Indian Journal of Chemical Technology Vol. 6,September 1999, pp. 247-255

Mathematical models for coal devolatilization and temperature distribution in coke ovens

Y R Popat & P D Sunavala*

Department of Chemical Engineering, Indian Institute of Technology, Bombay, Powai, Mumbai 400 076, India

Received 4 January 1999; accepted 7 June 1999

Merrick's models have been employed to study the rate of devolatilization and the physical properties of the charge, e.g. , bulk density, true density, porosity, specific heat, thermal conductivity and heat of reaction as a function of the tem­perature of carbonization. The equation. for unsteady state heat transfer by conduction was employed to evaluate the tem­perature-time distribution in a coke oven charge. The paper gives the tesults of computer calculations for low .and high vol atile Jharia coking coals of India.

For two centuries following the introduction of coke making, the conditions necessary for the' production of coke of an acceptable quality for metallurgical purposes remained more of an art than a science. Al­though the coking process has remained basically un­changed for a century, yet, even now there are many areas in which the mechanisms occurring have not been fully defined and remain unquantified. Nearly 95% of the total production of iron in the world comes through the blast furnace route, which requires for its operation hard, strong metallurgical coke. Al­though alternative technologies such as us~ of formed coke briquettes in conventional blast furnaces and direct reduction processes for iron manufacture re­quiring neither blast furnace nor coke oven technol­ogy have made some inroads, it is certain that the highly developed conventional coke oven cum blast furnace route will continue in t; e forceable future essentially because of its large productivity and economies of scale.

Mathematical modelling is a predictive technology. Although the coking process is a highly developed technology', mathematical modelling can widen the scope and applicability without resorting to expensive and time consuming experimentation. Three impor­tant models are considered in this paper.

Model for rate of devolatilization of coal It is well known that as devolatilization takes

place, the semi-coke gradually gets transformed into

*Present addres~ : Fl at No. 22, Mehta Mahal, Dadar Main Road (D. Phalke Road ), Mumbai 4000 14

coke. The strength of the ultimate coke depends upon the 'cracks and fissures that are formed perpendicular to the side walls during this transformation process. The rate of devolatilization is one such parameter which controls the strength of the coke. Hence a wider range of coal blends for making coke can be studied from the standpoint of rate of devolatilization.

Merrick postulates that devolatilization can be de­scribed by four parallel reactions defining the release of primary volatile matter, methane, carbon monoxide and hydrogen as shown in Eqs (I )-(4),

U ~ U' + primary volatile matter U~U'+C~

U~U'+CO

U'~U'+H2

(\) (2) (3)

... (4)

w~ere U denotes coal, U' denotes semi-coke or coke, and the primary volatile matter includes Tar, H20 , CmHn, CO2, NH3 and H2S species.

In line with Fitzgerald's2 treatment, Merrick l.3 as­sumed that the evolution of each of the above men­tioned four species can be described by a first order equation of the form shown in Eq. (5),

dm/dt = K (mo-m) ... (5)

where mo is the final yield of each of the four species on daf coal basis and m is the yield at time t, and K is the reaction rate constant.

Expressing the reaction rate constant in terms of the Arrhenius factor, Eq . (5) was written in the fonn of Eq. (6) where the activation energy E lies in the range 200 - 400 MJ/kg mo l,

248 INDIAN 1. CHEM . TEC HNOL. , SEPTEMBER 1999

0·90 000..------- --- ----- ---, Tolcl VM ( M~r ritt ) in Jhorioc.oal (lV) : 21 ·04-/. Totol VM ( Meorr il1 ) in ~oria(oal (l'/ ) & 19·51'/.

l ,.rnpe!o tu r 01 Srmi· Cok.;C _

Fig. I- Rate or dcV()la tili zati on fo r low and hi gh volatile Jhari a coa ls (R ate uf heatl'll! = 3 KJminl

i M

E CT. -" ~

~ .. ,. 0 U

I

'E .. oJ)

