Empirical models for the rate of lignite liquefaction

Fuel Processing Technology, 4 (1981) 191--216

191

Elsevier Scientific Publishing Company, Amsterdam -- Printed in The Netherlands

EMPIRICAL MODELS FOR THE RATE OF LIGNITE LIQUEFACTION

SANDRA K. HALEY, JERRY A. BULLIN and RAYFORD G. ANTHONY Department of Chemical Engineering, Texas A&M University, College Station, TX 77843 (U.S.A.)

(Received July 7th., 1980; accepted October 20th, 1980)

ABSTRACT In this study, samples of Texas lignite were ground, sieved and charged with pure tetralin into a batch reactor. A fluidized sand bath was used to control reaction temperatures at 350, 375, and 400°C. Reaction times from 5 to 60 minutes were used. The times included a two-minute heat-up period. Reaction pressures, which were monitored with a pressure transducer connected to a chart recorder, varied between 2 and 15 MPa. Product gases were analyzed on a gas chromatograph and the product liquids were filtered, and analyzed by gel permeation chromatography. Lignite conversion, tetralin conversion to naphthalene, and the weight of gaseous product were calculated. Hydrogen gas was not charged to the reactor. Because of significant scatter in the data, both lignite conversion and tetralin conversion were cross-plotted to yield a set of smooth data. By using these data, numerous rate equations with concentration terms having integral exponents were fitted for rate constants and activation energies. The lignite conversion was described by rate equations which were second order with respect to lignite concentration and first or zero order with respect to tetralin concentration. Tetralin conversion rate models were first order in lignite, first order in tetralin; and second order in lignite, zero order in tetralin. Statistical tests indicated that these two sets of equations fit the data equally. The total gas production was fitted as a linear function of the reaction variables (time, temperature, pressure) and of the lignite and tetralin conversion.

SCOPE AND OBJECTIVES Previous studies [3--7, 9,13--15, 21,23, 25] on coal liquefaction ranged from bituminous to brown coals in solvents such as tetralin and hydrogenated creosote oil with and w i t h o u t catalyst. A number of researchers attempted to model their results and to predict product yields. This research used Texas lignite from the Wilcox formation. Previous dissolution studies were conducted with lignite, bituminous, and subbituminous coals mined in other states. The methods of analysis employed on the reaction products were different and considered more efficient than conventional methods. Rate models for a range of experimental conditions were developed to predict the conversions of tetralin and lignite. Finally, a new model to predict the grams of gas produced per gram of lignite charged was devised. 0378-3820]81/0000--0000/$02.50 © 1981 Elsevier Scientific Publishing Company

192

Results of this study, in particular the rate expression, could be used in the design of a suitable reactor for liquefaction of lignite to a useful fuel. Also, the information obtained will provide a basis for comparison of future research on the liquefaction of Texas lignite. EXPERIMENTAL

Experimental apparatus The liquefaction experiments were conducted in T-shaped reactors constructed of stainless steel, type 316. The main b o d y of the batch reactor is a 6 inch {15.2 cm) cylinder, 5/8-inch O.D. with Swagelok fittings on both ends. Midway along the cylinder extends 6 inches (15.2 cm) of 1/4-inch stainless steel tubing tapering to 18 inches (45.6 cm) of 1/8-inch stainless steel tubing. At the end of this tubing is a stainless steel T-joint with a gas sampling valve on the branched end and a Viatran pressure transducer (Model 103) attached to the top. The transducer, in turn, is connected to a Fisher Recordall (Series 5000) strip-chart recorder. The total void volume of the reactor system is estimated to be 17 ml. A diagram of the reactor and pressure transducer is ~

S

Viatran pressure ansducer

connected to strip chart recorder

w

. ~

\

gas--sampling vatve

18 in

1/8 in,OD

(1in= 2.54cm)

Fig. 1. T - r e a c t o r w i t h Viatran pressure t r a n s d u c e r .

193 presented in Fig. 1. The reactor configuration was obtained from Exxon Research and Engineering and was initially designed by Dr. P. Maa. A Techne SP 21 fluidized bath with a Techne TC4B temperature controller (Series 230) was used to heat the reactor and maintain a preselected reaction temperature. The bath was filled with Alundum 120. The composition of the gas produced was determined using a Carle analytical gas chromatograph (Model l l l H , Series S). A molecular sieve and a Porapak N were the two columns utilized. The chromatograph was coupled to a Hewlett-Packard (Model 3385A) automation system which was used for peak integration and data reduction. A complete description of the analysis of lignite-derived gases by automated gas chromatography has been reported by Philip et al. [17]. To separate the coal liquids into fractions, a gel permeation chromatograph (GPC) system was employed. This system consisted of a Waters Associate Model ALC/GPC 202 liquid chromatograph equipped with a Model R 401 refractometer, a UV detector, and two 100 A pStyragel columns. A Model UK6 injector was used to load a 200-#1 sample into the column. Distilled reagent grade tetrahydrofuran (THF) was used as the GPC solvent. Details on the separation of coal-derived liquids by the GPC are presented by Philip and Anthony [16]. A Gow-Mac gas chromatograph, Model 69-550, with thermal conductivity detectors was used in the analysis of the coal liquid fractions. The oven temperatures were manually programmed and commercially available helium was purified and used as the carrier gas.

Preparation of lignite The lignite utilized in this study was obtained from Freestone County in Central Texas. An analysis of the lignite was performed b y Agricultural Analytical Services of Texas A&M University. The results are presented in Table 1. Before the experimental runs, lignite samples were ground and sieved through 100 mesh net in a glovebox containing a water-saturated argon atmosphere. Moisture and ash analyses were performed each time a new lignite sample was ground. The results of these analyses are shown in Table 2.

