Reaction temperature of solid particles undergoing an endothermal volatilization. Application to the fast pyrolysis of biomass

Pergamon

Biomos.~ and Bioenerg~ Vol. 7, Nos. Id, pp. 49-60, 1994 Copyright 0 1995 Elsevier Science Ltd Printed in Great Britain. All rights rcwwd 0961_9534(94)ooo46_8 0961-9534/94 $7.00 + 0.00

REACTION TEMPERATURE OF SOLID PARTICLES UNDERGOING AN ENDOTHERMAL VOLATILIZATION. APPLICATION TO THE FAST PYROLYSIS OF BIOMASS J. LkDb Laboratoire des Sciences du Genie Chimique, CNRS-ENSIC, 1, rue Grandville, B.P. 451, 54001 Nancy Cedex, France Abstract-The present paper describes the thermal conditions under which a solid particle (biomass) undergoes an endothermic decomposition caused by an external heat flux. The results derived from a mathematical model concern two extreme cases of conditions following the size of the particle (chemical and ablation regimes). The sensitivity of the results is studied as a function of several experimental parameters (particle size; heat transfer coefficient; heat source temperature) and chemical characteristics (kinetics and enthalpy). The sensible parameter governing the reaction temperature is the activation energy. The enthalpy has a minor effect except on heating rates. The reaction temperature is always much lower than the heat source temperature. In the chemical regime it is shown that after a simple heating phase, the temperature at which the reaction starts, varies between relatively close limits (less than 80 K). A temperature stabilization is then observed as the decomposition proceeds in such a way that the reaction may be considered as quasi-isothermal mainly for high enthalpies. In the ablation regime, the particle shrinks rapidly at a constant velocity, the reaction occurring inside an external thin layer. The reaction temperatures and heating rates are always lower than in the chemical regime. Data derived from previous experiments on fast pyrolysis of wood (ablation conditions) are in good agreement with the predictions of the model (reaction temperature, ablation rate and ablation layer thickness). The results bring confirmation of the effect of fusion observed during the thermal decomposition of biomass. Keywords-Fast pyrolysis; pyrolysis modeling; reaction temperature; biomass; ablation regime; chemical regime; endothermal reaction of solids.

particular example of this type of reaction. The primary products formed are probably liquids The endothermal decomposition of solid par- or gases (certainly steam, CO, C02) with no ticles constitutes an important domain of chem- major quantity of solid formed (no char) if these istry in the case of reactions of the type liquids are very efficiently eliminated.‘-” Some S + Fluid ---) Products.’ Also important are the authors have also proposed a model in which reactions of simple decomposition of the type biomass would decompose in these conditions S --+ Products (pyrolysis of organic compounds; as in a fusion (roughly constant decomposition mineral products decomposition; . . .).”Many temperature). It appeared valuable to develop a models have been proposed in the literature to model describing the decomposition of solid represent the complex first type of gas-solid biomass particles and to find a possible theoretireactions. Models dealing with the simpler type cal explanation of this phase change phenomof thermal volatilization are curiously more enon. The second purpose of this paper is to scare.2 The problem is generally treated in the observe how the effective reaction conditions assumption of no mass transfer limitation and are theoretically modified when different parthe authors usually consider the competition ameters are varied. The situations correspondbetween chemical and heat transfer processes in ing to very fine and very large particles will be order to estimate times of consumption of par- particularly considered. In order to approach ticles.2,5 Few works have been devoted to the the fast pyrolysis conditions, many authors study of effective reaction temperature in fast work in conditions of high external heat transfer heating conditions and to its variation as a coefficients and/or heat source temperature. The function of imposed parameters.6 The case of sensitivity of the overall behavior of the reacting biomass fast pyrolysis can be considered as a solid to these parameters will be finally studied. 1. INTRODUCTION

