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Continuous-Distribution Kinetic Analysis for Asphaltene Hydrocracking Yoichi Kodera,* Teruo Kondo, Ikuo Saito, Yoshiki Sato, and Koji Ukegawa National Institute for Resources and Environment, 16-3 Onogawa, Tsukuba, Ibaraki 305-8569, Japan Received May 17, 1999. Revised Manuscript Received October 27, 1999
Kinetic analysis of macromolecular conversion has many difficulties such as definition of rate of conversion and molecular-weight determination. Continuous-distribution kinetic analysis has been proposed for kinetic evaluation of asphaltene hydrocracking. Asphaltene has the molecularweight distribution (MWD) spanning continuously in the wide range. A gel permeation chromatography (GPC) is a practical and convenient method to observe MWDs of reaction mixtures during the conversion. A mathematical model was presented using simple schemes of chemical reactions representing overall reactions to interpret experimental results. The weights and MWDs of asphaltene components were converted into the corresponding zeroth moment (molar concentration) and first moment (mass concentration), and the time-dependent changes of these moments gave the apparent kinetic parameters of the overall reactions.
1. Introduction Continuous-distribution kinetic analysis was demonstrated to evaluate asphaltene hydrocracking at each reaction temperature. One of the important subjects in the studies on macromolecular conversion is to examine the rate of reaction for the optimization of reaction conditions. This could be a rate of molecular-weight lowering of macromolecules or a rate of formation of a specific product. GPC with a refractive-index (RI) detector is an effective method to monitor the changes of MWDs of a macromolecular reaction. On the basis of time-dependent changes of MWDs of reaction mixtures, continuous-distribution kinetics has been developed for kinetic analysis of macromolecular reactions such as polymer degradation.1-4 The purpose of this paper is to demonstrate the continuous-distribution kinetic model for asphaltene hydrocracking. Asphaltene hydrocracking was performed at three different temperatures, and overall rates of hydrocracking were obtained in which the rates were defined by simplified schemes of chemical reactions. The degradation of a reactant to the corresponding products was monitored as the molecular-weight lowering by GPC/RI after separation of asphaltene components from the reaction mixtures. The kinetic model mathematically shows the changes of moments with reaction time during the conversion. The kinetic parameters are obtained with the experimental results of time-dependent changes of moments calculated from * Author to whom correspondence should be addressed. Fax +81298-58-8408. E-mail:
[email protected]. (1) Sezgi, N. A.; Cha, W. S.; Smith, J. M.; McCoy, B. J. Ind. Eng. Chem. Res. 1998, 37, 2582-2591. (2) Gloor, P. E.; Tang, Y.; Kostanska, A. E.; Hamielec, A. E. Polymer 1994, 35, 1012-1030. (3) Browarzik, D.; Koch, A. J. Macromol. Sci. 1996, A33, 1633-1641. (4) Kodera. Y.; McCoy, B. J. AIChE J. 1997, 43, 3205-3214.
continuous-distribution curves, namely, the MWDs of reaction mixtures. Typically, there are two types in continuous-distribution kinetic models for macromolecular conversion such as degradation and polymerization. One is in this paper. Macromolecular degradation is expressed in one or more reaction schemes, and a time-differential equation using rates of reactions is deduced for each component that is quantitatively analyzed. The mathematical operation using the continuous-distribution function is carried out to derive a mathematical model according to defined reaction schemes. Kinetic parameters are obtained by comparing time-dependent changes of the moments with mathematical results. The statistical treatment is the second example of the continuous kinetics.5 Gamma distribution or the other distribution functions such as Gaussian and Poisson distribution approximate the molecularweight distribution curve of a reaction sample. The timedependent changes of the curve are expressed by the changes of distribution parameters of functions.6 This approach can simulate the changes of the molecularweight distribution of a reaction mixture during reaction. On the other hand, discrete models also have some successful examples such as simulation for processing of petroleum distillates.7 The discrete model describes reactions of chemical components, separately identified by analytical methods such as gas chromatography. The excellence is in the comprehensive and detailed description on the conversion of each component based on its reactivity and physical properties such as the boiling point when precise identification of the components and (5) Dotson, N. A.; Galva´n, R.; Laurence, R. L.; Tirrell, M. In Polymerization Process Modeling; VCH Publishers: New York, 1996; p 50. (6) Wang, M.; Smith, J. M.; McCoy, B. J. AIChE J. 1995, 41, 15211533. (7) Quann, R. J.; Jaffe, S. B. Chem. Eng. Sci. 1996, 51, 1615-1635.
