Energy & Fuels 1994,8, 89Q-895
890
Dynamics of the Extract Molecular Weight Distribution in Supercritical Extraction of Coal: Continuous-Mixture Kinetics Ming Wang, Chunjie Zhang, J. M. Smith, and Ben J. McCoy* Department of Chemical Engineering, University of California, Davis, California 95616 Received August 24, 199P
This paper presents a method of exploring the kinetics of supercritical tert-butyl alcohol extraction of coal. Molecular weight distributions (MWDs) of extraction products of bituminous coal are interpreted with a model based on continuous-mixture kinetics. A continuous-flow reactor, in which supercriticaltert-butyl alcohol contac6 a differential bed of coal particles, provides sequential samples that are analyzed by HPLC gel permeation chromatography to obtain the time-dependent MWD data. The observed MWDs of the reaction products and their precursors in the coal macromolecular network are described by three gamma distributions. At temperatures below 360 "C the MWDs maintain a similar shape during the semibatch extraction, indicating that the first-order rate constant is independent of molecular weight. The results of MWDs for runs with coal extract as feed provide experimental evidence that secondary reactions, such as repolymerization and cracking, are negligible at extraction conditions.
Introduction Extraction with a supercritical solvent has advantages over pyrolysis (occurring in a gas that has low solvent power) or thermolysis in a liquid (where mass transport resistance may obscure chemical kinetics). A supercritical fluid has transport coefficients that are gaslike and solvent properties that are liquidlike. Supercritical extraction thus has the advantage of low mass-transfer resistance combined with good so1vency.l In the experiments we describe, a semibatch reactor allows molecular products of thermal decomposition of coal to be transported rapidly out of the coal matrix and swept away by the flowing solvent. Thus, secondary reactions of the solubilized molecules are negligible, and kinetics of the extraction can be determined. When the number of chemical species involved in a chemicalprocess reachesa large number, e.g., 102or greater, it is convenient to consider a property of the components to be a continuous variable. For example, the molecular weight, the number of carbon or oxygen atoms, or the boiling point of the different species can be considered a continuum of values, rather than discrete n ~ m b e r s . ~One a line of inquiry is to formulate and solve the equations governing the chemical kinetics, or thermodynamics, of the continuous mixture and to test the theory by experimentally measuring the frequency of occurrence of the continuous variable (e.g., the molecular weight distribution). Another program is to average the governing equations to obtain relations for lumped variables that can be measured experimentally for the bulk mixture. Both these approaches have been explored for continuousmixture thermodynamics. The theoretical issues of continuous mixture and lumping kinetics for chemical reactions have been addressed in numerous mathematical studies, but their use to interpret experimental data has been limited.415 Prasad et aL3simulated the rate processes a Abstract published
in Advance ACS Abstracts, June 1, 1994. (1)Kerehaw, J. R.J. Supercritical Fluids 1989,2,35. (2)h i s , R.;Gavales, G. R. Philos. Tram. R . SOC.London 1966,A260, 351. (3)Praaad, G. N.; Agnew, J. B.; Sridhar, T. AIChE J . 1986,32,1277.
of coal liquefaction based on the continuum concept. In that model, two indices, the number of carbon atoms and the number of oxygen atoms, served as continuous variables. In the present work we apply concepts from continuous-mixture kinetics to thermolyticcoal extraction. Some essential ideas of continuous-mixture kinetics provide a framework for the theoretical analysis of the data given below. The averaging, or lumping, procedure shows how the kinetics governing the MWDs can lead to overall, lumped rate expressions used in most studies of coal thermolysis. The overlapping groups of extractable compounds in the coal matrix in some cases present complications for lumping mathematics. However, the low-temperature data (2' I360 "C)are readily explained by first-order expressions with rate coefficients that are independent of molecular weight (MW) and identical for the three groups of extractable compounds. The lumping in this case provides overall first-order rate expressions with the same rate coefficient. In this paper experimental MWD data for coal extraction at 340 and 360 "C in a differential flow reactor are interpreted by assuming that decomposition reaction rate expressions are continuous with molecular weight and three groups of chemical species are extracted simultaneously. The three groups are represented as gamma distributions in molecular weight.6 The data support the hypothesis that the first-order rate coefficient is independent of MW and that as a consequence the MWD has a similar shape during the time of extraction. As the analysis of thermolysis at higher temperatures is more complex,' to introduce the concepts of continuous-mixture kinetics to coal extraction we focus on low-temperature results (2' I360 "C)in the discussion. (4) Astarita, G.; Sandler, S. I. Kinetic and Thermolytic Lumping of Multicomponent Mixtures; Elsevier: Amsterdam, 1991. (5)Sapre, A. V.;Krambeck, F. J. Chemical Reaction in Complex Mixtures; Van Noetrand Reinhold New York, 1991. (6) Darivakis, G. S.;Peters, W. A.; Howard, J. B. AIChE J. 1990,36, 1189. (7)Wang, M.;Zhang, C.; Smith, J. M.; McCoy,B.J. AIChE J. 1994, 40 (l),131.
