A Simplified Pyrolysis Model of a Biomass Particle Based on

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A Simplified Pyrolysis Model of a Biomass Particle Based on Infinitesimally Thin Reaction Front Approximation Y. Haseli,* J. A. van Oijen, and L. P. H. de Goey Combustion Technology, Department of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands ABSTRACT: This paper presents a simplified model for prediction of pyrolysis of a biomass particle. The main assumptions include (1) decomposition of virgin material in an infinitesimal thin reaction front at a constant pyrolysis temperature, (2) constant thermophysical properties throughout the process, (3) negligible effect of volatiles flow. The formulation is presented for various stages of thermally thin and thermally thick slab particles. In each phase, the energy conservation is applied for the particle in a simple enthalpy balance form and the enthalpy of particle is computed at a volumetric mean temperature. The accuracy of this new model has been examined by comparing the predictions with various experiments of slab particles found in the literature as well as the predictions of a comprehensive model, in terms of mass loss rate, surface and internal temperatures, and conversion time. The results show that the model prediction is qualitatively and quantitatively in a satisfactory agreement with measured values. Comparing the outcome of the simplified model and a comprehensive model in terms of the conversion time of beech and spruce wood particles at high external heat fluxes reveals fair agreement between these two models. These multiple validations indicate that the presented model can be employed in design codes for practical applications. Typical numerical results are further presented to highlight the effect of the prescribed pyrolysis temperature on mass loss rate and surface temperature of both thermally thick and thin particles. The extension of the model for other particle shapes is outlined.

1. INTRODUCTION Interest in renewable energy sources has been increasing worldwide due to the limited availability of fossil fuels and their significant contribution to polluting our societies. Biomass has been known as an attractive renewable energy source due to its accessibility in most parts of the world. The energy content of biomass can be extracted using well-established techniques such as directly burning it in a power plant furnace or converting it to other forms like biofuels, hydrogen, or syngas. Whether the energy from biomass is released directly in a combustor or it is converted to other byproducts, the primary stage of thermochemical conversion of biomass is pyrolysis, which may begin at moderate temperatures (above 200 °C). During this process, the virgin material decomposes to volatiles and char residue. A substantial amount of research has been conducted on the subject of biomass pyrolysis by means of experimental and numerical investigations to increase the knowledge of various physical and chemical processes involved in the biomass pyrolysis. Along with many experimental studies on kinetics and decomposition of various types of biomass (see the review by Scott et al.1), several numerical models have been developed during the past decades. The reader may access the recent state of the art in refs 2−19. Excellent literature review on biomass pyrolysis modeling has also been given by Di Blasi.20,21 The common feature of the detailed numerical models reported in the literature is that the transport equations are usually described one-dimensionally and combined with a kinetic scheme representing chemistry of the virgin biomass decomposition. Two and three-dimensional models have rarely been reported; see ref 22. The advantage of these models is that they allow calculating a variety of parameters such as solid and © 2012 American Chemical Society

gas phase densities, temperature, pressure, velocity within the porous matrix and formation of main byproducts (light gases, tar, and char) in space and time. Such advanced models enable one to get a deeper understanding of the physics of the pyrolysis process on the scale of a single particle. In practical applications, the usage of detailed models would be at the cost of large computational efforts and time, in particular, when dealing with the design of combustors and gasifiers where a large number of particles undergo thermochemical conversion. For many industrial applications, designers are commonly interested in only a few parameters such as average temperature and/or temperature at the surface of particle, rate and the amount of particle mass loss, ignition time at which particle begins to decompose, and total duration of the conversion process. To capture the main characteristics of the pyrolysis of solid fuels with optimized computational efforts requires one to employ less complex models. Lu et al.23 and Bharadwaj et al.24 examined the accuracy of a lumped model (treating particle as a whole) and found that even for small particles significant errors may be caused in the predictions indicating that the intraparticle effects need to be accounted for in a pyrolysis model. Therefore, pyrolysis models for design purposes should be as simple as possible subject to meeting the satisfactory accuracy of computation. A literature survey reveals several simplified models reported by various researchers for prediction of the main characteristics of a pyrolyzing particle; e.g. see refs 25−38. The solution methodology and the range of applicability of these simple Received: December 20, 2011 Revised: April 20, 2012 Published: April 25, 2012 3230

dx.doi.org/10.1021/ef3002235 | Energy Fuels 2012, 26, 3230−3243

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models differ from one study to another. A common feature of simplified modeling studies is that the initial partial differential form of transport equations is transformed into a set of ordinary differential equations (ODE). Further, most past studies on this subject concerns with thermally thick particles in that pyrolysis begins at the exterior surface of particle before particle center temperature deviates from its initial value. The treatment of a thermally thin particle (in which pyrolysis begins after the center temperature has started a heating process) based on the assumption of infinitesimal rate of pyrolysis at a thin reaction front has not been previously discussed in the literature. The objective of the present paper is to introduce a simpler pyrolysis model compared to past studies for both thermally thick and thin particles assuming that the pyrolysis takes place at a prescribed temperature in an infinitely thin layer which propagates into interior layers of particle. The analysis is based on applying the conservation of energy for a charring particle and calculating the enthalpy of particle using a mean particle temperature. The idea is to derive a set of simple algebraic equations (rather than ODEs as in nearly all past studies) to predict key process parameters including burning rate, conversion time, surface temperature and heat flux. The accuracy of the model will be examined by comparing its prediction with different sets of experimental data found from the literature.

