976
Ind. Eng. C h e m . Res. 1989, 28, 976-982
Vermeulen, J. Contribution 1 1'Btude de l'analyses des systgmes reactionnels complexes. Application au craquage thermique d'hydrocarbures. Ph.D. Dissertation, Ecole Centrale des Arts et Manufactures de Paris, 1980. Volkan, A.; April, G. C. Survey of Propane Pyrolysis Literature. Znd. Eng. Chem. Process Des. Deu. 1977, 16(4),429-435.
Woinsky, S. Kinetics of thermal cracking of high molecular weight normal paraffins. Process Des. Deu. 1968, 74, 529-538.
Received for review March 21, 1988 Revised manuscript received October 25, 1988 Accepted February 25, 1989
A General Model for Coal Dissolution Reactions John M. Shaw* and Ernest Peters Metals and Materials Engineering Department, T h e University of British Columbia, Vancouver, British Columbia, Canada V 6 T 1 W5
Direct Coal Liquefaction has been treated as a purely kinetic process previously. Reaction rates have been related to intrinsic rates of product formation from specific coals. Process variables, such as solvent composition, the rate of interphase mass transfer, the intensity of turbulence, and catalysis are not included in these models, even though process variables have been shown to play an important role in determining the rates of liquefaction reactions, particularly with dense coal slurries. T h e impact of process variables on total coal conversion is quantified in the present model by subdividing the reaction scheme into an initial mass-transfer-controlled interval, followed by a second kinetically controlled one. This reaction scheme is consistent with experimental findings. Few coefficients are employed, and similar sets of coefficients describe the liquefaction behavior of different coals in a single solvent or a single coal in different solvents. T h e results from eight verification trials, involving six coals liquefied under a broad range of reaction conditions and in three different reactor types, are presented. Coal undergoes a complex sequence of physical and chemical processes as it is dissolved and hydrogenated in Direct Coal Liquefaction reaction environments. Droege et al. (1981) observed that coal particles swell when initially exposed to a sovlent under pressure and swell at elevated temperatures. This swelling has been shown to be a consequence of coalsolvent interactions (Weinberg and Yen, 1980; Hombach, 1980; Shibaoka et al., 1979) and/or the onset of thermal decomposition (Habermehl et al., 1981). Both mechanisms of particle swelling lead to rapid solvent absorption and the initiation of liquefaction reactions. Since coal is not structurally homogeneous (Yarzab et al., 1980; Smith and Cook, 1980) and constituent macerals exhibit a broad range of reactivities (Shibaoka et al., 19791, a number of reactions occur simultaneously. Reactive macerals dissolve quickly. The reactions are substantially complete within 2-10 min or high-temperature contact time (Whitehurst et al., 1980; Thurgood et al., 1982). These reactions, frequently associated with the cleavage of ether linkages (Kuhlmann et al., 1981; Carson and Ignasiak, 1980) and the hydrogenation of the resultant free radicals (Curran et al., 1967; Vernon, 1980; Petrakis and Grandy, 1980; Franz and Camaioni, 1980), are highly exothermic. In poor hydrogen-donor solvents or in donor-depleted sovlents, polymerization reactions also occur. These reactions may involve free-radical solvent-molecule or radical-radical interactions (Whitehurst et al., 1980) and can lead to the formation of high molar mass liquid products or coke (Derbyshire and Whitehurst, 1981). These products can be re-hydrogenated subsequently (Shalabi et al., 1979) because coal radicals, stabilized by initial dissolution reactions, may possess additional reactive linkages (Mohan and Silla, 1981) but the space-time yields of light oil or naphtha products are reduced. Less reactive macerals dissolve slowly. These reactions are typically
* Current address: Department of Chemical Engineering and Applied Chemistry, University of Toronto, Toronto, Ontario, Canada M5S 1A4.
