Kinetics of Thermal and Catalytic Coal Liquefaction with Plastic

1444

Ind. Eng. Chem. Res. 1997, 36, 1444-1452

Kinetics of Thermal and Catalytic Coal Liquefaction with Plastic-Derived Liquids as Solvent Weibing Ding, Jing Liang, and Larry L. Anderson* 3290 MEB, Department of Chemical and Fuels Engineering, University of Utah, Salt Lake City, Utah 84112

Results of a kinetic study of thermal and catalytic (Fe impregnated on coal) liquefaction of DECS-6 coal with plastic-derived liquids (PDL) as solvent have been obtained. The experimental work was conducted in 27-cm3 horizontally shaken microreactors at temperatures of 360-400 °C with isothermal reaction times ranging from 0 to 180 min. The reaction pressure was about 2000 psig H2, and the solvent-to-coal weight ratio was 2:1. Experimental data were correlated by a kinetic model which assumed the reaction pathways: coal to preasphaltenes, coal to asphaltenes, coal to gas + oil, preasphaltenes to asphaltenes, preasphaltenes to gas + oil, and asphaltenes to gas + oil. It was shown that this reaction model fit experimental data reasonably well at the conditions used, and the six rate constants exhibited Arrhenius-type temperature dependence. Some reactions were also carried out at a higher temperature (420 °C) to validate the model at reaction conditions other than conditions used for obtaining the kinetic parameters. Direct coal liquefaction reactions were predominant for both thermal and catalytic DECS-6 coal liquefaction with PDL as solvent, although the catalyst promoted consecutive reactions to a larger extent. Introduction The addition of hydrogen is necessary for coal liquefaction as coal is relatively lower in hydrogen content when compared with other fuels, e.g., petroleum. The conversion of coal to liquids is generally perceived to proceed via free-radical mechanisms. Reactive radical fragments are formed by thermally rupturing scissile bonds and by hydrogenolysis (Vernon, 1980). Once formed, fragments are either stabilized by hydrogen addition or recombined to form polymeric products. Two external sources of hydrogen are available to meet these demands. These are donor hydrogen in the solvent and gaseous molecular hydrogen. The solvents used for coal liquefaction were mostly hydroaromatics (tetralin, isotetralin), aromatics (naphthalene, anthracene oil, phenanthrene, pyrene), naphthenics (decalin), phenolic compounds (phenol, cresol), and their combinations (Clarke et al., 1984; Winschel et al., 1986; Tagaya et al., 1989; Takemura et al., 1989; Mochida et al., 1990; Bedell and Curtis, 1991). These relatively expensive solvents prevent coal liquefaction from becoming a commercial process. Coprocessing of coal with waste plastics could significantly alter the process economics (Warren and El-Halwagi, 1995). It is expected that, during coprocessing, the hydrogen-rich fragments from degraded waste polymers will react with coal in one way or another to yield higher quality liquid products than could be obtained with coal alone. We have developed two-stage coprocessing of coal with plastic and reported that waste plastic-derived liquids (PDL) can be utilized as solvent for thermal or catalyzed coal liquefaction (Ding et al., 1996a). As an iron precursor, ammonium iron(III) sulfate dodecahydrate was found to be very effective in increasing the liquid yields of catalytic hydroliquefaction of Blind Canyon coal (Yuen and Anderson, 1994). The present work was aimed to quantitatively evaluate the effects of PDL and this novel iron catalyst. The study of the kinetics of thermal liquefaction of coal in a solvent has a long history, dating back to 1934

