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Statistical and mathematical analysis of the catalytic hydrogenating depolymerization of benzene-insoluble coal extract fraction
Statistical and mathematical analysis of the catalytic hydrogenating depolymerization of benzene-insoluble coal extract fraction Bohdan
Radomyski
and Jerzy Szczygiet
Institute of Chemistry and Technology (Received 3 April 1981)
of Petroleum
and Coal, Wroclaw,
Poland
This Paper presents a statistical and mathematical analysis of hypotheses concerning the autoclave hydrogenating depolymerization of coal extract fractions insoluble in benzene. From comparison of theoretical and experimental data the most probable reaction mechanism was selected. (Keywords:
coal; hydrogenation;
catalysis)
Hydrogenating catalytic depolymerization of coal extract is one of the stages in the production of liquid fuel from coal. The subject of this Paper was the hydrogenation of the heaviest group component of coal extract, i.e., benzene-insoluble fractions. The investigations aimed to determine the effects of process parameters such as temperature, pressure and reaction time on raw material depolymerization and on the formation of products of smaller mean molecular weight (i.e., asphaltenes, gases and oils) which were the desired products. Optimum values of process parameters were determined using a statistical approach and, by assuming that reaction occurred between particular groups of compounds treated as chemical individuals, an hypothesis concerning the mechanism of conversion was formulated. Problem formulation
The kinetics of coal hydrogenation have been the subject of many studies. Weller et al.’ performed vitrinite hydrogenation in an autoclave in the presence of stannic sulphide/ammonium chloride mixture and concluded that the conversion of coal to oils involved consecutive reactions and that asphaltenes constituted intermediate products. Potgieter’, investigating the mechanism of noncatalytic hydrogenation of hard coals in the presence of tetralin, concluded that oil components may be formed both directly from coal organic substance and by means of a consecutive reaction through asphaltenes. Yoshida and Maekawa3 arrived at a similar conclusion when hydrogenating coal in an autoclave in the presence of red mud from the Bayer alumina process, as catalyst. Schwager4 found, based on chemical composition and, particularly, on C/H ratios of group components, that the mechanism of coal conversion is a consecutive process passing through carboids and asphaltenes. Neavel’, Shah6 and Whitehurst’ are of the opinion that in the process of coal hydrogenation asphaltenes, oils and gases form by means of simultaneous reactions. Different views on the kinetics of coal hydrogenation result from different process conditions. This Paper presents the results of a study of the kinetics of the hydrogenating depolymerization of benzene0016-2361/84/121687FO7$3.00 @ 1984 Butterworth & Co. (Publishers) Ltd
insoluble coal extract fractions in the presence of cobalticmolybdic catalyst. Such a study makes it possible to programme and control this process to achieve the highest possible product yield. Due to the complex character of the raw material, reaction effects were measured by the change in yield of compound groups treated as individual compounds. The following groups of compounds are distinguished : 1. Compounds insoluble in benzene, denoted ‘C 2. Asphaltenes, soluble in benzene but insoluble in paraffin and cycloparafin hydrocarbons, denoted ‘A 3. Oils, soluble in paraffin and cycloparaflin hydrocarbons, denoted ‘0 4. Gases, denoted ‘G The kinetics of the process are analysed by assuming that the reaction takes place between these groups which are treated as individual chemical compounds. STATISTICAL
METHOD
The effects of three independent variables, temperature, pressure and time of reaction, on the process (i.e., dependent variable y) were investigated and assumed to take the following form: ~=b,+b,xl+b,x,+b3x3+bl,xl,+b,3x13+b23~23 +
b, 1x12 + bZ2x22 + b33x32
(1)
b,, are model coefficients.
where: b,... Based on the derived equation, the process was optimized with regard to its parameters. Then a preliminary analysis, which can be tested at the next stage of investigations by constructing a definite kinetic model, was carried out. To simplify the analysis of the multinomial expression, Equation (1) was developed into the so-called canonic form, as follows: Y- Y,=B,,X1Z+B22X22+B33X32
(2) where: Y,=value of objective function in the centre of a new co-ordinate system; X1,X2,X3 = independent variables of a canonic equation related to variables from Equation (1) (x,;c2sc3 =non-singular linear conversion); B, 1,B22,B33 =coefficients of canonic equation.
FUEL,
1984,
Vol
63, December
1687
Hydrogenating
depolymerization
of coal extracts: B. Radomyski
The conversion of a multinomial equation into a canonic form is executed in two stages: (1) translation of a coordinate system centre into point S (stationary point), which disposes of the linear terms of the equation; and (2) turning of the coordinate system through a definite angle thus eliminating scalar products. Canonic Equation (2) simplifies the production of a graphical form of response surface. This produces isolines of numerical values of the response function in the system of two variables with a fixed numerical value of the third independent variable. The resulting regression equation was used for the analysis of depolymerization of benzeneinsoluble fractions by means of a Hoerl’s crest line’. This method makes it possible to find one general optimum or several local optima, and also allows ready analysis of the process on two-dimensional diagrams irrespective of the problem dimensions. On these diagrams the changes of particular variables can be observed as the function of radius R = (XT +x: +x:)“’ in order to maximize the output function. The calculation technique of this method relies essentially on the multiple solution of the set of equations written in matrix form: [(% I -2M
[(2b,,-b;; 13)3 )-/!I b
[
b 13
where:
A = (b3 + blsxl
1 Experimental
iI3 _zj]
results of catalytical
(MPa)
(ks.1
A,
A*
673
29.4
733