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enough data of the chemical and physical properties are available. Discrete models of asphaltene conversion were reported by the Monte Carlo method,8,9 applying differential equations of a detailed kinetic model, using parameters from detailed kinetic and structural data of reactant and reaction products. However, it is exhaustive work and sometimes impossible to determine chemical structures and reactivities of asphaltenes and their reaction products. Asphaltene has a complex structure and it is difficult to observe every chemical and physical event during the conversion and to obtain all parameters for the detailed kinetic models. One cannot kinetically describe degradation of a specific asphaltene such as the one we used as a reactant because of the complex structure, the high molecular weight, and the insufficient data on chemical and physical properties of components. The easier method of kinetic analysis was required to evaluate the asphaltene conversion in our reaction system, and we have applied continuous-distribution kinetics to asphaltene hydrocracking. 2. Reaction Model of Asphaltene Hydrocracking Mild reaction conditions including a selection of a catalyst were chosen so that liquid products were given as the major products and also the formation of gaseous products and coke were negligible with respect to their weights and molar amounts compared with those of the liquid products. Then, asphaltene and aliphatic components are analyzed and examined in our kinetic model. Asphaltene component is usually defined as one of the lumped groups based on its solubility to a solvent, an insoluble fraction to large excess amount of hexane or heptane. Its structure is considered to be a fused ring called a unit-sheet of saturated and unsaturated rings with side-chains attached to the rings and linkage, which is aliphatic hydrocarbon between the unit-sheets.8 We use this solubility-lumped group as one of the chemical components, which have fused-aromatic structures. Another solubility-lumped group is the components which are soluble to hexane and the chemical components are considered to be paraffins and olefins, which are derived from side-chains and linkages. Asphaltene hydrocracking involves complex events. Chemically, it could include bond scission of aliphatic chains (liberation of a linkage and a side-chain from aromatic rings and chain-scission within an aliphatic chain), hydrogenation of aromatic rings, ring-opening of saturated rings, their reverse reaction such as dehydrogenation of aromatic rings, and recombination via radical addition to unsaturated moieties. Physically, it could include asphaltene dispersion dissolving in a solvent (diffusion), the adsorption and desorption of hydrogen to a catalyst and, catalyst activation and deactivation, and vaporization and condensation of products. We now simplify the complex events to three sets of reaction schemes: (A) the cleavage of a linkage between fused-ring units, (B) side-chain liberation from fused rings, (C) random-chain scission of aliphatic compounds, and their reverse reactions. Terms used in this paper (8) Neurock, M.; Nigam, A.; Trauth, D. M.; Klein, M. T. Chem. Eng. Sci. 1994, A24, 4153-4177. (9) Trauth, D. M.; Stark, S. M.; Petti, T. F.; Neurock, M.; Klein, M. T. Energy Fuels 1994, 8, 576-580.