(Asbury, 1934). Due to the complexity of products from coal liquefaction, lumped parameter kinetic models have been used successfully to describe coal liquefaction processes. According to a method for characterizing coal liquefaction products, two main kinds of lumped parameters were used: one was based on solubility and the other was based on boiling range. Coal liquefaction kinetics were also studied based on H-NMR analyses (Schindler, 1996). As bench-scale batch processes were dominant in the coal liquefaction research, the method based on solubility was favored by many workers. Weller et al. (1950, 1951) first proposed essentially linear reaction pathways: coal to asphaltene, followed by asphaltene to oil. Thereafter, this simplistic series thermal reaction model was extensively developed to various combinations of series and parallel reaction pathways (Liebenberg and Potgieter, 1973; Cronauer et al., 1978; Shalabi et al., 1979; Mohan and Silla, 1981; Abichandani et al., 1982, 1984). Kinetics of catalytic coal liquefaction was further investigated by many researchers (Ruether, 1977; Gollakota et al., 1985; Pradhan et al., 1992; Suzuki, 1994). Recently, Keogh et al. (1991, 1994) studied the production of three lumped parameters (oils + gases, preasphaltenes + asphaltenes, and insoluble organic matter) as a function of a severity index, defined in terms of reaction temperature and time. They deduced reaction pathways for a large number of high-volatile bituminous coals during either thermal or catalyzed liquefaction. They found that neither the quality of the liquefaction solvent nor the addition of a catalyst affected the thermal pathway but did alter reaction rates. We have lumped the reaction products as gas + oil, asphaltenes, preasphaltenes, and char. Several reaction pathways were tested based on the experimental data. It was found that a valid kinetic model for both thermal and catalytic reactions was the same as the one proposed by Shalabi et al. (1979) but with some modifications. The mechanisms of thermal and catalytic reactions were investigated based on the context of the model. Experimental Section

* To whom correspondence should be addressed. Phone/ Fax: (801)581-5162. E-mail: [email protected]. S0888-5885(96)00568-4 CCC: $14.00

Materials. Blind Canyon (Utah) DECS-6 coal (60 mesh) was obtained from the Penn State Coal Sample © 1997 American Chemical Society

Ind. Eng. Chem. Res., Vol. 36, No. 5, 1997 1445

Reaction Procedure. Liquefaction reactions were carried out in 27-cm3 tubing reactors at 360-400 °C, about 2000 psig H2 (reaction pressure) for 0-180 min. The reactors were charged with a 1:2 ratio by weight of dry coal or iron-loaded coal and solvent. The reactors were purged with nitrogen and then pressurized with hydrogen to an initial pressure of 1000 psig at room temperature. The tubing reactor was attached to a shaft, was placed into a preheated fluidized sand bath, and reached the desired temperature in about 4 min. The moment when the tubing reactor reached the desired reaction temperature was designated as a reaction time of zero. When the reactions were completed, the tubing reactor was quenched in a water bath to room temperature in about 1 min. The reactors were depressurized, and the gases were vented. As illustrated in Figure 1, other liquefaction products were separated into oil (pentanesoluble), asphaltenes (benzene-soluble but pentaneinsoluble), preasphaltenes (THF-soluble but benzeneinsoluble), and char (THF-insoluble) by sequential Soxhlet extraction. As gaseous products came from both coal and solvent, it was difficult to determine how much gas was from coal depolymerization. Therefore, the reaction products were lumped as gas + oil, asphaltenes, preasphaltenes, and char. Product fractions were defined on a dry-ash-free basis as shown below:

char (U):

U ) (WTI - Wcat - Wash)/Wmaf

preasphaltenes (P): asphaltenes (A):

P ) (WBI - WTI)/Wmaf A ) (WPI - WBI)/Wmaf

oil + gas (+losses) (L): Figure 1. Schematic flowsheet of coal liquefaction products fractionation.

Bank and was ground to pass through a 100 mesh Tyler series screen using a ball mill grinder under nitrogen. Ground coals were dried under vacuum at 100 °C for 6 h, kept overnight at room temperature, stored in glass bottles sealed with nitrogen, and then put in a refrigerator for future use. The proximate analysis of the coal is 5.84% ash, 44.50% volatile matter, and 49.66% fixed carbon. The ultimate analysis of the coal sample was 81.72% carbon, 6.22% hydrogen, 1.56% nitrogen, 0.40% sulfur, and 10.10% oxygen. Iron-loaded DECS-6 coal was prepared by incipient wetness impregnation. Ammonium iron(III) sulfate dodecahydrate, obtained from Aldrich Chemical Co., was used as the precursor of iron. After impregnation, the resulting coal was dried at the same conditions as mentioned above. The weight ratio of iron to moisture-free coal was 1.12:100. The solvent, plastic-derived liquids, was obtained from depolymerization of high-density polyethylene (HDPE) in a 150-cm3 autoclave reactor at 435 °C, for a reaction time of 60 min, under nitrogen (Ding et al., 1996b). The boiling point distribution of the solvent was obtained by simulated distillation according to ASTM D2887-89 and D5307-92. The internal standard used was a mixture of nearly equal amounts of n-C16, n-C17, and n-C18. The analysis was performed on a HP-5890 series II gas chromatograph with FID detector, using a petrocol B column (6 ft long and 0.125 in. o.d.). The results of simulated distillation of the solvent are 52.1% lower-boiling fractions (BP < 325 °C) and 46.4% heavy gas oil + vacuum gas oil fractions (BP from 325 to 538 °C).

