1170
. 31,1170-1176 Ind. Eng. Chem. Res . 1992,
Frevel, L. K.; Gilpin, J. 0. A. Carbonate Synthesis from Alkylene Carbonates. US Patent 3,642,858, 1972; Chem. Abstr. 1972, 76, 991402. Fujinami, T.; Sato, S.; Sakai, S. A Facile Preparation of Dialkyl Carbonates from Potassium Carbonate and Alkyl Bromides by using Organostannyl Compound as a Catalyst. Chem. Lett. 1981, 749-752. Green, M. J. Transesterification Process. Eur. Pat. Appl. EP 150,962, 1986; Chem. Abstr. 1986,104,129505~. Hallgren, J. E.; Mathews, D. R. 0. The Reactions of Carbon Monoxide and Phenols Promoted by Palladium Complexes. J. Organomet. Chem. 1979, 175 (l), 135-142. Hoffman, W. A,, 111. Convenient Preparation of Carbonates from Alcohols and Carbon Dioxide. J. Org. Chem. 1982,47,5209-5210. Illuminati, G.; Romano, U.; Tesei, R. Aromatic Carbonates. Ger. Offen. 2,528,412, 1975; Chem. Abstr. 1976, 84, 121495h. Iori, G.; Romano, U. Preparation of Phenolic Ethers. UK Patent Appl. 2026484, 1980; Chem. Abstr. 1980, 93,167894b. Knifton, J. F. Process for Cosynthesis of Ethylene Glycol and Dimethyl Carbonate. US Patent 4,661,609,1987; Chem. Abstr. 1987, 107,39225e. Lissel, M.; Dehmlow, E. V. Phasentransfer-Katalytische Herstellung von Kohlensaureestern Ohne Verwendung von Phosgen. Chem. Ber. 1981,114, 1210-1215. Lissel, M.; Rohani-Derfuli, A.; Vogt, G. Reactions with Dimethyl Carbonate. Part 3. 1Applications and Mechanisms of Mono or Bis Methylation of Aromatic Amines with Dimethyl Carbonate. J. Chem. Res. (S) 1989, 312. Merger, F.; Towae, F.; Schroff, L. Aralkyl and Alkyl Phenol Ethers. Ger. Offen. 2,729,031, 1979; Chem. Abstr. 1979, 90,137482m. Mizuno, T.; Nakamura, F.; Egashira, Y.; Nishiguchi, I.; Hirashima, T.; Ogawa, A.; Kambe, N.; Sonoda, N. Facile Synthesis of Carbonates from Alcohols and Carbon Monoxide Promoted by Elemental Sulfur. Synthesis 1989,636-638.
Otera, J.; Dan-oh, N.; Nozaki, H. Novel Template Effects of Distannoxane Catalysts in Highly Efficient Transesterification and Esterification. J. Org. Chem. 1991, 56, 5307-5311. Perrin, D. D.; Armarego, W. L. F. Purification of Organic Chemicals. In Purification of Laboratory Chemicals, 3rd ed.; Pergamon: Oxford, England, 1988; Chapter 3, pp 65-309. Proux, Y.; Pellergrina, M. Preparation of Organic Carbonates by Transesterification of Carbonic Acid Diesters in the Presence of Crown Ethers or Cryptand Phase Transfer Catalysts. Fr. Pat. 2,2608,812, 1989; Chem. Abstr. 1989, 110, 215192q. Romano, U.; Tesei, R.; Mauri, M. M.; and Rebora, P. Synthesis of Dimethyl Carbonate from Methanol, Carbon Monoxide and Oxygen Catalysed by Copper Compounds. Ind. Eng. Chem. Prod. Res. Deu. 1980, 19, 396-403. Tobita, M.; Niizeki, J. Dialkyl Carbonic Acid Esters. Jpn. Kokai Tokkyo Koho J P 79148,726,1980; Chem. Abstr. l980,92,214901t. Tundo, P.; Trotta, F.; Morgalio, G.; Ligorati, F. Continuous-Flow Processes under Gas-Liquid Phase-Transfer Catalysis (GL-PTC) Conditions: The Reaction of Dialkyl Carbonates with Phenols, Alcohols, and Mercaptans. Ind. Eng. Chem. Res. 1988, 27, 1565-1571. Victor, M. Aromatic Carbonates. Ger. Offen. DE 3,445,552 1985; Chem. Abstr. 1985, 104, 50647~. Yamazaki, N.; Nakahama, S.; Higashi, F. Polymers Derived From Carbon Dioxide and Carbonates. Ind. Eng. Chem. Prod. Res. Deu. 1979, 18 (4), 249-252. Yoshino, T.; Kijima, I.;Ochi, M.; Sampei, A.; Sai, S. Synthesis of Aryl Titanate. Kogyo Kagaku Zasshi 1957,60, 1124-1125. Zuckermann, J. J. The Reaction Tin with Dihydric Phenols. The Direct Synthesis of Tin (11) Heterocycles. J. Chem. SOC.1963, 1322-1324.