2. DESCRIPTION OF THE PROCESS Consider a dry slab biomass particle with a thickness of L that is exposed to a hot environment. The particle is initially at temperature T0 ( tp,ini. Thus, upon initiation of the pyrolysis process, the particle is divided into three regions: char layer (0 < x < xc), virgin biomass undergoing heating up process (xc < x < xt), and virgin biomass which is still at the initial temperature (xt < x < L). By continuation of the pyrolysis process, the thermal wave and the char front penetrate into the particle until xt reaches the back face. Beyond this moment, the rest of the process is the same as 3231


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effect may however be implicitly accounted for in the thermophysical properties of char. In general, the conversion of a solid particle may occur at two extreme limits: the regime of shrinking density and the regime of shrinking core. The models describing these two limiting cases; i.e. shrinking density model (SDM) and shrinking core model (SCM) have been widely used in the literature of twophase gas−solid reaction systems; e.g. see refs 41 and 42. The suitability of employing SDM or SCM strictly depends on the operational regime of a converting solid particle. For the case of a pyrolyzing biomass particle at high temperatures, it is unlikely that SDM appropriately represents the particle conversion. On the basis of the results of refs 3, 23, and 24, it is necessary to account for the intraparticle gradients so the application of SDM (assuming a homogeneous process) can cause significant errors in the model prediction. Thus, the application of SDM is limited to the regime of slow pyrolysis where the particle decomposition occurs homogenously. In such a case, perhaps one may adapt the formulation of Thurner and Mann43 which has been recently modified by Van de Velden et al.44 where the particle is treated as a whole. On the other hand, it is possible to employ SCM for describing the pyrolysis of biomass particle in that the temperature gradient inside particle can also be taken into account in the formulation. In this case, it is assumed that the pyrolysis takes place at a very thin layer where the temperature is Tp, dividing the particle into two regions: biomass and char. This treatment is proven to yield reasonable results when modeling pyrolysis of biomass particles at high heating conditions.33−35 Although, in reality virgin biomass decomposes with different degrees inside a pyrolyzing particle, shrinking (unreacted) core model assumes that the volumetric integration of biomass decomposition takes place in a singlesheet at the interface of char and biomass regions. As will be discussed shortly below, this treatment allows one to describe the conservation of energy in a simple conduction heat transfer equation. 3.1. Thermally Thin Particle. 3.1.1. Preheating up Stage. Consider a slab biomass particle shown in Figures 1a which is initially at temperature T0 and suddenly exposed to a hot nonoxidative environment maintained at a uniform temperature. The particle will therefore begin to heat up so that a thermal penetration will form at the front surface. The net heat flux at the surface of the particle is

Figure 2. Schematic representation of a pyrolyzing thermally thick particle.

the thermally thin particle as depicted in Figure 2c and d. In summary, the following processes take place in a thermally thick particle: (1) Initial heating up (Figure 2a) (2) Heating-pyrolysis (Figure 2b) (3) Pyrolysis (Figure 2c) (4) Postpyrolysis heating up (Figure 2d) In the following section, a simplified model is presented for various stages of the conversion process explained above.

″ = qext ″ − h(Ts − T∞) − σε(Ts 4 − T∞4) qnet

(1)

From the principle of conservation of energy the net change in the enthalpy of the particle over an incremental time would be the same as the net heat received at the surface of the particle. Hence,

3. FORMULATION As the objective of the present paper is to establish a particle model as simple as possible which can capture the main characteristics of a pyrolyzing biomass particle, we need to base our formulation on certain simplifying assumptions. As is common in most simplified modelse.g. see refs 33−35 and 38the thermophysical properties and particle size are assumed to be constant during the entire process. Worthy of mentioning is that even in comprehensive modeling studies,4−8,12,19 most thermophysical parameters are treated as constants. Following the works of Peters,4 Sadhukhan et al.,11 Babu and Chaurasia,14 Bilbao et al.,39 and Koufopanos et al.,40 the effect of convective flow of gaseous byproducts on total particle enthalpy balance is not considered in this study. This

″ A dt dH = qnet

(2)

where A denotes the cross-sectional area. Equation 2 is rewritten in terms of temperature as follows. ″ dt ρB c p L dTm = qnet

(3)

B

where Tm represents the mean temperature of the particle defined as Tm = 3232

1 V

∫0

V

T dV ′ =

1 L

∫0

L

T dx

(4)


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The transient heating up schemed in Figure 1a is subject to three boundary conditions: −kB(∂T/∂x)|x=0 = q″net; kB(∂T/ ∂x)|x=xt = 0; T|x=xt = T0. To calculate a mean temperature using eq 4, one needs to account for the spatial temperature gradient within the particle. On the basis of the detailed simulation results,2,3 various functions can be employed for approximation of the spatial temperature; e.g. exponential, power, polynomial. In the current formulation, we assume that the spatial temperature profile inside the particle at each instant can be approximated with a quadratic function, because it can satisfy the above three boundary conditions. Thus, T(x) would obey T = T0 +

2 ″ ⎛ qnet x⎞ x t ⎜1 − ⎟ 2kB ⎝ xt ⎠

Ts = Ts, L +

(12)

This formulation is valid until the surface temperature rises up to Tp at the time tp,ini. 3.1.2. Pyrolysis Stage. Soon after the surface temperature has reached the pyrolysis temperature, the particle is divided into char layer with thickness xc, and biomass layer with length L − xc as depicted in Figure 1c. The temperature at the biomass/char interface, where pyrolysis is assumed to takes place at infinitesimal rate, is Tp. Consistent with the analysis presented for the heating up stage, the conservation of energy for char and biomass regions are written. Hence, Biomass region (xc ≤ x ≤ L)

(5)

The surface temperature is obtained from eq 5 with x = 0. Hence, Ts = T0 +

(ρc p)B d[(L − xc)(Tm,B − Tp)] = qB,″ x dt c

″ xt qnet

=

⎛ 1⎜ L ⎜⎝

∫0

= T0 +

∫0

xt

xt

(6)

