Ind. Eng. Chem. Res. 1989,28, 255-259
255
KINETICS AND CATALYSIS Reactions in and with Supercritical Fluids: Effect of Phase Behavior on Dibenzyl Ether Pyrolysis Kinetics Benjamin C. Wu, Michael T. Klein,* and Stanley I. Sandler Department of Chemical Engineering, University of Delaware, Newark, Delaware 19716
The effects of phase behavior on dibenzyl ether (DBE) pyrolysis kinetics were probed in a series of experiments a t 375 "C with different toluene loadings. The conversion of DBE (initial loading of 0.076 g/cmR3) after 30 min decreased from approximately 90% for neat pyrolysis to 50% at a toluene loading of 0.21 g/cmR3. This decrease is attributed to the dilution and diminution of the amount of DBE in the faster reacting liquid phase as the toluene loading is increased. T o interpret our data, we have calculated the phase behavior using the Peng-Robinson equation of state and a flash algorithm. The extreme pressure and temperature dependence of the density of a fluid near its critical point has generated considerable interest in the use of supercritical fluid (SCF) solvents in extraction (Eisenbach et ai., 1983; Schneider, 1983; Maddocks and Gibson, 1977; Maddocks et al., 1979; Amestica and Wolf, 1984; Barton, 1983; Towne et al., 1985) and reaction (Subramaniam and McHugh, 1986; McHugh and Occhiogrosso, 1987; Squires et al., 1983; Simmons and Mason, 1972) processes. The chemistry and kinetics of reactions in SCF solvents are affected by the solvent properties as a result of their influence on the thermodynamics of the transition state and the phase behavior of the mixture. Also, participation of the SCF solvent in the reaction has been observed (Townsend et al., 1988; Lawson and Klein, 1985; Abraham and Klein, 1985; Townsend and Klein, 1985). The literature provides an indication of the importance of these solvent effects. The role of the SCF solvent can be loosely categorized as either a participant or a reaction medium. Various SCF solvents have been suggested to participate in ionic (Ross and Blessing, 1979a,b; Anta1 et al., 1987) and solvolytic (Townsend et al.,1988; Lawson and Klein, 1985; Abraham and Klein, 1985; Townsend and Klein, 1985) mechanisms. As reaction media, SCF solvents can influence reactions through diffusion limitations (Abraham and Klein, 1987; Helling and Tester, 1987), pressure effects (Simmons and Mason, 1972; Johnston and Haynes, 1987),and electrostatic interactions (Townsend et al., 1988; Johnston and Haynes, 1987). Some of our previous studies (Townsend et al., 1988; Lawson and Klein, 1985; Abraham and Klein, 1985; Townsend and Klein, 1985) have been directed toward determining the influence of SCF solvent density on the reactions of coal model compounds. In these studies, the apparent water density was varied by charging different amounts of water into a constant volume reactor, while maintaining other reaction parameters constant. The results for the reaction of guaiacol (Lawson and Klein, 1985) and benzylphenylamine (Abraham and Klein, 1985) were qualitatively similar: the conversion initially decreased with increasing water loading and then increased after passing through a minimum. The increase at higher water loadings was attributed to an increase in the hydrolysis 0888-5885/89/2628-0255$01.50/0
rate; however, the cause of the initial decreases was unclear. Here, we show that the occurrence of two equilibrium fluid phases can explain this initial decrease in conversion. The importance of the phase behavior of systems involving supercritical fluids in kinetic analyses has been emphasized by McHugh and Occhiogrosso (1987). The present report, therefore, focuses on the influence of phase equilibria on the kinetics of reactions in SCF solvents. Dibenzyl ether (PhCHzOCHzPh)was chosen as a probe reactant because it is prototype coal model compound whose global chemistry and elementary steps of reaction have been well-studied (Brucker and Kolling, 1965; Cronauer et al., 1979; Schlosberg et al., 1981a,b; Gilbert and Gajewski, 1982; Simmons and Klein, 1985; Townsend and Klein, 1985; OMalley et al., 1985). Toluene was selected as the SCF solvent because the phase behavior of the DBEftoluene system can be predicted adequately by using the Peng-Robinson equation of state and because toluene shares structural features with dibenzyl ether (DBE) and its pyrolysis products. The pyrolysis of DBE to toluene and benzaldehyde being essentially irreversible ( K , -lo"), the selection of this reaction system allowed emphasis to be placed on the phase equilibrium aspects of the problem.