49

50

J. LkDt 2. THEORETICAL MODEL

2.1. Basic assumptions

The basic assumptions valid for both extreme cases of the chemical and ablation regime studied here are: ?? The reaction is of the type S+ Fluids ( + Gases). ?? The fluid products escape freely towards the external surface without any diffusional resistante. This is a simplification of the actual situation where pyrolysis liquids and steam have been observed to migrate in counterflow through the capillaries of still unreacted parts of large particles of biomass (in the case of the ablation regime). It can be reasonably supposed that the relative amount of these products is small compared with that being rapidly removed from the pyrolysis zone. ?? At the same time, it is assumed that the remaining solid shrinks in order to keep a constant density p.* This shrinking velocity is denoted as U. In these conditions, heat conductivity J and heat capacity C, are also assumed to be constant. The results will be compared with results obtained elsewhere4 using the other assumption of a constant size of the particle and hence a decrease of the overall density. ?? The chemical rate, I, of decomposition of the solid is defined as the mass of solid transformed per unit time and per unit solid volume. The chemical rate is assumed to obey an Arrhenius type law: r = pA exp( - E/R, T). ?? The reaction is endothermic with an enthalpy per unit mass AH (>O) supposed to be independent of temperature. ?? The solid particle initially at T, (no reaction) is suddenly immersed into a hot medium at TP where it is heated by convective transfer (heat transfer coefficient h) before and during reaction. ?? In order to simplify the mathematical treatment, only the case of infinite slab shaped particles (initial half length L,) is considered. Other shapes could be studied without important changes in the qualitative results. Reaction thus causes shrinking along one single dimension. After immersion in the hot medium, there exists a temperature profile inside the particle T (z, t ) and a shrinking velocity profile u (2, t ). They can be obtained from the mass and energy balances written at a particle level as shown in Ref. [2].

2.2. Basic balance equations (dimensional)

The coordinate axis z is attached to the outer surface of the particle and directed towards its center (Fig. 1). Mass balance.

au

pY&+r=o,

(1)

r = pA exp( - E/R, T).

(2)

with The initial and boundary conditions are: t = 0, u = 0, L = L,, z = ok a = ov dL z = Ly Us = &

(3) 1.

Heat balance. a2T

aT

dT

L,Z,=rAH+puCPz+pCPat.

(4)

The initial and boundary conditions are: t=O,

T=T,,

z =O,-Lg=h(T,- T,),

z=L,

aT -=o. aZ

1

(5)

It is instructive to write these equations in reduced form based on dimensionless numbers depending on initial and intrinsic conditions of the reaction, mainly L,, and Tp.

Fig. 1. Temperature and shrinking velocity profiles in a particle (dimensional).

51

Endothermal volatilization of solid particles

coordinate: x = z/L, (reduced half size of the slab: e = L/L,,. ?? Reduced temperature: y = T/T,. ?? Reduced time: 8 = tr,/p. ?? Reduced

(6) (7)

(8)

rp is the theoretical rate of reaction at T,: rp = Ap exp( -E/R, T,) = Ap exp( - y ).

(9)

t, (=pC,L,,/h) is a characteristic time of heat exchange between the particle and the outside medium. K is usually lower than 1. 2.3. Basic balance equations (dimensionless) With these defined parameters, eqns (l)-(5) are then written as follows. Mass balance.

y is the activation criterion. For most reactions of this type, 5 < y < 50.4 ?? Reduced

rate of reaction:

g+w=o,

o=o,

o=O,z!=l,

( 1 0 )

x = 0,

V = 0,

shrinking velocity: u = pu/L,r, (11) ?? Thermicity criterion: H = AH/C, T, . (12)

x =e,

de O=de’

W=rjr,=exp(-p-l+). ?? Reduced

Practically H may vary from 0 to about 1O.4 ?? Thermal

Biot number: BiT = hL,/il.

Thiele modulus at T,:

Mp = r,LiC,/A = t,/t,.

(14)

Mp compares two characteristics times: t7 (= pC, L i/A) the heat penetration time and t, ( = p/r,) the reaction time at Tp . Small Mp values associated with small Bif numbers indicate that the reaction occurs in chemically controlled regime. High Mp values do not necessarily indicate that the reaction occurs in the ablation regime (i.e. reaction limited to a very thin layer close to the surface) if the reaction temperature is much lower than T,, as seen later. Ablation is observed in the case where large BiT numbers are associated with large M values (M being defined at true reaction temperature). ?? Damkohler

number:

K = BiTIMp = hlr,L,C, = t,/t,.

(17)

Heat balance.

(13)

It brings information on the means of particle heating: a high value of BiT (large heat transfer and particle size values and low solid conductivity) indicate that the particle is only heated in an external thin layer, whereas small values of BiT (< 0.1) indicate that heating is controlled by external heat transfer resistance with uniform temperature profile inside the particle, as would be obtained with low heat transfer coefficient h, small particle size L, and/or large particle conductivity 1. However this parameter is insufficient to define the type of consumption of the particle. It must be associated with the following Thiele modulus. ?? Thermal

(16)

(15)

2 = Ml -Y,),

x=0,

--

x=e,

g=o.

(19)

2.4. Solution in the first limit case: chemical regime

In this case, the temperature is uniform inside the particle at any moment, implying that both BiT and M (at T) are small. The rate of reaction is independent of the abscissa and equation (16) becomes: de v =a = -ew. u is a function of both conversion and temperature. In that case, the value of y is the solution of the following simple dimensionless heat balance:

Q

dy

-=HW+m MPe

(21)

with = B&.(1 -Y).

