Predictive models and operation guidance system for iron ore pellet induration in traveling grate–rotary kiln process

Computers and Chemical Engineering 79 (2015) 80–90

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Predictive models and operation guidance system for iron ore pellet induration in traveling grate–rotary kiln process Xiao-hui Fan, Gui-ming Yang ∗ , Xu-ling Chen, Lu Gao, Xiao-xian Huang, Xi Li School of Minerals Processing and Bioengineering, Central South University, Changsha 410083, Hunan, China

a r t i c l e

i n f o

Article history: Received 16 July 2014 Received in revised form 29 January 2015 Accepted 27 April 2015 Available online 4 May 2015 Keywords: Predictive models Iron ore pellets Traveling grate Rotary kiln Operation guidance

a b s t r a c t Thermal state of iron ore pellets in industrial traveling grate–rotary kiln process cannot be revealed straightforward, which is unfavorable for field operations. In this study, coupled predictive models of pellet thermal state within traveling grate and rotary kiln were established. Based on the calculated temperature profiles, predictive model of pellet compression strength was also established to assist in process optimization. All the models proposed were validated by the industrial data collected from a domestic plant, and the results show that grate model possesses a high accuracy, kiln model is considered to be accurate to within 10–15% of actual values, and strength model can identify the variation of pellet strength caused by the thermal changes. The proposed models were embodied into an operation guidance system developed for a large-scale pelletizing plant, and the system running results illustrate that the predictive models and expertise rules established can optimize the process very well. © 2015 Elsevier Ltd. All rights reserved.

1. Introduction In the past few decades, iron-making industry in China has soared up due to the rapid development of economy. According to China Steel Association, the domestic production of pig iron exceeded 700 Mt in 2013. Besides the production, burdens of blast furnace have improved from sinter ores of low basicity incorporated with lump ores to sinter ores of high basicity incorporated with acid iron ore pellets. These two main factors lead to an increase of pellet production in China. Fig. 1 shows the iron ore pellet production at home and abroad together with domestic pig iron production in the past 10 years. Processes of producing iron ore pellets mainly include vertical shaft furnace, moving grate and traveling grate–rotary kiln. Although the investment and operating cost of shaft furnace is low, this process is confronted with market shrink due to its low productivity and the requirement of magnetite. Moving grate process requires special alloys that are comparatively expensive and rarely produced in China, thus its application is restricted. Traveling grate–rotary kiln process has the advantages such as large handle capacity, multiple fuel capacity and good adaptability to various materials, and it has become a major process of producing iron ore pellets in the domestic recently.

∗ Corresponding author. Tel.: +86 0731 8830542; fax: +86 0731 8710225. E-mail address: [email protected] (G.-m. Yang). http://dx.doi.org/10.1016/j.compchemeng.2015.04.035 0098-1354/© 2015 Elsevier Ltd. All rights reserved.

A main task of operating grate–kiln system is to stabilize the thermal state and to guarantee a good pellet consolidation. Undoubtedly, accurate measurements of gas/solid temperature within these two devices are fundamental to a better control of this process. Even though many types of equipments have been installed to efficiently monitor the process variables in most pelletizing plants, thermal state of pellet bed remains opaque. Another criterion concerning is pellet strength, at present, mechanical strength of iron ore pellets cannot be measured until they are discharged from the cooler (there exists about half a production cycle between pellet roasting and strength measurement). This hysteretic feedback of product quality may be adverse to the operations especially at highly fluctuating thermal state. In such cases, predictive models on pellet thermal state and pellet strength need to be constructed to assist in optimizing the grate–kiln operations. In the present work, adopting the mass and heat balance equations and certain kinetic expressions of corresponding phenomena, predictive models on thermal state within grate–kiln process were established. The coupling of grate model and kiln model, which has been less discussed previously, was particularly realized to visualize the entire thermal process. Prediction of pellet strength based on time–temperature profile was conducted as well. Finally, an industrial instance of the established models was given, in which an operation guidance system containing predictive models and expertise rules was developed to optimize the production of a domestic pelletizing plant.

X.-h. Fan et al. / Computers and Chemical Engineering 79 (2015) 80–90

A Ai AF b1 b2 Cg Cp CO2 COe 2 dp di De e DH O 2

gas–pellet apparent contact area, m−1 area per unit kiln length, m stoichiometric air–fuel ratio, mass basis thickness of refractory bricks, m thickness of steel shell, m specific heat of gas, J/(kg K) specific heat of pellet, J/(kg K) concentration of oxygen, kg/m3 equilibrium concentration of oxygen, kg/m3 pellet diameter, m diameter of rotary kiln, m hydraulic diameter of the kiln, m effective diffusivity of water, m2 /s

diffusivity of oxygen, m2 /s radiactive heat transfer coefficient flame length, m superficial gas flow rate, kg/(m2 s) momentum flow rate of fuel, kg m/s2 momentum flow rate of primary air, kg m/s2 heat transfer coefficient within grate, J/(m2 s K) heat transfer coefficient within kiln, J/(m2 s K) bed depth in rotary kiln, m thermal conductivity of gas, J/(m s K) thermal conductivity of pellet, J/(m s K) first order rate of magnetite oxidation, m/s mass transfer coefficient of oxygen, m/s mass transfer coefficient of water vapor in the gas, m/s mF mass flow rate of fuel, kg/s mass flow rate of gas, kg/s mg ms mass flow rate of solid, kg/s mpa mass flow rate of primary air, kg/s MVF materials volumetric flow rate, m3 /s rotational speed of kiln, r/s n Nu Nusselt number P gas pressure, Pa Prandtl number Pr rm radius of unreacted magnetite core, m rp radius of pellet, m radius of wet core of the pellet, m rw R radius of rotary kiln, m Rfuel rate of fuel combustion, kg/s Rm rate of magnetite oxidation, kg/(m3 s) Rw (Rcd ) rate of water evaporation/condensation, kg/(m3 s) ReD axial Reynold’s number Rep pellet Reynold’s number Rew angular Reynold’s number time, s t Ti temperature, K u moving velocity of pellet in the kiln, m/s wP pellet moisture content, mass% moisture content of the gas, kg/m3 Wg Wge equilibrium concentration of water vapor between gas and pellet, kg/m3 y bed height in traveling grate, m position along kiln axis, m z DO2 Eri FL G GF Gpa heff hi H kg kp km kO2 kw