Receiued for reuiew July 9, 1991 Accepted January 6, 1992
Development of a Pulse-Injection Short Contact Time Coal Liquefaction Flow Reactor William D. Provine, Nicholas D. Porro, Concetta LaMarca, Michael T. Klein,* Henry C. Foley, and Kenneth B. Bischoff Department of Chemical Engineering, University of Delaware, Newark, Delaware 19716
Charles G. Scouten, Donald C. Cronauer, and A. Martin Tait Research and Development Department, Amoco Oil Company, Naperville, Illinois 60566
A well-mixed reactor was developed to study the initial reaction pathways and mechanisms of direct coal liquefaction. This pulse-injection flow vessel exploits the reactor residence time distribution to obtain an isothermal series of samples of well-defined holding times from 10 to 900 s. The reactor design also allowed for quick and efficient procurement of optimally spaced and sized samples. The operation of this reador is illustrated using both model compound and coal liquefaction experiments.
Direct coal liquefaction typically involves mixing the coal with a “donor” solvent to form a slurry that is then heated for 1800-5400 s (30-90 min) at 400-450 “C under 500-2000 psig of hydrogen pressure. The hydrogen-deficient coal abstracts hydrogen from the donor solvent or hydrogenrich structures in the coal to form liquids that are subsequently upgraded to more desirable light distillates. Throughout, retrograde reactions unfavorably compete by producing heavy products. Retrograde reactions convert desirable small product molecules into less-desirable larger macromolecules. This can occur either by recombination of two small product molecules or by addition of these product molecules back onto the unconverted coal macrostructure. Work by Shim (1984) and others shows that retrograde reactions are important even at short reaction times. Indeed, retrograde reactions can have the net effect of converting relatively weak bonds that are potentially cleavable into strong bonds 0888-588519212631-1170$03.00/0
that are more difficult to cleave. As a result, retrograde reactions can influence the liquefaction behavior observed at longer reaction times. This motivated keen interest in the chemistry of both the coal and its liquid products at short reaction times, where it would be most fruitful to attempt to unravel the competing contributions of forward and retrograde reactions. Such previous studies have been hampered by equipment limitations. Batch liquefaction studies often use tubing bomb or autoclave reactors (Cassidy et al., 1989; Maa et al., 1984). Results from these reactors can be confounded by large temperature fluctuations during the initial stages of liquefaction. Flow liquefaction has been studied in tubular or autoclave reactors (Brunson, 1979, Laine et al., 1985; Gibbins et al., 1990). Generally, these provide a single global residence time for a given system flow rate. Also, donor solvent vaporization through tubular flow reactors can obscure the actual residence time within 1992 American Chemical Society
Ind. Eng. Chem. Res., Vol. 31, No. 4,1992 1171 the reactor (Brunson, 1979). The foregoing motivated the design and construction of a novel, laboratory-scale reactor for the study of short contact time direct coal liquefaction. The pulse-injection flow reactor described herein exploits the reactor residence time distribution to obtain a series of samples of welldefined holding or reaction times. This reactor achieves isothermal operation and allows procurement of optimally sized solid and liquid samples over a small duration of sampling. The key design challenges were to obtain (1) isothermal and isobaric operation, (2) a well-defined residence time for each sample, Le., a minimum sampling duration, (3) a sufficient amount of coal-derived material in each sample, and (4) rapid injection of the coal into the reactor. The object of this paper is to describe the design and operation of the reactor system as well as to present some preliminary results.