associated with methyl group cleavage, although some ether linkages have also been shown to have low reactivities (Carson and Ignasiak, 1980). Dissolved molecular hydrogen (Vernon, 1980), hydrogen-donor species present in the solvent (Abichandani et al., 1982; Cronauer et al., 1978), or molecular species hydrogenated in situ (Derbyshire et al., 1982) can act as hydrogen sources for liquefaction reactions. Shaw and Peters (Shaw and Peters, 1984) show that molecular hydrogen can be a more effective hydrogenation reagent than tetrahydronaphthalene for initial dissolution reactions. However, the rate of radical formation increases rapidly in the temperature range 350-450 " C (Ross and Blessing, 1979). At low temperatures within this range, radical formation occurs slowly and donor solvents can hydrogenate and stabilize radicals as they form. Liquefaction reactions, conducted under these conditions, are insensitive to the presence or pressure of molecular hydrogen (Derbyshire et al., 1982) and the solvent-to-coal ratio (Mochida et al., 1979). A t higher temperatures, the observed rates of liquefaction reactions are sensitive to solvent composition, the rate of catalytic solvent rehydrogenation, and the pressure of molecular hydrogen (Derbyshire et al., 1982; Rudnick and Whitehurst, 1981), and polymerization reactions become more significant (Mochida et al., 1979). Polymerization/coking reactions have also been shown to occur at long mean residence times (Bickel and Thomas, 1982). These reactions can occur homogeneously or heterogeneously (Painter et al., 1979). Shaw and Peters (1989) suggest that polymerization reactions arise primary in a persistent dispersed liquid phase. The reaction models for coal dissolution, cited on Table I, vary in complexity but treat coal dissolution as a purely kinetic process. These models contain between 2 and 34 fitted constants, and the complexity of the predictions varies accordingly. There is little agreement on the dissolution mechanism(s), and unrelated sets of parameters are required for each model depending on the reaction conditions. The parameter sets for the models proposed
0888-~885/89/2628-0976$01.50/0 0 1989 American Chemical Society
Ind. Eng. Chem. Res., Vol. 28, No. 7 , 1989 977 Table I. Coal Liauefaction Reaction Models kinetic no. of models schemeo parameters assumptions simple models first-order kinetics C-A+O 2 Hill et al., 1966 a single thermal decomposition coal is best characterized Curran et al., 1967 as comprising two different reactive species ~~
Liebenberg and Pitgieter, 1973
/.
A
C
'
Yoshida et al., 1976
W
solvent
Utah
tetralin
Pittsburg
tetralin
coal produces A and 0 by separate reaction sequences
bituminous tetralin
6
coal produces A and 0 by separate reaction sequences
Japanese
anthracene oil
red mud and sulfur added as catalysts
gas generation ignored
Illinois No. 6
tetralin
the authors propose two models: (1) based on chromatographic separation of liquids; (2) based on solubility separation model 2 fits the data better a batch reactor was used
complex models Mohan and Silla, 1981 AR
c
(2)
-
A
10
large fragments react reversibly to form lighter components
14
reactions occurring in the preheater are not included the reversible reaction C * P is not truely reversible; P can form coke, which cannot be distinguished from coal all reactions are first order and irreversible no distinction made for reactions in the preheater
3 P *O
Gertenbach et al., 1989
C*P
Cronauer et d . , 1978
G
12
tA
C-A
Shaw and Peters, G 1989 t C
- MO
10 LO
1'HO W
all reactions involving coal are first order hydrocracking reactions are zeroth or first order
irrversible first order reaction kinetics Singh et al., 1982
G
Lo
\t/
MO
8 . W --C'IOM'
SRC
1
HO
-
-
1 'SAC ASH
HO
comments
4
0
C - A - 0
coal
34
efforts were made to fit the model to the data of other researchers; the fit was poor even with their own data the model predicts a significant increase in oil yield in plug flow reactors Bell Ayre hydrogenated completely different set of subbituanthracene oil parameters fitted the minous results for the two solvents hydrogenated a Dlun flow Dreheater - phenanthrene oil -foliowed by a CSTR was employed Big Horn process-derived a plug flow preheater subbituliquid followed by a CSTR was minous employed a proprietary catalyst was used dispersion number was a parameter and varied with slurry rtd and H2 flux Kentucky tetralin short heat-up time batch experiments were performed Kentucky No. 9
2-staee kinetics: Pohatan (i)-instantaneous breakup No. 5 of coal to fixed fractions of various components (ii) slow conversion of SRC and HO to lighter components irreversible first-order kinetics preheater has no impact on kinetics
250 OC vacuum
cut of SRC I1 1iquid s
vacuum tower bottoms from SRC I1 plant
a plug flow preheater and a CSTR were employed this model has been used to stimulate the SRC I1 process
"A = asphaltenes, AR = aromatics, B = byproduct gases C = coal, E = ethers, G = gases, H = hydrolysis, HO = heavy oil, IOM = inert organic matter, LO = light oil, M = multifunctionals, MO = middle oil, N = nitrogens, 0 = oil, P = pre-asphaltenes, SRC = solvent refined coal, W = water.