19.6
673
19.6
733
9.8
x1
of the benzene-insoluble
Temperature (K) Pressure (MPa) Reaction time (ks)
0
+1
673 9.8 0.0
JO3 19.6 7.2
733 29.4 14.4
part of coal extract”
Xfoa) 1.8
69.2 18.1
3.0 21.5
0.7 41.3
19.1
3.6 7.2
14.0
23.6
44.0
19.1 18.4
13.9 13.6
15.8 10.5
51.0 56.6
19.3 19.3
80.4 28.5 20.0
2.8 32.0 37.1 49.4 53.3
15.6 16.4
14.1
1.2 23.1 26.0 19.7 15.0
16.5 17.6
1.8 3.6 7.2 14.4
84.0 41.5 23.6 16.8 13.1
0.4 26.5 36.9 32.7 29.6
1.5 16.8 23.5 34.4 40.9
14.1 15.2 16.0 16.1 16.4
4.1 21.8 25.3
11.4 11.8 12.1
27.5
12.4 4.1 5.3 6.4 7.4
A,
1.8 3.6 7.2 14.4
14.4
16.9
0
84.1
0.4
3.6 7.2 14.4
65.8 62.0 59.5
0.6 0.6 0.6
0
91.6 88.1 82.6 71.7
0.2 0.5 2.1 2.6
4.1 6.1 8.9 18.3
3.6
84.6 78.0
0.7 1 .o
4.5 9.8
7.2 14.4
75.2 73.3
0.4 0.6
12.7 13.5
11.2 11.7 12.6
0 3.6 7.2 14.4
93.9 87.7 85.7 81.5
0.3 0.8 0.8 0.9
2.3 4.4 5.3 8.4
3.5 7.1 8.2 9.2
3.6 7.2 14.4
time was measured starting from the moment when the assumed values of reaction conditions
FUEL, 1984,
-1
Gas (wt%)
0
9.8
f;]
Oil (wt%)
0
1688
ranges in real and coded units
Asphaltene (wt%)
0
a Reaction
Table 2 Parameters
Benzeneinsoluble (wt%)
14.4
29.4
=-[
depolymerization
(K)
673
To generate a multinomial model of the second order all available results of the previous experiments (Table 1) were used for optimization. The experiments were performed in a shaking autoclave of 0.2 dm3 volume capable of operation under 39.2 MPa (400atm) at 773 K (460°C). The range of parameters in encoded and real quantities is given in Table 2 from which it follows that the transition from natural quantities to encoded ones is determined by the following relations:
x3
Reaction time
29.4
x [f;]
+ bZ3xZ)/(x3).
Pressure
JO3
EXPERIMENTAL
x2
Temperature
733
This relation results from the equating of derivatives dy/ax with zero. By solving a given set of equations repeatedly for different value of A, which is changed optionally within a certain range, one obtains the values of (vectors) and hence radii XlJ2sc3 R = (xl2 +x22 +x32)4 for which the objective function reaches a maximum or minimum value.
-Al
b 12
Table
and J. Szczygie%
Vol 63, December
had been reached
10.2
Hydrogenating
depolymerization
of coal extracts: B. Radomyski and J. SzczygiaI
A, - 703
x1 =
30
x = A, - 19.6 2
(4)
9.8
r-I
A, - 7.2 x3=7.2
Regression coefficients of the assumed equation (tested for adequacy) calculated on MC ODRA-1305 are given in Table 3 together with the values of correlation coefficients, Y. Statistical interpretation of hydrogenation insoluble fractions
of benzene-
A detailed analysis of the effect of particular parameters on the change of output quantities (conversion, content of asphaltenes, oils and gases) can be performed from Figures l-5, which were plotted by graphplotter MC ODRA-1305 using the canonic form of regression equation. Depolymerization in the temperature range 673-733 K at p=29.4 MPa depends to only a small degree on temperature and, in practice, after 7.2 ks the conversion Table 3 Regression coefficients Y Coefficient bo 61 bz 6s 611 btz 61s bzz 62s 63s r
Conversion (%) 44.8 1 .B7 27.49 17.26 0.92 -0.61 -5.6 15.88 5.44 -18.36 0.97
I
I I I I I
1
f (ks)
-
c
I I I I I I I
L-1 Figure 2
lsolines of asphaltenes content in reaction product (wt%) as a function of temperature (7) and reaction time (t). Pressure, p=29.4 MPa
of the assumed equation
Benzeneinsoluble (wt%)
Asphaltenes (wt%)
Oil (wt%)
Gas (wt%)
55.91 -1 .B7 -27.49 -17.26 -0.92 0.61 5.6 -15.88 -5.44 18.36 0.97
3.37 -3.60 8.53 1.67 2.58 -3.23 -2.84 6.65 -0.22 -5.17 0.76
31.27 3.43 15.23 14.18 -2.41 2.85 -2.19 4.87 6.35 -12.11 0.93
9.45 2.06 3.74 1.41 0.76 -0.21 -0.56 4.37 -0.68 -1.11 0.99
718-/l
-
T(k)
T Figure 3 lsolines of oil content in reaction product (wt%) as a function of temperature (T) and pressure (p). Reaction time, t=3.6 ks
Figure
1
temperature
lsolines of conversion (%) as a function of (T) and reaction time (t). Pressure, p=29.4
MPa
reaches 90% (see Figure 1). A specific change in the time for the asphaltene content to reach the maximum indicates that the depolymerization of benzene-insoluble fractions to oil is a consecutive process taking place through asphaltenes (Figure 2). However, since there is a high content of oil after 3.6 ks (Figure 3) it may be supposed that the direct reaction of depolymerization of benzene-insoluble fractions into oil contributes much to the production of oils at least in the initial period of the reaction, and that a higher content of oil under corresponding conditions of temperature and pressure after 14.4 ks (Figure 4) probably results from a secondary depolymerization of asphaltenes to oils, since this occurs
FUEL, 1984,
Vol 63, December
1689
Hydrogenating
depolymerization of coal extracts: 8. Radomyski and J. Szczygie+
values are obtained by maintaining 703 K temperature and increasing pressure and reaction time. A similar profile of changes can be observed during the maximization of oil yield, though a longer time of reaction is necessary and a favourable effect of temperature rise can be noticed. This suggests a consecutive depolymerization, though direct formation of oils from benzene-insoluble fractions cannot be excluded, as is testified by the considerable quantities of oil present during the initial period of reaction, MATHEMATICAL
ANALYSIS
The possible kinetic models are represented by sets of differential equations resulting from the application of the law of conservation of mass. A general form of these equations is given below: X=X(x).K
Figure 4 lsolines of oil content in reaction product (wt%) as a function of temperature (T) and pressure (p). Reaction time, t=14.4 ks
(4)
where: K= vector of reaction rate constants = 1 x s; s = the number of possible reactions in the assumed kinetic model; X(x)=matrix of concentration of group components % by weight, equal to i xs with the elements defined from the law of conservation of mass for the assumed set of reactions; and X = vector of concentration of derivatives of particular components with time. After analytic differentiation of Equation (4) with initial conditions : X,(O) = 100, X,(O) = X,(O), X,(O) = 0
T
(5)
P(MPa) (k) / t(ks)
t 0
1.0
0.5
1.5
R