Experimental Method DBE was pyrolyzed in 316 stainless steel "tubing bomb" reactors with a volume of 0.59 cm3. The reactors consisted of one lf4-in.Swagelok port connector and two 1/4-in.end caps. In all experiments, 0.045 g of DBE; 0.005 g of a demonstrably inert (Townsend and Klein, 1985) internal standard, biphenyl; and a predetermined amount of solvent were loaded volumetrically into "tubing bombs" with an Eppendorf digital pipet (3t1%); the loadings were verified with a Mettler AE200 balance (*0.1 mg). The reactors were heated to, and maintained at, a reaction temperature of 375 f 2 "C in a fluidized sand bath for 30 min. The reactions were then quenched by immersing the tubing bombs in a room-temperature (-20 "C) water bath. The reaction products were recovered by three consecutive acetone washes. The products were then identified by GC/MS and quantified on an HP 5580 GC equipped with a 50-m DB-5 fused silica capillary column and flame ion0 1989 American Chemical Society
256 Ind. Eng. Chem. Res., Vol. 28, No. 3, 1989
I
ET;
:eR
Toluene Loading (gkm
V o K ]
)
Equilibrium Flash Calculation Scheme
n
/
50
0.05 0.10 0.20
.~ 0
Experimental
0.0
0.2
40
30
0.6
0.4
0.8
1.0
Mole Fraction Toluene
Figure 2. Phase behavior of DBE/biphenyl/toluene system at 375
"C.
update P with Newton-Raphson technique
actual volume ?
V
I
(3
1 I
J
FINISHED
Vapor 0 "
Figure 1. Flow diagram of modified flash calculation.
ization detector. Response factors were estimated by analyzing standard mixtures.
DBE/Toluene Phase Behavior The object of the phase equilibrium calculation was to estimate the pressure and the number and composition of equilibrium phases. The computational method, detailed in the Appendix section, was based on a flash vaporization calculation (King, 1980) where the temperature, pressure, and composition of the feed stream are known and the phase split and compositions of the subsequent phases are calculated. When applied to our tubing bomb reactors, where the pressure was not measured directly, the constant reactor volume replaced the pressure as input. Figure 1 outlines the computational method. The pressure was estimated initially as that of an ideal gas. The resulting volume was then calculated based on the phase split and phase densities provided by the flash vaporization calculation. The Newton-Raphson method was then used to adjust the estimated pressure until the actual reactor volume was obtained. The Peng-Robinson equation of state was used to describe the nonidealities in both phases in this calculation. The results of the calculation for the DBE/biphenyl/ toluene system at an experimental DBE and biphenyl loading of 0.045 and 0.005 g, respectively, are shown in Figure 2 as a pseudo-P-x diagram (two-dimensionalP-x diagrams are meaningful only for binary systems). Biphenyl was, however, present in sufficiently low amounts (" .-
W
W
-I
m n
C
m n
0.00017
-
P u)
u)
0
E 0.0001 6
i
..
I
0.04
.
i
.
I
0.12
.
I
'
I
I 0.00004
0.20
Toluene Loading (gkm
\)
Figure 4. Effect of toluene loading on phase split of DBE.
at a pressure of approximately 5 atm. The addition of toluene had two immediate effects. First, the DBE concentration in the liquid phase was diluted, as shown in Figure 3, because some of the solvent entered the liquid phase. Second, the number of DBE moles in the liquid phase decreased, as some of the DBE dissolved in the toluene-rich vapor phase. This is shown in Figure 4. - The phase split and compositions were found by using the inverse lever rule at each point of Figure 2. At a toluene loading of 0.21 g/cmR3, or a mole fraction of 0.85, the system exited the vapor-liquid two-phase region. The pressure at this point was approximately 47 atm.
