New Approaches in Coal Chemistry - American Chemical Society

conducted in a 2 lb/hr, 1" ID χ 8 ft long downflow tubular reactor in the range ... k i 0 e. " E i / R T for all i. Regression Technique. A minimizat...
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12 The Kinetics of Flash Hydrogenation of Lignite and Subbituminous Coal 1

B.L.

BHATT ,

P. T. F A L L O N , and M . STEINBERG

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Process Sciences Division, Department of Energy and Environment, Brookhaven National Laboratory, Upton, N Y 11973

A reaction model, based on a single coal particle surrounded by H2 gas, is developed for the hydrogenation of lignite and subbituminous coal. Conversion data from experiments conducted at various pressures, temperatures, particles residence times and gas residence times are correlated to calculate activation energies and to obtain one set of kinetic parameters. A single object function formulated from the weighted errors for the four dependent process variables, CH4, C2H6, BTX, and Oil yields, was minimized using a program containing three independent iterative techniques. The results of the nonlinear regression analysis for lignite show that a first-order chemical reaction model with respect to carbon conversion, satisfactorily describes the dilute phase hydrogenation. Data obtained from experiments using subbituminous coal are correlated using similar techniques. Results from data analysis of the two types of coals are compared. The mechanisms, rate expressions, and design curves developed can satisfactorily predict conversions to various products at different conditions and hence can be used for scale-up and reactor design.

F l a s h h y d r o g é n a t i o n i s a short residence time (1 to 10 sec) gas-phase, n o n - c a t a l y t i c process i n which p u l v e r i z e d c o a l i s r a p i d l y heated ( 2 0 , 0 0 0 - 3 0 , 0 0 0 ° C/sec) i n hydrogen to obtain l i q u i d and gaseous hydrocarbons d i r e c t l y . Experiments were conducted i n a 2 l b / h r , 1" ID χ 8 f t long downflow tubular reactor i n the range of 5 0 0 ° to 900°C and 500 to 3000 p s i H2 pressure for North Dakota L i g n i t e and New Mexico subbituminous c o a l (L). The ultimate analyses of these coals are given i n 1

Current address: Air Products and Chemicals, Inc., P.O. Box 427, Marcus Hook, PA 19061. 0097-6156/81/0169-0201$05.00/0 © 1981 American Chemical Society

Blaustein et al.; New Approaches in Coal Chemistry ACS Symposium Series; American Chemical Society: Washington, DC, 1981.

NEW

202

APPROACHES IN

COAL CHEMISTRY

Table I . An o n - l i n e process gas chromatograph analyzed the gas stream f o r 10 components every 8 minutes from sample taps l o c a t e d at i n t e r v a l s of 2 f e e t along the length of the r e a c t o r C?.). The heavier hydrocarbon products (> C9), c o l l e c t e d i n l i q u i d product condensers, were measured at the end of each experiment.

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M o d e l l i n g . The f l a s h hydrogénation i s assumed to take place v i a the f o l l o w i n g r e a c t i o n steps: C ( i n coal) + H

2

-^->

CH

+ H

2

-^->

C*

C ( i n coal) + H

2

-^->

C H

+ H

2

-^6->

C*

C ( i n coal) + H

2

-^*->

BTX

+ H

2

-^->

CH

4

C ( i n coal) + H

2

-i^->

Oils + H

2

-^->

CH

4

4

2

6

C* designates the non-reactive elemental carbon contained i n the char product. The chemical r e a c t i o n i s assumed to be the r a t e c o n t r o l l i n g step. T h i s assumption i s j u s t i f i e d i n the D i s c u s s i o n of R e s u l t s . The r e a c t i o n s are considered to be f i r s t order with respect to f r a c t i o n of carbon remaining i n c o a l as w e l l as converted to hydrocarbons and m order with respect to H p a r t i a l pressure. The d e t a i l s of the development of the model i s reported elsewhere (2). The experimental data c o r r e l a t e d was obtained from d i l u t e phase operation i n an excess of hydrogen atmosphere, so the p a r t i a l pressure of hydrogen was considered to be approximately equal to the t o t a l system pressure and was assumed constant along the length of the reactor. For isothermal c o n d i t i o n s , d i f f e r e n t i a l equations set up from m a t e r i a l balances of each component can be solved a n a l y t i c a l l y to o b t a i n the r e l a t i o n s h i p s i n Table I I . Arrhenius behavior of the rate constant with temperature was assumed as f o l l o w s : tn