Experimental method An undried ground sample of the lignite in a one to one ratio (by weight) with the solvent, technical grade tetrahydronaphthalene (tetralin) was charged into a T-shaped batch reactor. An additional 0.92 g of tetralin was added to o c c u p y the dead space in the 1/4-inch and 1/8-inch tubing extending above the cylindrical part of the reactor. This added tetralin was not in contact with the lignite so it was n o t considered in the weight of tetralin charged as a reactant. A pressure transducer connected to a chart recorder was

194 TABLE 1 Lignite analysis [ 2 ] BTU/lb. (MFB) a

H~O (Wt. %)

S (MFB) (Wt. %)

Ash (MFB) (Wt. %)

7,530 7,650

29.3 29.2

1.6 1.4

27.2

ASHb Weight % Na~ O

Ass 03

CaO

Fe2 03

SiO2

NiO

A1203

1.1 0.8

0.0014 0.0013

3.7 3.3

3.6 3.0

48.5 49.6

0.02 0.01

34.4 33.4

aMFB -- Moisture Free Basis. bMetal oxides formed by oxidation of mineral matter in lignite; reported as percent metal in ash. TABLE 2 Moisture and ash analyses of ground lignite Experimental runs

H20 (Wt. %)

Ash (WB) a (Wt. %)

Ash (MFB) b (Wt. %)

31a--44 58--68 71--75 1S--94 96--102

19.7 23.0 18.1 25.2 22.0

24.5 36.0 38.1 32.7 31.2

30.5 46.7 46.5 43.7 40.0

a WB -- wet basis. bMFB moisture free basis. Runs 31a--44 lignite was ground in a water-saturated air atmosphere. Runs 58--102 lignite was ground in a water-saturated argon atmosphere. -

-

a t t a c h e d t o the r e a c t o r in o r d e r t o r e c o r d the pressure t h r o u g h o u t the reaction. In m o s t of the e x p e r i m e n t a l runs, the r e a c t o r was p u r g e d with argon b e f o r e being securely sealed and l o w e r e d into the t e m p e r a t u r e - c o n t r o l l e d fluidized sand bath. The r e a c t o r was n o t agitated d u r i n g reaction. A f t e r a pre-selected r e a c t i o n time, the r e a c t o r was r e m o v e d f r o m the sand b a t h and l o w e r e d i n t o a q u e n c h d r u m c o n t a i n i n g water. A f t e r pressure within t h e r e a c t o r had stabilized, a gas sample was t a k e n and a n a l y z e d on the Carle GC gas c h r o m a t o g r a p h . T h e final pressure in the T - r e a c t o r at r o o m temperature p e r m i t t e d t h e moles o f gas p r o d u c e d to be calculated. Figure 2 diagrams the p r o c e d u r e . T w o d i f f e r e n t p r o c e d u r e s were used in the separation and analysis o f the

195 I LignitiSample ]

I Technical Tetralin Grade 1

I sampleground & seived 1 moisture & ash analysis performed

I sample & I chargedweighed to reactor

i

I sample & J chargedweighed to reactor

' p....... t....d.... ' I lattached & reactor flushedwith argon

½ reactor loweredinto sandbath

reactiontemperature,pressure and time recorded

reactor quenched

reactor pressure at room tempera-

!

|

ture noted

total moles of I1 gas calculated

I .lyzedgas sampleon ana- I GC

'liquid-solidproducts

eparated & analyzed I

I ligniteconversion calculated I

I

tetralinconversion I calculated

Fig. 2. Liquefaction experimental procedure.

solid--liquid products. In runs numbered 31a--66, the solid and liquid residues were flushed out of the reactor with tetrahydrofuran (THF) into a cellulose thimble. The residues were then extracted in a soxhlet extractor with THF for three to six hours. The weight of the solid residue was determined and a moisture analysis performed. The liquids remaining in the THF solution were rotary-evaporated to remove the solvent. All volatiles were also removed. The residue was vacuum sublimed to 260°C. The remaining portion was mostly tar while the sublimed portion consisted of products having a boiling point of less than 500°C. These were considered the high-boiling point liquids in this study. These liquids were analyzed using a SP 2100 column on the Gow-Mac gas chromatograph with temperature programming. From the results of this analysis, the conversion of the tetralin to naphthalene was calculated. A schematic of this procedure is presented in Fig. 3. In runs numbered 6"/--102, the liquid and solid residues were scraped from

196

the reactor into a 2 ml course, flitted-glass funnel and suction-filtered. The recovered liquids were further filtered through a 0.5 p m Milipore filter. Gel permeation chromatography separated the filtrate into three fractions: the nonvolatiles, the high-boiling point liquids and the tetralin/napthalene portion The first fraction was discarded while the high-boiling point liquids and the tetralin/naphthalene fraction were analyzed on the SP 2250 and the SP 2100 columns of the Gow-Mac gas chromatograph, respectively. From these analyses lignite conversion to liquids and tetralin conversion to naphthalene were calculated. Figure 4 shows a flow chart of this procedure. A total of forty-eight experiments were performed: thirty-seven at 400°C, six at 350°C and five at 375°C. Reaction times ranged from 5 to 60 minutes including an estimated 2 minute heat-up period. The reaction pressure was roughly predetermined (less than 8 MPa, 8 to 12 MPa, or greater than 12 MPa) by the amount of lignite charged to the reactor. Resulting lignite conversion varied between 1 and 73 percent, while tetralin conversion to naphthalene ranged from 1 to 37 percent. Gas production varied from 0.03 to 0.09 grams per gram of lignite charged. These data are presented in Table 3.

Liquidand Solid[ Products ] i placedin cellulose I thimbl....tracted withTHF ~r

~--]' rotaryevap°ratedll

w~hed~

I~oist......lysis'I ihigh,b.p. liquidsI IvolatilesI porf.... d

[

II

andtar+

ligniteconversion] calculated [ I

Iisublimed ~

Jland++l

I

tetralin conversion calculated Fig. 3. Procedure for separation and analysis of solid-liquid products in runs 31a--66.

197

Liquld and Solid . Products

---~suctlon-filtered

~r

, ~

resJ~

~r

non-volatiles

high

b,p.llquids

[lignite conversion[ | calculated I ]p*oduct distribution II tetrali........ ion I [ ....ined II calculated ] Fig. 4. Procedure for separation and analysis of solid-liquid products in runs 67--102.

TABLE 3 E x p e r i m e n t a l d a t a used in m o d e l l i n g Run No.

31a 31b 32a 32b 32c 33a 33b 34 41a 4tb

Rxn time (rain)

13 23 13 13 23 3 3 23 13 58

Mean rxn press (MPa) 2.97 2.94 2.45 4.62 5.54 1.86 3.44 4.74 5.37 6.22

XL

0.193 0.238 0.104 0.221 0.300 0.010 0.030 0.315 0.306 0.500

ZT

0.098 0.130 0.104 0.111 0.134 0.056 0.030 0.134 0.108 0.239

C Lo

C To (g/g)

G/W~

(g/g)

0.401 0.384 0.358 0.353 0.350 0.531 0.365 0.358 0.356 0.364

0.599 0.616 0.642 0.647 0.650 0.469 0.635 0.642 0.644 0.636

0.0724 0.0767 0.0736 0.0505 0.0554 0.0710 0.0425 0.0571 0.0439 0.0798

(g/g)

198 42a 42b 43a 43b 44 58 59 60 61 63 64 65 66 67 68 71 75 a 1S a 77 2S a 3S a 82 4S a 85 86 5S a 87 88 90 92 93 94 96 98 99 100 102

