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Solid state pyrolyses Part 2: Solid state kinetics studied by pyrolysis—gas chromatography
Journal of Analytical and Applied Pyrolysis, 19 (1991) 15-27 Elsevier Science publishers B.V., Amsterdam
15
Solid state pyrolyses Part 2: * Solid state kinetics studied by pyrolysis-gas chromatography Lars Carlsen *, Anders Feldthus and Peter Bo ** ~ornb~tio~ department, Rise Nationai ~~rato9,
OK-4000 Roskilde ~~e~rnark~
(Received 21 June, 1990; accepted in final form February 6, 1991)
ABSTRACT The applicability of pyrolysis-gas chromatography to isothermal solid state kinetic studies is discussed based on a model comprising primary formation of volatiles and a non-volatile fraction, the latter being converted into volatiles and an eventual non-p~ol~able fraction in secondary reactions. The n th order kinetic approach to solid state reactions is illustrated by studies on the pyrolysis of coal. The significance of the obtained activation parameters, including the activation entropy, is discussed. Coal; gas chromatography;
pyrolysis; solid state kinetics.
INTRODUCTION
It is generally accepted that in connection with the possible characterization of polymers, e.g. by their thermal stability, or with the study of hydrocarbon formation from coals and kerogens, kinetic investigations are crucial. Thus, in the field of petroleum generation studies, activation parameters, i.e. activation energies and frequency (pre-exponential) factors, are fundamental requirements needed to carry out successful basin-modelling I131. In a recent paper we suggested a rather simple approach to solid state kinetics, based on the assumption that the overall reaction could be formulated by a single n th order reaction [3]. The applicability of this approach was illustrated by a study on the decomposition kinetics of polystyrene [3]. However, the study unequivocally demonstrated the inadequacy of this simple model when more chemically complicated systems such as coals and kerogens were investigated [3]. * For part 1, see ref 3. ** Present address: Haraldsborgvej 016%2370/91/$03.50
54, DK-4000 Roskilde, Denmark.
0 1991 Elsevier Science Publishers B.V.
16
It appears reasonable to assume that reactions taking place in the solid state at pyrolysis temperatures do not follow “nice” kinetic laws with integer reaction orders. As a variety of products typically is generated by pyrolysis of e.g. polymers, synthetic as well as naturally occurring such as coals, kerogens etc., it is suggested that the overall reaction, leading to volatile products, can be described by nth order kinetics, n possibly being fractional. In the simple case [3], where all solid material is converted directly to volatiles, the solid state kinetics can be based on the following rate equation:
d(A) = -k(A)” dt
-
which gives rise to the follo~ng
integral expression
where C is the amount of product formed and A, is the original total amount of pyrolyzable material, k and n are the rate constant and the reaction order, respectively. Since the method is based on gas chromatographic (FID) detection, the measurable products are the generated volatile hydrocarbons only. Thus, if consecutive and parallel reactions are operating, e.g. producing a second solid phase, which (consecutively) can be converted into volatiles, the system becomes rather complicated. In addition a reaction which directly converts the starting material into a non-volatile and non-pyrolyzable product may operate. Finally, a possible release of trapped volatile material in the starting material also has to be considered. On this background we propose the following general model for the degradation of solid polymeric material.
P
k
V
/’ \ k
Q&A
k,
“2
s
kA
S’
Scheme 1
A denotes the starting material, whereas V and S are the volatile and solid products of the primary reactions. Reactions 3 and 4 of the solid S may consecutively lead to volatiles, V, and a solid product S’, which is assumed not to be converted into volatiles. A non-volatile product Q, generated directly from A, which is not consecutively converted into volatiles is also taken into account. It should be noted that Q, as well as S’, also represent products, which do not give rise to a FID signal (see experimental section),
17
Finally, the parallel reaction of P into volatiles is considered, P being trapped volatile material in the starting material A. A similar type of model has recently been proposed by Skala et al. in a study on oil shale pyrolysis [4].
THEORY
The kinetic evaluation of the system will in the following be discussed based on the assumption that all reactions are considered to be of nth order, ni not necessarily being an integer. According to the above reaction scheme, the system can kinetically be described in the following way dA dt=
- k,A”’ - k,A”= - k,A”’
dS = + k,An2 - k,S”’ - k,Sn4 dt
dV = + k,A”’ + k,S”’ + k,P”X dt
dP dt = -k,P”X
dQ = dt
+kSAn5
dS’ = +k4Sn4 dt
It is important to note that this model describes overall reactions, i.e. no distinction is made between the various chemical components being evolved during the pyrolysis. Thus, all quantities are mass measures or relative mass measures, i.e. relative to the mass of some component that does not change during the pyrolysis. The set of coupled first order differential equations are solved numerically by a Runge-Kutta method [5], reaction rates (ki), reaction orders (n,) and initial values of A, P and S being specified as input parameters.
EXPERIMENTAL
The coal sample studied was obtained from the Dutch Coalbank (200 US 38). The C/H ratio of the coal was estimated at 14.8. For our studies the coal sample was pulverized, the applied fraction having an average particle diameter I 50 pm.
