) 

where Eb is the pellet bed porosity. 

3.2 Oxidation in the Rotary Kiln 

The transport and reaction of (h in the cascading pellet bed in the kiln is complicated by the 

intermittent tumbling action of the pellets induced by the rotating action of the kiln. A 

simple, novel approach was used here that provided satisfactory results, while avoiding the 

difficult, rigorous approach of previous modeling efforts (Young, et al., 1979). 

This approach is based on the mathematical description of a cascading bed in a rotary kiln : 

developed by Saeman (1951). The number of cascades per kiln revolution is 

8 
c, = . _,(wb) sm -

2R 

(23) 

where R is the radial position of the pellet in the bed, and Wb is the width of the top of the 

bed, as shown in Figure 3: 

Wb = 2R, sin 1/> (24) 

The axial velocity of a 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 of inclination, <)> 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 of cascades per unit bed length is 

(26) 

The pellets do not necessarily travel along an arc of radius R as suggested by eqs 23 and 

25. However, the average number of cascades is independent of radial position in the bed. 

This model assumes that all of the 02 in 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 02 from the secondary air above the bed when the covered pellets become 

exposed. The concentration of 02 per cascade in the 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 of times the bed turns over and the average concentration in the bed. This gives the 

average moles of 02 reacted per cascade: 

9 
.. 

• .. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

• 

• 

• 

-

-

-

'tfiJ 

--~-----

(27) 

The differential form of eq 27, with substitution from eq 26 gives the moles of Oz reacted 

per unit kiln length: 

dN o, _ [ 02 ]b ebL,Ab sin 1/1 

dz- Wb(O+ lp"coslf>) 

In this case, the heat of the magnetite oxidation reaction per unit length is 

The total moles of magnetite oxidized is 4No2

: 

The total moles of magnetite oxidized per pellet is: 

(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) 

where rei is the average pellet core radius feeding the kiln. The assumption of complete Oz 

consumption with each cascade was verified here with the shrinking core model for each 

cascade at various temperatures and Oz compositions typically found during kiln operation 

(Potts, 1991) . 

10 
4. Heat Transfer 

The primary mechanism of heat transfer in the preheat furnace and cooler is convection 

between the secondary air and pellet bed. The principle heat transfer mechanism 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 

Thermal energy is liberated during the combustion of natural gas in the burner zone of the 

kiln. ill this study, natural gas is assumed to be pure methane. Approximately 10% of the 

stoichiometric air required for complete combustion is premixed with the fuel in the burner 

(Zahl, et al., 1995). The rest of the oxygen required for coi:pplete combustion is supplied 

as secondary air. The combustion rate and flame shape are governed by the flux of air to 

the flame stream from the secondary air. 

The flame and secondary air streams were modeled as perfectly mixed plug flows, with no 

inter stream mixing, except for a constant flux of entrained gas from the secondary air 

stream to the flame stream. The material 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 Pt is 

the perimeter of the flame: 

(35) 

where Rt is the local flame radius. 

11 
This approach is similar to that of Jenkins and Moles (1981), Gorog, et al. (1983), and 

Silcox and Pershing (1990), except these 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 of the 

kiln, but the cross sectional area of the flame was permitted to vary as a function of the 

flame and secondary air stream volumetric flow rates and temperatures. Assuming ideal 

gas behavior and uniform pressure, the cross sectional area of the flame is 

(36) 

where At is the total cross seCtional area of the kiln above the'pellet bed: 

A• = R?[ n--0.5(2¢ -sin2¢)] (37) 

The radius of the flame is: 

(38) 

As the flame stream entrains the secondary air, the radius grows, increasing the rate of 

. entrainment In the limit of z ~ 0, this model reduces to the semi-empirical expression for 

gas entrainment rate by a jet in 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 of the pellet bed is defined in terms of the mass flow rate of 

the bed and the cross sectional area of the kiln that is occupied by the bed: 

12 
(40) 

where Pp is the pellet density. The cross sectional area of the bed is: 

(41) 

where Rr is the inside radius to the kiln refractory lining. Saemon's (1951) predicted the 

velocity of the pellet based on angle of repose and inclination: 

u = ( ~~ )[ 8 + arctan( R, c~s cf> )cos cf> }1- cohp )'

12 

• 0.5R;(2cf>-sin2cf>)sincf> 

(42) 

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

' 

superficial velocity are found by solving the nonlinear eqs 40-42 simultaneously for cj> and 