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are defined as follows: asphaltene, A(x), is a hexaneinsoluble component of molecular weight x, and Aliphatic components, P(x), are alkanes and alkenes of molecular weight x. Asphaltene is considered to have a fused-ring unit and side-chains attached to the ring structure. A side-chain linked to another fused-ring unit is called a linkage and the other is called a side-chain. The fused aromatics involve both saturated rings and unsaturated rings. Random bond-scission is assumed for the cleavage of linkages between fused-ring units (Scheme A), the side-chain cleavage from a fused ring (Scheme B), and bond-scission of aliphatic hydrocarbons (Scheme C) because of the possible random-distribution features of MWDs of fused-rings and linkages. Recombination of intermediary radicals is considered for each scheme. ka
A(x) {\ } A(x′) + A(x - x′) k A
kb
} P(x′) + A(x - x′) A(x) {\ k B
kr
} P(x′) + P(x - x′) P(x) {\ k R
(A)
(B)
(C)
Scheme A is an overall description of linkage-scission and stabilization of the resulting radical. One may involve dissolution of asphaltene into a solvent within this scheme depending on the reaction conditions. Although physical phenomena like dissolution might influence some elementary reactions, the changes of the amounts of lumped groups, A(x) and P(x), were defined by the simplified chemical transformation and the overall rates of the transformation were examined. We assume sufficient activity of the molybdenum catalyst to hydrogenation of radicals with sufficient supply of hydrogen by the use of the oil-dispersed catalyst in a well-stirred batch reactor, resulting the negligible formation of coke. As known empirically, molybdenum catalyst has no activity for hydrogenation of aromatic rings, C-C bond cleavage, and ring-opening reaction of an alicyclic ring. Negligible hydrogenation of aromatic rings was confirmed by the observation of the small consumption of hydrogen in each run (2-5.1 mmol/gasphaltene) and no λmax shift of chromatograms of the reaction mixtures at 450 °C from the chromatogram of a reactant asphaltene using a HPLC-diode array UV detector. Negligible formation of coke and gas was confirmed by the weight of toluene-insoluble fraction and GC analysis. Then, liquid products and hexaneinsoluble fractions of the liquid prducts were analyzed and kinetic analysis of the reaction was performed on the basis of the MWDs of aliphatic and asphaltene components. Based on the schemes A, B, and C, the distribution balance equations for asphaltene, a(x,t), and aliphatic components, p(x,t), are given as shown in eqs 1 and 2. A mathematical technique similar to a mathematical treatment of the polystyrene decomposition4,10 was used for random-chain scission of each reaction scheme. (10) Kodera, Y.; Cha, W. S.; McCoy, B. J. Prepr. Pap.sAm. Chem. Soc. Div. Fuel Chem. 1997, 42, 1003-1007.
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∫0∞a(x′) a(x - x′) dx′ + ∞ ∞ 2 ka∫x a(x′) Ω(x,x′) dx′ -2 kAa(x) ∫0 a(x′) dx′ ∞ kba(x) + kB∫x a(x - x′) p(x′) dx′ + ∞ ∞ kb∫x a(x′) Ω(x,x′) dx′ - kBa(x)∫0 p(x′) dx′ (1)
∂a/∂t ) -kaa(x) + kA
∫x a(x′) Ω(x,x′) dx′ - kBp(x)∫0 a(x′) dx′ ∞ krp(x) + kR∫0 p(x′) p(x - x′)dx′ + ∞ ∞ 2kr∫x p(x′)Ω(x,x′) dx′ - 2kRp(x)∫0 p(x′) dx′ (2)
∂p/∂t ) kb
∞
∞
Applying the moment operation, ∫∞0 [ ]xndx,11,12 to the integro-differential equations 1 and 2 yield
da(n)/dt ) [(2Zn0 - 1)ka + (Zn0 - 1)kb]a(n)+ n
(nj)a(j)a(n-j) - 2a(n)a(0)] + ∑ j)0
k A[
n
kB[
(nj)p(j)a(n-j) - a(n)p(0)] ∑ j)0
(3)
dp(n)/dt ) kbZn0a(n) - kBp(n)a(0) + (2Zn0 - 1)krp(n) + n
k R[
(nj)p(j)p(n-j) - 2p(n)p(0)] ∑ j)0
(4)
where Zn0 ) 1, 1/2, or 1/3 for n ) 0, 1, or 2. Zeroth moments (n ) 0) are governed by the differential equations 5 and 6,
da(0)/dt ) (ka - kAa(0))a(0)
(5)
When radical quench for aliphatic components is sufficient (kr . kR), eq 4 gives