L ) 1.0 - (U + P + A)

where WTI is the weight of THF-insoluble products; Wcat is the weight of catalyst used, if any; Wash is the weight of ash in coal; Wmaf is the moisture and ash free weight of the starting coal; WBI is the weight of benzeneinsoluble products; and WPI is the weight of pentaneinsoluble products. All experiments were performed in duplicate or triplicate; repeatability of the results was (2.5% for total conversion and for gas + oil yield. Results and Discussion Kinetic Model. The following reaction model was found to be valid for both thermal and catalytic coal liquefaction with PDL as solvent. preasphaltenes (P) k1

coal (C)

k5

k4

k2

asphaltenes (A) k6

k3

gas + oil (L)

Three assumptions were made for this model: (1) All reaction steps were first order and irreversible. (2) The rate constants fit the Arrhenius law. (3) Hydrogen is present in excess. The rates of disappearance and formation of lumped components in the batch reactor can be presented as the sum of thermal reaction rates for the products and are listed in the Appendix. The initial conditions for all species need to be known for integrating the above equations. Shalabi et al. (1979) took initial values of preasphaltenes, asphaltenes, and gas + oil as zero. Such a treatment may not reflect the nature of the isothermal reactions. In this study, the initial conditions for char, preasphaltenes,

1446 Ind. Eng. Chem. Res., Vol. 36, No. 5, 1997

Figure 2. Experimental (data points) and model-fitted product distributions (lines) for DECS-6 coal liquefaction with plastic-derived liquids as solvent in a tubing reactor at 360 °C, ∼2000 psig H2.


asphaltenes, and gas + oil fractions were obtained from the solubility of coal, which just achieved isothermal reaction temperature, i.e., at t ) 0, P ) p0, A ) a0, and L ) l0, where p0, a0, and l0 are preasphaltenes, asphaltenes, and gas + oil fractions obtained from the reactions at isothermal reaction temperatures at a reaction time of 0 min. As all the organic coal may not be converted to liquefaction products (Shalabi et al., 1979), the reactive fraction of coal (denoted by r) is less than 1. This reactive fraction is not only a function of temperature and solvent used (Cronauer et al., 1978) but also a function of the catalyst used. The insolubles in THF obtained in the longest run (i.e., 180 min) were taken as the unreactive fraction (denoted by 1 - r) of coal at the reaction conditions. Therefore, the initial conditions for the reactive fraction of coal was represented by:

at t ) 0,

C ) C0 ) r - (a0 + p0 + l0)

Let U denote char in the reactor, at any reaction time t,

U(t) ) C(t) + (1 - r) when t ) 0, U0 ) 1 - (a0 + p0 + l0).

(1)

The solutions of the differential equations (A1)-(A4), coupled with eq 1, are listed in the Appendix. The NL2SOL program (Dennis et al., 1981), based on an adaptive nonlinear least-squares algorithm, was used to estimate parameters k1-k6 by regression analysis. The objective function is N

F(k1,...,k6) )

1

(R(k1,...,k6)iTR(k1,...,k6)i) ∑ i)12

(2)

where

R(k1,...,k6) )

x(Ai - Ai)2 + (Pi - Pi)2 + (Li - Li)2 + (Ui - Ui)2 Ai, Pi, Li, and Ui are experiment data, Ai, Pi, Li, and Ui are data calculated from the model, and i ) 1, ..., N, where N is the number of experimental observations. The algorithm realized by NL2SOL was explained in detail by Dennis et al. (1981, 1983). There are two advantages to using this method. First, convergence from poor starting guesses is promoted, because NL2SOL uses a model/trust-region technique along with an adaptive choice of the Hessian model. Second, on large residual problems (in which F(x) is relatively large),