The pyrolyses were carried out using a PYROLA-85 foil pulse pyrolyzer (PYROL ab, Lund, Sweden). Samples of approximately 5-10 pg were used. In the case of polystyrene the samples were applied to the platinum foil of the pyrolyzer in THF solution, whereas the coal samples were applied as a suspension in pentane. The pyrolyzer was connected to a Hewlett-Packard HP-5890 gas-chromatograph in combination with an HP-5895A work-station. The pyrolysis products were passed directly, i.e. without any separation, to the FI detection of the gas-chromatograph through a 40 cm fused silica tube (uncoated, deactivated, id. 0.32 mm) [3,6]. The temperature of the transfer tube was kept at 300 o C. The pyrolyses were carried out as so-called sequential pyrolyses [7], i.e. the pyrolysis temperature and time was chosen in a way that each pyrolysis afforded only fractional decomposition of the sample. Typically 8-12 pyrolyses of the same sample were carried out. The remaining pyrolyzable part of material was eventually volatilized by pyrolysis at very high temperatures, 1200-1400 K. It is emphasized that the actual pyrolysis time in each of the pyrolyses in the sequence (in the present study typically 1.5 s) is significantly longer than the corresponding temperature rise time (typically 8-10 ms). Thus the technique has to be regarded as isothermal pyrolysis. The kinetic evaluation was carried out applying the computer code KIN2LIB [8], which is based on a Runge-Kutta procedure for solving coupled first order differential equations [5]. The program is developed using the built-in facilities of the HP-5895A work-station and designed to read the report-files, giving the integrated GC-results, directly. The program calculates and plots the time dependent amounts of each of the six involved components together with the experimental values of V, obtained from the gas chromatographic analysis of the volatiles produced during the pyrolysis. As a guide for the otherwise manual fitting of the calculated data to the experimental data, the program finally calculates the sum of the squared differences between the experimental data points and the calculated amounts of volatiles at the same time, as well as the mean, minimum and maximum deviation between experimental and calculated values, the latter two being expressed as percentages of the experimentally obtained value. The amount of combined pyrolyzate, V, is taken as the accumulated integrated peak-integrals, the total amount of pyrolyzable material being the final accumulated integral value obtained following the eventual volatilization of any remaining pyrolyzable material. Thus, the sum of the initial values of A, S and P equals the final accumulated integral value of V found during the pyrolysis plus the sum of the eventual amounts of Q and S’. The latter two values are, however, not experimentally determined, but found by an iterative procedure. In a forthcoming paper we will describe the fitting procedure in detail as part of a parameter study [9].
19
It should be noted that the model presented in this paper includes the original simple model [3];the latter is achieved applying k, # 0 and ki( i = 2-5) = k, = 0.
RESULTS AND DISCUSSION
In our previous paper we studied the overall kinetics of the pyrolytic degradation of polystyrene (MW 37,~) 131. Based on the simple A -+ Y model, i.e. complete and direct volatilization of the starting material A into volatiles I’, we estimated the rate constant at 768 K as 6.47 x 10m5 s-l, the reaction order being 1.65. The result was obtained based on a least-squares fit [3]. Applying the extended model described in the present paper for the polystyrene case, using the above given values for k and n, resulted in the plot depicted in Fig. 1, visualizing the expe~ment~ly and theoretically evaluated formation of volatiles (V) and the simukaneous theoretically estimated variation in the solid and non-volatile materials (A, S, S’). Not surprisingly, it is immediately noted by visual inspection that an almost perfect fit of the calculated amount of volatiles generated to the experimental data is obtained. This is further verified by the calculated deviations. The maximum and minimum deviations between the experimentally and th~retically obtained values were calculated to 5.14% (point #1) and 0.58% (point #3), respectively.
1
Y;
28 TIME
(sec.
38
f
Fig. 1. Kinetic evaluation of polystyrene (MW 37.~) pyrolysis, T = 768 K, pulse: 2.0 s).
pyrolysis (approx. 10 pg, sequential
20
1
2.0E4:
a
1.8E4: 1.6E4: 1.4E4: 1 .2E4: 10000: 8000: 6000: 4000: 2000: I
, 0
‘.
,
5
‘.
!
I
10 (mln.1
Tlmc
.’
.I,
15
‘. 20
1.2E4-
b
10000-
e000-
6000-
4000-
2000-
0-,
.’ 0
I
,I
.I
,I
1,
L,
10
,_
,,
. .
,,
,,
20 Time
:
; 30
(mtn.) _
3.0E4-
c
2.0E4-
Fig. 2. Sequential pyrolyses (pulse: 1.5 s) of (a), non-extracted coal (T= 853 K); (b), pyridine-extracted coal (T = 843 K); (c), methylene chloride-extracted coal (T = 803 K).
21
Turning to coal pyrolysis we encountered several problems, due to the complex nature of the material, when attempting to apply the simple A + V model [3]. In sum these problems comprise the presence of volatiles trapped in the coal matrix (cf. the molecular-macromolecular, ‘host-guest’, coal model as described in ref. lo), as well as formation of less- and non-volatile material, i.e. tar and char [lo-121 as primary pyrolysis products. Some of these products will, however, by increased pyrolysis temperature or at the original pyrolysis temperature, with a lower rate constant be converted into volatiles in secondary pyrolysis reactions. The first of these problems, which causes a disproportionately high apparent volatile formation during the first pyrolysis period, can be circumvented to a certain extent by studying solvent-extracted coal samples. However, we found that solvent extraction apparently does not remove quantitatively all volatile material trapped in the coal matrix. This is demonstrated by the ~~ornato~ap~c traces depicted in Figs. 2(a)-2(c), visualizing sequential pyrolyses of (a), non-extracted; (b), pyridine-extracted; and (c) methylene chloride-extracted coal samples, respectively. In all three cases disproportionately high amounts of volatiles are observed to be formed during the first pyrolysis, although this tendency appears less pronounced in the cases of the solvent-extracted coal samples. The more effective technique to remove the volatile fraction in the coal sample prior to pyrolysis of the coal matrix was found to be the~ovapo~zation. The sample under investigation (5-10 pg) was thermolyzed at 525-550 K for approximately 100 s (sequence of 5 x 20 s). Subsequently the temperature was raised to the actual pyrolysis temperature requested to promote the pyrolysis of the coal matrix. The resulting sequential pyrolysis is visualized in Fig. 3. It is immediately noted that the disproportionately high first peak no longer appears. Thus, for our kinetic evaluation (vide
7000 6000: 5000: 4000: 3000: 2000: 1000: D)
c
‘ 15
1.
I
20 Time
i 25 (min.
I
I
1 30
I
I 35
1
Fig. 3. Sequential pyrolysis of thermovaporized
coal (T= 825 K, pulse: 1.5 s).