dp(0)/dt ) kba(0) + (kr - kBa(0))p(0)
(6)
Integration of eq 5 with the initial conditions a(0)(t ) 0) ) ao(0) gives
a(0)(t) ) kaao(0) exp(kat)/{ka + ao(0)kA[exp(kat) - 1]} (7)
dp(1)/dt ) (1/2)kba(1) - kBa(0)p(1)
(10)
The summation of first moments for asphaltene and aliphatic components gives
d[a(1) + p(1)]/dt ) 0
(11)
confirming the conservation of reactant asphaltene mass. Experimentally, this equation is valid for the negligible amounts of reaction products such as gas and coke escaping from the reaction mixtures, which are subject to GPC analysis. 3. Experimental Section Sample and Catalyst. Reactant asphaltene used in this study is a hexane-insoluble fraction of Arabian Light vacuum residuum. The chemical structure of asphaltene was briefly discussed by elemental and NMR analyses.13 The asphaltene was precipitated with a 40-fold excess of n-hexane, stirred for 24 h and separated with a centrifuge, and dried under vacuum at 50 °C for 24 h. Molybdenum dithiocarbamate, ((C8H17)2NC)2S6Mo2O2, was purchased from Asahi Denka Inc. (Tokyo) and was used as a Decalin solution in molybdenum concentration of 0.1%. Hydrocracking. Asphaltene (3 g) was suspended with 15 g of Decalin with 0.1% molybdenum catalyst and heated at 380-420 °C for 30 to 120 min under hydrogen gas (5 MPa) in a 110 cm3-autoclave equipped with a mechanical stirrer. Reaction period starts after the temperature reached the operation temperature, when the time is 0 min. After the reaction, the autoclave was cooled to room temperature and gaseous products were vented off and analyzed with a gas chromatograph. Reaction mixtures were filtered to separate solid and liquid. The solid was extracted with toluene to obtain coke, which is defined as a toluene-insoluble substance. Liquid products were analyzed by HPLC-GPC using a RI detector. Analysis. The reactant asphaltene and liquid products were diluted with THF and analyzed with a GPC apparatus (Polymer Laboratories, two 7.5 × 300 mm columns of Mixed-E 10 µm with a guard column maintained at 40 °C; HewlettPackard 1050 pump, Shimadzu RID-6A RI detector, and Shimadzu SPD-M10A diode-array UV detector). Molecular weights were calibrated by polystyrene standards. Adding 40fold of hexane and centrifuging the mixture separated the asphaltene components. The asphaltene obtained was dissolved in THF for GPC analysis.
4. Results and Discussion
(9)
Asphaltene components were examined experimentally and mathematically. Hexane-insoluble fractions were treated as asphaltene components and the other parts of reaction mixtures were treated as aliphatic components. Percent recoveries of the asphaltene components were defined as the weight ratio of hexaneinsoluble fractions to a reactant asphaltene. The percent recoveries were 84.3 (0 h), 76.4 (0.5 h), 71.6 (1 h), and 65.1% (2 h) at 380 °C, 70.4, 63.4, and 56.6% at 400 °C, and 60.2, 56.6, and 48.7% at 420 °C. Coke (tolueneinsoluble fraction) was recovered at 0.00 (0.5 h) to 0.01% (2 h) at 380 °C, 0.30 to 2.01% at 400 °C, and 2.59 to 3.38% at 420 °C. Gas formation was also very small relative to the amount of the reactant asphaltene (0.2 wt % at 380 °C for 0.5 h and 2.6 wt % and 420 °C for 2 h).
(11) McCoy, B. J.; Subramaniam, B. AIChE J. 1995, 41, 317-323. (12) McCoy, B. J.; Madras, G. AIChE J. 1997, 43, 802-810.
(13) Kondo, T.; Sato, S.; Matsumura, A.; Saito, I. In Proceedings of JECAT′97, Tsukuba, Japan; 1997, pp 335-340.
a(0)(t f ∞) ) ka/kA Applying eq 7 to 6 and integration with the initial condition p(0)(t ) 0) ) po(0) under the approximation, kr . kR and kB ≈ kA, give eq 8.
p(0)(t) ) ka exp(krt){ao(0)kb[exp((ka - kr)t) - 1] + (ka - kr)po(0)]}/{(ka - kr)[ka + ao(0)kA (exp(kat) - 1)]} (8) First moments (n ) 1) are given as follows:
da(1)/dt ) -(1/2)kba(1) + kBa(0)p(1)
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Figure 1. MWDs of reaction mixtures in the reaction at 380 °C.
