Ind. Eng. Chem. Process Des. Dev. 1985, 2 4 , 1125-1132 Leathard, D. A.; Purneil, J. H. R o c . R . SOC. London A 1968, 306, 553. Levy, J. H.; Stuart, W. I.Proceedings First Australian Workshop on Oil Shale, Lucas Heights, May 1983, p 135. Lin, M. C.; Back, M. H. Can. J . Chem. 1966, 4 4 , 2389. Lin, M. C.; LaMler, K. J. Can. J . Chem. 1966, 4 4 , 2927. McFarlane, I.; Rankine, J.; Walker, D. R. Southern Pacific Petroleum Report to Shareholders, Sydney, NSW, April 27, 1979. Miirdichian, V. “Organic Synthesis-Volume 2”; Reinhoid: New York, 1957. Murray, J. B.; Evans, D. G. Fuel 1972, 57, 290. Mushrush, G. W.; Haziett, R. N. Naval Research Lab. Report No. 8630 Washington, DC, Sept 21, 1982. Raley, J. H. Fuel 1980, 59, 419. Regtop, R. A.; Crisp, P. T.; Ellis, J. Fuel 1982. 67, 185. Robinson, W. E. I n “Organic Geochemistry”; Eglinton, G.; Murphy, M. T. J., Ed.; Springer-Verlag: Berlin, 1969. Robinson, W. E. I n “Oil Shale”; Yen, T. F.; Chiiingarian, G. V. Ed.; Elsevier: Amsterdam, 1976. Sakai, T.; Soma, K.; Sasaki, Y.; Tominga, H.; Kunugi, T. I n “Advances in Chemistry No. 97, Refining Petroleum for Chemicals”; American Chemical Society: Washington, DC, 1970.
1125
Sandei, R. S.; Waicheski, P. J. Fuel 1981, 6 0 , 644. Saxby, J. D. I n “Oil Shale”; Yen, T. F.; Chiiingarian, G. V., Ed.; Elsevier: Amsterdam, 1976. Saxby, J. D. fuel 1981, 60, 994. Saxby, J. D.; Riley, K. W. Nature (London) 1984, 308, 177. van de Meent, D.;Brown, S. C.; F’hiip, R. P.; Simoneit, B. R. T. Geochim. Cosmochim Acta 1980, 44, 999. van de Meent, D.; de Leeuw, J. W.; Schenck, P. A. I n “Advances in Organic GeOChemlStry 1979”; Douglas, A. G.; Maxwell, J. R.; Ed.; Pergamon: London, 1980. Voge, H. H.; Good,G. M. J . Am. Chem. SOC. 1949, 7 1 , 593. Wallman, P. H.; Tamm, P. W.; Spars, B. G. I n “Oil Shale, Tar Sands and Related Materials”; Stauffer, H. C., Ed.; Symposium No. 163; American Chemical Society: Washington, DC, 1981. Weichman, B. E.; Knight, J. H. US. Patent 4 133 741, 1979. Young, D. A. “Decomposition of Soilds”; Pergamon: London, 1966.
Received for review March 12, 1984 Revised manuscript received October 23, 1984
Oil Shale Pyrolysis. 2. Kinetics and Mechanism of Hydrocarbon Evolution John M. Charlesworth Materials Research Laboratories, P.0. Box 50, Ascot Vale, Victorla, 3032 Australia
The evolution of hydrocarbons from a variety of oil shales and kerogen concentrate has been measured by using flame ionization detection, with the aim of monitoring the kinetics under both isothermal and nonisothermal cond%ions. The isothermally measured behavior shows that a single rate law does not operate at temperatures below 500 O C . Above 500 OC the interpretation of data is complicated by the delay in achieving thermal equilibrium before appreciable reaction occurs. The application of some of the more commonly used rate expressions for soli-phase decompositions suggests that the mechanism progresses from a diffusion-controlled reaction, through a phaseboundary process, to a reaction governed by nucleation and growth. Removal of the minerals does not appear to change the mechanism, but the rate of reaction is increased. I n the case of nonisothermal measurements at heating rates from 1 to 40 deg min-’, the kinetics can be adequately described by a simple first-order rate expression, together with the appropriate time-temperature transformation. The discrepancy between the two techniques is discussed in terms of the approximations and inaccuracies involved in measuring and processing the results.