by Mohan and Silla (1981) are temperature dependent, even if the coal, the solvent, and all other process variables remain fixed. The model proposed by Cronauer et al. (1978) requires two unrelated sets of parameters to describe the dissolution behavior of a single coal in two different solvents. The extreme specificity of these models limits their utility with respect to process design and development studies and reflects the impact of the reaction
environment on coal dissolution kinetics.
Proposed Reaction Model The proposed reaction model, Figure 1,conforms with cited experimental observations and is not radically different in appearance from previous models. If one compares this model to those listed on Table I, for example, it would be best described as a combination of the models
978 Ind. Eng. Chem. Res., Vol. 28, No. 7 , 1989 The coal-solvent interfacial area, A ’, varies appreciably with solvent composition and coal type, and the coal fraction reported initially as unreacted material, U1, can be approximated as
and is defined as
Uz E kl - k,D[H] C3AL 2
Figure 1. Proposed two-stage reaction model.
proposed by Curran et al. (1967) and Singh et al. (1982). The major differences between the model proposed here and those proposed previously are related to the factors that control the rates of various dissolution reactions (Shaw and Peters, 1989) rather than differences in the reaction scheme per se. A fraction of the coal (coal 1) undergoes “instantaneous” thermal decomposition, yielding a spectrum of liquefaction products which includes gases, liquids, partially converted material, and coke. The fraction of the coal or lignite participating in these reactions is assumed to depend solely on coal composition, while the product distribution is assumed to depend on the rate of hydrogen transfer to the coal particles and the solubility of liquefaction products in the carrier solvent. In the absence of dissolved gaseous hydrogen, for example, the fraction of the coal reported initially as liquid would decline, and the fraction reported as coke would increase, as polymerization and condensation reactions are more likely to occur under these conditions. The fraction occurring initially as partially converted material, which is insoluble in the carrier solvent, contributes to the formation of a dispersed fluid phase. The remainder of the coal (coal 2) undergoes slow thermal decomposition into the various liquefaction products. The material occurring at the dispersed phase initially polymerizes or is converted on subsequent reaction, depending on the rate of hydrogen transfer to the dispersed phase and variations in solvent composition with time. The rate of hydrogen transfer to the dispersed phase is proportional to the dissolved hydrogen concentration and inversely proportional to the mean droplet diameter, which is determined by the intensity of turbulence. Solvent composition is altered by adduct formation and catalytic hydrogenation and hydrogenolysis reactions (Guin et al., 1978, 1979; Weigold, 1980).
Formulation of the Model Thermal Decomposition of Reactive Macerals. Thermal decomposition of the most reactive species present in a coal is rapid and is modeled as instantaneous. In the absence of dissolved gaseous hydrogen, these reactions may lead to the formation of insoluble adducts. In the presence of hydrogen, a greater fraction of the coal reports as converted material. The extent of the reduction in unconverted material is proportional to the rate of hydrogen transfer to the coal particles. The rate of hydrogen transfer per unit mass of coal, K’, can be related to the external Sherwood number (cf. Clift et al. (1978)) of the coal particles:
K‘ =
ShoDIH]A’ Psolvent aoPcoal
(1)
(2)