Greek symbols kiln inclination angle, rad ˛ voidage of pellet bed εb εi emissivity

air b cp e F g m g

vg 1 2 Hw Hm  ϕ d

 ˚i

density of air, kg/m3 bulk density of pellet bed, kg/m3 density of combustion product, kg/m3 equivalent density of gas, kg/m3 equivalent density fuel, kg/m3 gas density, kg/m3 density of magnetite, kg/m3 gas viscosity, Pa s gas velocity, m/s thermal conductivity of refractory bricks, W/(m K) thermal conductivity of steel shell, W/(m K) enthalpy of evaporation/condensation, kJ/kg enthalpy of magnetite oxidation, kJ/kg pellet sphericity, taken to be 0.9 filling angle, rad dynamic repose angle, rad filling degree of pellet in the kiln empirical constant, taken to be 0.15 heat flux per unit kiln length, W/m

Subscripts g, p, w, s, a gas, pellet, wall, solid, ambient wi, wo, wu, wc inner, outer, uncovered, covered wall rgw, rgs, rws, rwa gas/wall, gas/solid, wall/solid, wall/atmosphere radiation cgw, cgs, cws, cwa gas/wall, gas/solid, wall/solid, wall/atmosphere convection

800 700

Production (Million ton)

Nomenclature

81

600

Global iron ore pellets Domestic iron ore pellet Domestic pig iron

500 400 300 200 100 0

2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013

Year Fig. 1. Pig iron and iron ore pellet production in past ten years.

2. Previous investigations As understood, grate–kiln process is a combination of horizontally moving grate and circumferentially rotating kiln. Mathematical simulations on pellet thermal state within moving grate can be seen in many literatures (Barati, 2008; Majumder et al., 2009; Sadrnezhaad et al., 2008; Thurlby et al., 1979), since moving grate process accounts for two thirds of the world’s installed pelletizing processes capacity. The mathematical models are mass and heat balance equations incorporated with kinetic expressions of physical and chemical phenomena, which includes evaporation and condensation of pellet moisture, oxidation of magnetite, combustion of coke breeze, calcination of lime or dolomite, pellet shrinkage, etc. Rotary kilns are ubiquitous fixtures of the metallurgical and chemical process industries, the mathematical models of rotary kiln generally involve solid motion (Boateng and Barr,

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1996; Puyvelde, 2006), heat transfer (Barr et al., 1989; Senegacnik et al., 2007; Shi et al., 2008; Tomaz and Filho, 1999), kinetics of chemical reactions such as pyrolysis, calcination, solid clinkering (Mujumdar et al., 2007; Ortiz et al., 2005; Patisson et al., 2000a) and fuel combustion. Similarly, overall model of rotary kiln is established via mass and heat balance equations, as reported in Marias (2003), Mujumdar and Ranade (2006), and Patisson et al. (2000b). Besides the thermal state, prediction of pellet strength during roasting is also important to operators. Methods such as neural network (Dwarapudi et al., 2007; Umadevi et al., 2012) and statistical analysis have been reported. These models are practical but can hardly elucidate the effect of thermal state on pellet strength, thus lacking universality. Some researches (Wynnyckyj and Fahidy, 1974; Batterham, 1986) characterized the pellet densification as the improvement of pellet strength and proposed the kinetic formalisms using time–temperature profiles within moving grate. However, pellet roasting in rotary kiln is quite different from static heat-hardening within moving grate, and the application of this model in industrial rotary kiln has not been verified. Grate model and kiln model have been intensively investigated, but the coupling of two models has been less discussed. Even though it is possible to adopt separate grate model and separate kiln model to reveal the entire grate–kiln process, grate–kiln process is an integrated system in which thermal state of one device will greatly affect the operations of both two devices, several problems may occur when two models are not coupled: (1) Calculated results of grate model ought to be the boundary conditions of kiln model and vise versa. Separation of these two models may lead to the inconsistent or even contradictory boundary results. In such cases, the entire model accuracy will decline. (2) The core of steady-state optimization is to seek a group of manipulated parameters via mathematical models to maximize economic benefits. This work is generally carried out using Pareto multi-criteria optimization based on process simulation (discussed in our coming paper). When the influence of one model on the other model is not considered, the real optimization of entire thermal process will be unavailable. (3) Predictive model of pellet strength is based on the accurate time–temperature profile. Thermal state obtained by separate models may reduce the reliability of pellet strength prediction. Henceforth, an incorporation of grate model and kiln model was conducted in this paper. In addition, the main physical and chemical phenomena occurred in rotary kiln of iron ore pellets are different from that of aluminum oxide, cement or petroleum coke, the kinetic conditions should be elucidated. 3. Process description The schematic figure of grate–kiln–cooler process for iron ore pellets is shown in Fig. 2. Processing of green pellets prepared from pelletizer is accomplished by three equipments: traveling grate (drying and preheating), rotary kiln (roasting) and circular cooler (cooling). A typical traveling grate can be divided into four zones: up-draught drying (UDD), down-draught drying (DDD), temperate pre-heating (TPH) and pre-heating (PH), and circular cooler is generally divided into three zones (C1, C2 and C3) to attain hot gas of different temperature. Roasting of iron ore pellets is realized in rotary kiln with kiln end connected to PH and kiln head connected to C1. Fuels including pulverized coal and natural gas are injected into the kiln through nozzle and burner-blower to supply heat for the whole system. To optimize energy consumption, off-gas from C1 is re-circulated to rotary kiln, and off-gas from kiln end is

utilized for preheating and down-draught drying of iron ore pellets through PH auxiliary ventilator and DDD exhauster. Off-gas from C2 is re-circulated to TPH through TPH exhauster while off-gas from C3 is re-circulated to UDD. Green pellets are charged to the feed end of grate at certain bed height to be dried and pre-heated, then the pre-heated pellets enter rotary kiln to be roasted. Similar to cement kiln, inclination and rotation of the kiln impel the pellets to move forwards and circumferentially simultaneously to realize uniform roasting. The roasted pellets discharged from kiln head subsequently enter circular cooler at certain bed height, and the cooled pellets are finally transported to storage place by belts. Considering that cooling process has less effect on pellet strength compared to drying and heating, pellet induration in circular cooler is not considered herein.