"0 ~ <II C .. 0

.x :; CD

8GOr----------------~

700

60

500

'00 a

Jharia ( LV)

(VM = 21.04'''')

lharia . (HV)

(VM = 29. 50'/, )

200 400 600 SOO 1000 1200 1400

T.mpora lur. of S . mi-Cok.,·C _

Fig. 2-Bulk densities o f semi -cokes from low and high volatile lhari a coals

. . . (6)

The yi eld of tota l volati le matter was expressed in terms of the ultimate analysis of coal on daf basis as shown in Eq . (7),

mo (Tota l VM ) = 16H + 0 . 14 0 + N + S - 0.573 .. . (7)

The reac ti on rate constant Ko was found to vary with temperature in accordance with Eq. (8),

Eq. \6) was numerically integrated fo r a heati ng rate of 3 K/min using the val ue of mo (Total VM) given by Eq. (7) to gi c the cumulat ive yield of vo latile matter

Table l~ompos i t ion of lhari a low and high volatile coals4

lharia Low lhari a High Volatile Volatile

(LV ) (HV)

Coalfield ' lharia Jhari a Colliery Khas Jayrampur Pathagori a Scam XI/XII V Measures Barakar Rani ganj Moisture, % 1.4 2.4 Ash, % 2 1. 3 23 .5 Vol atile Matter, % 24 .2 31.1 Fixed Carbon , % 53. 1 43.0 Caking Index 17 24 Cdmm) , % 89.8 85 .7 Hdmmf, % 5..0 5.7

Odmmf, % 2.6 5.6 Ndmnlf, % 1.9 2.5

SUnlIT. % 0. 7 0.5 Volat ile Matter, % 21.04 29.51 (Mcrrick . Eg .7)

as a function of temperature. T he predicted cumula­tive yields of vo latile matter were differentiated to give the rates of devolatilization (dVMldT, or dVMldt) which are illustrated for low and high volatile Jharia coking coals in Fig. 1.

T he composition of low and high volatile Jharia . coking coals taken in thi s study are shown

4 in

Table 1. It will be noted from Fig.1 that differences in the

rates of devolatilization between the low volatile Jharia coal (VM = 21.04%) and the high volatile Jharia coal (VM = 29.5 1 %) are most marked in the early stages of devolatilization . (It may be noted that the above mentioned yie lds of vo latile matter were calculated from Merrick's Eq . 7 which are less than the volatile matter from proximate analysis and con­forms more nearly to actual yie ld of volati le matter ill practice). Secondly, the rates of devolatil ization reach a maximum between 440 and 480oe, the increase in the volatile matter conten t of coal being accompanied by an increase in the maxi mum rate of devolatiliza­tion and a decrease in the temperature at which the maximum occurs . Beyond 500oe, the rates of devola­tilization converge. Tn all cases lne evolu tion of pri­mary vo latile matter "ppear<;! be completed by 6000e although secondary vol a ti k matter continues to he re leased unti I 1000' C.

~tuc! J es h,;ve abo iLdicatcd tha: as the heal ing -ate was increaseJ from { Kimin to '.( t(/min, the tem­perature at whic 1 maximum rate ,, ( de vulatil ization occurs increases with ' Icating late .

POPAT & SU NAVALA: MATHEMATICAL MODELS FOR COAL DEVOLATILIZATION 249

2200,------------------------------.

i 210 0

M

~200 ~

0 1900 u

" x .3 1800 , E ~ 1700

.~ 1600 '" c

~ 15 00

" ~ ~

14 00

1300

Jharia(LY)

I 2 00 t=~::;=~~__!:_::-:-~:-::-~:_:__..L..--.L--.-J o 200 Tompora llrr~ of 50mi _ Co l<2,oC __

Fig. 3-Truc ciL: nsily of semi-cokes from low and high volatile JhJria coa ls

100',-------------------------------.