Ind. Eng. Chem. Res., Vol. 28, No. 3, 1989 257
DBE Pyrolysis Mechanism The elementary steps of DBE pyrolysis have been summarized by Gilbert and Gajewski (1982). This RiceHerzfeld chain mechanism includes initiation (with rate constant k , ) to a benzyl (pl) radical and a benzyl alcohol (pz) radical, which propagate the chain through hydrogen abstraction (k2)from DBE. The thus-derived DBE radical (pl)undergoes p scission (k3) to benzaldehyde and the benzyl radical (pl) chain carrier. Termination is by all combinations (k4, k,, and k6) of pl, p2, and p1radicals. For long kinetic chains (rp/rI>> l),toluene and benzaldehyde are the only appreciable products, and thus abstraction by p2 becomes a chain-transfer step that renders initiation equivalent to generation of two p1 radicals. Use of the steady-state and long-chain approximations allows derivation of an analytic solution for the reaction rate as d[DBE] r=-= dt
Effect of Toluene Loading on DBE Conversion 1.0
w m
,
I
0.4
- Model Prediction 0.0
0.00
0.10
0.20
Toluene Loading (gicm ) Figure 5. Effect of toluene loading on DBE conversion at 375 OC: experimental data and model prediction.
Experimental Results and Discussion
which, after the reasonable approximation that the termination rate constants are equal except for the statistical factor for self-collision,i.e., k4 k5/2 k6 = kt, simplifies to
- -
The experimental results of DBE pyrolysis at different toluene loadings are presented in Figure 5. At a reaction time of 30 min, the conversion was approximately 90% at neat conditions and decreased to 50% at a loading of 0.21 g/cmR3. This decrease is consistent with the trend observed by Lawson and Klein (1985) and Abraham and Klein (1985). The flash calculations detailed above offer some insight into the interpretation of the kinetics. These calculations established that two phases exist in the tubing bomb for all loadings studied. At neat conditions, the pyrolysis of DBE in the high-concentration ([DBE] 3.5 M) liquid phase accounted for greater than 99.9% of the global reaction rate. Although the DBE in the vapor phase constituted 20% of the total DBE, the relatively small [DBE] of -0.02 M caused the vapor-phase reaction rate to be negligible in comparison. The addition of toluene lowered [DBE] in the liquid phase and caused more DBE to appear in the vapor phase. The consequence to the global reaction rate was 2-fold. First, the liquid-phase reaction rate decreased due to the decrease in [DBE] by dilution. Second, DBE dissolved into the supercritical toluene phase where DBE reaction was slower. Although both of these effects also caused the vapor-phase reaction rate to increase, the fraction of the overall DBE pyrolysis occurring in the vapor phase was negligible, and therefore the increased rate in the vapor phase had little impact on the overall kinetics. The four rate constants, kv’, kv”, kL’, and kL”, were determined by using the downhill simplex method of Nelder and Mead (1965). The minimized function was (Xexp - XmdeJ2.The model conversions were calculated by numerically integrating eq 4 in conjunction with the flash calculation. At the start of each time step, a flash calculation was performed using the global composition of the previous time step. The global concentrations were then updated as the reaction described by eq 4 progressed. This phase equilibrium/reaction kinetics simulation therefore mimicked the reaction dynamics in the tubing bomb. The regression yielded the values kv’ = 0.00895 M-1/2 s-l, kv” = 5.83 X M-l, kL’ = 0.00298 M-lf2s-l, and kL” = 9.84 X M-l, which provide the model prediction shown in Figure 5. The apparent reaction order of n = 3/2 is consistent with Gilbert and Gajewski’s (1982) report of n = 1.43 over the temperature range 310-350 “C. A comparison of kv’ and kL‘ suggests that the reaction rate constant in the liquid phase is one-third of that in the vapor phase. This could be due to a diffusional limitation
