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Transition between regimes in the degradation of thermoplastic polymers
Polymer Degradation and Stability 64 (1999) 359±367
Transition between regimes in the degradation of thermoplastic polymers Colomba Di Blasi1 Dipartimento di Ingegneria Chimica, Universita degli Studi di Napoli ``Federico II'' P.le V. Tecchio, 80125 Napoli, Italy Accepted 20 March 1998
Abstract The pyrolysis regimes of thermoplastic polymers (polyethylene) are examined through a mathematical model, including transport phenomena and chemical reactions. Depolymerization and melting are followed by devolatilization. Surface regression, property variation, heat convection and conduction are properly taken into account. Simulations are carried out for external heating conditions corresponding to ®xed-bed reactors, hot-plate contact and ®re-level radiation exposures. Only very slow external heat transfer rates, associated with low reactivity of the fuel, give rise to a pure kinetic control. For conditions of interest in ®xed-bed reactors and radiative heating, a transition from a thermally thin to a thermally thick regime is observed, as the sample size is increased. Two regimes can be established during hot-plate contact, namely an ablative regime or again a thermally thick regime, depending on the relative importance between internal heat transfer and chemical reaction kinetics. # 1999 Elsevier Science Ltd. All rights reserved. Keywords: Pyrolysis; Thermoplastic polymers; Modelling
1. Introduction The thermal and oxidative degradation of solids is important in the ®elds of ®re safety science and chemical reaction engineering. Indeed, the rates of solid devolatilization and/or charring are key parameters in the assessment of material ¯ammability and also largely determine the reactor size and throughput in the thermochemical conversion of biomass and plastic waste. In particular, pyrolysis, that is, the thermal decomposition of the solid fuel in the absence of oxidizing agents, is not only an independent process but also the ®rst step in combustion and gasi®cation. Pyrolysis reactions can be roughly identi®ed as primary solid degradation and secondary reactions of volatile products, which may occur within both the reacting solid and the heating/ reacting environment. Kinetic studies of the thermal degradation of charring and non-charring polymers can be classi®ed into three main groups [1]: 1. one step global models, based on weight loss curves, which assume a constant ratio between volatiles and char; 1
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2. multi-reaction models, where numerous reactions correlate product distributions (cellulosic fuels) or describe chain initiation, depropagation and termination paths (synthetic polymers); 3. semi-global models, which include both primary and secondary reactions and lump the pyrolysis products into three groups (tar, gas and char). Apart from the multi-reaction schemes developed for synthetic polymers, the above models are simpli®ed descriptions of thermal degradation kinetics, but semiglobal models are retained to be suitable for engineering applications. In general, the rupture of chemical bonds occurs according to a variety of mechanisms. For instance, three classes of synthetic polymers have been identi®ed [2]: (1) those which degrade completely with breaking of the main chain (melting or thermoplastic polymers with 99% volatile (alkenes) yields, i.e. PMMA); (2) those which undergo rupture of side fragments with the formation of both volatiles (aromatics) and char (PVC); (3) cross-linked polymers, whose main degradation product is char. On the other hand, cellulosic materials degrade through two main competitive pathways [3], ring scission and end-group depolymerization. The ®rst, leading to char and gas formation, is favoured at low temperatures (below 550±570 K), whereas the
0141-3910/99/$ - see front matter # 1999 Elsevier Science Ltd. All rights reserved. PII: S0141 -3 910(98)00134 -7
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second, leading to tar production, is favoured at higher temperatures. It should be noted that whether thermal degradation is the limiting step or not depends on the conversion conditions and the nature of the polymer. Primary solid degradation is strictly coupled to heat transfer, while secondary degradation is aected by both heat and mass transfer. Therefore, conversion characteristics and product distribution are, in general, the result of a strong interaction between chemical and physical processes. They are dependent on three main parameters: (1) the heating rate of the solid; (2) the residence time of the solid particles and the evolved pyrolysis products within the reaction environment, and (3) the reaction temperature, all dependent on numerous variables (nature of the solid fuel, particle size, reactor type, etc.). Slow-conventional pyrolysis of cellulosic materials (slow heating rates, low temperatures and long residence times) is applied to produce high char yields. Fast or ¯ash pyrolysis (very high heating rates) is associated with a high reduction in the solid residual yield. In this case, there could be two dierent objectives, that is, the production of a maximum gas or liquid yield. For both cellulosic [4] and plastic [5] waste, gas production processes are favoured by high temperatures and signi®cant volatile residence times, whereas processes for the attainment of high liquid yields should operate at low temperatures and reduced residence times. The speci®cation of the pyrolysis characteristics (fast or slow) does not correspond to the de®nition of the processes controlling the conversion, i.e., chemistry or heat and mass transfer. In this study conversion regimes of thermoplastic polymers are introduced and results of numerical simulations are presented for the single particle system directly and indirectly heated, as no detailed study is currently available for this class of fuels. 2. Thermal regimes The simplest approach in the de®nition of the thermal regimes of solid degradation should take into account the mechanisms of internal and external heat transfer and the chemical reaction. External heat transfer to the solid is always important and, in general, all the mechanisms (convection, radiation, conduction) contribute to a certain extent. Schematically, two main modalities of solid pyrolysis can be de®ned, on the basis of the prevalent heat transfer mechanisms, namely convective/radiative pyrolysis (indirect heating) or contact (ablative) pyrolysis (direct heating). The ®rst is usually established in ®xed-bed reactors and under ®re conditions. Heat transfer through conduction, by contact of the solid fuel with a hot surface or hot sand, takes place in ablative and circulating ¯uid-bed reactors. Furthermore, single-particle experiments on contact pyrolysis,
by means of the so-called hot-plate technique, were ®rst carried out by Shultz and Dekker [6], to simulate the high-temperature pyrolysis of propellants. Successive studies also considered some other synthetic polymers, with the main aim of investigating ¯ash pyrolysis kinetics. A ®rst-basis analysis of the dierent regimes can be made assuming a one-step global pyrolysis reaction and a pure heat conduction equation, which allow the characteristic times [7,8] to be de®ned in relation to: external convective heating (hc , external heat transfer coecient) %cp ; 1 tv hc external radiation (Qr , intensity of the radiative heat ¯ux, Ti , temperature dierence) Ti %cp ; 2 trad Qr hot-plate heating (hw , global heat transfer coecient) tw
%cp ; hw
3
internal conduction (l, thermal conductivity) tc
%cp 2 ; l
chemical reaction (rp , reaction rate) % tr rp
4
5
(% and cp are the density and speci®c heat of the solid, is a characteristic length which varies with the heating modality). Characteristic numbers can be introduced to de®ne the dierent regimes. The Biot number, Bi, is a measure of the importance of the internal heat conduction time with respect to the external heat transfer time. Thus, for the case of indirect (convection and radiation) and direct (hot plate contact) heating, it can be de®ned as: t c hc ; 6 Bi tv l tc Qr ; 7 Bi trad lTi tc hw : 8 Bi l tw Two limit conditions can be observed, depending on the values of the Bi number: (I) Bi 1, that is, the internal heat transfer rate is much faster than the external heat transfer rate and the thermal conversion process is dominated by the external heat transfer supply; (II) Bi 1, that is, the internal heat transfer rate is much slower than the external heat transfer rate and thus internal heat transfer is controlling. In order to determine the conversion regime, the characteristic heat transfer times should be compared
