Elsevier Scientific Publishing Company, Amsterdam -- Printed in The Netherlands .... development and close temperature control is required to ensure consistent.
International Journal o f Mineral Processing, 6 (1979) 43--64
43
© Elsevier Scientific Publishing Company, Amsterdam -- Printed in The Netherlands
DEVELOPMENT AND VALIDATION OF A MATHEMATICAL MODEL FOR THE MOVING GRATE INDURATION OF IRON ORE PELLETS J.A. THURLBY l, R.J. BATTERHAM 1 and R.E. TURNER 2 x Commonwealth Scientific and Industrial Research Organization, Division o f Mineral Engineering, Clayton, Victor&, (Australia) 2 Hamersley Iron Pry. Ltd., Dampier, Western Australia (Australia)
(Received August 16, 1978); accepted January 26, 1979)
ABSTRACT
Thurlby, J.A., Batterham, R.J. and Turner, R.E., 1979. Development and validation of a mathematical model for the moving grate induration of iron ore pellets. Int. J. Miner. Process., 6: 43---64. A mathematical model is described for the induration of iron ore pellets on a moving grate. The validity of the model has been demonstrated, both for the performance of an operating plant and for the firing of pellets in a laboratory pot grate furnace. The model permits calculation of pellet bed temperature profiles and the resulting product quality, together with overall heat and mass balances for the induration machine. Indications are also given of the occurrence and extent of the spalling that can occur during removal of both free and chemically combined water in the drying stages. The work has demonstrated the significant effect of gas composition on pellet temperatures and indicated that difficulties can arise when comparing plant data with that from laboratory pot grate simulators.
INTRODUCTION Pelletizing is o n e o f the t w o c o m m o n a g g l o m e r a t i o n processes used f o r u p g r a d i n g iron-ore fines and installed c a p a c i t y in m o v i n g grate pelletizing p l a n t s a l o n e e x c e e d s 120 million t o n n e s p e r a n n u m (Traice a n d L a p p i n , 1973). M o s t o f this is in s t r a i g h t grate i n d u r a t o r s , c o m m o n l y o f at least 3 million t.p.a, c a p a c i t y , in which d r y i n g a n d t h e r m a l h a r d e n i n g of t h e pellets is c o m p l e t e d on a m o v i n g strand. T h e s t r a i g h t grate i n d u r a t i o n process is highly i n t e r a c t i v e with significant t r a n s p o r t a n d p r o d u c t q u a l i t y m e a s u r e m e n t delays ( B a t t e r h a m e t al., 1977). I n d u r a t o r p e r f o r m a n c e a n d pellet q u a l i t y can be i n f e r r e d f r o m t e m p e r a t u r e profiles in a p e l l e t bed, b u t as these are n o t a m e n a b l e to m e a s u r e m e n t on the p l a n t , p r o c e s s design a n d o p t i m i z a t i o n has b e e n f a c i l i t a t e d b y t h e use o f l a b o r a t o r y p o t - g r a t e " s i m u l a t o r s " . H o w e v e r t h e s e h a v e i n h e r e n t technical l i m i t a t i o n s ( T h o m a s a n d Clark, 1 9 7 4 ) a n d d o n o t a l l o w f o r process interactions, n o r d o t h e y d i r e c t l y p r o v i d e h e a t a n d mass b a l a n c e d a t a suitable f o r p l a n t use, a n d m o r e sensitive a n d c o m p l e t e process analysis is possible
44
by off-line mathematical modelling. To obtain accurate temperature profiles, the model must accommodate the evaporation of free water and chemical reactions such as the decomposition of goethite, kaolinite and carbonates. Changes in both the free and combined water contents of the feed pellets, or the drying rates dictate the division of the machine between drying and firing, thus significantly affecting the capacity of a machine of fixed size. Temperature profile calculations along moving beds of iron ore pellets have been reported by several authors (Young, 1963; Lobanov et al., 1972; Ball et al., 1973; Lobanov et al., 1974; Voskamp and Brasz, 1975; Pape et al., 1976; Cross et al., 1977) but validation, when discussed, has been incomplete. Product quality estimation and prediction of spalling have not been attempted in these models despite their demonstrated importance (Baker et al., 1973), and only two representations of the complete process have been reported (Voskamp and Brasz, 1975; Lebelle et al., 1975). Voskamp and Brasz simulated a six-zone machine, calculating temperature profiles and process gas flows and approximation methods used to reduce computing time were an important feature of their work. For each zone lumped parameters