Background The essential strategy was to operate the reactor in a pulse-injection, or "wash-out", mode. This mode allowed procurement of samples which, after the pulse, could be taken at times representative of the time allowed for reaction. In the limiting case, the reactor behavior would approach that of the ideal continuous stirred tank reactor (CSTR) which is spatially uniform in both concentration and temperature. This uniformity can be at the microscopic level (micromixed CSTR, the standard approximation) or, for viscous systems, such as in polymerization, at a more macrosopic level (macromixed CSTR) (Danckwerts, 1953; Zwietering, 1959). Operation of the reactor vessel under well-mixed operating conditions would provide fluid elements having reaction times with a probability given by the exponential residence time distribution function. All of the reactant coal would be injected at t = 0, and product samples would be taken at times t > 0 representative of the time spent in the reactor. The reaction would convert coal to coal liquids, and samples would contain time-dependent concentrations of coal plus coal liquids, C(t),given by the classic well-mixed response to a pulse input to a CSTR
where 7 is the mean residence time and Co is the initial concentration of coal in the reactor after injection. Operation of the reactor in this pulse-injection mode requires that the system initially be lined-out at the operating temperature and pressure before the coal is injected into the reactor at the arbitrary time zero. The initial isothermality is accomplished by a flow of solvent into the reactor. This flow of solvent also minimizes the thermal shock caused by the injected "cold" coal charge. As the reaction progresses, the solvent flow washes the coal-containing mixture out of the reactor where the reactions are quenched and a continuous series of samples are produced. Performing experiments in this wash-out mode provided special challenges for product sampling. Analytical chemistry requirements (NMR, solvent extraction, GPC, elemental analysis, and low-temperature ash analysis) dictated a reactor design for samples containing at least " x g" of coal and coal products ( C ( t ) )in both the liquid and solid phases. Because of the exponential depletion of the total coal-derived material in the reactor, this size requirement ultimately dictated the reactor design. The key design variables were the volume of the reactor (V), mean residence time ( T ) , the initial charge of coal of the reactor (Wo),and the total run time (tJ.
Variables
COnStraintS
B4Wh
Volume
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I
t
Maximum
Maximum Charge of Coal
1:5 CoalSolvent
Ratio
200 B
I
I
t 1
(+)
W"= . f.,.._
o
-
Mean Residence Time
I
'
60 900 S I
Figure 1. Logic diagram for short contact time coal liquefaction reactor design (2' I 450 "C, P I 1800 psig).
Operation of the reactor in the pulse-injection, or wash-out, mode depletes the amount of coal in the reactor. Both reaction kinetics and the residence time distribution contribute to this depletion. In order to obtain samples for quantitative analysis of the kinetics of the conversion of coal to coal liquids, short sample durations (tD)were sought. This required an estimate of the smallest sample duration that could generate x g of coal plus coal liquids. This was determined using the time dependence of the concentration of the coal-derived material (C in units of g/cm3) within the reactor, provided by eq 1with the initial condition C(t=O) = Co = (1- Ao)Wo/V (2) representing the pulse nature of a typical experiment. Since the coal initially contains mineral matter (Ao = low-temperature ash fraction = 0.14 for a typical Illinois no. 6 coal), eq 2 shows that only (1- A,) Woof the coal can liquefy. Thus, eq 3 provides the time dependence of the (3) coal-derived material concentration. This permits calculation of the sample size (2)required to capture the minimum amount, x , of solid plus liquid product needed for analytical workup. This is given by eq 4, which in turn
specifies the sample duration, tD,as in eq 5, where Q (cm3/s) is the volumetric flow rate. Together, eqs 4 and 5 allowed design of the liquefaction unit with moderate constraints on the allowable volume, coal charge, and mean residence time.