″ − qC, ″ x ) dt (ρc p)C d[xc(Tm,C − Tp)] = (qnet

T dx +

∫x

c

T dx ) t

⎞ ⎡ ⎞2 ⎤ q″ ⎛ ⎢T + net x ⎜1 − x ⎟ ⎥ dx + T (L − x )⎟ 0 t ⎟ ⎢⎣ 0 2kB t⎝ xt ⎠ ⎥⎦ ⎠

″ xt 2 qnet 6kBL (7)

d ″ (q ″ xt 2) = 6αBqnet dt net

−kB(∂TB/∂x)|x = xc = −k C(∂TC/∂x)|x = xc +ṁ ″Δhp

Applying approximate time integration (i.e., assuming = 0.5(q″net + q″0)t) to eq 8 leads to ⎛ q″ ⎞ 3αB⎜⎜1 + 0 ⎟⎟t ″ ⎠ qnet ⎝

q″net dt

ṁ ″ = ρB

Δx dxc ≈ ρB c Δt dt

TB = Tp + ϕ1(x − xc) −

″L qnet 3kB

(10)

⎛ 3αB ⎞ ⎜ ⎟q ″ d t ⎝ L ⎠ net

ϕ1 2(L − xc)

(x − xc)2

(11)

(17)

kBϕ1 + ṁ ″Δhp

(xc − x) kC q ″ + kBϕ1 + ṁ ″Δhp (xc − x)2 + net 2xck C

TC = Tp −

Thus, the particle conservation of energy reads ″ L) = d(3kBTs − qnet

(16)

where Δt is a very small increment of time. Let us approximate the spatial temperature profile in each layer with a quadratic function. Applying appropriate boundary conditions at the particle surface, back face, and the location of x = xc leads to the following temperature profiles in char and biomass layers.

(9)

where q0″ denotes the net heat flux at t = 0. In the second phase of the heating up process as depicted in Figure 1b, the thermal wave has already reached the back face while Ts is still less than Tp. If we undertake a similar procedure and repeat eqs 2−7 for the second phase of the preheating stage, the following expression is obtained for the particle mean temperature. Tm = Ts −

(15)

where Δhp denotes the specific heat of pyrolysis (negative when endothermic and positive when exothermic), and ṁ ″ represents the decomposition rate per unit particle surface area perpendicular to x-coordinate.

(8)

∫ t0

(14)

where Tm,B, Tm,C, q″C,xc, and q″B,xc denote mean temperature of biomass layer, mean temperature of char layer, heat flux transferred from char layer to the biomass/char interface, and heat flux received by the biomass layer at the interface, respectively. On the other hand, the conservation of energy at the biomass/char interface implies that the net heat received by the biomass region is equal to the heat transferred from the char region to the interface minus (plus) the endothermic (exothermic) heat of pyrolysis. Hence,

L

A combination of eqs 7 and 3 yields

xt =

(13)

Char region (0 ≤ x ≤ xc)

2kB

With the temperature profile given in eq 5, the mean particle temperature is found using eq 4. Hence 1 Tm = ( L

α L ″ − qL″) + B (qnet ″ + qL″)(t − tL) (qnet 3kB 2kBL

(18)

In eqs 17 and 18, ϕ1 is a time-dependent coefficient for which a relationship can be obtained by applying a similar analysis to the biomass region. First, using eq 19, we determine the mean temperature in the biomass layer as follows.

The initial condition for this problem is that at t = tL (the time at which the thermal wave reaches the back face), Ts = Ts,L (to be determined from eq 6). So, integrating eq 11 from tL to t, and assuming a mean value for qnet ″ equaling (qnet ″ + qL″ )/2 yields 3233


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Tm,B = = Tp +

ϕ1 3

∫x

Article L

T dVB =

c

1 L − xc

∫x

L

thermophysical properties should be replaced with those of char. Thus, the surface temperature is obtained from α L ″ + qp″)(t − t p) Ts = Tsp + (q ″ − qp″) + C (qnet 3k C net 2k CL

T dx

c

(L − xc)

(19)

(26)

Substituting eq 19 into eq 13 and computing q″B,xc with the aid of eq 17 yields (ρc p)B d[ϕ1(L − xc)2 ] = −3kBϕ1 dt

where tp is the conversion/pyrolysis time (including heating up stage) and Tsp and qp″ are the surface temperature and net heat flux at the time tp. 3.2. Thermally Thick Particle. For a thermally thick particle, all subprocesses are the same as those of a thermally thin particle except the second phase of the process. Unlike in the thermally thin particle (Figure 1) where the thermal wave rapidly reaches the back face of the particle before initiation of the pyrolysis at the front surface, in the thermally thick particle (Figure 2) the surface temperature attains the pyrolysis temperature while still xt < L. In this section only the formulation of the second stage of a thermally thick particle will be presented. The procedure is very much similar to that presented in section 3.1.2. The conservation of energy within the biomass (xc < x < xt) and the char (0 < x < xc) regions are described by eqs 13 and 14, respectively. It can be shown that the temperature profile within the char layer would be exactly the same as given in eq 18 and the mean temperature in this region would be the same as given in eq 22. This means that the time and space integration of eq 14 would lead to exactly the same result given in eq 24. On the other hand, the temperature profile in the biomass region undergoing a heating up process would be somewhat similar to eq 17 with L replaced with xt and ϕ1 given by eq 27.

