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Ind. Eng. Chem. Res. 1998, 37, 2582-2591
KINETICS, CATALYSIS, AND REACTION ENGINEERING Polyethylene Pyrolysis: Theory and Experiments for Molecular-Weight-Distribution Kinetics Naime A. Sezgi, Wang S. Cha, J. M. Smith, and Ben J. McCoy* Department of Chemical Engineering and Materials Science, University of California, Davis, California 95616
A novel reactor for pyrolysis of a polyethylene melt stirred by bubbles of flowing nitrogen gas at atmospheric pressure permits uniform-temperature depolymerization. Sweep-gas experiments at temperatures 370-410 °C allowed pyrolysis products to be collected separately as reactor residue (solidified polyethylene melt), condensed vapor, and uncondensed gas products. Molecular-weight distributions (MWDs) determined by gel permeation chromatography indicated that random scission and repolymerization (cross-linking) broadened the polymer-melt MWD. Observing the repolymerization reaction is difficult if the condensate and melt are not recovered separately as in the described experiments. The C1-C5 uncondensed gas products were formed by chain-end scission, according to the continuous-distribution theory proposed to interpret the experimental data. The mathematical model accounts for the mass transfer of vaporized products from the polymer melt to gas bubbles. The driving force for mass transfer is the interphase difference of MWDs based on equilibrium at the vapor-liquid interface. The chain-end-scission activation energy and preexponential were determined to be 35 kcal/mol and 1.14 × 108 s-1, respectively. The data did not permit determination of the random scission and repolymerization rate coefficients. Introduction Pyrolysis of plastics is well-known as an analytical procedure and is also a potential method for recycling polymers. Unlike thermolysis in dilute solution, where solubilized polymers undergo chain scission to products that mostly remain in the constant-volume liquid phase, pyrolysis usually refers to a melted plastic thermally depolymerizing to lower molecular-weight (MW) compounds that vaporize and reduce the melt volume. The vaporization process makes pyrolysis kinetics more complex and difficult to characterize quantitatively than solution-phase thermolysis. Wall1 argued that molecular vaporization can control the weight loss during plastics pyrolysis. He showed that combining kinetic theory and vapor-pressure thermodynamics yields activation energies for vaporization on the order 18-50 kcal/mol for alkanes of chain length 19-94. Because chain-scission activation energies are also in this range, determining the rate-controlling process may not be straightforward. A recent review2 of low-temperature pyrolysis (T < 450 °C) states that most chemical-reaction kinetics studies of pyrolysis were performed by standard thermogravimetric analysis (TGA). Weight-loss data for a small polymer mass (a several milligram sample) of polymer in a small heated crucible comprise the primary information for determining pyrolysis kinetics. The review, in a critical discussion of several models for analyzing TGA data, pointed out that the observed weight loss in pyrolysis involves evaporation of low-MW products. Any low-MW molecules initially in the polymer will also evaporate. The empirical power-law rate
expression employed in most studies to fit TGA weightloss data is considered valid only at large polymer conversions, where random scission of the remaining lower-MW polymer molecules yields products that can vaporize. The widespread use of the simple power-law model is a probable reason2 that reported rate coefficients differ by a factor of 10. Reported kinetic parameters (preexponential factor and activation energy) for polyethylene also cover a wide range. Westerhout et al.2 proposed a random-chain-dissociation (RCD) model, based on evaporation of depolymerization products less than a certain chain length. In a subsequent paper3 on screen-heater pyrolysis, the RCD model was further described. For the screen-heated system, as well as for thermogravimetry, mass transfer of vaporized depolymerization products can strongly influence rate measurements. Such interphase mass transfer depends on a driving force that should account for equilibrium at the vapor-liquid (melt) interface. Evaluation of a flow reactor with entrained polymer particles4 showed that melted particles tended to stick to the reactor walls, making their residence times unpredictable. Seeger and Gritter5 studied pyrolysis of 1-mg samples of polyethylene and n-alkanes with programmed temperature rise under hydrogen sweep gas. Gas chromatographic analysis of the volatilized reaction products yielded a carbon-number distribution. Recognition of the key role of the volatilization process was a result of this work. Ng et al.6 used nitrogen sweep gas for polyethylene pyrolysis and catalytic cracking, noting that volatile products were purged from the reactor and prevented from reacting. In other investigations of
S0888-5885(98)00106-7 CCC: $15.00 © 1998 American Chemical Society Published on Web 05/21/1998
Ind. Eng. Chem. Res., Vol. 37, No. 7, 1998 2583