Figure 2. MWDs of asphaltene in the reaction at 380 °C.
Figure 1 shows MWDs of the reactant asphaltene and the reaction in the experiments at 380 °C. Polystyrene standards (Mp ) 418-43900) were used for molecularweight calibration for asphaltene and aliphatic components. Figure 2 shows MWDs of the reactant asphaltene and asphaltene components given in the experiments at 380 °C. Peaks of Decalin and THF were skimmed from the original chromatograms by nonlinear regression with exponential function using the computer software Igor-Pro (Wavemetrics, Inc.). Coke and gas were neglected in moment calculations because of the negligible amounts to the total moments of reaction mixtures. The nth moment of the MWDs of asphaltene component is defined as
a(n)(t) )
∫0∞xna(x,t) dx
(12)
where, x is molecular weight, t is a reaction time, and a(x,t) is distribution function. In the numerical analysis, a(x,t) is a value by which the peak intensity in chromatograms of GPC is divided by molecular weight, and normalized. The sum of the value of a(x,t) in the entire molecular-weight range gives total molar concentration of the asphaltene, which is zeroth moment at the time t. The molecular weights of asphaltene were determined with polystyrene molecular-weight standards instead of the absolute molecular weights of asphaltene itself in GPC analysis. We cannot use conventional methods to discuss the kinetics of the asphaltene hydrocracking because it is difficult to determine molecular weights
Figure 3. Zeroth moment of asphaltene.
of asphaltenes. Viscometry cannot be applied due to the unknown constants of the Mark-Houwink-Sakurada equation for the asphaltene, and the light-scattering method cannot be applied to asphaltene due to the serious absorption of laser beam. It was not practical for our experiments to use a vapor pressure method, which provides weight-average molecular weights, because it requires large amounts of samples and it does not provide the information of number-average molecular weight giving molar concentration of asphaltene. To obtain ka, zeroth moments of asphaltene were calculated based on the MWDs at 380, 400, and 420 °C as shown in Figure 3. The value at 0 min is not a zeroth moment of an original asphaltene but a zeroth moment of asphaltene component separated from the reaction mixture heated to reach to the temperatures of 380, 400, or 420 °C. To obtain ka values at each temperature, nonlinear regression with eq 7 was applied to the experimental results of a(0)(t). The ka values were given as 4.34 × 10-2, 4.96 × 10-2, and 5.60 × 10-2 min-1sPS at 380, 400, and 420 °C, respectively. The kA values were given as 1.29 × 102, 1.26 × 102, and 96.9 min-1sPS at 380, 400, and 420 °C, respectively. The adjunct, sPS, means that the rate based on the molecular concentration calculated by molecular-weight calibration with polystyrene standards. Experimental results would involve analytical and experimental errors. GPC results have errors in MWDs ((0.12% in elution time and (0.42% in signal intensity) and reaction temperatures have fluctuation ((3 °C). These errors influence the zeroth moment, a(0), of asphaltene in Figure 3. In Figure 3, model fitting did not fit experimental results well at 420 °C. This would be mainly due to undergoing degradation of paraffins, which is ignored in the mathematical model. As known generally, paraffin degradation is not observed less than about 380 °C under an inert atmosphere, while paraffins undergo thermal degradation almost over 410 °C. It was shown experimentally in the results of our polyethylene thermal decomposition.11 The errors in elution time give errors of the molecular weights of compounds in eluates. The error in molecular weight was estimated at (3.4% at reaction time 0 min, 420 °C, when the weight-average molecular weight of the reactant is 5375.6. Nonlinear regression of the plots gave the gradients of a(0), ka, with the errors (6.8% at time 0 min. Figure 4 shows an Arrhenius plot of ka giving linear relationship of ln ka
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Figure 4. Arrhenius plot of ka.
