Theoretical and Experimental Study on Spontaneous Ignition ofLignite during the Drying Process in a Packed BedXuezhong Gao,† Chengbo Man,† Shangjian Hu,† Xueyuan Xu,‡ and Defu Che*,†

†School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China‡Shanghai Boiler Works Ltd, Shanghai 200245, China

ABSTRACT: Lignite is a kind of coal which has high moisture content and needs to be dried before being utilized. Lignite has agreat spontaneous ignition tendency due to its high volatile content and porous structure. Spontaneous combustion may takeplace if heat accumulates within the coal layer due to low temperature oxidation, presenting a serious risk during lignite drying. Inthis paper, a calculation method is developed to predict the spontaneous ignition of lignite during the drying process in a packedbed dryer. The basic principle of this method is that the spontaneous ignition is determined by the combination of convectiveheat transfer between the gas flow and the particles and the heat generated by the oxidation reactions. The heat generation can beobtained from the differential scanning calorimetry (DSC) curve of the thermogravimetry combustion experiment. The heat lossis obtained by calculating the heat transfer coefficient between the lignite particles and the gas flow. Hence, provided thetemperature, the velocity, and the oxygen concentration of the drying gas, together with the size parameters of the particles andthe bed, are given, whether the spontaneous ignition occurs or not can be predicted. Moreover, the critical inlet gas temperature,below which the spontaneous ignition will not occur, can be determined as long as the DSC curve is obtained. Numerousexperiments have been carried out in a lab-scale reactor. The experimental results were used to verify the calculated results, andthe deviations are acceptable.

1. INTRODUCTION

Coal is the primary source of energy, fueling around 40% of thepower stations around the world. It is worldwide realized thatcoal will still be the most important energy source in thecoming years, maybe until 2100.1,2 Coals are mainly classifiedinto anthracite, bituminous coal, and lignite. Anthracite andbituminous coal are usually used for electricity generation.Although lignite is not used as widely as anthracite andbituminous coal in power stations until recently because of itshigher moisture content, greater tendency to combustspontaneously, high degree of weathering, and dustingcharacteristics, it will be exploited more intensively for its lowprice and low sulfur content with the increasing demand forelectricity in the future.2,3 The high moisture is the main factorthat restricts widespread use of lignite. It leads to hightransportation costs, low thermal efficiency, and potential safetyhazards. Therefore, drying is necessary for lignite beforetransportation and other processes.4

Besides the conventional thermal drying technologies, suchas pulse combustion, vacuum, fluid bed, rotary, and superheatedsteam drying,5 numerous new technologies have been proposedfor drying lignite recently. RWE Power AG6,7 developed thefluidized bed drying with waste heat utilization (WTA), inwhich the waste heat is recycled to dry the lignite. Numericaland experimental investigations at a semi-industrial scale facilityon the characterization of Greek predried lignite’s combustionbehavior were carried out by Agraniotis et al.8,9 Bergins etal.10−12 developed the mechanical thermal dewatering (MTE)process, in which the lignite was heated to 150−210 °C andthen the water was removed nonevaporatively by theapplication of mechanical pressure. The MTE process is ableto produce a low porosity coal with low spontaneous ignition

tendency.13 Many researchers performed studies on upgradingof low rank coal with solvent.14,15 Kakaras et al.16 presented thecomputer simulation studies for the integration of an externaldryer into a steam cycle of a Greek lignite power plant as atypical test to demonstrate the potential of the dryingtechnologies for power generation. This study provides amethod for evaluating the feasibility of integrating the dryersinto the power stations.Although a number of new technologies have been

developed, the most common method of lignite drying isevaporative drying, in which the moisture is heated by hot air,combustion gases, superheated steam, or other heating mediumuntil evaporating. The commonly used dryers include packedbed, fluidized bed, vibrated bed, and rotary dryers. Packed beddryer is one of the most common types of industrial dryers.5,17

In packed bed dryers, the heating medium flows through thewet particles on the bed and drives off the moisture. Packed beddryer is widely applied because of its compact construction andsimple design, low-temperature operation, and high drying rateper unit volume. However, the great spontaneous ignitiontendency becomes a principal difficulty associated with lignitedrying due to the high volatile content and porous structure.18

As well-known to all, a higher heating medium temperaturemakes a higher drying rate, but also leads to a higherspontaneous ignition risk, which is not expected. Therefore, itis necessary to develop a calculation method to predict thespontaneous ignition of lignite during the drying process.

Received: July 21, 2012Revised: October 7, 2012Published: October 9, 2012

Article

pubs.acs.org/EF

© 2012 American Chemical Society 6876 dx.doi.org/10.1021/ef3012239 | Energy Fuels 2012, 26, 6876−6887

Many investigators have focused on spontaneous ignition ofcoals. It is commonly agreed that the low-temperatureoxidation leads to the spontaneous ignition of coals.19 Previousstudies suggest that the low-temperature oxidation occurs inseveral steps. At low temperature up to 60 °C, the coal absorbsoxygen physically and releases absorption heat. If thetemperature reaches 60−70 °C, the chemical adsorption willoccur and coal−oxygen complexes will be formed on the coalsurface. In the range of 70−150 °C, these complexesdecompose, and at around 150 °C a new set of coal−oxygencomplexes will be formed exothermically. Finally, when thetemperature rises to the ignition point, a runaway ignition eventcan ensue.19−22