22
infra) we used thermovaporized samples. By comparing the amounts of volatiles liberated during the sequential pyrolysis of non-extracted and thermovaporized coal samples, we estimated the amount of volatiles, i.e. trapped material in the samples to be 8-U%. Thus, for the fitting procedure we assumed the initial values of A, P, and S to be A, = 77-84, P, = 8-15 and SO= 8% of the final accumulated integral values of V, V, formed during the pyrolysis, respectively. For the fitting procedure in the case of thermovaporized samples the values of A, and S,, were consequently set equal to 92 and 8% of Vr, respectively. The eventual adjustment of A, and S, by adding the theoretically estimated values corresponding to S’ was achieved by an iterative procedure (see experimental section). The second problem mentioned above, i.e. the operation of the secondary formation of volatiles as well as the eventual non-pyrolyzable fraction, from primary generated less- and/or non-volatile products, i.e. the S + V and S + S’ reactions, cannot be remedied without application of other techniques supplementary to the flash pyrolysis studies [3]. Thus, we are forced to apply the reaction parameters for the four reactions A + V, A + S, S + V, and S --) S’ for the kinetic evaluation. In addition the reaction P + V must be brought into play in cases where non-extracted samples are studied. In order to evaluate the applicability of the model in this respect, we carried out pyrolyses on a thermovaporized coal sample. In Fig. 3 the chromatographic trace following sequential pyrolysis at 825 K is shown.
TIME
Fig. 4. Kinetic evaluation of the pyrolysis pyrolysis, T = 825 K, pulse: 1.5 s).
(Sec.)
of thermovaporized
coal (5-10
pg, sequential
23
0
5
I0 TItlE
Fig. 5. Kinetic evaluation of the pyrolysis pyrolysis, T = 825 K, pulse: 1.5 s).
I5 (sec.
20
1
of non-extracted
coal (S-10
fig, sequential
The rather significant abundance of the final peak corresponding to the eventual volatil~ation (at 1375 K) reflects the eventual formation of volatiles in the secondary pyrolysis, i.e. the S -+ V reaction, of primary generated less-volatile material. In Fig. 4 the resulting close-to-perfect fit is visualized applying k, = 1.21 x 1O-4 s-l, k2 = 2.1 x 10m4 s-l, k, = 4.0 X 10v6 s-l, and k4 = 1.1 X 10e5 S -’ corresponding to the A + V, A 3 S, S -+ V, and S + S’ reactions, respectively. The corresponding reaction order was estimated as n, = 1.62, n2 = 1.65, n3 = 1.65, and n4 = 1.62. The calculated ma~mum and minimum deviations between the experimental and theoretical obtained values were calculated to 3.13% (point #2) and 0.18% (point #ll), respectively. Since the only difference between the kinetic evaluation of the pyrolyses of the thermovaporized and the non-extracted coal samples is the additional operation of the P -+ V reaction in the latter case, it should be possible to evaluate the sequential pyrolysis of the non-extracted coal sample at 825 K applying the above given rate constants and reaction orders adding the parameters k, and n, corresponding to the P -+ V reaction. Hence, assuming a ~imolecul~ release of the trapped volatiles, i.e. n, = 1.0 and a rather high rate constant, k, = 5.0 s-l we obtained a close-to-perfect fit (Fig. 5), the calculated maximum and minimum deviations between the experimentally and theoretically obtained values amounting to 1.80% (point #2) and 0.02% (point # 3), respectively. In order to estimate activation parameters for the single reactions involved in the coal pyrolysis according to the proposed model, we studied sequential pyrolyses of thermovaporized coal samples in the temperature
24
range 813-848 K. The kinetic evaluations were based on the assumptions that within the relatively narrow temperature range, the involved reaction orders are constants and that the initial amount of S is a constant, in the -5
A +V -7 i .5
-9
-11
-13 0.00116
0.00116
-5
I
0.00116 -5
0.00120
,
0.00116
0.00116 I
0.00116
0.00120 I
0.00120
0.00122 I
0.00122 I
0.00122
0.00121 I
0.00124 I
0.00124
Fig. 6. Arrhenius plots for the four reactions A +V, A-+& S+V, and S-+S’ involved in the pyrolysis of thermovaporized coal (5-10 pg, sequential pyrolysis, T = 813-848 K, pulse: 1.5 s).