(22)

The elimination of reduced time between eqns (20) and (22) leads to:

dv H Kc1 -Y) -=_r V= 1, y = Yo). de e

(23)

J. LkDk

52

wler surface

Numerical resolution of eqn. (23) gives the evolution of the particle temperature as a function of its size for given values of the three parameters H, y and K. Notice that substituting the reduced size e by the conversion yield X(X = 1 - /) equation (23) becomes:

KU

dy

-Y)-H

dX=(l-X)W

1-X’

center

(24)

This result is similar to the equation derived in the case of a sphere reacting in the chemical regime but with the assumption of an unchanging size [4]:

(25) (B is a number describing the evolution of p and C, as a function of X, B = 1 for X = 0). 2.5. Solution in the second limit case: ablation regime

In this case, the temperature and shrinking velocity decrease very sharply in a thin layer close to the external surface of the particle, while the particle core remains cold [2]. It has been shown that in such conditions, these parameters reach very rapidly stationary profiles with the shrinking of the particle occurring at a constant linear velocity, as the reaction proceeds. These stationary profiles are the solutions of equations (16) and (18) becoming in these conditions:

Fig. 2. Temperature and shrinking velocity profiles in a particle (dimensionless) in the case of the ablation regime. Dotted lines correspond to approximated profiles chosen for the model.

Besides numerical resolution, approximate analytical solutions can be obtained by the integration of equation (28) providing an assumption is made on the shapes of the profiles y(x) and v(x) (Fig. 2). Let us define arbitrarily the depth of the ablation layer as the abscissa where (dv/dx), represents only 1% of its value (dv/dx), at the surface of the particle: ($$( $)S=o.ol =;, or: ))Ys-Ye

- -dv = w dx ’

-=4.6. YeY,

with (27)

with

x=e,

dy

--= dx Bid*

dy

Ys-Ye

-.Y,),

y=y,, x=0.

- Ye %4.6* Y

(32)

From the flux condition at x = 0 [equation (29)], the thickness e can be approximately calculated by:

P

x=0,

(31)

In a first approximation, equation (3 1) allows the calculation of the temperature gradient y, - y, in the ablation layer when surface temperature is known, since T, approaches T,: Ys

-&$=HW+v$,

(30)

(29)

4.6 yf

e=BiT(l -y,)%yBi,(l -y,)’

(33)

In this ablation layer, the velocity profile is assumed to be linear between x = 0 (v = 0) and

53

Endothermal volatilization of solid particles

x = e (u = uc) and thus the temperature profile is uniform (y,): 0 < x < e,

dv dx = - W, = constant.

large size of the particle (BiT and Mp are both very large and the results must be independent of L,).

(34) 3. RESULTS OF SIMULATIONS

For x > e, the velocity profile is constant (uc). The result is the same as supposing that the reaction occurs between x = 0 and x = e as in the chemical regime conditions, with preheating for x > e without any reaction. Such an assumption may be justified by the results derived elsewhere:3*4v6 a small particle immersed in a hot medium first undergoes a simple heating until a given reaction temperature TR is reached where the reaction begins suddenly and then proceeds under almost isothermal conditions. The results presented in the following sections will bring other evidence of this assumption. The integration of eqn. (28) between 0 and d:

The mathematical expressions derived above will be solved in the case of the very fast primary decomposition (volatilization) of cellulose. The standard parameters used in these calculations are: External conditions: h = 103Wm-‘K-’ Tp = 1200 K. Solid properties: ‘“,“‘3 1 = 0.2 W m-’ K-‘, C, = 2800 J kg-’ K-l, p = 700 kg mP3, Lo = 10m5 m. Characteristics of the reaction: AH = 40,000 J kg-‘,‘3*‘4 A = 2 83 x lOI s-’ 6,10,“,‘5 E/R, = 29,000 K 1 ’

leads for each term to:

($(1-Y,))

(-Hu,) (0) (0) MYo-Y,N

and from the integration of eqn. (34) to the following solutions:

$%l -YJ=UYo-Ye-H),

(36)

P

v,= - W,e.

(37) Using the value of e given by eqn. (33) one obtains: 4.6 yf H+y,-y,--

.

Y

(38) When the parameters BiT, Mp and y are known, eqn. (38) allows the calculation of a rough estimate of reaction temperature y,. The term 4.6 yf /y in the second member is often low compared to H + y, - y, and to neglect it has only minor effects on the calculation of the temperature T, (maximum 3 K error). It is noticed that eqn. (38) introduces a new dimensionless member: Bi:/M, which is independent of the initial size L,, of the particle. Accordingly, T, is independent of L,, a logical consequence of the ablation regime where reaction occurs in a very thin layer compared to the

The corresponding calculated standard dimensionless numbers are then: BiT = 0.05;

H = 0.01;

y = 24;

K = 5.7 x lo-“;

Bi$/M, = 2.8 x 10m9.