containing physical property variables were assigned values which were chosen to give agreement between calculated and plant gas flows and temperatures. The work described forms part of a joint research and development programme of Hamersley Iron Pty. Ltd. and the C.S.I.R.O. The objective is to develop and validate a model which will accurately predict machine performance under a wide range of operating conditions. The ability to predict spalling (i.e. the explosion of pellets into small fragments and dust due to excessive internal water vapour pressures (Baker et al., 1973)) and product quality is regarded as essential and necessitates a more detailed approach than that of Voskamp and Brasz. Iterative procedures are necessary to handle the effects of gas properties as a function of temperature and composition and to adjust flowrates to match required pressure drops. The main assumptions are constant bed voidage and height throughout the machine, and uniform gas distribution across the bed. No magnetite is present in the feed stock so it was not necessary to allow for its oxidation. The present work has indicated that drying can be adequately represented without modelling internat pellet processes, and therefore temperature and moisture gradients within individual pellets have been ignored. Longitudinal heat transfer through the bed has also been ignored as the temperature gradients are negligible compared with those in the vertical direction.
45 PROCESS MODELLING CONCEPTS
Features o f the induration process In the straight grate induration process "green" pellets containing 7--91~ free moisture are spread evenly onto a layer of previously fired pellets on the moving grate. This hearth layer and side layers of the same material protect the grate structure from excessive temperatures. Grate speed and/or bed height are adjusted according to the green pellet feedrate. Usually the first stage of drying is updraught which avoids condensation in the b o t t o m of the bed, thus minimizing pellet deformation due to the weight of the bed. Removal of free and chemically combined water are critical phases for most ores. The rate of heat transfer to pellets at all bed levels must be low enough to avoid an unacceptable degree of spalling which can cause severe local reduction in bed permeability as well as contribute to fan wear and environmental problems. Most of the water removal is accomplished in drying zones, using outlet gas from the firing and cooling zones with supplementary heat from burners as required. The firing stage is controlled so that the b o t t o m of the green pellet bed reaches a sufficiently high temperature for adequate final pellet strength development and close temperature control is required to ensure consistent product quality and to avoid overheating the grate. An "after-firing" zone is c o m m o n l y employed in which the green pellets in the lower portion of the bed reach their maximum temperature, by the transfer of heat from hardened pellets in the upper portion. This is accomplished using hot air from the cooling zone with no supplementary heating. Design and operation of the cooling stage is aimed at efficient recovery and utilization of heat from the bed and grate. High temperature air is used in the firing and after-firing zones. Lower temperature air from the final stages of cooling is used for drying. Hamersley Iron's indurator at Dampier, which is simulated in this paper, and shown diagrammatically in Fig. 1, is of Dravo-Lurgi design with 400 sq. metres grate area travelling across 60 windboxes each 2.0 metres long. H a m m o n d (1970) has given a description of the complete Dampier pellet plant which includes a full description of this indurator.
Moving bed heat transfer model Gas composition varies along the length of the machine and, where drying occurs, humidity changes with vertical position in the bed. For convenience calculations can be based on dry air flowrate (Fa) i.e.:
Fa = Fgw/(1 + X n + X c +Xwv)
(1)
where Fgw is the flowrate of moist gas; Xn, Xc and Xwv are respectively, the excess nitrogen, carbon dioxide and water vapour contents of the gas expressed as a fraction of the dry air contained in the gas.
46
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W S.
24-36
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W.B 44-60
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COOLING AIR W.B. EXHAUST~
HOOD -SEAL
/J
'
-M DUST SYSTEM
2
UPDRAUGHT DRYING
"
W.B RECUP. W.B. RECUP. NO1 NO,2
Fig. 1. Dampier indurator.