0 1994 American Chemical Society
Energy & Fuels, Vol. 8, No. 4,1994 891
Dynamics of Supercritical Extraction of Coal
Theory Since a differential semibatch reactor is used in this study, further reactions of the products from the thermal decomposition of the coal macromolecular network are negligible. The products are generated directly from the coal network and then carried away from the reactor. The rate of extraction determines the rate of product formation. In the present continuous-mixture approach the MW is considered to be a continuous variable. If x is the MW, then the MWD is ci(x,t), where at time t ci(x,t) dz is the concentration in the MW interval ( x , x dx). The integral over all x is the lumped concentration, expressed in units of mass (kilograms) of extractable compounds per mass (kilogram) of coal sample. A central question of continuous-mixture kinetics is whether the reaction order is preserved by the lumping procedure. We follow Aria8 in answering this question for kinetics that describe coal thermolytic extraction when secondary reactions are negligible. For the flow reactor used here the residence time is too short for further (secondary) reactions of the extract molecules to occur. We generalizethe earlier development8by consideringthat several groups of chemical species are extracted simultaneously from the coal. If the process consists of parallel reactions of nth-order at each molecular weight, x , then the governing differential equation for the differential coal batch is
+
dci(x,t)/dt = -ki(x) [ci(~,t)l”
coi(x) = moiyi(llr’ exp(-yi)/bir(ai)
ci(x,t) = cOi(x)[l (n - l)cOi(x)”’ki(x)t~l/‘”-” (2)
-
where in the limit as n 1 ci(x,t) approaches an exponential. The averaged, or lumped, concentration is given by
(8)
whereyi = ( x -xoi)/bi. The zero moment of the distribution is moi. The average position of the peak, xi = xgi + aiai, and its variance, bi2 = @i2, are the first and second moments. The position of the peak maximum is xpi = xoi + &(cui - 1). The distribution is equivalent to that used by HOand Ariag if @i= 1/aiand moi = 1. In the limit as ai m, C&) = moi6(x - xoi), SO that only components having a single MW are reacting, and the rate coefficient has a constant value at that MW. With the solution for ci(x,t), i.e., the case when n = 1 in eq 2, we can integrate to obtain the lumped concentration, -+
C(t) = z s o m c i o ( xexp(-kIixt) ) dx = z C i ( t ) I
(1)
with initial condition ci(x,t=O)= c d x ) . The rate coefficient is ki(x) and the subscript i refers to the ith group of compounds that react. The solution is
+
constant with x , then the resulting lumped kinetics can be other than first order. Ho and Ariag showed how lumping firsborder continuous-mixture kinetics can lead to any reaction order between one and two, depending on the initial condition. We apply their reasoning here to the polyaromatic groups extracted from coal. Considerthat the rate coefficient is proportional to MW, Le., ki(x) klix, where kli is independent of x . A general initial MWD that covers many possible forms for Coi(x) is the gamma distribution (or Pearson Type I11 distributionlo),
(9)
I
with Ci(t) = m,(l
+ @zit)”‘
(10)
The rate expression is obtained by differentiation, dC/dt = x d C i / d t
(11)
where
(3) This equation simplifies to a power-law rate expression, and
The lumped nth-order kinetics equation corresponding to this system, dC(t)/dt = -K[C(t)l”
(5)
with initial condition C(t=O) = CO,has the solution C(t) = C,[1+ (n - 1)Co”’Kt1’/‘”-”
(6)
where K is the rate constant. The solutions for C ( t ) and the lumped expression of ci(x,t) are identical when
cOi(x)”’ki(x) = KC,“’
(7)
Thus, for first-order kinetics (n = 1)we must have ki(x) = K, independent of molecular weight, for the lumped expression to be first order. If the rate coefficient is not (8)Aria, R. AIChE J. 1989, 36, 539.