It must be noticed that the parameters BiT and K are defined for studying the chemical regime alone. For the ablation regime, the useful parameter is Bi:/M, [eqn. (38)]; it is independent of the particle size Lo. In these conditions, both the Biot and Thiele numbers must be high enough to represent an ablation regime (for example: BiT = 50 and Mp = 8.9 x 10” correspond to Lo = lo-*m in this standard case). It results that the comparison between the chemical and the ablation regimes will be made on the basis of the same values of h, Tp, 1, C,, p, AH, A, E/R, and Bi :/M,. On the other hand, Lo values will be different in order to take into account the necessary different values of BiT and Mp for each regime. Results obtained with other values of these parameters will be given in order to observe their relative sensitivity. 3. I. Chemical regime Figure 3, derived from the numerical resolution of eqn. (23), shows the variations of the

54

J.

t.iDk

0.8 0.7 0.6 -

H = O.Ol(slnndard case)

0.5 0.4 0.3 0.2 0.1 0

0.4

I

0.5

0.6

I

0.7

0.8

I

0.9

Y

1

1

Fig. 3. Theoretical profiles of reduced size L = L/L,, as a function of reduced temperature y = T/T, for different values of the thermicity criterion H (H = AH/C, T,).

reduced size G of the particle as a function of its reduced temperature y. It appears that &’ is unchanged until a certain value of y where the reaction suddenly occurs. This is in agreement with other results3.6 showing that the behaviour of a solid particle undergoing an endothermal decomposition may be separated into two sequences: simple heating followed by reaction with an apparent stabilization of the solid temperature. For the standard case, the variation of y between 10% and 90% of conversion yield is only 0.062. Figure 3 shows also that if the reaction starts at about the same temperature whatever H (Cl), the stabilization effect increases as H increases, a logical consequence of the strong coupling between heat flux transferred from the hot medium to the particle and heat flux absorbed at a certain rate by the endothermal reaction. For H = 0, no heat is absorbed by the reaction and external heat flux is only used for heating the remaining solid. In that case, the stabilization is only an apparent effect due to the fact that the reaction occurs during a relatively short time. For intermediate values of H, coupling of heat fluxes and short time of reaction join their effects to increase the phenomenon of temperature stabilization. For high enough H values, eqn. (23) is the difference between two great terms of the same order of magnitude and dy/d/ may be neglected (as shown in ref. [4]). Then eqn. (23) becomes: H>0.5,

t=K;;ya? H

(3%

In these conditions, this expression gives a very good approximation of the variation of e with y. Moreover, the curve e(y) is so steep that y may be considered constant (isothermal reaction) up to high conversion yields. This constant reaction temperature y, may then be calculated by an excellent approximation from eqn. (39) with ip = 1:4

WR K 1-y,=

(40)

the quasi-constant reaction temperature being a function of a new dimensionless number H/K.

It could also be shown that the curves of Fig. 3 would be quantitatively very close in other hypotheses: other shapes of particles (spheres; cylinders; . . .) and/or assumption of a constant size of the particle during the reaction [eqn. (25)]. In any case, a bad knowledge of the reaction enthalpy has only a minor effect on the reduced reaction temperature: for e = 0.5, y = 0.64 (H = 0) and y = 0.598 (H = 1). Figure 4 shows the influence of K [indirectly the influence of h and/or L,, eqn. (IS)] on the phenomenon. It is shown that multiplying or dividing K by a factor of 10 leads to a maximum variation of only 5% of the y values. Figure 5 illustrates the influence of h (or Lo), AH and r, on the variation of reaction temperature compared to the standard case: Multiplying or dividing h or L,, by a factor of 10 produces a 40 K difference temperature.

??

55

Endothermal volatilization of solid particles

Fig. 4. Theoretical profiles of reduced size G = L/LO as a function of reduced temperature y = T/T, for different values of the dimensionless parameter K (K = h/r,&C,). ?? Multiplying

AH by a factor of 100 only produces a decrease of 50 K (roughly the same effect as h/10). ?? For e = 0.5, there is a difference of only 30 K for a 600 K difference of the hot medium temperature T, .

Confirming the theoretical results previously obtained,4 Fig. 6 shows that the sensible parameter in the calculation of reaction temperature is the activation energy of the reaction represented by the parameter y, even if the overall shapes of the curves are still unchanged.

These results show that the strong increase of h or decrease of L,, (always in conditions of small BiT number) or increase of Tp have only small influences on the reaction temperature. These observations associated with the temperature stabilization effect, bring a clear explanation of the “fusion” effects reported by several author&” during biomass pyrolysis.