25
present case set equal to 8%. In Fig. 6, the Arrhenius plots (In k vs l/T) for the reactions A + V, A + S, S + V, and S + S’, respectively, are displayed. In all cases it is noted that In k vs l/T give rise to straight lines. Based on a least square procedure the activation parameters were estimated to be: (1) A + V: E, = 55.6 + 7.0 kcal/mol, In k,, = 24.6 + 4.2 s-‘; (2) A + S: E, = 83.0 + 6.0 kcal/mol, In km2 = 42.3 + 3.6 s-l; (3) S -+ I? E3 = 28.4 + 4.6 kcal/mol, In k,, = 4.8 + 2.8 s-‘; and (4) S + S’: E4 = 59.9 + 12.5 kcal/mol, In k,, = 24.8 + 7.6 s-l, respectively, based on 11 measurements. The obtained data appear to be in good agreement with kinetic parameters previously reported for the formation of hydrocarbons from coals, kerogens and shale [13-151. Thus, Burnham et al. reported activation parameters (E,/ln k,) for the eight Argonne Premium Coals in the range 46.9 kcal/mo1/27.8 s-l-62.8 kcal/mo1/39.7 s-l and for a series of kerogens from 43.3 kcal/mo1/24.6 s-l-55.2 kcal/mo1/32.8 s-l, both studies applying distributed activation energy models [13,14]. Evaluation of hydrocarbon evolution from Colorado oil shale, applying a single 1.51-order reaction led to E, = 49.3 kcal/mol and In k, = 28.9 s-l [15]. However, it is emphasized that these data correspond to the overall formation of hydrocarbons, therefore not describing the single steps presented in our model. It is noted that the standard errors, especially in the case S + S’, seem unsatisfactorily high. We are aware of this problem, which we hope to remedy by an improved fitting procedure [9]. However, it appears crucial that the actual pyrolysis temperatures for the single pyrolyses in the sequence remain absolutely constant, which unfortunately constitutes a problem with no present cure. A second quite interesting feature is the actual mutual values of the estimated activation parameters. In this context it is, first of all, interesting to note that the relations between the activation energies and the corresponding frequency factors agree nicely with the so-called autocorrelations of kinetic parameters in coal and char reactions recently reported by Essenhigh and Misra [16]. Secondly, at least at first sight, it may appear somewhat thought-provoking that the activation energy for the primary process A + S is apparently 25-55 kcal/mol higher than those for the primary process A + V and the secondary processes S + V and S + S’. However, the answer to this is to be sought in the frequency factors and, hence, the reaction entropy AS* = R (In k, - ln(kT/h)) k and h being the Boltzmann and the Planck constants, respectively [17]. At
573 K the term ln(kT/h) equals 12.8 s-l. Obviously the primary reactions proceed with highly positive activation entropies (AS& = 23 and 59 e.u., respectively), whereas the secondary reaction S + I/ exhibits a significant negative activation entropy (AS& =
26
- 16 ea.). AS& for the S --) S’ reaction was estimated to be 24 e.u. This is in accordance with the assumption that the primary processes in the pyrolysis of coal involve cleavage of C-H and C-C bonds in the coal matrix [18-221, causing, in terms of entropy, a significantly increased degree of disorder in the system. For comparison, rupture of the central C-C bond in 1,Zbiphenyl ethane proceeds with an activation energy of approximately 50 kcal/mole and a logarithmic frequency factor of ca. 21.5 s-l (see ref. 20), the latter corresponding to an activation entropy of ca. 17 e.u. A broad selection of elementary reactions of coal pyrolysis has been reported by Gavalas et al. [21,22]. The S + I/ process, on the other hand, apparently requires transition states of a high degree of order, which possibly could be associated with the formation of ring-containing compounds by cyclization processes. Thus, it appears obvious that the single sets of activation parameters (E,/ln k,) and, hence, the rate equation (k = k,exp( - EJRT)) has to be considered in order to evaluate the relative importance of the single reactions at a given temperature (see ref 13). To further elucidate these features the possible variations in the product composition following the single pyrolyses in the sequence have to be studied in detail. Studies along this line will be reported separately [23]. In summary it can be concluded that pyrolysis-gas chromatography constitutes an attractive alternative approach (e.g. to techniques using the parallel first-order reaction model) to studies of solid state kinetics. However, it is emphasized that only overall, but not the individual elemental reactions involved, are elucidated, the composite nature of the operating processes being reflected in the non-integer values of the reaction orders. Thus, overall activation parameters for the single steps are obtained, in contrast to the distribution of activation energies obtained using the parallel first-order reactions approach. The relation between these approaches will be discussed in a forthcoming paper.
ACKNOWLEDGMENT
The work has been financed through the research programme the Danish Department of Energy.
EFP88 of
REFERENCES 1 Cs. Sajgo and J. Lefler, in G. Buntebarth and L. Stegena (Editors). Lecture notes in Earth Sciences, Vol. 5: Paleogeothermics, Berlin, 1986, p. 119. 2 J.J. Sweeney, A.K. Bumham and R.L. Braun, A model of hydrocarbon generation for type I kerogen: Application to the Uinta Basin, Utah, UCRL-94245, Lawrence Livermore National Laboratory, Livermore, CA, 1986.
27 3 L. Carlsen, A. Feldthus and P. Bo, J. Anal. Appl. Pyrolysis, 15 (1989) 373. 4 D. Skala, H. Kopsch, M. Sokic, H.J. Neumann and J.A. Jovanovic, Fuel, 69 (1990) 490. 5 H. Margenau and G.M. Murphy, The Mathemati~ of Physics and Chemistry, 2nd Ed., Van Nostrand, Princeton, 1956. 486 pp. 6 H. Alden, G. Eklund, J.R. Pedersen and B. Stromberg, J. Anal. Appl. Pyrolysis, 9 (1985) 75. 7 I. Ericsson, J. Chromatogr. Sci., 16 (1978) 340. 8 P. Bo, A. Feldthus and L. Carlsen, unpub~sh~. 9 A. Feldthus and L. Carlsen, to be published. 10 N.E. Vanderborgh, J.M. Williams, Jr. and H.-R. Schulten, J. Anal. Appl. Pyrolysis, 8 (1985) 271. 11 P.R. Solomon, D.G. Hamblen and R.M. Carangelo, in K.J. Voorhees (Editor), Analytical Pyrolysis. Techniques and Applications, Butte~orths, London, 1984, p. 121. 12 G.J. Lawson, in R.C. Mackenzie (Editor), Differential Thermal Analysis, Vol. 1, Academic Press, London, 1970, p. 705. 13 A.K. Bumham, M.S. Oh, R.W. Crawford and A.M. Samoun, Energy and Fuels, 3 (1989) 42. 14 A.K. Bumham, R.L. Braun and H.R. Gregg, Energy and Fuels, 1 (1987) 452. 15 R.L. Braun and A.K. Bumham, Fuel, 65 (1986) 218. 16 R.H. Essenhigh and M.K. Misra, Energy and Fuels, 4 (1990) 171. 17 R.H. Lowry and K.S. Richardson, Mechanism and Theory in Organic Chemistry, Harper and Row, New York, 1976. 18 J.H. !&inn, Fuel, 63 (1984) 1187. 19 P.J.J. Tromp, Coal Pyrolysis. Basic Phenomena Relevant to Conversion Processes, PhDThesis, University of Amsterdam, 1987. 20 J.M. Charlesworth, Ind. Eng. Chem. Process Des. Dev., 24 (1985) 1125. 21 G.R, Gavalas, P.H.-K. Cheong and R. Jain, Ind. Eng. Chem. Fundam., 20 (1981) 113. 22 G.R. Gavalas, R. Jain and P.H.-K. Cheong, Ind. Eng. Chem. Fundam., 20 (1981) 122. 23 A. Feldthus and L. Carlsen, to be published.