polyethylene pyrolysis, the condensed reaction products were collected and analyzed by gas chromatography.7,8 In polyethylene melt processing Johnston and Morrison9 considered the relative influences of thermal scission and cross-linking (repolymerization). Unsaturated groups decreased with increasing repolymerization and increased with increasing chain scission. For the most part, empirical reaction-kinetics expressions for weight loss due to volatilization of lower-MW depolymerization products were applied in polymer pyrolysis studies. The mathematical models usually disregarded mass-transfer resistance for volatile depolymerization products. The dynamics of the MWDs of polymer and vapor have not been addressed, nor have MWD measurements been reported. Understanding the chain-scission reactions that produce lower-MW volatile products is obviously required for a fundamental quantitative description of pyrolysis. Attempts have been made to model random-chain scission, but chain-end scission, which accompanies random scission, has been ignored. Repolymerization, giving higher-MW products during pyrolysis, has also been neglected. The present objective is to describe a novel experimental method for studying pyrolysis and a new mathematical model combining mass-transfer, interfacial vapor-liquid equilibrium, and chain-scission processes. We describe experiments for a polyethylene melt decomposing at pyrolysis temperatures to form lower-MW evaporating compounds. These products are swept away by flowing inert gas into a cooled flask where condensed vapors are trapped. The MWDs of reactor residue and semisolid condensate (wax) are determined by HPLC gel permeation chromatography (GPC). Noncondensable gases (C1-C5) are analyzed downstream by gas chromatography. Population balance equations, incorporating random and chain-end scission as well as liquid-vapor mass transfer, are applied to polymer melt, vapor, condensable vapor, and gas. A MWmoment method applied to the governing integrodifferential equations allows formulation of ordinary differential equations for zeroth moments (molar concentrations), first moments (mass concentrations), and second moments of melt, vapor, condensate, and gas MWDs. Growth of high-MW compounds in the reactor melt is evidence of repolymerization, which is represented by the reverse of random scission. Low-MW molecules, whether initially in the polymer or produced by depolymerization, evaporate from the melt. The distribution-kinetics model describes a mass decrease of the polymer melt due to losses of condensable vapor and noncondensable gas produced by random- and chain-end scission, respectively. Comparisons and relationships with simpler experiments and less-detailed models indicate the benefits of this approach. Experiments Polyethylene pyrolysis experiments were conducted at atmospheric pressure under nitrogen gas at 370, 390, 400, and 410 °C. The diagram of the experimental apparatus (Figure 1) shows a polymer melt in the heated reactor (immersed in a molten-salt bath) and vapor carried to the condenser vessel (immersed in an ice bath) by flow of nitrogen sweep gas. The gas flows through 1/16-in. stainless steel tubing, 3.4 m of which is coiled and immersed in the molten salt so that the gas
Figure 1. (A) Schematic drawing of the experimental apparatus: (1) nitrogen cylinder, (2) valve, (3) rotameter, (4) heater, (5) stirrer, (6) reactor, (7) thermocouples, (8) molten-salt bath, (9) ice bath, (10) soap-bubble meter, (11) controllers, (12) digital thermometer readout. (B) Sketch of the apparatus for the mathematical model showing the notation for volumes, molar MWDs, and flow rate.
temperature reaches the bath temperature. Nitrogen enters at the reactor base through a 1/2-in.-diameter, 316 stainless steel frit (Supelco) with 2-µm pores, which disperse the gas but prevent backflow of the polymer melt. Connecting tubes are 10.5-mm-internal-diameter stainless steel tubing. The exit gas flow rate (0.25 cm3/ s), measured by water displacement from an inverted graduated cylinder, was not affected by small amounts of gaseous products and was thus constant during the experiment. Observations made by looking down into the open reactor during a preliminary pyrolysis experiment confirmed that the HDPE melt was well-mixed by approximately 1-mm gas bubbles rising through the melt. This eliminates the potential problem of uneven heating that can occur in unstirred pyrolysis systems. The molten-salt bath is a mixture of potassium nitrate, sodium nitrite, and sodium nitrate in a molar ratio of 7:7:1, stirred by an agitator (Fisher Scientific StedFast stirrer model SL 600) and heated by a 3-kW element (Omega TBL-A-131/240V). The bath temperature was measured with a Type J thermocouple (Omega) and controlled to (1 °C by a temperature controller. The stainless steel reactor of internal volume 10 cm3 is fitted into a steel protective sleeve lined with a steel shot (3.4mm diameter) to improve heat transfer. The volume available to condensable vapor, Vv ) 64 cm3, includes reactor and condenser vapor spaces and a connecting tube. The volume available to noncondensable gas, Vg ) 324 cm3, includes Vv and the tube leading away from the condenser.
2584 Ind. Eng. Chem. Res., Vol. 37, No. 7, 1998
Each experiment was performed by immersing the reactor and inlet tube coils into the molten-salt bath set at the reaction temperature. The reactor holds 2 g of unreacted polyethylene pellets. The reactor reaches the reaction temperature in less than 20 min, as measured by a thermocouple inserted in the reactor. Measurement of reaction time was begun when the temperature reached 300 °C. The stainless steel tube leading from the reactor to the condenser vessel was wrapped with heating tape to maintain a temperature 5 °C higher than the reaction temperature. This prevented condensation in the tubing. The tube temperature was measured with a Type K thermocouple (Fisher Chemicals) and controlled to (3 °C with a Thermolyne 45500 power controller. After the reaction time (1, 2, or 3 h) the reactor was immediately removed from the bath and cooled in ice water. The cooled pyrolysis products at the end of an