90

80

;:. _ - 7

" " ~ 60 u

; 50 <J1

. 20

10

Jharia (!iV)

1hario (LV)

~

O~-~~--~--~--~--L---L---L-~ o 200 400 600 1000 1200 1400

T.mpora tur. of S.mi- Coko , °c _

Fig. 4-Porosil Y of semi-co kes from low and high volatile Jhari a coal<,

Models for physical properties of coals :vlany physical propert ies used in beat 1 ransfer cal­

CUI:JtIOIlS such as thermal conductivity, specific heat, true and bulk densit ies o f coa)s, vary with tempera­ture and hence for accurate calculation the study of their variation with temperature is important.

2300

2200

2100

i 2000

~ 1900

'" .... ...... -: laoo .. .>t 0 u , 1700 ·e ..

<J1 _ 1600 0

" ~ 1500

~ .[ 1400 III

'" 6 1300 .. c

" g 1200 ;; .E

1 roo

~ ~ f I

200 400 600 800 1000 1200 1400 T<lmporatll"tof !)omi-Coko,oC ~

Fig. 5--Instant specific heats of semi -cokes from low and high volatile 1haria coals

Bulk density 1.3

The variation of bulk density with temperature of carbonization was calcu lated using the formula shown in Eq. (9),

P = po Y/(0 .875 - 0.00.0137 Podry) kg/m3 .. . (9)

where po = Initial bulk density of wet charge kg/m 3

(assumed equal to 767.1 kg/m3)

Podry = Initial bulk density of dry charge, kg/m3

(assumed equal to 750 kg/m3) .

Y = Yield of coke, kg/kg

The results for low and high volatile Jharia coking coals is shown in Fig. 2. As can be seen the bulk den­sity decreases from the onset of devolatilization at about 350°C. The high volatile Jharia coal (VM =

29.5%) obviously has a larger drop in bulk density than the low volatile Jharia coal (VM = 21.04%). The decrease in lJulk density is simu ltaneously accompa­nied by shrinkage.

True den~ity of serni cokes"

The most sat isfactory correlation for tI ue dellsity of coals was reported by Ergun et al. 5 as shown in .Eq. (10),

250 INDIAN J. CHEM. TECHNOL. , SEPTEMBER 1999

O.4,r-----------------,

i ~ 0·2 .!:! u o co a: (;

'0 ~ 0.1 co

. ~

E " E

" u

Jhorlo.(L V)

Jh.arta, (HV)

o~~~~~~~~~~~~~__=~ o 200 'T¢mperotur. of Scmi- Coke I ~ _

Fig. 6--Cumulative heats of reaction during carbonization of low and high volatile Jharia coals

1 0.00084H -=0.00044+-------- m3/kg do ~+H+Q+!i+_S

12 16 14 32 ... (10)

However, Eq. (10) predicts higher values for semi­cokes and the following relation given by Eq. (11) was proposed by Merrick for semi-cokes,

_1 =0.001388+ 0.0000769 3/k do eON s m g

-+H+-+-+-12 16 14 32

... (II) The results calculated for semicokes obtained on car­bonization of low and high volatile Jharia coking coals at various temperature is shown in Fig. 3. It will be noted that the semi-coke from Jharia coal consis­tently shows about 20-50 kg/m3 higher true density which increases from about 1250 kg/m3 at 4000e to about 2050 kg/m3 at 1200°C.

Porosity of semi-cokesl,3

The porosity, el is related to the bulk density p and the true density, d, by the Eq . (1 2) as,

e = I - E.. d

... ( 12)

As carbonization proceeds, p decreases and d de­creases upto a temperature of about 10000e as shown in Figs 2 and 3. Hence in accordance with Eq . (1 2) e increases upto about 1000°C. Th is is shown for po-

'" E ..... ~ .. ... o U

4

I 2 'e JI '15 ?: ~ u

" -g 1 o w

200 400 600 800 1000 1200 1400 rcmpcrdlurc , of Sami-Cokc:C _

Fig. 7-Thermal conductivity of semi-coke from low and high volatile lharia coals

rosity of semi-cokes obtained by carbonization of low and high volatile Jharia coking coals in Fig. 4. The porosity of lump coke at the resolidification tem­perature is given by Eq. (13) as,

... (13)

The resolidification temperature (1) is given by Eq. (14) as,

... (14)

where T max is the temperature at which maximum rate of devolatilization takes place (Fig. I).