(20a)

or, after expanding the left-hand side and rearranging, dϕ1 ϕ1

=

−3αB dt 2

(L − xc)

+

2 dxc L − xc

(20b)

Assuming a mean value for xc in the first term on the right-hand side of eq 20b over a small time increment Δt as xc̅ = [xc(t) + xc(t − Δt)]/2, a solution of eq 20b results as follows. ⎡ L − xc(t − Δt ) ⎤2 ⎡ 3αBΔt ⎤ ⎥ ϕ1(t ) = ϕ1(t − Δt )⎢ ⎥ exp⎢ − ⎣ L − xc(t ) ⎦ ⎣ (L − xc̅ )2 ⎦ (21)

Notice that eq 21 is subject to the initial condition t = tp,ini and ϕ1 = −qp,ini ″ /kB. Similarly, the following relationship is obtained for the mean temperature of the char layer. Tm,C = Tp +

″ − 2kBϕ1 − 2ṁ ″Δhp qnet 6k C

xc

(22)

So, eq 14 can be rewritten using eq 22 and with the aid of eq 18 for determination of q″C,xc. Hence d [(q ″ − 2kBϕ1 − 2ṁ ″Δhp)xc 2] dt net ″ + kBϕ1 + ṁ ″Δhp) = 6αC(qnet

⎛ Tp − T0 ⎞ ϕ1 = −2⎜ ⎟ ⎝ xt − xc ⎠

Thus, the energy conservation equation in the biomass region experiencing a heating process leads to

(23)

Considering an average value for the terms inside the bracket on the right-hand side of eq 23 and integrating with respect to the time from tp,ini to t results in xc =

⎛ q ″ + kBϕ + ṁ ″Δhp ⎞ 1 ⎟⎟(t − t p,ini) 3αC⎜⎜ net ″ − ϕ q 2 k ⎝ net B 1 − 2ṁ ″Δhp ⎠

d(xt + 2xc) =

6αB dt xt − xc

(28)

Integrating eq 28 over a small time increment Δt gives xt(t ) = xt(t − Δt ) +

(24)

6αBΔt − 2[xc(t ) − xc(t − Δt )] xt̅ − xc̅ (29)

It is obvious that initially (i.e., t = tp,ini) xc = 0. At each instant, the surface temperature is determined from eq 18 with x = 0. Hence ⎛ q ″ − kBϕ1 − ṁ ″Δhp ⎞ ⎟xc Ts = Tp + ⎜ net 2k C ⎝ ⎠

(27)

where xt̅ and xc̅ denote mean values of the thermal penetration and the char layer thicknesses, respectively, over the time increment of Δt. Notice that the initial conditions required for solving the second phase of the thermally thick particle pyrolysis are that at t = tp,ini, xc = 0 and xt = xt(tp,ini), where the thermal penetration depth at the commencement of the pyrolysis is obtained from the previous stage (preheating stage). To be able to fully solve the pyrolysis problem at this stage, one would need to also use eqs 16, 24, 25, and 1. 3.3. Numerical Solution. The first step for numerically solving the equations of the simplified model described in previous sections is to define whether the particle is thermally thin or thick. Initially, particle undergoes a heating up process so one needs to simultaneously solve eqs 1, 6, and 9. For a thermally thin particle, the calculations continue until xt equals L at the characteristic time tL. Upon satisfaction of xt = L, one needs to solve eqs 1 and 12 to compute the net heat flux and

(25)

We have five unknownsṁ ″, ϕ1, xc, Ts, and q″netand five coupled algebraic equations which need to be solved simultaneously at each time step from the initiation of pyrolysis at the surface of particle until the char front reaches the back face. 3.1.3. Postpyrolysis Heating Up. After all biomass has completely decomposed to the pyrolysis byproducts, the remaining material in particle is char and the problem reduces to a simple conduction heat transfer problem as shown in Figure 1d. The solution of the postpyrolysis heating up would be identical to that of the second phase of the heating up stage as described in section 3.1.1 with a difference that all 3234


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temperature at the particle surface during the prepyrolysis heating up stage. When the surface temperature attains the assigned pyrolysis temperature at the time tp,ini, the solution algorithm switches so that eqs 1, 16, 21, 24, and 25 are solved numerically through a trial-and-error method. For the thermally thick particle, the solution method is initially is the same as explained above for the thermally thin particle. That is, one needs to first solve eqs 1, 6, and 9 from the time t = 0 until tp,ini. Beyond this moment, the solution algorithm consists of simultaneously solving eqs 1, 16, 24, 25, and 29 until thermal penetration reaches the back face at t = tL. Between t = tL and t = tp, the pyrolysis problem is identical to that of the thermally thin particle whence a set of eqs 1, 16, 21, 24, and 25 are solved.

4. MODEL VALIDATION The formulation of the simplified model presented in the preceding section is accomplished by adapting certain simplifying assumptions and approximations. To examine the accuracy of the model, the validation is carried out in two stages, which includes assessment of the preheating model and the entire pyrolysis model. In the upcoming subsection, the computations of the simplified preheating model are compared with those of an ODE (ordinary differential equation) model and a PDE (partial differential equation) model. Upon validation of the preheating model, the accuracy of the simplified pyrolysis model will be examined by comparing the predictions of the model against different sets of experimental data found in the literature as well as the computations of a comprehensive model of a pyrolyzing single wood particle. 4.1. Validation of the Preheating Model. The first phase of particle decomposition includes a heating up process until the surface temperature reaches a pyrolysis temperature. The capability of the simplified model is assessed by comparing the history of the surface temperature obtained from three models: the simplified model, an ODE model, and a PDE model. The comparison is carried out for both thermally thick and thermally thin particles. For each case, two different heating conditions are considered: (1) Particle is heated up in a hot environment maintained at a uniform temperature; (2) Particle is heated up by an external heat flux. The thermophysical properties used in the computations are as follows: ρB = 700 kg/m3, cpB = 2000 J/kg·K, kB = 0.35 W/m·K, T0 = 300 K, Tp = 700 K, h = 20 W/m2·K, ε = 0.9. The ODE model is, in fact, a set of equations described in section 3.1.1 excluding those obtained from approximate time integration. Furthermore, the PDE model is the simple transient heat conduction equation defined as (∂T/∂t) = αB(∂2T/∂x2). The comparison between three models is depicted in Figures 3 and 4 for thermally thick and thermally thin particles, respectively. The first main observation from Figures 3 and 4 is that the predictions of the simplified and ODE models are perfectly coincident. This leads us to conclude that the treatment of approximate time integration does not cause significant error. On the other hand, for the case of thermally thick particle (Figure 3), the solution of either of simplified or ODE model leads to a little overprediction of the surface temperature and slightly underprediction of the time of pyrolysis commencement compared to the PDE solution. In the case of thermally thin particle (Figure 4), all three models predict almost identical surface temperature history in both heating conditions depicted in Figure 4a and b.