where 4i = (1+ ai)/ai. As ai increases from one to infinity, the order of the lumped kinetics expression decreasesfrom two to one. For the general case when several groups, i, react independently, no simple overall kinetics expression appears. One can, however,perform the lumping operation numerically and determine a reaction expression by numerical fitting. For our experimental procedure, the extractable component MWD and concentration of coal, c(x,t) and C(t), are not measured directly. Rather, the concentrations of solubilized extract (both MWDs and lumped concentrations) in the solvent leaving the reactor are monitored with time. The time evolution of these concentrations is described by mass balances written for the reactor. Consider that the concentration of reaction products originating from coi in a semibatch reactor is ui(x,t). The average residence time based on the reactor volume of the (9) Ho, T. C.; Aria, R. AZChE J. 1987, 33, 1050.
(10)Abramowitz, M.; Stegun, I. A. Handbook of Mathematical NBS Washington, DC, 1968; Chapter 26.
htnctiorrcr;
Wang et al.
892 Energy & Fuels, Vol. 8, No.4,1994
fixed bed of coal is r , and the bed void fraction is e. The mass balance equation for a continuous flow, semibatch reactor is written
where Q is the volumetric flow rate of solvent andf[~i(x,t)l represents the rate expression. The use of a differential bed of fine coal particles allows the reactor analysis to be simplified considerably. The convective term in the mass balance can be approximated as the volumetric flow rate multiplied by the gradientless concentration in the fixed bed. For the experimental conditions the residence time in the heated zone of the reactor is much less than the characteristic reaction time (reciprocal of the rate coefficient). Thus, the accumulation term can be neglected, and the mass balance becomes simply
1.0
1
1 4 6 mln
t45
I
mln
The lumped extract concentration is
Various rate expressions can be hypothesized for f[cj(x,t)] and substituted into the equation for U t ) . Similar to the discussion above for the coal batch extraction, one concludes that only for special cases will simple lumped mass-balance expressions be found for U(t). For example, a t temperatures 360 O C and below, the rate is first-order with rate coefficients, ko, independent of x and identical for the extractable groups (Figure 1). For this case it is straightforward to demonstrate that the lumped rate is first-order with rate coefficient equal to ko;thus, u(x,t) = koco(x)exp(-kot)/Q
(17)
and
where co(x) is the summation of cgi(x) and CO is the summation of Coi. These equations can be compared with the lumped, reactor-exit concentration.
ExperimentB The experimental apparatus and procedure have been described previously.7JlJa Supercriticalfluid extraction of Illinois No. 6 coal is conductedin a fixed-bed reactor with flowingsolvent. The followingultimate analysis was provided for the IllinoisNo. 6 coal: carbon, 65.49%;hydrogen, 4.56; nitrogen, 1.11%;sulfur, 4.52%; oxygen, 8.16%; ash, 16.16%. The coal samples were prepared by sieving to a particle size range of (6-8)X lo-' m and stored under water to prevent oxidation. The lumped, reactorexit concentration is measured by spectrophotometricabsorbauce in a flow cuvette. We selected tert-butyl alcohol as the solvent, since it does not interfere with the UV absorbance of aromatic coal-extractionproducts. The coal is pretreated with supercritical tert-butyl alcohol at 300 OC to remove physicallyextractable constituents. The extraction process is carried out at constant pressure, 6.8 MPa, and constant flow rate, 0.17 cms/s. The temperature of the reactor was raised quickly to extraction (11)Zhang, C.; Smith, J. M.; McCoy, B. J. Supercritical Fluid Engineering Science, ACS Symposium on Supercritical Fluide; ACS Symp.Ser. 199S, 514,363. (12) Wang,M.; Smith, J. M.; McCoy, B. J. Energy h e l e 1993, 7,78.