experiment are solid polymer remaining in the reactor, semisolid condensate in the condenser vessel, and gas. Gas product was collected at 20-min intervals during the experiment and analyzed by GC (Perkin-Elmer model 8500; J&W Scientific capillary alumina column, 30 m × 0.53 mm). Reactor and condenser vessels were separately weighed before and after each experiment to determine the final polymer and condensate masses. Each product was dissolved at 90 °C in 100 mL of HPLC reagent-grade 1,2,4-trichlorobenzene (TCB; Fisher Scientific) and analyzed by HPLC-GPC. A mixture of dissolved polymer melt and condensate was prepared by mixing 10 mL of each solution. Before GPC analysis, all samples were again diluted 5-30-fold to maximize sensitivity. The HPLC system (Hewlett-Packard 1050) consists of a 100-µL sample loop, a precision pump, and a refractive-index detector (Hewlett-Packard 1047A). Two GPC columns (Waters 10674, 300 mm × 7.5 mm) packed with cross-linked styrene-divinylbenzene copolymer beads (10-µm diameter) were used in series. The eluent TCB was pumped at a constant flow rate of precisely 1.00 mL/min. Column and detector temperatures were maintained at 50.0 °C. The calibration curve (retention time versus MW) was determined with n-hexane, pentadecane, triacontane, and pentacontane (Aldrich) as calibration standards. The calibration results were checked by determining the feed-polymer MWD before each series of sample analyses. The raw polyethylene served as a standard to determine when recalibration was required. Conversion of GPC retention time to MW in a MWD was computed by a spreadsheet computer program. Knowing the mass of the polymer and the volume of the solvent allows calculation of MWD as mass/MW. Mass MWDs are reported in this work as g/MW normalized for 1.00 g of initial sample (area under mass MWD represents 1.00 g). Molar MWDs can be calculated by dividing each mass MWD by MW. MW moments of these molar MWDs are represented as P(n) (the units are mol for n ) 0 and mass for n ) 1). The respective molar concentration moments are expressed on a volume basis, p(n) ) P(n)/V. The feed polymer was high-density polyethylene (Polysciences) of nominal MW 700, density 0.94 g/cm3, and melting point range 93-97 °C. For depolymerization by a free-radical mechanism, chain branching increases the reaction rate due to the higher stability of tertiary radicals relative to secondary and primary
radicals. For this reason, low-density polyethylene (LDPE) will depolymerize at a higher rate than highdensity polyethylene (HDPE). The actual values of Mn and Mw for feed HDPE were determined by HPLC-GPC as 542 ( 28 and 677 ( 31. These average values and standard deviations were obtained by analyzing the initial HDPE four times during the 8 weeks of experimentation. The uncertainty in the average MW determined by GPC is thus estimated at (6%, and the uncertainty of reactor mass measurements determined by replicate runs is (2%. Distribution-Kinetics Model The experimental apparatus (Figure 1B) shows a polymer melt in the heated reactor, vapor flow to the condenser vessel, and flow of inert nitrogen sweep gas. The subscripts m, v, c, and g denote liquid melt, condensable vapor, condensate, and noncondensable gas products, respectively. Polymer melt volume, Vm, decreases with reaction time by evaporation of low-MW components, and condensate volume, Vc, increases. Volume changes of the relatively large vapor volume, Vv, and gas-product volume, Vg, are negligible. The gas flow rate, Q, was constant. MWDs (mol/(vol‚MW)) are defined10,11 so that, at time t, p(x,t) dx is the molar concentration (mol/volume) of a compound having values of MW x in the range x to x + dx. Moments of MWDs are defined as integrals over x,
p(n)(t) )
∫0∞p(x,t) xn dx
(1)
The zeroth moment (n ) 0) is the time-dependent total molar concentration (mol/volume). The first moment, p(1)(t), is the mass concentration (mass/volume). The normalized first moment (average MW) and second central moment (variance of the MWD) are given respectively by pavg ) p(1)/p(0) and pvar ) p(2)/p(0) - [pavg]2. The polydispersity index is defined as the ratio of mass (or weight) average MW, Mw ) p(2)/p(1), to molar (or number) average MW, Mn ) pavg; thus, D ) p(2)p(0)/[p(1)]2. The three moments, p(0), pavg, and pvar, provide shape characteristics of the MWD and can be used to construct the MWD mathematically. Population balances12 for the MWDs shown in Figure 1B are based on mass balances; that is, the accumulation rate is equal to the net generation by reaction minus the net loss by flow or mass transfer. The masstransfer rate from the polymer melt to vapor bubbles, described by an overall mass-transfer coefficient, κ(x) ) κ0 - κ1x, is assumed to decrease linearly with MW to account for lower mass-transfer rates of higher-MW components. The interphase mass-transfer driving force is given by pm - pv/K, where pm, pv, and K are all functions of x so that the driving force depends on the particular component that is evaporating. The vaporliquid phase equilibrium constant is assumed to decrease with MW according to an inverse polynomial
K(x) ) K0/(1 +
ajxj) ∑ j)1
(2)
These expressions for κ(x) and K(x) permit mathematical solutions to the mass balance equations through MW moments.
Ind. Eng. Chem. Res., Vol. 37, No. 7, 1998 2585
Simultaneous random-scission and repolymerization reactions can be written as kd
P(x′) S P(x) + P(x′-x)
for polymer melt d(Vmpm(n))/dt ) -κ0[pm(n) - (pv(n) + κ1[pm(n+1) - (pv(n+1) +
(A)
ka
ajpv(n+j))/K0] + ∑ j)1
ajpv(n+1+j))/K0] + ∑ j)1
Vm[-kdpm(n)(n - 1)/(n + 1) - 2kapm(n)pm(0) +
( nj )pm(j)pm(n-j) - kspm(n) + ks∑( nj )(-xs)jpm(n-j)] ∑ j)0 j)0
ka