where kl is expected to be on the order of unity and k , is a lumped parameter combining solvent and coal properties. The coal fraction occurring at the dispersed phase initially is more difficult to estimate. Shaw and Peters (1989) found that an optimum catalyst level to stirring rate ratio exists when coal or lignite is liquefied in a stirred autoclave. This effect was attributed to the existence of an optimum ratio of catalytic solvent hydrogenation to uncatalyzed dispersed-phase hydrogenation. At the optimum ratio of these reactions, the amount of material occurring at the dispersed liquid phase is minimized. If one considers possible kinetic schemes for these two reactions, the rate of catalytic sovlent hydrogenation, R1, is proportional to the amount of catalyst present and the dissolved molecular hydrogen concentration and can be expressed as
Rl
MJHI
(3)
The initial rate of dispersed-phase hydrogenation, R P ,is proportional to the rate of hydrogen transfer to the dispersed phase: DIHIShdropPsolvent R2 a
2 ddrop Pdrop
(4)
Mean drop diameter is determined by the intensity of turbulence. The relationship between turbulence and drop diameter is well defined for stirred tanks (Taverides and Stamatoudis, 1980) where the maximum drop diameter is inversely proportional to the stirring rate raised to the power 1.2; Le., ddrop F-’.’. If the mean drop diameter is proportional to the maximum diameter, the reaction rate ratio becomes
fi2
DShdro$
2’4Psolvent
and the fraction of a coal occurring at the dispersed phase initially, U2,is proportional to some function of the ratio C = M,./F*.*
(6)
Equation 7 is a simple empirical function which conforms with the experimental observation of an optimum value for C. The total coal conversion increases initially with
U2 = k3D[H1[exp(-k,C )
+ k , exp(-h4Co,,)C1
(7)
the ratio C but declines in the presence of excessive catalytic solvent hydrogenation. Combining eq 2 and 7 yields the total coal fraction occurring as unconverted material at zero time, U:
u = u1 4- u2
(8)
Kinetically Controlled Dissolution Reactions. Equations 2 and 7 describe the disposition of coal components at zero time. A kinetic expression for the second-stage reactions is defined in a straightforward manner. The reaction rates for the dispersed phase and the slowly
Ind. Eng. Chem. Res., Vol. 28, No. 7, 1989 979 reacting coal components cannot be distinguished. So, the reaction kinetics for these two types of material are combined in a single kinetic expression. First-order irreversible reaction kinetics, a typical assumption in coal dissolution models, is also employed in this model. Thus, ak,/at = - ~ k 5
(9)
where k5 is the reactive fraction of the initially unconverted coal. It would be natural, at this point, to assert that the rate constant, K , has an Arrhenius temperature dependence. This assumption is frequently made, despite the arbitrary definition of the rate constant. One would not expect such a rate constant to exhibit an Arrhenius temperature dependence. However, pseudo-Arrhenius behavior can be realized if the rate constant is correlated as
The form of eq 10 suggests that only the aggregate behavior of a coal follows an Arrhenius pattern and that the observed rates reflect the fact that coal constituents that do not react initially are more refractory than the parent coal. This equation conforms with the findings of Szladow and Given (1981),who showed that the apparent activation energy for liquefaction reactions increases with the extent of conversion. Shaw and Peters (1989) showed that molecular hydrogen is a key reagent in the initial stage of coal dissolution. A simple kinetic expression accounting for the role of hydrogen Kl
H2 coal-coal
K4
e2(coal radical)
+ coal radical
K3
(2' ) (3' 1
Hacoal
can be resolved using the steady-state hypothesis for the hydride radical concentration to yield for all coals. The normalized activation energy, E I R , for coal dissolution reactions in the presence of hydrogen is therefore at least 26 200 K, the energy required to form a hydride radical. In the absence of molecular hydrogen, the rate of product formation via reaction with a donor species, D, can be approximated from a comparable mechanism: D
+ coal radical
K6
H-coal + H'
== 2(coal radical) K5
+ D'
(4')
K4
coal-coal H'
HATCREEKB
,
~
M DDLE K A
FORES-BURG1
a
FORESTBURGZ
I
W R O N CREEK2 BVRONCREEKI
'
1
0 20 40 60 80 EXPERIMENTAL CONVERSION WT%
0
I00
Figure 2. Parity plot for the verification trials.