4. Model description In essence, the target of pellet production is to realize efficient heat exchange between gas and pellets with the prerequisite of satisfactory pellet quality. According to the moving directions of gas and solid, heat transfer within traveling grate is cross-current while heat transfer within rotary kiln is counter-current.

4.1. Traveling grate 4.1.1. Grate model Due to the requirement of BF burdens that sinter ores of high basicity (R = 1.8 − 2.2) are incorporated with acid oxidized pellets (R < 0.3), most iron ore pellets produced in China are acid. Generally, coke or fluxes such as limestone and dolomite are not added in the pelletization, therefore, coke combustion and lime calcination within the pellets are not considered here. For acid iron ore pellets, main physical–chemical phenomena occurred in traveling grate include evaporation and condensation of moisture, oxidation of magnetite, desulphurization and bed slump caused by pellet shrinkage. According to the model proposed by Hoffman and Finkers (1995), the changes in bed voidage caused by the reduction of pellet size are not considerable, therefore bed slump or pellet shrinkage is not considered. Given that sulfur content of pellet feed in most pelletizing plants is very low (<0.1%), the influence of desulphurization on thermal state is neglected here. Several assumptions were made in establishing predictive model of traveling grate: (1) The process reaches steady state; (2) Pellet bed is regarded as porous packed bed of equal sized balls; (3) Temperature gradient within the pellet is ignored; (4) Conduction and radiation between gas/solid can be represented by a comprehensive heat transfer coefficient and heat losses are neglected. Heat balance equation for gas phase is expressed as Eq. (1) and heat balance equation for solid phase is expressed as Eq. (2). GCg

∂Tg = −heff A(Tg − Tp ) − 0.5 × Rw Hw + 0.5 ∂y × (Rm Hm + Rcd Hw )

b Cp

(1)

∂Tp = heff A(Tg − Tp ) − 0.5 × Rw Hw + 0.5 ∂t × (Rm Hm + Rcd Hw )

(2)

Coefficient 0.5 here indicates that the heat generated by reactions is distributed equally between gas/solid. The comprehensive

X.-h. Fan et al. / Computers and Chemical Engineering 79 (2015) 80–90

83

Fig. 2. Schematic view of typical grate–kiln cooler system.

heat transfer coefficient is calculated by Eq. (3) and heat transfer area is calculated by Eq. (4). Nu =

heff dp kg

 Re 1/2

= 2.0 + 0.6

p

εb

Pr 1/3

(3)

Rcd = kw A(Wg − Wge )

6(1 − εb ) A=  · dp

(4)

Drying of iron ore green pellets has been intensively investigated and can be represented by mathematical models given in Cumming and Thurlby (1990) and Tsukerman et al. (2007). It is recognized that drying of green pellets can be split into three stages using two critical moisture contents, namely constant rate stage, first falling rate stage and second falling rate stage. In the initial step of drying, pellet surface temperature quickly increases to dew point with evaporation front remaining on the pellet surface, saturated vapor concentration between gas/solid does not vary and humidity gradient is a constant. Throughout the first stage, drying rate is independent of pellet moisture content and is only related to hot gas property. When pellet moisture content drops below the first critical value, evaporation front moves within the pellet and vapor diffusion through the dry shell begins to play a rate limiting step. Drying rate in this stage decreases as pellet moisture content decreases. Last stage occurs at the end of drying when pellet moisture drops below second critical value. The dry shell is pretty thick and vapor diffusion becomes extremely difficult. Since rate expression of the third stage is complicated and its effect on pellet temperature is relatively small, the drying of green pellet bed is simplified into two stages with rate expressions given in Eqs. (5) and (6). Rw = kw A(Wge − Wg ) for wp ≥ critical value Rw =

A(Wge − Wg ) e (1/kw ) + (rp (rp − rw )/2rw DH

2O

)

for wp < critical value

(5) (6)

The equilibrium concentration of water vapor between gas/solid hinges upon the pellet surface temperature. This correlation can be obtained by fitting the saturated vapor density at different temperature, as formulated in Eq. (7). The value of critical moisture content is an important parameter in dividing rate stages, it was taken to be 120 kg/m3 (which is 5.45% considering a bulk density of 2200 kg/m3 for green pellets) in Hasenack et al. (1975) and taken to be 5% of pellet bed in Patisson et al. (1990). Hence, the critical value is assumed to be 5.2% of green pellets by weight in this study.

⎧ 1.23 × 10−6 exp(T /28.41) − 0.020 p ⎨

Wge =

⎩

for Tp ≤ 373.15 K

8.57 × 10−4 exp(Tp /51.39) − 0.677 for 373.15 K < Tp ≤ 473.15 K 5.20 × 10

−3

The condensation of water vapor occurs once vapor content of the gas surpasses the saturated vapor concentration, the condensation rate is assumed to be proportional to humidity gradient and its kinetic expression is given in Eq. (8).

exp(Tp /62.64) − 2.031 for Tp > 473.15 K

(7)

(8)

As reported in Barati (2008), the oxidation of magnetite comprises three steps: transfer of oxygen from the bulk gas to the pellet surface, pore diffusion through the hematite layer and interfacial surface reaction with the magnetite particles. The unreacted core model is adopted to describe the oxidation and its rate equation is given as Eq. (9) based on mixed control mechanism. Rm =

e ) 29A(CO2 − CO2 1 kO2

+

rp 2 1 rm 2 km

+

rp DO2

 rp rm



(9)