C. Di Blasi / Polymer Degradation and Stability 64 (1999) 359±367
with those associated with chemical reaction. For case (I) (Bi 1), the characteristic times of external heat transfer (the slowest process) should be compared with the characteristic reaction time. This is usually done through the Damkohler number, which for the cases of interest can be expressed as: tr hc ; t v r p cp tr %Qr ; Da trad rp Ti %cp tr hw : Da t w r p cp Da
9 10 11
Thus, for Bi 1, two regimes can be observed: (IA) the thermally thin regime (Bi 1 and Da 1), when conversion occurs under the external heat transfer control, (IB) the pure kinetic regime (Bi 1 and Da 1), when conversion occurs under the control of the chemical kinetics. For case (II) (Bi 1), the characteristic time associated with internal heat transfer (the slowest process) should be again compared with the characteristic time of chemical reaction. This is usually done by means of the thermal Thiele number: Th
tc %cp 2 =l rp 2 cp : tr l %=rp
12
Thus, for Bi 1, two regimes can be observed: (IIA) the thermally thick regime (Bi 1 and Th 1), when conversion occurs under the chemical kinetic control, (IIB) the ablation regime (Bi 1 and Th 1), when conversion occurs under the control of internal heat transfer. It is worth observing that the classi®cation given above is only qualitative because the exact de®nition of characteristic variables, i.e., characteristic length, reaction rate, etc., cannot be made a priori. Also, only the thermal eects have been roughly considered, but the role played by mass transfer, which is known to aect the extent of secondary reactions, in some cases may become controlling for both char and non-char forming polymers. In the following sections the thermal regimes of pyrolysis are discussed for a melting polymer, through numerical simulations of a detailed mathematical model. 3. Mathematical model The pyrolysis kinetics of polyethylene (PE), as representative of thermoplastic polymers, are considered. The mechanism is the same as in Di Blasi (1997) [9]. The ®rst step describes the formation of condensended-
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phase species, S , with a reduced degree of polymerization and no mass loss, while the second is pertinent to the devolatilization (V) process: S !k0 S !k1 V
13
(no distinction is made between condensable and noncondensable volatile products). The problem considers a one-dimensional slab (x is the spatial coordinate) heated on both sides. Given the symmetry of the problem only half particle is considered (initial half-thickness 0 ). The reduction in the degree of polymerization is associated with a phase change (from the solid to the molten state) but transport phenomena of the ¯uid phase are not taken into account (devolatilization is faster than mass transport). The most restrictive assumption is that of no resistance to mass transfer. This condition is usually met only for severe thermal conditions, when the reaction zone is very thin, thus facilitating the escape of volatile products [10]. Further assumptions are: no secondary reactions of volatile pyrolysis products, local thermal equilibrium, negligible accumulation of vapor mass and enthalpy in the condensed phase (this assumption is usually indicated as ``quasi-steady'' gas phase and has been shown [11] not to aect simulation results in the absence of secondary reactions). Properties vary linearly from the virgin polymer values to those of the molten phase, while the total volume decreases proportionally to the total condensed-phase mass (S and S ), that is, the regression rate is proportional to the degradation rate of S . The conservation equations are written for the virgin (S) and the molten phase S polymer as: @MS ÿK0 MS ; @t
14
@MS K0 MS ÿ K1 MS : @t
15
The total volume V (that is, the sample half-thickness ) decreases linearly with the mass of the condensed-phase species: V MS MS ; 16 V0 0 M0 where V0 0 and M0 are the initial volume and mass of the specimen. New condensed-phase densities are also evaluated as: %S MS =V; %S MS =V. The energy conservation, as in all models published to date, is written with the assumption of negligible kinetic and potential energy, by the replacement of internal energy with enthalpy and neglecting the enthalpy ¯ux due to species diusion: @T @ U%V T @ @T Q r ÿ cV l ; 17 s c s @t @x @x @x where
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Qr K0 %S hS K1 %S hS ;
18
l kS 1 ÿ kS ;
19
MS =M0 ;
20
%s cs %S cS %S cS
21
(l is the thermal conductivity, c the speci®c heat, U the volatile velocity and H the reaction enthalpy). The vapor mass ¯ux is determined from the continuity equation integrated along the sample length: x 22a %V U m K1 %S dx: 0
Thus, the volatile mass ¯ux, leaving the regreding surface of the solid, is: 22b ms K1 %S dx: 0
Initially, the specimen is at ambient conditions (T T0 ) and properties are those of the virgin polymer. The external heating conditions are varied so as to reproduce the dierent regimes and correspond to those usually achieved in ®xed-bed and ablative/circulating ¯uid-bed reactors and exposures to ®re-level heat ¯uxes. In the ®rst case (chemical reactors) the external heat transfer (x ) rate can be expressed by means of a global heat transfer coecient, hp , and the boundary condition for the enthalpy equation is: l @T ÿhp T ÿ Te ; 23a @x where Te is the temperature of the reacting environment. The expression of hp varies with the conversion unit. For ®xed-bed reactors the following correlation [12] is usually applied: hp
2:06cb %b Ub ÿ0:575 ÿ2=3 Re Pr ; b
4. Results Properties used for PE are the same as in Di Blasi (1997) [9]. The data for the ®rst-order depolymerization process (K0 ) are [14]: A 6:19 104 sÿ1 ; E 17 kcal/ mol, whereas the ®rst-order rate of the devolatilization process (K1 ) for medium density PE is described [15] by A 5:2 1011 sÿ1 and E 48 kcal/mol. These data clearly show that the ®rst reaction is not rate limiting. However, it is an arti®ce to describe variations in the physical properties (melting), taking place before devolatilization. Simulations have been carried out for heating conditions corresponding to ®xed-bed reactors (Eq. (23a)Eq. (24)) by varying the external temperature from 773 to 1273 K and for initial particle half thicknesses, , equal to 0.05 and 0.5 cm (the Re number is based on the initial particle size and the gas velocity through the bed is always taken equal to 100 cm/s). The in¯uence of the external heat transfer rate on the conversion process has been investigated for 0:5 cm through simulations which take into account the variation of the particle size in the ®xed-bed heat transfer coecient (Eq. (23a)Eq. (24)) and for radiative heating (Eq. (23b)) and external temperatures as above. Contact pyrolysis (Eq. (23a)Eq. (25)) has been simulated for 2:5 cm and the results compared with the case of ®xed-bed heating, carried out for the same particle size. Fig. 1 reports the weight loss curves for ®xed-bed heating, 0:5 cm and external temperatures in the range 873±1273 K (constant Re number). As expected, the conversion time becomes successively shorter as the external temperature is increased, but all curves are similar in shape. For low and intermediate conversion levels (50±60%), the global rate of degradation continuously increases with time, followed by almost instaneous
24
where Re and Pr are the Reynolds and Prandtl numbers, referred to the single particle, "b the porosity of the bed and cb , %b and Ub , the speci®c heat, the density and the velocity of the gas through the bed, respectively. For contact pyrolysis [13] it has been suggested: hp 0:0017p W=m2 K
25 5
7
where the applied pressure is in the range 10 ÿ 10 Pa. For radiative heating, the boundary conditions at x become: l @T ÿe T4 ÿ T4e : @x
23b
At x 0 it is assumed that the temperature gradient is zero, which corresponds to symmetry conditions. The moving boundary problem, described by Eqs. (14)±(23) is solved numerically through implicit, ®nitedierence approximations.