Spontaneous ignition is a complex physiochemical processincluding turbulent flow, heat and mass transfer, phasetransition, and chemical reaction. To determine the sponta-neous ignition tendency of coals, the investigators haveemployed various methods, such as the Frank−Kamenetskiimethod, crossing point temperature method, activation energymethod, etc. In addition to the elemental tests mentionedabove, more and more attention has been paid to thespontaneous ignition of coal in its mining, transportation,storage, and treatment. Fierro et al.23 focused on spontaneouscombustion in coal stockpiles. They identified that ventilation,size segregation of particles, and angle of the slopes of thestockpile are the most important considerations in safestockpiling and suggested that low angle slope and goodventilation could make the coal stockpiles safer. Hull et al.24

studied the spontaneous combustibility of a coal pile inconfined storage and confirmed the importance of bedcompaction in enhancing the safety of the coal pile in confinedspaces. Besides, much work has been done to investigate thegas products in the coal spontaneous combustion. In order toprovide scientific basis for the forecast of coal spontaneouscombustion in the early stage, Wu25 et al. measured theconcentration of significant gases released by the coal samplesat different temperatures and found that CO can be regarded asthe significant gas of spontaneous combustion. Pone et al.26

studied the gas products in the spontaneous combustion in twocoalfields of South Africa. This study identified that burningcoal released toxic gases and greenhouse gases includingbenzene, toluene, xylene, ethyl benzene, methane, and carbonoxides.As mentioned above, most previous studies focus on the

spontaneous ignition of coals in coal stockpiles, in which theheat generated from the low temperature oxidation reactions istransported by diffusion and natural convection of the air.However, the conclusions of these studies may be not suitablefor the spontaneous ignition of lignite during the drying processin the packed bed because the heat transportation in the packedbed dryer is mainly caused by forced convection of the heatingmedium. Moreover, in the coal piles, low temperature oxidationof the coal is the primary source of heat leading to thespontaneous ignition. In comparison, during the drying processin the packed bed, the heat from the hot drying medium ismuch more than that of the low temperature oxidation of thecoal. Therefore, the spontaneous ignition of coal could occurmore easily and earlier in the packed bed dryer than in the coalpile. Thus, the method of significant gas analysis, which hasbeen used in coal mines to predict the spontaneouscombustion,26 is not applicable to the lignite drying processin the packed bed dryer. Hence, a method to predict thespontaneous ignition of lignite during the drying process in the

packed bed dryer is requested. Insufficient research has beendone on this topic. van Blijderveen27 et al. studied thespontaneous ignition of wood, char, and RDF (refuse derivedfuel) in a lab scale packed bed. In their work, the effect ofprimary air flow velocity, particle size, moisture content, andaddition of inert to the fuel bed on the spontaneous ignitionbehavior of several solid fuels was presented. However, onlyqualitative analysis was obtained in their work, quantitativeanalysis is still needed.It has been mentioned that the incidence of spontaneous

ignition of lignite in the drying process is very high. It dependson many factors, including temperature, particle size, volatilecontent, moisture content, and the drying time, etc.19,28,29

These parameters are important to the design of dryers. In thispaper, theoretical calculation and experimental research ondrying and spontaneous ignition of lignite samples in a packedbed dryer was performed. The influential factors includingtemperature, flow rate, oxygen content of drying medium, layerheight, and particle size related to the spontaneous ignition areevaluated. The results of this study are expected to provideguidance for design and operation of packed bed dryers oflignite.

2. EXPERIMENTAL SECTION2.1. Coal Analysis. The lignite used in this study was obtained

from Pingzhuang Mine, Inner Mongolia, China. The proximateanalysis of the raw coal is given in Table 1. It can be seen that the

moisture content, ash content, and volatile matter of this lignite arevery high while the calorific value is very low because of the lowcontent of its fixed carbon.

2.2. Thermogravimetry Experiment. Temperature program-ming thermogravimetry was used in the combustion experiments ofthe lignite. A thermogravimetry differential scanning calorimetry (TG-DSC) balance rod was applied in this study. Generally, a coal sampleof 10 ± 0.1 mg was put into an Al2O3 container, which was then placedin the Setaram simultaneous thermal analyzer Labsys Evo. In thepresent study, the samples’ physical and chemical changes in thetemperature range of 460−560 K were focused on because thespontaneous ignition took place right in this range. According toprevious experiments, the heating rate has insignificant effect on theresults of TG-DSC experiments in the temperature range of 460−560K. Therefore, all the experiments were carried out at a constantheating rate of 20 K·min−1 in the temperature range of 300.15−1273.15 K with a preset O2−N2 gas flow rate of 50 mL·min−1. Theexperiments of the oxygen concentration effect on coal combustionreactivity proceeded at oxygen concentration of 10%, 15%, and 21%.

2.3. Packed Bed Experiment. The lignite was ground and sievedinto three size groups (1−3, 3−5, and 5−7 mm) and then keptairproof in glass containers at room temperature, respectively. Theschematic diagram of the experimental system is shown in Figure 1.The reactor is a lab-scale packed bed dryer with the height of 300 mmand the inner diameter of 30 mm, as shown in Figure 2. The reactor isinsulated with 20 mm of glass wool to ensure no radial temperaturegradients inside the dryer. The primary air is heated by an electricheater and fed from the bottom of the packed bed reactor. Then, thehot gas flows through the bed and dries the lignite particles. Thetemperature of the gas is maintained at the desired value by thetemperature controller and the flow rate is controlled by the mass flow