Introduction The rate of thermal decomposition of oil shale has been studied extensively in recent times, and a review of the topic, covering work prior to 1978, has been presented by Rajeshwar et al. (1979). Since then a number of other significant contributions to the area have been published, including investigations by Campbell et al. (1978, 1980), Shih and Sohn (1980), Noble et al. (1981), Wallman et al. (1981), and Rajeshwar and Dubow (1982). Most recently a comparison of the pyrolysis behavior of key oil shales from eight countries has been presented by Nuttall et al. (1983). Due to the complexity of the chemical structure of kerogen, a mechanistic theory capable of describing the fundamental bond rupture and propagation steps at elevated temperatures is still not available. Because of this, most of the relationships that have been developed to describe the kinetics have essentially phenomenological foundations. Furthermore, there appears to be substantial disagreement among many of the proposed models, particularly in terms of those parameters that are normally considered to characterize the reaction. For example, measurements of activation energy for the decomposition range from approximately 20 to 240 kJ mol-’ in the 15 examples cited by Rajeshwar et al. (1979). Nuttall et al. 0196-4305/85/1124-1125$01.50/0
(1983) report that for Rundle oil shale the activation energy varies from approximately 30 to 160 kJ mol-l, depending on the method of analysis of the experimental data. In general, expressions involving first-order kinetics are the most popularly applied rate laws; however, Rajeshwar and Dubow (1982) have recently fitted a variety of more complex equations to the pioneering kinetic data produced by Hubbard and Robinson (1950). Variations such as these are partially attributable to the different reaction schemes, which may include up to 10 separate steps (Shnackenberg and Prien, 1953). Many of the intermediate species and products, such as bitumen, oil, and gas, are poorly defined in terms of their chemical identity, and this almost certainly leads to confusion when interpreting results. Other problems stem from the lack of uniformity in the experimental procedures adopted by various workers. In particular, particle- and sample-size variations can lead to differences in the rate at which the shale achieves thermal equilibrium with the surroundings. This may become critical at high temperatures where the rate of reaction can be faster than the rate of heating. Recently Rajeshwar and Dubow (1982) criticized the approaches that had been adopted in previous studies on the fundamental theoretical grounds that the pyrolysis of oil shale kerogen involves the 0 1985
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reaction of a solid, leading to both gaseous and solid products, and that homogeneous reaction mechanisms are not applicable. Most importantly, concepts such as concentration and reaction order do not have the same physical significance in solid decompositions as they do in solution or gas-phase reactions, where reacting species are freely mobile and randomly distributed throughout the system. These workers chose to reanalyze earlier kinetic data using the rate expressions developed to explain the decomposition reactions of crystalline solids. In these systems, the majority of reactions can be described by the following equation (Jacobs and Tompkins, 1955)
The reaction velocity is normally given by da/dt = k ( T ) f ( l - a )
(1)
where a is the fractional degree of reaction, k(T) is a rate constant dependent on temperature, and f(1- a)depends on the rate-limiting step and the topochemistry, Le., geometrical arrangement of chemical species. Under certain conditions, this rate-limiting step will take place at an interface between the product and reactant phases and determine the speed at which the interface moves into the reactant. The area of the interface thus becomes analogous to concentration in homogeneous kinetics, and the function f(1 - a) is simply the area expressed as a fraction of the original area at a = 0. In other situations it may occur that the reaction results in the formation of localized regions of solid product in the bulk of the reactant. Under these circumstances the interfacial area, and hence f(1- a),depends on the laws of nucleation and growth. This type of process is likely to happen when the molecular volume of B is greatly different from that of A, which leads to a deformation in the structure. The resulting strain energy must be added to the free energy change for the reaction and, depending on the magnitude of the effect, further reaction will take place at the interface between the phases in preference to other sites. Thus the reaction becomes autocatalytic at the points of initial reaction, and the product phase spreads outwards. The factors that determine the rate of growth include the shape of the nuclei, the possibility of overlap with other nuclei, and the rate of formation of new nuclei (Young, 1966). Obviously, any attempt to extrapolate the behavior of a crystalline material to an amorphous substance, such as kerogen, must be accompanied by some justification on the basis of the known transformations that occur during heating. Recently, solid-state 'H NMR has been used to study the molecular changes induced by heating a lamosite type oil shale (Lynch et al., 1983). Measurements of the second moment of the proton signal indicate a