15
Solid state pyrolyses Part 2: * Solid state kinetics studied by pyrolysis-gas chromatography Lars Carlsen *, Anders Feldthus and Peter Bo ** ~ornb~tio~ department, Rise Nationai ~~rato9,
OK-4000 Roskilde ~~e~rnark~
(Received 21 June, 1990; accepted in final form February 6, 1991)
ABSTRACT The applicability of pyrolysis-gas chromatography to isothermal solid state kinetic studies is discussed based on a model comprising primary formation of volatiles and a non-volatile fraction, the latter being converted into volatiles and an eventual non-p~ol~able fraction in secondary reactions. The n th order kinetic approach to solid state reactions is illustrated by studies on the pyrolysis of coal. The significance of the obtained activation parameters, including the activation entropy, is discussed. Coal; gas chromatography;
pyrolysis; solid state kinetics.
INTRODUCTION
It is generally accepted that in connection with the possible characterization of polymers, e.g. by their thermal stability, or with the study of hydrocarbon formation from coals and kerogens, kinetic investigations are crucial. Thus, in the field of petroleum generation studies, activation parameters, i.e. activation energies and frequency (pre-exponential) factors, are fundamental requirements needed to carry out successful basin-modelling I131. In a recent paper we suggested a rather simple approach to solid state kinetics, based on the assumption that the overall reaction could be formulated by a single n th order reaction [3]. The applicability of this approach was illustrated by a study on the decomposition kinetics of polystyrene [3]. However, the study unequivocally demonstrated the inadequacy of this simple model when more chemically complicated systems such as coals and kerogens were investigated [3]. * For part 1, see ref 3. ** Present address: Haraldsborgvej 016%2370/91/$03.50
54, DK-4000 Roskilde, Denmark.
0 1991 Elsevier Science Publishers B.V.
16
It appears reasonable to assume that reactions taking place in the solid state at pyrolysis temperatures do not follow “nice” kinetic laws with integer reaction orders. As a variety of products typically is generated by pyrolysis of e.g. polymers, synthetic as well as naturally occurring such as coals, kerogens etc., it is suggested that the overall reaction, leading to volatile products, can be described by nth order kinetics, n possibly being fractional. In the simple case [3], where all solid material is converted directly to volatiles, the solid state kinetics can be based on the following rate equation:
d(A) = -k(A)” dt
-
which gives rise to the follo~ng
integral expression
where C is the amount of product formed and A, is the original total amount of pyrolyzable material, k and n are the rate constant and the reaction order, respectively. Since the method is based on gas chromatographic (FID) detection, the measurable products are the generated volatile hydrocarbons only. Thus, if consecutive and parallel reactions are operating, e.g. producing a second solid phase, which (consecutively) can be converted into volatiles, the system becomes rather complicated. In addition a reaction which directly converts the starting material into a non-volatile and non-pyrolyzable product may operate. Finally, a possible release of trapped volatile material in the starting material also has to be considered. On this background we propose the following general model for the degradation of solid polymeric material.
P
k
V
/’ \ k
Q&A
k,
“2
s
kA
S’
Scheme 1
A denotes the starting material, whereas V and S are the volatile and solid products of the primary reactions. Reactions 3 and 4 of the solid S may consecutively lead to volatiles, V, and a solid product S’, which is assumed not to be converted into volatiles. A non-volatile product Q, generated directly from A, which is not consecutively converted into volatiles is also taken into account. It should be noted that Q, as well as S’, also represent products, which do not give rise to a FID signal (see experimental section),
17
Finally, the parallel reaction of P into volatiles is considered, P being trapped volatile material in the starting material A. A similar type of model has recently been proposed by Skala et al. in a study on oil shale pyrolysis [4].
THEORY
The kinetic evaluation of the system will in the following be discussed based on the assumption that all reactions are considered to be of nth order, ni not necessarily being an integer. According to the above reaction scheme, the system can kinetically be described in the following way dA dt=
- k,A”’ - k,A”= - k,A”’
dS = + k,An2 - k,S”’ - k,Sn4 dt
dV = + k,A”’ + k,S”’ + k,P”X dt
dP dt = -k,P”X
dQ = dt
+kSAn5
dS’ = +k4Sn4 dt
It is important to note that this model describes overall reactions, i.e. no distinction is made between the various chemical components being evolved during the pyrolysis. Thus, all quantities are mass measures or relative mass measures, i.e. relative to the mass of some component that does not change during the pyrolysis. The set of coupled first order differential equations are solved numerically by a Runge-Kutta method [5], reaction rates (ki), reaction orders (n,) and initial values of A, P and S being specified as input parameters.
EXPERIMENTAL
The coal sample studied was obtained from the Dutch Coalbank (200 US 38). The C/H ratio of the coal was estimated at 14.8. For our studies the coal sample was pulverized, the applied fraction having an average particle diameter I 50 pm.