Table 1. Proximate Analysis of Pingzhuang Lignite

totalmoisturewt %

inherentmoisture wt

%, ad

fixedcarbon wt%, ar

volatilematter wt%, daf

ashcontentwt %, ar

calorificvalue

MJ·kg−1, ar

33.3 8.55 25.86 44.61 20.02 12.03

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controller. The nitrogen can be mixed into the air to investigate theoxygen content effect.The reactor is placed on the electric balance to measure the loss of

sample mass in the drying process. Six K-type thermocouples are used.The lowest one is set under the gas distributor to monitor the inlet gastemperature and the other five are set in the packed bed at 20, 70, 120,170, and 220 mm above the gas distributor to monitor the temperatureinside and above the bed. The weights and temperatures are recordedby seconds.2.4. Experimental Procedures and Programs. At the beginning

of every experiment, the hot gas was fed into the dryer to preheat thereactor until the inlet gas temperature reached the expected value.Then, the samples were put into the reactor and the drying startedwhile the inlet gas temperature was kept constant. The loss of samplemass and temperatures in the bed were monitored. When the samplemass appeared to drop rapidly and the temperatures in the bed rosesharply, it could be decided that spontaneous ignition took place. Theinlet gas temperature was set to be different under different workingconditions to determine the critical point of spontaneous ignition.

As mentioned before, three sample size groups (1−3, 3−5, and 5−7mm) were prepared to study the effect of the particle size on thecritical gas temperature and the spontaneous ignition temperature. Tostudy the effect of primary gas flow velocity on the critical gastemperature and spontaneous ignition temperature, a number ofexperiments have been carried out at four gas flow velocities (0.2, 0.3,0.4, and 0.5 m·s−1). By mixing the nitrogen into the air, three oxygenconcentrations of 21%, 15%, 10% were used to investigate the oxygencontent effect. Moreover, different bed heights were also used inexperiments to study the bed height effect. The experimentalconditions were shown in Table 2. It should be noted that a number

of experiments at various inlet gas temperatures were carried out todetermine the critical spontaneous ignition temperature, which are notlisted in every detail here. Instead, the temperature range in which theexperiments were performed is shown in Table 2.

3. SPONTANEOUS IGNITION THEORY3.1. Single Particle Model. In the experiments, the coal

samples in the packed bed were dried by the hot gas from thebottom to the top, so particles at the bottom were dried first.Then, the dry particles went on to be heated by the hot gaswhile the particles at high level were still being dried. In thiscase, the bed can be divided to the dry area and the wet area.When the temperature of particles in the dry area became highenough, low-temperature oxidation occurred and the particleswould be heated by the heat gained from the oxidationreactions. Finally, the temperature of dry particles will be higherthan that of the surrounding gas. In this case, the energybalance of the particles consists of two parts: the heat gainedfrom the oxidation reactions and the convective heat transferbetween the primary gas flow and the particles.27,30,31 To modelthe energy balance of a single particle, the followingsimplifications were used: (1) The particle is taken as aspherical particle. In most models about coal particles, theshape of the particles is usually assumed to be spherical tosimplify the calculation and the deviation is acceptable as longas the equivalent diameter is selected reasonably. (2) Theconditions within the lignite particle are independent of angle,so a one-dimensional mathematical model can be used. (3) Theprocess is treated as steady because the temperature of theparticle is increasing slowly before ignition. (4) The heat gainedby the reactions is treated as a uniform inner heat source Φ inthe particle. Precisely, the inner heat source is not uniform dueto the internal diffusion and temperature distribution within theparticle. However, these two factors can be neglected if thereaction rate is controlled by the reaction step and the internalthermal resistance is much smaller than the external thermalresistance. By calculating, the value of the Thiele modulus φ,

Figure 1. Schematic diagram of the experimental packed bed dryersystem 1, air pump; 2, nitrogen; 3 and 4, mass flow controller; 5,electrical heater; 6, temperature controller; 7, packed bed; 8,thermocouples; 9, gas distributor; 10, gravity sensor; 11, dataacquisition unit; 12, computer.

Figure 2. Packed bed reactor.

Table 2. Experimental Conditions

oxygenconcentration

(%)

particlesize(mm)

gas flow velocity at293.15 K, 1 atm

(m·s−1)

heightof bed(mm)

inlet gastemperature (K)

21 3−5 0.2 150 458.15−463.1521 3−5 0.3 150 460.15−465.1521 3−5 0.4 150 463.15−468.1521 3−5 0.5 150 463.15−468.1521 1−3 0.3 150 458.15−463.1521 5−7 0.3 150 460.15−465.1521 3−5 0.3 100 460.15−465.1521 3−5 0.3 200 458.15−463.1515 3−5 0.3 150 473.15−478.1510 3−5 0.3 150 483.15−488.15

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which can describe the relationship between diffusion andreaction rate in porous particles, is in the range of 2 × 10−5−1× 10−4 s−1. This indicates that the reaction rate is controlled bythe reaction step. The Biot number (Bi) in the present work isin the range of 0.00875−0.58, which means that the heatconduction within particles is much faster than the heatconvection away from the outer surface. Therefore, the uniforminner heat source can be assumed.32,33 The energy conservationequation of a particle is represented by

λ + Φ =⎛⎝⎜

⎞⎠⎟r r

rT

r1 d

d

d

d0p 2

2 p

(1)

The boundary conditions are given by

= =rTr

0,dd

0(2)

λ= − = −r RT

rh T T,

d

d( )p p

pp g (3)

where λp is the thermal conductivity of dry lignite, Tp is thetemperature of particle, Tg is the temperature of gas, Rp is theparticle radius, and h is the convective heat transfer coefficient.Solving these three equations, the heat flux at the radius of r canbe expressed as follows:

= Φqr31 (4)

On the particle surface

= ΦqR

31p

(5)

The convective heat transfer flux between the gas and theparticle can be expressed as

= −q h T T( )2 p g (6)

The relationship between q1 and the temperature T is obtainedby solving the differential scanning calorimetry (DSC) curveand represented by the curve L in Figure 3. Qualitative analysiswill be introduced in the following sections.