Flame Steam 

In the case of complete combustion, the reaction stoichiometry is equimolar: 

CH4 + 202 -7 C02 + 2H,O (43) 

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

streams is governed by the NO formation and combustion reactions. A differential material 

balance for each of the combustion reactants and products in the flame stream is: 

dF -' = v,y0 P1N, dz ' 

(44) 

where 'lli is the combustion reaction coefficient for species i in terms of 02. A 

stoichiometric amount of fuel is assumed to be completely com busted with the air entrained 

by the flame. During combustion, the coefficients of the various species are: CI4 = -112; 

13 
.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

• 

• 'tit 

'tit 

= 

Oz = 0; COz = 1/2; HzO = 1. The post combustion coefficients are: CI4 = 0; Oz = 1; C02 

=0; HzO = 0 . 

The differential species balances for the non-combustion species in the flame steam are: 

dF; PN A- -=y. f + ,s. dz ' 8 ' 

(45) 

where Si is the rate of generation of species i in equation 9 based on the stoichiometry of the 

overall NO reaction: 

N2 +02 ~2NO (46) 

A differential energy balance for the flame stream includes the flux of enthalpy from the gas 

stream: 

(47) 

where q' rf is the net rate of thermal radiation to the flame per unit length. 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 of formation at a reference temperature, T0 • The initial flame 

temperature was assumed to be the 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 per unit length between tbe secondary air and 

the surrounding kiln wall and pellet bed. The heat transfer coefficients of Tscheng and 

Watkinson (1979) were used to predict the convective heat transfer rates between the gas, 

and the pellet bed and kiln wall. The secondary air stream enthalpies are defined similarly 

to eq 48. 

Pellet Bed 

The thermal energy balance around the pellet bed involves heat transfer between the bed 

and the kiln wall, secondary air, flame stream, and the heat released from the exothermic 

reaction of magnetite oxidation : 

(51) 

where mb is the mass flow rate of the pellet bed, 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 

length from the wall to the bed, q'rb is the net radiation per unit length to the bed, and q' ox 

is the heat generated per unit length by the magnetite oxidation reaction in the bed. 

The pellet bed was modeled as an inner core of pellets surrounded by an outer mantle of 

pellets, as suggested by Thornton and Batterham (1982). The heat transfer between the 

bed mantle and core is 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 heat conduction and steady-state operation: 

(53) 

where q'bw , q' gw, and q' rw are the heat transfer rates per unit 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 transfer through the wall normal to the axis is 

(54) 

where R8 is the inside radius of the kiln shell, Ro is the outside shell radius, 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 

transfer coefficient correlation for free convection from a rotating cylinder recommended 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 of the kiln wall, pellet bed, and flame is based 

on the net radiation approximation method of Thornton and Batterham (1982). A weakness 

of this 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 ±0.3 kiln 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. It was 

also assumed that no radiation transmits through the three bodies. 

The thermal radiation emission rate from each surface i is 

(57) 

Of the net energy arriving at a surface, G, pG is reflected, and (1-p )G is absorbed. The 

total rate of energy per unit length leaving surface i is 

(58) 

Considering all the surfaces, the total incident radiation per unit 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 by a body (surface) per unit area is 

q;, =(1-p1)G1 -E, (60) 

where Pt and Pt, are the perimeters of the 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 in the 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 of gases above the pellet bed was modeled as a perfectly 

stirred tank. The energy balance under steady state operation becomes: 

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 of convective and conductive heat 

transfer resistances: 

18 
UA= 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 preheater refractory thickness, /';.w is the preheater wall thickness, hi 

is the internal heat transfer coefficient, how is the external wall free convection heat transfer 

coefficient, hot is the external top free convection heat transfer coefficient and K is the wall 

or refractory thermal conductivity. 

The outside surface temperature was calculated from an energy balance across the boundary 

layer outside the furnace: 

(64) 

The inside surface temperature was calculated in a similar manner: 

(65) 

The results in a system of non-linear algebraic equations in Tg, Tsi and T80 which must be 

solved simultaneously by a trial and error technique such as Newton's method. 

The bed of pellets traveling along the grate was treated as 5 discrete layers of uniform 

thickness, similar to the approach of Thurlby (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 heat transfer coefficient, the differential tern perature change across a layer 

is: 

(66) 

19 
r . 

• .. 

• ' 

• 

• 

• 

,' . ._ 

-

• 

• 

• 

• 

• 

.. 