Figure 6 Extreme conversion values and corresponding values of temperature, a; pressure, b; and reaction time, c; versus R Figure 5 lsolines of gas content in reaction product (wt%) function of temperature (T) and reaction time (t). Pressure, p=29.4 MPa
as a PCMF :its, .(k) / 733 -29L
at the time when the level of benzene-insoluble fractions is already fixed. From Figure 5 it can be seen that the major portions of gases form in the initial period of depolymerization before stabilization of reaction conditions, i.e., before time denoted as 0. The analysis of regression equations by Hoerl’s method confirmed the above hypothesis. Figures 6 and 7 are the final effect of the processing by Hoerl’s method. They represent extreme values of conversion and oil content as functions of experimental area radius, the centre of which was point 703 K, 19.6 MPa, 7.2 ks. Also, numerical values of particular parameters related to the extreme value of given radius are marked in these figures. High conversion
1690
FUEL, 1984,
Vol 63, December
718 -24.:
703 -19.6
Figure 7 Extreme yield of oil and corresponding values of temperature, a; pressure, b; and reaction time, c; versus R
Hydrogenating
depolymerization
of coal extracts:
6. Radomyski
and J. Szczygie#
and through variations of Lagrange constants, a relationship is obtained between the concentrations of particular substances and time for each kinetic model: xi=fi(K,t) i= l-4 (6) Estimation of reaction rate constants for a definite temperature was carried out based on the minimization of F,(K,rO)=
f:
(7)
i [Xij-Xij(tj)]’
j=li=l
where: Xij=experimental value of the concentration of the ith component at the jth moment of time; Xij(tj) = value of the ith component concentration at the jth moment of time calculated from the model; and t, = induction time. To find the minimum of Equation (7) the gradient method of a non-linear optimization after FlecherDawidon’ was used. When selecting a possible kinetic model and its particular constituent reactions, the following requirements were taken into account: 1. Hypothetical models should more or less comply with intuition and a general knowledge of hydrogenating depolymerization. 2. They should provide for the content of all defined groups of compounds at each moment of time and at any temperature and pressure. 3. They should be as simple as possible. Changes in the content of asphaltenes, which reach as a maximum, confirmed experiment, made it possible to reduce the range of investigations to these kinetic models which promised good description of the change in content of these group components with time. The following models were verified by experimental data: G M
K3
/ K4 C+iF-A
T
K3
L-!!cLT II
For particular definite forms: -(C-Cl) 0
Equation
-(C-C,)
IY
-(C-C,)
-(A)
-(C&
0
0 (C-C,)
0
0 -(C-Cf)
7
(1) takes the following
(‘4)
0
(C-C,)
jK4K5
III
models
0
-(C-C,)
(C-C,)
-(A)
0
0
0 (A)
(C-CJ) 0
HI K3
x
HI
K4
K5
Kl
K2
K3
-(C-C,)
0 0 (C-c/) -(C-C,)
0
(A) 0 -(A) 0
-(C-Cf)
0 (C-C,) 0 -(C-C,)
(C-C,)
-(A)
0
0 0
(A) 0
0 (C-C,)
-(C-C,)
(C-C,) 0
21 6
252
288
of the reaction product (wt%) versus Figure 8 Composition reaction time for 733 K and 29.4 MPa. Lines for scheme I: a, benzene insoluble; b, asphaltene; c, oil; d, gas. Experimental points: 0, benzene insoluble; x, asphaltene; A, oil; 0, gas
I””
90
c
-0.3140
I
36
72
10 8
14 4 180 Time (ks)
21 6
25 2
28.8
Where: 0=0 concentration. The solutions of systems (I-A)(IV-A) are equations describing the change in concentration of particular group components with time according to the assumed model. Calculated numerical values of reaction rate constants for 673-733 K and 29.4 MPa for the investigated models are given in Tuble I.
versus experimental data The theoretical curves calculated for model (I), repre(1-A) sented in Figure 8, describe well the changes in concentrations with time offractions insoluble in benzene, the same is true for asphaltene and oil contents. Only the changes in gas content show disagreement; calculated values for gases within the investigated range of tempera(II-A) ture, 673-733K, are too low at the beginning of the reaction, and increase with time, exceeding the experimental value after a certain time. It appears that this results from an incorrect assumption of the reaction model. The (III-A) asphaltenes which condense to fractions insoluble in benzene are the source not only of oils but also of gases; thus it appeared advisable to examine the consecutive model for fractions insoluble in benzene decomposing into oils. It was likely that by assuming a consecutive reaction the above discrepancy with gas contents could be (IV-A) avoided. Models
I[ 1 Kl
'
K3 K5 K2
(A) -(C-C,) -(A) 0 0 0
14 4 180 Time (ks)
Kl
0
x
10.8
T CsA%O
CxAK2-0
I
72
of the reaction products (wt%) versus Figure 9 Composition reaction time for 733 K and 29.4 MPa. Lines for scheme II: a, benzene insoluble; b, asphaltene; c, oil; d, gas. Experimental points: 0, benzene insoluble; x, asphaltene; A, oil; 0, gas
G
G
K3
36
-0.2970
FUEL, 1984,
Vol 63, December
1691
Hydrogenating
depolymerization
of coal extracts: B. Radomyski
Equations of (II) gave a better description of the changes in gaseous components except for the initial period of time, though the calculated values still overestimated the experimental results (Figure 9). The calculated content of asphaltenes reached a maximum higher than that determined by experiment; this appeared too early and afterwards the asphaltene yield quickly approached zero, thus underrating experimental results. Oils are also badly described -their content is underrated up to 3.6 ks of reaction time and overstated thereafter. Therefore, it appears that if a consecutive mechanism of depolymerization of benzene insoluble fractions into oils is operating, then model (II) is incomplete. The addition of direct formation of oil from benzene-insoluble fractions favourably affects the description of the changes of particular group compounds (model (III); Figures IO, II and 12). Gases are satisfactorily described with the exception of the initial reaction period. For the benzeneinsoluble fraction the theoretical curves do not show the tendency to overstate the results, because of the reaction C-0, and the contents are described with a smaller error. The changes in asphaltene content are still not precisely described by model (III), but better however than by model (II). The maximum in asphaltenes is reached after