58 58 58 23 3 58 3 13 13 58 13 23 58 3 58 33 43 33 43 13 33 43 33 43 43 43 43 58 3 58 33 43 58 33 43 13 23

4.55 3.98 6.66 8.71 4.84 12.8 10.2 14.7 11.6 10.2 9.90 9.79 8.58 6.35 9.20 8.83 11.8 9.76 11.4 15.9 13.4 10.3 6.70 6.10 6.99 12.1 8.10 10.0 7.19 7.60 10.5 8.10 7.80 7.29 7.60 10.1 12.1

0.400 0.446 0.456 0.388 0.124 0.721 0.331 0.568 0.607 0.665 0.579 0.742 0.701 0.755 0.460 0.501 0.931 0.589 0.578 0.557 0.505 0.504 0.381 0.272 0.512 0.185 0.432 0.139 0.518 0.312 0.229 0.419 0.378 0.355 0.237 0.289

0.214 0.217 0.194 0.149 0.054 0.184 0.031 0.154 0.140 0.266 0.214 0.234 0.264 0.070 0.269 0.213 0.186 0.368 0.156 0.161 0.137 0.151 0.130 0.143 0.060 0.147 0.023 0.089 0.008 0.151 0.055 0.039 0.106 0.081 0.094 0.046 0.064

0.350 0.351 0.356 0.336 0.357 0.304 0.291 0.291 0.289 0.288 0.292 0.293 0.291 0.309 0.302 0.301 0.303 0.301 0.303 0.312 0.297 0.295 0.287 0.295 0.296 0.291 0.295 0.293 0.297 0.297 0.294 0.292 0.317 0.321 0.320 0.329 0.320

0.650 0.649 0.644 0.664 0.643 0.696 0.709 0.709 0.711 0.712 0.707 0.707 0.709 0.691 0.698 0.699 0.697 0.699 0.697 0.688 0.703 0.705 0.713 0.705 0.704 0.709 0.705 0.707 0.703 0.703 0.706 0.708 0.683 0.679 0.680 0.671 0.680

Reaction temperature: Runs 31a--87 400°C Runs 88--94 350°C R u n s 9 6 - - 1 0 2 375°C

XL XT

= c o n v e r s i o n o f lignite t o liquids

= c o n v e r s i o n o f t e t r a l i n to n a p h t h a l e n e = initial c o n c e n t r a t i o n of lignite (g lignite (m.a.f.)/total g) C~: = initial c o n c e n t r a t i o n of t e t r a l i n (g t e t r a l i n / t o t a l g) T o t a l g= grams t e t r a l i n + grams lignite (m.a.f.) c h a r g e d t o r e a c t o r = w e i g h t o f gas p r o d u c e d at 24°C/.weight o f lignite c h a r g e d (m.a.f.) a R u n s m a d e b y S a n d r a Haley; o t h e r s were m a d e by Peggy Moede.

C~

G/W°L

0.0834 0.0967 0.0484 0.0313 0.0420 0.0570 0.0432 0.0742 0.0619 0.0741 0.0587 0.0683 0.0681 0.0464 0.0917 0.0686 0.0942 0.0525 0.0526 0.0540 0.0772 0.0637 0.0588 0.0583 0.0459 0.0648 0.0376 0.0476 0.0327 0.0586 0.0422 0.0316 0.0505 0.0422 0.0519 0.0524 0.0348

199

CROSS-PLOTTING THE DATA The lignite and tetralin conversions were cross-plotted in order to smooth the data which showed significant scatter. The scatter was apparently caused by the heterogeneous nature of lignite. Lignite and tetralin conversions were plotted as a function of the mean reaction pressure as shown in Figs. 5 and 6. Smooth curves were drawn through the points and, at five reaction pressures, conversions were read from the smooth curves at each reaction time. These conversions were plotted against the reaction time for each selected pressure. Again, smooth curves were drawn through the points, as in Figs. 7 and 8. Next, conversions were read from these plots at each reaction time, and for the same five reaction pressures and replotted onto the conversion--pressure graphs. The final smooth curves were drawn and a set of internally consistent smooth data were selected for use in future modelling. The data were smoothed by inspection and the use of french curves.

90

Q

3 rain

~13 C) 23 80

D 58 initial curve final

70

~

curve

WI

_~ x ~

u.J

0 o w I-

40

oJ

71

2

4 MEAN

1

J"

6

8

REAC11ON

PRESSURE ,

1

I

10

12

MPa

Fig. 5. Cross-plot o f lignite c o n v e r s i o n at 4 0 0 ° C .

4--

8-

12

16--

~

1

-

-

1

MEAN

.~-----~/

G

REACTION

I 4

i

Q

2

~

.

curve

final

[ ] 58 __ __ initial curve

~

I

~

0

~

~

~ ~

[]

~

80 -

I 6

8

~

I

®

~

10

PRESSURE , MPa

®

[]

12

I

~

10

20

30

40

s0

-

I 10

REACTION

20

[

[ ] 12.2

I TIME,

30

i min

40

I 50

Fig. 7. Smoothed lignite conversion at 400°C

z

uJ

0

->

~

0

60

70

O10.1

8.1

,~

4.1 MPa

(~ 6.1

~

O 23

3 min

A13

Q

Fig. 6. Cross-plot of tetralin conversion at 400°C.

~-

<

z

u

o

--

24 --

~z 20

z"

28

32 --

36 --

I 60

O 0

201

<~ 4.1 MPa

32

0

6.1

A

e.1

~ 10.1 f;'112.2

28

-~ O O

20--

z_ ~

16

12

8

4

10

20

30

REACTION TIME

40

50

60

rain

Fig. 8. S m o o t h e d tetralin c o n v e r s i o n at 400°C. MODEL DEVELOPMENT

The integral method of analysis as described by Holland and Anthony [10] was used in the development of kinetic models to describe the reaction behavior of both lignite and tetralin. Two general forms for these models were assumed as follows.

C~L dXL/dt = k, Cia I CT b'

(1)

and

C~ dXT/dt = h2 Ci~' CTb2

(2)

Dividing eqn. (1) by eqn. (2) yields 0

C L dXL 0

C w dZT

where

-

k

CI~ CTb

(3)

202 k = k~/k2 a

=

a 1 -a

2

b = bl-b2

Equation (3) may also be written in terms of the conversions C~ dX L

- k C~a C~ b (1 - X L ) a (1 - X T ) b CT d Z T .