tributions, which match distributions found in complex reactors, can be digitized and combined with the model. Simple distributions, such as the plug flow distribution, can be resolved analytically to yield 70 conversion = 100 - 100U(e-"k5
+ 1.0 - k5)
(13)
Verification of the Model The reaction model was verified by regressing sets of batch coal liquefaction data with an unbiased objective function, (coal
€=El
- (coal
(coal conversion),xptl (14)
2H'
K6
H'
100
+ coal radical
K3
(2')
Hscoal
(3' )
rH.coal= 2K4[D][coal radical]
(12)
using steady-state assumptions as The activation energy for reaction 4 is dependent on the type of species involved. Normalized activation energies range from 9000 to 20000 K when tetralin is the donor species. Residence Time Distributions. The final equation required in order to complete the model is one that couples the slurry residence time distribution with the kinetic expression, eq 10. Arbitrary slurry residence time dis-
The value of this function was minimized by using a suite of nonlinear optimization programs. Data sets were obtained from Shaw and Peters (1989), Shalabi et al. (1979), McElroy (1982), and Szladow and Given (1981). Liquefaction data obtained from the flow apparatus were excluded from these tests because coal conversion, mean residence time, and residence time distributions for slurries and reactor temperature profiles are too poorly defined in these reactors. The reaction conditions and reactor configurations associated with the data sets selected from the literature are listed on Table 11. Six coals (three bituminous and three subbituminous coals) and three reactor types are represented. Hydrogen solubilities and diffusion coefficients, in various coal liquefaction media, and the density of coal liquids are the principal physical properties required by the model. These data are frequently unavailable, and a number of approximations were employed. The solubility of molecular hydrogen in coal liquids was estimated by using the correlation of Shaw, (1987). Diffusion coefficients for hydrogen in tetralin were estimated (Reid et al., 1977). Diffusion coefficients in other solvents were assumed to be proportional to these calculated values. The hydrogen concentration in the various solvents was assumed to be equal to or proportional to the saturated hydrogen concentration.
Results and Discussion The overall fit of the model is illustrated on Figure 2. The model accurately predicts total conversion values, for a variety of bituminous and subbituminous coals, in diverse reaction environments-Table 111. Only at long mean residence times does the model appear to diverge from the experimental data as exemplified by Figure 3. This divergence arises because the model does not account for possible physical interactions between the solvent and
980 Ind. Eng. Chem. Res., Vol. 28, No. 7, 1989 Table 11. Data Sets Selected for Model Verification no. of coal data pts reaction conditions Fies Mine KY Seam No. 9 13 solvent = tetralin: temn = 350., 275. 400 - - O C-:, (high-volatile bituminous) hydrogen pressure = 13.2 MPa; analysis solvent = THF -___ Hat Creek A 15 solvent = tetralin; temp = 350, 375, 400, 425 OC; (subbituminous) hydrogen pressure = 5.5 MPa (cold); analysis Hat Creek B 17 solvent = pyridine (subbituminous) Szladow and shaken microreactor Middle Kittanning 23 solvent = tetralin; temp = 340, 355, 370 385, 400 Given, 1981 (high-volatile bituminous) "C; hydrogen pressure = 0.00 MPa; analysis solvent = pyridine Shaw and slurry-injected, Forestburg (subbituminous) 25 solvents = SRC oil and 70 wt % SRC oil + 30 wt Peters, 1989 2000-mL P P I autoclave, Byron Creek 21 % tetralin; temp = 375, 400, 425 OC; hydrogen (oxidized bituminous) fitted with a magnetically pressure = 5 MPa (cold); analysis solvent = T H F driven stirrer ref Shalabi e t al., 1979
reactor slurry-injected, 300-mL A. E. Autoclave; -D = 3.2 cm; -F = 25 s-l McElroy, 1982 shaken microreactor containing steel balls
I
.
S
Table 111. Optimum Parameters parameters coal Fies Mine (HVB) Hat Creek A (SB) Hat Creek B (SB) Middle Kittanning (HVB) Forestburg (SB) Byron Creek
(B)
solvent tetralin tetralin tetralin tetralin SRC oil SRC oil T H N SRC oil SRC oil + T H N
+
kl 1.00 0.9123 1.00 0.8832 1.00 1.00 1.408 1.755
kz 0.009 244 0.040 20 0.02207
k3
0.01932 0.040 19 0.046 53 0.05652
308.7 361.9 189.9 101.3
k6
k4
284.9 504.5 4881.0 6.9
X
EIR
k6
0.7355 3.28 X 1OI6 0.6774 ,1.553 X lOI5 0.5179 2.63 x 1015 1.0 1.437 X lo6 0.8276 2.85 x 1014 0.8031 3.49 x 1014 0.5517 1.885 X 1013 0.3424 6.579 X 1013
lo6
26 200 26 200 26 200 11800 26 200 26 200 26 200 26 200
av absolute error, % 2.0 3.0 5.8 4.8 3.2 2.7 4.7 4.9
,
......................... ...............................