Referring to Fig. 2, at any position in the pellet bed (or in the grate) the rate of convective heat transfer from the gas to the solid is given by: ~qcv
-~-=
h d A ( Tg - Ts)
(2)
where h and dA are the local heat transfer coefficient and surface area respedtively. The heat balance across an element (illustrated in Fig. 2) for the gas is given by: - F a (Cga + X w v C w v ) a_Tg = h ~ ( T ¢ az
- Ts)
(3)
and that for the solid material (which also receives heat by radiation and conduction from surrounding material) by: a w A H v = h d A ( T g - Ts) + -~qo dm(Cs + M C w ) aTs - ~ + a-O - d + ~qr "a0
(4)
where Cga is the specific heat of dry gas per unit mass of contained air; Cs, Cw and Cwv are the specific heats of solid, water and waper vapour respectively; M is the moisture content of the solid; dm is the dry mass of solid and AHv the heat of vapourization of free water or the effective heat of decomposition for the removal of combined water. The above equations are solved in finite difference form with position along the machine derived as a function of time and machine speed. The
47 NOTATION
Latin Symbols A Cga, Cgw Cs, Cw, Cwv dp
f Fa Fgw G h AHv kgw km m M, Mi, M o
,52 qt qcv, qcd, qr
Tb Tg, Tgi, Tgo, Tgav
Ts, Tsi, Tso, Tsar
U V Aw
Ax
x~ x~ Xwv, Xwvi, Xwvo
Xsg, Xss Az Zm ax
= surface area for h e a t or mass t r a n s f e r = specific h e a t of dry gas per u n i t mass of c o n t a i n e d air, a n d m o i s t gas, respectively = specific h e a t of dry solid (pellet or grate), w a t e r a n d w a t e r v a p 0 u r , respectively = pellet diameter = pellet specific h e a t f a c t o r = dry air f l o w r a t e = m o i s t gas f l o w r a t e = m o i s t gas f l o w r a t e / s u p e r f i c i a l area = convective heat transfer coefficient = h e a t of v a p o u r i z a t i o n or r e a c t i o n = t h e r m a l c o n d i m t i v i t y o f m o i s t gas = mass t r a n s f e r c o e f f i c i e n t for initial stage o f drying = dry mass o f solid c o n t a i n e d in e l e m e n t = w a t e r c o n t e n t at a n y p o i n t in bed, i n c o m i n g a n d o u t g o i n g w a t e r c o n t e n t for e l e m e n t , respectively = pressure d r o p across e l e m e n t = total heat transferred = h e a t t r a n s f e r r e d by c o n v e c t i o n , c o n d u c t i o n a n d r a d i a t i o n , respectively = n o m i n a l t e m p e r a t u r e at w h i c h v a p o r i z a t i o n OCCURS = gas t e m p e r a t u r e at a n y p o i n t in bed, i n t o a n d o u t o f e l e m e n t , a n d average gas t e m p e r a t u r e for e l e m e n t , respectively = solid t e m p e r a t u r e a t a n y p o i n t in bed, i n c o m i n g , o u t g o i n g a n d average solid t e m p e r a t u r e for e l e m e n t , respectively = superficial gas v e l o c i t y = grate s p e e d = mass o f w a t e r r e m o v e d f r o m pellets in element = l e n g t h of e l e m e n t or s e g m e n t = c a r b o n d i o x i d e c o n t e n t o f gas = excess n i t r o g e n c o n t e n t of gas = h u m i d i t y at a n y p o i n t in b e d a n d h u m i d i t y o f gas e n t e r i n g a n d leaving e l e m e n t , respectively s a t u r a t i o n h u m i d i t y at gas b u l k t e m p e r a t u r e a n d at solid surface t e m p e r a t u r e , respectively = height of element = total bed height =
m2 k J kg -1 °C-1 k J kg -1
m [0] kg m i n -1 kg m i n -1 kg m -2 rain -1 k J m -2 C-l m i n -1 k J (kg w a t e r ) -1 k J m -1 rain -1 °C-1 kg m -2 rain-1 kg kg (kg dry solid) -1
N m -2 kJ kJ °C °C
°C
m m i n -1 m m i n -1 kg m kg (kg air) -1 kg (kg air) -1 kg (kg air) -1
kg (kg air) -1 m m
Greek Symbols = f r a c t i o n o f h e a t t r a n s f e r r e d to pellet used for d r y i n g
°C-1
[0 ]
48 [0] kg m-1 min -1 [0] kg m -3 min
= bed voidage = viscosity of moist gas = shape factor = density of moist gas = segment residence time
c Pgw Pgw A0
Dimensionless Groups Nusselt number (hdp/kgw) ---Prandtl number (Pgw Cgw/k~w ) Reynolds number (Gdp/Pgw) =
Nu
Pr Re
z I /=
__
SEGMENTn×
A.