steady increase in molecular mobility commencing at room temperature and nearing a plateau at approximately 250 "C. Apparent hydrogen contents measured during the same experiment did not decline until around 350 "C. It can be concluded from this that kerogen exhibits a broad glass transition of the type encountered in highly cross-linked synthetic organic polymers (Nielsen, 1969) followed by the escape of degraded molecules about 100 "C later. Therefore the degrading structure which needs to be considered is that of a rubber rather than a liquid, glass, or crystal. In such a structure, it is probable that any large induced strains could a t least be partially relieved by molecular relaxation of the network chains. However, due to constraints imposed by the cross-links, large-scale rearrangement in a short time appears unlikely, and the
radicals formed by the rupture of the most thermally labile bonds should therefore be restricted in their interaction with other parts of the structure. As the gas-phase pyrolysis of hydrocarbons is known to occur by a free radical chain reaction mechanism (Fabuss et al., 1964),the concept of reaction centers growing in size from an initiation site in the kerogen with an interface between reactants and products appears to be possible. Additional support of this comes from the results presented in part 1 of this work (Charlesworth, 1985) concerning the time-dependent composition of the vapors produced during isothermal laboratory retorting of oil shale. It was shown in this study that the 1-alkene to n-alkane ratio does not vary as markedly as expected if a homogeneous reaction mechanism was operational. One of the aims of the present study is to test the validity of the heterogeneous reaction kinetics hypothesis by using rapid heating conditions and flame ionization detection (FID) of the total organic fraction evolved from the shale. Experimental Section The modified gas chromatograph used to measure the retorting kinetics has been described in detail in part 1 of this work. In essence, the apparatus consisted of a temperature-controlled microretort directly coupled to an FID. Milligram amounts of shale or kerogen concentrate were rapidly deposited on the hot retort inner surface, and the time or temperature dependence of the pyrolysis reaction was measured by the amount of evolved organic vapors. Cold-surface measurements were obtained by retaining the sample in the probe after insertion into the retort. The composition of the Rundle and Hartley Vale shale samples has been listed in part 1 of this work. Microanalysis of the Green River shale gave the following results: (ash free) 71.6% C, 8.7% H, 2.2% N, 3.1% S, and 14.4% 0 (by difference), 49% ash. Particle-size fractionations in the range 53-2000 pm were performed by sieving. Smaller size range samples were obtained by sedimentation in methanol. Samples of -53pm Rundle shale that had been ashed at 550 "C were impregnated with 20% n-octatriacontane (CS8rz-alkane) under a pressure of 150 MPa at 100 "C with a KBr disk press. Results and Discussion Isothermal Measurements. Allred (1966) has reported that the process of oil evolution during oil shale pyrolysis can be regarded as the sum of two separate steps. The first involves degradation, with an activation energy of 46 kJ mol-', and the second involves evaporation of the products, with an activation energy of 39 kJ mol-'. As the temperature increases, this latter process is claimed to be the rate-determining step. Wall et al. (1970) have measured the rates of molecular vaporization of several pure linear alkanes ranging from CI9 to Cg4. They report that the kinetics are zero order throughout and that the energy of evaporation is proportional to the two-thirds power of the number of carbon atoms. For n-octatriacontane at 400 "C, the calculated activation energy is 101 kJ molT1. In order to estimate the significance of the evaporation process in the overall kinetic scheme, a representative model was chosen consisting of ashed shale impregnated under pressure with n-octatriacontane, The fractional evaporation curves for this material at several temperatures are shown in Figure 1. Up to 300 "C the evaporation is indeed relatively slow; however at 400 "C the half-life is less than 15 s, and above 450 "C the rate is too fast to accurately measure. The half-lives for oil evolution from the oil shales and kerogen concentrate at temperatures from 400 to 600 "C are listed in Table I. Clearly, at least for temperatures
Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 4, 1985 1127
+ A 0
m
" 0
0.5
10
1.5 TIME, t (minutes)
300'C 350'C 40OoC 4 5 0 ~
2.0
EXTRACTED HARTLEY VALE SHALE
3.0
Figure 1. Plots of the extent of evaporation of n-octatriacontane from a shale ash matrix as a function of time and temperature. Table I. Half-Lives for Isothermal Pyrolyses temp, "C 400 425 450 475 500 525 550 575 600
tip, min Rundle Hartley kerogen Vale
Rundle 18.8 8.5 2.1 1.40 0.67 0.43 0.28 0.20 0.15
7.6 3.1 1.5 0.90 0.63 ND" 0.29 ND ND
59.2 11.5 5.9 1.62 0.79 0.63 0.38 0.28 0.19
RAW HARTLEY VALE SHALE
Green River 29.5 8.6 3.5 1.12 0.59 0.47 0.35 0.22 0.14
J
0
Table 11. Heat Transfer and Particle Size Effects on Half-Life at 450 O C N,/cold surface: He/hot surface: size, um min min 2.1 f 0.2 2.3 f 0.2 2.4 f 0.2 2.6 f 0.2 2.8 k 0.2 3.1 f 0.2
16
20
TIME ( m i n u t e s )
Figure 2. Pyrolysis curves illustrating the rapid evaporation of extractable organics.
"ND = not determined.