Fig. 1. Weight loss curves for ®xed-bed heating conditions ( 0:5 cm, Te in the range 873±1273 K).
C. Di Blasi / Polymer Degradation and Stability 64 (1999) 359±367
devolatilization of the remaining part of the fuel. This behavior can be easily explained through the spatial pro®les of temperature, densities (S and S ) and vapor mass ¯ux, m, which are qualitatively similar for external temperatures above 873 K. An example of the process dynamics is given in Figs. 2 and 3 for Te 1273 K and 0:5 cm. After a short transient, pertinent to the heating of a thin fuel layer below the heated surface, the process is characterized by the simultaneous propagation of a melting and a devolatilization front, resulting in the continuous regression of the surface exposed to heating. Apart from the initial and ®nal stages of the degradation process, the variations in the temperature at the regressing surface are small (temperatures varies from 821 K for t 35 s to 844 K for t=125 s), but the propagation of the reaction fronts along the particle thickness is highly unsteady. Indeed, the extension of the devolatilization region, identi®ed through the pro®les of the vapor mass ¯ux (values dierent from zero), enlarges and the temperature of the particle continuously increases. Thus, the vapor mass ¯ux leaving the particle surface, ms , also continuously increases with time. More precisely, for times shorter than 100 s, ms increases almost linearly, corresponding to the ®rst region of the weight loss curve. The size of the devolatilization zone becomes very large towards the end of the degradation process, that is, when particle heat-up conditions are attained. This process is associated with a very rapid increase in amount of volatile released in the gas phase and is responsible for the second region observed in the weight loss curves. It is possible that, at this stage, intra-particle mass transfer limitations are not negligible, as assumed in the mathematical treatment of the problem. The formation of the condensed-phase, reaction intermediate, S , becomes active for temperatures slightly
Fig. 2. Spatial pro®les of temperature for ®xed-bed heating, Te 1273 K and 0:5 cm.
363
Fig. 3. Spatial pro®les of volatile mass ¯ux (solid lines) and density (dashed lines) of species S for ®xed-bed heating, Te 1273 K and 0:5 cm.
above 400 K, a value close to the softening temperature of PE. Reduction in the degree of polymerization and variation in the physical properties reach completion for temperatures of about 620 K. The devolatilization process is much slower, with rates that attain signi®cant values only for temperatures of about 750 K. The large spatial gradients of temperature and the smooth devolatilization front indicate that, for 0:5 cm and external temperatures above 873 K, PE conversion takes place under the control of chemical kinetics and for conditions of internal heat transfer rates much slower than the external heat transfer rates, that is, in the thermally thick regime. It is worth noting that the process dynamics are qualitatively the same, and the increase in the external heat transfer rate results in higher temperatures at the solid surface (Fig. 4) and, on the average, with progressively higher regression rates. The particle dynamics for 0:5 cm are signi®cantly dierent from above, when the external temperature is below 873 K. An example, for Te 773 K, is shown in Figs. 5±7 through the spatial pro®les of temperature, density of species S and vapor mass ¯ux. Because of the reduced rate of external heat transfer, no signi®cant devolatilization takes place before the complete melting of the particle. This process is associated with the presence of a thermal front, propagating through the particle, that is, with a thermally thick regime. It is completed within the ®rst 180 s. For times slightly shorter (160 s) surface regression (devolatilization) begins and the spatial temperature gradients becomes negligible, though the temperature values continuously increase in time. Hence, the process occurs in a thermally thin regime. However, though spatial temperature variations are small, conversion is still characterized by the continuous regression of the surface, given the
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C. Di Blasi / Polymer Degradation and Stability 64 (1999) 359±367
Fig. 4. Surface temperature as a function of the time (referred to the time needed for conversion of 90%) under ®xed-bed heating conditions ( 0:5 cm, Te in the range 873 ÿ 1273 K).
Fig. 6. Spatial density pro®les of species S for ®xed-bed heating, Te 773 K and 0:5 cm.
exponential dependence of the devolatilization rate on temperature. Again, the process is highly unsteady, as shown by the pro®les of the vapor mass ¯ux. Apart from very short times, as a consequence of the thermally thin regime, the extension of the devolatilization region coincides with the whole particle thickness, but the values of ms go through a maximum. Indeed, at short times, they increase because of the increase in both the reaction temperature and the size of the devolatilization region. However, as the surface regression becomes signi®cant, the eects of the reduction in the size of the devolatilization region overcome those of temperature increase and ms decreases. External temperatures below 773 K are not of practical interest in thermochemical conversion processes, because of the reduced reactivity of the fuel and the case
discussed above can be considered as the limit condition in terms of thermal behavior. Therefore, in practical applications for external temperatures above 773 K and particle sizes above 1 cm conversion takes place in a thermally thick regime. The case of smaller particle sizes should also be examined because it can be expected that, when the size of the melting region becomes large, the particle will not retain the original shape and the size of the melting and reacting regions can be signi®cantly smaller than predicted by the model. Spatial gradients are successively reduced as the particle is made thinner. This clearly appears from the pro®les of temperature and density of S , reported Fig. 8 and obtained for 0:05 cm and Te 1273 K, when compared with the corresponding case obtained for 0:5 cm (Figs. 2 and 3). The process can be divided
Fig. 5. Spatial pro®les of temperature for ®xed-bed heating, Te 773 K and 0:5 cm.
Fig. 7. Spatial pro®les of volatile mass ¯ux for ®xed-bed heating, Te 773 K and 0:5 cm.
C. Di Blasi / Polymer Degradation and Stability 64 (1999) 359±367
365
Fig. 8. Spatial pro®les of temperature and density of species S for ®xed-bed heating, Te 1273 K and 0:05 cm.