90
80 70 c 60 -
-2.06
0
3.6
7.2
10 8 14.4 Trme (ks)
18.0
21.6
25.2
28.8
Figure 10 Composition of the reaction products (wt%) versus reaction time for 733 K and 29.4 MPa. Lines for scheme III: a, benzene insoluble; b, asphaltene; c, oil; d, gas. Experimental points: 0, benzene insoluble; x, asphaltene; A, oil; 0, gas
and J. Szczygie+
70 2
60
$
50
t z 8
40 30 20 10 I
-0.3390
I
3.6
7.2
I
10 8
I
I
I
14 4 18.0 Time (ks)
21.6
Composition of the reaction products (wt%) Figure 12 reaction time for 673 K and 29.4 MPa. Lines for scheme
I
25.2
I 288
versus
III: a, benzene insoluble; b, asphaltene; c, oil; d, gas. Experimental points: 0, benzene insoluble; x, asphaltene; A, oil; 0, gas
5.4,3.6 and 1.8 ks at 673,703 and 733 K, respectively. After
reaching the maximum the asphaltene content decreases slowly in keeping with experimental results. The calculated numerical values of reaction rate constants K, for C-0 (Tab/e 4) show that the major portion of oils forms by way of direct decomposition of benzene-insoluble fractions. In Figures 10,lI and 12a broken line represents the change with time of the content of oils coming only from the reaction C-+0. The remaining oils are formed through asphaltenes; in practice they form after z 1.8 ks of reaction. After 28.8 ks the fractions of oils coming directly from fractions insoluble in benzene amount to 65.0, 59.2 and 56.0% at 733, 703 and 673 K, respectively. Model IV, which includes a balance between benzeneinsoluble fractions and asphaltenes, gives a quantitatively worse description of the gases formed, which reach a maximum. The remaining groups of compounds are satisfactorily described. It is characteristic that according to this model the contents of benzene-insoluble fractions increase slightly with longer reaction times. Negative values of reaction rate constants for reaction B-+C (Table 4) disqualify model IV as not true.
CONCLUSIONS Consideration of qualitative and quantitative descriptions of changes in content with particular groups of compounds judged by model errors (Table 4) suggest the adoption for the catalytic hydrogenation of benzeneinsoluble fractions of the model represented below (model III). s .ci 50 ki g 40 o
G K3
_____________________-_---
30
-0.29
I
0
3.6
7.2
10.8 14.4 Time (Its)
18.0
21 6
25.2
28.8
Figure 11 Composition of the reaction products (wt%) versus reaction time for 703 K and 29.4 MPa. Lines for scheme Ill: a, benzene insoluble; b, asphaltene; c, oil; d, gas. Experimental points: 0, benzene insoluble; x, asphaltene; A, oil; IJ, gas
1692
f Kl C-A-0
FUEL, 1984,
Vol 63, December
K2 K5
t
The analysis of the suggested kinetic models confirmed the conclusions of the statistical analysis of experimental data concerning oils formation directly from benzeneinsoluble fractions, and allowed a quantitative determination of contribution to the reaction of oils formation from benzene-insoluble fractions and asphaltenes. Explanation of distortions in the description of production by the suggested models needs further studies.
Hydrogenating Table
4
Reaction
rate constants Scheme
Reaction
rate
for different
I (K)
673
703
733
Kl
0.0149
0.0157
0.0264
K2
-
-
K3
0.0050 0.0031 0.0108
0.00884 0.0032 0.0234
10.80
10.94
K4
KS Model errors= (%) a Model
errors
measurements
calculated
from
of depolymerization Scheme
Temperature
constant (min-1)
schemes
depolymerization
673
703
733
0.0168 0.0059 0.0434
0.0217 0.0052 0.0073 -
0.0379 0.0208 0.0134 -
8.59
24.64
24.9
2 3 4 5
Scheme (K)
673
703
733
0.0556 0.0293 0.0207 -
0.0153 0.0016 0.0066 0.0098
0.0160 0.0021 0.0105 0.0227
0.0266 0.0042 0.0207 _ 0.0406
23.01
8.58
9.99
6.59
values
of the contents
Temperature
IV (K)
673
703
733
0.0151 0.0022 0.0074 -0.0014 0.0097
0.0157 0.0029 0.0113 -0.0015 0.0225
0.0267 0.0054 0.0222 -0.0022 0.399
9.23
9.92
6.72
of all the group
components
for all
at the temperature
REFERENCES 1
Ill
Temperature
and calculated
and J. Szczygiel
errors Scheme
(K)
of the experimental
and model
II
Temperature
differences
of coal extracts: B. Radomyski
Weller, S., Polipetz, M. G. and Friedman, S. Ind. Eng. Chem. 1951, 43, 1572; 1951,43,1575 Liebenberg, B. J. and Potgieter, H. G. J. Fuel 1973, 52, 130 Yoshida, R. and Maekawa, Y. Fuel 1976,55,337 Schwager, I. and Yen, Teh Fu Fuel 1978,57,100 Neavel, R. C. Fuel 1976,55,237
6
7 8 9 10
Shah, Y. T., Cronauer, D. C., McIlvried, H. G. and Parashos, I. A. lnd. Eng. Chem. Process Des. Dev. 1978, 17(3), 288 Whitehurst, D. D. and Mitchell, T. 0. Am. Chem. Sot. Div. Fuel Chem., Preprints 1976, 21(5), 127 Hoer], E. Gem. Eng. Progr. 1959, 55(1 l), 69 Findeisen, W., Szymanowski, J. and Wierzbicki, A. ‘Calculation methods of optimization’, PWN, Warszawa, 1977 Stolarski, M. PhD Thesis, Wroclaw, Poland, 1979
FUEL, 1984, Vol 63, December
1693
Radomyski
and Jerzy Szczygiet
Institute of Chemistry and Technology (Received 3 April 1981)
of Petroleum
and Coal, Wroclaw,
Poland
This Paper presents a statistical and mathematical analysis of hypotheses concerning the autoclave hydrogenating depolymerization of coal extract fractions insoluble in benzene. From comparison of theoretical and experimental data the most probable reaction mechanism was selected. (Keywords:
coal; hydrogenation;
catalysis)
Hydrogenating catalytic depolymerization of coal extract is one of the stages in the production of liquid fuel from coal. The subject of this Paper was the hydrogenation of the heaviest group component of coal extract, i.e., benzene-insoluble fractions. The investigations aimed to determine the effects of process parameters such as temperature, pressure and reaction time on raw material depolymerization and on the formation of products of smaller mean molecular weight (i.e., asphaltenes, gases and oils) which were the desired products. Optimum values of process parameters were determined using a statistical approach and, by assuming that reaction occurred between particular groups of compounds treated as chemical individuals, an hypothesis concerning the mechanism of conversion was formulated. Problem formulation