Equation 6 is the straight line M in Figure 3. The slope of Mdepends on the convection conditions, and M intersects withabscissa axis at T0,g. If T0,g is low, the line M and the heatgeneration curve L have two intersecting points, i.e., point 1and point 2. Both points are at equilibrium because the heat

generation is equal to the heat loss at these two points. But thetwo conditions are different.At the intersection point 2, if the temperature is reduced

slightly, it will be reduced continuously because the heatgeneration due to the oxidation is smaller than the heat loss dueto the convection between the gas and the particle. If thetemperature is raised slightly, it will rise continuously becausethe heat generation will be greater than the heat loss. Therefore,any perturbation of temperature around point 2 will make thereaction depart from equilibrium state. The intersection point 2is at an unstable equilibrium state. At point 1, if the temperatureis reduced, it will get back to this point because the heatgeneration will be greater than the heat loss. If the temperatureis raised, it will also fall back to point 1 because the heatgeneration will be smaller than the heat loss. Therefore, theintersection point 1 is at a stable equilibrium state.With the rise of T0,g, the line M moves rightward until the

position M′. The line M′ is tangent to the curve L at the point i,which is the limit position of stable state. If the gas temperatureT0,g is raised further, there will be no intersection of the heatgeneration curve and the heat loss curve. The heat generation isalways greater than the heat loss, and the temperature will risecontinuously. So the tangent point i is referred to as ignitionpoint, and the corresponding temperature Ti,p is known asignition temperature of the lignite particle.

3.2. Calculations of Spontaneous Ignition. 3.2.1. HeatGeneration. To obtain the heat generation from eq 5, the valueof Φ should be determined first.34 Thermogravimetry experi-ments under different oxygen concentrations were carried out,and the differential scanning calorimetry (DSC) curves wereobtained. DSC curves can indicate the endothermic andexothermic power of the samples.35 Figure 4 shows the DSC

curve of 10 mg lignite samples at the constant heating rate of 20K·min−1 in the temperature range of 303.15−1273.15 K withthe particle size of 100−125 μm and a preset O2−N2 gas flowrate of 50 mL·min−1. The oxygen concentration is 21%.As shown in Figure 4, endothermic reaction did not occur

until the sample temperature reached T0. When the sampletemperature was higher than T0, exothermic reaction started. Asmentioned above, it is the low temperature oxidation of lignitethat generates the heat. The object of this work is to study thespontaneous ignition of the coal sample, which happened at lowtemperature, so the DSC curve in the temperature range of T0− T0 + 100 was focused on. To make analysis easy, the

Figure 3. Spontaneous ignition of lignite particle.

Figure 4. DSC curve of the lignite combustion in atmosphere of 21%O2.

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exothermic power obtained from the DSC curve is representedas qm, then the value of Φ, which has been defined in section3.1, can be calculated by the following expression:

ρΦ =

q

mmp

(7)

where m is the mass of the samples and ρp is the density of thedry particles. The parameter Φ can represent the heatgeneration of the particles per unit volume. The heatgeneration Φ under different working conditions is shown inFigure 5.

It can be seen from Figure 5 that, under the oxygenconcentration of 21%, the exotherm begins at the temperaturearound 460 K. The heat generation due to the low temperatureoxidation of the samples increases with the increase of thesample temperature. With the decrease of oxygen concen-tration, the initial exothermic temperature increases and theexothermic power at the same temperature decreases. The mainreason is that the reaction rate of low temperature oxidationdecreases with the decrease of oxygen concentration. By fittingthe three DSC curves in Figure 5, the expression of Φ by theindependent variable of Tp under different oxygen concen-trations will be

Φ = − −ke b T c/( )p (8)

The values of k, b, and c are shown in Table 3.

3.2.2. Heat Loss. The heat loss can be obtained from eq 6provided the convective heat transfer coefficient is determined.However, the convective heat transfer coefficient h between theflowing gas and the particles is difficult to determine. Generally,the convective heat transfer coefficient h can be calculated bythe following equation:34,35

ε= + −Nu Nu[1 1.5(1 )]bed p (9)

ε= +Nu FPe

Pr2

/p 6 (10)

where Nubed is the Nusselt number of the bed and Nup is theNusselt number of a single particle. The factor F depends onRe, Pr, and the free stream turbulence level, and it can becalculated by the following correlation:34

εε

= ++ − −

⎛⎝⎜

⎞⎠⎟F

Re PrPr Re

0.664 10.0557( / )

1 2.44( 1)( / )

0.3 2/3

2/3 0.1

2

(11)

However, some researchers34−36 have pointed out that in therange of low Peclet numbers (Pe < 100), the experimentallyobtained particle-to-fluid heat transfer coefficient in packed bedmay be some orders of magnitude below the values predictedfrom the above equations. The Peclet number is used toindicate the relative proportions of convection and diffusion,and it can be calculated as follows:

ρ λ=Pe D C v/pp ,g g (12)

where v is the velocity of the flowing gas in the empty crosssection of the packed bed and Cp,g is the heat capacity of thegas. The present experiments were all carried out in the rangeof Pe < 100, and thus, h obtained from eq 9 must be correctedby a simple model created by Martin et al.34 The modelconsists of a packed bed with a average void fraction of ε, whichis 0.48 in the present study. In the bed, a small part of the totalcross-sectional area is assumed to have a larger void fractionand this part is called the bypass. The Nusselt numbers of bothparts are calculated and then the apparent overall transfercoefficient can be obtained from the following equation:34