3.2. Ablation regime Table 1 gives a few values of y, and y, (and corresponding T, and T,) for the ablation regime, calculated from eqns (32) and (38) in comparison with the corresponding y, values numerically calculated from eqn. (23) (Fig 3-5)

I

600K W3OK

I

I = IZOOK (Standard case)

0

I

I

I

0.1

0.2

I

0.3

1

I

I

I

I

0.4

0.5

0.6

0.7

0.8

2 0.9

I

Fig. 5. Variations of effective reaction temperature T(K) as a function of reduced size / = L/L,, of the particle. Sensitivity to several operating parameters.

J.

56

LtDk

0.9 -

0.0 0.7 0.6 05 0.4 0.3 02 0.1 /-

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Fig. 6. Theoretical profiles of reduced size I = L/L, as a function of reduced temperature y = T/T, for different values of the activation criterion y (y = E/r, T,).

in the chemical regime for 5% and 95% conversion. The influence of H is less important in ablation, while the influence of TP and h are more important. Whatever the case, the domain of reaction temperatures observed in ablation is always smaller than in the chemical regime; the differences are sometimes greater than 100 K. These deviations are small for high enthalpies where the fraction of flux used for

preheating (ablation case) becomes relatively less important. 3.3. Reaction and shrinking times. Heating rates 3.3.1. Ablation regime. Shrinking velocity is easily calculated from eqns (33) and (37): 4.6 y: v/=-w ‘V&(1 -Y,)

Table 1. Calculated values of y and corresponding effective reaction temperature of the solid (cellulose: i, = 0.2 W me2 K-‘; C, = 2800 J kg-’ K-l; p = 700 kg rne3) for different operating parameters. The standard case corresponds to: h = 1000 W m-* K-‘; Tp = 1200 K; AH = 40,000 J kg-‘; A = 2.83 x 1Or9 s-r; E/R, = 29,000 K. In other cases, only one parameter is changed compared to this standard case. The standard particle size L,, = 10 x lo-” m is useful for describing the chemical regime alone (the ablation regime depends on the dimensionless parameter Bi:/M, which is independent of L,) Ablation regime Chemical regime (vO = 0.25)

Standard case h x 10 (h = 104Wm-*K-r)

h/10 (h = 100Wm-2K-‘)

T,=!XlOK Tp= 15OOK

AH=0 AH x 10

(AH=4x 10SJkg-‘) AH x 50 (AH =2x 106Jkg-‘) AHxlOO (AH =43 x 106Jkg-‘)

$K) 0.515 618 0.562 674 0.475 570 0.666 599 0.423 635 0.515 618 0.512 614 0.505 606 0.501 601

T,J;:K) 0.580 696 0.641 768 0.529 635 0.745 670 0.477 716 0.579 695 0.575 690 0.567 680 0.561 673

y (l = 0.95) T (K) 0.597 716 0.630 756 0.567 680 0.783 705 0.487 730 0.598 718 0.594 713 0.586 703 0.577 692

y (t = 0.05) T (K) 0.682 818 0.722 866 0.645 774 0.883 795 0.557 835 0.689 827 0.656 787 0.628 754 0.618 742

(41)

51

Endothermal volatilization of solid particles

or, in dimensional form: (42) It is a constant value in steady state conditions of ablation. Equation (42) shows that U, is proportional to the inverse of h (T, - T,). But in the same time, T, increases with this heat flux (see Table 1) in such a way that u, is globally an increasing function of it (see Table 2). A few values are reported in Table 2 with the corresponding estimation of ablation layer thickness a (a = eL,) given by: a=

4.61T;

(43)

+TP- T,) g The time for total consumption is roughly proportional to L, and may be very large for high particle size (a basic condition for ablation assumption). It is yet possible to calculate the time t, corresponding to a total consumption of the ablation layer, i.e. the necessary time for the surface to cover the distance a (from temperature T, to temperature T,):

h = lo4 W me2 K-‘. High enthalpies considerably lower the heating rate. 3.3.2. Chemical regime. The calculation of shrinking velocity is more difficult since, as was shown in eqn. (20), it is proportional to W which is now a function of y, itself a function of the time. It is then difficult to compare this rate with the steady-state values in ablation. It is the same for the calculation of total consumption time, t,, for which analytical calculations are not directly possible. Besides numerical resolution, simplified solutions may be obtained for estimating t,. In all cases studied in this work and for H 6 0.05, it can be shown that in a first approximation, the product W& (0) increases linearally with P from e2 = 1 to roughly 0.02, under which limit, the velocity falls very rapidly. In the linear domain, the variation law can be written as: H < 0.05, -g = W{=lx(l -e*>.