and irreversible chain-end scission as
(7)
ks
P(x) 98 Q(xs) + P(x-xs)
(B)
for vapor d(Vvpv(n))/dt ) κ0[pm(n) - (pv(n) +
where Q(xs) is a monomer or oligomer of mass xs. The rate expressions for reactions A and B have been related to radical mechanisms.13 The random-scission rate should increase with the number of bonds that can be cleaved. Hence, kd should generally increase12 with x. Polymerization rates, according to the equal-reactivity approximation,14 are independent of MW. The chainend scission rate is essentially proportional to the number of chain ends and is thus independent of the chain length and of x, the MW of a macromolecule.10 The stoichiometric kernels are 1/x′ for random scission and δ[x-(x′-xs)] and δ(x-xs) for the two products of chain-end scission.10 Rate expressions for reactions A and B have been applied previously in polymer degradation studies.10,13,15,16 We consider that random-scission and repolymerization reactions, as well as chain-end scission, occur in the polymer melt with rate coefficients kd(x), ka, and ks, respectively. The random-scission rate coefficient is considered a function of x, whereas the two other coefficients are independent of x. The vapor is dilute as it is swept out of the reactor. Hence, no significant reaction occurs in the vapor. If composition is assumed uniform at any time throughout the gas bubbles and the liquid, the mass balances are as follows:
for polymer melt
∫x
ajpv(n+1+j))/K0] - Qpv(n) ∑ j)1
(8)
for condensate d(Vcpc(n))/dt ) Qpv(n)
(9)
for noncondensable gas products d(Vgpg(n))/dt ) Vmksxsnpm(0) - Qpg(n)
(10)
For n ) 0 the differential equations are molar balances:
for polymer melt d(Vmpm(0))/dt ) - κ0[pm(0) - (pv(0) + κ1[pm(1) - (pv(1) +
ajpv(j))/K0] + ∑ j)1
ajpv(j+1))/K0] + ∑ j)1
Vm[kd - kapm(0)]pm(0) (11) for vapor d(Vvpv(0))/dt ) κ0[pm(0) - (pv(0) + κ1[pm(1) - (pv(1) +
ajpv(j))/K0] ∑ j)1
ajpv(j+1))/K0] - Qpv(0) ∑ j)1
(12)
for condensate
∂(Vmpm)/∂t ) -κ(pm - pv/K) + Vm[-kd(x) pm(x) + 2
κ1[pm(n+1) - (pv(n+1) +
ajpv(n+j))/K0] ∑ j)1
∞
kd(x′) pm(x′) (1/x′) dx′ -
2kapm(x)pm(0)
d(Vc pc(0))/dt ) Qpv(0)
+
for noncondensable gas products
∫0xpm(x′) pm(x-x′) dx′ - kspm(x) + ∞ ks∫x pm(x′) δ[x-(x′-xs)] dx′]
(3)
∂(Vvpv)/∂t ) κ(pm - pv/K) - Qpv
(4)
ka
d(Vgpg(0))/dt ) Vmkspm(0) - Qpg(0)
for vapor
for condensate ∂(Vcpc)/∂t ) Qpv
(5)
for noncondensable gas products ∂(Vgpg)/∂t ) Vmks
∫x pm(x′) δ(x-xs) dx′ - Qpg ∞
(13)
(6)
We first consider that kd is constant with x and comment later on the effect of a linear dependence on x. Applying the moment operation, ∫∞0 [...]xn dx, to each equation yields11 the following differential equations:
(14)
Molar production of gas products is quasi-steady-state because the molar concentration of polymer (and therefore of chain ends) is relatively constant. Thus, the lefthand side of eq 14 vanishes, and the molar flow rate of gas products out of the equipment is
Qpg(0) ) Vmkspm(0)
(15)
The molar amount of vapor is also relatively constant, d(Vvpv(0))/dt ) 0. Adding together molar balances for the polymer melt, vapor, and condensate shows that moles of polymer in the melt and in the condensate, Pm(0) + Pc(0) ) Vmpm(0) + Vcpc(0), change according to the rate
d(Pm(0) + Pc(0))/dt ) Vm[kd - kapm(0)]pm(0)
(16)
As the mass transfer terms cancel by addition, eq 16 represents the increase in moles due to random scission
2586 Ind. Eng. Chem. Res., Vol. 37, No. 7, 1998
and the decrease due to repolymerization reactions. This result is valid for any mass-transfer expression that allows the moment operation. For chain-end scission, the molar concentration of reactant polymers is unchanged, and hence ks does not appear in eq 16. For n ) 1 the differential equations are mass balances:
for polymer melt d(Vmpm(1))/dt ) - κ0[pm(1) - (pv(1) + κ1[pm(2) - (pv(2) +
ajpv(j+1))/K0] + ∑ j)1
ajpv(j+2))/K0] - Vmksxspm(0) ∑ j)1
(17)
for vapor d(Vvpv(1))/dt ) κ0[pm(1) - (pv(1) + κ1[pm(2) - (pv(2) +
ajpv(j+1))/K0] ∑ j)1
ajpv(j+2))/K0] - Qpv(1) ∑ j)1
Figure 2. Change of polymer-melt mass, Pm(1) (g), with time at four pyrolysis temperatures.
(18)
for condensate d(Vcpc(1))/dt ) Qpv(1)
(19)
for noncondensable gas products d(Vgpg(1))/dt ) Vmksxspm(0) - Qpg(1)
(20)
If these four mass balance equations are added, terms cancel so that the rate of change of the total mass, mtot ) Pm(1) + Pv(1) + Pc(1) + Pg(1), equals the loss of gas products in the outflow,
dmtot/dt ) -Qpg(1) thus recovering the overall mass balance for the equipment. Because dPg(1)/dt is vanishingly small, from eq 20 and the definition of the polymer melt MW, Mnm, we have
dmtot/dt ) -ks(xs/Mnm)Pm(1)
(21)
According to this equation, the rate of change of the total polymer mass is first-order in melt mass, Pm(1) ) Vmpm(1). This is a rationale for the first-order rate expression that is frequently applied to calculate rate coefficients for pyrolysis data.2 The calculation, however, is usually based on polymer melt mass, Pm(1), rather than total mass, mtot, according to the supposed first-order expression
dPm(1)/dt ≈ -ks apPm(1)
(22)
Equation 22 ignores the vaporization contribution to weight loss and lumps all chain-scission processes into one rate constant. Therefore, this expression is an approximation to the realistic rate. Initial conditions for polymer melt and condensate MWDs are pm(x,0) and pc(x,0) and, for moments, pm(n)(0) and pc(n)(0). The mass-transfer expression appearing in eqs 3 and 4 accounts for loss of low-MW molecules by vaporization that are initially in the melt. Experimental Results Experimental results demonstrate how MWDs of reactor polymer and vaporized depolymerization prod-
Figure 3. Change of condensate mass, Pc(1) (g), with time at four pyrolysis temperatures.