30-53 53-106 106-250 250-600 600-1000 1300-2000
12
8
4
1.9 f 0.2 2.1 f 0.2 1.8 f 0.2 1.8 f 0.2 1.9 f 0.2 2.0 f 0.2
" See experimental section. below 500 "C, the oil shale pyrolysis is an order of magnitude slower than the c38 n-alkane evaporation. As essentially all the pyrolysis products from these shales are below size c38, it appears unlikely that the evaporation process is a rate-limiting factor. Further evidence for this comes from an examination of the behavior of samples before and after they have been solvent extracted. Figure 2 illustrates the normalized FID response, as a function of time, for Hartley Vale shale retorted at 450 "C. The sharp peak occurring early in the vapor from the raw sample, which is absent in the extracted sample, can be attributed to the rapid evaporation of the 2.7% of organic material not chemically bonded to the kerogen network. One of the most significant factors reported to influence the kinetic behavior is the shale particle size. Allred (1964) concluded that doubling the particle diameter increases the time required for 95% pyrolysis by a factor of 4. Reports by Wallman et al. (1981) and Haddadin and Mizyed (1974) also suggest that both the rate and extent of pyrolysis are increased upon reduction of particle size. These effecb have been interpreted as indicating a physical process controlling the reaction rate. The data in Table I1 show that the rate, as measured by the half-life at 450
1.0
r
0.8
0.6 a GREEN RIVER
0.4
0
'4oooc
425'C 45OoC A 475'C A 500'C 0 525'C 55OoC
Y
0.2
+ n 0
0.5
1.0
1.5
2.0
2.5
t4,> Figure 3. Reduced time plots for the pyrolysis of Green River shale.
"C, for the pyrolysis of Rundle shale may or may not vary with the shale size depending on the experimental conditions employed. In the set of data where a variation in rate is exhibited, the samples were retained in the insertion probe after being introduced into the retort and a relatively nonthermally conductive sweep gas had been employed. In the second series the samples were deposited directly onto the hot retort surface, and helium sweep gas was used. I t must be concluded that the particle-size effect under the first set of conditions is related to a heat diffusion phenomenon rather than to any chemical effect. The first step in the analysis of the time-conversion data is to determine if the same kinetic law applies throughout the entire temperature range. The most appropriate
Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 4, 1985
1128
0
0
05
10
15
20
05
1.5
1.0
25
t/t,,,
Figure 4. Reduced time plots for the pyrolysis of Rundle shale and kerogen concentrate.
25
20
tit,,,
Figure 5. Reduced time plots for theoretical kinetic models listed in Table 111.
Table 111. Kinetic Models for Solid-state Decompositions funcn eq type ref (1) Diffusion-Controlled Reactions D1 (a) a2 = k t one-dimensional Shewmon (1963) D2 (a) (1 - a ) In (1 - two-dimensional Valensi (1935) a ) = kt
(2) Phase-Boundary-Controlled Reactions Sharp et al. (1966) kt Pz (a) 1 - (1 - a)ll3 = sphere Sharp et al. (1966) kt
PI (a) 1 - (1 - a)lI2= cylinder
N1 ( a )
= kt" n = 1, 2, 3, 4
(3) Nucleation power law
0
Wischin (1939)
(4) Nucleation and Linear Growth N 2 (a) In [ a / ( l - a)]= branching Prout and Tompkins kt (1944) (5) Nucleation and Bulk Growth N 3 (a) [-ln (1 - a ) ] 1 / 2 two-dimensional Avrami (1941) = kt
method for assessing this is the reduced time technique first suggested by Sharp et ai. (1966) and later used by Rajeshwar and Dubow (1982). Measurements for Green River and Rundle shale, and kerogen concentrate, are represented in this manner in Figures 3 and 4, respectively. The Hartley Vale data (not shown) produced similar results. In these figures, the experimental time scale at each temperature has been divided by the time at an arbitrary level of reaction, which in all instances is 50% conversion. Provided the same general law is obeyed throughout the range of temperatures, all the data should fall on a single master curve. In practice, the curves change from convex to sigmoidal, converging to a single master curve only above 500 "C. The general shape of the reduced timeconversion plots gives an indication of the types of mechanisms that are occurring (Sharp et al., 1966). These may be broadly classified into the following five categories: (1) diffusion-controlled reactions, (2) phase-boundarycontrolled processes, (3) nucleation-controlled processes, (4) reactions with nucleation and linear growth of nuclei, and (5) processes governed by nucleation and bulk growth of nuclei. Some of the most commonly employed models in each of these categories are presented in Table 111. With the exception of the Prout-Tompkins relationship, which cannot be represented on a scale involving tl 2, these equations, and a simple first-order plot, are shown in
5
15
10
20
25
30
TIME, t (minutes)
Figure 6. Plot of the diffusion control function, D 2 ( a ) against , time for the three shales at 400 "C. 05 -
04
- 03 - 02 01
3
0
1
2
3
4
5
6
7
TIME t ( m i n u t e s )
Figure 7. Plot of the phase-boundary function, PI (a),against time for the three shales at 450 "C.