Reactor Design The logic that organized the reactor design is detailed in Figure 1. The design was based on minimizing the sample duration, tD,over the course of an experiment while maintaining at least x = 2 g of coal-derivedmaterial in each sample. The three main design variables were reactor volume, initial charge of coal, and mean residence time. Volume. The range of allowable reactor volumes, V , was, in principle, dependent on the initial charge of coal, Wo,since processing constraints limit the ratio of coal to solvent that can be charged to the reactor. From a processing standpoint, a dilute stream was preferable since entrained solids tend to scour metal surfaces and reduce the lifetime of valves in the sampling manifold. Since the
1172 Ind. Eng. Chem. Res., Vol. 31, No. 4,1992
optimal volume depends on the flow rate and contact time, the volume was set to the commercially available lo00 cm3 without loss of an optimal design. Initial Charge of Coal. The maximum charge of coal to the reactor was constrained by the processing issues stated above; the m i n i u m charge of coal was constrained by the analytical chemistry requirements. It was also desired that the donor solvent remain in excess during the course of an experiment and therefore was not a kinetic limitation to conversion of the coal. Therefore, the ratio of coal to solvent was held to a maximum 15 ratio. This set the maximum coal charge at 200 g. The solvent to coal ratio continuously increases due to the pulse injection of the coal and the continuous feed of solvent to the reactor. For all practical purposes, the solvent to coal ratio is considered infinite. The minimum charge of coal was deduced from the maximum allowable sample duration specified from the need to obtain quantitative kinetics. This was set at tD(max)= 30 s, which is 5% of the mean residence time for tf = 600 s. Therefore, the initial charge of coal was constrained as 50 g IW oI 200 g. Mean Residence Time. The final design variable, i.e., the flow rate of fresh solvent into the reactor (or, equivalently, the mean residence time with the now-fmed reactor size of 1000 cm3), was determined by minimizing the sample duration of eq 5. At one extreme, the required sample duration is high for large flow rates or small mean residence times. This is due to the high wash-out of the coal from the reactor, which causes the coal concentration within the reactor to drop rapidly. As a consequence, the length of the window for obtaining initialkinetic information narrow8 as the flow rate increases. At the other extreme of low flow rates, or equivalently large mean residence times, the coal concentration within the reactor is maintained at a high level over an extended period of time since the coal is flushed from the reactor slowly. The low flow rate leads to a large sample duration in order to capture sufficient coal-derived material in each sample. The foregoing suggests the existence of an optimal flow rate for a given total run time (tf). Operation at this flow rate would produce sharp samples containing the required amount of coal-derived material. The calculation of this flow rate, for a given final sample time, was provided by the derivative (13tD/d7)Wo,t=tf:This is shown in eq 6. Solution of eq 6 shows the optimal mean residence time to be equal to the total run time, Le., 7,,t. = tP
These concepts are summarized in Figure 2 as a plot of sample duration vs mean residence time with W o= 140 g, x = 2 g, and a variety of final sample times (tf= 0,300, 600, 900 s). Clearly, the sample duration, tD, achieves a minimum which corresponds to 7 = t p Also,it is noticeable that a smaller than optimal mean residence time will hamper quantitative kinetic analysis more than a larger one due to the sharp increase in sample duration with small changes in mean residence time. The present study of short contact time coal liquefaction sought kinetics information from samples taken throughout the range of 10-900 s. Therefore, the pulse-injection reactor system was designed for a mean residence time ( 7 = V / Q )range of 60-900 s. Given that the flow rate was specified by the time of the final sample, early samples could be of smaller duration
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and still provide x g/sample. This would allow for a policy of increasing tD through to the find sample. The resulting trajectory of tDis shown in Figure 3. However, operation in this mode was considered less practical than one leading to constant sample sizes because of equipment component variations and the need for flexibility in operation from run to run. Thus, for ease in analysis and operation of the reactor system, a constant sample size policy was used in practice.