Figure 3. Comparison of the predicted surface temperature by three models: (a) thermally thick particle (L = 30 mm, qext = 75 kW/m2); (b) thermally thick particle (L = 10 mm, T∞ = 900 K).

On the basis of the results of Figures 3 and 4, it can be concluded that approximating the spatial temperature profile with a quadratic function may lead to a negligible overprediction of the surface temperature of a thermally thick particle, whereas it has almost no influence on the surface temperature history of a thermally thin particle. 4.2. Validation of the Pyrolysis Model. The validation of the pyrolysis model is carried out by comparing its predictions with five different sets of experiments of various wood particles reported in the literature as well as the computations of a comprehensive model of a pyrolyzing single wood particle published by the authors earlier.2,3 The comprehensive model has further been used in a particle combustion model.45 The thermophysical properties employed in the simulations are those reported in the relevant sources used for validation of the model or given in the literature (see Tables 1 and 2). The correlation proposed by Milosavljevic et al.46 is used for calculating the enthalpy of pyrolysis. It is proven to be a sufficient relationship, which allows producing accurate predictions when used in a pyrolysis model.3 4.2.1. Burning Rate. The first set of validation is carried out using the experiments reported by Spearpoint and Quintiere.33 These data are obtained from the pyrolysis of different wood species of 50 mm thickness exposed to incident 3235


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Table 2. Thermophysical Properties Used for Validations in Figures 6−9

Table 1. Thermophysical Properties33 Used for Validations in Figure 5 Douglas fir

Red Oak

Redwood

Tp [K] T0 [K] T∞ [K] kB [W/m·K] kC [W/m.K] ρB [kg/m3] ρC [kg/m3] cpB [J/kg·K] cpC [J/kg·K] h [W/m2·K] ε L [mm]

657 300 400 0.4 0.2 502 50 3000 1500 10 0.95 50

577 300 400 0.44 0.2 753 75 3600 1500 10 0.95 50

648 300 400 0.22 0.2 354 50 3000 1500 10 0.95 50

Figure 6

Figure 7

Figure 8

Figure 9

648 300 400 0.6 0.45 462 60 4000 2000 10 0.95 25.4

523 300 1625 0.2 0.06 650 33 2500 1200 15 0.95 0.16

523 300 400 0.3 0.1 450 60 2000 1100 15 0.85 30

623 300 400 0.3 0.15 380 80 1150 1000 24 1 38

heat fluxes of 25−75 kW/m2 with their grain oriented either parallel or perpendicular to the incident heat flux. Most of the tests were conducted for an exposure time of 25 min. All samples were tested in a Cone Calorimeter with horizontal orientation. Figure 5 plots comparisons between the measured and the predicted burning rates for slabs of Douglas fir (Figure 5a), Red Oak (Figure 5b), and Redwood (Figure 5c) particles with incident heat flux of 75 kW/m2 (Douglas fir and Red Oak woods) and 50 kW/m2 (Redwood) radiated along the grain. Spearpoint and Quintiere33 presented only the first 600 s of each test for clearly identifying the growth and decay stages of the conversion process. The prediction of the presented simplified model is qualitatively in a good agreement with the experimental trend of the burning rate history in all three cases. In addition, the model successfully captures the burning rates at early stages including the measured time and amount of the maximum burning rate. The computed mass loss rate in the decay phase of the conversion is underpredicted. As outlined by Spearpoint and Quintiere,33 the back face effect may play a role due to incomplete insulation, but the formulation assumes no heat exchange at this location with the surrounding. A further possible reason for underprediction of the burning rate in later stages may be the assumption of constant thermophysical properties and negligible virgin biomass and char density gradients along the particle, which are not taken into account in the presented model. The second validation is carried out using the measured mass loss rate history reported by Wasan et al.26 The data were obtained from pyrolysis test of a 25.4 mm plywood particle exposed to an external heat flux of 50 kW/m2. Figure 6 compares the predicted mass loss history during the entire decomposition process with the measured data. The model prediction is in a satisfactory agreement with the experiments both qualitatively and quantitatively. As can be seen, the mass loss rate takes a peak twice during the particle pyrolysis; first at the early stage and then in the final stage of conversion. The predicted time and the quantity of these peaks are within ±5.5% and −4% of the corresponding measured values, respectively. Further model validation is related to the comparison of the predicted and measured mass loss of a 160 μm flake-like sawdust particle pyrolyzed at a reactor temperature of 1625 K. The experimental data are reported by Lu et al.5 The comparison is depicted in Figure 7 where the prediction of the detailed pyrolysis model of Lu et al.5 is also represented.

Figure 4. Comparison of the predicted surface temperature by three models: (a) thermally thin particle (L = 1 mm, qext = 90 kW/m2); (b) thermally thin particle (L = 1 mm, T∞ = 1273 K).

property

property Tp [K] T0 [K] T∞ [K] kB [W/m·K] kC [W/m·K] ρB [kg/m3] ρC [kg/m3] cpB [J/kg·K] cpC [J/kg·K] h [W/m2·K] ε L [mm]

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Figure 6. Comparison of the predicted and measured mass loss rate of a 25.4 mm pine particle exposed to 50 kW/m2 heat flux.