(4)

After variables separation and rearrangement, (5) is obtained (1 - X L ) -a d X L

=

C~a-1 ~Wf'°b+l (1 - X T ) b dX T

(5)

Various combinations of -2, - 1 , 0, 1 and 2 for a and b were assumed and eqn. (5) was integrated to give a series of models relating the conversion of lignite to the conversion of tetralin. Each model was analytically integrated, linearized, and the relative rate constant, k was evaluated. The rate constant is a function of pressure as well as the initial concentrations of the lignite and tetralin. SAS (Statistical Analysis Systems) was employed to fit all models to the smoothed data. After fitting, the models were rearranged to the form: X T = f(XL)

(6)

and a set of predicted XT'S was generated for each experimental run at 400°C. Statistical tests as described by A n t h o n y [1] were performed on each model in order to discriminate between the degrees of fit. The four tests utilized were: (1) sum of squares, (2) significance of regression, (3) lack of fit, (4) correlation coefficient. In the first test, the sum of squares, SS, was calculated as n

SS = E (ZT, cal - Zw, exp )2 i=1

(7)

where n equals the number of data points. A criterion for passing this test was arbitrarily set based on an estimate of the scatter of the data. Significance of regression tests the hypothesis that all of the parameters in the model are equal to zero. This Freg value is determined as n

i=1

(8)

Freg = n

(XT, ex p - XT, c a l ) 2 / ( n - p i=I

l)

203 where X T is the average of all experimental X T values and p equals number of parameters. If Freg is larger than the table value selected, then the hypothesis is rejected. As expected, all models passed this test. The lack of fit test is probably the most discriminating and, therefore, the most useful of the four tests considered. It tests the Hypothesis that the model is adequate (i.e. more terms are not required). The value to be calculated is, Flof =

-

- 02

-kr)

/(kr-p-1)o 2

(9)

where kr = number of replicate experiments and 0 2 = variance of pure error associated with X T. If Flo f is less than the table value, then the hypothesis is not rejected. The final test involves the determination of R 2, the correlation coefficient. It is defined as R 2 = ~ (XT, ca1 - ,YT) 2

(XT, exp - .~T) 2

(10)

i=l In this analysis, an R 2 greater than 0.80 was considered adequate (1.0 is a perfect fit). Due to the scatter in the experimental data an R 2 greater than 0.90 would be impossible to achieve with the simple models that were considered. Upon obtaining a set of satisfactory rate models based on ratios, a series of lignite rate models were analyzed. Equation (1) is the general form for the lignite rate model. Since the conversion of tetralin can be expressed as a function of the conversion of lignite, eqn. (1) can be written in terms of lignite conversion

C~ dXL/dt = kl C~a' C~b' (1 - XL) al (f(XL)) bl

(11)

Rearrangement of this equation yields

(1 - xt,)-°, (f(XL))b ' dX L = h, C~a'

_,

c 6,

dt

(12)

Combination of values of - 2 , - 1 , 0, 1 and 2 were tested on a~ and b~. Each of the best rate models was used to express f ( X L). Once substituted, eqn. (12) was analytically integrated to give an expression for lignite conversion in terms of time. Next, the expression was linearized and least squares utilized to determine the rate constant, k 1, as a function of the reaction pressure. For each lignite model considered, the rate form was numerically integrated for each experimental run at 400°C to produce a set of predicted lignite conversions. The same statistical tests were performed and the best models selected. To promote further discrimination (1) data at other temperatures were added and

204

(2) initial concentrations of lignite and tetralin were included. Curve-fitting was performed on experimental data rather than smoothed data. The smoothed data had assumed constant initial concentrations for lignite and tetralin. The best rate models based on ratios and the better lignite rate models were refitted and retested. Since data at other temperatures were added, the relative rate constant, k, and the lignite rate constant, kl, had to be evaluated as functions of the reaction temperature as well as the reaction pressure. Tetralin rate equations were then developed. Two approaches were used. In the first, the tetralin rate model was estimated by dividing the best lignite model by the ratio model, that is dXT = dXL/d~t dt dXL/dX w

(13)

The resulting tetralin models were integrated and statistical tests were performed. The second approach was similar to the method employed in determining the lignite rate models. Equation (6) was rearranged to obtain XL : f(XT)

(14)

and then substituted into eqn. (2) to obtain

C~, d X T / d t

= k2 C~,a: C~b2 (f(Zw)) a* ( 1 - Z w ) b2

(15)

As in the lignite rate development, combinations of - 2 , - 1 , 0, 1, and 2 were selected for a2 and b2 while the rate constant, an exponential function of reaction temperature and of mean reaction pressure, was fitted. For a set of (a2, b2 ) eqn. (15) was integrated and rearranged to solve explicitly for the rate constant k. The functional form for k was substituted and the equation linearized by use of logarithms. DISCUSSION OF RESULTS

The method employed in this study to develop rate equations involved dividing the rate equation for lignite by the rate equation for tetralin to obtain a ratio rate model interrelating these two components parametrically. Figure 9 illustrates this relationship for the smoothed data which was used in curvefitting the ratio models. The five best models were selected and re-fitted using the actual experimental data at all three reaction temperatures. The parameter associated with the reaction pressure was n o t re-fitted (i.e. the value resulting from the smoothed data was retained). Table 4 contains the results of the re-fits (with criteria for S S and R 2 being 0.05 and 0.85, respectively). Model 12 is the best model with Model 1 the second best. Model 12 indicated a linear relationship between the conversions of lignite and tetralin, which was not observed in Fig. 9. Figure 10, however, suggests a

8

1 12

1 16

[ 20

1 24

I 28

CONVERSION, %

Fig. 9. Smoothed lignite-tetralin relationship.

TETRALIN

o

~

4

0 1

0

l

I 12

I 16

TETRALIN CONVERSION, %

8

O ~/

I

20

I

/

I 24

Fig. 10. Experimental lignite-tetralin relationship.