Figure 5. Arrhenius plots for the rate constants: thermal liquefaction of DECS-6 coal with plastic-derived liquids as solvent. Table 1. Rate Constants for Thermal Liquefaction Pathways

k1 (coal f preasphaltenes) k2 (coal f asphaltenes) k3 (coal f gas + oil) k4 (preasphaltenes f asphaltenes) k5 (preasphaltenes f gas + oil) k6 (asphaltenes f gas + oil)

360 °C

parameters (h-1) 380 °C

400 °C

activation energy (kcal/g‚mol)

frequency factor (h-1)

0.2168 0.3057 0.4963 0.0151 0.0109 0.0075

0.3102 0.4064 0.5893 0.0287 0.0251 0.0156

0.5041 0.698 0.8902 0.0593 0.0501 0.0353

18.0 17.6 12.5 29.2 32.6 33.1

6.541 × 105 3.394 × 105 9.229 × 103 1.749 × 118 1.987 × 109 1.890 × 109

NL2SOL often works much better than the GaussNewton or Levenberg-Marquardt method alone. Thermal Liquefaction. Coal liquefaction experiments were carried out in the 27-cm3 tubing reactor at 360, 380, and 400 °C, at eight times (0, 5, 15, 30, 60, 90, 120, and 180 min). As shown in Figures 2-4, the model-predicted curves for the amount of char, the production of preasphaltenes, asphaltenes, and gas + oil against isothermal reaction time agree reasonably well with the experimental data for the coal-solvent system. The six rate constants evaluated by nonlinear leastsquares regression are listed in Table 1. Based on the kinetic parameters, Arrhenius plots were obtained and are shown in Figure 5. It is obvious that the data lie on a straight line for each parameter. The activation energies and frequency factors, which are listed in Table 1, were calculated from the slopes and intercepts of

these straight lines according to the Arrhenius equation (Levenspiel, 1972). The values of the rate constants k1, k2, and k3 indicate the importance of the direct coal conversion reaction to preasphaltenes, asphaltenes, and gas + oil, respectively. The extent of hydrocracking reactions, preasphaltenes f asphaltenes, preasphaltenes f gas + oil, and asphaltenes f gas + oil, is reflected by the magnitudes of k4, k5, and k6, respectively. As seen in Table 1, it is interesting to note that k4, k5, and k6 are much smaller than k1, k2, and k3, indicating the predominance of the direct conversion reactions. Shalabi et al. (1979) studied the kinetics of Kentucky No. 9 bituminous coal liquefaction with tetralin as solvent. They also found that the magnitude of k values for direct coal conversion is about 1 order larger than that of k values for indirect coal conversion reactions. This indicates that the quality of the liquefaction solvent has no major effect on the

1448 Ind. Eng. Chem. Res., Vol. 36, No. 5, 1997 Table 2. Comparison of Kinetic Parameters reactor technique coal solvent

Mohan et al., 1981

Cronauer et al., 1978

Shalabi et al., 1979

this work

batch nonisothermal (390-450 °C) Illinois No. 6 (bituminous) tetralin

CSTR isothermal (400-470 °C) Belle Aye (subbituminous) hydrogenated anthracene oil

batch isothermal (350-400 °C) Kentucky No. 9 (bituminous) tetralin

batch isothermal (360-420 °C)a DECS-6 (bituminous) HDPE-derived liquids

reactionb coal f preasphaltenes coal f asphaltenes coal f oil (+gas) preasphaltenes f asphaltenes preasphaltenes f oil (+gas) asphaltenes f oil (+gas) a

E (kcal/g‚mol)

k0 (h-1)

E (kcal/g‚mol)

k0 (h-1)

29.3 18.9 19.8 29.2

109

1.49 × 1.44 × 105 1.71 × 105 2.05 × 107

13.8 15.6 14.1 12.8

2.81 × 1.12 × 104 3.11 × 103 9.66 × 102

29.0

1.14 × 107

16.0

1.42 × 103

103

E (kcal/g‚mol)

k0 (h-1)

29.0 30.0 40.0

2.25 × 8.34 × 106 1.21 × 1010 106

E (kcal/g‚mol)

k0 (h-1)

18.0 17.6 12.4 29.2 32.6 33.1

6.54 × 105 3.39 × 105 9.23 × 103 1.75 × 108 1.99 × 109 1.89 × 109

The model was extrapolated to 420 °C; see Model Validation section in this paper. b E is activation energy, and k0 is frequency factor.