Figure 6. Arrhenius plot of kb.
Figure 5. First moment of asphaltene.
versus 1/T. As the activation energy, 6 ( 3 kcal/mols PS was obtained in consideration of fluctuation of the reaction temperature and the errors in ln ka. The changes of the first moments are shown in Figure 5. The kb values were obtained with first moments of asphaltene, a(1)(t), which are the weight ratio of asphaltene components recovered as hexane-insoluble fractions to the weights of reactant asphaltene. Equation 9 was simplified to eq 13 under assumptions ka, kb . kr at the early stage of hydrocracking neglecting reverse reactions of schemes A, B, and C.
a(1)(t) ≈ ao(1)[1 - (kb/2)t]
(13)
Applying eq 13 to the first moments in Figure 5 gives rate coefficient kb at each temperature. The kb values were 1.83 × 10-3, 2.31 × 10-3, and 2.60 × 10-3 min-1 at 380, 400, and 420 °C, respectively. First moments of asphaltene could be affected by temperature fluctuation during reaction. Arrhenius plots of ln kb versus 1/T give linear correlation as shown in Figure 6. The activation energy was given at 8 ( 1 kcal/mol with the error by fluctuation of T. In the mathematical model, molecular-weight dependence of rate coefficient of reaction is not considered. It is assumed that the reactant asphaltene dissolves in a solvent at the reaction temperature and that the dissolution does not influence the reaction rate of the
degradation. The rate of degradation in this paper is the overall rate of the defined reaction scheme and the results would include the reactions in both vapor and liquid phases. Thus, the resulting kinetic parameters differ from parameters obtained in decomposition of a hydrocarbon under controlled reaction conditions. It should be noted that the rates ka, kA, and activation energy by ln ka were obtained from the change of molar concentration with time, in which polystyrene molecular-weight standards were used for determination of molecular weights of asphaltenes. The activation energy is not absolute activation energy but a relative value of temperature effect on reaction rate. We cannot use conventional methods to discuss the kinetics of the asphaltene hydrocracking because it is difficult to determine molecular weights of asphaltenes. Viscometry cannot be applied due to the lack of the constants of Mark-Houwink-Sakurada equation for the asphaltene and light-scattering method cannot be applied to asphaltene due to the serious absorption of the laser beam. It was not practical in our experiments to use a vapor pressure method, which provides weight-average MWs, because it requires large amounts of samples and it does not provide the information of number-average MW giving molar concentration of asphaltene. For some purposes, one may use thermogravimetric analysis (TGA). This method is not suitable for asphaltene hydrocracking in solution because the present reaction is in solution using a catalyst with stirring. The continuous-distribution kinetics in this paper is based on MWDs and shows the mathematical relation of MWDs to rate coefficients defined in reaction schemes although some of the kinetic parameters are relative values which cannot be compared with the conventional data because of the use of polystyrene molecular-weight standards. This paper provides a versatile method for the discussion of the kinetics of the conversion of complex macromolecules. Kinetic analysis using absolute molecular weights of macromolecules will be examined with time-of-flight mass spectrometer (TOFMASS) soon. Conclusion Continuous-distribution kinetic analysis was applied to asphaltene hydrocracking using simplified schemes for describing overall rates of hydrocracking on the basis
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of time-dependent changes in moments. This procedure provides a practical method of kinetic evaluation for asphaltene conversion, indicating changes of degradation rates by temperature difference of 20 K. Evaluation of the other reaction conditions such as H-donor effects are promising. GPC/RI using polystyrene molecularweight standards was used to obtain MWD because other analytical methods such as light-scattering cannot be used.
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Acknowledgment. The authors are grateful to Prof. McCoy, Department of Chemical Engineering & Materials Science, University of California, Davis. The kinetic study in this paper has been developed to apply to asphaltene hydrocracking, based on the kinetic studies of one of the authors, Y. Kodera, who had worked for him as a visiting researcher. EF990089Y