Figure 5 on a reduced-timescale. A qualitative comparison of the shapes of these curves with the experimental results illustrated in Figures 3 and 4 appears to show a progression from a diffusion-controlled reaction at the lower temperatures, through a phase-boundary-limited reaction, or first-order reaction, around 450 "C, to one of the types of nucleation-controlled mechanism at 500 "C and above. The data at 400 "C and 450 "C for all three oil shales is plotted according to the functions Dz ( a ) and PI ( a ) in Figures 6 and 7, respectively. The close agreement suggests that at low reaction temperatures the rate is determined by the ease with which the reacting species can diffuse
Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 4, 1985 1129 Table IV. Activation Energies and Frequency Factors for Bond Rupture in Selected Organic Compounds" calculated rate constants, sec-l reaction E , kJmol-I log A 400 OC 500 "C 1.6 X 2.6 x 10-14 418 14.7 CH4 CH3. + H* 356 15.8 1.5 X lo-'* 5.6 x 10-9 C2H6 2CH3CH3COCH3 CH3CO. + CH3. 299 14.3 1.3 X lo4 1.3 X lo4 1.9 x 10-8 1.9 x 10-5 298 15.4 (CH3OCHJZ + 2CHsOCHz. 2.0 x 104 1.5 x 10-3 286 16.5 ((CH3)C)z 2(CH3)3C* 6.0 X lo4 3.9 x 10-5 280 14.5 CH3COOCH&H6 -.+ CH3COO. + C6H5CHz. 1.7 x 10-7 7.7 x 10-6 264 13.7 C2H5CH2CSH5 -+ C2H5. + C6H5CH2. 1.6 X lo4 4.1 x 10-5 241 12.9 C H ~ N H C H ~ C ~ H CH3NH S + C&CH2. 9.2 x C H ~ S C H ~ C ~-.+HCHSS. S + C6H5CH2' 215 13.5 6.5 x 10-4 C S H ~ C H ~ C H Z C ~2CsH&H2. H~ 200 9.3 5.5 x 10-7 5.6 x 10-5
-
+
+
+
+
+
Average values from collected data presented by O'Neal and Benson (1973).
1.5 0 RUNDLE A
G R E E N RIVER
0 HARTLEY VALE
1.0
I 0.5 0 25
0
I
I
I
05
10
15
TIME
I *
20
t (minutes)
Figure 8. Plot of the nucleation function, N3 (a), against time for Rundle shale above 475 "C.
through the network. This may be an indirect consequence of the bimolecular nature of the transfer reaction, which must cause some depletion of reactants in the immediate vicinity of the initiation site. At 450 "C, possibly because of the more rapid escape of gaseous products, additional thermodynamic advantage is gained by the reaction propagating at a phase boundary. The results for the Rundle shale at and above 475 "C are plotted in Figure 8 according to the Avrami function N3 (a).At 500 "C and above, it appears that a two-dimensional nucleation and growth mechanism is consistent with the data. In this particular process, as the nuclei grow larger they overlap one another, causing growth to cease. The analogy can be made with the random throwing at disks onto a plane surface, with the uncovered surface representing the unreacted material (Mampel, 1940). The values of the slopes of the lines in Figure 8 for Rundle shale, and also for the Hartley Vale and Green River shale kinetic data plotted in the same fashion, show an Arrhenius type dependency on temperature (Figure 9). The Rundle and Green River shales, which are both classified as lamosites, have essentially identical activation energies of 70 kJ mol-', while the Hartley Vale torbanite gives a value of 81 kJ mol-'. Interpretation of these data must be made with caution as a model consisting of nucleation and growth involves the arithmetic average of the activation energies for each process (de Bruijn et al., 1981). Nucleation will occur when fluctuations in the local energy of the system are great enough to allow for initiation of a growth center. In kerogen these are almost certainly the sites of the weakest chemical bonds. Growth of nuclei will occur by the less selective destruction of bonds at the interface between the kerogen and its degradation products. For this process to
2\
\\ \.
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Chem. Process Des. Dev., Vol. 24, No. 4, 1985
such a process. Furthermore, the overall order of the reaction ranges from unity to 3 / 2 in a complex dependency on temperature and pressure. It is therefore only possible to state that in the present systems the activation energy should fall between values for the rupture of the weakest bonds in the network and the fission and transfer reactions outlined in part 1 of this work. A further complicating factor that may contribute to the apparently low activation energy is the reduction in the ratio of rates of heat transfer and reaction above 500 "C. This effect is difficult to quantify and can never be entirely eliminated when attempting to perform isothermal experiments. However, it is noteworthy that the rate of decomposition of mineral-free kerogen is not significantly different from that of the undemineralized sample above 500 " C , in spite of the fact that the mineral matter is a better conductor of heat than the organic matter (Thien et al., 1968). The smaller activation energy for the lamosite shales compared to the torbanite can be rationalized in terms of the greater proportion of 0, N, and S in the former materials (see part 1). The selection of reactions listed in Table IV in general show lower activation energies where heteroatomic or aromatic compounds are involved compared to the rupture of simple saturated hydrocarbons. The data for the demineralized shale show that the mechanism is essentially the same as the undemineralized shale; however, the rate of pyrolysis below 500 "C is much faster. In this temperature region the diffusion- and phase-boundary-controlled mechanisms are operating, and it is probable that initiation will occur a t the particle surface. The large increase in porosity that must result when the mineral matter is removed should therefore multiply the number of initiation sites. The equality of reaction rates above 500 "C can be explained by the increasing importance of nucleation and growth throughout the bulk of the kerogen or by the rate-limiting influence of slow heat transfer. Nonisot hermal Measurements. Although isothermal measurements show that a single rate expression does not apply in the 400-500 "C region, it may still be possible to derive useful information about the reaction by nonisothermal methods. If there are a total of n mechanisms competing in this temperature range, the rate of conversion can be expressed as
where
(z)
k i ( T ) = A ; exp -
c
350
400
If it is assumed that all the processes have the same activation energy, i.e., E = El = E2 = ... = E, (4) then
In order to convert the rate expression from one involving time as the variable to a solely temperature-dependent equation, the following relationship has been widely used, in accordance with the usual mathematical rules for partial differentiation.