ucts vary with time. Typical pyrolysis experiments measure only loss of polymer mass due to evaporation of depolymerization products and unreacted low-MW polymer. The present approach provides two measurements of reactor polymer mass (Figure 2) and of condensate (Figure 3) at the end of each experiment. One measurement is by weighing and the other is by the first moment of the MWD, which requires that the weight be known. As the measurements are not independent, reactor polymer mass and condensate mass calculated by the two methods coincide. Reactor polymer mass decreases as condensate increases, and their sum decreases with time due to gas product loss (Figure 4). The mass of gaseous products (Figure 5) is found by subtracting the sum of polymer melt and condensate masses from the initial polymer mass. Figures 2, 3, and 5 show that polymer vaporization and gas production are significant. For example, at 410 °C and 3 h, 24% of the original polymer remains in the reactor while 64% is condensate and 12% gaseous products. As temperature and time increase, the reactor polymer mass decreases while condensate and gas-product masses increase. The time dependences of polymer-melt mass, condensate mass, combined mass, and product-gas mass were approximated as second-order polynomials (Figures 2-5). The rate of gas production is nearly constant during the 3-h experiment (Figure 5), indicating that chain-end scission occurs throughout the pyrolysis. If noncondensable gas were produced only by random scission, one would expect the gas production rate to
Ind. Eng. Chem. Res., Vol. 37, No. 7, 1998 2587
Figure 4. Change of combined polymer-melt and condensate masses, Pm(1) + Pc(1) (g), with time at four pyrolysis temperatures.
Figure 6. Effect of pyrolysis time on the MWD of the polymer melt, pm(x,t), at 400 °C pyrolysis temperature.
Figure 5. Change of cumulative gas-product mass, Ng (g), with time at four pyrolysis temperatures.
Figure 7. Change of the zeroth moment, Pm(0) (mol), of the polymer melt with time at four pyrolysis temperatures.
increase as the average MW decreased and smaller-MW molecules were produced. The condensate accumulation rate increases with the gas flow rate, as indicated by eqs 5, 9, 13, and 19. Higher flow rates cause the mass of the reactor melt to be smaller and the mass of the condensate to be larger. The influence of flow rate is greater at higher temperatures and longer reaction times. As the reaction temperature approaches the boiling point of the polymer melt, vaporization increases. In the absence of sweep gas flow we observed polymer-melt boiling at 430 °C, which is the upper temperature limit for the experiments. GC analysis of gaseous products indicated that the gas composition was independent of flow rate and was unchanged over the experimental ranges of temperatures and reaction times. This is further confirmation that gas is produced by chain-end scission occurring during the entire pyrolysis time. The averages of several analyses provided the mole fractions: 11% methane, 19% ethane, 22% propane, 20% butane, and 27% pentane. From molar composition the numberaverage MW of the gas was 38 ( 1. MWDs of polymer remaining in the reactor after different pyrolysis times at 400 °C are shown in Figure 6. The increase of polymer molecules of large MW is evident, demonstrating that repolymerization occurs. Polymer of lower MW is also produced by random scission (Figure 6) and after vaporizing is carried over into the condenser vessel. Similar behavior was re-
Table 1. Number- and Weight-Average Molecular Weights, Mnm, Mwm, Mnc, and Mwc, of Polymer Melt and Condensate, Respectively, at Experimental Reaction Times and Temperaturesa 0h
1h
2h
3h
Mnm Mwm Mnc Mwc Mnm Mwm Mnc Mwc Mnm Mwm Mnc Mwc Mnm Mwm Mnc Mwc
370 °C
390 °C
400 °C
410 °C
542 677 na na 524 665 395 469 571 771 406 511 581 773 354 428
542 677 na na 608 820 372 457 700 1021 409 495 816 1265 380 465
542 677 na na 590 792 366 456 703 979 352 431 840 1240 356 461
542 677 na na 635 848 337 398 705, 732 992, 1104 357, 335 432, 398 1159 2084 356 457
a Replicate values at 410 °C and 2 h indicate the uncertainty. At 0 h there is no condensate.
vealed by MWDs for other pyrolysis temperatures. The moles of reactor polymer, Pm(0), decrease with time (Figure 7), not only because low-MW products are vaporized but also because repolymerization occurs. The increase in the average MW (Table 1) indicates that the increase of polymer molecules by chain scission is more than compensated by the decrease due to repolymerization. Chain-end scission to produce gas products does not change the polymer molar concentration.15,16
2588 Ind. Eng. Chem. Res., Vol. 37, No. 7, 1998
Model Interpretation of Data
Figure 8. Effect of pyrolysis time on the MWD of condensate, pc(x,t), at 400 °C pyrolysis temperature.