Fig. 10. Spatial pro®les of volatile mass ¯ux for ®xed-bed heating, Te 773 K and 0:05 cm.
into two stages. In the ®rst, melting and devolatilization take place simultaneously and are associated with signi®cant spatial temperature gradients (thermally thick regime). In the second, devolatilization of the already melted polymer takes place, with low spatial temperature variations (thermally thin regime), though devolatilization still occurs with the propagation of a regression front. The dynamics of a thin particle ( 0:05 cm) under ®xed-bed heating conditions and low temperature (773 K) are shown through Figs. 9 and 10, in terms of spatial pro®les of temperature and vapor mass ¯ux. Similar to the case of 0:5 cm, particle heating and melting take place in the presence of relatively large spatial temperature gradients. Again, devolatilization, starting for times of about 5 s, takes place with no signi®cant spatial
temperature gradients but, in this case, variations of temperature with time are also very small (for the whole duration of the devolatilization process the particle temperature varies from 750 to 765 K). From the thermal point of view, this behavior can be associated with a pure kinetic control, though this is not rigorously true, as devolatilization is still associated with the existence of a regression front. However, the size of the devolatilization region always coincides with the whole particle thickness and ms decreases linearly as time increases. Extensive simulations have not been carried out, but it is expected that conversion under pure kinetic control requires particles even smaller than 1 mm, a condition of no interest in ®xed-bed conversion. The conversion regime is highly dependent on the external heating conditions. As for ®xed-bed heating, it should be noted that the characteristic particle size does not remain constant in the expression for the global heat transfer coecient, but it continuously decreases as a consequence of the conversion process. Also, the heating conditions of ®xed-bed reactors can be signi®cantly dierent from particle exposure to radiation, which is the main external heat transfer mechanism during ®res. A comparison for these dierent conditions is given in Fig. 11, through the weight loss curves in the temperature range 973±1273 K, as simulated for 0:5 cm and ®xed-bed conditions with the initial particle size (a) and with the current particle size (b) in the Re number (Eq. (24)) and radiative heating (c). No dierence is seen between cases (a) and (b) for small conversion levels, but the process is on the whole faster for case (b). The weight loss curves, simulated for radiative heating, are similar in shape to the cases of ®xed-bed heating, though the characteristics times of the process are different, mainly for low and high temperatures. At low temperature, radiative heating results in slower external
Fig. 9. Spatial pro®les of temperature for ®xed-bed heating, Te 773 K and 0:05 cm.
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C. Di Blasi / Polymer Degradation and Stability 64 (1999) 359±367
Fig. 11. Weight loss curves for ®xed-bed heating conditions with constant (a, solid lines) and variable (b, dashed lines) particle size in the Eq. (24) for the heat transfer coecient and for radiative heating (c, dashed-dotted lines) ( 0:5 cm, Te in the range 973 ÿ 1273 K).
Fig. 12. Spatial pro®les of temperature for several times for ®xed-bed heating (dashed lines, hp given by Eq. (24)) and ablative pyrolysis (solid lines, hp 0:4 cal/cm2s, eqn. Eq. (25)), for Te 1273 K and 2:5 cm.
heat transfer rates, whereas the contrary is observed at high temperatures. However, given the large sample sizes of interest in ®re conditions, it can be understood that no signi®cant variation should be expected in the thermal conversion regimes. The case of conversion in the ablative regime (values of the external heat ¯uxes typical of ablative/circulating ¯uid-bed reactors or hot plate contact) is only brie¯y analyzed here, mainly with the purpose of a comparison with the case of ®xed-bed heating, as ablative pyrolysis has already been discussed in detail elsewhere [7,16]. The dynamics of the temperature ®eld, for hp 0:4 cal/ cm2 K, 2:5 cm and Te 1273 K, are shown in Fig. 12, where the case of ®xed-bed heating is also included. Though, for both cases and times suciently dierent from the beginning and the completion of the process, the regression front propagates with an almost constant rate, the values of this variable as well as the temperature at the surface are highly dierent (values of the regression rate are about 26 times slower and surface temperatures about 300 K lower for ®xed-bed heating). Furthermore, while for the case of ®xed-bed heating, the process is unsteady, because of a continuous increase in the extension of the vaporizing region and thus in the amount of volatiles evolved from the sample (thermally thick regime), high external heat transfer rates (ablative regime) give rise to a truly quasisteady process. Indeed, the thermal and the reacting waves propagate through the solid at a uniform rate, which is established after very short transients, associated with the beginning of the conversion process. The thickness of the reaction layers remains constant for the whole duration of sample conversion. As expected, ®nite thicknesses eects become important towards the completion of the process, when degradation takes place
along the remaining part of the sample. Also, the (maximum) temperature attained by the molten intermediate at the sample surface, Ts , is lower than Te and it is maintained until complete conversion. The process remains qualitatively the same as Te is decreased, but the surface temperature becomes successively lower and the reaction zone thicker, so that a thermally thick regime is again possible for low external temperatures. A reduction in the applied pressure also causes a transition from the ablative to the thermally thick regime. Another important observation is that in the ablative regime, the particle size does not aect the conversion regime, as long as it is larger than the size of the reaction zone. 5. Conclusions A numerical model has been developed to investigate the dierent regimes and characteristics of thermoplastic material pyrolysis for both indirect and direct external heating. For external heating rates and particle sizes of interest in ®xed-bed reactors and ®re conditions, pyrolysis takes place in a thermally thick or a thermally thin regime. Though for conditions far from the initial and ®nal transients, the surface regression rate may show only small variations, the process is never quasisteady, because the size of the reaction zone continuously varies in time. Also, a pure kinetic regime is never achieved, unless temperatures associated with very slow reactivity of the material are considered. High external heat transfer rates (hot-plate contact, ablative reactors) give rise to particle conversion in the ablative regime, through a quasi-steady process. Indeed, a constant-size, very thin reaction zone is seen to propagate
C. Di Blasi / Polymer Degradation and Stability 64 (1999) 359±367
with a constant rate through the virgin solid. However, reductions in the applied pressure and /or temperature again result in a thermally thick regime. Further developments should take into account the description of mass transfer limitations in the evolution of pyrolysis products. Indeed, the dynamics of volatile bubble formation and migration through the molten layer of the degrading particle as well as intra- and extra-particle activity of secondary reactions may be important processes in product distribution, mainly for slow heating rates. Furthermore, the extension of single particle models to the treatment of chemical reactors should be considered. References [1] Di Blasi C. Progress in Energy and Combustion Science 1993;19:71.
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[2] Kashiwagi T. Twenty-Fifth Symposium (Int.) on Combustion. Pittsburgh: The Combustion Institute, 1994. p.1423. [3] Sha®zadeh F. The chemistry of pyrolysis and combustion. In: Rowell R, editors. The chemistry of solid wood, Advances in Chemistry Series 207. Washington, DC: American Chemical Society, 1984. [4] Scott DS, Piskorz J, Bergougnou MA, Graham R, Overend RP. Ind Eng Chem Res 1988;27:8. [5] Scott DS, Czernik SR, Piskorz J, Radlein D. Energy and Fuels 1990;4:407. [6] Schultz RD, Dekker AO, Fifth (Int.) Symposium on Combustion. New York: Reinhold, 1955. p.260. [7] Lede J. Biomass and Bioenergy 1994;7:49. [8] Di Blasi C. Ind Eng Chem Res 1996;35:37. [9] Di Blasi C. J Anal Appl Pyrolysis 1997;40-41:463. [10] Hertzberg M, Zlochower IA, Combustion and Flame 1991;84:14. [11] Di Blasi C. Fuel 1996;75:58. [12] Yoon H, Wei J, Denn MM. AIChE J 1978;24:885. [13] Lede J, Panagopoulos J, Li HZ, Villermaux J. Fuel 1985;64:1514. [14] Baer AD. J. Fire and Flammability 1981;12:214. [15] Madorsky SL. J Polymer Sci 1952;9:133. [16] Di Blasi C. Chem Eng Sci 1996;51:2211.