(46)

The integration of equation (46) between the limits of validity gives: cr0 = 1.68~2,

(47)

or, in dimensional form: 2 ” = aA exp( - E/R, T,) ’ Let ATa:,lt, be the mean heating rate defined as the reaction occurs: R

a

Ts - Te

=s=Ts-Te ci

-=

(48)

When H is great enough, We is roughly independent of e* in about the same domain of d2.

(45)

t,

H

Table 2 shows that the heating rate varies in large limits when the conditions are varied and reaches values up to 1O’K SC’ for

20.5, -$ = w/=/l,

(49)

or, after integration: ge = 1

(50)

Table 2. Calculated values of shrinking velocity, a, and layer thickness, a (ablation regime) and time for total consumption I, (chemical regime). Comparison of the corresponding heating rates R, and R, in both regimes. Same values of the parameters as for Table I Ablation regime (y,, = 0.25) (mU;- I, Standard case h x IO (h = 104Wm-2K-‘) h/IO (h = IOOWm-‘K-‘)

r,=9OOK r,= 1500K AH=0 AHx50 (AH=2x 10”Jkg-‘) AH x 100 (AH=4x 106Jkg-‘)

6.92 x lO-4 4.89 x lo-’

(Ln) 30.5 4.3

9.39 x 1o-5

226

2.79 1.51 6.49 2.4

x x x x

1O-4 IO-’ 1O-4 1O-4

1.49 x 10-4

Ii, x a (mZ s-’ x 108)

Chemical regime R* (K ss’)

2.11 2.10

1771 106,114

2.12

27

62 20.1 30.3 28.2

I .73 3.13 I .97 0.68

320 5890 1646 630

21.3

0.41

394

(K?‘) a, B a = 7.2 x IO-’ 3.07 x 10-j 33,224 a = 5.8 x lO-6 3.81 x IO-’ 28.87 I 8.5 x IO-”

2.6 x IO-?

3615

a = 8.2 x 10m4 8.5 x IO-’ 8.8 x 10e9 2 x IO-’ a =9x IO-’ 2.46 x 10-j fi =4.4 x IO-* 2.51 x IO-?

10,588 52,500 44,309 203 I

p =2.3 x IO-’ 4.8 x IO-’

1042

a=

a=

J.

58

and in dimensional form: 1 ” = PA exp( -E/R, T,) ’

(51)

Whatever the case, t, is independent of the particle size L, in the chemical regime. Table 2 shows that these values are always much lower than 1. Of course, for given imposed parameters, the times for total consumption of the particle [ = L,/u,: see equation (42)] are always much greater in ablation than in chemical regime because of the corresponding large values of Lo. Let AT,/t, be the mean heating rate defined as the reaction occurs: R = 3 = T(t = 0.05) - T(t = 0.95) c

4

4

, (52)

T (l = 0.05) and T (/ = 0.95) being the temperatures of the solid at, respectively, 95% and 5% conversion yield (Table 1). Table 2 shows that heating rates are always much higher (except for very high h) in chemical regime where the sensitivity of h and Tp coefficients are much less important than in ablation. The effect of enthalpy is more pronounced in the chemical regime. It seems that the difference of heating rates between both regimes is lower as enthalpy increases (the fraction of heat flux used for preheating the still cold parts of the solid, is less important in ablation for high AH). 4. COMPARISON WITH EXPERIMENT

The comparison of these results with experiment is much easier in the case of the ablation regime. The results of typical ablation experiments have been previously published,‘0.“,‘3 Rods of wood were applied under known pressures on hot spinning disks in such conditions that the primary produced liquids were immediately eliminated from the wood surface. Measurements consisted of determining the shrinking velocity of the rods (time required for a known length to be consumed, u,), and the reaction thickness (estimation by microscopic measurement of the extent of darkness zone near the surface, a). The rods were long enough (several cm) for postulating ablation conditions. Following the applied pressure, values of h were roughly varied between 2000 and 50,000 W mm2 Km ‘. A mean reaction temperature was then estimated to be 739 K (“wood fusion temperature”). Table 1 shows that for

LkDk

h > 1000 W me2 K-‘, and with different AH and Tp values, the theoretical surface reaction temperature T, varies between the extreme values of 673 K and 768 K with a mean value of 720 K in excellent agreement. A very good agreement is also observed for the values of u,: Experiments [ 131: 7 x 10m4 < ul(m ss’) < 4 x 10e3, llO>a(~m)>20, u,a x constant = 8 x 10e8 m2 s-’ Table 2: 6.92 x 10m4 < ul(m ss’) < 4.89 x 10e3 30.5 > a (pm) > 4.3 U/Q z constant = 2.1 x IO-’ m2 s-’ The experimental values of a are higher than the calculated ones probably because the reaction of volatilization occurs significantly for temperatures higher than those corresponding to the first changes of wood colour. The theoretical value of the product u,a (=2.1 x 10e8 m2 ss’) is larger than the empirical estimation proposed elsewhereI and expected close to the thermal conductivity of the solid @/PC, x lo-’m2 s-l). 5. DISCUSSION AND CONCLUSION