Instantaneous specific heat of semi-cokel•3

The Einstein model has been used to calculate the variation of instantaneous specific heat of semi-coke as a function of temperature. The Einstein model IS

given by Eq. (15 ) as,

R[E(TK 1380) + 2E(TK 11800)] Ik K CON S J g - + H+-+-+-

c = ... (15)

12 1.6 l!1 32 where R is t)e gas constant and E, the Einstein fU i1~ '

tion given by Eq. ( : 6) as,

E(y) = e I/y I [y( e i /y - 1) f . " (16)

The resu lts for instantaneolls specific heats 0f cokes from low and high vo lati le Jhafia coking coals is

POPAT & SUNAVALA: MATHEMATICAL MODELS FOR COAL DEVOLATILlZATION 251

13 Ov~n SpecificationS

D~nw~h .~~Om

1200 'Noli thickness :~.05Qm~

Wall bul. donsity = 2Boo"g 1m3

Wa ll .p~cific hoot =UOO J I ~g K

1100 Wall th~rma l conduclivity .2 . 3 W/m K

Wall

300

200

Timtl for Carbonization t h -----...

Fig. 8--Temperature-time history for carbonization of low vola­tile Jharia coal

shown in Fig. 5. It is interesting to note that the pre­dictions indicate the existence of a maximum instan­taneous spec ific heat at about 400-450°C. Kirov6 at­tri butes this result to the volatile matter having a higher specific heat than that of fixed carbon. As the vol atile matter is removed, the specific heat can fall even though the specific heat of the carbon continues to ri se.

The specific heats predicted by Eq. (15) can be corrected for ash and moisture in semi-coke as shown in Eq. ( 17) as,

en = Wdaf C + W a Co + 4186 W on J/kg K ... (17)

HealS of reaction,·J

It is often observed that the centre of an oven charge becomes hotter than the walls towards the end of carbonizat ion indicating the existence of exother­mic reactions above about 650°C. Heat balances on a coke oven carr ied out by Lowry show that these exo­therm ic react ions provide approx imate ly 15-20% of the total heat required for carbonizat ion (equivalent to about 0.266-0.45 MJ/kg initial coal basis at ambient temperature ).

Ovon Spocifications

avon wIdth .O.450m 13 • O.O'SO m

• 2800 :1111 I ml

Wall spocifie hoot = 1200 J/kg K 'Noll !hormol conductivity. 2 .3W/mK

15.4h

O~ ____ L-~~~====~~~~ Wall 118 1/4 3/B C

Plano Plan~ Plano

Fig. 9--Distribution of temperature within coke oven charge at different time intervals for low volatile Jharia coal

Although the errors in these estimates are large, exothermic heats of reaction of this magnitude will clearly have a significant effect on the temperature­time history profile of a coke oven charge. However, no consistent relationship between heats of reaction and coal type is apparent. The use of differential thermal analysis in assessing the heats of carboniza­tion reactions is uncertain since the published results do not agree on the pattern of heat evolution.