0.0
0.5
t
b 1 4 5 min
1
nn 0
200
400
600
800
IO00 1200
Molecular Weight Figure 1. Experimentaldata and model calculationsfor MWDs at 340 O C and different times: symbol, experimental data; line, model calculations.
temperature (340 or 360 "C). Coal particles are small enough that intraparticle diffusion resistance is not significant,lJ and the solvent flow rate is large enough that external mass transfer resistance is negligible." Coal extract samples of 100 mL were collected at 10-mintime intervals during the extraction process and concentrated by evaporation of tert-butyl alcohol under vacuum. The MWDs of the extract, based on polystyrene molecular weight standards, were determined by using PLgel columns coupledwith a Hewlett-Packard1050HPLC. Two PLgel columns (Polymer Lab), 0.30 x 0.0075 m*, of 100- and 500-A pore size, respectively, packed with 5-mm cross-linked polystyrene-divinylbenzene copolymer, were used in series. The HPLC reagent gradetetrahydrofuran(THF,Baker Analyzed)was continuously pumped through the columna at a flow rate of 1.0 mL/min. The injected sample volume was 100 mL at a concentration about 0.2 % w/v. A variable-wavelengthspectrophotometric detector with a wide wavelength range (190-700 nm) was used. The wavelength 254 nm was chosen since it gives the maximum absorption for the coal-extract samples in THF. Experiments using pyridine, another common solvent for coal-derivedliquids, as mobile phase in the GPC measurements were performed. Measurements were made with the two solvents for the same mixture of extracts from runs at different temperatures. The GPC chromatogramswere nearly identical, thus confirmingthat results are not solvent specific. A refractive index detector also confiied the shapes of M W D indicated by the UV detector. The limits of the GPC method and the lack of calibration standard for coal-derived materials have been pointed out by
Energy & Fuels, Vol. 8, No. 4, 1994 893
Dynamics of Supercritical Extraction of Coal
I-l -10 U.uO14
0.0015
0.0016
0.0017
1IT
t i 40 min.
Figure 4. Arrhenius plot of the rate coefficients based on the data in Table 1.
t i 50 min.
t i 70
mln.
800
loo0 1200
0.5 nn "."
0
200
400
600
Molecular Weight Figure 2. Experimentaldata and model calculations for MWDs at 360 O C and different times: symbol, experimental data; line, model calculations. 14 I
4 c)
8
B H
xd
6 -
3
P
2-
0' 0
Zoo0
rlooo
6ooo
Boo0
1
looa,
Time (aec.)
Figure 3. Experimental data of total extract concentrations at 340 and 360 O C and their exponential fit based upon kilogram of initial coal sample mass. Bartle et al.lsJ4and Buchanan et al.16 Polystyrene MW standards provide only semiquantitative results for high-molecularweight coal producta.le For coal-derivedproducts of low MW (lessthan (13) Bartle, K. D.; Mulligan, M. J.; Taylor, N.; Martin, T. G.; Snape, C. E. Fuel 1984,63, 1556. (14) Bartle,K. D.; Mills, D. G.; Mulligan, M. J.; Ameachina, J. C.; Taylor, N. Anal. Chem. 1986,58,2403. (15) Buchanan, D. H.;Warfel, L. C.;Bailey, S.;Lucas, D. Energy Fuels 1988,2, 32.
a few thousand),however, Bartle et al.19 demonstrated that the retention behavior of polystyrenestandardsapproximatesclosely that of coal extracts. Recently, Larsen et al.17 showed that polystyrene MW standardswere quite good for coal-liquefaction products produced in the Wilsonville pilot plant. Since the molecular weight range of coal extracts in our experiments is very low (between100and lOOO), the calibrationwith polystyrene standards is adequate for our purposes. To test the effect of secondary reactions in the liquid phase, specialexperimentswere conducted in the differentialsemibatch reactor. Four liters of coal extractwas introduced as feed solution to the reactor at 6.8MPa and at various temperatures and flow rates. The experimental monitoring procedures are similar to those for the extraction runs. Two samples of 100 mL were collected for each set of experimental conditions. The MWDs of these sampleswere comparedwith the feed solution to test the secondary reaction effect. The resulting MWDs did not vary, even when depleted coal particles were present in the reactor.