Figure 7. Comparison of the prediction of the simplified model with the experiment and the prediction of the Lu et al. model5−mass loss of a 160 μm sawdust particle at a reactor temperature of 1625 K.

experimental trend. As pointed out by Lu et al.,5 this is possibly due to the irregular shape and size distribution of the particles which are not accounted for in neither of the models. 4.2.2. Temperature. The accuracy of the model has also been examined by reproducing the temperature of thick slab particles undergoing pyrolysis at the surface and internal locations. The first set of data is taken from the work of Grønli and Melaaen47 who experimentally studied the pyrolysis of birch, pine, and spruce particles in a bell-shaped glass reactor using a xenon arc lamp as a radiant heat source. The total times of exposure were 300 and 600 s. The experimental results of spruce particle, among other species, of 30 mm length were chosen for validation of their pyrolysis model (which did not account for particle shrinkage). The particle was heated parallel with the grain and showed the lowest axial shrinkage at both low and high heat fluxes compared to pine and birch samples. Shown in Figure 8 are the predicted temperature histories at the surface and 4 mm below the surface using the simplified model compared with the experimental values as well as the computations obtained from the comprehensive model2,3 for an

Figure 5. Comparison of the predicted and measured burning rate of 50 mm particle exposed to 75 kW/m2 (a and b) and 50 kW/m2 (c) heat flux: (a) Douglas fir; (b) Red Oak; (c) Redwood.

The prediction of the present model is well comparable with that of the comprehensive model of Lu et al.5 The trend of the mass loss history is reasonably captured by the simplified model. The predicted conversion time is 0.305 s which is fairly comparable to the measured value 0.350 s. The slope of mass loss curve predicted by both models is steeper than the 3237


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Figure 9. Comparison of the predicted and measured white pine particle temperature at the surface and at the location of 5 mm beneath the surface (L = 38 mm; q″ext = 40 kW/m2).

Figure 8. Comparison of the predicted and measured (area between the broken lines) spruce particle temperature at the surface and at the ″ = 80 kW/m2 location of 4 mm beneath the surface (L = 30 mm; qext heat flux).

were studied by means of a comprehensive pyrolysis model. The detailed description of this model can be found in refs 2 and 3. It assumes that a virgin biomass decomposes to light gases, tar and char through three parallel reaction pathways. On the basis of this kinetic scheme, one-dimensional (1D) transport equations are described on the basis of principles of energy, mass, and momentum conservation. The comprehensive model, validated against a wide range of experiments, allows one to observe time and space evolution of many parameters such as temperature, solid density, gas phase density, porosity, velocity of gaseous flow within the pores, etc. The conversion time of beech and spruce wood slab particles predicted by the simplified and the comprehensive models is illustrated in Figure 10. Four different data sets can be observed in this figure. For each wood type, one set of conversion times is related to a constant external heat flux of 100 kW/m2 and various particle sizes in the range of 300−1500 μm, whereas another set is for a particle thickness of 1000 μm and varying heat flux in the range of 100−300 kW/m2. The range of particle

exposure time of 600 s and an incident heat flux of 80 kW/m2. As seen, the prediction of the simplified model compares well with the detailed model, and it is capable of reproducing the time evolution of the temperature at different positions. In particular, it can be observed that the surface temperature predicted by the simplified model matches that resulted from the comprehensive model. The pyrolysis temperature assigned for producing the graphs depicted in Figure 8 was chosen 250 °C according to the experimental results of Grønli48 obtained from the pyrolysis of spruce wood. To reinsure the capability of the simplified model for reproducing the temperature experiments, another set of data reported by Kashiwagi et al.49 is used for additional model validation. They conducted gasification experiments of thermally thick white pine wood with 38 mm cube samples at three different atmospheres of nitrogen, 10.5% oxygen/ 89.5% nitrogen, and air under the nonflaming conditions at a thermal radiant heat flux of 25−69 kW/m2. For the purpose of comparison of the simplified pyrolysis model, only the measurements obtained in the nitrogen atmosphere are chosen. A comparison of the predicted and measured temperature history at the surface and 5 mm beneath the surface of a white pine sample exposed to a 40 kW/m2 external heat fluxparallel to the grainis shown in Figure 9. The computed graphs are obtained assuming a pyrolysis temperature of 350 °C. Similar to the previous case (Figure 8), the trend of predicted temperature histories compare well with the experiments. At early stages of the process, the temperature is overpredicted owing to the moisture content of the sample, as the model does not account for particle drying. At the later stages of the decomposition, however, the predicted temperature histories at the surface and 5 mm depth match very well with the measured values. 4.2.3. Conversion Time. A further key process parameter is conversion/pyrolysis time, which is of great importance for designers of reactors operating at high heating conditions where thermochemical conversion of small (millimeter size) particles takes place. In a previous study by Haseli et al.,3 the effects of particle size and external radiant heat flux on conversion time and final char yield of beech and spruce woods

Figure 10. Comparison of the predictions of the simplified and the comprehensive models in terms of conversion time (s) of beech and spruce wood particles. 3238


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parameters such as external heat flux and particle size, which may be used as a useful tool in the absent of experimental data. Their results show that at a high heating rate, the pyrolysis temperature is higher. The effect of prescribed pyrolysis temperature on model predictions have further been investigated for both thermally thick and thermally thin beech wood particles (700 kg/m3) exposed to an incident heat flux of 50 kW/m2. The thickness of thermally thick particle is chosen to be 10 mm and that of thermally thin particle is assigned as 1 mm. In both cases, it is assumed that the final char density is 70 kg/m3 (90% conversion). The time evolution of burning rate and surface temperature are examined for Tp = 573, 623, 673, and 723 K. The results are depicted in Figures 11and 12. Figure 11 illustrates the effect of pyrolysis temperature on burning rate history. For a thermally thick particle (Figure 11a), the trends of the graphs are similar to those shown in Figure 6. There exist two distinctive maximum mass loss rates at early and late stages of decomposition. At a lower value of Tp, the global mass loss peak takes place at the early phase of pyrolysis.

size and external heat flux are chosen from ref 3 which is similar to the condition of industrial combustors. The regime of particles in all these cases is thermally thin. Simulations were carried out for the situation that both the front surface and back face of particle are exposed to the above heat flux, so that the calculations were performed for half of the particle assuming a symmetry condition at the particle center. The comparisons shown in Figure 10 reveal the acceptable capability of the simplified model for predicting the conversion time of small particles. Form this graph, the accuracy of the simplified model is within ±20% of the comprehensive model. These results indicate that the model introduced in this paper can be effectively used for practical design purposes.