Transition between regimes in the degradation of thermoplastic polymers Colomba Di Blasi1 Dipartimento di Ingegneria Chimica, Universita degli Studi di Napoli ``Federico II'' P.le V. Tecchio, 80125 Napoli, Italy Accepted 20 March 1998
Abstract The pyrolysis regimes of thermoplastic polymers (polyethylene) are examined through a mathematical model, including transport phenomena and chemical reactions. Depolymerization and melting are followed by devolatilization. Surface regression, property variation, heat convection and conduction are properly taken into account. Simulations are carried out for external heating conditions corresponding to ®xed-bed reactors, hot-plate contact and ®re-level radiation exposures. Only very slow external heat transfer rates, associated with low reactivity of the fuel, give rise to a pure kinetic control. For conditions of interest in ®xed-bed reactors and radiative heating, a transition from a thermally thin to a thermally thick regime is observed, as the sample size is increased. Two regimes can be established during hot-plate contact, namely an ablative regime or again a thermally thick regime, depending on the relative importance between internal heat transfer and chemical reaction kinetics. # 1999 Elsevier Science Ltd. All rights reserved. Keywords: Pyrolysis; Thermoplastic polymers; Modelling
1. Introduction The thermal and oxidative degradation of solids is important in the ®elds of ®re safety science and chemical reaction engineering. Indeed, the rates of solid devolatilization and/or charring are key parameters in the assessment of material ¯ammability and also largely determine the reactor size and throughput in the thermochemical conversion of biomass and plastic waste. In particular, pyrolysis, that is, the thermal decomposition of the solid fuel in the absence of oxidizing agents, is not only an independent process but also the ®rst step in combustion and gasi®cation. Pyrolysis reactions can be roughly identi®ed as primary solid degradation and secondary reactions of volatile products, which may occur within both the reacting solid and the heating/ reacting environment. Kinetic studies of the thermal degradation of charring and non-charring polymers can be classi®ed into three main groups [1]: 1. one step global models, based on weight loss curves, which assume a constant ratio between volatiles and char; 1
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2. multi-reaction models, where numerous reactions correlate product distributions (cellulosic fuels) or describe chain initiation, depropagation and termination paths (synthetic polymers); 3. semi-global models, which include both primary and secondary reactions and lump the pyrolysis products into three groups (tar, gas and char). Apart from the multi-reaction schemes developed for synthetic polymers, the above models are simpli®ed descriptions of thermal degradation kinetics, but semiglobal models are retained to be suitable for engineering applications. In general, the rupture of chemical bonds occurs according to a variety of mechanisms. For instance, three classes of synthetic polymers have been identi®ed [2]: (1) those which degrade completely with breaking of the main chain (melting or thermoplastic polymers with 99% volatile (alkenes) yields, i.e. PMMA); (2) those which undergo rupture of side fragments with the formation of both volatiles (aromatics) and char (PVC); (3) cross-linked polymers, whose main degradation product is char. On the other hand, cellulosic materials degrade through two main competitive pathways [3], ring scission and end-group depolymerization. The ®rst, leading to char and gas formation, is favoured at low temperatures (below 550±570 K), whereas the
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second, leading to tar production, is favoured at higher temperatures. It should be noted that whether thermal degradation is the limiting step or not depends on the conversion conditions and the nature of the polymer. Primary solid degradation is strictly coupled to heat transfer, while secondary degradation is aected by both heat and mass transfer. Therefore, conversion characteristics and product distribution are, in general, the result of a strong interaction between chemical and physical processes. They are dependent on three main parameters: (1) the heating rate of the solid; (2) the residence time of the solid particles and the evolved pyrolysis products within the reaction environment, and (3) the reaction temperature, all dependent on numerous variables (nature of the solid fuel, particle size, reactor type, etc.). Slow-conventional pyrolysis of cellulosic materials (slow heating rates, low temperatures and long residence times) is applied to produce high char yields. Fast or ¯ash pyrolysis (very high heating rates) is associated with a high reduction in the solid residual yield. In this case, there could be two dierent objectives, that is, the production of a maximum gas or liquid yield. For both cellulosic [4] and plastic [5] waste, gas production processes are favoured by high temperatures and signi®cant volatile residence times, whereas processes for the attainment of high liquid yields should operate at low temperatures and reduced residence times. The speci®cation of the pyrolysis characteristics (fast or slow) does not correspond to the de®nition of the processes controlling the conversion, i.e., chemistry or heat and mass transfer. In this study conversion regimes of thermoplastic polymers are introduced and results of numerical simulations are presented for the single particle system directly and indirectly heated, as no detailed study is currently available for this class of fuels. 2. Thermal regimes The simplest approach in the de®nition of the thermal regimes of solid degradation should take into account the mechanisms of internal and external heat transfer and the chemical reaction. External heat transfer to the solid is always important and, in general, all the mechanisms (convection, radiation, conduction) contribute to a certain extent. Schematically, two main modalities of solid pyrolysis can be de®ned, on the basis of the prevalent heat transfer mechanisms, namely convective/radiative pyrolysis (indirect heating) or contact (ablative) pyrolysis (direct heating). The ®rst is usually established in ®xed-bed reactors and under ®re conditions. Heat transfer through conduction, by contact of the solid fuel with a hot surface or hot sand, takes place in ablative and circulating ¯uid-bed reactors. Furthermore, single-particle experiments on contact pyrolysis,
by means of the so-called hot-plate technique, were ®rst carried out by Shultz and Dekker [6], to simulate the high-temperature pyrolysis of propellants. Successive studies also considered some other synthetic polymers, with the main aim of investigating ¯ash pyrolysis kinetics. A ®rst-basis analysis of the dierent regimes can be made assuming a one-step global pyrolysis reaction and a pure heat conduction equation, which allow the characteristic times [7,8] to be de®ned in relation to: external convective heating (hc , external heat transfer coecient) %cp ; 1 tv hc external radiation (Qr , intensity of the radiative heat ¯ux, Ti , temperature dierence) Ti %cp ; 2 trad Qr hot-plate heating (hw , global heat transfer coecient) tw
%cp ; hw
3
internal conduction (l, thermal conductivity) tc
%cp 2 ; l
chemical reaction (rp , reaction rate) % tr rp
4
5
(% and cp are the density and speci®c heat of the solid, is a characteristic length which varies with the heating modality). Characteristic numbers can be introduced to de®ne the dierent regimes. The Biot number, Bi, is a measure of the importance of the internal heat conduction time with respect to the external heat transfer time. Thus, for the case of indirect (convection and radiation) and direct (hot plate contact) heating, it can be de®ned as: t c hc ; 6 Bi tv l tc Qr ; 7 Bi trad lTi tc hw : 8 Bi l tw Two limit conditions can be observed, depending on the values of the Bi number: (I) Bi 1, that is, the internal heat transfer rate is much faster than the external heat transfer rate and the thermal conversion process is dominated by the external heat transfer supply; (II) Bi 1, that is, the internal heat transfer rate is much slower than the external heat transfer rate and thus internal heat transfer is controlling. In order to determine the conversion regime, the characteristic heat transfer times should be compared