The condensate MWD (Figure 8) reveals a symmetric increase of moles, supporting the notion that reaction products simply evaporate from the melt and without significant reaction condense in the cooled flask. Calculations by eq 13 show the vapor molar concentration is only 2% of the polymer melt molar concentration, which confirms the negligible contribution of vapor degradation. The moles of condensate, Pc(0), increase with time (Figure 9) due to accumulation of condensed vapor. The moles of mixed polymer and condensate, Pm(0) + Pc(0), are constant with time (Figure 10), as the decrease in Pm(0) is compensated by the increase in Pc(0). While not shown, MWDs of the mixture varied with time in an unsystematic manner, revealing a loss of information on mixing reactor polymer with condensate. MWDs also indicate that compensating effects diminish the observable effect of repolymerization on the higher-MW region for the mixed polymer and condensate. This justifies the two-vessel pyrolysis apparatus to recover condensate separately from the reactor melt. An experiment at 410 °C and 2-h reaction time was duplicated on different days to determine reproducibility. The replicate data (Figures 7, 9, and 10) indicated the maximum uncertainty in moles was (8%, due mainly to random errors in the GPC analysis. Branching in the HDPE polymer would cause an increased degradation rate in the early stages of pyrolysis, as already mentioned. Such an effect would be difficult to detect in the present experimental apparatus because up to 20 min is required for the reactor to reach the bath temperature. To suppress radical-chain reactions, an experiment at low temperature, 300 °C, was conducted for 3 h. For an activation energy of 31 kcal/mol, the chain-scission rate at 300 °C is less than 6% of the rate at 370 °C. Thermal initiation rates, which have much higher activation energies, would be even smaller13 and would produce negligible radicals. With this experiment we therefore expected to measure evaporation of low-MW polyethylene from the initial sample only. Indeed, the polymer-melt MWD indicated negligible chain scission and repolymerization. After the 3-h experiment, the reactor residue and condensate weights were 0.914 and 0.072 g/g of initial HDPE, and thus no gas was produced. The observations are consistent with the proposed overall interpretation of the experimental process.
Application of the proposed model to interpret experimental data requires a mass-transfer expression that allows MW moments to be formulated. We found that the vapor-liquid equilibrium constant could be represented by an inverse 6th-degree polynomial, K(x) ) K0/ (1 + a1x + a2x2 + a3x3 + a4x4 + a5x5 + a6x6). The coefficients ai, determined from the best fit to alkane phase-equilibrium data17 for K, are given in Table 2. Figure 11, 1/K versus x, demonstrates that the inverse polynomial correlates the data well. Parameters in the mass-transfer coefficient, κ(x) ) κ0 - κ1x, can be determined from correlations18,19 for liquid-to-bubble mass transfer. Values of κ0 are displayed in Table 3. In the present approach, explicit expressions for K(x) and κ(x) are not applied to the experimental data. Following application of the moment operation, masstransfer terms cancel when melt and condensate moment equations are added. Thus, numerical values of coefficients in the mass-transfer polynomial expressions will not directly affect final results or conclusions. Relative amounts of reactor residue and condensate, however, do depend on the mass-transfer rate and therefore on the sweep-gas flow rate. Density of the polyethylene was determined by heating 1.00 g of raw HDPE in a graduated conical tube and measuring the volume in the temperature range 151295 °C. The weight of the tube and contents did not change, indicating there are no vaporization losses in this temperature range. The density (g/cm3) as a function of temperature (°C) was fitted with a 2nddegree polynomial,
Fm ) 0.999-0.0016T + 2 × 10-6T2
(23)
and extrapolated to 410 °C to calculate polymer-melt volumes from melt mass (Figure 12). After an experiment, weights of reactor residue and condensate were determined by weighing reactor and condensate vessels with their contents and subtracting weights of the empty vessels. Polymer-melt volume as a function of time, Vm(t), was determined from reactor residue mass (Figure 2) and density (eq 23). Values of Vm versus time at four reaction temperatures (Figure 13) are well approximated by straight lines. The condensate volume, Vc(t), was calculated from condensate mass (Figure 3) and density, measured as 0.81 g/cm3. Values of Vc versus time at four reaction temperatures (Figure 14) are fitted with 2nd-order polynomials. The mass rate of gas production equals the loss rate of polymer. If Ng(t) represents cumulative moles of gas of MW, Mng, then the difference between the initial polymer mass and the sum of melt and condensate masses is
NgMng ) Pmo(1) - (Pm(1) + Pc(1))
(24)
where gas-product MW, Mng ) 38, was independent of temperature and pyrolysis time. Cumulative moles of gas product increase nearly linearly with time at all temperatures (Figure 5), in accord with
Ng ) Qpg(0)t
(25)
when Q and pg(0) are constant. The rate coefficient for gas production by chain-end scission was calculated
Ind. Eng. Chem. Res., Vol. 37, No. 7, 1998 2589 Table 2. Coefficients for the Vapor-Liquid Phase Equilibrium in the Inverse Polynomial K(x) ) K0/(1 + a1x + a2x2 + a3x3 + a4x4 + a5x5 + a6x6) T
K0
a1
a2
a3
a4
a5
a6
370 °C 390 °C 400 °C 410 °C
10.1 -115 -20.6 -12.1
-0.00711 -0.154 -0.0460 -0.0371
-0.000 370 0.004 19 0.000 832 0.000 555
6.58 × 10-6 -4.87 × 10-5 -7.90 × 10-6 -4.51 × 10-6
-4.12 × 10-8 2.65 × 10-7 3.87 × 10-8 1.99 × 10-8
1.16 × 10-10 -7.10 × 10-10 -9.86 × 10-11 -4.73 × 10-11
-1.14 × 10-13 6.81 × 10-13 9.20 × 10-14 4.24 × 10-14
Figure 9. Change of the zeroth moment, Pc(0) (mol), of the condensate with time at four pyrolysis temperatures.