-
d [DBE] r=-dt
-- k ’[DBEI3l2 1 + k”[DBE]
1
k2
+ -[DBE] k3
(2) In principle, then, the concentration of DBE therefore dictates not only the reaction rate but also its order. Potentially, the apparent reaction order could be 3/2 in the gas phase because of the relatively low [DBE] and 1/2 in the more concentrated liquid phase. Application of this rate expression to the present system required the concentrations in each phase and the phase split. The global rate was the volume average of the reaction rate in each phase: k’[DBE]v3/’ = “1 + k”[DBEIV
’
+
~’[DBE]L~/~ (3) ‘L1 k”[DBEIL
+
The rate constants for the elementary steps and, therefore, k ’and k I‘ are not expected to be the same in the liquid and vapor phases. However, few reacting systems have been studied in both the vapor and liquid phases. Stein et al. (1982) investigated the pyrolysis of bibenzyl in the liquid and gas phases and attributed the lower rate constants in the liquid phase to cage effects. Moore and Pearson (1981) suggest that liquid-phase diffusional limitations may restrict the rates of encounter and disencounter of potential reacting pairs, thereby affecting the reaction rate constants. The general global rate shown in eq 3 was therefore modified to eq 4 which contains four rate constants, two for each phase. The corresponding pairs, (kv’ and kL’) and (kv” and kv”), can in principle be related through the Moore and Pearson (1981) formalisms. kv’[DBE]v3/2 r = 1 + kv” [DBEIv4’
+
kL’ [DBEIL3l2 kL” [DBEIL+L
1
+
(4)
258 Ind. Eng. Chem. Res., Vol. 28, No. 3, 1989
in the liquid phase. However, the reaction rate in the liquid phase is still more than 2 orders of magnitude greater by virtue of concentration differences. The significance of this work can be viewed from two perspectives. In the first perspective, kinetics analysis of reactions in supercritical fluids clearly requires calculation of the number and composition of equilibrium phases. Fundamental information such as reaction order and Arrhenius parameters would otherwise be obscured. That is, single-phase analysis of chemistry actually occurring in multiple phases would be inappropriate “early” averaging. A second processing perspective is also germane. Industrial-scale reactors will involve whatever number and compositions of equilibrium phases the overall process economics dictate. Their design, scale-up, and optimization, therefore, require thermodynamics as well as kinetics analysis. It is noteworthy that pressure can be used as an optimizing process variable since it can control the number and composition of equilibrium phases.
Conclusions The conversion of dibenzyl ether after pyrolysis for 30 min at 375 “C at a DBE loading of 0.076 g/cmR3 was suppressed from 90% under neat conditions to 50% with a toluene loading of 0.21 g/cmR3. The suppression of the overall reaction rate can be explained by the existence of both vapor and liquid phases. The addition of supercritical toluene diluted [DBEIL and diminished the amount of DBE in the faster reacting liquid phase. Nomenclature A = Peng-Robinson parameter E = Peng-Robinson parameter F = moles in feed (set to 1 mol) K = x/y L = fraction of total moles in liquid phase P = pressure, atm T = temperature, K T , = critical temperature, K T , = reduced temprature = T / T , V = fraction of total moles in vapor phase X = conversion Z = compressibility a = Peng-Robinson parameter b = Peng-Robinson parameter f = fugacity, atm k = rate constant r = reaction rate, M-l x = liquid mole fraction y = vapor mole fraction z = total mole fraction
stead of pressure as the input along with temperature and component loadings. The initial pressure, estimated from the ideal gas law, was used as the initial estimate. Through the flash calculation, the phase split and the resulting volumes of each phase were calculated. The pressure was then adjusted by using the Newton-Raphson technique until the volume converged on that of the reactor. In the algebraic approach to a flash calculation, three sets of equations were solved: component mass balance: x ~ L+ yiV = ziF overall mass balance:
(A21
L+V=F phase equilibrium: Ki = Y J X i =
(A31
@>/@iV
This involved solving a system of 2n+2 equations with 2n+2 unknowns where n was the number of components present. The adopted convergence method involved specifying (1) Cyi - Exi = 0 and (2) f? = fiv. The calculation scheme first initialized L I F = V / F = 0.5 and set Ki as Pmk/P.To derive the first convergence, criteria A 1 and A3 were combined to yield zi
?(Ki- l ) ( V / F )
+ 1= o
(A4)
z;K~ = 4 ( K i- l)(V/F)
+ 1= O
(A5)
=
and
Therefore, the convergence criterion became zi(Ki - 1) = (Ki - I)( V / F ) + 1 = 0
(A6)
Then, with eq A6, the correct L and V were calculated iteratively by using the Newton-Raphson technique. The liquid and vapor fugacities were then calculated as either fiL =
(A7)
Xi@’iLP
or
fiV = y$’iVP
(AS)
The fugacity coefficient was derived from the PengRobinson equation of state as bi = -(Z bm
Greek Letters a = Peng-Robinson parameter 6 = Peng-Robinson interaction parameter @ = fugacity coefficient 4 = volume fraction w = accentric factor
In
Subscripts and Superscripts i = component I = initiation L = liquid phase V = vapor phase P = propagation R = indication of reactor volume
where
@i
- 1)- In (2 - B )
+
I
with am = CCyivjaij i
Appendix Modified Flash Calculation. The computational method used a flash calculation that accepted volume in-
(AI)
l
bm = Cyibi
ai, = (1- Gii)(aiaj)l/z and
i
izj
Ind. Eng. Chem. Res., Vol. 28, No. 3, 1989 259 Helling, R. K.; Tester, J. W. Oxidation Kinetics of Carbon Monoxide in Supercritical Water. Energy Fuels 1987, 1, 417-423. Johnston, K. P.; Haynes, C. Extreme Solvent Effects on Reaction Rate Cons@ts at Supercritical Fluid Conditions. MChE J. 1987, 33, 2017-2026.
K
= 0.37464
+ 1 . 5 4 2 2 6 ~- 0 . 2 6 9 9 2 ~ ~
and
b=
0.07780RTc
pc
The Peng-Robinson equation of state was chosen because it was useful for correlating vapor-liquid equilibrium data of coal model compound/polar solvent systems (Thies, 19851, albeit with fitted binary interaction parameters. The dearth of phase equilibrium data for the present systems precludes estimating binary interaction parameters. The fugacities of each component must be the same in both phases. If they do not agree, then Ki's are updated as When the fugacities have converted, the calculation is complete. Registry No. Dibenzyl ether, 103-50-4; toluene, 108-88-3.
Literature Cited Abraham, M. A.; Klein, M. T. Pyrolysis of Benzylphenyl Amine Neat and with Tetralin, Methanol, and Water Solvents. Znd. Eng. Chem. Prod. Res. Deu. 1985, 24, 300. Abraham, M. A.; Klein, M. T. Solvent Effects During the Reaction of Coal Model Compounds, ACS Symp. Ser. 1987, 329, 67-76. Amestica, L. A.; Wolf, E. E. Supercritical Toluene and Ethanol Extraction of an Illinois No. 6 Coal. Fuel 1984, 63, 227-230. Antal, M. J., Jr.; Brittain, A.; DeAlmeida, C.; Ramayya, S.; Jiben, C. R. Heterolysis and Homolysis in Supercritical Water. ACS Symp. Ser. 1987,329, 77-86. Barton, P. Supercritical Separation in Aqueous Coal Liquefaction with Impregnated Catalyst. Znd. Eng. Chem. Process Des. Deu. 1983,22, 589-594.
Brucker, R.; Kolling, G Brennst. Chem. 1965, 46, 41. Cronauer, D. C.; Jewell, D. M.; Shah, Y. T.; Modi, R. J. Mechanism and Kinetics of Selected Hydrogen Transfer Reactions Typical of Coal Liquefaction. Znd. Eng. Chem. Fundam. 1979,18,153-162. Eisenbach, W.; Gottsh, P. J.; Niemann, N.; Zosel, K. Extraction and Supercritical Gases: The First Twenty Years. Fluid Phase Equilib. 1983, 10, 315-318. Gilbert, K. E.; Gajewski, J. J. Coal Liquefaction Model Studies: Free Radical Chain Decomposition of Diphenylpropane, Dibenzyl Ether, and Phenyl Ether via p-Scission Reactions. J. Org.Chem. 1982,47, 4899-4902.