−1

Gas flow rate through the packed bed in traveling grate is controlled by the pressure drop between hoods and wind boxes, as described by Ergun equation. This formula is used as constrained conditions for numerical solution of grate model. −

1.75g (1 − εb )v2g 150(1 − εb )2 g vg ∂P = + 3 2 ∂y dp εb  dp ε3b 

(10)

Water evaporation/condensation and oxidation of magnetite will change the gas and solid constituents. These changes are related to the rate of reactions, and mass balance equations are adopted as well. 4.1.2. Numerical solution of grate model The partial differential equations described above are solved simultaneously using an explicit finite difference technique similar to Barati (2008) and Majumder et al. (2009). Regular grids of orthogonal coordination system are adopted to discretize the computational region. The results of each computation are assigned to the next leading element as the initial value. Iteration in each section of traveling grate is the same except that UDD section is started from the bottom and other sections are started from the top. An iterative loop using the hood/wind-box gas flow rate as the iterative variable is adopted and iteration is running until the calculated pressure drop across the bed height attains sufficient convergence with the measured pressure drop. 4.2. Rotary kiln Mass and heat transfers in rotary kiln are complicated. Solid pellets move forwards and circumferentially simultaneously, meanwhile, the injected fuel combusts and hot gas exchanges heat with the moving pellets. Oxidation of magnetite continues while abrasion and collision of particles may cause pellet breakage and

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ring formation. In this study, oxidation of magnetite is neglected considering a weak oxidative atmosphere in the kiln, this assumption leads to a small error on temperature profile since oxidation degree of acid iron ore in the kiln using pulverized coal is generally less than 5%. Ring formation is partly attributed to high wall temperature (Pisaroni et al., 2012) and has been simply formulated in Peng et al. (2009). However, the essence of ring formation is still a controversy and its thickness distribution along kiln axis is hard to simulate, this phenomenon is also not considered. Several assumptions on establishing predictive models of rotary kiln are: (1) The process reaches steady state; (2) Solid movement obeys plug flow pattern described in Klose and Schinkel (2004); (3) Grain shrinkage is ignored and pellets are seen as unbroken throughout the roasting; (4) Axial convective heat transfer and axial radiative heat transfer are ignored; (5) Pellet is spherical and its diameter is fixed; (6) One-dimensional approach is used and rotary kiln is divided into a number of slices each of which has a uniform temperature. 4.2.1. Solid motion Local depth of the solid bed is a prerequisite to calculate the heat transfer area. A schematic figure of cross section and axial section of rotary kiln is depicted in Fig. 3. Several numerical models are available to predict the depth profiles (Gupta et al., 1991; Hogg et al., 1974; Kramers and Croockewit, 1952; Saeman, 1951) and the one proposed by Saeman (1951) is the most widely used, as given in Eq. (11). −1.5 3 tan d tan ˛ dH = − · MVF · (R2 − (H − R)2 ) 4 n dz cos d

(11)

where MVF is the material volumetric flow and can be estimated via the moving speed and bed height of traveling grate. The differential equation is solved with the initial condition that bed depth at kiln head equals to the dam height (for kiln without a dam, bed depth at kiln head is taken to be the diameter of single pellet). Analytical solution for the axial solid transportation proposed by Liu et al. (2009) is adopted in this study. Residence time together with temperature profile of pellets has great impact on pellet quality. Prediction of mean residence time (MRT) in rotary kiln based on particulate trajectory models can be seen in many literatures (Chatterjee et al., 1983; Perron and Bui, 1990; Yan et al., 2002). At the given depth profile, the velocity of the solid materials at any axial position is expressed as Eq. (12) and MRT can be evaluated by integrating this velocity expression (Kramers and Croockewit, 1952). u(z) =

2 · MVF (ϕ(z) − sin ϕ(z)) · R2

(12)

4.2.2. Heat transfer As reported in Patisson et al. (2000b), heat exchange forms in a cross section of rotary kiln include radiation from gas to inner wall, radiation from gas to the exposed solid, radiation from inner wall to the exposed solid, radiation from outer wall to ambient atmosphere, convection from gas to inner wall, convection from gas to the exposed solid, convection from the wall to the solid with which it is in contact and convection from outer wall to ambient atmosphere. Considering a high flowing velocity of gas phase, the gas/wall conduction and gas/solid conduction are neglected. Calculations of heat exchange items are given as below. To simplify the calculations and ensure on-line computational speed, the variations of circumferential wall temperature are ignored (Twi = Twu = Twc ). 4 ˚rgw = Awu Ergw (Tg4 − Twu ) with

˚rgs = As Ergs (Tg4 − Tp4 ) with



Awu = dwi −

As = dwi sin

ϕ 2

ϕ 2



(13) (14)

4 ˚rws = As Erws (Twu − Tp4 )

(15)

4 ˚rwa = Awo εwo (Two − Ta4 ) with

Awo = dwo

(16)

˚cgw = hcgw Awu (Tg − Twu )

(17)

˚cgs = hcgs As (Tg − Tp )

(18)

˚cwa = hcwa Awo (Two − Ta )

(19)

˚cws = hcws Awc (Twc − Tp ) with

Awc

ϕ = dwi 2

(20)

In radiation phenomena, the radiative heat transfer coefficients can be calculated using correlations given by Manitius et al. (1974). Ergs = εg εs ,

Ergw = εg εw ,

Erws = εw εs (1 − εg )

(21)

The emissivities of pellets, inner wall and outer wall are all taken to be 0.9. The emissivity of gas theoretically depends on gas species (especially CO2 and H2 O) and their concentrations, together with the presence of dust. Since the contribution of dust is difficult to evaluate, emissivity of gas is taken to be 0.35 in this study. In convection phenomena, the heat transfer coefficients have been extensively discussed. For convection between gas and solid and convection between gas and wall, Tscheng and Watkinson (1979) proposed the empirical correlations which are widely cited: hcgs = 0.46 · hcgw = 1.54 ·

kg 0.535 0.104 · ReD · ReW · −0.341 De

(22)

kg −0.292 0.575 · ReD · ReW De

(23)