Reactor Operation The resulting process flow diagram is illustrated in Figure 4. The major components of the system are listed in detail in Table I. Generally, the flow of material is from left to right in Figure 4,i.e., from the feed reservoir to the waste vessels. Construction material limitations constrain the system temperature to 1450 "C (valve seats) and the system pressure to 11800 psig (waste and solvent recovery vessels). Fresh solvent flows from a 26.5-L (7.0 U.S.gal) feed reservoir through a metering feed pump, where it is pressurized to the operating pressure (commonly, 900 psig). The solvent is fed through an oil circulation preheater where it is heated to 150 "C. It then enters an electrically heated zone where its temperature is raised to approximately 200 "C. Then, by passage through a 0.95-cm (3/e-in.)air-operated ball valve (9 or 10 on Figure 4),the solvent either enters the reactor through a bypass line or through a 500-cm3 coal-charging bomb. The coal is injected into the reactor by diverting the pressurized solvent so as to blow a 1.75-cm (11/16-in.),lo00 psig rupture disk installed in the line between the coal charging bomb and the reactor. The loaded bomb contains
Res., Vol. 31, No. 4, 1992 1173
Sampling Yanlfold (7 rampbr)
Fresh Solvent
L E O Figure 4. Pulse-injection short contact time coal liquefaction reactor system flow sheet. Table I. Major Components of Reactor component 1000-cm3(L)Magne drive stirred autoclave 3.5-kW heater, bottom flush valve, Model BC0100SS06AG16D program logic controller, Model TI-100 metering feed pump, explosion proof, Model 7120-SE, 3.33 cm3/s at 2000 psig mass flow controller and display, Model 5850TRP, 5896 data acquisition computer, PS/2 Model 30-286 autoclave temperature controller, Model MTCPKCSOO data acquisition analog input board, Model DT2805, DT707-T 4.0-gal waste vessel oil preheater with temperature controller, Model CX2P3N25H2X 2.5-gal solvent recovery vessel air-operator 3/8-in. ball valve (450 OC at 2000 psig), Model 20SC6071-OIF-HT data acquisition software, Asystant+ software 7.0-gal feed reservoir, Model 73-07 back-pressure regulator, Model SD-91XW air-operated l/,-in. ball valve (150 OC at 2000 psig), Model SS-S62PS4-133NC manual l/,-in. ball valve (150 "C at 2000 psig), Model SS-S62PS4 three-way solenoid valve, Model D-19, D-49 injection rupture disk assembly
System manufacturer Autoclave Engineers Texas Instrument Pulsafeeder Brooks Instruments IBM Autoclave Engineers Data Translation Hoke Gaumer Co. Hoke Autoclave Engineers Asyst Software Alloy Products Co. Grove Co. Swagelok Swagelok Automatic Switch Co. Koch and Associates
a coal slurry (coal to solvent mass ratio = 1:2) that enters the reactor almost instantaneously for a 50-g charge. The injection of the coal is controlled from the program logic
controller which sends an electronic signal to the solenoid valves that release air to the appropriate air-operated ball valves. Efficient heat transfer to the autoclave maintains a high-temperature, near-isothermal environment. The feed (pure tetralin) is preheated to between 200 and 225 "C, and the remaining heat requirements are met from a customized 3.5kW adjustable output heater obtained with the autoclave. At a flow rate of 1.67 cm3/s of fresh tetralin to the reactor, the system maintains 420 "C within the reactor with maximum fluctuation of 15 "C during the entire length of an experiment. On exit from the reador, samples are quenched to 1150 "C with a countercurrent water heat exchanger and collected in a sampling manifold assembly. Two sets of sample cylinders (labeled 1-7 on Figure 4) were needed. One set handled 0-60-sexperiments, and the others handled 0-600-s experiments. A sample size of 50 cm3 was taken for samples spanning across a 600-s run, whereas a sample size of 15 cm3was taken for final times of less than 60 s. Thus,the sampling manifold is modular in the sense that the sample cylinders (15 and 50 cm3) are interchangeable, depending on the experiment. This held the sample duration to a maximum of 30 s for a 600-srun (tr = 600 s) and 5 s for a 60-s run (tf = 60 s) while ensuring that each sample contained at least 2 g of coal-derived material. The sampling manifold was automated with 0.64-cm (ll4-in.) air-operated ball valves connected to three-way solenoid valva controlled by a programmed logic controller (PLC). This allowed samples to be obtained very rapidly and with minimal error since air-operated valves close very rapidly (under 1.0 s). This feature is very important when