,:' /
.
Legend DATA 8 7 3 K 648 K
,
623 K
/7
PREDICTED thll) w o r k PREDICTED ~~
20 0
20
40
BO
BO
100
120
140
REACTION TIME min
0
50
100
150
200
REACTION TIME mln
Figure 3. Detailed comparison between model predictions and experimental data for Middle Kittanning coal.
Figure 4. Detailed comparison between model predictions and experimental data for Fies Mine coal.
partially reacted material. The physical properties of these two phases change over time, and these changes can lead to an increase or decrease of product solubility in the carrier solvent. Nevertheless, the results confirm the generality of the proposed two-stage reaction model. Shalabi et al. (1979), for example, fitted a single-stage coal dissolution model to their liquefaction results. The model, shown in Table I, correlates total conversion values with seven parameters obtained by regressing product distribution data. Even in this case, the model proposed here fits the data better, Figure 4, and employs only four adjustable parameters. The inadequacy of the single-stage model is particularly evident at temperatures greater than 623 K. Clearly, mass-transfer-controlled (effectively instantaneous) decomposition, followed by slow kinetically controlled dissolution, provides a general framework for analyzing coal dissolution reactions. The optimum parameter sets for the batch verification trials, Table 111, also confirm the generality of the proposed two-stage reaction model. Despite the large differences in the chemical composition and structure of these coals and the many differences in the reaction environments, the liquefaction behavior can be characterized in a consistent and coherent manner.
The frequency factor for the rate constant, k6,for example, varies from 2.85 X 1014 s-l for the more slowly reacting subbituminous coals up to 3.28 X 1015s-l for the more quickly reacting high-volatile bituminous coals. The only exceptions are Middle Kittanning coal, which was reacted in the absence of hydrogen and has a different reaction path, and Byron Creek coal, which is a partially oxidized bituminous coal and consequently is expected to react more slowly (Cronauer et al., 1984). The value of parameter kl,for a number of coals, suggests that little or no coal is converted during the fiist stage of reaction, in the absence of molecular hydrogen, and that the amount of organic material reported initially as unconverted coal may exceed the mass of MAF coal added to the reactor, due to adduct formation. If the liquefaction results for Middle Kittanning coal most closely resemble this situation, then kl may overestimate the extent of adduct formation, in some cases. The kl values reported for Byron Creek coal are clearly too large. This is an understandable shortcoming of a semiempirical model. The maximum coal fraction that is predicted by the model to enter the dispersed phase is also proportional to the initial rate of hydrogen transfer to the coal. The model only detects marginal material which can occur a t either
Ind. Eng. Chem. Res., Vol. 28, No. 7, 1989 981 the liquid or dispersed phase. The constant of this proportionality, k,, varies from 101.3 to 361.9. Thus, the coal fraction reporting to the dispersed phase varies correspondingly from 6 to 40 wt %, depending on operating conditions. This projection has a number of design implications for coal liquefication reactions and is currently under investigation. With the inclusion of solvent properties in the kinetic model, it was expected that similar or identical sets of coefficients would fit dissolution data for a single coal liquified in different solvents. This expectation was only partially met with the present model. The dissolution behavior of Forestburg coal in two solvents is well correlated with similar sets of coefficients. Greater similarity may have been obtained had pertinent solvent properties been available. However, the divergent dissolution behavior of Byron Creek coal in the same two solvents confirms that it is necessary to perform a t least a limited number of experiments with each solvent system, even if solvent properties are included in the reaction model. More successful aspects of this reaction model include (i) provision for the impact of turbulence and catalysis, or changes in these parameters, on dissolution kinetics; eq 7 provides an adequate representation of these phenomena; and (ii) provision for changes in solvent properties on the availability of molecular hydrogen, which may vary with the degree of slurry-phase axial mixing operating pressure, etc. Both of these considerations are essential elements in the development of appropriate reactor designs. Successful elimination of the activation energy for coal dissolution as a coal or solvent-dependent variable, if hydrogen is present in the reaction, is of equal importance, as it helps to elucidate the mechanism for coal dissolution. Clearly, this model provides a sound basis for the development of more detailed process and kinetic models. Summary The novel