However, when Eq. (23) is applied to large-scale pellet rotary kiln, the calculated value of hcgw is very low (less than 5 W m−2 K−1 ), which is inconsistent with those reported in Patisson et al. (2000b), Guen et al. (2013) and Kreith and Black (1980). Hence, it is taken to be equal to hcgs in the present work instead. For natural convection between outer wall and ambient air, the heat transfer coefficient is taken to be 0.26 W m−2 K−1 (Ozisik, 1985). For the convection from the wall to the solid with which it is in contact, the heat transfer coefficient is calculated by Eq. (24) (Yi, 2007).



hcws =

1



( · dp /kg ) + 1/2

kp · b · Cp · ω/



(24)

4.2.3. Fuel combustion Fuel is injected and burnt to provide heat for the system, factors such as burner type, fuel type, temperature of secondary air, pct primary air and burner momentum all contribute to the flame length and heat transfer in the flame zone. Xiao et al. (1991) supposed that fuel combusts at a rate related to its axial position within the flame length (obeys normal distribution within the flame), as expressed in Eq. (25). Rfuel (z) =

1.5mF FL



1−

4(z − 0.5FL )2 FL2



(25)

On the flame length, Xiao et al. (1986) took it to be 320–500 times of the outlet diameter of the burner and field operators empirically take it to be 3 times of the kiln inner diameter. Based on Beer’s equation (Beer and Chigier, 1972), Gorog et al. (1983) took into account the burner diameter, fuel flow rate and primary air flow rate, and proposed a model to calculate the flame length, as given in Eq. (26). Fuel types considered in this expression (fuel oil, natural gas and producer gas) do not include pulverized coal which is a main fuel for grate–kiln process in China, but since fine coal particles are injected with air of high momentum, the influence of fuel type on applying this model is neglected. According to our calculating trials for several industrial kilns, the flame length obtained using the above three methods are quite close. Eq. (26)

X.-h. Fan et al. / Computers and Chemical Engineering 79 (2015) 80–90

85

Fig. 3. Cross section and axial section of rotary kiln.

can reflect other operating parameters, and it is reported to be in good agreement with flames measured and considered to be accurate to within 20 pct of actual values (Gorog et al., 1983), therefore it is selected in this study.



6 · (mF + mpa )

FL =

[(GF + Gpa ) e ]0.5

with B =

· (1 + B) ·

e √ cp · air

AF · mF − mpa mF + mpa and e = mF mF /F + mpa /air

(26)

4.2.4. Balance equations Taking the pseudo steady-state operation within each subdivided slice, temperature profiles of gas, solid and wall can be obtained along kiln axis by adopting heat balance equations. For gas phase: −mg Cg

dTg = Rfuel (z) · Hfuel − (˚rgw + ˚rgs + ˚cgw + ˚cgs ) dz

(27)

For pellet phase: ms Cp

dTp = ˚rgs + ˚cws + ˚cgs + ˚rws dz

(28)

For wall phase: ˚cgw + ˚rgw − ˚cws − ˚rws = ˚rwa + ˚cwa

(29)

At steady state, conductive heat flux passing through refractory brick and steel shell is equal to the convective heat flux from outer wall to the ambient atmosphere, as expressed in Eq. (30). Since the thickness of refractory lining and steel plate are small compared to the kiln diameter, steady conduction of cylindrical multilayer is approximated to be steady conduction of planar multilayer. The inner wall temperature which satisfies this correlation is acquired by an iterative procedure. Awi ·



Twi − Two b1 /1 + b2 /2



= ˚rwa + ˚cwa

(30)

As pulverized coal and natural gas combust in the kiln, the flow rate and composition of gas change along kiln axis. These changes are related to the combustion rate and the types of fuel used. Mass balance is adopted in each slice at the same time during the calculation of the temperature profiles.

and the gas balance equation from different directions. For the subsequent iteration, the temperature profiles are assumed to be linear combinations of the previously assumed and computed profiles (successive approximation). This method guarantees that one is always starting from known initial conditions (Riffaud et al., 1970), but it appears to converge very slowly, with axially propagating disturbance on the profiles computed in the subsequent iterations (Manitius et al., 1974). Another method is BDF (backward differentiation formulas), in which the unknown gas temperature at kiln end is assumed and all equations are integrated simultaneously in one direction. To hit the boundary conditions at kiln head, the initial conditions are iteratively modified (Barrozo et al., 1998; Lacerda et al., 2005). In this study, the latter method is adopted and the entire computational diagram of kiln model is depicted in Fig. 4. 4.3. Model coupling As discussed in Section 2, it is vitally important to consider the coupling characteristic of grate–kiln process for on-line prediction of thermal state and steady-state optimization, thus the incorporation of grate model and kiln model is conducted. Kiln end is connected to PH section of traveling grate, the pellets discharged from PH section become the feeds of rotary kiln, and off-gas exhausted from kiln end is re-circulated to the gas hood of PH section. Therefore, computed pellet temperature at the end of PH section is assigned as initial feed temperature of kiln model, and computed gas temperature at kiln end is assigned as initial gas temperature of grate model (PH section). Two compartment models are coupled using computational algorithm depicted in Fig. 5. The program firstly assumes the gas temperature of PH hood (Tg[hood]), and calculates the entire thermal state within traveling grate using this assumed condition together with other measured variables to obtain the discharged pellet temperature. Then this value is taken to be the initial condition of kiln model, and the entire thermal state within rotary kiln is calculated using the computational diagram shown in Fig. 4 to obtain the gas temperature at kiln end (Tg[kiln]). Tg[hood] is supposed to be equal to Tg[kiln] due to the connection of PH section and kiln end, if their difference is out of the reasonable range, a modification of Tg[hood] proportional to this difference is carried out and the entire calculation is repeated until it converges. 4.4. Pellet strength