1174 Ind. Eng. Chem. Res., Vol. 31, No. 4, 1992
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where W, = initial charge of biphenyl (g) and p = density of reactor fluid (g/cm3). For the distribution of eq 10, this simplifies to Wso= PQWS,T (12)
-CDBE - --CDBE~ exp [-k t ] cs cs, Note that the unreactive standard provided a direct measure of the RTD, which had the effect of removing the RTD from the kinetics analysis for DBE. Equation 9 thus allowed estimation of the DBE disappearance reaction rate
where wso is the weight fraction of biphenyl in the reactor at t = 0. The right-hand side of eq 12 amounted to 17.6 g while the experimental injection, W,, was 19.7 g. Thus, 90% of the standard was recovered via the flow out of the reactor. The holdup within the reactor at the end of the DBE/tetralin run (t = 1500 s) contained 0.85 g of biphenyl; eq 10 would suggest 0.30 g. This experimental holdup of biphenyl adds to its measured washout to give a total material balance of 93% . In short, the pyrolysis of DBE in tetralin showed that the reactor can be reasonably well mixed and possesses characteristicsresembling a continuous stirred tank reactor (CSTR) for a liquid feed. This encouraged further experiments with an actual coal. Coal Liquefaction Experiments. The liquefaction of an Illinois no. 6 coal (Amoco) was conducted at 390 "C and an operating pressure of 900 psig of nitrogen gas. The feed rate to the reactor was 7.5 cm3/s (at standard conditions of T = 0 "C and P = 775 psig) of nitrogen gas and 1.94 cm3/s of fresh tetralin ( T = 500 8 ) . A 1000 psig rupture disk was used to charge the reactor with 50 g of coal. It took 51 s to overpressurize the disk. The coal liquefaction data thus derived are used to show the operability of the reactor for actual coal liquefaction experiments as well to present representative NMR analyses of both the solid and liquid components of liquefaction. The reactor operating temperature and pressure profiles are shown in Figure 7. On injection, the reactor experi-
Ind. Eng. Chem. Res., Vol. 31, No. 4, 1992 1175
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Figure 9. Solid-state CP/MAS 13C NMR of residual solids after liquefaction of an Illinois no. 6 coal at 390 O C .
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Figure 7. Reactor temperature and pressure profile for a coal liquefaction experiment at 390 OC.
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Figure 8. Conversion kinetics of an Illinois no. 6 coal after liquefaction at 390 OC with tetralin.
enced a 300 psig pressure spike which subsided within 5 s to 900 f 50 psig. The oscillation of 50 psig is due to the opening and closing of the diaphragm of the back-pressure regulator. The coal produced a 20 "C temperature drop in the reactor upon injection, but within 20 s the reactor was again at the set point of 390 f 2 "C. The slight increase in the reactor temperature before injection occurred because the cold solvent (200 "C) flow in the reactor was temporarily suspended while the pressure built up in the coal charging bomb. Samples were taken at t = 2,23,57,88,119, and 151 s; analyses presented herein include low-temperature ash analysis, solid-state CP/MAS 13CNMR spectroscopy, and liquid-phase 'H NMR spectroscopy. The low-temperature ash analysis (LFE Corp., Model LT-302 asher) determined the fraction of mineral matter in each solid sample, and the coal conversion was determined by tracking the fraction of mineral matter in the residual solids as a function of reaction time. Conversion, on a moisture and ash-free basis (maf basis), is defined by
The dependence of conversion on reaction time is shown in Figure 8. These results show that the reactor produces solid samples which have very limited conversion at the earliest stages of liquefaction. This allows the focus to be placed on the initial bond breaking f bond forming reactions. Figures 9 and 10 summarize the NMR analyses of the coal liquefaction run. Figure 9 summarizes a solid-state 13C NMR analysis (Chemagnetics M-100s spectrometer) that shows a pronounced decrease in aromaticity (aromatic carbon = 75-175 ppm NMR, aliphatic carbon = 25-75
20
40
60
80 Time (s)
100
120
140
160
Figure 10. Proton NMR of liquid phase after liquefaction of an Illinois no. 6 coal in tetralin at 390 O C .