In reality it is impossible to imagine the physical significance of a change in the degree of conversion as the time
600
500 550 TEMPERATURE, T (OC)
450
Figure 10. Conversion-temperature plots for Rundle shale a t various heating rates. The solid line represents best fit values from eq 12.
1.5
10
a
-m \
05 -
\
O / 12
1.3
15
14
1000/T
(K-')
Figure 11. Plot of nonisothermal data for Rundle shale a t three conversion levels according to eq 10.
is held constant; hence most workers hold that for practical purposes the transformation can be represented by da - 1da _ (7) dT-Fdt where 0 is the linear rate of temperature increase (Tang and Chaudhri, 1980). It therefore follows that a
(3)
1 OCIminute
da = iJTexp( c A f , ( l - a) P
g)
dT
(8)
i=l
As a first approximation, Tang and Chaudhri (1980) have suggested that the integral of the exponential in eq 8, which has no analytical solution, can be replaced by
s,'exp( g)d T =
RT
Therefore, for data measured a t the same level of conversion, but at different heating rates, Le., a(T1)= a ( T z ) , PI # &, it follows that log
0.4573 1 pzPi = T( E $) -
Figure 10 illustrates conversion profiles a t five heating rates ranging from 1to 40 deg min-l for Rundle shale. The data at 2070,50%, and 80% conversion are plotted according to eq 10 in Figure 11. Linear regression gives an activation energy of 184 kJ molw1. More sophisticated models have been tested and compared by Nuttall et al. (1983) using nonisothermal TGA data for a large selection
Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 4, 1985
tivation energy of 164 kJ mol-' and a frequency factor of 5.2 X lo8 s-l. However, in the same study the basic Coats and Redfern approach (eq 12) gave activation energies more than 100 kJ mol-' lower than those found in this work and also lower values for Green River shale compared to those reported by Shih and Sohn (1980). The question also remains as to why the nonisothermal approach should show that a first-order rate law can be used to fit the data in the 400-500 "C range, yet isothermal experiments clearly indicate that the mechanism changes over the same span. A possible explanation is that the isothermal measurements are not truly isothermal and that equilibrium is not maintained due to temperature gradients within the sample. However, the relatively long half-lives up to 500 "C and the lack of any appreciable particle-size effect at 450 O C tend to suggest that this does not become a rate-limiting factor at temperatures below 500 "C. A second possibility is that the transformation from time to temperature, given by eq 7, is invalid and that a more complex operation is involved. In the absence of any obvious evidence to support this argument (see Tang and Chaudhri, 1980),it must be rejected. A final explanation is that the assumptions involved in eq 2 are incorrect and that a more accurate relationship is the following:
-14
-15
- 16
-
$1.
-17
I
v
c
a
1131
-18
iJ:
':"
-19
L_/
-c
- 20
-21
-22 12
13
14
1.5
1.6
1000/T ( K - ' )
Figure 12. Entire nonisothermal data plotted according to eq 12.