The model assumes that the exothermic heat of re­act ion above 650°C Catl be evaluated from the cumu­

lative yields of the secondary volatile matter species C H4, CO and H2 on daf initial coal basis and 2 is the cumulative heat of reaction on daf initial coal basis as shown in Eq . ( 18) as,

2 0 = 6.234 x 106 m(CH4) - 4 .243 x 106 m(CO)

( 18)

The cumulat ive yie lds of CH4 , CO and H2 on daf initial coal basis were eva luated by correlations drawn from experimental data as shown in Eqs ( 19), (20) and (21) as,

252 INDIAN 1. CHEM. TECHNOL., SEPTEMBER 1999

Own 5pccff icaHons o..on wid1h :O.'SOm Wall th ickfHISS :: O. 0'50 rn Wall bulk d<zns i!y =1BOO.~/mJ Wall .poe;1;c hoot =1100 J/k9 II C.ntr~

11 00

tlOOO

I 900

~ 80

10

I.J , 'e 70 .. <II

. 0 . 50

" :; ~ 500 " a

S ~ .00

JOO

200

100

Wal! thqrmol conductivity.: 2.3W/mK

___ --..:W~ac:.:...I1-_---~<::::....l Wall

~~~~~~-~8~~10-'~12~~'~~~1~5-~18~ Time for Carbonization, h ~

Fig. 10--Temperature-lime history for carbonization of high vola­tile Jhari a coal

[ J })2.38

- (T - 350) m(CH4) = 0.06 1- eXPl 324 .. . (19)

-(T - 350) [ { })

2.63

m(CO) = 0.35 0 1- exp 420 . . .. (20)

- (T - 350) [ { })

2.5

m(H2) = (0.034 - 0.3H) 1- exp 455

... (21) The results of the ca lculat ions for low and high vola­tile Jharia coking coals is shown in Fig. 6 which indi­cate an exothermic reaction in the range 650-1200°C wh ich causes the centre of the charge to get heated above the wall temperature towards the end of the coking period .

In the model it is assumed that the release of heat of reaction fo llows a first order reaction as shown in Eq. (22) as,

.. . (22)

where Z" - Ultimate heat of reaction at time t.. given by Eq .( 18) (J /kg daf initial coal basis)

Z - Cumulative heat of reaction at time, t (Jlkg, daf initial coal basis), and

K,- Rate constant assumed to vary exponen­tially with temperature according to Ar­rhenius equation (S·I).

Thermal conductivity of charge A general equation for estimating the thermal con­

ductivity of two-phase systems in which either the solid or the fluid is the continuous phase was pro­posed by Russell7 and shown in Eqs (23) and (24) as,

K 213 K 1 2/3 Kpart =

coal P + gas ( -P ) 2 / 3 2/3 ~/rn1(

K eoaJ (P -p)+Kgas(l-p +p) Kgas

(23)

and jJ = I - e (24)

where Kparh Kgas and Keoal are the thermal conductivi­ties of the particulate charge, gas and solid coal re­spectively.

Below the resolidification temperature, T" given by (Eq. 14), the charge is effectively particulate and the thermal conductivity of the two-phase system IS

given by Eq. (25) as,

K K Kpart = coal gas ~ 1m K

Keoal e+Kgas(l-e) ... (25)

The thermal conductivity of wet charge can be cal­culated as shown in Eq. (26) as,

Kwet = Kpart + emoist (Kwaler - Kpa(1) ~/m K ... (26)

where' e,oois is the volume fraction of charge occupied by moisture and Kwaler is the thermal conductivity of water taken to be 0.6 W ImK .

Above the resolidification temperature the solid phase is continuous and the thennal conductivity of the two-phase system is given by Eq. (27) as,

... (27)

Eqs (26) and (27) have been used to calculate the thermal conductivi ty of semi-coke using the fo llow­ing Eqs (28) - (30) for Kgas and Eq . (31 ) for Keoal '

Kgas = 7.83xI0-5 h (for TK < 700 K) ~/mK .. . (28)

Kgas = 1.095xlO·3 h -0 .7 12 (for 700 K ~ TK ~ 1 WOK) W /mK .. . (29)

Kg .. = 4.48x I 0-4 TK ( for 11 OOK < TK ) ~/mK '" (30)

POPAT & SUNAVALA: MATHEMATICAL MODELS· FOR COAL DEVOLATILIZATION 253

Own Spczcilicatlon

o..n width .0.450'111 Wall ltIickn.. .0·050m Woll bulk density .Z800klllm) '#jail .p~cilic heat .1200 J I kll II Wall th~,mol conduct i.ity~ ·3W/mK

300

200

100

ol ______ ~~==~~~==~~~~ v'(] 11 1/8 1/4 3/8