ppm NMR) during the first minute of liquefaction. The representative liquid-phase proton NMR analysis (Bruker AM-250 spectrometer) shows an increase in the condensed aromatic (7.25-9.0 ppm NMR) and olefinic protons (5.90-6.90 ppm NMR) during that time period. This suggests that the early stages of liquefaction of this Illinois no. 6 coal might involve the cleavage of cross-linkages, followed by the sequences of hydrogen abstraction and /3-scission pathways that transfer small molecules from the solid to the liquid phase. It is also possible that an aromatic-rich mobile phase is liberated in the early stages of liquefaction.
Summary A short contact time coal liquefaction flow reactor was designed, constructed, and operated. The system included a 1000-cm3autoclave that can handle a 50-200-g charge of coal with a mean residence time of 60-900 s. Isothermal and isobaric conditions were achieved within 20 s after injection. This system generates product samples with at least 2 g of coal-derived material. The reactor performance was probed by studying the pyrolysis of dibenzyl ether in tetralin. The residence time distribution of the unreactive biphenyl showed a close approach to theoretical CSTR characteristics for a liquid feed. Also, the good agreement between the present and independent kinetic parameters suggest high reliability of the reactor. Preliminary coal liquefaction experiments showed that information can be obtained on both liquid and solid samples. Thus reaction of not only the coal liquids but also reaction of the solid coal itself can be probed. Of note, the solid-phase aromaticity dropped initially while the liquid-phase aromaticity increased. Acknowledgment We acknowledge the financial support of Amoco Oil Co. and the National Science Foundation (MTK PYI Award
1176
Ind. Eng. Chem. Res. 1992, 31, 1176-1182
BCS8451240). Also, the research on which this project is based was financed in part by the State of Delaware as authorized by the State Budget Act of Fiscal Year 1988. We would also like to acknowledge the helpful suggestions of Bob Lumpkin, Ken Robinson, and Al Van der Klay of Amoco and Bill Calkins and Rowena Torres-Ordonez of the University of Delaware. Also, we would like to thank Mary Jacintha and Cecil Dybowski of the University of Delaware for the solid-state CP/MAS 13CNMR analyses. Nomenclature A. = fraction of mineral matter in original coal, t = 0 A, = fraction of mineral matter at time t C = concentration of coal plus coal-derived material in the reactor (g/cm3) CDBE = concentration of dibenzyl ether (mol/cm3) C D B b = concentration of DBE at t = 0 (mol/cm3) Cs = concentration of biphenyl (mol/cm3) C, = concentration of biphenyl at t = 0 (mol/cm3) P = reactor pressure (psig, 900 psig = 6.3 MPa) Q = flow rate (cm3/s) tD = sample duration (8) t = contact or reaction time (8) tf = total run time = final sample time (8) T = reactor temperature ("C) V = volume of reactor (cm3) W , = initial charge of coal to reactor (9) w s = weight fraction of biphenyl in reactor wso = weight fraction of biphenyl in reactor at t = 0 W , = initial charge of biphenyl to reactor (g) W , = weight of solid collected in each sample (g) x = amount of concentrated coal-derivedmaterial needed for analytical workup (g) Z = sample size (cm3)
Greek Symbols p = density (g/cm3) T = mean residence time (9) = V/Q Registry No. DBE, 103-50-4; PhMe, 108-88-3; PhCHO, 10052-7.