coal liquefaction reaction model, presented and verified in this paper, has been shown to provide a general framework for describing the dissolution behavior of coals in a variety of reaction environments and reactor configurations. The model can be used to (i) extrapolate and interpolate results from existing data sets, the fitted data span, in most cases, the high- and low-temperature regions identified by Mohan and Silla (1981), etc.; (ii) extend existing data sets to include other catalysts, with few additional experiments; The optimum catalyst to turbulence ratio must be determined experimentally; and (iii) model the impact of residence time distribution variations, as long as the modified solvent properties are known or can be estimated. Retrogressive reactions are considered to be a reflection of a liquid-liquid insolubility problem involving the solvent and the initial liquefaction products arising from instantaneous decomposition of a coal. The tendency for larger coal-derived molecules to precipitate progressively with time as the solvent undergoes hydrogenolysis reactions is not modeled and cannot be modeled until more general theories for liquid-liquid solubility are developed. Retrogressive reactions can play an important role in determining the liquefaction reaction sequence. Under conditions where retrogressive reactions are significant, the model is not applicable. A second restriction, envisioned when the model was formulated, is that the transition zone between labile hydrogen and molecular hydrogen masstransfer control of the initial “instantaneous” liquefaction reactions would be difficult to model. The model has been shown to work well if either of these modes of reaction
dominate, but the transition zone, occurring over a range of hydrogen concentrations, not yet identified, must be found and quantified if the model is to be rendered as general as possible. Acknowledgment The financial support provided by British Columbia Research Ltd., in the form of a B. C. Research Fellowship for J. M. Shaw, and NSERC, through strategic Grant 0164, is gratefully acknowledged. Nomenclature A’ = coalsolvent interfacial area per unit volume of coal, cm2 D = diffusivity of molecular hydrogen in a solvent, cm2 s-’; reactor diameter, cm, eq 5 and 6 d, d , ;io, ddrop = particle diameter, average particle diameter, initial average mean particle diameter, and average drop diameter, cm F = stirring frequency, Hz [HI = molecular hydrogen concentration in the continuous liquid phase, mol-kg-’ K’ = rate of hydrogen transfer per unit mass of coal, molskg-’ ki = constants for the coal dissolution reaction model M , = mass of added catalyst present, g R1, R2 = reaction rates defined by eq 3 and 4, respectively Sh, Sho, &drop = Sherwood number, average initial particle Sherwood number, Sherwood number of the droplets evolving from the coal particles, and average droplet Sherwood number U , U1, U2 = total coal fraction occurring as unconverted material initially, coal fraction occurring as unreacted material initially, coal fraction occurring at the dispersed phase initially
so,
Greek Letters t = error function defined by eq 1 4 K = first-order rate constant, s-l Pt Pcoal, Pdrop, Psolvent
= density, g cm-3
R e g i s t r y No. Tetralin, 119-64-2.
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Received for review May 11, 1987 Accepted J u l y 22, 1988
MATERIALS AND INTERFACES Effective Boundary Area of Decomposition and Dissolution of Agglomerated Lead Carbonate Kenichi Miyasaka, Kanako Ueda, and Mamoru Senna* Faculty of Science and Technology, Keio University, Hiyoshi, Yokohama 223, Japan
Mechanically activated, fine powdered aggregates were additionally compressed into agglomerates to examine the effective boundary area of the dissolution and decomposition reactions. The effective boundary area for the dissolution reaction was confirmed to be the external area around the aggregates or agglomerates, which tended to disintegrate themselves during the reaction. T h e decomposition reaction, on the other hand, was not restricted by the external surface area. Instead, the limiting extensive dimension was similar t o the intercrystallite boundary area. Energy storage as a result of mechanical activation is well-known (Heinicke, 1984; Miyasaka and Senna, 1985). The reactivity of such mechanically activated fine powders is often predominated by the availability of the stored energy (Miyasaka and Senna, 1987). The effective boundary area is of no less importance, as was already discussed (Miyasaka and Senna, 1986). In spite of the 0888-5885/89/2628-0982$01.50/0
general recognition of the above-mentioned, experimental studies aimed at the separation of parameters affecting the rate of solid-state reaction are scarce. A real rate process of the solid-state reaction using mechanically activated, fine powdery materials can never be expressed by any models comprising an ensemble of separated spherical particles. Existence of agglomerates 6 1989 American Chemical Society