20--

_~ 3o

~ 50

~

6o

g

_

I

~

,o

80

8.7-12.2

1.5--5.1 MPa 5,2--8.6 /

4 r~ 12.3 --15.7

3~ 80

6.1

~ 8.1 I m10"1 1~12.2

A

10 2A

(~ 4.1 MPa

. /|

b~ O O1

206

TABLE 4 Ratio rate models with temperature dependence General form of model d X L / d X w = k (1 -XL) a ( 1 - X T ) b where k = k 0 exp(APn) expB(1]T-1/Ta ) Model No.

a

b

ko

al

0

1

2

0

-1

3

1

1

8

1

1

a12

0

0

1.78 -+0.36 1.64 ±0.34 1.77 ±0.38 1.63 -+0.34 1.70 -+0.35

A

0.649 -+0.216 0.517 ±0.277 1.12 -+0.21 0.989 -+0.260 0.588 ±0.213

B

7436 ±1741 8521 ±1803 5985 ±1810 7069 -+1799 7963 -+1765

#1

Freg Flo f #2 #3

R2 #4

Test # passed

0.0522

287

2.16

0.864

2,3,4

0.0521

219

2.16

0.830

2,3

0.1160

197

5.04

0.814

2

0.0792

251

3.40

0.848

2,3

0.0494

259

2.03

0.852

1,2,3,4

SS

aBest models. Pn = mean reaction pressure (MPa)/12.2 TO = 673.15 K; T = reaction temperature, K freg (97.5% confidence table value) = 5.4 Flo f (97.5% confidence table value) = 3.8 S S - based on tetralin conversion (difference between experimental and calculated values) Note: Curve-fitting was performed with experimental data, holding the value of A constant at the value determined with smooth data. linear relationship w h e n the conversions for the actual e x p e r i m e n t a l data are plotted. F o r this reason, b o t h Models 12 and 1 were used t o p r e d i c t tetralin c o n v e r s i o n in the s u b s e q u e n t curve fitting o f the lignite rate equations. T h e lignite rate m o d e l s were f i t t e d using the s m o o t h e d d a t a first and t h e n the e x p e r i m e n t a l data. As with the ratio models, the p a r a m e t e r on pressure o b t a i n e d in the s m o o t h e d - d a t a fits was r e t a i n e d while t h e p a r a m e t e r on temp e r a t u r e a n d t h e rate c o n s t a n t were fitted. F o r b o t h s m o o t h e d and experim e n t a l data, the s a m e t h r e e lignite rate m o d e l s a p p e a r e d b e t t e r t h a n the others. Table 5 c o n t a i n s a selection o f the lignite rate m o d e l s c o n s i d e r e d with Models 2, 3, and 6 n o t e d as the best. The criteria f o r S S and R 2 are 0.8 and 0.71, respectively. Tetralin rate e q u a t i o n s were curve-fitted in a similar m a n n e r , a n d the results are s h o w n in Table 6. Based o n S S criterion o f 0.15 and R 2 criterion o f 0.71, the best m o d e l s were 4 a n d 14. It m u s t be n o t e d t h a t in Tables 6 - - 1 0 , t and Pn are n o r m a l i z e d variables. The variable t was n o r m a l i z e d b y dividing t h e r e a c t i o n time by the m a x i m u m r e a c t i o n time o f 58 minutes. Similarly, Pn was n o r m a l i z e d b y dividing the m e a n r e a c t i o n pressure b y the m a x i m u m m e a n r e a c t i o n pressure o f 12.2 MPa based on s m o o t h e d data.

207 TABLE 5 Lignite rate models with initial concentrations and temperatures General form of model C~ dXL/dt = k I eL al Cw bl where k I = k01 exp(AiPn) exp[B x( 1 / T - 1 / T o ) ] Model No.

aI

b~

1

1

0

a2

2

0

a3

3

0

4

1

1

a6

2

1

8

1

2

12

0

1

14

0

2

lnk01

-0.823 _+0.250 0.143 _+0.295 1.10 "_+0.38 b-0.243 _+0.248 c-0.307 _+0.495 0.726 -+0.297 0.339 -+0.249 -1.22 _+0.24 -0.641 -+0.241

A~

1.52 -+0.35 2.31 _+0.41 3.19 _+0.53 1.40 _+0.34 1.44 +0.58 2.20 -+0.41 1.27 _+0.34 0.692 _+0.333 0.556 _+0.333

B~

-6360 _+2243 -7664 _+2650 -9365 -+3441 -7348 _+2228 -6983 -+2543 -8748 -+2665 -8363 _+2232 -6396 _+2165 -7308 -+2163

#1

Freg Flof #2 #3

R2 #4

Test #'s passed

1.04

107

22.6

0.704

2

0.771

113

16.7

0.716

1,2,4

0.691

111

15.0

0.711

1,2,4

0.940

112

20.4

0.713

2,4

0.950

111

20.7

0.711

2,4

0.714

118

15.5

0.724

1,2,4

0.862

115

18.7

0.719

2

2.08

91

45.0

0.669

2

1.75

95

38.0

0.679

2

SS

a Best models bUsing #12, Table 3 c Using #1, Table 3 Pn = mean reaction pressure (MPa)/12.2 t = reaction time (min)/58.0 CO= initial concentration of reactant, g/g T = reaction temperature, K T O= 673.15 K Freg (97.5% confidence table value) = 5.4 Flo f (97.5% confidence table value) = 3.8 Note: Models 6--14 were fit using Model 12, Table 4. Note: Curve-fitting and statistical tests are based on the experimental data. Table 7 c o n t a i n s a s u m m a r y of the best lignite, tetralin, and ratio models d e v e l o p e d i n t h i s s t u d y . N o t e , if M o d e l 6 f o r l i g n i t e a n d M o d e l 1 4 f o r t e t r a l i n are d i v i d e d , t h e n t h e f o r m o f r a t i o M o d e l 1 is o b t a i n e d . S i m i l a r l y , if M o d e l 2 f o r l i g n i t e a n d M o d e l 1 4 f o r t e t r a l i n are d i v i d e d , t h e r a t i o M o d e l 1 2 is o b tained. Ratio Model 8 c o n s i d e r e d a good fit previously, occurs w h e n Model 2 f o r l i g n i t e is d i v i d e d b y M o d e l 4 f o r t e t r a l i n . T h e a v e r a g e a n d m a x i m u m deviations between the experimental and the predicted conversions for the lignite a n d t e t r a l i n m o d e l s are s h o w n i n T a b l e 7. T h e s e d e v i a t i o n s d o n o t i n c l u d e t h o s e d a t a p o i n t s j u d g e d as " b a d " b a s e d o n m a x i m u m d e v i a t i o n f r o m t h e s m o o t h c u r v e s . T h e p r e s u m p t i o n is t h a t t h e d e v i a t i o n w a s r e l a t e d t o e x p e r i -

208 TABLE 6 T e t r a l i n rate m o d e l s w i t h initial c o n c e n t r a t i o n s a n d t e m p e r a t u r e s General f o r m o f m o d e l

C~ dXT /dt = k~ CLa~ CT b2 w h e r e k ~ =k0~ e x p ( A 2 P n ) e x p [ B 2 ( 1 / T - 1 / T 0 ) ] Model No.

a~

b2

1

0

1

2

0

2

3

0

3

a4

1

1

6

1

2

8

2

1

12

1

0

a14

2

0

lnk02

-0.933 -+0.233 -0.359 ±0.231 0.215 ±0.242 0.0318 ±0.244 0.993 ±0.347 0.607 ±0.253 -0.541 -+0.237 0.418 ±0.337