2

k

i

a

k

i0

e

"

E

i /

R

T

for a l l i

Regression Technique. A minimization program 'MINUIT* (^) was used on CDC 7600 to f i t the equations to the data and f i n d the unknown parameters. Three d i f f e r e n t minimization algorithms, Monte C a r l o , Simplex, and V a r i a b l e M e t r i c , a v a i l a b l e i n MINUIT, were used f o r the c o r r e l a t i o n . A s i n g l e object f u n c t i o n was formulated f o r the four

Blaustein et al.; New Approaches in Coal Chemistry ACS Symposium Series; American Chemical Society: Washington, DC, 1981.

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BHATT E T A L .

Flash

203

Hydrogénation

TABLE I ULTIMATE ANALYSIS (WT PCT DRY) OF LIGNITE AND SUBBITUMINOUS COALS

Carbon Hydrogen Oxygen* Nitrogen Sulfur Ash

*By 1) 2)

North Dakota Lignite

New Mexico Subbituminous

59.0 4.0 25.5 0.9 0.6 10.0 100.0

59.3 4.2 16.8 1.2 0.8 17.7 100.0

difference From Baukal Noonan Inc. Mines, P.O. Box 879, Minot, N. Dakota 58701 From Western Coal Co. Mines, P.O. Box 509, Farmington, N. Mexico 87401

Blaustein et al.; New Approaches in Coal Chemistry ACS Symposium Series; American Chemical Society: Washington, DC, 1981.

NEW APPROACHES IN COAL CHEMISTRY

204

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TABLE I I

gs

k

1234 - k

«gs

k

1234 ~ 6

u

[C H ] 2

6

[BTX]

k

*»gs 1234 • - k k

[0il8]

»

r-^

u



1

k

u

2

g 8

e - 6 H2 k

k

Ug

e " 7 H P

e " 8 H2 k

P

H

-e

2

-e - 1234P "

P

k

7

g s 1234 " 8 k

H

5

2



*.

H

8

-

e

ÎS. - e gs

~ 1234 ^ k

Ρ

C

Η "

u

Blaustein et al.; New Approaches in Coal Chemistry ACS Symposium Series; American Chemical Society: Washington, DC, 1981.

«

T S

12.

BHATT ET

Flash

AL.

205

Hydrogénation

Weighting f a c t o r s i n v e r s e l y p r o p o r t i o n a l to the variance of each dependent v a r i a b l e were used (]L'· To take i n t o account the v a r i a b l e number of data points a v a i l a b l e f o r each dependent v a r i a b l e , weighting f a c t o r s were taken p r o p o r t i o n a l to the number of data p o i n t s and can then be represented as f o l l o w s : W

±

«

f o r i - 1,2,3,4. Σ(Υ

±

-

Y)