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with those associated with chemical reaction. For case (I) (Bi 1), the characteristic times of external heat transfer (the slowest process) should be compared with the characteristic reaction time. This is usually done through the Damkohler number, which for the cases of interest can be expressed as: tr hc ; t v r p cp tr %Qr ; Da trad rp Ti %cp tr hw : Da t w r p cp Da
9 10 11
Thus, for Bi 1, two regimes can be observed: (IA) the thermally thin regime (Bi 1 and Da 1), when conversion occurs under the external heat transfer control, (IB) the pure kinetic regime (Bi 1 and Da 1), when conversion occurs under the control of the chemical kinetics. For case (II) (Bi 1), the characteristic time associated with internal heat transfer (the slowest process) should be again compared with the characteristic time of chemical reaction. This is usually done by means of the thermal Thiele number: Th
tc %cp 2 =l rp 2 cp : tr l %=rp
12
Thus, for Bi 1, two regimes can be observed: (IIA) the thermally thick regime (Bi 1 and Th 1), when conversion occurs under the chemical kinetic control, (IIB) the ablation regime (Bi 1 and Th 1), when conversion occurs under the control of internal heat transfer. It is worth observing that the classi®cation given above is only qualitative because the exact de®nition of characteristic variables, i.e., characteristic length, reaction rate, etc., cannot be made a priori. Also, only the thermal eects have been roughly considered, but the role played by mass transfer, which is known to aect the extent of secondary reactions, in some cases may become controlling for both char and non-char forming polymers. In the following sections the thermal regimes of pyrolysis are discussed for a melting polymer, through numerical simulations of a detailed mathematical model. 3. Mathematical model The pyrolysis kinetics of polyethylene (PE), as representative of thermoplastic polymers, are considered. The mechanism is the same as in Di Blasi (1997) [9]. The ®rst step describes the formation of condensended-
361
phase species, S , with a reduced degree of polymerization and no mass loss, while the second is pertinent to the devolatilization (V) process: S !k0 S !k1 V
13
(no distinction is made between condensable and noncondensable volatile products). The problem considers a one-dimensional slab (x is the spatial coordinate) heated on both sides. Given the symmetry of the problem only half particle is considered (initial half-thickness 0 ). The reduction in the degree of polymerization is associated with a phase change (from the solid to the molten state) but transport phenomena of the ¯uid phase are not taken into account (devolatilization is faster than mass transport). The most restrictive assumption is that of no resistance to mass transfer. This condition is usually met only for severe thermal conditions, when the reaction zone is very thin, thus facilitating the escape of volatile products [10]. Further assumptions are: no secondary reactions of volatile pyrolysis products, local thermal equilibrium, negligible accumulation of vapor mass and enthalpy in the condensed phase (this assumption is usually indicated as ``quasi-steady'' gas phase and has been shown [11] not to aect simulation results in the absence of secondary reactions). Properties vary linearly from the virgin polymer values to those of the molten phase, while the total volume decreases proportionally to the total condensed-phase mass (S and S ), that is, the regression rate is proportional to the degradation rate of S . The conservation equations are written for the virgin (S) and the molten phase S polymer as: @MS ÿK0 MS ; @t
14
@MS K0 MS ÿ K1 MS : @t
15
The total volume V (that is, the sample half-thickness ) decreases linearly with the mass of the condensed-phase species: V MS MS ; 16 V0 0 M0 where V0 0 and M0 are the initial volume and mass of the specimen. New condensed-phase densities are also evaluated as: %S MS =V; %S MS =V. The energy conservation, as in all models published to date, is written with the assumption of negligible kinetic and potential energy, by the replacement of internal energy with enthalpy and neglecting the enthalpy ¯ux due to species diusion: @T @ U%V T @ @T Q r ÿ cV l ; 17 s c s @t @x @x @x where
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Qr K0 %S hS K1 %S hS ;
18
l kS 1 ÿ kS ;
19
MS =M0 ;
20
%s cs %S cS %S cS
21
(l is the thermal conductivity, c the speci®c heat, U the volatile velocity and H the reaction enthalpy). The vapor mass ¯ux is determined from the continuity equation integrated along the sample length: x 22a %V U m K1 %S dx: 0
Thus, the volatile mass ¯ux, leaving the regreding surface of the solid, is: 22b ms K1 %S dx: 0
Initially, the specimen is at ambient conditions (T T0 ) and properties are those of the virgin polymer. The external heating conditions are varied so as to reproduce the dierent regimes and correspond to those usually achieved in ®xed-bed and ablative/circulating ¯uid-bed reactors and exposures to ®re-level heat ¯uxes. In the ®rst case (chemical reactors) the external heat transfer (x ) rate can be expressed by means of a global heat transfer coecient, hp , and the boundary condition for the enthalpy equation is: l @T ÿhp T ÿ Te ; 23a @x where Te is the temperature of the reacting environment. The expression of hp varies with the conversion unit. For ®xed-bed reactors the following correlation [12] is usually applied: hp
2:06cb %b Ub ÿ0:575 ÿ2=3 Re Pr ; b
4. Results Properties used for PE are the same as in Di Blasi (1997) [9]. The data for the ®rst-order depolymerization process (K0 ) are [14]: A 6:19 104 sÿ1 ; E 17 kcal/ mol, whereas the ®rst-order rate of the devolatilization process (K1 ) for medium density PE is described [15] by A 5:2 1011 sÿ1 and E 48 kcal/mol. These data clearly show that the ®rst reaction is not rate limiting. However, it is an arti®ce to describe variations in the physical properties (melting), taking place before devolatilization. Simulations have been carried out for heating conditions corresponding to ®xed-bed reactors (Eq. (23a)Eq. (24)) by varying the external temperature from 773 to 1273 K and for initial particle half thicknesses, , equal to 0.05 and 0.5 cm (the Re number is based on the initial particle size and the gas velocity through the bed is always taken equal to 100 cm/s). The in¯uence of the external heat transfer rate on the conversion process has been investigated for 0:5 cm through simulations which take into account the variation of the particle size in the ®xed-bed heat transfer coecient (Eq. (23a)Eq. (24)) and for radiative heating (Eq. (23b)) and external temperatures as above. Contact pyrolysis (Eq. (23a)Eq. (25)) has been simulated for 2:5 cm and the results compared with the case of ®xed-bed heating, carried out for the same particle size. Fig. 1 reports the weight loss curves for ®xed-bed heating, 0:5 cm and external temperatures in the range 873±1273 K (constant Re number). As expected, the conversion time becomes successively shorter as the external temperature is increased, but all curves are similar in shape. For low and intermediate conversion levels (50±60%), the global rate of degradation continuously increases with time, followed by almost instaneous
24
where Re and Pr are the Reynolds and Prandtl numbers, referred to the single particle, "b the porosity of the bed and cb , %b and Ub , the speci®c heat, the density and the velocity of the gas through the bed, respectively. For contact pyrolysis [13] it has been suggested: hp 0:0017p W=m2 K
25 5
7
where the applied pressure is in the range 10 ÿ 10 Pa. For radiative heating, the boundary conditions at x become: l @T ÿe T4 ÿ T4e : @x
23b
At x 0 it is assumed that the temperature gradient is zero, which corresponds to symmetry conditions. The moving boundary problem, described by Eqs. (14)±(23) is solved numerically through implicit, ®nitedierence approximations.