The kinetics of coal hydrogenation have been the subject of many studies. Weller et al.’ performed vitrinite hydrogenation in an autoclave in the presence of stannic sulphide/ammonium chloride mixture and concluded that the conversion of coal to oils involved consecutive reactions and that asphaltenes constituted intermediate products. Potgieter’, investigating the mechanism of noncatalytic hydrogenation of hard coals in the presence of tetralin, concluded that oil components may be formed both directly from coal organic substance and by means of a consecutive reaction through asphaltenes. Yoshida and Maekawa3 arrived at a similar conclusion when hydrogenating coal in an autoclave in the presence of red mud from the Bayer alumina process, as catalyst. Schwager4 found, based on chemical composition and, particularly, on C/H ratios of group components, that the mechanism of coal conversion is a consecutive process passing through carboids and asphaltenes. Neavel’, Shah6 and Whitehurst’ are of the opinion that in the process of coal hydrogenation asphaltenes, oils and gases form by means of simultaneous reactions. Different views on the kinetics of coal hydrogenation result from different process conditions. This Paper presents the results of a study of the kinetics of the hydrogenating depolymerization of benzene0016-2361/84/121687FO7$3.00 @ 1984 Butterworth & Co. (Publishers) Ltd
insoluble coal extract fractions in the presence of cobalticmolybdic catalyst. Such a study makes it possible to programme and control this process to achieve the highest possible product yield. Due to the complex character of the raw material, reaction effects were measured by the change in yield of compound groups treated as individual compounds. The following groups of compounds are distinguished : 1. Compounds insoluble in benzene, denoted ‘C 2. Asphaltenes, soluble in benzene but insoluble in paraffin and cycloparafin hydrocarbons, denoted ‘A 3. Oils, soluble in paraffin and cycloparaflin hydrocarbons, denoted ‘0 4. Gases, denoted ‘G The kinetics of the process are analysed by assuming that the reaction takes place between these groups which are treated as individual chemical compounds. STATISTICAL
METHOD
The effects of three independent variables, temperature, pressure and time of reaction, on the process (i.e., dependent variable y) were investigated and assumed to take the following form: ~=b,+b,xl+b,x,+b3x3+bl,xl,+b,3x13+b23~23 +
b, 1x12 + bZ2x22 + b33x32
(1)
b,, are model coefficients.
where: b,... Based on the derived equation, the process was optimized with regard to its parameters. Then a preliminary analysis, which can be tested at the next stage of investigations by constructing a definite kinetic model, was carried out. To simplify the analysis of the multinomial expression, Equation (1) was developed into the so-called canonic form, as follows: Y- Y,=B,,X1Z+B22X22+B33X32
(2) where: Y,=value of objective function in the centre of a new co-ordinate system; X1,X2,X3 = independent variables of a canonic equation related to variables from Equation (1) (x,;c2sc3 =non-singular linear conversion); B, 1,B22,B33 =coefficients of canonic equation.
FUEL,
1984,
Vol
63, December
1687
Hydrogenating
depolymerization
of coal extracts: B. Radomyski
The conversion of a multinomial equation into a canonic form is executed in two stages: (1) translation of a coordinate system centre into point S (stationary point), which disposes of the linear terms of the equation; and (2) turning of the coordinate system through a definite angle thus eliminating scalar products. Canonic Equation (2) simplifies the production of a graphical form of response surface. This produces isolines of numerical values of the response function in the system of two variables with a fixed numerical value of the third independent variable. The resulting regression equation was used for the analysis of depolymerization of benzeneinsoluble fractions by means of a Hoerl’s crest line’. This method makes it possible to find one general optimum or several local optima, and also allows ready analysis of the process on two-dimensional diagrams irrespective of the problem dimensions. On these diagrams the changes of particular variables can be observed as the function of radius R = (XT +x: +x:)“’ in order to maximize the output function. The calculation technique of this method relies essentially on the multiple solution of the set of equations written in matrix form: [(% I -2M
[(2b,,-b;; 13)3 )-/!I b
[
b 13
where:
A = (b3 + blsxl
1 Experimental
iI3 _zj]
results of catalytical
(MPa)
(ks.1
A,
A*
673
29.4
733
19.6
673
19.6
733
9.8
x1
of the benzene-insoluble
Temperature (K) Pressure (MPa) Reaction time (ks)
0
+1
673 9.8 0.0
JO3 19.6 7.2
733 29.4 14.4
part of coal extract”
Xfoa) 1.8
69.2 18.1
3.0 21.5
0.7 41.3
19.1
3.6 7.2
14.0
23.6
44.0
19.1 18.4
13.9 13.6
15.8 10.5
51.0 56.6
19.3 19.3
80.4 28.5 20.0
2.8 32.0 37.1 49.4 53.3
15.6 16.4
14.1
1.2 23.1 26.0 19.7 15.0
16.5 17.6
1.8 3.6 7.2 14.4
84.0 41.5 23.6 16.8 13.1
0.4 26.5 36.9 32.7 29.6
1.5 16.8 23.5 34.4 40.9
14.1 15.2 16.0 16.1 16.4
4.1 21.8 25.3
11.4 11.8 12.1
27.5
12.4 4.1 5.3 6.4 7.4
A,
1.8 3.6 7.2 14.4
14.4
16.9
0
84.1
0.4
3.6 7.2 14.4
65.8 62.0 59.5
0.6 0.6 0.6
0
91.6 88.1 82.6 71.7
0.2 0.5 2.1 2.6
4.1 6.1 8.9 18.3
3.6
84.6 78.0
0.7 1 .o
4.5 9.8
7.2 14.4
75.2 73.3
0.4 0.6
12.7 13.5
11.2 11.7 12.6
0 3.6 7.2 14.4
93.9 87.7 85.7 81.5
0.3 0.8 0.8 0.9
2.3 4.4 5.3 8.4
3.5 7.1 8.2 9.2
3.6 7.2 14.4
time was measured starting from the moment when the assumed values of reaction conditions
FUEL, 1984,
-1
Gas (wt%)
0
9.8
f;]
Oil (wt%)
0
1688
ranges in real and coded units
Asphaltene (wt%)
0
a Reaction
Table 2 Parameters
Benzeneinsoluble (wt%)
14.4
29.4
=-[
depolymerization
(K)
673
To generate a multinomial model of the second order all available results of the previous experiments (Table 1) were used for optimization. The experiments were performed in a shaking autoclave of 0.2 dm3 volume capable of operation under 39.2 MPa (400atm) at 773 K (460°C). The range of parameters in encoded and real quantities is given in Table 2 from which it follows that the transition from natural quantities to encoded ones is determined by the following relations:
x3
Reaction time
29.4
x [f;]
+ bZ3xZ)/(x3).