2

±

R e s u l t s of Regression A n a l y s i s . For s i m p l i f i c a t i o n , i t was assumed that a l l a c t i v a t i o n energies f o r i n i t i a l formation of hydrocarbons from c o a l are the same, i . e . E^ » E = E3 = E4. A r a t i o n a l e f o r t h i s i s that during decomposition, c o a l i s i n e q u i l i b r i u m with the same t r a n s i t i o n complex r e g a r d l e s s of the f i n a l products. Data from 83 experimental runs, w i t h H / c o a l weight r a t i o of about 1, using North Dakota L i g n i t e , were c o r r e l a t e d . D e t a i l s of the c o r r e l a t i o n f o r the l i g n i t e are reported elsewhere ( . For New Mexico subbituminous c o a l , data from 47 experimental runs, a l s o with H / c o a l weight r a t i o of about 1, were c o r r e l a t e d . For these runs, 166 data p o i n t s , corresponding to d i f f e r e n t l o c a t i o n s i n the r e a c t o r , were a v a i l a b l e f o r CH4, C H$ and BTX c o n c e n t r a t i o n s . O i l data, obtained from the t o t a l amount of o i l c o l l e c t e d i n the condensors, were a v a i l a b l e f o r 17 runs. Estimated values of various parameters f o r subbituminous c o a l are tabulated i n Table I I I , along with those found f o r l i g n i t e . The order of magnitude of the parameters i s the same f o r both c o a l s . C o r r e l a t i o n c o e f f i c i e n t s and standard e r r o r s f o r the subbituminous coal are tabulated i n Table IV. The standard e r r o r of 8% carbon conversion f o r CH4 seems to be high, but because of higher amounts and v a r i a t i o n i n the CH4 data, a c o r r e l a t i o n c o e f f i c i e n t o f 0.92 i s obtained, i n d i c a t i n g e x c e l l e n t c o r r e l a t i o n . The c o r r e l a t i o n of the o i l data i s b e t t e r compared to those of C H £ and BTX data. Using Student's t s t a t i s t i c s , hypothesis: p»0 was tested . I t was found that the hypothesis P«0 can be r e j e c t e d at the 0.005 s i g n i f i c a n c e l e v e l . I t t h e r e f o r e appears almost c e r t a i n that the % carbon conversions to CH4, C H , BTX and O i l s can be r e l a t e d to r e a c t i o n temperature, H p a r t i a l pressure, p a r t i c l e residence time, and gas residence time by the correlations. Using F i s h e r ' s Ζ transformation (*L), 95% confidence l i m i t s f o r the o v e r a l l c o r r e l a t i o n c o e f f i c i e n t f o r the subbituminous c o a l were 0.70 < r < 0.84. A s e n s i t i v i t y a n a l y s i s was performed on the c o r r e l a t i o n . The k i n e t i c parameters and c o r r e l a t i o n c o e f f i c i e n t s were estimated f o r Ν » 166, 156, 146, and 136 with N = 17, 16, 15,

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2

2

2

2

2

2

6

2

4

Blaustein et al.; New Approaches in Coal Chemistry ACS Symposium Series; American Chemical Society: Washington, DC, 1981.

Blaustein et al.; New Approaches in Coal Chemistry ACS Symposium Series; American Chemical Society: Washington, DC, 1981.

7 0

5 0

0 >

e

c

8 e c

sec sec" ~ sec

s

sec ~

s e c

1

J

8

e

c

k80> k80» s e c " Ε ( E ^ thru E4), c a l / g mole E5, c a l / g mole E$, c a l / g mole Ε7» c a l / g mole Eg, c a l / g mole m (power of Pj

k

1 0

k , k20» 30» k4 k , k60> k ,

0.14

1 6

9

1 0

0.15

1 0

1 6

9

1

6

6

6

1

6

6

5.5 χ 106 6.7 χ 1 0 6.3 χ 1 0 4.0 χ 1 0 4.8 χ 10 1.7 χ 1 0 1.5 χ 10 6.9 χ 1 0 43,200 20,900 55,000 51,100 84,700

New Mexico Subbituminous

6

5

5.0 χ 10 7.5 χ 1 0 4.4 χ 10 4.6 χ 1 0 5.2 χ 10 1.7 χ 1 0 1.6 χ 10 4.6 χ 1 0 42,700 20,100 54,200 50,300 84,200

North Dakota L i g n i t e

ESTIMATED VALUES OF VARIOUS PARAMETERS

TABLE I I I

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12.