A2

B2

-0.0459-13103 ±0.308 ±2000 -0.171 -13970 -+0.319 ±2074 -0.295 -14866 ±0.334 ±2167 0.629 -12397 -+0.338 ±2198 1.42 -11323 -+0.48 -+3127 0.513 -13282 ±0.351 ±2279 0.747 -11535 ±0.329 ±2137 1.52 -10400 ±0.467 ±3034

SS #1

Freg #2

Flo f #3

R2 #4

Test # ' s passed

0.241

90.0

10.7

0.669

2

0.206

92.7

9.2

0.673

2

0.183

93.4

8.1

0.675

2

0.143

86.2

6.3

0.657

1,2

0.316

38.5

14.2

0.461

2

0.453

67.8

20.4

0.601

2

0.158

85.7

7.0

0.656

2

0.134

73.6

5.9

0.620

1,2

aBest models Pn = m e a n r e a c t i o n pressure ( M P a ) / 1 2 . 2 t = reaction time (min)/58.0 C o = initial c o n c e n t r a t i o n o f r e a c t a n t , g/g T = reaction temperature, K To = 673.15 K Freg (97.5% c o n f i d e n c e t a b l e value) = 5.4 Flof (97.5% c o n f i d e n c e t a b l e value) = 3.8 N o t e : M o d e l s 4 - - 1 4 were fit using M o d e l 12, T a b l e 4. N o t e : Curve-fitting a n d statistical tests are b a s e d o n t h e e x p e r i m e n t a l data.

mental error. The statistical tests in Tables 4--6, however, were run on all experimental data points resulting in the low R 2 values and the failure of m a n y of the lack-of-fit tests. If the five worst data points for lignite and the five worst data points for tetralin are removed from the statistical analysis, then R 2 terms increase to those listed in Table 7. Figures 11 and 12 are the scatter plots for lignite Model.6 and tetralin Model 4. These predicted versus experimental plots show a scatter of points about a 45 ° line, indicating the models selected appropriately describe the data. Error bands of 7 and 5 percent have been drawn in Figs. 11 and 12, respectively. These error bands represent, with 95 percent confidence, the expected deviation of the conversions due to pure (or experimental} error. These deviations were determined from the results of one set of three replicate experiments and three sets of two replicate experiments.

209 TABLE 7 Best kinetic models

Ratio Models:

dXL/dX T

Average deviation

Maximum deviation

Table 4 # 12:

dXL - k dX w

1.8%

5.1%

Table4 #1:

dX L - k(1-Xw) dX T

1.9%

5.5%

Lignite Rate Models:

dXL/dt

Table5 #6:

o dXL 02 o C L dt - k~ C L C T (1-- XL )2 ( 1 - XT)

Table5 #2:

0 dXL 05 C L dt - kl CL ( 1 - X L ) 2

Tetralin Rate Models:

dXw/dt

o dXT o Table 6 # 4! C T dr- ks C L C°T(1-XL)(1-XT) Table 6 # 14: C~ dXT 05 d ~ - - = ks CL (1-XL)2 Model Table Table Table Table

R2 5 5 6 6

# # # #

6 2 4 14

0.829 0.818 0.814 0.785

aAverage deviation 7.53% 7.97% 3.14% 3.03%

Maximum deviation 21.0% 22.3% 7.7% 7.6%

aAverage deviation refers to expected error on predicted values of the conversion. For example, in Table 5 # 6, the lignite conversion predicted would be (X L cal × 100) -+ 7.53 percent. The rate constants and activation energies determined for the lignite and t e t r a l i n r a t e e q u a t i o n s a r e c o m p a r e d t o l i t e r a t u r e v a l u e s in T a b l e 8. T h e l i g n i t e rate constants obtained in this study are significantly larger than the others tabulated, suggesting a possible catalytic effect due to the mineral matter contained in Texas lignite. In the cases of Maekawa [12] and Shalabi [22], kinetics considered were first order parallel mechanism. The rate constants for these parallel reactions were added and then recorded. The tetralin rate c o n s t a n t s f o r M o d e l 4, s h o w n in T a b l e 6 c o m p a r e f a v o r a b l y w i t h t h o s e o f Potgieter [19] who used a catalyst. T h e a c t i v a t i o n e n e r g i e s f o r b o t h l i g n i t e a n d t e t r a l i n r a t e m o d e l s a r e in t h e s a m e r a n g e as t h o s e r e p o r t e d b y o t h e r i n v e s t i g a t o r s , in p a r t i c u l a r , W i s e r [ 2 4 ] a n d G u i n [ 8 ] . W i s e r ' s e x p e r i m e n t a l s y s t e m w a s s i m i l a r t o t h e o n e in t h i s s t u d y . G u i n u t i l i z e d c r e o s o t e oil, r a t h e r t h a n t e t r a l i n , as a s o l v e n t .

40

•

-'

/

10

/'.

/

/

20

/

o/

LIGNITE

/

/

"/

•

/ /

/

/•

40

/ /

CONVERSION--exp,

30

/

/' /

/

"/

~

%

"

/

/

50

./ /. •

•

/

/

60

" /

"////

• "// •

I

Fig. 11. S c a t t e r p l o t for lignite rate m o d e l 6, Table 5.

10

~ 3o

~-

~.

I

so

so

70

80

70

/

4

[/~

8•

/~ /

;

I 12

/

"/

•

~//~

16

I

:///

I 20

/

CONVERSION-- exp, %

"...

TETRALIN

I 8

I /

/.

4

• ,

///'~.'"/ / •

/

/

/

"Y

./"

0~"

/

"Y

/

I 24

•

"/ /

Fig. 12. S c a t t e r p l o t for t e t r a l i n rate m o d e l 4, Table 6.

~

~~

t)

~=

16

= 12 o

-~

]

-

~,2o-

24

2a

pa o

211 TABLE 8 Comparison of rate constants and activation energies to literature values Source

Order of rate eqn.

Rate constants (min -~) Lignite

Table 4 # 6 Table 4 # 2 Table 5 # 4 Table 5 # 14 Liebenberg and Potgieter [ 11 ] Maekawa [ 12 ] (k, + k~) Shalabi [ 22 ] (k, + k~ + k3) Potgieter [ 19 ] (cobalt-oxide catalyst)

3 2 2 2

Source

Order of rate eqn.