Pressure
JO3
EXPERIMENTAL
x2
Temperature
733
This relation results from the equating of derivatives dy/ax with zero. By solving a given set of equations repeatedly for different value of A, which is changed optionally within a certain range, one obtains the values of (vectors) and hence radii XlJ2sc3 R = (xl2 +x22 +x32)4 for which the objective function reaches a maximum or minimum value.
-Al
b 12
Table
and J. Szczygie%
Vol 63, December
had been reached
10.2
Hydrogenating
depolymerization
of coal extracts: B. Radomyski and J. SzczygiaI
A, - 703
x1 =
30
x = A, - 19.6 2
(4)
9.8
r-I
A, - 7.2 x3=7.2
Regression coefficients of the assumed equation (tested for adequacy) calculated on MC ODRA-1305 are given in Table 3 together with the values of correlation coefficients, Y. Statistical interpretation of hydrogenation insoluble fractions
of benzene-
A detailed analysis of the effect of particular parameters on the change of output quantities (conversion, content of asphaltenes, oils and gases) can be performed from Figures l-5, which were plotted by graphplotter MC ODRA-1305 using the canonic form of regression equation. Depolymerization in the temperature range 673-733 K at p=29.4 MPa depends to only a small degree on temperature and, in practice, after 7.2 ks the conversion Table 3 Regression coefficients Y Coefficient bo 61 bz 6s 611 btz 61s bzz 62s 63s r
Conversion (%) 44.8 1 .B7 27.49 17.26 0.92 -0.61 -5.6 15.88 5.44 -18.36 0.97
I
I I I I I
1
f (ks)
-
c
I I I I I I I
L-1 Figure 2
lsolines of asphaltenes content in reaction product (wt%) as a function of temperature (7) and reaction time (t). Pressure, p=29.4 MPa
of the assumed equation
Benzeneinsoluble (wt%)
Asphaltenes (wt%)
Oil (wt%)
Gas (wt%)
55.91 -1 .B7 -27.49 -17.26 -0.92 0.61 5.6 -15.88 -5.44 18.36 0.97
3.37 -3.60 8.53 1.67 2.58 -3.23 -2.84 6.65 -0.22 -5.17 0.76
31.27 3.43 15.23 14.18 -2.41 2.85 -2.19 4.87 6.35 -12.11 0.93
9.45 2.06 3.74 1.41 0.76 -0.21 -0.56 4.37 -0.68 -1.11 0.99
718-/l
-
T(k)
T Figure 3 lsolines of oil content in reaction product (wt%) as a function of temperature (T) and pressure (p). Reaction time, t=3.6 ks
Figure
1
temperature
lsolines of conversion (%) as a function of (T) and reaction time (t). Pressure, p=29.4
MPa
reaches 90% (see Figure 1). A specific change in the time for the asphaltene content to reach the maximum indicates that the depolymerization of benzene-insoluble fractions to oil is a consecutive process taking place through asphaltenes (Figure 2). However, since there is a high content of oil after 3.6 ks (Figure 3) it may be supposed that the direct reaction of depolymerization of benzene-insoluble fractions into oil contributes much to the production of oils at least in the initial period of the reaction, and that a higher content of oil under corresponding conditions of temperature and pressure after 14.4 ks (Figure 4) probably results from a secondary depolymerization of asphaltenes to oils, since this occurs
FUEL, 1984,
Vol 63, December
1689
Hydrogenating
depolymerization of coal extracts: 8. Radomyski and J. Szczygie+
values are obtained by maintaining 703 K temperature and increasing pressure and reaction time. A similar profile of changes can be observed during the maximization of oil yield, though a longer time of reaction is necessary and a favourable effect of temperature rise can be noticed. This suggests a consecutive depolymerization, though direct formation of oils from benzene-insoluble fractions cannot be excluded, as is testified by the considerable quantities of oil present during the initial period of reaction, MATHEMATICAL
ANALYSIS
The possible kinetic models are represented by sets of differential equations resulting from the application of the law of conservation of mass. A general form of these equations is given below: X=X(x).K
Figure 4 lsolines of oil content in reaction product (wt%) as a function of temperature (T) and pressure (p). Reaction time, t=14.4 ks
(4)
where: K= vector of reaction rate constants = 1 x s; s = the number of possible reactions in the assumed kinetic model; X(x)=matrix of concentration of group components % by weight, equal to i xs with the elements defined from the law of conservation of mass for the assumed set of reactions; and X = vector of concentration of derivatives of particular components with time. After analytic differentiation of Equation (4) with initial conditions : X,(O) = 100, X,(O) = X,(O), X,(O) = 0
T
(5)
P(MPa) (k) / t(ks)
t 0
1.0
0.5
1.5
R
Figure 6 Extreme conversion values and corresponding values of temperature, a; pressure, b; and reaction time, c; versus R Figure 5 lsolines of gas content in reaction product (wt%) function of temperature (T) and reaction time (t). Pressure, p=29.4 MPa
as a PCMF :its, .(k) / 733 -29L
at the time when the level of benzene-insoluble fractions is already fixed. From Figure 5 it can be seen that the major portions of gases form in the initial period of depolymerization before stabilization of reaction conditions, i.e., before time denoted as 0. The analysis of regression equations by Hoerl’s method confirmed the above hypothesis. Figures 6 and 7 are the final effect of the processing by Hoerl’s method. They represent extreme values of conversion and oil content as functions of experimental area radius, the centre of which was point 703 K, 19.6 MPa, 7.2 ks. Also, numerical values of particular parameters related to the extreme value of given radius are marked in these figures. High conversion