BHATT E T AL.

Flash

Hydrogénation

207

and 14 r e s p e c t i v e l y . The c o r r e l a t i o n c o e f f i c i e n t s obtained are tabulated i n Table V. The c o r r e l a t i o n c o e f f i c i e n t s do not show any s i g n i f i c a n t change (< 5% v a r i a t i o n ) i n d i c a t i n g that the c o r r e l a t i o n i s good. Design curves were developed i n the range of the experimental data from the k i n e t i c parameters and r a t e expression, using a T e k t r o n i x i n t e r a c t i v e graphic terminal connected with CDC 6600. F i g u r e s 1, 2 and 3 show percent carbon conversion to C H 4 v s . r e a c t o r length, gas residence time, and p a r t i c l e residence time, at v a r i o u s temperatures and pressures. For pressures of 1500 p s i and 2500 p s i , maxima i n C H 4 y i e l d s are found w i t h i n the range of the experiments. C H 4 y i e l d increases and occurs at l e s s e r residence times as the temperature i n c r e a s e s . Figures 4, 5, and 6 show percent carbon conversion to C 2 H 6 , BTX and O i l s , r e s p e c t i v e l y v s . r e a c t o r length f o r v a r i o u s temperatures at 1500 p s i . The maximum y i e l d s of these products decrease and occur at l e s s e r residence times as the temperature i n c r e a s e s . Maximum y i e l d s of various products and necessary operating c o n d i t i o n s are tabulated i n Table VI. Maximum y i e l d s from subbituminous c o a l are found at 2500 p s i , which i s the highest pressure used i n experiments f o r that c o a l . For comparison purposes, l i g n i t e y i e l d s are a l s o tabulated f o r 2500 p s i , though some experiments were conducted at 3000 p s i with the l i g n i t e , o b t a i n i n g higher y i e l d s . For both c o a l s , the C H 4 maximum i s found at higher temperature and occurs at shorter residence times, compared to C 2 H 5 , BTX and O i l s . Higher maximum y i e l d s of CH4 and BTX and s l i g h t l y lower maximum y i e l d s of C 2 H 5 and O i l s were obtained f o r the subbituminous c o a l compared to the l i g n i t e . Maximum % carbon conversion to C H 4 v s . pressure i s p l o t t e d i n Figure 7. The maximum C H 4 conversion shows a l i n e a r increase with increase i n pressure f o r both c o a l s . At a l l pressures, the maxima are found at 900°C and the subbituminous c o a l maximum y i e l d s to C H 4 are higher than those from the lignite. D i s c u s s i o n of Results and Conclusions. The r e s u l t s of r e g r e s s i o n a n a l y s i s show that a chemical r e a c t i o n model, f i r s t order with respect to f r a c t i o n a l carbon conversion, with a production and a decomposition step f o r each of C H 4 , C 2 H 5 , BTX and O i l s , s a t i s f a c t o r i l y describes the d i l u t e phase f l a s h hydrogénation of both l i g n i t e and subbituminous c o a l . The a c t i v a t i o n energy estimates of > 20,000 cal/gmole j u s t i f y the assumption that chemical r e a c t i o n i s the rate c o n t r o l l i n g step. The a c t i v a t i o n energy f o r the i n i t i a l formation of hydrocarbons was 42,700 cal/gmole f o r l i g n i t e and 43,200 cal/gmole f o r subbituminous c o a l , with estimated e r r o r s of only 50-80 cal/gmole. This i n d i c a t e s that the e r r o r i n v o l v e d

Blaustein et al.; New Approaches in Coal Chemistry ACS Symposium Series; American Chemical Society: Washington, DC, 1981.