The pyrolyses were carried out using a PYROLA-85 foil pulse pyrolyzer (PYROL ab, Lund, Sweden). Samples of approximately 5-10 pg were used. In the case of polystyrene the samples were applied to the platinum foil of the pyrolyzer in THF solution, whereas the coal samples were applied as a suspension in pentane. The pyrolyzer was connected to a Hewlett-Packard HP-5890 gas-chromatograph in combination with an HP-5895A work-station. The pyrolysis products were passed directly, i.e. without any separation, to the FI detection of the gas-chromatograph through a 40 cm fused silica tube (uncoated, deactivated, id. 0.32 mm) [3,6]. The temperature of the transfer tube was kept at 300 o C. The pyrolyses were carried out as so-called sequential pyrolyses [7], i.e. the pyrolysis temperature and time was chosen in a way that each pyrolysis afforded only fractional decomposition of the sample. Typically 8-12 pyrolyses of the same sample were carried out. The remaining pyrolyzable part of material was eventually volatilized by pyrolysis at very high temperatures, 1200-1400 K. It is emphasized that the actual pyrolysis time in each of the pyrolyses in the sequence (in the present study typically 1.5 s) is significantly longer than the corresponding temperature rise time (typically 8-10 ms). Thus the technique has to be regarded as isothermal pyrolysis. The kinetic evaluation was carried out applying the computer code KIN2LIB [8], which is based on a Runge-Kutta procedure for solving coupled first order differential equations [5]. The program is developed using the built-in facilities of the HP-5895A work-station and designed to read the report-files, giving the integrated GC-results, directly. The program calculates and plots the time dependent amounts of each of the six involved components together with the experimental values of V, obtained from the gas chromatographic analysis of the volatiles produced during the pyrolysis. As a guide for the otherwise manual fitting of the calculated data to the experimental data, the program finally calculates the sum of the squared differences between the experimental data points and the calculated amounts of volatiles at the same time, as well as the mean, minimum and maximum deviation between experimental and calculated values, the latter two being expressed as percentages of the experimentally obtained value. The amount of combined pyrolyzate, V, is taken as the accumulated integrated peak-integrals, the total amount of pyrolyzable material being the final accumulated integral value obtained following the eventual volatilization of any remaining pyrolyzable material. Thus, the sum of the initial values of A, S and P equals the final accumulated integral value of V found during the pyrolysis plus the sum of the eventual amounts of Q and S’. The latter two values are, however, not experimentally determined, but found by an iterative procedure. In a forthcoming paper we will describe the fitting procedure in detail as part of a parameter study [9].
19
It should be noted that the model presented in this paper includes the original simple model [3];the latter is achieved applying k, # 0 and ki( i = 2-5) = k, = 0.
RESULTS AND DISCUSSION
In our previous paper we studied the overall kinetics of the pyrolytic degradation of polystyrene (MW 37,~) 131. Based on the simple A -+ Y model, i.e. complete and direct volatilization of the starting material A into volatiles I’, we estimated the rate constant at 768 K as 6.47 x 10m5 s-l, the reaction order being 1.65. The result was obtained based on a least-squares fit [3]. Applying the extended model described in the present paper for the polystyrene case, using the above given values for k and n, resulted in the plot depicted in Fig. 1, visualizing the expe~ment~ly and theoretically evaluated formation of volatiles (V) and the simukaneous theoretically estimated variation in the solid and non-volatile materials (A, S, S’). Not surprisingly, it is immediately noted by visual inspection that an almost perfect fit of the calculated amount of volatiles generated to the experimental data is obtained. This is further verified by the calculated deviations. The maximum and minimum deviations between the experimentally and th~retically obtained values were calculated to 5.14% (point #1) and 0.58% (point #3), respectively.
1
Y;
28 TIME
(sec.
38
f
Fig. 1. Kinetic evaluation of polystyrene (MW 37.~) pyrolysis, T = 768 K, pulse: 2.0 s).
pyrolysis (approx. 10 pg, sequential
20
1
2.0E4:
a
1.8E4: 1.6E4: 1.4E4: 1 .2E4: 10000: 8000: 6000: 4000: 2000: I
, 0
‘.
,
5
‘.
!
I
10 (mln.1
Tlmc
.’
.I,
15
‘. 20
1.2E4-
b
10000-
e000-
6000-
4000-
2000-
0-,
.’ 0
I
,I
.I
,I
1,
L,
10
,_
,,
. .
,,
,,
20 Time
:
; 30
(mtn.) _
3.0E4-
c
2.0E4-
Fig. 2. Sequential pyrolyses (pulse: 1.5 s) of (a), non-extracted coal (T= 853 K); (b), pyridine-extracted coal (T = 843 K); (c), methylene chloride-extracted coal (T = 803 K).
21
Turning to coal pyrolysis we encountered several problems, due to the complex nature of the material, when attempting to apply the simple A + V model [3]. In sum these problems comprise the presence of volatiles trapped in the coal matrix (cf. the molecular-macromolecular, ‘host-guest’, coal model as described in ref. lo), as well as formation of less- and non-volatile material, i.e. tar and char [lo-121 as primary pyrolysis products. Some of these products will, however, by increased pyrolysis temperature or at the original pyrolysis temperature, with a lower rate constant be converted into volatiles in secondary pyrolysis reactions. The first of these problems, which causes a disproportionately high apparent volatile formation during the first pyrolysis period, can be circumvented to a certain extent by studying solvent-extracted coal samples. However, we found that solvent extraction apparently does not remove quantitatively all volatile material trapped in the coal matrix. This is demonstrated by the ~~ornato~ap~c traces depicted in Figs. 2(a)-2(c), visualizing sequential pyrolyses of (a), non-extracted; (b), pyridine-extracted; and (c) methylene chloride-extracted coal samples, respectively. In all three cases disproportionately high amounts of volatiles are observed to be formed during the first pyrolysis, although this tendency appears less pronounced in the cases of the solvent-extracted coal samples. The more effective technique to remove the volatile fraction in the coal sample prior to pyrolysis of the coal matrix was found to be the~ovapo~zation. The sample under investigation (5-10 pg) was thermolyzed at 525-550 K for approximately 100 s (sequence of 5 x 20 s). Subsequently the temperature was raised to the actual pyrolysis temperature requested to promote the pyrolysis of the coal matrix. The resulting sequential pyrolysis is visualized in Fig. 3. It is immediately noted that the disproportionately high first peak no longer appears. Thus, for our kinetic evaluation (vide
7000 6000: 5000: 4000: 3000: 2000: 1000: D)
c
‘ 15
1.
I
20 Time
i 25 (min.