Plan. Plana Plana

Fig. II-Distribution of temperature within coke oven charge at different time intervals for high volatile Jharia coal

-[ 0.016 1 tl2 Kcoal - CON S - 0.105 (Td W/mK -+ H+ - + - + --12 16 14 32

... (31)

After resolidification, radiative heat transfer is possi­ble both across pores within coke lumps and along the fissures separating the lumps. The mean radiation path length within coke lumps can be taken to be the mean pore intercept. Hence the overall effective thermal conductivity for dry particulate charge (be­low T,) is given by Eqs (32) and (34) and for continu­ous solid phase charge (above Tr) is given by Eqs (33) and (34) as,

K = K part + K,ad

or K = K coke + K,ad

where K,ad = 1.82 x 10.7 e ,ad Xrad TK3

(32)

(33)

(34)

and e rad is the effective area porosity of the bulk mate­rial corresponding to the mean radiation path, Xrad.

The results for thermal conductivities of semi­cokes obtained from low and high volatile Jharia coking coal s are shownjn Fig.7 which shows almost

a linear increase in the thermal conductivity of 0.2 W/mK at 400 K to about 3.8 W/mK at 1300 K.

Charge temperature-time historyl,3 The temperature-time history model consists of the

solution of equation for unsteady state heat transfer by conduction to predict the temperature distribution in the charge at different intervals and different planes and thus permits a study of the inhomogenei­ties in the coke during the coke forming stage and at the end of the coking period due to temperature gra­dients. Furthermore the energy consumption and pro­ductivity are also related to the charge temperature­time history.

Assumptions i) The charge is assumed to be homogeneous ini­

tially and to remain uniform in planes parallel to the oven wall throughout the carbonization pro­cess.

ii) The local effects of fissuring, curvature of the coke at the wall end of the charge and non­uniformities in bulk densities caused by any seg­regation are neglected.

iii) The charge temperature at any specified dis­tance from the wall as predicted by the model is assumed to be constant along the whole length of the coke oven.

iv) The steam generated by boiling cannot condense and moves towards the oven wall, and in doing so, gets heated to the resolidification tempera­ture (about 500°C). This results in a predicted mean temperature of 580°C for the carboniza­tion gases which is in fair agreement with the measured values.

v) The heat transfer by conduction is assumed to take place between only one refractory wall and half the width of the oven charge.

vi) The temperature at the outer surface of the re­fractory is assumed constant. However, in pro­grammed heating of ovens, this temperature, IS

assumed to be a prescribed function of time.

Numerical solution of the heat conduction equation for a dry charge

The followingS one-dimensional heat conduction Eq. (35) was used to calculate the charge tempera­ture-time history as,

pc d T = ~ ( K d T) + Q dt dx dx

. .. (35)

254 INDIAN 1. CHEM. TECHNOL., SEPTEMBER 1999

where Q = Rate of heat release (W/m J ) from the car­

bonization reactions and calculated by Eq.(36) as, d Z W

Q = Po Wdof - - •. . (36) dl m J

where Q = Cumulative heat release at time t (J/kg, daf initial coal basis) and Wdaf = mass fraction of daf coal

in charge. The phys ical properties Po, C, K and Z were predicted by the mode ls described in section' dealing with model s for physical properties of coals.

The numerica l so lution of the heat conduction Eq. (35) can be obtained by using a modified Crank­Nicholson approximation as discussed below. Eq. (35) can be expressed in terms of diffusivities as shown in Eq . (37),