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208

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TABLE IV CORRELATION COEFFICIENTS AND STANDARD ERRORS FOR THE SUBBITUMINOUS COAL RESULTS

Correlation Coefficient

8.0 3.2 2.9 0.7

0.92 0.66 0.72 0.81 0.78

CH4 C H BTX Oils Overall 2

Standard E r r r o r , %C Conversion

6

TABLE V RESULTS OF THE SENSITIVITY ANALYSIS FOR THE SUBBITUMINOUS COAL CORRELATION COEFFICIENT

Ν

N

166 156 146 136

17 16 15 14

4

CH4

C2H6

BTX

Oils

0.92 0.92 0.92 0.92

0.66 0.65 0.64 0.66

0.72 0.71 0.69 0.69

0.81 0.84 0.81 0.80

Overall

Blaustein et al.; New Approaches in Coal Chemistry ACS Symposium Series; American Chemical Society: Washington, DC, 1981.

0.78 0.77 0.76 0.77

BHATT E T A L .

Flash

209

Hydrogénation

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12.

Figure 1.

Flash hydrogénation of subbituminous coal: pressure = flow rate ~ 1 Ib/h; coal feed rate ~ 1 lb/h.

500 psi; H

Blaustein et al.; New Approaches in Coal Chemistry ACS Symposium Series; American Chemical Society: Washington, DC, 1981.

t

NEW APPROACHES IN COAL CHEMISTRY

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210

Figure 2.

Flash hydrogénation of subbituminous coal: pressure = flow rate ~ 1 Ib/h; coal feed rate ~ 1 Ib/h.

1500 psi; H

Blaustein et al.; New Approaches in Coal Chemistry ACS Symposium Series; American Chemical Society: Washington, DC, 1981.

t

BHATT E T AL.

Flash

211

Hydrogénation

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12.

Figure 3.

Flash hydrogénation of subbituminous coal: pressure = flow rate ~ 1 Ib/h; coal feed rate ~ 1 lb/h.

2500 psi;

Blaustein et al.; New Approaches in Coal Chemistry ACS Symposium Series; American Chemical Society: Washington, DC, 1981.

H

t

NEW APPROACHES IN COAL CHEMISTRY

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212

Blaustein et al.; New Approaches in Coal Chemistry ACS Symposium Series; American Chemical Society: Washington, DC, 1981.

Flash

213

Hydrogénation

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BHATT E T AL.

Figure 5.

Flash hydrogénation of subbituminous coal: pressure = flow rate ~ 1 Ib/h; coal feed rate ~ 1 lb/ h.

1500 psi; H

Blaustein et al.; New Approaches in Coal Chemistry ACS Symposium Series; American Chemical Society: Washington, DC, 1981.

t

214

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NEW APPROACHES IN COAL CHEMISTRY

Figure 6.

Flash hydrogénation of subbituminous coal: pressure = flow rate ~ 1 Ib/h; coal feed rate ~ 1 Ib/h.

1500 psi; H

Blaustein et al.; New Approaches in Coal Chemistry ACS Symposium Series; American Chemical Society: Washington, DC, 1981.

t

Blaustein et al.; New Approaches in Coal Chemistry ACS Symposium Series; American Chemical Society: Washington, DC, 1981.

Conditions

Pressure, p s i Temp., °C Reactor Length, f t S o l i d r e s . time, sec Gas r e s . time, sec

Operating

2500 900 3.5 3.9 16.6

2500 900 4.5 5.0 21.4

2500 750 8 8.8 38.0

2500 750 8 8.8 38.0

2500 725 8 8.8 38.0

2500 750 8 8.8 38.0

2500 700 8 8.8 38.0

2500 700 8 8.8 38.0

30 33 51

44

51

49

76

70

Total

6

5

Oils

8 3

8

3

8

1 0

1

5 10

7 7

9 14

0

9 9

9 14

10

2

BTX

6

2

2

C H

9

11

25

18

25

73

67

CH4

26

Lignite

Subbit.

Lignite

SubbJ

Max. O i l s

Subbit.

Max. BTX Lignite

6

Subbit.