King, J. D. Separation Processes; McGraw-Hill: New York, 1980. Lawson, J. R.; Klein, M. T. Influence of Water on Guaiacol Pyrolysis. Ind. Eng. Chem. Fundam. 1985,24, 203. Maddocks, R. R.; Gibson, J. Supercritical Extraction of Coal. Chem. Eng. Prog. 1977, 73, 55-63. Maddoch, R. R.; Gibson, J.; Williams, D. F. Supercritical Extraction of Coal. Chem. Eng. Prog. 1979,4945. McHugh, M. A,; Occhiogrosso, R. N. Critical-mixture Oxidation of Cumene. Chem. Eng. Sci. 1987,42, 2478-2481. Moore, J.; Pearson, R. Kinetics and Mechanisms; Wiley and Sons: New York, 1981. Nelder, J. A.; Mead, R. A Simplex Method for Function Minimization. Comput. J. 1965, 7, 308. OMalley, M. M.; Bennett, M. A.; Simmons, M. B.; Thompson, E. D.; Klein, M. T. Isotope Labelling as a Probe for Free-radical Reactions during Dibenzyl Ether Thermolysis. Fuel 1985, 64, 1027-1029.
Ross, D. S.; Blessing, J. E. Alcohols as H-donor in Coal Conversion 1. Base Promoted H-Donor to Coal by Methyl Alcohol. Fuel 1979b,58,432-437.
Ross, D. S.; Blessing, J. E. Alcohols as H-donor in Coal Conversion 2. Base Promoted H-Donor to Coal by Isopropyl Alcohol. Fuel 1979, 58, 438-442.
Schlosberg, R. H.; Ashe, T. R.; Pancirov, R. J.; Donaldson, M. Pyrolysis of Benzyl Ether under Hydrogen Starvation Conditions. Fuel 1981a, 60, 155. Schlosberg, R. H.; Davis, W. H.; Ashe, T. R. Pyrolysis Studies of Organic Oxygenates. 2. Benzyl Phenyl Ether Pyrolysis under Batch Autoclave Conditions. Fuel 1981b, 60, 201. Schneider, G. M. Physicochemical Aspects of Fluid Extraction. Fluid Phase Equilib. 1983, 10, 141-157. Simmons, M. B.; Klein, M. T. Free-Radical and Concerted Reaction Pathways in Dibenzyl Ether Thermolysis. Znd. Eng. Chem. Fundam. 1985,24, 55. Simmons, G. M.; Mason, D. M. Pressure Dependency of Gas Phase Reaction Rate Coefficients. Chem. Eng. Sci. 1972, 27, 89. Squires, T. G.; Venier, C. G.; Aida, T. Supercritical Fluid Solvents in Organic Chemistry. Fluid Phase Equilib. 1983,10, 261-268. Stein, S. E.; Robaugh, D. A.; Alfieri, A. D.; Miller, R. E. Bond Homolysis in High Temperature Fluids. J . Am. Chem. SOC.1982,104, 6567-6570.
Subramaniam, B.; McHugh, M. A. Reactions in Supercritical Fluids-A Review. Znd. Eng. Chem. Process Des. Deu. 1986,25, 1-12.
Thies, M. Vapor-Liquid Equilibrium of Model Coal-derived Compounds with Methanol at Elevated Temperatures and Pressures. Ph.D. Dissertation, University of Delaware, Newark, 1985. Towne, S. E.; Shah, Y. T.; Holder, G. D.; Deshpande, G. V.; Cronauer, D. C. Liquefaction of Coal Using Supercritical Fluid Mixture. Fuel 1985,64, 883-889. Townsend, S. H.; Klein, M. T. Dibenzyl Ether as a Probe into the Supercritical Fluid Solvent Extraction of Volatiles from Coal with Water. Fuel 1985, 64, 635-8. Townsend, S. H.; Abraham, M. A.; Huppert, G. L.; Klein, M. T.; Paspek, S. C. Solvent Effects during Reactions in Supercritical Water. Znd. Eng. Chem. Res. 1988, 27,143-149. Received for review August 11, 1988 Accepted November 28, 1988