Figure 11. Inverse of the vapor-liquid equilibrium coefficient, 1/K(x), as a function of MW for high-MW alkanes at four temperatures and fitted with 6th-degree polynomials. Table 3. Mass-Transfer Coefficients, K0 (cm/s), for Gas Bubbles in HDPE Melt at Three Temperatures According to Calderbank and Moo-Young18 and Hughmark19 Calderbank and Moo-Young Hughmark
370 °C
390 °C
410 °C
0.000 177 0.000 340
0.000 174 0.000 337
0.000 168 0.000 331
Figure 10. Zeroth moment, Pm(0) + Pc(0) (mol), of combined polymer melt and condensate which is constant with time at four pyrolysis temperatures.
from eqs 15 and 25, rewritten as
Ng/Pm(0) ) kst
(26)
Stated another way, the rate of loss of mass from the system equals the rate of generation of noncondensable gas by chain-end scission in the polymer melt. For the four temperatures, Figure 15 shows H ) Ng/ Pm(0) plotted versus t. As expected, slopes increase with temperature. At higher reaction times, however, the experimental points indicate an increasing slope. This implies that the reaction rate increased with time, which was not anticipated. Several possible causes are suggested. The increase might be caused by a catalytic effect of small amounts of coke that accumulate with time, especially at higher temperatures. Another possible contribution to increased noncondensable gas products could be random chain scission, which is accounted separately from chain-end scission. More likely, the accumulation of branched polyethylene formed by repolymerization9 would increase the radical con-
Figure 12. Polymer-melt density, Fm (g/cm3), as a function of temperature.
centration and thus accelerate the chain-end scission reaction rate.1 It is also possible that GPC measurement of MW is adversely affected by the presence of branched polyethylene. When all the data in Figure 15 are regressed as straight lines, the slopes yield an average value of ks at each temperature. The chain-end scission rate coefficient, in terms of its prefactor and activation energy, is expressed as
ks ) As exp(-Es/RT)
(27)
The energy of activation, Es ) 35 kcal/mol, and the prefactor, As ) 1.14 × 108 s-1, were determined from the Arrhenius plot (Figure 16), where ln ks is plotted
2590 Ind. Eng. Chem. Res., Vol. 37, No. 7, 1998
Figure 16. Arrhenius plot for a polyethylene chain-end scission rate coefficient. Figure 13. Change of polymer-melt volume, Vm (cm3), with time at four pyrolysis temperatures.
Figure 14. Change of condensate volume, Vc (cm3), with time at four pyrolysis temperatures.
Figure 15. Plot of H ) Ng/Pm(0) versus time at four pyrolysis temperatures. The slope of each line is the chain-end scission rate coefficient, ks.
versus 1/T. The effect of increasing slope on the rate coefficient can be reduced by considering smaller reaction times. If we use only 0-, 1-, and 2-h points in Figure 15, rate coefficients provide Arrhenius parameters of 20 kcal/mol and 1.33 × 103 s-1. According to eq 16, random scission and repolymerization rate coefficients, kd and ka, should be determinable from the intercept and slope, respectively, of the plot of (1/Pm(0)) d(Pm(0) + Pc(0))/dt versus pm(0). However, the polymer-melt molar concentration, pm(0) ) Pm(0)/Vm, was nearly constant at a given temperature, because
Pm(0) and Vm decrease proportionately. Consequently, uncertainties in the volume and zeroth moment produced poor regressions. Owing to the uncertainties inherent in the GPC of polyethylene with RI detection, we conclude that random scission and repolymerization rate coefficients cannot be determined from current experimental data. This conclusion is unchanged if the polymer-melt, zeroth-moment equation (eq 11) with its mass-transfer term is applied. The difficulty is in the rate expressions for random scission and repolymerization, which are 1st and 2nd-order, respectively, (kd kapm(0))pm(0). Evaluation of kd and ka requires highly accurate data for molar concentration, pm(0). If we consider that the random-scission rate coefficient increases linearly with MW, kd(x) ) kd1x, then the term involving kd in eq 7 is changed. The moment is increased by 1 order, thus, kd1pm(n+1)(n - 1)/(n + 1). This sole effect on the moment equations does not alter the results or conclusions. An approximate estimate of the chain-end scission rate coefficient can be determined from the mass of the polymer melt, Pm(1). By applying eq 22, we calculated an approximate rate coefficient, ks ap, at each reaction temperature from the slope of ln[Pm(1)(t)/Pm(1)(0)] versus time. The Arrhenius plot of these rate coefficients gave the activation energy of 31 kcal/mol and prefactor 1.35 × 106 s-1. Compared with other reports, these values are smaller than recommended values. For example, Westerhout et al.2 for HDPE suggested 50 kcal/mol and 1013 s-1. Owing to the compensating effects of the activation energies and prefactors, the value of ks ap for the current study would be identical with that of Westerhout et al.2 at about 340 °C. The reason for the difference in rates may be attributed to the different polyethylene samples and different reactors. Our bubbling-melt reactor is obviously unlike the typical thermogravimetric apparatus. Conclusions The analysis and results of this investigation are for a two-phase, plastics-pyrolysis process with polymer degradation occurring in the polymer melt. Lower-MW products of random scission volatilize by mass transfer and are condensed downstream. The driving force for mass transfer depends on the vapor-liquid equilibrium, for which volatility decreases with increasing MW. Capturing and analyzing the condensable vapors separately from the reactor polymer facilitates the analysis and interpretation of reaction data. The MWDs of polymer and condensate, determined by HPLC-GPC,