Figure 6. Experimental (data points) and model-fitted product distributions (lines) for iron-loaded DECS-6 coal liquefaction with plasticderived liquids as solvent in a tubing reactor at 360 °C, ∼2000 psig H2.

thermal pathway. However, different solvents resulted in different coal conversions. Under the same reaction conditions, coal conversions were 81.4% and 47.5% when tetralin or the PDL was used as solvent, respectively (Ding et al., 1996a). This confirms the statement that the primary difference in the observed pathway for the different liquefaction solvents is the magnitude of the maximum conversion obtained for the coals: the better the donor ability, the higher the maximum conversion obtained by the coal (Keogh et al., 1991). One of the interesting results of this study is that the reaction coal f gas + oil is more favorable although the order of magnitude of k1, k2, and k3 is about the same. This supports the proposal for the existence of a “mobile” phase in the macromolecular network of coal (Schindler, 1989). The cross-links in bituminous coal are believed to contain short aliphatic and ether bridges. There are also some loosely held and easily broken alkyl side chains attached to the clusters of aromatic and hydroaromatic rings (Wiser, 1977). It has been reasonably well established that when temperature reaches 400 °C, the pyrolytic breakup of the coal matrix begins mostly during the first several minutes (Figure 4). A large number of concurrent and competitive chemical reactions occur during the liquefaction process, such as thermolysis, hydrogen abstraction, dealkylation, cleavage of bridges between structural units, desulfurization, dehydration, and ring opening. This is reflected by an increase of k1, k2, and k3 values with an increase in temperature from 360 to 400 °C (Table 1).

Table 2 lists a comparison of kinetic parameters obtained in this study with those calculated by other workers (Cronauer et al., 1978; Shalabi et al., 1979; Mohan et al., 1981). There are no kinetic data existing in the literature for DECS-6 coal to make an extremely valid comparison. The closest situations are chosen to make the best comparison that can be made so far. Generally, the activation energies obtained by this work are consistent with those of other workers. The small discrepancy may be due to different definitions for lumped products and different coal/solvent systems used. Catalytic Liquefaction. Catalytic coal liquefaction with plastic-derived liquids as solvent is a more practical method for coprocessing coal with plastics (Ding et al., 1996a). One of the primary objectives of this work was to quantitatively measure the function of the iron catalyst for DECS-6 coal liquefaction with PDL as solvent. When obtaining k1-k6 by using the NL2SOL program, we found that the number of experimental data sets (six or eight sets) had virtually no effect on the final k1-k6 values. Therefore, we ran catalytic experiments at only six times (0, 15, 30, 60, 120, and 180 min). Figures 6-8 compare predicted and experimental results for the catalytic DECS-6 coal liquefaction with PDL as solvent at 360, 380, and 400 °C, respectively. The values of the rate constants, as well as activation energies and frequency factors, which were obtained from Arrhenius plots (Figure 9), for catalytic coal


Figure 7. Experimental (data points) and model-fitted product distributions (lines) for iron-loaded DECS-6 coal liquefaction with plasticderived liquids as solvent in a tubing reactor at 380 °C, ∼2000 psig H2.