Results and Discussion The experimental results for 340 and 360 O C show MWDs whose shapes are similar at different times; i.e., the average molecular weight is invariant with time (Figures 1 and 2). Such behavior can be described by assuming that the rate coefficient for the first-order rate expression is independent of MW. T w o types of parameters appear in this model: those in the three gamma functions describing the initial MWDs of extractable polyaromatic units in coal, and the rate coefficients for the extraction of the extractable group. It was reported6 that the range of (Y is 1.3-3.0,but the most likely value is 2. In our simulations we fixed ai = 2 for the three gamma functions. Based on eq 17 and the shape of experimental MWDs at the two temperatures, the parameters Xoi, Pi, and moi were estimated by minimizing the deviations between MWD data and model computations. The relationships between totally lumped extract concentration, U ( t ) and , extraction time at 340and 360"Care shown in Figure 3. The lumped concentrations are determined by the flow-through spectrophotometer at the reactor exit. To determine ko, the time-dependent concentration data were fitted by an exponential expression based on the lumped expression for U(t) (eq 18). The values of the first-order rate coefficients at the two temperatures are displayed in Table 1. Figure 4 shows the Arrhenius plot (16) Solomon,P.R.;Serio,M.A.;Suuberg,E. M.Prog.EnergyCombuut. Sci. 1992, 18, 133. (17) Larsen, J. W.; Lapucha, A. R.; Wernett, P. C.; Anderson, W. R. Energy Fuels 1994,8, 258.
Wang et al.
894 Energy & Fuels, Vol. 8, No. 4,1994 0.015
0.010
I t
Feed Extract
T=360'C P = 6.8 MPa t = 18.5 min. 0
200
400
600
800
1200
IO00
X
(a)
2 0.015
T= 400 'C P = 6.8 MPa t = 18.5 min.
E
\
.-
-
2
v
J
Y
Molecular Weight 0
Figure 6. Experimentalresulta of MWDs at 360 and 400 "C for the runs with coal-extract feed. 0
200
400
600
800
loo0
1200
X
(b)
Figure 5. Comparison of model calculations and experimental data of MWDs for two samples: (a) T = 340 "C,t = 56 min; (b) T = 360 "C,t = 30 min. Table 1: Values of Coal Conversion and the First-Order Rate Constant T (K) conversion (dmf) rata constant, ki (8-l)
0
0.OOO 15 0.OOO 22 0.OOO 30 0.OOO 37
0.066 0.10
613 633 653' 673'
Values for the rate constant are from Wang et al.'