4.2.5. Numerical solution of kiln model The numerical solution of kiln model is implemented with the boundary conditions that gas/pellet temperature at kiln end or kiln head are specified. Several methods have been reported to hit the boundary conditions. One method consists of assuming the initial temperature profiles and integrating the pellet balance equation

Stability control of thermal state is fundamental to stabilizing pellet quality at the given raw materials. However, raw materials in some domestic pelletizing plants are frequently changed due to the market price and resource supply, in addition, production inference caused by operations or equipments are unavoidable even at

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Start Compute gas composition at kiln end based on air/fuel draught Initial guess of gas temperature at PH hood (Tg[hood]) Compute Tp at PH discharged end using grate model Set Tp as initial condition of kiln model Compute gas temp at kiln end using kiln model (Tg[kiln]) ΔT=Tg[hood]-Tg[kiln] ΔT
Modify Tg[hood] using αΔT N

Y Store and display End Fig. 5. Computational diagram the coupled algorithm.

pellet strength discussed in this paper refers to compression strength. According to Batterham (1986), pellet strength at the end of the induration can be estimated via the time-temperature profile (pellet temperature varying with heating time), as given in Eq. (31).

 Qp = 0

t

A0 exp T

 −E  RT

· (Qf − Q ) dt

(31)

where Qp is pellet strength at the end of the induration, T is heating temperature, E is activation energy of roasting (−E/R is taken to be 5940 K), Qf is final strength that would be attained after a long time of roasting at temperature T, Q is strength parameter of pellets during the induration and A0 is constant for given pellet feed and it is taken to be 28,340. This model was primarily developed for static heat hardening of pellets on moving grate. For grate–kiln system, pellet temperature profiles within two devices can be estimated by the coupled model proposed in this study, and residence time on the grate can be obtained via moving speed while residence time in rotary kiln can be estimated by Eqs. (11) and (12). However, the application of this model to industrial grate–kiln process requires further verification.

Fig. 4. Computational diagram of entire kiln model.

the fixed materials. In such cases, thermal state will fluctuate and pellet quality becomes unstable. It is acknowledged that accurate on-line prediction of pellet quality can reduce the occurrence of this situation to a certain degree. Important indices of pellet quality include compression strength, abrasion index and TFe (total content of iron). TFe is greatly determined by the chemical compositions of raw materials used and not closely related to the thermal state, it is not discussed herein. Both compression strength and abrasion index represent the mechanical strength of pellets, but technicians in the domestic plants pay more attention to compression strength. Hence, the

5. Case study The coupled predictive models proposed herein have to be delicately validated before being applied. In this section, validation of grate model, kiln model and strength model using the production data of a large-scale industrial grate–kiln process was given. In order to testify the reliability and utility of model prediction in optimizing the pellet production, these models were embodied into an operation guidance system developed for a domestic pelletizing plant. System functions and the running results were described at the end of this section. It should be noted that, models established herein are based on mass and heat transfer principles, and they can be applied to any grate–kiln system more than this industrial instance.

X.-h. Fan et al. / Computers and Chemical Engineering 79 (2015) 80–90 Table 1 Apparatus parameters of the reference grate–kiln process. Traveling grate Grate width UDD length DDD length TPH length PH length

Table 3 Value range of process parameters corresponding to a throughput of 600 t/h.

Rotary kiln 5.666 m 12.20 m 12.20 m 12.20 m 24.40 m

Inner diameter Kiln length Thickness of refractory Thickness of steel lining Inclination angle

6.858 m 45.72 m 0.25 m 0.04 m 4◦

Table 2 Physical and chemical properties of green pellet feed. Chemical composition/%

Characteristics of green pellets

TFe FeO CaO MgO SiO2 Al2 O3 S P

Pellet moisture content Dropping number Compression strength Pellet size Bulk density Pellet porosity Bed voidage Dynamic repose angle

64.70 9.57 0.22 0.19 5.34 0.41 0.068 0.019

87

10 wt.% 4.5 times/pellet 12.3 N/pellet 10–15 mm 2200 kg/m3 0.27 0.39 42◦

5.1. Study object The study object is the grate–kiln process of Ezhou pelletizing plant attached to Wuhan Iron & Steel Group Minerals Company in China. Table 1 is the apparatus geometries of traveling grate and rotary kiln, and these parameters are kept constant during modeling. In the reference plant, iron ore concentrates are milled and blended prior to pelletization, and then ∼2% of bentonite is added as binder. Green pellet moisture content is controlled at ∼10% and qualified pellets are transported to traveling grate. The physical and chemical properties of green pellet feed are given in Table 2. Properties of pellet feed are assumed to be constant and the operation guidance system developed in this study is to optimize the operations at the given pellet feed. Inputs of the coupled predictive models are on-line data available from field DCS (distributed control system). A brief introduction of measured variables is given as follows: (1) Traveling grate is covered at the top with gas hoods and at the bottom with wind boxes, the gas temperature and gas pressure of hoods and boxes in each section are available; (2) Five sensors of bed height are installed along grate width at the feed end of grate; (3) Gas temperature at kiln end and pellet temperature at kiln head are available by thermal couple and pyrometer signal; (4) Moving speed of the grate, fuel injected rate and kiln rotational speed are available. In general, the main controlled variables are thermal states of PH and rotary kiln, and these are chosen to directly influence the quality of pre-heated and roasted pellets. The manipulated variables are pellet feed charging rate, air/fuel draft through the kiln, rotational speed of the kiln and fuel injected rate. Some common values of measured variables for the reference plant are listed in Table 3. 5.2. Model validation A comparatively completed validation of the model requires measuring temperature inside the moving bed or inside the rotary kiln, which is rather impractical for an industrial grate–kiln process. In order to testify the reliability of our model, several detection points were specially added, as marked in Fig. 2. Five thermal couples were installed in traveling grate to continuously measure the outlet gas temperature at pellet bed surface, one thermal couple was installed to measure the temperature at kiln head, and portable infrared thermometer was utilized to intermittently measure the temperature at kiln wall. On-line production data were successively