I
I
1 30
I
I 35
1
Fig. 3. Sequential pyrolysis of thermovaporized
coal (T= 825 K, pulse: 1.5 s).
22
infra) we used thermovaporized samples. By comparing the amounts of volatiles liberated during the sequential pyrolysis of non-extracted and thermovaporized coal samples, we estimated the amount of volatiles, i.e. trapped material in the samples to be 8-U%. Thus, for the fitting procedure we assumed the initial values of A, P, and S to be A, = 77-84, P, = 8-15 and SO= 8% of the final accumulated integral values of V, V, formed during the pyrolysis, respectively. For the fitting procedure in the case of thermovaporized samples the values of A, and S,, were consequently set equal to 92 and 8% of Vr, respectively. The eventual adjustment of A, and S, by adding the theoretically estimated values corresponding to S’ was achieved by an iterative procedure (see experimental section). The second problem mentioned above, i.e. the operation of the secondary formation of volatiles as well as the eventual non-pyrolyzable fraction, from primary generated less- and/or non-volatile products, i.e. the S + V and S + S’ reactions, cannot be remedied without application of other techniques supplementary to the flash pyrolysis studies [3]. Thus, we are forced to apply the reaction parameters for the four reactions A + V, A + S, S + V, and S --) S’ for the kinetic evaluation. In addition the reaction P + V must be brought into play in cases where non-extracted samples are studied. In order to evaluate the applicability of the model in this respect, we carried out pyrolyses on a thermovaporized coal sample. In Fig. 3 the chromatographic trace following sequential pyrolysis at 825 K is shown.
TIME
Fig. 4. Kinetic evaluation of the pyrolysis pyrolysis, T = 825 K, pulse: 1.5 s).
(Sec.)
of thermovaporized
coal (5-10
pg, sequential
23
0
5
I0 TItlE
Fig. 5. Kinetic evaluation of the pyrolysis pyrolysis, T = 825 K, pulse: 1.5 s).
I5 (sec.
20
1
of non-extracted
coal (S-10
fig, sequential
The rather significant abundance of the final peak corresponding to the eventual volatil~ation (at 1375 K) reflects the eventual formation of volatiles in the secondary pyrolysis, i.e. the S -+ V reaction, of primary generated less-volatile material. In Fig. 4 the resulting close-to-perfect fit is visualized applying k, = 1.21 x 1O-4 s-l, k2 = 2.1 x 10m4 s-l, k, = 4.0 X 10v6 s-l, and k4 = 1.1 X 10e5 S -’ corresponding to the A + V, A 3 S, S -+ V, and S + S’ reactions, respectively. The corresponding reaction order was estimated as n, = 1.62, n2 = 1.65, n3 = 1.65, and n4 = 1.62. The calculated ma~mum and minimum deviations between the experimental and theoretical obtained values were calculated to 3.13% (point #2) and 0.18% (point #ll), respectively. Since the only difference between the kinetic evaluation of the pyrolyses of the thermovaporized and the non-extracted coal samples is the additional operation of the P -+ V reaction in the latter case, it should be possible to evaluate the sequential pyrolysis of the non-extracted coal sample at 825 K applying the above given rate constants and reaction orders adding the parameters k, and n, corresponding to the P -+ V reaction. Hence, assuming a ~imolecul~ release of the trapped volatiles, i.e. n, = 1.0 and a rather high rate constant, k, = 5.0 s-l we obtained a close-to-perfect fit (Fig. 5), the calculated maximum and minimum deviations between the experimentally and theoretically obtained values amounting to 1.80% (point #2) and 0.02% (point # 3), respectively. In order to estimate activation parameters for the single reactions involved in the coal pyrolysis according to the proposed model, we studied sequential pyrolyses of thermovaporized coal samples in the temperature
24
range 813-848 K. The kinetic evaluations were based on the assumptions that within the relatively narrow temperature range, the involved reaction orders are constants and that the initial amount of S is a constant, in the -5
A +V -7 i .5
-9
-11
-13 0.00116
0.00116
-5
I
0.00116 -5
0.00120
,
0.00116
0.00116 I
0.00116
0.00120 I
0.00120
0.00122 I
0.00122 I
0.00122
0.00121 I
0.00124 I
0.00124
Fig. 6. Arrhenius plots for the four reactions A +V, A-+& S+V, and S-+S’ involved in the pyrolysis of thermovaporized coal (5-10 pg, sequential pyrolysis, T = 813-848 K, pulse: 1.5 s).