Table 2: Parameter Values for the Gamma Distributions (a = 2)
T 613 K
0.0033 kglkg of coal 0.032 kglkg of coal 0.029 kglkg of coal O.Oo80 kg/kg of coal = 0.049 kglkg of coal moa 0.041 kg/kg of coal mol
T 633 K
81
20
8 2 = 62 88
120
81 = 20 8 2 62
6s 120
%oi=
120
xm = 170 xw = 275 %01 120 ~ t m 170 xw = 275
of the rate coefficients, which gives an energy of activation E , = 58 kJ/mol. The gamma distribution parameters, provided in Table 2, show that increasing the temperature changes only the zero moments. The concentrations for each group of extractable compounds, moi, increase due to the greater extraction a t higher temperatures. The comparison of the calculated and experimental MWDs is shown in Figure 5 for two samples. Figures 1 and 2 show the model calculations for five values of time and at each temperature. Only time is allowed to vary during the course of the evolution of the MWDs; the
parameters for the initial MWD in the coal and the rate coefficients are constant. The agreement between the experimental data and the model calculations is consistently good for all samples during the course of a run, thus supporting the validity of the explanation of coal thermolytic extraction that we have proposed. The above model represents only the primary reactions of coal extraction. The effect of secondary reactions was tested by feeding extract in solvent to the reactor. Figure 6 shows the resulting MWDs at different temperatures for the runs with coal extract feed. The results are normalized so that the area below the curve is unity. No evidence of repolymerization to form larger molecular products is observed in the temperature range of our study. However, the extract can degrade to lower molecular products if the residence time is long enough. At 360 "C, secondary reactions are not significant even with a residence time of 18.5 min. At 400 "C,the secondary reactions are substantial for a residence time of 18.5 min. In the thermolytic extraction runs, however, the residence time is around 10 8, much smaller than that needed to observe secondary reactions. A rough estimation shows that the secondary reactions can be neglected during the extraction runs. Figure 7 shows the results of 400 "C and different residence times. At the largest residence time (92.5 min), the MWD distinctly shifts to lower MWs. The MW moments of the gamma distributions, displayed in Table 2, suggest an interpretation based on the structure of coal7 that follows Darivakis et al.S The zero moment, mgi (i = 1,2,3), gives the amount of each group. The largest value of mgi is for the second group, and the smallest value is for the first group. The first moment of a MWD is the average MW, fj = xgi + agi. The value of f l for group 1 is 155, for group 2 E2 = 284, and for group 3 3 3 = 517. The second central moment, or variance (ui2
Energy & Fuels, Vol. 8, No.4, 1994 895
Dynamics of Supercritical Extraction of Coal 0.015
0.010
Feed Extract
peratures 340 and 360 OC the MWDs maintain a similar shape during the semibatch extraction. This indicates that first-order kinetics dominate and that the rate coefficient is independent of molecular weight. The lumped extract concentration is monitored at the reactor exit by continuous UV absorbance spectrophotometry. Both MWD and lumped concentration data are described by consistent expressions based on the same rate coefficient. The MWDs for the runs with coal extract feed illustrate that secondary reactions are negligible in the semiflow reactor.
Acknowledgment. The financial support of Pittsburgh Energy Technology Center Grant DOE DE-FG2290PC90288 and the University of California UERG is gratefully acknowledged. Notation concentration distribution of ith group of extractable polyaromatic units in coal, kg/kg of coal MW initial concentration distribution of ith group of extractable polyaromatic units in coal totally lumped concentration of extractable polyaromatic units for ith group in coal, kg/kg of coal the summation of Ci(t) activation energy for the extraction reactions rate coefficients for extractable groups, 8-1 proportional constant in the expression for rate coefficient rate constant for the lumped nth-order kinetics equation zero moment of gamma function in eq 8, kg/kg of coal pressure, MPa flow rate of solvent, mS/s time, s temperature, K concentration distribution of extract products from ith extractable group in coal based on kg of dried coal sample, kg/ms MW totally lumped extract concentration of extract products from ith extractable group, kg/ms the summation of Ui(t) molecular weight the minimum molecular weight for group i in the gamma function
Figure 7. Experimental results of MWDs at 400 "C and different residence times for the runs with coal-extract feed. = CY#), denotes the span of the MWD. When CY is fixed, then pi denotes the heterogeneity of the polyaromatic structure of coal. Larger & values indicate a higher probability of finding kinetically dissimilar bonds within the coal structure. The present conceptual model of coal is thus in general agreement with earlier conclusions.6
Conclusion A continuous-flow extraction reactor, in which supercritical tert-butyl alcohol contacts a differential bed of coal particles, provides sequential coal-extract samples that are analyzed by HPLC gel permeation chromatography to obtain time-dependent MWD data. The coal extraction experimental data support an interpretation of the results based on considering the molecular weight of extraction products as a continuous variable. This continuous-mixture theory suggests that three groups of coal components are extracted independently. At tem-
Greek Letters ai Bi
e 7
parameter in the gamma function for ith extractable group, eq 8 parameter in the gamma function for ith extractable group, eq 8 bed void fraction residence time based on reactor volume, s