φ νν

φν

= + * − +−

− *⎜ ⎟

⎛⎝⎜

⎞⎠⎟

⎛⎝

⎞⎠

Nu Nu Nu Nua H1 1 1 1

Pe 1

1

bed 1 2 1

1 bed

2

(13)

where Nu1 and Nu2 are the Nusselt numbers of the two parts inthe bed, a1 is the surface area per volume of the section withlow void fraction, Hbed is the total height of the bed, ν is thebypass flow rate ratio, and φ* is the specific surface area ratio.To calculate the criterion numbers Re, Pr, and Pe, the

characteristic temperature Tf and characteristic length should bedetermined first. In the present experiments, the temperature ofthe gas was elevated by only several degrees as the gas flowedthrough the dry area of the bed, so the characteristictemperature Tf was chosen according to the inlet gastemperature T0,g. In addition, the same Tf was chosen underthe conditions with the same oxygen concentration. Then thecharacteristic length should be determined. It is the size and theshape of the particles that have an effect on the convective heattransfer coefficient, so the equivalent diameter Dp of particle istreated as the characteristic length. In this work, the equivalentsurface area diameter, which is the diameter of the spherepresenting the same surface as that of the particle, is taken asthe equivalent diameter Dp. However, the shape of the particlesis irregular and the number of the particles is huge. Therefore,1000 particles were selected randomly and their breadth,length, and thickness are measured, and then, Dp and the voidfraction ε of the bed are calculated according to Allen37 andMasuda.38

Figure 5. Heat generation of the samples.

Table 3. Parameters of Fitted DSC Curves

oxygenconcentration (%) k b c

correlationcoefficient

21 3.41 × 108 773.06 353.99 0.9992715 2.79 × 108 751.31 359.73 0.999310 1.65 × 108 640.44 374.93 0.99913

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The parameters of different working conditions were shownin Table 4. The parameters for calculation depending on thecharacteristic temperature and the particle size are listed inTables 5 and 6, respectively.

It can be seen that the heat transfer coefficient increases withthe increase of the gas flow velocity and the particle size. Thedecrease of the bed height can also lead to the increase of theheat transfer coefficient. All the factors will be discussed indetail in the following sections.3.2.3. Calculation of Spontaneous Ignition Temperature.

Combining eqs 5, 6, and 8, the heat generation and heat loss ofparticles in the dry area per unit outer surface area can beexpressed as

= − −qD

k6

e b T c1

p /( )p

(14)

= −q h T T( )2 p g (15)

For the particles of 3−5 mm, the gas flow velocity of 0.3m·s−1 and the oxygen concentration of 21%, eqs 14 and 15 areplotted in Figure 6. The spontaneous ignition point i is thetangent point of the heat generation curve and the heat losscurve, thus

=

=

⎧⎨⎪

⎩⎪

q q

q

T

q

T

d

d

d

d

1 2

1

p

2

p (16)

This equation can be expressed in detail as follows:

= −

−=

− −

− −

⎧

⎨⎪⎪

⎩⎪⎪

⎛⎝⎜⎜

⎞⎠⎟⎟

Dk h T T

bT c

Dk h

6e ( )

6e

b T c

b T c

p /( )p g

p

2p /( )

p

p

(17)

The particle temperature Ti,p and gas temperature Ti,g at thespontaneous ignition point can be calculated by eq 16.The spontaneous ignition points of all the experimental

conditions were calculated. The effects of the gas flow velocity,the particle size, the oxygen concentration, and the bed heightwill be discussed in the following sections.

3.3. Heat Transfer in the Packed Bed. The reactor usedin the experiments is a cylinder with the height of 300 mm andthe inner diameter of 30 mm. The temperature at the centralaxis was focused on because it was the highest in the bed andthe spontaneous ignition probably happened right there. Toreduce the radial temperature gradients inside the dryer, thereactor is insulated with glass wool of 20 mm. Furthermore, theaxial heat flux due to the convection between gas and particlesis much greater than the radial heat flux.27 Therefore, the radialtemperature gradients at the central axis can be assumed to beflat and the system can be treated as one-dimensional. The one-dimensional system is shown in Figure 7; the gas with thetemperature of T0,g flows through the bed and heats theparticles. When the particles at the bottom were dried andheated to a certain temperature, the oxidation would take place.If T0,g is not high enough, the thermal equilibrium would finallybe reached, just like point 1 in Figure 3. When the particles at ahigher level were dried, it also would reach a thermalequilibrium at a higher temperature. Therefore, all the particlesin the dry area are at stable equilibrium states. The temperature

Table 4. Parameters under Different Conditions

bed height(mm)

oxygenconcentration (%)

particle size(mm)

equivalentdiameter (mm)

gas flow velocity at 20 °C, 1atm (m·s−1)

characteristictemperature (K)

convective heat transfer coefficient(W·m−2·K−1)

150 21 3−5 4.1 0.2 463.15 15.15150 21 3−5 4.1 0.3 463.15 22.63150 21 3−5 4.1 0.4 463.15 30.05150 21 3−5 4.1 0.5 463.15 37.43150 21 1−3 2.5 0.3 463.15 14.87150 21 5−7 5.8 0.3 463.15 34.26200 21 3−5 4.1 0.3 463.15 17.03100 21 3−5 4.1 0.3 463.15 33.7150 15 3−5 4.1 0.3 478.15 22.71150 10 3−5 4.1 0.3 488.15 22.79