A model has been developed to describe the behavior of solid particles undergoing a reaction of decomposition (volatilization) under conditions where no residual solid by-product is expected to be formed. The fluid products are supposed to be immediately eliminated with no possibility of subsequent reaction inside the solid matrix. These are the main basic conditions for fast pyrolysis. Two extreme cases have been considered: the chemical regime (reaction occurs in the whole volume of a small particle where the temperature is uniform); and the ablation regime (reaction occurs in a very thin layer close to the surface of a big particle). In the chemical regime, the temperature at which the reaction starts varies between relatively narrow limits (68G756 K) even for very different external conditions and is only slightly dependent of the value of enthalpy. A stabilization of solid temperature is then observed as the reaction proceeds until total consumption, this effect increasing as enthalpy increases (the

Endothermal volatilization of solid particles

reaction may be considered quasi isothermal for high AH). In the ablation regime, the particle shrinks rapidly at a constant velocity with a steady-state profile of temperature in the ablation layer. The reaction temperature is always lower than in the chemical regime and is also moderately dependent on the chosen conditions, especially with enthalpy. These results give a theoretical explanation of the “fusion-like” phenomenon reported by several authorP’ to describe the fast pyrolysis of biomass. This type of behaviour would be probably observed for every reaction of the type S -+ Fluids: if the fluids are liquids, the phenomenon looks like a fusion; if they are gases it looks like a sublimation. The temperature stabilization is the result of two phenomena. The first phenomenon is a competition between heat flux required for heating the solid and heat flux required by the reaction occurring at a certain rate. The second phenomenon is that the reaction occurs during a short time and the temperature has no time to increase to a large extent (this second reason explains the apparent stabilization effect also observed for the case of AH = 0). The reaction temperatures reported in Table 1 are of the same order of magnitude as the measured “fusion temperature” of 739 K ‘OJ’ bringing an indirect proof of the validity of the kinetics constants chosen for the reaction. Another good agreement is also observed in the values of theoretical and measured parameters characterizing ablation: shrinking velocity uI and thickness of reaction layer a. For a given enthalpy, the product u,a (m’s_‘) is roughly constant whatever the other parameters. As already mentioned for other types of reactions,4 the sensitive parameter is the activation energy of the reaction, whose variation leads to very important effects on reaction temperature. A bad knowledge of the enthalpy of the reaction has only little influence on the calculation of reaction temperature in both regimes (mainly in ablation) but highly influences the estimation of heating rates that tend to become identical for high AH. In order to approach the fast pyrolysis conditions many authors report work in conditions of high heat transfer coefficients and/or high hot medium temperature. These results show that the increase of these parameters may have different consequences. On reaction temperature, there are only moderate effects

59

if h and Tp are increased, whatever the regime. On heating rates, the effects are very important in both regimes mainly in the case of ablation. In any case, the effective reaction temperature is very different from the external hot medium temperature Tp. The ratio y of these temperatures may be very small, mainly for high Tp (y = 0.487, i.e. T = 730 K for T,, = 1500 K in the chemical regime). Assuming that biomass decomposes at Tp would lead to considerable errors even for very thin particles (chemical regime). For given working parameters, reaction temperatures and heating rates may be significantly different in each regime. This means that if the solid may decompose according to several possible chemical processes characterized by different activation energies, selectivity and hence the nature of the products may be different depending upon the initial size of particles (very fine or very large).

NOMENCLATURE

a A B

BiT CP e E h H K r L LO M MD

Q r YP 4 4 R, t

t

d

tc 4 tP

t, T

Ablation layer thickness (m) Pre-exponential factor (Arrhenius law) (s-l) Dimensionless number describing the evolution of p and C, as a function of X (L, constant) Thermal Biot number (= hL,/I ) Heat capacity (J kg-’ K-‘) Ablation layer thickness (= a/Lo) Activation energy (J mol-‘) External heat transfer coefficient (Wm-*K-l ) Thermicity criterion (=AH/C, T,) Dimensionless number ( = h /r, LOC, = $Jf,) Reduced size of the particle (= L/L,) Half thickness of the particle (m) Initial half thickness of the particles (m) Thermal Thiele modulus at T (=rL i C,IE.) Thermal Thiele modulus at T,, (= r,, La Cpll) Reduced heat flux density Rate of reaction at T (kg m-j s-‘) Rate of reaction at Tp (kg m-j 5’) Heating rate in ablation regime (K ss’) Heating rate in chemical regime (K s-‘) Gas constant (J mol-’ Km’) Time (s) Time for total consumption of ablation layer a (s) Reaction time in chemical regime (s) Characteristic time of heat exchange (‘P C,L”III) (s) Characteristic reaction time at T,