Ind. Eng. Chem. Res., Vol. 37, No. 7, 1998 2591
permit important features of the physical and chemical reaction processes to be better understood and interpreted. For example, MWDs show that random scission and repolymerization compensate each other, which cannot be perceived readily if experimental distributions are not available. The mathematical model applied to the experimental data was based on distribution kinetics, by which population-balance equations for MWDs are formulated as mass balances. These integrodifferential equations for melt, vapor, condensate, and gas were converted to ordinary differential equations by a MW-moment method. The resulting set of equations could be used to interpret the experimental data, although random scission and repolymerization rate coefficients could not be determined. A separate chainend scission process produces low-MW noncondensable gases (C1-C5) of average MW 38. The chain-end scission rate coefficient, ks ) As exp(-Es/RT), was computed from data at different temperatures, yielding Es ) 35 kcal/mol and As ) 1.14 × 108 s-1 for HDPE. Approximate rate parameters, based on an empirical rate expression first-order in reactant mass, were found to be 31 kcal/mol and 1.35 × 106 s-1. Compared to other approaches, this study provides a more detailed description of pyrolysis. The reactor apparatus and analytical instrumentation are more complex than is typical for pyrolysis. More data are available for analysis, which requires a more comprehensive mathematical model for interpretation. The model provides a framework for understanding the significant processes in polymer-melt pyrolysis: random scission and repolymerization, chain-end scission, and evaporation of volatile depolymerization products. The approach has potential for application to other pyrolytic processes, including those enhanced by catalysis. Acknowledgment Financial support from the Scientific and Technical Research Council of Turkey for the visiting status of Dr. N. A. Sezgi and from the Korea Science and Engineering Foundation for Dr. W. S. Cha is gratefully acknowledged. Research funding by Pittsburgh Energy Technology Center Grant No. DOE DE-FG22-94PC94204 is acknowledged. We thank Dr. Giri Madras and Yoichi Kodera for helpful discussions and Ben Chal and Mike Darrett for assistance with experiments. Literature Cited (1) Wall, L. A. Pyrolysis of Polymers. In Pyrolysis of Polymers; Hilado, C. J., Ed.; Fire and Flammability Series; Technomic: Westport, CT, 1976; Vol. 13, p 67. (2) Westerhout, R. W. J.; Waanders, J.; Kuipers, J. A. M.; Van Swaaij, W. P. M. Kinetics of the Low-Temperature Pyrolysis of
Polyethene, Polypropene, and Polystyrene Modeling, Experimenal Determination, and Comparison with Literature Models and Data. Ind. Eng. Chem. Res. 1997a, 36, 1955. (3) Westerhout, R. W. J.; Balk, R. H. P.; Meijer, R.; Kuipers, J. A. M.; Van Swaaij, W. P. M. Examination and Evaluation of the Use of Screen Heaters for the Measurement of the High-Temperature Pyrolysis Kinetics of Polyethene and Polypropene. Ind. Eng. Chem. Res. 1997b, 36, 3360. (4) Westerhout, R. W. J.; Kuipers, J. A. M.; Van Swaaij, W. P. M. Development, Modelling and Evaluation of a (Laminar) Entrained Flow Reactor for the Determination of the Pyrolysis Kinetics of Polymers. Chem. Eng. Sci. 1996, 51, 2221. (5) Seeger, M.; Gritter, R. J. Thermal Decomposition and Volatilization of Poly(R-olefins). J. Polym. Sci. 1977, 15, 1393. (6) Ng, S. H.; Seoud, H.; Stanciulescu, M.; Sugimoto, Y. Conversion of Polyethylene to Transportation Fuels through Pyrolysis and Catalytic Cracking. Energy Fuels 1995, 9, 735. (7) Ishihara, Y.; Nanbu, H.; Ikemura, T.; Takesue, T. Catalytic Decomposition of Polyethylene Using a Tubular Flow Reactor System. Fuel 1990, 69, 978. (8) Ohkita, H.; Nishiyama, R.; Tochihara, Y.; Mizushima, T.; Kakuta, N.; Morioka, Y.; Ueno, A.; Namiki, Y.; Tanifuji, S.; Katoh, H.; Sunazuka, H.; Nakayama, R.; Kuroyanagi, T. Ind. Eng. Chem. Res. 1993, 32, 3112. (9) Johnston, R. T.; Morrison, E. J. Thermal Scission and CrossLinking during Polyethylene Melt Processing. In Polymer Durability; Clough, R. L., Billingham, N. C., Gillen, K. T., Eds.; ACS Symposium Series 249; American Chemical Society: Washington, DC, 1996; p 651. (10) Wang, M.; Smith, J. M.; McCoy, B. J. Continuous Kinetics for Thermal Degradation of Polymer in Solution. AIChE J. 1995, 41, 1521. (11) McCoy, B. J.; Madras, G. Degradation Kinetics of Polymers in Solution: Dynamics of Molecular Weight Distributions. AIChE J. 1997, 43, 802. (12) Madras, G.; Chung, G. Y.; Smith, J. M.; McCoy, B. J. Molecular Weight Effect on the Dynamics of Polystyrene Degradation. Ind. Eng. Chem. Res. 1997, 36, 2019. (13) Kodera, Y.; McCoy, B. J. Continuous-Distribution Kinetics of Radical Mechanisms for Polymer Decomposition and Repolymerization. AIChE J. 1997, 43, 3205. (14) Dotson, N. A.; Galvan, R.; Laurence, R. L.; Tirrell, M. Polymerization Process Modeling; VCH Publishers: New York, 1996. (15) Madras, G.; Smith, J. M.; McCoy, B. J. Degradation of Poly(methyl methacrylate) in Solution. Ind. Eng. Chem. Res. 1996a, 35, 1795. (16) Madras, G.; Smith, J. M.; McCoy, B. J. Thermal Degradation of Poly(R-methylstyrene) in Solution. Polym. Degrad. Stab. 1996b, 52, 349. (17) HYSYS Version 1.0, Integrated System of Engineering Software; Hyprotech Ltd.: Calgary, Canada, 1995. (18) Calderbank, P. H.; Moo-Young, M. B. The Continuous Phase and Mass-Transfer Properties of Dispersions. Chem. Eng. Sci. 1961, 16, 39. (19) Hughmark, G. A. Holdup and Mass Transfer in Bubble Columns. Ind. Eng. Chem. Process Des. Dev. 1967, 6, 218.
Received for review February 19, 1998 Revised manuscript received April 13, 1998 Accepted April 14, 1998 IE980106R