2

Max. C H

Lignite

% C Conv. to

Max. CH4

MAXIMUM CARBON CONVERSIONS TO VARIOUS PRODUCTS AT 2500 PSI

TABLE VI

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APPROACHES IN

COAL CHEMISTRY

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NEW

Figure 7. Flash hydrogasification of coal: maximum percentage of carbon conversion to CH vs. pressure (at 900°C). Solid residence time (t ); gas residence time (t ); North Dakota lignite (O ); New Mexico subbituminous ( Q ) h

e

g

Blaustein et al.; New Approaches in Coal Chemistry ACS Symposium Series; American Chemical Society: Washington, DC, 1981.

12.

BHATT E T A L .

Flash

217

Hydrogénation

i n the assumption, that a l l the a c t i v a t i o n energies f o r i n i t i a l formation of hydrocarbons from c o a l are the same (Εχ - E E3 * E ) i s probably s m a l l . The values of these a c t i v a t i o n energies estimated are comparable to the mean a c t i v a t i o n energy o f 48,700 cal/gmole found by Anthony (Z) f o r d e v o l a t i l i z a t i o n of Montana L i g n i t e and the a c t i v a t i o n energy of 48,900 cal/gmole found by Bhatt (υ.) f o r h y d r o p y r o l y s i s of North Dakota L i g n i t e . The k i n e t i c parameters (k5Q, k^Q, kjQ, E5, E5, E7) corresponding to the decomposition steps f o r CH , C H^ and BTX are found to be almost the same f o r both l i g n i t e and subbituminous c o a l , as expected. The pre-exponential f a c t o r s f o r o i l s are d i f f e r e n t f o r the two c o a l s , probably due to some d i f f e r e n c e i n nature of the o i l s produced. The pre-exponential f a c t o r s (k^Q, 20> 30> k o ) f o r i n i t i a l decomposition of subbituminous c o a l are found to be d i f f e r e n t than those f o r l i g n i t e . At optimum c o n d i t i o n s , subbituminous c o a l produces more CH and BTX and s l i g h t l y l e s s C H £ and O i l s than l i g n i t e . The power of the hydrogen p a r t i a l pressure, m, was about +0.14 to +0.15. T h i s i n d i c a t e s a small i n c r e a s e i n % carbon conversion to hydrocarbons with Increase i n hydrogen p a r t i a l pressure. The c o r r e l a t i o n f o r subbituminous c o a l with o v e r a l l c o r r e l a t i o n c o e f f i c i e n t 0.78, having 95% confidence l i m i t s of 0.70 and 0.84, i s considered good. The mechanism, r a t e expressions, and the design curves developed s a t i s f a c t o r i l y represent the experimental data and hence can be used f o r scale-up and r e a c t o r design. The model developed might be a p p l i c a b l e to other types o f c o a l while the r e g r e s s i o n technique used i s a p p l i c a b l e to any experimental data f o r c o r r e l a t i o n . The model was developed from experiments conducted i n a downflow r e a c t o r , where gas residence times are g r e a t e r than s o l i d residence times. The model may not be able to p r e d i c t residence time e f f e c t i n a f l u i d bed or upflow r e a c t o r where s o l i d residence times are greater than gas residence times. But i t does g i v e u s e f u l i n f o r m a t i o n f o r pressure and temperature e f f e c t s i n these r e a c t o r s . β

2

4

4

2

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k

k

4

4

2

Literature Cited 1.

Fallon, P.T., Bhatt, B., and Steinberg, M. "The Flash Hydropyrolysis of Lignite and Subbituminous Coals to both Liquids and Gaseous Hydrocarbon Products"; Brookhaven National Laboratory; BNL 26210; presented at the 178th National Meeting of the American Chemical Society: Washington, D.C., 1979. 2. Steinberg, Μ., Fallon, P., Dang, V., Bhatt, B., Ziegler, Ε., and Lee, Q. "Reaction and Process Engineering for the Flash Hydropyrolysis (FHP) of Coal"; Brookhaven National Laboratory; BNL 25232; presented at 71st Annual Meeting of the American Institute of Chemical Engineers: Miami Beach, Florida, 1978. Blaustein et al.; New Approaches in Coal Chemistry ACS Symposium Series; American Chemical Society: Washington, DC, 1981.