d T = ~ (D d T) d 1 + R d 1 . . . (37) d x d x Pc

Let the region of interest be considered to be divided

into n e lements of width &, if the temperature at the mid-po ints of each of these elements at TI ... Tn at

time 1 and 8 1 ... 8" at time 1 + I'1t, where I'1t is a small time increment, then Eq. (37) can be expressed as shown in Eq. (38),

8-T = lD;' +1 (8 i+1 - 8 i ) - Dii_1 (8 i - 8 i_1 ) J + Qi I'1t

, , & 2 /1'11 PiCi

(38) where Dii+ 1 is the average diffusivity of the i1h element between temperatures T; and Ti+1 and T ii.1 the average diffusivities of the succeeding element between tem­peratures T i . 1 and T i . Eqs (38) can be rearranged in the form as shown in Eq .(39) ,

where li = _Di i. 1 6.t/ t1./ mi = I + (Di

i.1 + Di i+l) 1'1//& 2 Il i = -Di

i+1 1'1//& 2

Pi = Ti + (1'11 Qi)/(PiC;) uC

... (39)

(40) (41)

(42) (43)

Eqs (40) to (43 ) can be written in matrix notation and so lved numerically fo r pred icting the charge tem­perature-time hi story. The computed results are shown for low volati le Jharia coal in Figs 8 and 9 lIsed fo r hi gh vo lati le Jharia coa l in Figs 10 and II .

The predicted charge temperature-time hi story and the di stri bution o f tempera ture within the charge at vari ous time interva ls exh ibit some main features like rapid hea ting of the charge to 1000°C and the tem­perature gradi en t reversa l towards the end of carboni­za ti on due to exotherm ic heat of reaction, which are

also exh ibited in experimental oven tests. The ex­trapolation of the curves indicates an excess of about 100-150°C in the temperature at the centre of the charge over wall temperature. The increment in tem­perature gradient between 700-900oe may also be partly due to decrement in the instantaneous specific heat of semi-coke in this range.

Conclusions Merrick's original PLil program 1 was converted to

Pascal and applied to one low volatile and one high volatile Jharia coking coal. The results lead to the following conclusions,

i) The rates of devolatilization reaches a maximum between 440-480oe , the increase in the volatile matter content of the coal being accompanied by an increase in the maximum rate of devolatilization and a de­crease in the temperature at which the maximum oc­curs. Beyond 500oe, the rates of devolatilization con­verge and in all cases the evolution of primary vola­tile matter appears to be complete by 600°e.

ii) The bulk density decreases from the onset of devo latil ization at 350°e.

iii) The true density increases from about 1250 kglm3 at 4000 e to about 2050 kglm3 at 1200°e.

iv) The instantaneous specific heat attains a maxi­mum value between 400-450°e.

v) The exothermic heats of reaction observed above 6500 e appear to result mainly from the forma­tion of methane.

vi) The thermal conductivities shows a linear in­crease in values from 0.2 W/mK at 400 K to about 3.8 W/mK at 1300 K .

vii) The charge temperature-time history obtained by a numerical sol ution of the unsteady state heat conduction equation shows the characteristic features obtained in experimental oven tests, like rapid Initial heating of charge to loooe and an increase in the temperature of the centre of the charge by about 100-150"e over the wall temperature on account of exo­thermic heat of reaction.

viii) High carbonizing temperatures increase the throughput (kg coke/mlh) by decreasi ng the coki ng period but it a lso increases the energy consumption (MJ/kg) due to increased heat losses. In programmed heating of coke ovens, the heat input to the heating flues is decreased at a contro lled rate throughout the coking period and charge centre temperature is not a llowed to exceed 1050°e. Such programmed heating systems can permit high throughput rates with high