Table 5. Calculation Parameters under DifferentCharacteristic Temperatures

characteristictemperature

(K)

heat capacityof the gas(J·kg−2·K−1)

gasdensity(kg·m−3)

particle thermalconductivity(W·m−1·K−1)

gas viscosity(kg·m−1·s−1)

463.15 1024 0.7625 0.03855 2.57 × 10−5

478.15 1027.2 0.7388 0.03964 2.62 × 10−5

488.15 1029.6 0.7244 0.04032 2.65 × 10−5

Table 6. Calculation Parameters under Different ParticleSizes

particle size(mm)

outer surface area per unitbed volume (m−1)

specific surfacearea ratio

bypass flowrate ratio

1−3 1248 0.05 0.193−5 760.98 0.13 0.295−7 537.93 0.24 0.40

Figure 6. Determination of the spontaneous ignition point.

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of the gas and particles will change only with the height beforespontaneous ignition occurs.39

Take the height at the gas distributor as the height of 0, theenergy balance in an infinitesimal element of dH at the heightof H can be expressed as follows:

ρ = −C vT

HH ha T T H

d

dd ( ) dpg ,g

gp g (18)

where a is the outer surface area of particles per unit bedvolume and the value of a can be determined by the followingequation:

ε= −a

D6(1 )

p (19)

where Dp is the equivalent diameter of the particles, ε is thevoid fraction of the bed.Combining eqs 14, 15, and 18, the following equation can be

obtained:

ρ− =− − − −

⎛⎝⎜

⎞⎠⎟T

kD

h

akD

C vHd

6e

6e db T c b T c

pp /( ) p

g p,g

/( )p p

(20)

By solving the eq 20, the relationship between the particletemperature Tp and the height H can be expressed as follows:

∫ ρ+

−=−

⎛⎝⎜⎜

⎞⎠⎟⎟

kbD

h T cT

akD

C vHe

6 ( )d

6b T c/( ) p

p2 p

p

g p,g

p

(21)

Denote the left item as ∫ f(Tp) dTp; the value of this item canbe calculated by plotting the curve of f(Tp) and integrating it.Thus, the particle temperature at the height of H can becalculated as long as the inlet gas temperature is determined.Considering extreme condition, that is, the spontaneousignition occurs at the top of the bed, it can be expressed as

= =H H T T, ibed p ,p (22)

= =H T T0, p 0,p (23)

Then eq 21 can be derived as follows:

∫ ρ+

−= −−

⎛⎝⎜⎜

⎞⎠⎟⎟

kbD

h T cT

akD

C vHe

6 ( )d

6( 0)

T

Tb T c/( ) p

p2 p

p

g p,gbed

i

0,p

,pp

(24)

In eq 24, T0,p is the particle temperature at the inlet, Ti,p is theparticle temperature at the spontaneous ignition point, Hbed isthe total height of the lignite bed. Because there is littledifference between the particle temperature and gas temper-ature at the inlet, T0,p was treated as the inlet gas temperature,which can be expressed as T0,p = T0,g. The condition indicatedby eq 24 is the extreme condition that the spontaneous ignitionwill not occur with lower inlet gas temperatures. By solving eq24, the lowest inlet gas temperature that can reach spontaneousignition can be determined. This temperature, which can beexpressed as Tc,g, is the critical inlet gas temperature, thatmeans, spontaneous ignition will not take place with lower inletgas temperatures.

4. RESULTS AND DISCUSSION4.1. Results by Calculations. The particle and gas

temperatures at the spontaneous ignition points and the criticalinlet gas temperatures are calculated under different conditions.The effect of gas flow velocity, oxygen concentration of the gas,and particle size will be discussed in the following sections.

4.1.1. Effect of Gas Flow Velocity. Figure 8a shows thechange of particle temperature Ti,p and gas temperature Ti,g at

Figure 7. One-dimensional system of the bed.

Figure 8. Particle and gas temperature at spontaneous ignition point with different gas flow velocities.

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the spontaneous ignition point with the primary gas flowvelocity. It can be seen that both the particle temperature andthe gas temperature needed for spontaneous ignition to occurincrease with the increasing gas flow velocity. It is reasonable tobelieve that the gas with higher velocities takes more heat awayfrom the particles due to the better convective heat transfer.37,40

Clearer explanation is shown in Figure 8b. With the oxygenconcentration at 21% and the particle size in the range of 3−5mm, the heat generation curve L is constant. The spontaneousignition point is the tangent point, and the particle temperatureTi,p is the temperature at this point. The line of heat lossintersects with abscissa axis at Ti,g, which is the gas temperatureat the spontaneous ignition point. The slopes of the heat losscurves are the heat transfer coefficients, which are listed inTable 4. The slope increases with the increasing gas flowvelocity. When the spontaneous ignition point moves right-ward, resulting from the increasing gas flow velocity, theignition temperature rises. It means that the spontaneousignition becomes more difficult. Therefore, the high gas flowvelocity in the packed bed dryer is of crucial importance,because it can not only provide a higher drying rate but alsoreduce the spontaneous combustion tendency.4.1.2. Effect of Oxygen Concentration. Decreasing the

oxygen concentration in the drying gas is one of the mosteffective methods to reduce the spontaneous combustiontendency.41 The temperatures of particle and gas at thespontaneous ignition points with the oxygen concentration of21%, 15%, and 10% are shown in Figure 9a. These calculations