Fig. 1. Weight loss curves for ®xed-bed heating conditions ( 0:5 cm, Te in the range 873±1273 K).
C. Di Blasi / Polymer Degradation and Stability 64 (1999) 359±367
devolatilization of the remaining part of the fuel. This behavior can be easily explained through the spatial pro®les of temperature, densities (S and S ) and vapor mass ¯ux, m, which are qualitatively similar for external temperatures above 873 K. An example of the process dynamics is given in Figs. 2 and 3 for Te 1273 K and 0:5 cm. After a short transient, pertinent to the heating of a thin fuel layer below the heated surface, the process is characterized by the simultaneous propagation of a melting and a devolatilization front, resulting in the continuous regression of the surface exposed to heating. Apart from the initial and ®nal stages of the degradation process, the variations in the temperature at the regressing surface are small (temperatures varies from 821 K for t 35 s to 844 K for t=125 s), but the propagation of the reaction fronts along the particle thickness is highly unsteady. Indeed, the extension of the devolatilization region, identi®ed through the pro®les of the vapor mass ¯ux (values dierent from zero), enlarges and the temperature of the particle continuously increases. Thus, the vapor mass ¯ux leaving the particle surface, ms , also continuously increases with time. More precisely, for times shorter than 100 s, ms increases almost linearly, corresponding to the ®rst region of the weight loss curve. The size of the devolatilization zone becomes very large towards the end of the degradation process, that is, when particle heat-up conditions are attained. This process is associated with a very rapid increase in amount of volatile released in the gas phase and is responsible for the second region observed in the weight loss curves. It is possible that, at this stage, intra-particle mass transfer limitations are not negligible, as assumed in the mathematical treatment of the problem. The formation of the condensed-phase, reaction intermediate, S , becomes active for temperatures slightly
Fig. 2. Spatial pro®les of temperature for ®xed-bed heating, Te 1273 K and 0:5 cm.
363
Fig. 3. Spatial pro®les of volatile mass ¯ux (solid lines) and density (dashed lines) of species S for ®xed-bed heating, Te 1273 K and 0:5 cm.
above 400 K, a value close to the softening temperature of PE. Reduction in the degree of polymerization and variation in the physical properties reach completion for temperatures of about 620 K. The devolatilization process is much slower, with rates that attain signi®cant values only for temperatures of about 750 K. The large spatial gradients of temperature and the smooth devolatilization front indicate that, for 0:5 cm and external temperatures above 873 K, PE conversion takes place under the control of chemical kinetics and for conditions of internal heat transfer rates much slower than the external heat transfer rates, that is, in the thermally thick regime. It is worth noting that the process dynamics are qualitatively the same, and the increase in the external heat transfer rate results in higher temperatures at the solid surface (Fig. 4) and, on the average, with progressively higher regression rates. The particle dynamics for 0:5 cm are signi®cantly dierent from above, when the external temperature is below 873 K. An example, for Te 773 K, is shown in Figs. 5±7 through the spatial pro®les of temperature, density of species S and vapor mass ¯ux. Because of the reduced rate of external heat transfer, no signi®cant devolatilization takes place before the complete melting of the particle. This process is associated with the presence of a thermal front, propagating through the particle, that is, with a thermally thick regime. It is completed within the ®rst 180 s. For times slightly shorter (160 s) surface regression (devolatilization) begins and the spatial temperature gradients becomes negligible, though the temperature values continuously increase in time. Hence, the process occurs in a thermally thin regime. However, though spatial temperature variations are small, conversion is still characterized by the continuous regression of the surface, given the
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C. Di Blasi / Polymer Degradation and Stability 64 (1999) 359±367
Fig. 4. Surface temperature as a function of the time (referred to the time needed for conversion of 90%) under ®xed-bed heating conditions ( 0:5 cm, Te in the range 873 ÿ 1273 K).
Fig. 6. Spatial density pro®les of species S for ®xed-bed heating, Te 773 K and 0:5 cm.
exponential dependence of the devolatilization rate on temperature. Again, the process is highly unsteady, as shown by the pro®les of the vapor mass ¯ux. Apart from very short times, as a consequence of the thermally thin regime, the extension of the devolatilization region coincides with the whole particle thickness, but the values of ms go through a maximum. Indeed, at short times, they increase because of the increase in both the reaction temperature and the size of the devolatilization region. However, as the surface regression becomes signi®cant, the eects of the reduction in the size of the devolatilization region overcome those of temperature increase and ms decreases. External temperatures below 773 K are not of practical interest in thermochemical conversion processes, because of the reduced reactivity of the fuel and the case
discussed above can be considered as the limit condition in terms of thermal behavior. Therefore, in practical applications for external temperatures above 773 K and particle sizes above 1 cm conversion takes place in a thermally thick regime. The case of smaller particle sizes should also be examined because it can be expected that, when the size of the melting region becomes large, the particle will not retain the original shape and the size of the melting and reacting regions can be signi®cantly smaller than predicted by the model. Spatial gradients are successively reduced as the particle is made thinner. This clearly appears from the pro®les of temperature and density of S , reported Fig. 8 and obtained for 0:05 cm and Te 1273 K, when compared with the corresponding case obtained for 0:5 cm (Figs. 2 and 3). The process can be divided
Fig. 5. Spatial pro®les of temperature for ®xed-bed heating, Te 773 K and 0:5 cm.
Fig. 7. Spatial pro®les of volatile mass ¯ux for ®xed-bed heating, Te 773 K and 0:5 cm.
C. Di Blasi / Polymer Degradation and Stability 64 (1999) 359±367
365
Fig. 8. Spatial pro®les of temperature and density of species S for ®xed-bed heating, Te 1273 K and 0:05 cm.