25
present case set equal to 8%. In Fig. 6, the Arrhenius plots (In k vs l/T) for the reactions A + V, A + S, S + V, and S + S’, respectively, are displayed. In all cases it is noted that In k vs l/T give rise to straight lines. Based on a least square procedure the activation parameters were estimated to be: (1) A + V: E, = 55.6 + 7.0 kcal/mol, In k,, = 24.6 + 4.2 s-‘; (2) A + S: E, = 83.0 + 6.0 kcal/mol, In km2 = 42.3 + 3.6 s-l; (3) S -+ I? E3 = 28.4 + 4.6 kcal/mol, In k,, = 4.8 + 2.8 s-‘; and (4) S + S’: E4 = 59.9 + 12.5 kcal/mol, In k,, = 24.8 + 7.6 s-l, respectively, based on 11 measurements. The obtained data appear to be in good agreement with kinetic parameters previously reported for the formation of hydrocarbons from coals, kerogens and shale [13-151. Thus, Burnham et al. reported activation parameters (E,/ln k,) for the eight Argonne Premium Coals in the range 46.9 kcal/mo1/27.8 s-l-62.8 kcal/mo1/39.7 s-l and for a series of kerogens from 43.3 kcal/mo1/24.6 s-l-55.2 kcal/mo1/32.8 s-l, both studies applying distributed activation energy models [13,14]. Evaluation of hydrocarbon evolution from Colorado oil shale, applying a single 1.51-order reaction led to E, = 49.3 kcal/mol and In k, = 28.9 s-l [15]. However, it is emphasized that these data correspond to the overall formation of hydrocarbons, therefore not describing the single steps presented in our model. It is noted that the standard errors, especially in the case S + S’, seem unsatisfactorily high. We are aware of this problem, which we hope to remedy by an improved fitting procedure [9]. However, it appears crucial that the actual pyrolysis temperatures for the single pyrolyses in the sequence remain absolutely constant, which unfortunately constitutes a problem with no present cure. A second quite interesting feature is the actual mutual values of the estimated activation parameters. In this context it is, first of all, interesting to note that the relations between the activation energies and the corresponding frequency factors agree nicely with the so-called autocorrelations of kinetic parameters in coal and char reactions recently reported by Essenhigh and Misra [16]. Secondly, at least at first sight, it may appear somewhat thought-provoking that the activation energy for the primary process A + S is apparently 25-55 kcal/mol higher than those for the primary process A + V and the secondary processes S + V and S + S’. However, the answer to this is to be sought in the frequency factors and, hence, the reaction entropy AS* = R (In k, - ln(kT/h)) k and h being the Boltzmann and the Planck constants, respectively [17]. At
573 K the term ln(kT/h) equals 12.8 s-l. Obviously the primary reactions proceed with highly positive activation entropies (AS& = 23 and 59 e.u., respectively), whereas the secondary reaction S + I/ exhibits a significant negative activation entropy (AS& =
26
- 16 ea.). AS& for the S --) S’ reaction was estimated to be 24 e.u. This is in accordance with the assumption that the primary processes in the pyrolysis of coal involve cleavage of C-H and C-C bonds in the coal matrix [18-221, causing, in terms of entropy, a significantly increased degree of disorder in the system. For comparison, rupture of the central C-C bond in 1,Zbiphenyl ethane proceeds with an activation energy of approximately 50 kcal/mole and a logarithmic frequency factor of ca. 21.5 s-l (see ref. 20), the latter corresponding to an activation entropy of ca. 17 e.u. A broad selection of elementary reactions of coal pyrolysis has been reported by Gavalas et al. [21,22]. The S + I/ process, on the other hand, apparently requires transition states of a high degree of order, which possibly could be associated with the formation of ring-containing compounds by cyclization processes. Thus, it appears obvious that the single sets of activation parameters (E,/ln k,) and, hence, the rate equation (k = k,exp( - EJRT)) has to be considered in order to evaluate the relative importance of the single reactions at a given temperature (see ref 13). To further elucidate these features the possible variations in the product composition following the single pyrolyses in the sequence have to be studied in detail. Studies along this line will be reported separately [23]. In summary it can be concluded that pyrolysis-gas chromatography constitutes an attractive alternative approach (e.g. to techniques using the parallel first-order reaction model) to studies of solid state kinetics. However, it is emphasized that only overall, but not the individual elemental reactions involved, are elucidated, the composite nature of the operating processes being reflected in the non-integer values of the reaction orders. Thus, overall activation parameters for the single steps are obtained, in contrast to the distribution of activation energies obtained using the parallel first-order reactions approach. The relation between these approaches will be discussed in a forthcoming paper.
ACKNOWLEDGMENT
The work has been financed through the research programme the Danish Department of Energy.
EFP88 of
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27 3 L. Carlsen, A. Feldthus and P. Bo, J. Anal. Appl. Pyrolysis, 15 (1989) 373. 4 D. Skala, H. Kopsch, M. Sokic, H.J. Neumann and J.A. Jovanovic, Fuel, 69 (1990) 490. 5 H. Margenau and G.M. Murphy, The Mathemati~ of Physics and Chemistry, 2nd Ed., Van Nostrand, Princeton, 1956. 486 pp. 6 H. Alden, G. Eklund, J.R. Pedersen and B. Stromberg, J. Anal. Appl. Pyrolysis, 9 (1985) 75. 7 I. Ericsson, J. Chromatogr. Sci., 16 (1978) 340. 8 P. Bo, A. Feldthus and L. Carlsen, unpub~sh~. 9 A. Feldthus and L. Carlsen, to be published. 10 N.E. Vanderborgh, J.M. Williams, Jr. and H.-R. Schulten, J. Anal. Appl. Pyrolysis, 8 (1985) 271. 11 P.R. Solomon, D.G. Hamblen and R.M. Carangelo, in K.J. Voorhees (Editor), Analytical Pyrolysis. Techniques and Applications, Butte~orths, London, 1984, p. 121. 12 G.J. Lawson, in R.C. Mackenzie (Editor), Differential Thermal Analysis, Vol. 1, Academic Press, London, 1970, p. 705. 13 A.K. Bumham, M.S. Oh, R.W. Crawford and A.M. Samoun, Energy and Fuels, 3 (1989) 42. 14 A.K. Bumham, R.L. Braun and H.R. Gregg, Energy and Fuels, 1 (1987) 452. 15 R.L. Braun and A.K. Bumham, Fuel, 65 (1986) 218. 16 R.H. Essenhigh and M.K. Misra, Energy and Fuels, 4 (1990) 171. 17 R.H. Lowry and K.S. Richardson, Mechanism and Theory in Organic Chemistry, Harper and Row, New York, 1976. 18 J.H. !&inn, Fuel, 63 (1984) 1187. 19 P.J.J. Tromp, Coal Pyrolysis. Basic Phenomena Relevant to Conversion Processes, PhDThesis, University of Amsterdam, 1987. 20 J.M. Charlesworth, Ind. Eng. Chem. Process Des. Dev., 24 (1985) 1125. 21 G.R, Gavalas, P.H.-K. Cheong and R. Jain, Ind. Eng. Chem. Fundam., 20 (1981) 113. 22 G.R. Gavalas, R. Jain and P.H.-K. Cheong, Ind. Eng. Chem. Fundam., 20 (1981) 122. 23 A. Feldthus and L. Carlsen, to be published.