of world oil shales. These widely accepted methods are derived from simple rate expressions, including the most common approach which assumes that the following first-order type can be substituted in eq 8. CAif(l - a ) = A ( l - C Y )
(11)
i=l
The Coats and Redfern (1964) approximation can then be applied, enabling the following equation to be derived. N_
A E In - - - (12)
E
RT
The entire set of nonisothermal data is plotted according to eq 12 in Figure 12. The second term on the left-hand side of eq 12 does not vary greatly with small changes in E hence the approximate value of 184 k J is used and a refined value determined from the slope of the line of best fit. The final values of E and A obtained in this way are 166 kJ mol-' and 2.8 X lo9 s-l, respectively. Figure 10 also shows a comparison between the experimental and calculated curves obtained by substituting the above values for A and E in eq 12. The agreement appears to be satisfactory and supports the analysis presented by Shih and Sohn (1980) in which a similar approach was used to interpret the nonisothermal rate of oil evolution from Green River shale. These workers found activation energies and preexponential factors that ranged from 181 to 199 kJ mol-' and 3.3 X 1O'O to 8.3 X 10" s-l, respectively, and approximate first-order kinetics operated throughout. The result also compares favorably with the parameters calcualted by Nuttall et al. (1983) using the multiactivation energy Anthony-Howard model (Anthony et al., 1975). For Rundle oil shale, these workers found an average ac-
It is implicit in this equation that at any chosen temperature the reaction may be treated as occurring by one rate-determining mechanism, rather than by the sum of a series of mechanisms. When the temperature is changed, the rate-determining step, and hence the mechanism, changes in a continuous fashion, and the variables a and T cannot be separated without detailed knowledge of f(1 - C Y , T). Thus the integration performed in eq 8 is not strictly valid and will lead to an approximate solution only. Some understanding of such a strong temperature dependence can be gained by comparing the temperature effect on the rate constants calculated from the data in Table IV. For example, the relative rate of initiation by bond rupture of dibenzyl and benzyl acetate is 9.2 at 400 "C and 1.4 at 500 "C. Hence the decomposition may be expected to depend on the relative proportions of these units, their proximity to a surface, and the composition of the surrounding network. Other effects that must be considered include the temperature dependency of the network viscosity and catalysis by reaction products. It should also be noted that instances of changes in the pyrolysis mechanism with temperature have been observed in the case of some inorganic solids. Hancock and Sharp (1972) have shown that the kinetics of the decomposition of BaC03 are governed by a diffusion-controlled mechanism from 961 to 1009 "C followed by a phase-boundary process from 1016 to 1035 "C. The decomposition of potassium azide also exhibits a number of strongly temperature-dependent mechanisms (Jacobs and Tompkins, 1952). The fundamental significance of nonisothermally derived kinetic parameters must therefore be treated with some caution; however, for the purpose of obtaining a working means of predicting the effects of heating rate on oil production, the method is valuable. Conclusions and Summary The rate of evaporation of high molecular weight hydrocarbons does not appear to be an important factor in the overall rate of oil evolution. Particle-size effects on the pyrolysis rate are related to the rate of heat transfer rather than to any physical transport phenomenon. Iso-
Ind. Eng. Chem. Process Des. Dev. 1985, 2 4 , 1132-1 136
1132
thermal measurements using a reduced time scale show that the pyrolysis mechanism is temperature dependent below 500 "C. Application of a variety of commonly used solid-state reaction expressions indicates that as the temperature increases the mechanism progresses from a diffusion-controlled reaction, through a phase-boundary process, to a reaction governed by nucleation and growth. Removal of the minerals does not change the mechanism; however, the half-life for the reaction is considerably reduced below 500 O C . Analysis of nonisothermal pyrolysis data does not require the use of a temperature-dependent rate law, and first-order kinetics with a single activation energy w ill fit the data. The apparent discrepancy between these two approaches is most likely related to the neglect of the temperature effect on the mechanism when transposing equations to enable integration to be carried out. Literature Cited Allred, V. D. Colo Sch Mines 0.1964, 5 9 , 47. Allred, V. D. Chem. Eng. Prog. Symp. Ser. 1966, 62, 5 5 . Anthony, D. A,; Howard, J. B.; Hottel, H. C.; Meissner, H. P. "Fifteenth SymDosium on Combustion"; The Combustion Institute: Pittsburgh, PA: 1975, p 1303. Avrami, M. J. Chem. Phys. 1941, 9 , 177. Campbell, J. H.;Koskinas, G. H.; Gallegos, G.; Greg, M. Fuel 1980, 59, 718. Campbell, J. H.; Koskinas. G. H.; Stout, N. D. Fuel 1978. 5 7 , 372. Charlesworth, J. M. Ind. f n g . Chem. Process Des. Dev. 1985, preceding paper in this issue. Coats. A. W.; Redfern, J. P. Nature (London) 1964, 201, 66. de Bruijn. T. J. W.; de Yong, W. A.: van den Berg, P. J. Thermochim. Acta 1981, 4 5 , 315. Fabuss, B. M.; Smith, J. 0.; Satterfield, C. N. I n "Advances in Petroleum Chemistry and Refining"; McKetta, J. J., Ed.: Interscience: New York. 1964.