Variable

Value

Grate moving velocity Grate bed height UDD wind-box temperature DDD hood temperature TPH hood temperature PH hood temperature Pressure drop in UDD Pressure drop in DDD Pressure drop in TPH Pressure drop in PH Kiln rotational speed Coal mass flow rate Natural gas flow rate Combustion air flow rate Pellet temperature at kiln head

5.78–6.88 m/min 130–170 mm 220–300 ◦ C 300–420 ◦ C 600–750 ◦ C 1100–1200 ◦ C ∼1500 Pa ∼1700 Pa ∼1000 Pa ∼1300 Pa 1.0–1.5 r/min ∼10 t/h ∼1500 m3 /h ∼15,000 m3 /h 1100–1300 ◦ C

collected every 5 min from field DCS for two weeks, then the records were screened using a steady-state criterion to constitute a steadystate data sample. This data sample were used as model inputs to predict the temperature profiles in traveling grate and rotary kiln, and the comparisons between predicted and measured results were subsequently carried out. The steady-state criterion adopted herein is that the values of process parameters listed in Table 3 fluctuate less than 5% for successive 30 min (which approximates to the residence time of pellets in grate–kiln process). At this criterion, steady-state records account for 25.52% of total production records. 5.2.1. Traveling grate The comparison results of traveling grate are shown in Fig. 6. The predicted data coincide well with the measurements at steady state. In DDD section, some measured values are high above the predicted values. This is mainly attributed to inappropriate prediction of pellet moisture content of second drying stage. The evaporation model divides the drying into two stages with second stage mainly occurring in DDD. However, toward the end of drying, drying rate actually becomes very low leading to an obvious increase of gas temperature while the predicted drying rate is comparatively high leading to a slight increase of gas temperature. From Fig. 6, deviations at high temperature seem to be larger than those at low temperature, which may be caused by the ignorance of heat losses in grate model. Furthermore, the errors in the thermal couple readings and inaccurate installing also contribute to the deviations. 5.2.2. Rotary kiln The comparison results at kiln head are shown in Fig. 7 where the number of data records is reduced to 554. This is because kiln head is connected to circular cooler and the temperature of gas hood in C1 has great effect on the temperature value of kiln head. Although the variation of this initial temperature has little effect on the entire temperature profile compared to the fuel combustion, it actually determines the measured value at kiln head where fuel combustion does not begin. Hence, in order to ensure the reliability of validation work, an extra selection of the above steady-state data sample was implemented by a constraint that C1 gas temperature varies within 1050–1100 ◦ C. From Fig. 7, predicted values are considered to be in agreement with detected values considering an error of 10–15%. Several factors contribute to this deviation: (1) Kiln model established in this study is one dimensional, the temperature detection point can not represent the whole cross-section of kiln head very well. (2) An implicit assumption of kiln model is that kiln head and kiln end are taken to be insulated, but axial heat losses at kiln head are not negligible in practice. (3) Pulverized coal, natural gas and primary air are injected from kiln head, and

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1000 PH2

o

Gas temperature ( C)

800

PH1

600 400 200

TPH 0

100

200

300

400

500

600

700

800

900

1000

1100

200 DDD

160 120 80

UDD 0

100

200

300

400

500

600

700

800

900

1000

1100

Serial number

o

Kiln head temperature ( C)

Fig. 6. Predicted (hollow point) and measured (solid point) gas temperature at different locations of traveling grate.

1200 1000 800 Prediction 600

0

Detection 100

200

300

400

500

600

Serial number Fig. 7. Predicted and measured gas temperature at kiln head.

3000

240 Carrier roller Rolling ring 200

Rolling ring Prediction1 Prediction2 Prediction3

160

120

Detection1 Detection2 Detection3

Compression strength (N/Pellet)

280

o

Outer wall temperature ( C)

320

Prediction Detection

2800 2600 2400 2200 2000

0 0

10

20

30

40

Distance from kiln end (m)

48

96

144

192

240

288

336

Serial time (hours) Fig. 9. Predicted and measured values of pellet compression strength.

Fig. 8. Calculated temperature profiles and measured temperature of kiln outer wall.

the turbulence or entrainment of material flux has great impact on the temperature detection. The temperature at kiln outer wall was measured by portable IR thermometer for further validation of kiln model, and the comparison results are shown in Fig. 8. Temperature measurement at the surface of rolling ring and carrier roller is neglected, since shell thickness at these positions is much larger. As seen, the predicted

values are in good agreement with the measured values along kiln axis considering the errors brought by IR thermometer and uneven thickness of steel shell/refractory lining. From Figs. 6–8, two-dimensional predictive model of traveling grate possesses a high accuracy while one-dimensional predictive model of rotary kiln is considered to be accurate within 10–15% of actual values at steady state. Since fluctuations in field production are unavoidable and our model is mainly applied to operation

X.-h. Fan et al. / Computers and Chemical Engineering 79 (2015) 80–90

89

Fig. 10. GUI of operation guidance system.

guidance rather than precise design, the temperature profiles containing certain deviations for the reference plant are acceptable. 5.2.3. Pellet strength To utilize Eq. (31) for the reference plant, final pellet strength varying with temperature should be acquired. Green pellets described in Table 1 were desiccated at 105 ± 5 ◦ C overnight and the dried pellets were roasted at different temperature for a sufficient time in an electric tube furnace. Based on our experimental results and the piecewise linear function given by Batterham (1986), the formalism of final strength is expressed in Eq. (32).