5. DISCUSSION The multiple validations of the simplified model against various experimental data and the prediction of a comprehensive model in terms of main process parameters lead to the conclusion that the presented model is sufficiently capable of predicting the mass loss (rate), surface temperature, and conversion time. Thus, it can be employed as an effective design tool for predicting the main characteristics of pyrolysis of biomass (and charring solid) particles of thermally thick and thermally thin. The main advantage of the simplified model compared to the comprehensive model is that it can be easily implemented into a reactor model and solved much quicker. In industrial reactors such as fluidized beds and entrained flow reactors, a designer needs to deal with thermochemical conversion of a large number of small particles in the order of 1 mm or less. The most important parameters to be calculated from a single particle model are the history of temperature and net heat flux at the surface and mass loss. The results of this study show that the presented model can be a useful tool for engineering applications. Given that the formulation and the results are presented for slab and flakelike particles, the same methodology can be applied for modeling pyrolysis of other shapes; i.e. cylinder and sphere. Appendix A describes the formulation procedure for a thermally thin cylindrical/spherical particle. Worthy of further discussion is the sensitivity of the model accuracy to thermophysical properties and other input parameters; the most rigorous one being the pyrolysis temperature. A wide range of values has been reported in the literature for this parameter. Galgano and Di Blasi37 suggest that it should be treated as an adjustable parameter leading to results comparable with experiments or a detailed model based on finite rate kinetics. Past study of Spearpoint and Quintiere33 indicates that Tp obtained from experimental tests is material and orientation dependent. For instance, they determined average ignition temperatures of 375 and 204 °C for Redwood with the external heat flux radiating along and across the grain, respectively. Another study by Moghtaderi et al.50 revealed that the ignition temperature depends on the external heat flux and moisture content. They measured ignition temperatures for Radiata pine wood for incident heat flux of 20−60 kW/m2 and moisture content of 0−30% and found a range of 298−400 °C. Moreover, Yang et al.51 reported a range of 190−310 °C for the ignition temperature of wood. As a result, a designer needs to carefully select a proper value for the pyrolysis temperature; otherwise, it may lead to insufficient accuracy of the simplified model predictions. Recently, Park et al.52 have proposed a correlation for estimating Tp as a function of process

Figure 11. Effect of pyrolysis temperature on burning rate history of a single (a) thermally thick particle (b) thermally thin particle, at an incident heat flux of 50 kW/m2. 3239


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The effect of Tp on the surface temperature is shown in Figure 12. The main observation is that for the thermally thick particle the surface temperature reaches thermal equilibrium with the surrounding before completion of the pyrolysis (Figure 12a), while for the thermally thin particle the surface temperature still rises after complete conversion of particle (Figure 12b). This is due to the influence of intraparticle thermal resistances which, in the thermally thick regime, are much greater than those in the thermally thin regime. This indicates that for the case of thermally thin, the rate of char penetration depth (dxc/dt) is faster than the rate of surface temperature rise.

6. CONCLUSION A simplified pyrolysis model of single biomass particle is presented which assumes that the decomposition of biomass takes place at a prescribed pyrolysis temperature in an infinitesimally thin plane dividing the particle into char and virgin layers. Two different pyrolysis regimes have been identified including thermally thin and thermally thick. In the former regime, a thermal wave initiated at the surface of the particle moves fast toward the back face such that the time of initiation of pyrolysis (tp,ini) is longer than the time at which the thermal penetration reaches the back face (tL). In the latter regime tL > tp,ini meaning that the decomposition begins at the surface while the thermal penetration wave still moves toward the back face. Different validations of the introduced model with a wide range of experimental data of slab particles as well as the predictions of a comprehensive model indicate that the presented model successfully captures the trend of the main process parameters. It is capable of predicting mass loss rate, surface and internal temperatures, and particle conversion time with sufficient accuracy acceptable for engineering purposes. The multiple validations of this model reveals that it can be adopted as a useful tool in reactor design codes for industrial applications, since computationally it is cheaper and easier to implement in a computational fluid dynamics (CFD) code compared to a comprehensive model.

Figure 12. Effect of pyrolysis temperature on surface temperature history of a single (a) thermally thick particle (b) thermally thin particle, at an incident heat flux of 50 kW/m2.

■

By increasing Tp, the first peak shifts in time, its quantity decreases, and the process becomes longer. Also, the global maximum burning rate takes place at the later stage of pyrolysis at higher values of Tp. In fact, at a higher Tp, the particle regime shifts toward thermally thin and the initiation time of pyrolysis increases (leading to an increased preheating phase) and gets closer to the time at which the back face temperature begins to heat up. When the pyrolysis temperature is lower, particle decomposition takes place faster than the case with a higher Tp. On the basis of the model assumption, the conversion of virgin material would happen as soon as the temperature reaches Tp. Thus, a higher Tp corresponds to a higher amount of heat required for virgin material decomposition and the process becomes slower. For a thermally thin particle (Figure 11b), the same general trend can be observed; that is, by increasing Tp, the process becomes slower and the mass loss rate reduces. Unlike the thermally thick particle, there exists only one maximum burning rate which takes place in the first half of the decomposition process. At higher values of Tp, the burning rate peak occurs later and its quantity becomes lower.