• 

-

• 

• 

• 

• 

... 

-

• 

• 

• 

• 

• 

• 

• 

--

• 

• 

• 

• 

• 

• 

• 

• 

• 

• 

• 

• 

• 

• 

-

• 

• 

where y is positive in the vertical down direction. Eq 66 was integrated over t'ly to give the 

following function of the gas temperature leaving bed layer j . 

(67) 

The total bed volume is divided by 5, the number of pellet 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 one used for the kiln wall: 

dT -"-= dz 

( djgj dTgj-l + djgj dTbj) l JTgj-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 pellet bed layer i is 

arbi q,c + qox 

dZ mbcp 

(69) 

The bed layer temperature was assumed to be uniform such that the convective heat transfer 

rate from the gas may be described in terms of the log-mean temperature difference: 

(70) 

where 

(71) 

The heat of the magnetite oxidation reaction is proportional to the rate of oxidation given in 

eq 21. 

20 
The preheater model 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 of the pellet bed 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 cooler to the kiln. 

21 
.. 

.. 

.. 

.. 

• 

.. • 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

... 

.. 

... 

... 

.. 

• .. 

.. 

.. 

• .. 

.. 

.. 

.. 

• 

• 

• 

3. Solve for the pellet bed temperature feeding the kiln, P2, and the gas temperature 

exiting the preheat furnace, G 1, with the preheat model equations. The temperature of 

the gas above the bed was calculated from the solution to the non-linear energy balance 

around the gases with NEWTONVS. The initial gas temperatures were calculated from 

the solution to the system of non-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 preheat feed gas temperature, G2, and the kiln exit pellet 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 secant method . 

The initial flame and wall energy balances were also solved numerically for the initial 

flame and wall temperatures using NEWTONVS. The system of first order ordinary 

differential equations was also solved numerically by the IEXVS method. The integral 

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 in G2 and G3 is achieved . 

At most 15 iterations on steps 3 through 6 were required to reach a converged solution . 

22 

'(, 

' 
6. Simulation Results 

The USS MinnTac plant 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 entrainment flux 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 

preheat furnace, rotary kiln, and cooler. 

The shrinking magnetite core radius profile is plotted with the pellet bed temperature profile 

in Figure 7. Most of the oxidation occurs in the preheat bed where 74% of the magnetite 

was gradually converted to hematite. Only 3.8% of the oxidation was estimated to occur in 

'the kiln where the secondary air is poorly mixed with the pellet bed. Potts (1991) reported 

a maximum of 5% oxidation of magnetite in the kiln. The rest of the magnetite is oxidized 

quickly in the presence of large 02 concentrations and high temperatures in the cooler. The 

heat released by the final oxidation causes the bed temperature to slightly increase before 

the pellets cool to their fmal temperature in the first stage of the cooler. 

, The temperature proftles of the pellet bed, kiln wall surface, and flame stream are shown 

together in Figure 8. The peak flame temperature of 2114 K occurred at approximately 16 

m into the kiln where the fuel is completely com busted. The pellet bed 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 at 7.5 to 12m. At 

the point of pellet discharge from the kiln, the simulation shows the flame stream and wall 

temperatures lower than the bed, due to convective cooling from outside the kiln. The 

23 

~-------~~ 
.-• .. 

• • 

.. 

-

.. 

-

.. 

.. 

.. 

-

~ 

.. 

.. 

-

.. 

.. 

-

.. 

• -

-

• 

• 

-

• 

-

-

• .. 

• • • • • • • • • • • • • 

• 

• 

• 

• 

• 

temperature of the 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 scale in the bottom plot. In the burner-zone, the diameter of the 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 

of NO formation in the burner zone, followed by rapid production of NO after the fuel is 

completely com busted and the hot combustion 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 of NOz 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 of NOx: 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 in the 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 air flow 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 air flow rate was decreased by 15%, the model simulation predicted an 

increase in the composition of N02 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 of 02 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 of N02. 

7. Conclusions 

The objective of this work was to investigate the simnltaneous phenomena of heat 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 of the flame formed from the 

constant flux of air from the secondary air. Also, accounting for NO formation provides an 

additional verification of heat transfer modeling in the kiln. 

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 of NOx requires smaller flame temperatures, shorter gas 

residence times, and lower Oz concentrations at the peak flame temperature. Based on a 

preliminary .study of the effects of the secondary air flow 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 of the endothermic 

calcination reactions and investigate process changes to decrease the residence times of Oz 

near the peak flame and air temperatures to reduce NOx . 