are carried out with the gas velocity of 0.4 m·s−1, using theparticles of 3−5 mm in size. It is obvious that both the particletemperature and the gas temperature are increased significantlywith the decreasing oxygen concentration. That is mainlybecause the heat generated by the low temperature oxidationdecreases with the decrease of oxygen concentration. The heatgeneration curves with the three oxygen concentrations areshown in Figure 9b. A similar trend for the changes of the heatgeneration with the increasing temperature can be observed.However, the curve of lower oxygen concentration is lower dueto the lower intensity of the oxidation reaction. Thecharacteristic temperatures under the three conditions are463.15, 478.15, and 488.15 K, respectively. The effect ofcharacteristic temperature on parameters ρg, Cp,g, μ, and λg isweak, so the three heat transfer coefficients are very close. Withthe same cooling ability of the flowing gases, it will be moredifficult for the lignite with less heat generation to reach thespontaneous ignition point. In Figure 9b, for the same heattransfer coefficients, the spontaneous ignition point movestoward high temperature zone with the decreasing oxygenconcentration.

4.1.3. Effect of Particle Size. In the industrial scale packedbed dryers, actually, the particles size may be in the range of20−30 mm. If the calculation of spontaneous ignitiontemperature for these particles was carried out, the internaldiffusion and temperature distribution within the particlesshould not be neglected. To simplify the calculation, theparticles in the range of 1−7 mm were selected in the present

Figure 9. Particle and gas temperature at spontaneous ignition point with different oxygen concentrations.

Figure 10. Particle and gas temperature at spontaneous ignition point with different particle sizes.

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study. The calculations on the Thiele modulus and Biotnumber of the particles with the size of 1−7 mm in section 3.1indicate that the internal diffusion and the temperaturedistribution within the particles are negligible. To study theeffect of particle size on the spontaneous ignition, the particlesare divided into three size groups (1−3, 3−5, and 5−7 mm).Although particles with different sizes have different outersurface area, particle size has insignificant effect on the heatgeneration because the oxidation reaction occurs on both theouter surface and the inner surface of the particles.27,30 Thecoal, especially the dried lignite, is porous. There are hugenumbers of holes in the lignite particles. For the particles usedin the experiments, the inner surface area is larger than theouter surface area by several magnitudes, so the oxidationreactions occur mainly at the inner surface and the heatgenerated by the reactions can be solved as a uniform innerheat source Φ.42,43 According to eq 17, the value of Ti,p

depends on the value of h/Dp. According to the parameterslisted in Table 4, the value of Dp/h under the particle size of 1−3, 3−5, and 5−7 mm are respectively 5948, 5517, and 5906,which are close to each other. Thus, the temperatures at thetangent point of the three conditions have negligible differencewith each other, which is shown in Figure 10a. Therefore, it canbe considered that in the range of 1−7 mm, the particle size hasinsignificant influence on the spontaneous ignition.19,38

4.1.4. Effect of Total Bed Height. The bed height is one ofthe most important design parameters of the packed bed dryers.Figure 11a shows the particle temperature Ti,p and gas

temperature Ti,g at the spontaneous ignition point against thebed height. These calculations are carried out with the gasvelocity of 0.3 m·s−1, using the particles of 3−5 mm in size. Itcan be seen that both the particle temperature and the gastemperature decrease with the increasing bed height, whichmeans the spontaneous ignition can take place more easily witha larger bed height. According to Table 4, the convective heattransfer coefficient between the flowing gas and the particlesdecreases with the increasing bed height. Thus, the heatgenerated by the low temperature oxidation can accumulatemore easily in the higher beds. Therefore, the slope of the heatloss curve shown in Figure 11b decreases with the increasingbed height and the spontaneous ignition point moves towardthe lower temperature.

4.2. Results of Packed Bed Experiment. In the presentexperiments, five thermocouples were placed in the packed bedat 20, 70, 120, 170, and 220 mm above the gas distributor andanother thermocouple was placed right under the gasdistributor. The inlet gas temperature and the temperaturesat different heights in the bed were measured. Moreover, thesample mass was weighed by the electronic balance. When thespontaneous ignition occurs, the exact temperature of thespontaneous ignition point can not be obtained because thespontaneous ignition may occur at any point in the bed, butthere are only five thermocouples in the bed. However, thenumber of the thermocouples is not crucial. Actually, morethermocouples will be also helpless since it is impossible tomeasure the temperature at every point in the bed. Therefore,

Figure 11. Particle and gas temperature at spontaneous ignition point with different bed heights.

Figure 12. Changes of temperatures at different positions and sample mass with the time.

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the inlet gas temperature T0,g, which is measured by the lowestthermocouples under the gas distributor, is made to be thecriterion of spontaneous ignition.Figure 12 shows the changes of temperatures at different

positions and sample mass with the time when the gas flowvelocity is 0.3 m·s−1, the particle size is in the range of 5−7 mm,and the oxygen concentration is 21%. Figure 12a was carriedout with the inlet gas temperature of 461 K, the mass of thelignite samples was kept constant at the end of the dryingprocess and no spontaneous ignition took place. Therefore, theexperiment with the inlet gas temperature of 1 K higher wascarried out. In Figure 12b, after the particles at a certain heighthad been dried, the particle temperature rose to a certaintemperature, which is higher than the inlet gas temperature. It

can be seen that the particle temperatures at the heights of 20,70, and 120 mm are kept constant at a certain value for a longtime. This means that the particles have reached a stableequilibrium state, which can be indicated by point 1 in Figure 3.However, as the gas flow was heated by the particles, point 1which was reached by the particles at higher level movedrightward until the spontaneous ignition occurred. In Figure12b, at about 1400 s, the temperature rose dramatically and themass of samples dropped rapidly, and it can be determined thatthe spontaneous ignition occurred. The temperature of Figure12b is determined as the critical inlet gas temperature.From Figure 12 and a series of relevant experiments, the

critical inlet gas temperatures under different conditions weredetermined and plotted in Figure 13. The critical inlet gas

Figure 13. Critical inlet gas temperature under different experimental conditions.