~ I Tg( . . . . . . 1) IXwv(nx,nz +1)
=1
/
ELEMENT (nx,nz) .
Y
LAYERnh
Tg(Jx nz)
Zmax
Xwv(nx,nz)
LAYER 1
j
l RESIDENCETIME:•O =•x
x P
Fig. 2. Division of pellet bed into elements. b e d is divided into layers, vertical s e g m e n t s a n d e l e m e n t s (see Fig. 2) a n d is c o n s i d e r e d to m o v e step-wise t h r o u g h t h e m a c h i n e . T h e inlet e l e m e n t o f the leading s e g m e n t is successively s u b j e c t e d t o gas at t h e f l o w r a t e s , inlet c o m p o s i t i o n s a n d t e m p e r a t u r e s o b t a i n i n g a l o n g t h e m a c h i n e . T h e s e g m e n t residence t i m e at each p o s i t i o n is p r o p o r t i o n a l t o the h o r i z o n t a l step size (i.e. t h e s e g m e n t length) a n d inversely p r o p o r t i o n a l t o m a c h i n e speed. E x t r e m e l y small e l e m e n t s m u s t be used if the driving f o r c e f o r convective h e a t t r a n s f e r within e a c h e l e m e n t is t a k e n as t h e d i f f e r e n c e b e t w e e n
49 the inlet gas and solid temperatures for the element. For a given accuracy element size can be increased and computation time reduced by estimating the mean driving force, as outlined below. The finite difference form of eq. 3 is: Fa(Cga + Z w v i C w v ) ( T g i - T g o ) - h A ( T g a v -
Tsav)
(5)
where Tgav and Tsar are respectively, the mean gas and solid temperatures for the element; i and o included as subscripts refer to element inlet and outlet conditions. Similarly for eq. 4 but, for the present, ignoring conduction and radiation: mf(Cs + MiCw)(Tso - Tsi)/AO = h A ( T g a v -
Tsar)
(6)
where f(C s + MiCw ) is an effective specific heat for the solid. Values for factor f, which accounts for heat used in free water or combined water drying can be estimated. Eqs. 5 and 6 can be combined to derive the gas temperature change across the element from the inlet gas and solid temperatures. They also yield the relationship between the temperature change of the solid and that of the gas. Thus: Tgo -- Tgi -
2(Tg i - Tsi ) [1 +Fa(Cg a + X w v i C w v ) A O / f m ( C s +MiCw)+ 2 F a ( C g a + X w v i C w v ) / h A ]
and:
(7)
Tso - Tsi = -
Fa (Cga + X w v i C w v ) A O fm(Cs + Mi C w )
(Tg o - Tgi)
(8)
Eqs. 7 and 8 allow computation of mean gas and solid temperatures (Tgav and Tsar) which are then used for the calculation of the heat transferred by convection. They may also be used for re-estimation of the values of physical properties which are initially calculated based on the temperatures of the solids and gases entering the element. Calculated outlet gas and solid temperatures for the element take into account the enthalpy of water vapour transferred to the gas as well as the heat transferred by radiation and conduction to the solid. The equations are: Tg o = Tg i - A q c v / [ F a ( C g a + X w v i C w v ) A O ]
(9)
and Tso =
A q t -- A w [ A H v + C w T b + Cwv(Tgo - Tb)] +mTsi(Cs +MiCw) m(Cs + MoCw)
(10)
where A W is the mass of water removed from the element (discussed below}. The outlet pellet moisture content M o and the outlet gas humidity, Xwvi, are calculated from A w; T b is the nominal drying temperature for free, goethite or other combined water. Heat transferred by radiation and con-
50 duction is calculated using the solid inlet temperature for the chosen element together with the corresponding temperatures for the elements immediately above and below. Conditions for free water drying vary considerably throughout the bed. Initially, when the pellet free water content is greater than about 757~ of the saturation value, diffusion of water vapour from the pellet surface is rate controlling. Hence: Aw/AO
= kmA(Xss-
Xwvi)
(11)
where k m is a mass transfer coefficient and Xss is the saturation humidity at the surface temperature (taken as the average pellet temperature). Subsequently the drying rate decreases and drying eventually involves gas temperatures above 100 ° C. Using data from drying tests on single pellets (Bowling and Thomas, pers. comm., 1977), it was found that: Aw/AO