Acknowledgments 

This work was sponsored by the Minnesota Department of Natural Resources and the Iron 

Ore Research Cooperative Program. 

Nomenclature 

A = cross sectional area 

a = pellet surface area per unit bed volume 

c = number of cascades 

Cp = heat capacity 

Cr = number of cascades per revolution 

D = gas diffusivity 

De = effective gas diffusivity 

E = emissive power per uuit length 

Ff = flame stream molar flow rate 

Fg = secondary air stream molar flow rate 

Fi = view factor for surface i 

G = radiation power incident on a surface per unit length 

26 
,j 

' q 

H = enthalpy 

Mlr = heat of magnetite oxidation reaction 

h = heat transfer coefficient 

J = total radiation emissive power per unit length 

k = mass transfer coefficient 

ki = reaction rate constant for reaction i 

L = length 

m = mass flow rate 

N = moles 

Ng = entrainment flux 

n = rotational velocity 

p = perimeter 

q ' = heat transfer rate per unit length 

R = kiln radius 

r = pellet radius 

s = reaction rate 

T = temperature 

u = overall heat transfer coefficient 

u = linear velocity 

w = width 

y = gas phase mole fraction 

z = preheat, kiln, cooler length coordinate 

Greek Symbols 

E = porosity or emissivity 

«!> = bed angle of repose, rad 

1C = thermal conductivity 

e = kiln angle of inclination, rad 

p = density 

(J = standard deviation or Stefan Boltzmann 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 or refractory 

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 of the 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, and Environment, McGraw-Hill, new York, pp. 

328-329, 1981. 

5. Fogler, H.S., Elements of Chemical 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 and Mass Transfer, 3rd ed., 

Wiley, New York, 1990 . 

11. Jenkins, B. G.; Moles, F.D., "Modeling of heat 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 of Nitrogen Chemistry 

in Combustion," Prog. Energy Combust. Sci., 15, pp.287-338, 1989 . 

28 
14. Monnot, G., Principles of Turbulent Fired Heat, Gulf Publishing Co., Houston TX, 

pp. 204-207' 1985. 

15. Nateson, K.; Philbrook, W.D., "Mathematical model for reaction rate and 

temperature profile during oxidation of magnetite 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 

of magnetite in the induration of iron ore pellets," Me talL 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 plant cooler," Ironmaking Steelmaking, 3, pp. 138-145, 

1976. 

19. Potts, R.D., "Induration of Taconite Pellets Using a Grate-Kiln System," 

AIME/University of Minnesota Mining Symposium, Duluth, MN, Jan. 8-9, 1991. 

20. Reid, R.C.; Prausnitz, J.M.; Poling, B.E., The Properties of Gases and Liquids, 4th 

ed., McGraw-Hill, New York, 1987. 

21. Ricou, F.P.; Spalding, D.B., "Measurements of entrainment by axisymmetrical 

turbulent jets," 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 of rotary kiln operating conditions and 

design on burden heating rates as determined by a mathematical model of rotary 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 of the complete grate/kiln iron-ore 

pellet induration 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., Air Pollution: 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 of iron 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 of Mines, NRRI, Minnesota DNR final report, September 

29, 1995. 

32. Zeldovich, Y.B.; Barenblatt, G.I., Librovich, V.B.; Makhviladze, G.M., The 

Mathemntical Theory of Combustions 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 of Sciences of the USSR, Moscow, 1947. 

30 
Preheater 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 

1st stage 

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 of inclination, 9, (b) angle of bed surface from the 

centerline, 'If, and (c) bed angle of repose, cjl • 

32 
Layer 1 

2 

3 

4 

5 

LayerS 

4 

3 

2 

1 

T 

out 

tl.y 

Figure 4. Preheat furnace bed discrete layers. 

T 

air 

fl.y 

Figure 5. Cooler bed discrete layers and gas temperatures. 

33 

.

.

~ 

.-

.-

~ 

~ 

.

.

.

.

.

.

.

.. 

trl

~ 

~ 

~ 

~ 

til

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 pellet bed temperature in the 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 

Post Burner Zone 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 1 0 15 20 25 30 35 40 

z (m) 

Figure 10. NO composition and flame temperature in the kiln . 

36 
Table 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 
Table IL 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