1690
FUEL, 1984,
Vol 63, December
718 -24.:
703 -19.6
Figure 7 Extreme yield of oil and corresponding values of temperature, a; pressure, b; and reaction time, c; versus R
Hydrogenating
depolymerization
of coal extracts:
6. Radomyski
and J. Szczygie#
and through variations of Lagrange constants, a relationship is obtained between the concentrations of particular substances and time for each kinetic model: xi=fi(K,t) i= l-4 (6) Estimation of reaction rate constants for a definite temperature was carried out based on the minimization of F,(K,rO)=
f:
(7)
i [Xij-Xij(tj)]’
j=li=l
where: Xij=experimental value of the concentration of the ith component at the jth moment of time; Xij(tj) = value of the ith component concentration at the jth moment of time calculated from the model; and t, = induction time. To find the minimum of Equation (7) the gradient method of a non-linear optimization after FlecherDawidon’ was used. When selecting a possible kinetic model and its particular constituent reactions, the following requirements were taken into account: 1. Hypothetical models should more or less comply with intuition and a general knowledge of hydrogenating depolymerization. 2. They should provide for the content of all defined groups of compounds at each moment of time and at any temperature and pressure. 3. They should be as simple as possible. Changes in the content of asphaltenes, which reach as a maximum, confirmed experiment, made it possible to reduce the range of investigations to these kinetic models which promised good description of the change in content of these group components with time. The following models were verified by experimental data: G M
K3
/ K4 C+iF-A
T
K3
L-!!cLT II
For particular definite forms: -(C-Cl) 0
Equation
-(C-C,)
IY
-(C-C,)
-(A)
-(C&
0
0 (C-C,)
0
0 -(C-Cf)
7
(1) takes the following
(‘4)
0
(C-C,)
jK4K5
III
models
0
-(C-C,)
(C-C,)
-(A)
0
0
0 (A)
(C-CJ) 0
HI K3
x
HI
K4
K5
Kl
K2
K3
-(C-C,)
0 0 (C-c/) -(C-C,)
0
(A) 0 -(A) 0
-(C-Cf)
0 (C-C,) 0 -(C-C,)
(C-C,)
-(A)
0
0 0
(A) 0
0 (C-C,)
-(C-C,)
(C-C,) 0
21 6
252
288
of the reaction product (wt%) versus Figure 8 Composition reaction time for 733 K and 29.4 MPa. Lines for scheme I: a, benzene insoluble; b, asphaltene; c, oil; d, gas. Experimental points: 0, benzene insoluble; x, asphaltene; A, oil; 0, gas
I””
90
c
-0.3140
I
36
72
10 8
14 4 180 Time (ks)
21 6
25 2
28.8
Where: 0=0 concentration. The solutions of systems (I-A)(IV-A) are equations describing the change in concentration of particular group components with time according to the assumed model. Calculated numerical values of reaction rate constants for 673-733 K and 29.4 MPa for the investigated models are given in Tuble I.
versus experimental data The theoretical curves calculated for model (I), repre(1-A) sented in Figure 8, describe well the changes in concentrations with time offractions insoluble in benzene, the same is true for asphaltene and oil contents. Only the changes in gas content show disagreement; calculated values for gases within the investigated range of tempera(II-A) ture, 673-733K, are too low at the beginning of the reaction, and increase with time, exceeding the experimental value after a certain time. It appears that this results from an incorrect assumption of the reaction model. The (III-A) asphaltenes which condense to fractions insoluble in benzene are the source not only of oils but also of gases; thus it appeared advisable to examine the consecutive model for fractions insoluble in benzene decomposing into oils. It was likely that by assuming a consecutive reaction the above discrepancy with gas contents could be (IV-A) avoided. Models
I[ 1 Kl
'
K3 K5 K2
(A) -(C-C,) -(A) 0 0 0
14 4 180 Time (ks)
Kl
0
x
10.8
T CsA%O
CxAK2-0
I
72
of the reaction products (wt%) versus Figure 9 Composition reaction time for 733 K and 29.4 MPa. Lines for scheme II: a, benzene insoluble; b, asphaltene; c, oil; d, gas. Experimental points: 0, benzene insoluble; x, asphaltene; A, oil; 0, gas
G
G
K3
36
-0.2970
FUEL, 1984,
Vol 63, December
1691
Hydrogenating
depolymerization
of coal extracts: B. Radomyski
Equations of (II) gave a better description of the changes in gaseous components except for the initial period of time, though the calculated values still overestimated the experimental results (Figure 9). The calculated content of asphaltenes reached a maximum higher than that determined by experiment; this appeared too early and afterwards the asphaltene yield quickly approached zero, thus underrating experimental results. Oils are also badly described -their content is underrated up to 3.6 ks of reaction time and overstated thereafter. Therefore, it appears that if a consecutive mechanism of depolymerization of benzene insoluble fractions into oils is operating, then model (II) is incomplete. The addition of direct formation of oil from benzene-insoluble fractions favourably affects the description of the changes of particular group compounds (model (III); Figures IO, II and 12). Gases are satisfactorily described with the exception of the initial reaction period. For the benzeneinsoluble fraction the theoretical curves do not show the tendency to overstate the results, because of the reaction C-0, and the contents are described with a smaller error. The changes in asphaltene content are still not precisely described by model (III), but better however than by model (II). The maximum in asphaltenes is reached after