Literature Cited Brunson, R. J. Kinetics of Donor-vehicleCoal Liquefaction in a Flow Reactor. Fuel 1979,58, 203. Cassidy, P. J.; Jackson, W. R.; Larkins, F. P.; Louey, M. B.; Rash, D.; Watkins, I. D. The Structure and Reactivity of Brown Coal 12. Timesampled Autoclave Studies: Reactor Design, Operation, and Characterization. Fuel 1989, 68, 32. Cronauer, D. C.; Jewell, D. M.; Shah, Y. T.; Modi, R. J. Mechanisms and Kinetics of Selected Hydrogen Transfer Reactions Typical of Coal Liquefaction. Ind. Eng. Chem. Fundam. 1979, 18, 153. Danckwerta, P. V. Continuous Flow Systems. Chem. Eng. Sci. 1953, 2, 1. Gibbins, J. R.; Kandiyoti, R. Development of a Flowing-Solvent Liquefaction Apparatus. Fuel Process. Technol. 1990, 24, 237. Korobkov, V. Yu.; Grigorieva, E. N.; Senko, 0. V.; Kalechitz, I. V. Kinetics and Mechanisms of Thermolysis of Dibenzyl Ether. Fuel Process. Technol. 1988, 19, 243. Laine, J.; Becerra, 0. A. Semi-continuous Flow Reactor Technique for Coal Liquefaction Studies. Fuel Process. Technol. 1985,11, 127. Maa, P. S.; Neavel, R. C.; Vernon, L. W. Tubing Bomb Coal Liquefaction Technique. Ind. Eng. Process Des. Dev. 1984, 23, 242. Shinn, J. H. From Coal to Single-stage and Two-stage Producta: A Reactive Model of Coal Structure. Fuel 1984,63, 1186. Simmons, M. B.; Klein, M. T. Free-Radical and Concerted Reaction Pathways in Dibenzyl Ether Thermolysis. Ind. Eng. Chem. Fundam. 1985,24, 55. Zwietering, Th. N. The Degree of Mixing in Continuous Flow Systems. Chem. Eng. Sci. 1959, 1 1 , 1.
Received for review June 10, 1991 Revised manuscript received December 3, 1991 Accepted December 31, 1991
A Graphical Method for Determining Pore and Surface Diffusivities in Adsorption Systems Peter G.G r a y and Duong D. Do* Department of Chemical Engineering, University of Queensland, S t . Lucia, Queensland 4072, Australia
The dynamics of adsorption in a single particle was modeled using two different mathematical formulations: two intrinsic diffusional resistances (macropore and surface diffusion) and one apparent diffusional resistance (pore diffusion). The relationship between the apparent and intrinsic diffusivities was determined and found to be a function of the adsorption isotherm nonlinearity. By combination of this relationship with an analytical solution of the pore (apparent) diffusion model, a method was developed whereby the macropore and surface (intrinsic) diffusivities could be determined directly from experimental adsorption uptake data without the need for any model fitting. This simple method was applied to experimentally measured adsorption dynamics of sulfur dioxide (Freundlich isotherm) and n-butane (Langmuir isotherm) on activated carbon, and was found to give macropore and surface diffusivities similar to that obtained using a full model fit. In many common gas- and liquid-phase adsorption systems the overall rate of the process is controlled by diffusional resistance. To make practical use of these adsorption processes, it is necessary to determine what diffusion mechanisms are acting and to quantify their respective diffusion coefficients. It is, therefore, advantageous to have a simple and quick method for determining these diffusivities from experimental adsorption dynamic
* Author to whom correspondence should be addressed.
data. The development of such a method is the objective of this work. The mechanisms acting over the macroscopic length scale of an adsorbent particle are macropore (molecular and/or Knudsen) diffusion and often surface (sorbedphase) diffusion. The macropore diffusion control model has been applied to many gas- and liquid-phase adsorption systems over a number of decades, where a standard formulation of this model is given by Ruthven (1984). As well as sorbate transport through the macropore void region
0888-5885/92/2631-ll76$03.00/00 1992 American Chemical Society