= ~(Aqt/[AH v +
Cwv (Tgi-- Tb) + Cw(Tb - Tsi)]A0
(12)
where × is the fraction of heat used for drying (typically a b o u t 0.7). Where the gas cools to below its dewpoint water condenses in the bed and: Aw/AO
=
Fa{Xsg - Xwvi)
(13)
where Xsg is the saturation humidity at the bulk gas temperature. Goethite decomposition is expressed in a rate equation of the Arrhenius type with constants calculated from data of Baker et al. (1973): Aw/AO
=
3.04.106 m exp [ - 1 2 0 0 0 / ( T s a r + 273)]
(14)
A similar equation is used to describe the elimination of other combined water. For Hamersley ores this is mainly by decomposition of kaolinite which commences at 500°C (Baker et al., 1972) compared with 300°C for goethite. As hardening and calcination of non-fluxed pellets involve only small amounts of heat they have been represented by step decreases in pellet temperatures when reaction temperatures are reached. The coefficient for heat transfer by convection to the pellet bed is calculated from: Nu
-~ 2 . 0 + 0 . 6 P r 1/3
(15a)
where e is the bed voidage. This equation is similar in form to that discussed by Ranz (1952) except for use of the modified Reynolds Number. Convective heat transfer to grate bars is calculated from: Nu
---
5.0
R e ~/2
(15b)
the coefficient resulting from pot grate furnace experiments. For the supporting structure a lower coefficient is used. As their thermal effects
51 are very significant the grate bars and supporting structure are each considered as four layers and the masses and heat .transfer areas of the corresponding element have been estimated for the particular grate design employed at Dampier. Gas property data was obtained from standard references (Hilsenrath et al., 1960; Hing et al., 1966; Bretsznajder, 1971; Maitland and Smith, 1972). Correlations for pellet specific heat have been derived from data of Bradshaw et al. (1970) and Coughlin et al. (1951). They are: Cs = 0.3416 + 1.324-10 -3 (Ts + 273) - 0.4032.10 -6 (Ts + 273) 2 for Ts < 677°C
(16a)
Cs = 1.111
(16b)
for 677°C < Ts < 777°C
Cs = 0.999 + 0.0461.10 -3 (Ts + 273)
for Ts > 777°C
(16c)
For the grate structure and bars specific heat is given by eq. 17, derived from data for an appropriate alloy steel (Smithells, 1967). Cs = 0.431 + 4.187-10 .4 Ts
(17)
Pressure drop across each bed element is calculated using an equation of the form proposed by Ergun (1952): Ap Az
150 Pgw(1 - e) 2 U -
3600(dpCs)2 e 3
1.75 Pgw(1 - e) ba +
3600 dp~se 3
(18)
where Pgw and Pgw are respectively the viscosity and density of the moist gas and U is the superficial gas velocity; dp and Cs are the mean pellet diameter and shape factor respectively. (Szekely and Propster, 1977) found that this equation gave good agreement with experimental results for iron ore pellets, using a value of 0.92 for the shape factor). Pressure drop across the grate has been equated to the pressure drop across a 2.5 cm layer of pellets immediately above the grate bars. Using calculated outlet gas conditions (temperature and humidity) for one element as inlet conditions for the next element, the above calculations are repeated for each element in the segment. If a total bed and grate pressure drop has to be met the air flowrate, Fa, is varied using the Modified Secant m e t h o d to accelerate convergence. The bed heat transfer and other calculations discussed below have been programmed in Fortran IV and are executed on a CDC Cyber 76 computer. Calculation o f process streams Solution of bed state equations requires known inlet gas temperatures and compositions. In some cases these are set externally but in others they are dependent on processes occurring elsewhere in the bed. In the straight