Fig. 10. Spatial pro®les of volatile mass ¯ux for ®xed-bed heating, Te 773 K and 0:05 cm.
into two stages. In the ®rst, melting and devolatilization take place simultaneously and are associated with signi®cant spatial temperature gradients (thermally thick regime). In the second, devolatilization of the already melted polymer takes place, with low spatial temperature variations (thermally thin regime), though devolatilization still occurs with the propagation of a regression front. The dynamics of a thin particle ( 0:05 cm) under ®xed-bed heating conditions and low temperature (773 K) are shown through Figs. 9 and 10, in terms of spatial pro®les of temperature and vapor mass ¯ux. Similar to the case of 0:5 cm, particle heating and melting take place in the presence of relatively large spatial temperature gradients. Again, devolatilization, starting for times of about 5 s, takes place with no signi®cant spatial
temperature gradients but, in this case, variations of temperature with time are also very small (for the whole duration of the devolatilization process the particle temperature varies from 750 to 765 K). From the thermal point of view, this behavior can be associated with a pure kinetic control, though this is not rigorously true, as devolatilization is still associated with the existence of a regression front. However, the size of the devolatilization region always coincides with the whole particle thickness and ms decreases linearly as time increases. Extensive simulations have not been carried out, but it is expected that conversion under pure kinetic control requires particles even smaller than 1 mm, a condition of no interest in ®xed-bed conversion. The conversion regime is highly dependent on the external heating conditions. As for ®xed-bed heating, it should be noted that the characteristic particle size does not remain constant in the expression for the global heat transfer coecient, but it continuously decreases as a consequence of the conversion process. Also, the heating conditions of ®xed-bed reactors can be signi®cantly dierent from particle exposure to radiation, which is the main external heat transfer mechanism during ®res. A comparison for these dierent conditions is given in Fig. 11, through the weight loss curves in the temperature range 973±1273 K, as simulated for 0:5 cm and ®xed-bed conditions with the initial particle size (a) and with the current particle size (b) in the Re number (Eq. (24)) and radiative heating (c). No dierence is seen between cases (a) and (b) for small conversion levels, but the process is on the whole faster for case (b). The weight loss curves, simulated for radiative heating, are similar in shape to the cases of ®xed-bed heating, though the characteristics times of the process are different, mainly for low and high temperatures. At low temperature, radiative heating results in slower external
Fig. 9. Spatial pro®les of temperature for ®xed-bed heating, Te 773 K and 0:05 cm.
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C. Di Blasi / Polymer Degradation and Stability 64 (1999) 359±367
Fig. 11. Weight loss curves for ®xed-bed heating conditions with constant (a, solid lines) and variable (b, dashed lines) particle size in the Eq. (24) for the heat transfer coecient and for radiative heating (c, dashed-dotted lines) ( 0:5 cm, Te in the range 973 ÿ 1273 K).
Fig. 12. Spatial pro®les of temperature for several times for ®xed-bed heating (dashed lines, hp given by Eq. (24)) and ablative pyrolysis (solid lines, hp 0:4 cal/cm2s, eqn. Eq. (25)), for Te 1273 K and 2:5 cm.
heat transfer rates, whereas the contrary is observed at high temperatures. However, given the large sample sizes of interest in ®re conditions, it can be understood that no signi®cant variation should be expected in the thermal conversion regimes. The case of conversion in the ablative regime (values of the external heat ¯uxes typical of ablative/circulating ¯uid-bed reactors or hot plate contact) is only brie¯y analyzed here, mainly with the purpose of a comparison with the case of ®xed-bed heating, as ablative pyrolysis has already been discussed in detail elsewhere [7,16]. The dynamics of the temperature ®eld, for hp 0:4 cal/ cm2 K, 2:5 cm and Te 1273 K, are shown in Fig. 12, where the case of ®xed-bed heating is also included. Though, for both cases and times suciently dierent from the beginning and the completion of the process, the regression front propagates with an almost constant rate, the values of this variable as well as the temperature at the surface are highly dierent (values of the regression rate are about 26 times slower and surface temperatures about 300 K lower for ®xed-bed heating). Furthermore, while for the case of ®xed-bed heating, the process is unsteady, because of a continuous increase in the extension of the vaporizing region and thus in the amount of volatiles evolved from the sample (thermally thick regime), high external heat transfer rates (ablative regime) give rise to a truly quasisteady process. Indeed, the thermal and the reacting waves propagate through the solid at a uniform rate, which is established after very short transients, associated with the beginning of the conversion process. The thickness of the reaction layers remains constant for the whole duration of sample conversion. As expected, ®nite thicknesses eects become important towards the completion of the process, when degradation takes place
along the remaining part of the sample. Also, the (maximum) temperature attained by the molten intermediate at the sample surface, Ts , is lower than Te and it is maintained until complete conversion. The process remains qualitatively the same as Te is decreased, but the surface temperature becomes successively lower and the reaction zone thicker, so that a thermally thick regime is again possible for low external temperatures. A reduction in the applied pressure also causes a transition from the ablative to the thermally thick regime. Another important observation is that in the ablative regime, the particle size does not aect the conversion regime, as long as it is larger than the size of the reaction zone. 5. Conclusions A numerical model has been developed to investigate the dierent regimes and characteristics of thermoplastic material pyrolysis for both indirect and direct external heating. For external heating rates and particle sizes of interest in ®xed-bed reactors and ®re conditions, pyrolysis takes place in a thermally thick or a thermally thin regime. Though for conditions far from the initial and ®nal transients, the surface regression rate may show only small variations, the process is never quasisteady, because the size of the reaction zone continuously varies in time. Also, a pure kinetic regime is never achieved, unless temperatures associated with very slow reactivity of the material are considered. High external heat transfer rates (hot-plate contact, ablative reactors) give rise to particle conversion in the ablative regime, through a quasi-steady process. Indeed, a constant-size, very thin reaction zone is seen to propagate
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with a constant rate through the virgin solid. However, reductions in the applied pressure and /or temperature again result in a thermally thick regime. Further developments should take into account the description of mass transfer limitations in the evolution of pyrolysis products. Indeed, the dynamics of volatile bubble formation and migration through the molten layer of the degrading particle as well as intra- and extra-particle activity of secondary reactions may be important processes in product distribution, mainly for slow heating rates. Furthermore, the extension of single particle models to the treatment of chemical reactors should be considered. References [1] Di Blasi C. Progress in Energy and Combustion Science 1993;19:71.
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[2] Kashiwagi T. Twenty-Fifth Symposium (Int.) on Combustion. Pittsburgh: The Combustion Institute, 1994. p.1423. [3] Sha®zadeh F. The chemistry of pyrolysis and combustion. In: Rowell R, editors. The chemistry of solid wood, Advances in Chemistry Series 207. Washington, DC: American Chemical Society, 1984. [4] Scott DS, Piskorz J, Bergougnou MA, Graham R, Overend RP. Ind Eng Chem Res 1988;27:8. [5] Scott DS, Czernik SR, Piskorz J, Radlein D. Energy and Fuels 1990;4:407. [6] Schultz RD, Dekker AO, Fifth (Int.) Symposium on Combustion. New York: Reinhold, 1955. p.260. [7] Lede J. Biomass and Bioenergy 1994;7:49. [8] Di Blasi C. Ind Eng Chem Res 1996;35:37. [9] Di Blasi C. J Anal Appl Pyrolysis 1997;40-41:463. [10] Hertzberg M, Zlochower IA, Combustion and Flame 1991;84:14. [11] Di Blasi C. Fuel 1996;75:58. [12] Yoon H, Wei J, Denn MM. AIChE J 1978;24:885. [13] Lede J, Panagopoulos J, Li HZ, Villermaux J. Fuel 1985;64:1514. [14] Baer AD. J. Fire and Flammability 1981;12:214. [15] Madorsky SL. J Polymer Sci 1952;9:133. [16] Di Blasi C. Chem Eng Sci 1996;51:2211.