Figure 8. Experimental (data points) and model-fitted product distributions (lines) for iron-loaded DECS-6 coal liquefaction with plasticderived liquids as solvent in a tubing reactor at 400 °C, ∼2000 psig H2. Table 3. Rate Constants for Catalytic Liquefaction Pathways

k1 (coal f preasphaltenes) k2 (coal f asphaltenes) k3 (coal f gas + oil) k4 (preasphaltenes f asphaltenes) k5 (preasphaltenes f gas + oil) k6 (asphaltenes f gas + oil)

360 °C

parameters (h-1) 380 °C

400 °C

activation energy (kcal/g‚mol)

frequency factor (h-1)

0.2315 0.3463 0.5412 0.0465 0.0302 0.0395

0.3201 0.4497 0.6123 0.0805 0.0615 0.0782

0.5112 0.7036 0.9415 0.153 0.1082 0.1227

16.9 15.1 11.8 25.4 27.3 24.3

1.516 × 105 5.439 × 104 5.856 × 103 2.691 × 107 8.044 × 107 9.626 × 106

liquefaction are given in Table 3. As observed from Tables 1 and 3, the addition of the Fe catalyst increased all six rate constants and decreased all six activation energies for each reaction pathway. It is generally accepted that the conversion of coal to liquids proceeds via a free-radical mechanism. Free radicals are produced by thermal scission of covalent bonds in the coal macromolecular structure in the initial stage, when the catalyst present rarely assists these coal depolymerization reactions. The formed radicals are either stabilized by hydrogen addition or regressively recombined to form polymeric products (i.e., THF-insolubles). For the thermal reaction in the absence of an excellent hydrogen donor solvent, such as tetralin, the transfer

of molecular hydrogen is limited; therefore, the amount of THF-insoluble is still high (Figures 2-4). However, increasing the coal conversion by adding the Fe catalyst indicated that this active Fe catalyst activated molecular hydrogen on the surface of the catalyst; thus, hydrogen may directly transfer to coal fragment radicals. Consequently, the rate constants for catalytic reactions were promoted. The results are also consistent with the understanding of the catalytic coal liquefaction mechanism proposed by Suzuki (1994). The small amount of increase in the k values for direct coal conversion reactions decreased in the order k3 > k2 > k1. However, there was at least a 2-fold increase in the rate constant groups between the thermal and


Figure 9. Arrhenius plots for the rate constants: catalytic liquefaction of DECS-6 coal (1.12 wt % Fe impregnated on coal) with plasticderived liquids as solvent.

Figure 10. Extrapolation of the product distribution experimental (data points) and model-fitted product distributions (lines) for DECS-6 coal liquefaction with plastic-derived liquids as solvent in a tubing reactor at 420 °C, ∼2000 psig H2.

catalytic runs for the consecutive reactions (preasphaltenes f asphaltenes, preasphltenes f gas + oil, asphaltenes f gas + oil) at 360, 380, and 400 °C. Moreover, for the catalytic reaction at 400 °C, the order of magnitude of k4-k6 reached the same order of magnitude of k1-k3. This indicated that consecutive reactions were strongly promoted by the Fe catalyst. If the catalytic rate constants k4-k6 are split into k4t + k4e, k5t + k5e, and k6t + k6e, respectively, where k4t, k5t, and k6t stand for thermal rate constants and k4e, k5e, and k6e represent effective rate constants caused by catalyst, the values of k4e, k5e, and k6e at 400 °C are 0.0937, 0.0581, and 0.0874, which are greater than the corresponding thermal rate constants k4t (0.0593), k5t (0.0501), and k6t (0.0353), respectively. k4e and k6e are larger than k5e. This trend is also observed for rate constants at 360 and 380 °C. Therefore, the Fe catalyst promoted the reaction pathway preasphaltenes f asphaltenes and asphaltenes f gas + oil to a larger extent than it did for preasphaltenes f gas + oil. The kinetic model fit the experimental data for both thermal and catalytic DECS-6 bituminous coal liquefaction very well. This suggested that the addition of Fe catalyst did not alter the reaction pathway defined by

the thermal process. The function of the Fe catalyst was only to selectively increase the rates of the reactions. Model Validation. To examine the validity of this kinetic model at higher temperatures, we applied it to the thermal and catalytic DECS-6 coal liquefaction with plastic-derived liquids as solvent at 420 °C. As observed in Figures 10 and 11, the model prediction and experimental results agreed within (3.1%. This convinced us that the model can be extrapolated to predict product distributions of DECS-6 coal liquefaction with PDL as solvent at temperatures at least as high as 420 °C. Conclusions Plastic-derived liquids can be utilized as solvent for Fe-loaded DECS-6 coal liquefaction. The experimental data were successfully correlated by the proposed kinetic model. The isothermal conditions were maintained not only experimentally but also mathematically. This simple but useful model can distinguish thermal and catalytic steps without adding more rate constants, and it can be applied within the temperature range from 360 to 420 °C. Moreover, the effects of reaction tem-