52 grate induration process, the flow of gases in the opposite direction to the bed movement forces the use of the two iterative procedures discussed below. Bed calculations are made far enough into the first cooling zone (see Fig. 1 ) to allow calculation of hood temperature in the after-firing zone. The assumption is made that air from the first part of the cooling zone goes to the last part of the after-firing zone (as shown on Fig. 1). The effect of hood leakage is included and, as in other parts of the machine, such calculations use the Modified Secant m e t h o d to accelerate temperature convergence. After-firing and cooling zone calculations are then repeated using successive substitution until hood temperatures have converged to within a few degrees. Calculations for the bed are continued to the end of the machine. Flowrates, compositions, enthalpies and temperatures of gases leaving the grate (or top of bed for updraught) are then determined for each length of the machine corresponding to one windbox. These data are then summed to give process stream flowrates and conditions. The effects of leakages into or out of the machine, above and below the grate, are included in these calculations as are the effects of h o o d sealing air and by-passing of gases through the seals between adjacent zones. Air bleeds required to meet specified fan temperatures are determined, allowances being made for duct heat losses. Having calculated the required process stream conditions, tempering air and fuel requirements are determined at each relevant windbox position, taking into account leakage, heat losses and oil fuel atomizing air. This completes one overall machine iteration. Successive substitutions of new bed inlet conditions are continued until satisfactory convergence of the air flowrate in each windbox is obtained. This variable is dependent on both inlet gas temperature and composition. Heat and mass balances are completed and finally a measure of quality is calculated. This takes the form of an Abrasion Index for the bed of pellets, which is the percentage of fines generated during tumbling of the pellets under standard conditions (ASTM Standard E279-69). A quality predictor is used that takes into account the time/temperature history of pellets at each bed level (Batterham and Thornton; publication pending). MODEL VALIDATION: COMPARISONS OF PREDICTED, LABORATORY AND PLANT RESULTS
Pellet heating and drying At present the 25 cm diameter Hamersley Iron pot grate simulator provides the best data for testing the model. This simulator is similar to that developed by the CSIRO Division of Process Technology and described elsewhere (Thomas and Clark, 1974).
53
Results from a typical simulator run, with a 45 cm bed of green pellets from the indurator feed conveyor on a 10 cm hearth layer, are shown in Figs. 3 and 4. The calculated temperatures shown are for an assumed bed voidage of 0.41, found to give the best overall agreement with the laboratory results. The actual bed voidage was not determined at the time but this value agrees with the 0.40--0.41 normally measured for green pellets poured without additional consolidation into a large cylindrical container. For the drying stage, calculated pellet temperatures tend to lag behind values measured in the pot grate simulator (Fig. 3). This effect may be attributed to the fact that as a considerable portion of the heat transferred to moist pellets is used for evaporation, pellet temperatures increase at a much lower rate than indicated by the thermocouples set in the bed. These thermocouples are heavily sheathed and designed to give a thermal response similar to that of dry pellets in the firing stage. By windbox 20 the actual and calculated temperatures in the top half of the bed agree well. In the b o t t o m half of the green pellet bed the temperature lag continues (see also Fig. 4) until after the predicted completion of free water drying at windbox 23. It is inferred from these comparisons of temperatures that free water drying is modelled satisfactorily. The data presented in Fig. 3 shows that the free water spalling predictions (based on critical water vapour flux rates) and the indications given by the spall detector installed on the simulator
26 °'r~240~-
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