Tetralin

11 MPa

16 MPa

0.266 0.16

0.646 0.415

1 0.0184

1

0.144

1

0.0372 0.157

0.042

0.043

Activation energies (kJ/mol) Lignite

Potgieter [ 19 ]

0.0311 0.101

0.023

1

3 2 2 2 1 1 2 1 1

14.3 MPa

0.0039

1

Table4 # 6 Table 4 # 2 Table5 # 4 Table 5 # 14 Shah [20] Wiser [ 24 ] Wiser [24 ] Guin [8] Potgieter [ 19 ]

10.8 MPa

Tetralin

72.8-+11 63.6 -+11 103 e9.2 86.6 +_12.7 192 65.3 120 87.9 (stannous chloride catalyst) (cobalt oxide catalyst)

55 142

T h e m e t h o d e m p l o y e d in d e v e l o p i n g t h e lignite a n d t e t r a l i n r a t e m o d e l s was more efficient than other methods attempted. By smoothing the data, good approximations for the best models and their corresponding rate cons t a n t s w e r e o b t a i n e d . T o j u s t i f y t h e s m o o t h i n g , all statistical tests w e r e b a s e d o n h o w well t h e m o d e l s fit t h e t r u e e x p e r i m e n t a l d a t a . B y f i n d i n g a r e l a t i o n s h i p b e t w e e n lignite c o n v e r s i o n a n d t e t r a l i n c o n v e r s i o n , t h e r a t e m o d e l s w o u l d be a n a l y t i c a l l y i n t e g r a t e d a n d t h e n c u r v e - f i t t e d . T h i s t e c h n i q u e w o u l d w o r k e q u a l l y well w i t h m o r e t h a n t w o c o m p o n e n t s , p r o v i d i n g t w o o f t h e c o m p o n e n t s are i n d e p e n d e n t . T h i s w o u l d c o r r e s p o n d t o a parallel m e c h a n i s m in w h i c h o n e r e a c t a n t f o r m s several p r o d u c t s . A p o s s i b l e r e a c t i o n s e q u e n c e f o r t h e l i q u e f a c t i o n o f lignite is c o n s i d e r e d t o be t h r e e parallel r e a c t i o n s in w h i c h c o a l f o r m s gases, oils a n d a s p h a l t e n e s .

212 TOTAL GAS PRODUCTION

The produced gases in the liquefaction runs were analyzed on a Carle GC gas chromatograph. A standard gas mixture was used to calibrate the chromatograph in order to convert areas on the chromatograph to gas composition. The major component in the gas produced, for all of the experimental runs, was carbon dioxide. On an oxygen, argon, nitrogen-free basis, the gas produced contained between 45 and 85 percent carbon dioxide. Other components included hydrogen, carbon monoxide, methane, ethane, ethylene, propane, propylene, and trace amounts of hydrogen sulfide. In some of the experiments, butanes and butylenes were also detected in trace quantities. Before modelling, the weight of gas produced was divided by the weight of lignite (maf) charged to the reactor. The weight of lignite charged varied considerably from run to run and normalization was used to determine the a m o u n t of gas produced as a function of other operating variables. The a m o u n t of gas produced was related to the reaction conditions and reactant conversions V = WG/W ~

=

f ( T , P , t , XL, X T )

where WG = weight of gas produced (g), W~ = weight of lignite (m.a.f.) charged to reactor (g). Before fitting, the variables were normalized Tn tn Pn Gn

= = = =

T/673.15 t/58.0 P/12.2 G/0.0967

Linear least squares was used to curve fit the coefficients, gi, in the following model Gn = g, Tn + g2tn +gaPn + g4XL +gsXT + g6Tntn + g~TnPn + ga TnXL + ggTnXT + glotnPn + gll tnXL + g,: tnXT + glaPnX L + glgPnX w + g l s X L X T

Four parameters were eliminated based on the parameter F-test provided in the o u t p u t from the SAS program. The model was then refitted and more parameters eliminated, one at a time, until the following model resulted in all parameters passing the 99.99% confidence test Gn = g l T n +g2tn + g6Tntn + gTTnPn + gaTnXL + ggTnXW + glaPnXL

where the values of the parameters were found to be gi = 0.624 + 0.111 g2 = - 1 . 6 8 + 1.26

213

g6 g7 g8 g9 g,3

= 1.87 + 1.31 = - 0 . 2 7 1 + 0.218 = - 0 . 9 3 6 + 0.429 = 1.51 -+ 0.69 = 0.812 +- 0.442

The R 2 value for this model is 0.965, which includes all data points in the analysis. Based on 42 of the 47 experimental runs, the average deviation was found to be 0.0072 g/g which is a b o u t 10%. This model gives, therefore, a fair estimation of the expected gas production. CONCLUSIONS AND RECOMMENDATIONS

Kinetic models were successfully developed to describe the reaction behavior of Texas lignite in the hydrogen donor solvent, tetralin. These models correlate temperatures from 350 to 400°C, pressures from 2 to 16 MPa, and reaction times from 3 to 58 minutes with conversions of lignite and tetralin. Further studies could define reaction with other donor solvents such as hydrogenated creosote oil, the effects of catalysts and reactivities of lignite samples from different locations. The conclusions drawn from this study are: 1. In the liquefaction of Texas lignite, the rate of conversion of lignite to coal liquids can be described by two models. The first model is second order with respect to lignite concentration and first order with respect to tetralin concentration. The second model is second order with respect to lignite. These models are statistically equivalent. One would, however, use the simpler equation. 2. The rate of conversion of tetralin to naphthalene can also be described b y two models. The first rate expression is first order on lignite, first order on tetralin. The second model is second order on lignite. 3. The activation energies obtained in the rate expressions for lignite and tetralin compare favorably with some literature values. The activation energies found in this study are 72.8 and 63.6 kJ/mol for the lignite models and 103 and 86.6 kJ/mol for the tetralin models. 4. The modelling m e t h o d used in this study may be used for modelling other systems. Smoothing the data through cross-plotting proved helpful although precision may be sacrificed. 5. The weight of gases produced in the liquefaction is a function of the reaction conditions and lignite and tetralin conversion. 6. The results of this study, in particular lignite rate Model 2 in Table 5, coupled with ratio rate Model 12 in Table 4, could be used in the design of a suitable reactor for the liquefaction of lignite. In general, the best ratio models, coupled with the lignite rate models, gave the best estimates of the lignite and tetralin conversions. 7. The variation in the reported reaction schemes in the literature indicates