(=plr,) (s)

Characteristic heat penetration time (=p C,L$i) (s) Temperature (K)

J. LkDk

60

Temperature in the assumption dy/d/ z 0 (K) Limit temperature of ablation layer (K) Initial temperature of the solid (K) External hot medium temperature (K) Reaction temperature (assumption of quasi isothermal temperature) (K) Surface temperature (K) Local shrinking velocity (m s-‘) Global shrinking velocity (m s-i) Reduced local velocity (= p u/L, rp) Reduced global velocity (= p u,/L, rp) Reduced rates of reactions at T, r,, T,, Ta, T, X Reduced abscissa (= z/L,) Conversion yield (= I - I) X Y?Ya~Ye,Yo9YR~Ys Reduced temperature at T, Ta, T,, To, TRI T,

Abscissa (m) Greek letters ;

j;H

0 I P

Proportionality coefficient [eqn. (46)] Proportionality coefficient [eqn. (49)] Activation criterion (= E/R T,) Enthalpy of reaction (J kgmf) Reduced time ( = tr, /p ) Thermal conductivity (W m-i K-i) Mass density (kg mm3)

4. J. Lede and J. Villermaux. Comoortement thermiaue et chimique de particules solides subissant une reaction de decomposition endothermique sous faction dun flux de chaleur externe, Can. J. Chem. Engng 71, 209 (1993). 5. D. L. Pyle and C. A. Zaror, Heat transfer and kinetics in the low temperature pyrolysis of solids. Chem. Engng Sci. 39, 147 (1984). 6. V. Kothari and M. J. Antal, Jr, Numerical studies of the flash pyrolysis of cellulose. Fuel 64, 1487 (1985). 7. J. P. Diebold. Ablative ovrolvsis of macroaarticles of biomass. Proc. Specialists’iVo&shop on Fast bvrolysis of Biomass, p. 237:Copper Mountain, Golden, CO.~Solar Enerev Research Institue. SERIICP.622.1096 fl980). 8. J. P.-Diebold, The cracking kinetics of depolymerized biomass vapors in a continuous reactor. Thesis T-3007. Colorado School of Mines, Golden, CO (1985). 9. H. Martin, J. Lede, H. Z. Li, J. Villermaux, C. Moyne and A. Degiovanni, Ablative melting of a solid cylinder perpendicularly pressed against a heated wall. Inr. J. Hear Muss Transfer 29, 1407 (1986). IO. J. Lede, H. Z. Li, J. Villermaux and H. Martin, Fusion like behaviour of wood pyrolysis. J. Anal. Appl. Pyrolysis 10, 291 (1987). II. J. Lede, H. Z. Li and J. Villermaux, Pyrolysis of biomass: evidence for a fusionlike phenomenon, In J. Soltes and T. A. Milne (eds) Pyrolysis Oils from Biomass, Producing, Analyzing and Upgrading, ACS Symp. Ser. 376, Chap. 7, p. 66 (1988).

12. J. Lede, F. Verzaro, B. Antoine and J. Villermaux, Flash pyrolysis of wood in a cyclone reactor. Chem. Engng Proc. 20, 309 (1986).

REFERENCES 1. J. Szekely, J. W. Evans and H. Y. John, Gas-Solid Reactions. Academic Press. New York (1976). 2. J. Villermaux, B. Antoine, J. Lede and F. Soulignac, A

new model for thermal volatilization of solid particles undergoing fast pyrolysis. Chem. Engng Sci. 41, I51 (1986). 3. J. Lede, H. Z. Li and J. Villermaux, Le cyclone: un reacteur chimique. Application a la reaction de decarbonatation de NaHCO,. Can. J. Chem. Engng 70, I I32 (1992).

13. J. Lede, J. Panagopoulos, H. Z. Li and J. Villermaux, Fast pyrolysis of wood: direct measurement and study of ablation rate. Fuel 64. 1514 (1985). 14. T. B. Reed, J. P. Diebold and R. Desrosiers, Perspectives in heat transfer requirements and mechanisms for fast pyrolysis.Proc. Specialists Workshop on Fast Pyrolysis of Biomass, p. 7. Copper Mountain, Golden, CO. Solar Enginery Research Institute, SERI/CP.622.1096 (1980). 15. A. G. W. Bradbury, Y. Sakai and F. Shafizadeh, A kinetic model for pyrolysis of cellulose. J. Appl. Polym. Sci. 23, 3271 (1979).