POPAT & SUNAVALA: MATHEMATICAL MODELS FOR COAL DEVOLATILlZATION 255

carbonizing temperature with minImum heat energy consumptions.

Nomenclature C = instantaneou s specific heat of daf coal or coke (J/kg K) Ca = instantaneous specific heat of ash (J/kg K) Cm = instantaneous specific heat of charge corrected for moisture

and ash (J/kg K) C = carbon content of daf coal (mass fraction) d = true density of coal or coke (kg/m3

)

du = true density of daf coal or coke (kg/m3)

D = thermal diffusivity (m2/s)

D ;~: = effective thermal diffusivity between i'h and i+l'h elements

of charge (mlls) Di

i.1 = effective thermal diffu sivity between i_l'h and i'h elements of charge (mll s)

e = porosity of charge (volume fraction) emui, = volume fraction of charge occupied by moi sture (e), = porosity of charge at resolidification temperature (volume

fraction ) E = activation energy (J/kg mol) E(y) = Einstein function of y H = hydrogen content of daf coal (mass fraction) K = effective thermal conductivity for dry particulate charge be-

low or above resolidification temperature (W/m K) K cnaJ = thermal conductivity of coal (W/m K) Kcuke = thermal conductivity of coke (W/m K) Kga., = thermal conductivity of gas (W/m K) Kparl = thermal conductivity of particulate charge (W/m K) K,ad = contribution of radiation to thermal conductivity (W/m K) Kwe, = thermal conductivity of wet charge (W/m K) Kwa,c,= thermal conduct ivi ty o f water (W/m K) K" = reaction rate constant (S- I)

Ii = coefficient in Eq .(40) m = cumulative yield of volatile matter species per mass of daf

initial coal mi = coefficient in Eq .(4 1) m(CH4 ) = cumulative yield of CH4 per mass of daf initial coal m(CO) = cumulative yield of CO per mass of daf initial coal m(H2) = cumulative yield of H2 per mass of daf initial coal m" = final yield of volatile matter species per mass of daf initial

coal ni = coefficient in Eq. (42)

N = nitrogen content of daf coal (mass fractio n) o = oxygen content of daf coal (mass fraction) p = (I - e) in Eq. 42 Pi = coefficient in Eq.(43) Q = heat generated in i 'h element of charge (W/m3

)

R = gas constant (831.4 J/kg mol K) t = time (s) T = temperature ("C) Ti = temperature in i'h element at time t (0C) TK = temperature (K) Tmax = temperature at which maximum rate of devolatilization

takes place «(lC) (D, = resolidification temperature (OC) Wa = ash content (mass fraction) Wdaf = daf content of coal or coke (mass fraction) Wm = moisture content (mass fraction) x = distance from the oven wall (m) Y = yield of coke per mass of initial charge (mass fraction) Z = cumulative heat of reaction at time t (J/kg, daf initial coal

basis) . Zo = ultimate heat of reaction at time t~ (J/kg, daf initial coal basis)

P = charge bulk density (kg/m3)

P i = bulk density in i 'h element of charge (kg/m3)

Po = initial wet charge bulk density (kg/m3)

P odry = initial dry charge bulk density (kg/m3)

8i = temperature in i'h element of charge at time 1+ I1t (0C)

8i.1 = temperature in i_l'h element of charge at time I+l1t (OC) 8i+1 = temperature in i+l'h element of charge at time t+l1t (0C)

References I Merrick D, Metallurgical Coke Manufacture - A Mathemati­

cal Study, Ph.D. Thesis, University of London, 1977.

2 Fitzgerald D, Eighth Arthur Duckham Research Fellowship Report, Institution of Gas Engineers, London (1957).

3 Merrick D, Fuel, 62 (1983) 534.

4 Indian Coals, Vol. 2 - Jharia Coalfield (Central Fuel Re-search Institute, Dhanbad, 1978) 6, 89.

5 Ergun S, Mentser, M & Howard, H C , Fuel, 38 (1959) 495 .

6 Kirov NY, BCURA Monthly Bulletin, 29 (1965) 33.

7 Russell H W , JAm Cer Soc, 18 (1935) 1.

8 Millard D J, J Inst Fuel, 28 (1955) 345.