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temperatures calculated by eq 24 are also plotted to comparethem with the measured ones.As shown in Figure 13, the critical inlet gas temperature

increases with the increasing gas flow velocity, the decreasingoxygen concentration, and the decreasing total bed height.Nevertheless, it has little relevance to the particle size. Theseresults are similar to those shown in Figure 8−11. Moreover,Figure 13e shows that the critical inlet gas temperaturedecreases with the increasing gas residence time in the packedbed, which reflects the combined effect of the bed height andgas flow rate. What should be concerned is the differencebetween the predicted temperatures and the measuredtemperature. It can be seen that under every conditionshown in Figure 13, the predicted temperature is lower thanthe measured temperature by only 10−20 K, which is anacceptable discrepancy. It can be believed that this discrepancyis not a random error since it is of regularity. It can bequalitatively explained that this discrepancy is mainly caused bythe simplifications we used in the single particle model. In themodel, the heat gained by the oxidation reactions is treated as auniform inner heat source Φ in the particle. Although thissimplification has been explained in section 3.1, the inner heatsource Φ will not be uniform in the real situation. In fact, thereis oxygen concentration gradient inside the particle due to thediffusion resistance and the oxygen concentration inside theparticle is lower than that at the outer surface.44 Therefore, theheat generated by oxidation reactions inside the particledecreases with the increasing distance to the outer surface.Denote the real inner heat source as Φ′ = f(r). It is hard to

obtain the exact expression of Φ′, but we can determine that Φ′< Φ. Thus, two curves of heat generation can be obtained,which are plotted in Figure 14. The calculated heat generation

curve is L, and the heat loss curve is M while the curve of realsituation are L′ and M′. Since the slope of M and M′ is thesame, the spontaneous ignition point of real situation has ahigher temperature. Actually, when determining the operatingparameters of a packed bed dryer, the margins are necessary.The inlet gas temperature is one of the most importantoperating parameters, for which a large margin will reduce thedrying rate and a small one may cause spontaneous ignition oflignite. A margin of 10−20 K is rational, which means thecalculated temperature can be directly used as the operatingtemperature of the packed bed dryer. Although there is adiscrepancy between the real and predicted situations, thetrends and the phenomena in the experiments can be predictedby the calculation method proposed in this paper. To make

more accurate predictions, further research on the detailedmechanism of the reactions is necessary.

5. CONCLUSIONSIn this paper, a calculation method is developed to predict thespontaneous ignition of lignite dried in the packed bed dryer.The critical inlet gas temperature of spontaneous ignition wascalculated. According to the results, the critical inlet gastemperature increases with increased gas flow velocity,decreased oxygen concentration, and decreased total bedheight. The particle size in the range of 1−7 mm hasinsignificant effect on the spontaneous ignition temperature.The critical inlet gas temperatures were also obtained from

lab-scale experiments under various working conditions.Compared to the calculated critical inlet gas temperatures,the experimental results are 10−20 K higher under almost allthe conditions, which is acceptable. For the packed bed drying,therefore, high gas flow velocity, low oxygen concentration ofthe gas, and small height of the bed are necessary to reduce thespontaneous combustion tendency of lignite.

■ AUTHOR INFORMATIONCorresponding Author*Tel.: +86-29- 82665185. Fax: +86-29-82668703. E-mailaddress: dfche@mail.xjtu.edu.cn.NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSThe financial support from Shanghai Boiler Works Ltd for thisresearch work is gratefully acknowledged.

■ NOMENCLATUREa = outer surface area per unit bed volume, m−1

a1 = outer surface area per volume of the section with lowvoid fraction, m−1

Bi = Biot numberCp,g = the heat capacity of the gas, J·kg−2·K−1

Dp = equivalent diameter of the lignite particles, mh = convective heat transfer coefficient, W·m−2·K−1

H = height in the bed, mHbed = total height of the bed, mm = mass of the samples, gNup = Nusselt number of single particleNubed = Nusselt number of the bedNu1 = Nusselt number of the section with low void fractionNu2 = Nusselt number of the section with high void fractionPe = Peclet numberPr = Prandtl numberq1 = heat generationq2 = heat lossqm = exothermic power in DSC curver = the radiusRp = equivalent radius of the lignite particles, mRe = Reynolds numberT = temperature, KTf = characteristic gas temperature, KTg = gas temperature, KTp = particle temperature, KT0,g = inlet gas temperature, KT0,p = particle temperature at the bottom of the bed, KTi,g = gas temperature at the spontaneous ignition point, K

Figure 14. Real and predicted situation of spontaneous ignition.

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Ti,p = particle temperature at the spontaneous ignition point,KTc,g = critical inlet gas temperature, Kv = gas velocity, m·s−1

Greek Symbolsε = void fraction of the bed, %λp = thermal conductivity, W·m−1·K−1

μ = viscosity, kg·m−1·s−1

ρg = density of the gas, kg·m−3

ν = bypass flow rate ratioφ* = specific surface area ratioφ = Thiele modulusΦ = inner heat source, W·m−3

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