214 that more research into the mechanism behind the liquefaction process is required before this process can be developed for large-scale production. 8. Because this research concentrated on the liquefaction of Texas lignite, it is further noted that most of the research being conducted at this time is on coals from other States. With the abundant resources of lignite in Texas, along with the limited research on this particular coal type, future work in coal dissolution studies should include lignite samples from other locations in Texas. More should be known concerning the effects of minerals on the yields and quality of liquids and gases derived from lignite. ACKNOWLEDGEMENTS The authors appreciate the financial support received from the Aluminum Company of America, D o w Chemical USA, The Center for Energy and Mineral Resources, the Texas Engineering Experiment Station and the Department of Chemical Engineering. The authors would also like to thank Mrs. Peggy J. Moede for her assistance in obtaining the data. NOTATION a A b B CO C Flof Freg g G k ko kr n p P R R2 SS t T W° X

coefficient for lignite concentration term parameter for pressure term coefficient for tetralin concentration term parameter for temperature term initial concentration of reactant concentration of reactant or product F-value calculated for lack of fit test F-value calculated for significance of regression test parameter in gas production equation weight of gas product/weight of lignite (m.a.f.) charged rate constant rate constant excluding temperature and pressure effects number of replicate experiments number of experimental data points number of parameters reaction pressure universal gas constant correlation coefficient sum of squares {experimental - calculated) reaction time reaction temperature initial weight of reactant charged to reactor average experimental conversion

02

variance of pure error

215

Subscripts cal exp

calculated experimental

G L n N T 1 2

p r o d u c e d gas lignite normalized naphthalene tetralin lignite rate equation tetralin rate equation

REFERENCES 1 Anthony, R.G., 1978. The use of statistics in the development of rate equations. Internal report from Chemical Engineering Department, Texas A&M University, College Station, Texas. 2 Anthony, R.G., 1976. In situ comminution or liquefaction of Texas lignites. TEES Publications, Tech. Bull., 76--3: 4. 3 Attar, A., 1978. The kinetics of coal liquefaction in a hydrogen donor solvent. Prepr. ACS Fuel Division, 23 (4) (Miami): 169. 4 Cudmore, J.F., 1977--78. Non-catalytic hydrogenation of Australian coals. Fuel Processing Technology, 1: 227. 5 Farcasiu, M., Mitchell, T.O. and Whitehurst, D.D., 1976. On the kinetics and mechanisms of solvent refining coal. Prepr. presented at 1976 Coal Chemistry Workshop, Standford Research Institute. 6 Given, P.H., Cronauer, D.C., Spackman, W., Lovell, H.L., Davis, A. and Biswas, B., 1975. Dependence of coal liquefaction behavior on coal characteristics. 1. Vitriniterich samples. Fuel, 54: 34. 7 Given, P.H., Cronauer, D.C., Spackman, W., Lovell, H.L., Davis, A. and Biswas, B., 1975. Dependence of coal liquefaction behavior on coal characteristics. 2. Role of petrographic composition. Fuel, 54: 40. 8 Guin, J.A., Tarrer, A.R., Taylor, Jr., L., Prather, J.W. and Green, Jr., S., 1976. Mechanisms of coal particle dissolution. Ind. Eng. Chem., Process Des. Dev., 15, 4: 400. 9 Guin, J.A., Tarrer, A.R., Pitts, W.S. and Prather, J.W., 1977. Kinetics and solubility of hydrogen in coal liquefaction reactions, In: Liquid Fuels from Coal. Academic Press, Inc., New York, NY. 10 Holland, C.D. and Anthony, R.G., 1979. Fundamentals of Chemical Reaction Engineering. Prentice Hall, Inc., Englewood Cliffs, NJ. 11 Liebenberg, B.J. and Potgieter, H.G.J., 1973. The uncatalysed hydrogenation of coal. Fuel, 52: 130. 12 Maekawa, Y., Ishii, T. and Takeya, G., 1977. The effect of hydrogen pressure on the hydrogenation reaction of coal. Journal of Chemical Engineering of Japan, 10 (2): 101. 13 Neavel, R.C., 1976. Liquefaction of coal in hydrogen-donor and non-donor vehicles. Fuel, 55: 237. 14 Philip, C.V. and Anthony, R.G., 1977. Characterization of liquids and gases obtained by hydrogenating lumps of Texas lignite. Prepr. of ACS Fuel Div., 22(5) (Chicago): 31. 15 Philip, C.V. and Anthony, R.G., 1978. Chemistry of Texas lignite liquefaction in a hydrogen-donor solvent system. Prepr. of ACS Fuel Div., 23 (4) (Miami, Florida): 196. 16 Philip, C.V. and Anthony, R.G., 1979. Separation of coal-derived liquids by gel permeation chromatography. Prepr. of ACS Fuel Div., 24 (3) (Washington, DC): 204.

216 17 Philip, C.V., Bullin, J.A. and Anthony, R.G., 1979. Analysis of lignite-derived gases by automated gas chromatography. Journal of Chromatographic Science, 17: 523. 18 Philip, C.V., Bullin, J.A. and Anthony, R.G., 1978. Hydrogenation of Texas lignite. TEES Publications, Tech. Bn., 78--2: 10. 19 Potgieter, H.G.J., 1973. Kinetics of conversion of tetralin during hydrogenation of coal. Fuel, 52: 134. 20 Shah, Y.T., Cronauer, D.C., McIlvried, H.G. and Paraskos, J.A., 1978. Kinetics of catalytic liquefaction of Big Horn coal, in V.W. Weekman, Jr. and Dan Luss (Eds.), Fifth Int. Syrup. on Chemical Reaction Engineering, Chemical Reaction Engineering-Houston, ACS Symp. series vol. 65, p. 303. 21 Shalabi, M.A., Baldwin, R.R., Bain, R.L., Gary, J.H. and Golden, J.O., 1977. Kinetics of coal liquefaction to preasphaltenes, asphaltenes, and oils. Colorado School of Mines, Golden, Colorado. 22 Shalabi, M.A., Baldwin, R.R., Bain, R.L., Gary, J.H. and Golden, J.O., 1979. Noncatalytic coal liquefaction in a donor solvent. Rate of formation of oil, asphaltenes, and preasphaltenes. Ind. Eng. Chem., Process Des. Dev., 18(3): 474. 23 Tarrer, A.R., Guin, J.A., Pitts, W.S., Henley, J.P., Prather, J.W. and Styles, G.A., 1977. Effect of coal minerals on reaction rates during coal liquefaction. In: Liquid Fuels from Coal. Academic Press, Inc., New York, NY. 24 Wiser, W.H., 1968. A kinetic comparison of coal pyrolysis and coal dissolution. Fuel, 47: 475. 25 Wiser, W.H., Anderson, L.L., Qader, S.A. and Hill, G.R., 1971. Kinetic relationship of coal hydrogenation, pyrolysis and dissolution. J. Applied Chem. Biotechnology, 21: 82.