Figure 11. Extrapolation of the product distribution experimental (data points) and model-fitted product distributions (lines) for ironloaded DECS-6 coal liquefaction with plastic-derived liquids as solvent in a tubing reactor at 420 °C, ∼2000 psig H2.

perature and isothermal reaction time were also well described by this model based on Arrhenius activation energies. The Fe catalyst increased all six rate constants and decreased activation energies, but it did not alter the reaction pathways defined for the thermal process. Direct coal liquefaction reactions were predominant for both thermal and catalytic DECS-6 coal liquefaction with PDL as solvent, although the Fe catalyst promoted the consecutive reactions (preasphaltenes f asphaltenes f gas + oil) greatly. For catalytic reactions, the order of magnitude of rate constants for consecutive reactions was the same as that of rate constants for direct conversion reactions at 400 °C. Acknowledgment We gratefully acknowledge the funding support from the U.S. Department of Energy through Consortium of Fossil Fuel Liquefaction Science and the University of Utah. Nomenclature A ) asphaltenes, or weight fraction of asphaltenes a0 ) weight fraction of asphaltenes at zero reaction time BP ) boiling point C ) coal, or weight fraction of coal C0 ) weight fraction of coal at zero reaction time E ) activation energy, kcal/mol F ) objective function to be minimized ki (i ) 1, 6) ) rate constant for coal liquefaction pathway k0 ) frequency factor, h-1 L ) gas + oil, or weight fraction of gas + oil l0 ) weight fraction of gas + oil at zero reaction time N ) number of experimental observations p0 ) weight fraction of preasphaltenes at zero reaction time P ) preasphaltenes, or weight fraction of preasphaltenes PDL ) plastic-derived liquids r ) reactive fraction of coal R(k1,...,k6) ) residual function t ) time, min U ) char, or weight reaction of char U0 ) weight fraction of char at zero reaction time Wash, WBI, Wcat, Wmaf, WPI, WTI ) mass of ash, benzeneinsoluble products, catalyst, maf coal, n-pentane-insoluble products, and tetrahydrofuran insolubles, g Greek Symbols R ) k1 + k2 + k3 β ) k4 + k5

Subscripts e ) effective t ) thermal

Appendix The rates of disappearance and formation are given by

d C ) -(k1 + k2 + k3)C dt

(A1)

d P ) k1C - (k4 + k5)P dt

(A2)

d A ) k2C + k4P + k6A dt

(A3)

d L ) k3C + k5P + k6A dt

(A4)

The solutions for the above equations are given by

U(t) ) (1 - r) + (r - a0 - p0 - l0) exp(-Rt)

(A5)

1 [(r - a0 - p0 - l0)k1 exp(-Rt)] β-R 1 [(r - a0 - p0 - l0)k1 + p0(R - β)] exp(-βt) β-R (A6)

P(t) )

A(t) ) (r - a0 - p0 - l0) exp(-Rt)[k1k4 + k2(β - R)] (β - R)(k6 - R) (r - a0 - p0 - l0)k1 + p0(R - β) k4 exp(-βt) (β - R)(k6 - β) k6 - k3 [a (β - k6) + p0k4] exp(-k6t) (k6 - R)(k6 - β) 0 k2k6 - k1k4 - k2β (r - l0) exp(-k6t) (k6 - R)(k6 - β) k6 - k5 (a k - p0k2) exp(-k6t) (A7) (k6 - R)(k6 - β) 0 1 L(t) ) 1 - (U(t) + P(t) + A(t)) where R ) k1 + k2 + k3 and β ) k4 + k5.

(A8)


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Received for review September 13, 1996 Revised manuscript received January 23, 1997 Accepted January 23, 1997X IE960568+ X Abstract published in Advance ACS Abstracts, March 1, 1997.

Kinetics of Thermal and Catalytic Coal Liquefaction with Plastic

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