Qf =

1550

for T < 1142 ◦ C

1550 + 15.49 × (T − 1142)

for T ≥ 1142 ◦ C

(32)

In order to validate this pellet strength model in industrial rotary kiln, prediction was triggered every 2 h and the model inputs were the weighted average of the data records in past 2 h. Compression strength of pellets at the outlet of circular cooler was measured manually every 12 h. The predicted and measured compression strength is shown in Fig. 9, as seen, the predicted values coincide very well with the measured values in successive production. This predictive model of pellet strength in rotary kiln based on temperature-time profile is able to identify the variation of pellet strength caused by the thermal changes. 5.3. Operation guidance system Although new techniques such as IR measurements and CCD (charged-couple device) image sensors have provided field operators with more insight information on the process, the interior thermal state still remains unknown, which impedes further optimization of the process. Predictive models on temperature profiles and pellet strength assist in visualizing the process at steady state and reducing the impact of information hysteresis. Based on the predictive models established above, an operation guidance system for iron ore pellet induration in traveling grate–rotary kiln process was developed (in Visual C++) and applied in Ezhou Pelletizing Plant. The basic function of this system is to predict the thermal state and stabilize the production (by expertise rules) at fluctuating state, and to realize the visualization of thermal state at less fluctuating state. The construction of expertise rules and

inference system will be discussed in our coming paper, and the GUI (graphical user interface) of process visualization is shown in Fig. 10. The system automatically identifies whether the current state reaches steady using the criterion mentioned in Section 5.2. If it is steady, model calculation is triggered to visualize the process. If it is highly fluctuating, model prediction is implemented and expert inference is triggered to search for appropriate operating rules. All the model results are displayed in graphics. In Fig. 10, Region A is the visualization of pellet moisture content along bed height and grate length, Region B is the visualization of oxidation degree of magnetite along bed height and grate length, Region C is the visualization of pellet temperature along bed height and grate length, Region D is the visualization of temperature profiles within rotary kiln and Region E is the prediction of compression strength of roasted pellets. Identification of thermal state and corresponding operation guidance is given in statements to optimize pellet production, as shown in Region F. This system has been running in the reference plant since October 2013. According to field operators, the guidance provided is satisfying and the predicted pellet strength is accurate to be within 200 N/pellet of measured values at normal production. From the production indices between October 2013 and April 2014, coal consumption was lowered by 0.38 kg per ton pellets, and the operation rate of rotary kiln was enhanced by 0.71% comparing with the same period of the year before. Suppose an annual production of 4 million tons and coal price of 500 RMB per ton, the system directly reduces energy costs by 760,000 RMB per year for the pelletizing plant. 6. Conclusions Industrial traveling grate–rotary kiln process is a complicated system that interior thermal state cannot be revealed straightforward. This limitation impedes the better control of pellet production. In accordance with the integrated characteristic of this process, the coupled predictive models of thermal state were established in this study, and operation guidance system containing model prediction was developed. The main conclusions are as follows: (1) Predictive models of temperature profiles in traveling grate and rotary kiln were established respectively, and model coupling

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of these two devices was particularly carried out. Validation by industrial data shows that grate model possesses a high accuracy while kiln model is considered to be accurate to within 10–15% of actual values at steady state. (2) Predictive model of pellet strength in rotary kiln was established based on the calculated results of coupled model. Validation by production data shows that predicted values coincide very well with measured values at the given raw materials. This model is able to identify the variations of pellet strength caused by thermal changes. (3) An operation guidance system comprising predictive models and expertise rules was developed and applied in a domestic pelletizing plant. Running results show that the system can reduce energy consumption and enhance the operation rate of rotary kiln. Acknowledgements The authors wish to thank the technicians in Ezhou pelletizing plant for the measurement support, and Mr. Tai-shan Chu of Changtian International Engineering Company for fruitful discussions. References Barati M. Dynamic simulation of pellet induration process in straight-grate system. Int J Miner Process 2008;89:30–9. Barr PV, Brimacombe JK, Watkinson AP. A heat-transfer model for the rotary kiln: part II. Development of the cross-section model. Metall Trans B 1989;20: 403–19. Barrozo MAS, Murata VV, Costa SM. The drying of soybean seeds in countercurrent and concurrent moving bed dryers. Drying Technol 1998;16:2033–47. Batterham RJ. Modeling the development of strength in pellets. Metall Trans B 1986;17:479–85. Beer TM, Chigier MA. Combustion aerodynamics. London: Applied Science Publishers; 1972. Boateng AA, Barr PV. Modeling of particle mixing and segregation in the transverse plane of a rotary kiln. Chem Eng Sci 1996;51:4167–81. Chatterjee A, Sathe AV, Mukhopadhyay PK. Flow of materials in rotary kilns used for sponge iron manufacture: part II. Effect of kiln geometry. Metall Trans B 1983;14:383–99. Cumming MJ, Thurlby JA. Developments in modeling and simulation of iron ore sintering. Ironmak Steelmak 1990;17:245–54. Dwarapudi S, Gupta PK, Rao SM. Prediction of iron ore pellet strength using artificial neural network model. ISIJ Int 2007;47:67–72. Gorog JP, Adams TN, Bricombe JK. Heat transfer from flames in a rotary kiln. Metall Trans B 1983;43:411–24. Guen LL, Huchet F, Dumoulin J, Baudru Y, Tamagny P. Convective heat transfer analysis in aggregates rotary drum reactor. Appl Therm Eng 2013;54:131–9. Gupta D, Khakhar DV, Bhatia SK. Axial transport of granular solids in horizontal rotating cylinders: part I. Theory. Powder Technol 1991;67:145–51. Hasenack NA, Lebelle PAM, Kooy JJ. Induration process for pellets on a moving bed. In: Proc. Mathematical process models in iron and steelmaking. The Metals Society; 1975. p. 6–16. Hoffman AC, Finkers HJ. A relation for the void fraction of randomly packed particle beds. Powder Technol 1995;82:197–203. Hogg R, Austin LG, Shoji K. Axial transport of dry powders in horizontal rotating cylinders. Powder Technol 1974;9:99–106. Klose W, Schinkel AP. Energy and mass transport processes in the granular bed of an indirectly heated rotary kiln. China Particuol 2004;2:107–12. Kramers H, Croockewit P. The passage of granular solids through inclined rotary kilns. Chem Eng Sci 1952;1:259–65. Kreith F, Black WZ. Basic heat transfer. New York: Harper and Row; 1980.

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