218

NEW

APPROACHES IN COAL CHEMISTRY

Downloaded by UNIV LAVAL on July 13, 2016 | http://pubs.acs.org Publication Date: October 26, 1981 | doi: 10.1021/bk-1981-0169.ch012

3.

Bhatt, B., Fallon, P.T., and Steinberg, M. "Reaction Modelling and Correlation for Flash Hydropyrolysis of Lignite"; Brookhaven National Laboratory; BNL 27574; presented at the 15th Intersociety Energy Conversion Engineering Conference: Seattle, Washington, BNL 27574R, 1980. 4. James, F., and Roos, M. "MINUIT - A System for Function Minimization and Analysis of the Parameter, Errors and Correlations"; Computer Physics Communications, 10, 1975, p 343-367. 5. Bhatt, B. "Kinetics of Coal Devolatilization and Hydropyrolysis"; Ph.D thesis; Polytechnic Institute of New York, 1980. 6. Spiegel, M.R. "Theory and Problems of Statistics"; Schaum's Outline Series; McGraw-Hill Book Company, 1961; p 344. 7. Anthony, D.B. "Rapid Devolatilization and Hydrogasification of Pulverized Coal"; Sc. D. Thesis; Dept of Chemical Engineering: Mass Institute of Tech., Cambridge, 1974. Nomenclature [BTX]

f r a c t i o n of carbon converted to benzene, toluene and xylene.

[BTX] p

mean o f [ B T X ]

[CH4]

f r a c t i o n of carbon converted to methane.

eX

[CH4]

mean o f [ C H 4 ]

e x p

e x p

e x p

[^2^6]

f r a c t i o n of carbon converted to ethane.

[ C H ] exp

mean o f [C2^6]exp

E, E^

a c t i v a t i o n energy,

F

object function

k^

r a t e constant, sec"*

k^o

pre-exponential f a c t o r , sec~*

ki234

βurn k]+k2+k3+k4, sec"*

m

order of r e a c t i o n with respect t o H2 gas

N, N-£

number of data p o i n t s

[Oils]

f r a c t i o n of carbon converted t o O i l s

2

6

cal/gmole

Blaustein et al.; New Approaches in Coal Chemistry ACS Symposium Series; American Chemical Society: Washington, DC, 1981.

12.

BHATT

Flash

ET AL.

[ O i l s ] exp

Hydrogénation

219

mean o f [ O i l s ] p e X

Downloaded by UNIV LAVAL on July 13, 2016 | http://pubs.acs.org Publication Date: October 26, 1981 | doi: 10.1021/bk-1981-0169.ch012

p a r t i a l pressure of hydrogen, p s i r

sample c o r r e l a t i o n c o e f f i c i e n t

R

gas constant, cal/gmole °K

ts

s o l i d residence time, s e c

T

temperature

U

8

gas v e l o c i t y , f t / s e c

u

s

u

°K

solid velocity, ft/sec

g 8

Wi Y, Y i .• Ϋ.

(absolute),

Y

U

ratio Ug/u

s

weighting

factors

dependent

variable

mean of Y

\

Greek l e t t e r ρ

t h e o r e t i c a l population c o e f f i c i e n t of c o r r e l a t i o n

Subscripts cal

calculated

value

exp

experimental

g

gas

i

ith

value

component s RECEIVED

solid June 16,

1981.

Blaustein et al.; New Approaches in Coal Chemistry ACS Symposium Series; American Chemical Society: Washington, DC, 1981.