90
80 70 c 60 -
-2.06
0
3.6
7.2
10 8 14.4 Trme (ks)
18.0
21.6
25.2
28.8
Figure 10 Composition of the reaction products (wt%) versus reaction time for 733 K and 29.4 MPa. Lines for scheme III: a, benzene insoluble; b, asphaltene; c, oil; d, gas. Experimental points: 0, benzene insoluble; x, asphaltene; A, oil; 0, gas
and J. Szczygie+
70 2
60
$
50
t z 8
40 30 20 10 I
-0.3390
I
3.6
7.2
I
10 8
I
I
I
14 4 18.0 Time (ks)
21.6
Composition of the reaction products (wt%) Figure 12 reaction time for 673 K and 29.4 MPa. Lines for scheme
I
25.2
I 288
versus
III: a, benzene insoluble; b, asphaltene; c, oil; d, gas. Experimental points: 0, benzene insoluble; x, asphaltene; A, oil; 0, gas
5.4,3.6 and 1.8 ks at 673,703 and 733 K, respectively. After
reaching the maximum the asphaltene content decreases slowly in keeping with experimental results. The calculated numerical values of reaction rate constants K, for C-0 (Tab/e 4) show that the major portion of oils forms by way of direct decomposition of benzene-insoluble fractions. In Figures 10,lI and 12a broken line represents the change with time of the content of oils coming only from the reaction C-+0. The remaining oils are formed through asphaltenes; in practice they form after z 1.8 ks of reaction. After 28.8 ks the fractions of oils coming directly from fractions insoluble in benzene amount to 65.0, 59.2 and 56.0% at 733, 703 and 673 K, respectively. Model IV, which includes a balance between benzeneinsoluble fractions and asphaltenes, gives a quantitatively worse description of the gases formed, which reach a maximum. The remaining groups of compounds are satisfactorily described. It is characteristic that according to this model the contents of benzene-insoluble fractions increase slightly with longer reaction times. Negative values of reaction rate constants for reaction B-+C (Table 4) disqualify model IV as not true.
CONCLUSIONS Consideration of qualitative and quantitative descriptions of changes in content with particular groups of compounds judged by model errors (Table 4) suggest the adoption for the catalytic hydrogenation of benzeneinsoluble fractions of the model represented below (model III). s .ci 50 ki g 40 o
G K3
_____________________-_---
30
-0.29
I
0
3.6
7.2
10.8 14.4 Time (Its)
18.0
21 6
25.2
28.8
Figure 11 Composition of the reaction products (wt%) versus reaction time for 703 K and 29.4 MPa. Lines for scheme Ill: a, benzene insoluble; b, asphaltene; c, oil; d, gas. Experimental points: 0, benzene insoluble; x, asphaltene; A, oil; IJ, gas
1692
f Kl C-A-0
FUEL, 1984,
Vol 63, December
K2 K5
t
The analysis of the suggested kinetic models confirmed the conclusions of the statistical analysis of experimental data concerning oils formation directly from benzeneinsoluble fractions, and allowed a quantitative determination of contribution to the reaction of oils formation from benzene-insoluble fractions and asphaltenes. Explanation of distortions in the description of production by the suggested models needs further studies.
Hydrogenating Table
4
Reaction
rate constants Scheme
Reaction
rate
for different
I (K)
673
703
733
Kl
0.0149
0.0157
0.0264
K2
-
-
K3
0.0050 0.0031 0.0108
0.00884 0.0032 0.0234
10.80
10.94
K4
KS Model errors= (%) a Model
errors
measurements
calculated
from
of depolymerization Scheme
Temperature
constant (min-1)
schemes
depolymerization
673
703
733
0.0168 0.0059 0.0434
0.0217 0.0052 0.0073 -
0.0379 0.0208 0.0134 -
8.59
24.64
24.9
2 3 4 5
Scheme (K)
673
703
733
0.0556 0.0293 0.0207 -
0.0153 0.0016 0.0066 0.0098
0.0160 0.0021 0.0105 0.0227
0.0266 0.0042 0.0207 _ 0.0406
23.01
8.58
9.99
6.59
values
of the contents
Temperature
IV (K)
673
703
733
0.0151 0.0022 0.0074 -0.0014 0.0097
0.0157 0.0029 0.0113 -0.0015 0.0225
0.0267 0.0054 0.0222 -0.0022 0.399
9.23
9.92
6.72
of all the group
components
for all
at the temperature
REFERENCES 1
Ill
Temperature
and calculated
and J. Szczygiel
errors Scheme
(K)
of the experimental
and model
II
Temperature
differences
of coal extracts: B. Radomyski
Weller, S., Polipetz, M. G. and Friedman, S. Ind. Eng. Chem. 1951, 43, 1572; 1951,43,1575 Liebenberg, B. J. and Potgieter, H. G. J. Fuel 1973, 52, 130 Yoshida, R. and Maekawa, Y. Fuel 1976,55,337 Schwager, I. and Yen, Teh Fu Fuel 1978,57,100 Neavel, R. C. Fuel 1976,55,237
6
7 8 9 10
Shah, Y. T., Cronauer, D. C., McIlvried, H. G. and Parashos, I. A. lnd. Eng. Chem. Process Des. Dev. 1978, 17(3), 288 Whitehurst, D. D. and Mitchell, T. 0. Am. Chem. Sot. Div. Fuel Chem., Preprints 1976, 21(5), 127 Hoer], E. Gem. Eng. Progr. 1959, 55(1 l), 69 Findeisen, W., Szymanowski, J. and Wierzbicki, A. ‘Calculation methods of optimization’, PWN, Warszawa, 1977 Stolarski, M. PhD Thesis, Wroclaw, Poland, 1979
FUEL, 1984, Vol 63, December
1693