Haddadin. R. A.; Mizyed, F. A. Ind. Eng. Chem. Process Des. Dev. 1974. 13, 332. Hancock, J. D.: Sharp, J. H. J. Am. Ceratn. SOC. 1972, 55, 74. Hubbard, A. B.; Robinson, W. E. U.S. Bur. Mines Rep. Invest. 1950, 4744. Jacobs, P. W. M.; Tompkins, F. C. Proc. R. SOC.London A 1952, 215, 265. Jacobs, P. W. M.; Tompkins, F. C. I n "Chemistry of the SolM State"; Garner, W. E., Ed.; Butterworths: London, 1955; Chapter 7. Lynch, L. J.; Webster, D. S.;Parks, T. "Proceedlngs, First Australian Workshop on Oil Shale", Lucas Heights, May 1983, p 139. Mampel, A. 2.Phys. Chem. Abt. A 1940, 187. 43, 235. Neilsen, L. E. J. Macromol. Scl. Rev. Macromol. Chem. 1969, C3(1 ) . 69. Nobie, R. D.; Harris, H. G.; Tucker, W. F. Fuel 1981, 6 0 , 573. Nuttali, H. E.; Guo, T. M.; Schrader, S.; Thakur, D. S. I n "Geochemistry and Chemistry of Oil Shales"; Miknis, F. P.; McKay, J. F., Ed.; ACS Symposium Series No. 230; American Chemical Society: Washington, DC, 1983. O'Neal, H. E.; Benson, S.W. I n "Free Radicals-Volume 2"; Kochi. J. K., Ed.; Wiley: New York, 1973; Chapter 17. Prout, E. G.:Tompklns. F. C. Trans. Faradsy SOC. 1944, 4 0 , 488. Rajeshwar, K.; Dubow, J. Thermochim. Acta 1982, 5 4 , 71. Rajeshwar, K.; Nottenburg, N.; Dubow, J. J. Mater. Sci. 1979, 14, 2025. Schnackenberg, W. D.: Prien, C. H. Ind. f n g . Chem. 1953, 4 5 , 313. Sharp, J. H.; Brindley, G. W.; Achar, B. N. N. J. Am. Ceram. SOC. 1966, 49, 379. Shewmon, P. G. "Diffusion in Solids";McGraw-Hili: New York, 1963. Shih, S. M.; Sohn, H. Y. Ind. Eng. Chem. Process Des. Dev. 1980, 19, 420. Tang, T. 8.; Chaudhri, M. M. J. Therm. Anal. 1980, 18, 247. Thien, S. S.;Carpenter, H. C.; Sohns, H. W. NBS Spec Publ. 1968, 302, 529. Valensi, G. Compt. Rend. 1935 201, 602. Wall, L. A.; Flynn, J. H.; Strauss, S. J. Phys. Chem. 1970, 7 4 , 3237. Wallman, P. H.; Tamm, P. W.; Spars, B. G. I n "Oil Shale, Tar Sands and Related Materials"; Stauffer, H. C., Ed.; ACS Symposium Series No. 163; American Chemical Society: Washington DC, 1981. Wischin, A. Proc. R . SOC.LondonA 1939, 172, 314. Woinsky, S.G. Ind. Eng. Chem. ProcessDes. Dev. 1968, 7 , 529. Young, D. A. "Decomposition of Solids"; Pergamon: London, 1966.
Received for review March 12, 1984 Accepted October 23, 1984
A Computer Algorithm for Optimized Control Patrlcla A. S. Ralston, Kelth R. Watson,+ Ashutosh A. Patwardhat!,$ and Pradeep B. Deshpande" University of Louisville, Louisville, Kentucky 40292
There is a continuing need for simple and efficient methods for finding optimized process and controller parameters. I n this paper, a computer algorithm is described which may be used to determine optimized process constants of an overdamped secondarder-plus dead-time model and optimum tuning constants of digital PID controllers. The algorithm should find use in on-demand identification and tuning applications.
Process identification and tuning methods are important in computer control applications. The identification procedure determines the process parameters which frequently change owing to changes in operating conditions, equipment fouling, etc. The tuning procedure finds updated tuning constants in the event that the process parameters have changed. The identification procedure of concern in this paper is based on experimental input-output data from the process. A suitable disturbance is introduced into the manipulated variable while the process is operating at steady state in manual, and the process output data are 'Currently at E. I. du Pont de Nemours & Co., Midlothian, VA. *Currently a t Colorado State University, Fort Collins, CO. 0 196-4305/85/1124-1132$01.50/0
recorded. The experimental output is compared with the predicted output of an assumed process model, and the process identification procedure is applied to determine the set of process parameters which minimize the error between observed and predicted outputs. Once new process constants are found, there may be a need to determine new controller constants. In this instance, the purpose of the optimization procedure is to determine the set of controller tuning constants which minimize a user-specified measure of error under the closed-loop response curve. Several methods are available for finding optimum tuning constants of digital controllers. Among them are the method of Gallier and Otto (1969) and Fertik (1975). These investigators have developed graphs which give optimum tuning constants as functions of process parameters. The effect of sampling is included in the form of 0 1985 American
Chemical Society