APPENDIX A. DERIVATION OF MODEL EQUATIONS FOR OTHER SHAPES The key difference between a slab particle and a cylindrical/ spherical particle is that the cross-sectional area of the thermal wave (in preheating phase) and reaction front (in pyrolysis phase) decreases from the surface towards the center in a cylindrical/spherical particle. The derivation of model equations is described only for the preheating and the pyrolysis phases of a thermally thin particle. The same methodology can be applied for a thermally thick particle. Thermally Thin Particle: Preheating up Stage. The conservation of energy for the virgin material obeys (ρc p)B dTm =

″ 2qnet R

dt

(A.1)

where R denotes the radius of cylinder. Using the boundary conditions and assuming a quadratic function for temperature within particle leads to eq 5. Thus, the mean temperature Tm is obtained as follows. 3240


Energy & Fuels Tm =

1 [ R2

∫0

Article

rt

2(R − rt)T dt +

∫r

⎡ R − rc(t − Δt ) ⎤3 ⎡ 8α Δt ⎤ B ⎥ ϕ1(t ) = ϕ1(t − Δt )⎢ ⎥ exp⎢ − ⎣ R − rc(t ) ⎦ ⎣ (R − rc̅ )2 ⎦

R

2(R − rt)T dt ]

t

(A.2)

(A.13)

where rt is the thermal penetration depth. Substituting eq 5 into eq A.2 and integrating, we get Tm =

″ qnet 12R2kB

Furthermore, integrating eq A.12 using a mean value of the terms inside the bracket on the right-hand side of eq A.12 at time tp,ini and t gives

(4Rrt 2 − rt 3) + T0

″ [4Rrc 2 − rc 3 − 12αCR(t − t p,ini)]qnet

(A.3)

A combination of eqs A.1 and A.3 yields

+ [3rc 3 − 8Rrc 2 − 12αC(R − rc)(t − t p,ini)]kBϕ1

″ (4Rrt 2 − rt 3)] = 24αBRqnet ″ dt d[qnet

= [12αC(R − rc)(t − t p,ini) − 3rc 3 + 8Rrc 2]ṁ ″Δhp

(A.4)

(A.14)

Consequently, applying approximate time integration to eq A.4 and rearrangement results in ⎛ q ″⎞ rt 3 − 4Rrt 2 + 12αBR ⎜⎜1 + 0 ⎟⎟t = 0 ″ ⎠ qnet ⎝

It is obvious that the rate of biomass conversion is determined from ṁ ″ = ρB

(A.5)

To obtain the thermal penetration depth at a given instant, one needs to solve eqs A.5, 1, and 6 simultaneously. The solution is valid until rt becomes equal to R at the time tR. In the second phase of the preheating phase (i.e., tR ≤ t ≤ tp,ini), Tm is obtained by undertaking a similar procedure as follows.

Tm = −

″ qnet 4kB

R + Ts

Sphere

The model equations for a thermally thin spherical particle equivalent to eqs A.5, A.8, A.13, and A.14 are as follows. ⎛ q″ ⎞ rt 4 − 5Rrt 3 + 10R2rt 2 − 30R2αB⎜⎜1 + 0 ⎟⎟t = 0 ″ ⎠ qnet ⎝

The conservation of energy for the particle is therefore represented as

Ts = TsR +

(A.7)

3αB 9R (q ″ − qR″) + (q ″ + qR″)(t − tR ) 20kB net 2kBR net

⎡ R − rc(t − Δt ) ⎤4 ⎡ 15α Δt ⎤ B ⎥ ϕ1(t ) = ϕ1(t − Δt )⎢ ⎥ exp⎢ − ( R − rc̅ )2 ⎦ ⎣ R − rc(t ) ⎦ ⎣

α R ″ − qL′′) + B (qnet ″ + qL′′)(t − tR ) (qnet + 4kB kBR

(A.13a)

(A.8)

Thermally Thin Particle: Pyrolysis Stage. The formulation procedure is the same as explained in section 3.1.2. One needs to calculate mean temperature for the char and biomass regions with a method described above considering the geometry of a cylindrical particle. We avoid repeating the derivation of Tm,C and Tm,B. The final results are Tm,C = Tp −

(kBϕ1 + ṁ ″Δhp)(15Rrc 3 − 4rc 4 − 20R2rc 2) ″ (10rc 2R2 − 5rc 3R + rc 4) + qnet ″ ](t − t p,ini) = 30αC[(R − rc)2 (kBϕ1 + ṁ ″Δhp) + R2qnet

■

kBϕ1 + ṁ ″Δhp ⎛ 8Rrc 2 − 3rc 3 ⎞ ⎜ ⎟ 2 12k C ⎝ 2Rrc − rc ⎠

ϕ1 4

(R − rc)

Notes

The authors declare no competing financial interest.

■

(A.9)

ACKNOWLEDGMENTS The financial support provided by the Dutch Technology Foundation STW through project BiOxyFuel No. 10416 is gratefully acknowledged.

(A.10)

■

(A.11)

″ (4Rrc 2 − rc 3) − (kBϕ1 + ṁ ″Δhp)(8Rrc 2 − 3rc 3)] d[qnet ″ R + (kBϕ1 + ṁ ″Δhp)(R − rc)] dt = 24αC[qnet

AUTHOR INFORMATION

*E-mail: [email protected].

The differential form of the heat transfer equation in char and biomass regions results as follows. d[ϕ1(R − rc)3 ] = −8αBϕ1(R − rc) dt

(A.14a)

Corresponding Author

q ″ ⎛ 4Rr 2 − rc 3 ⎞ ⎟ + net ⎜ c 12k C ⎝ 2Rrc − rc 2 ⎠ Tm,B = Tp +

(A.5a)

(A.8a)

Integrating eq A.7 yields Ts = Ts, R

(A.15)

A system of eqs A.13−A.15, 25, and 1 should be solved at each time interval for predicting the pyrolysis stage.

(A.6)

″ R + 4kBTs) = 8αBqnet ″ dt d( −qnet

drc Δr ≈ ρB c dt Δt

(A.12)

A solution of eq A.11 leads to 3241

NOMENCLATURE cp = specific heat, J/kg·K H = enthalpy, J h = convective heat transfer coefficient, W/m2·K k = thermal conductivity, W/m·K L = thickness/length of particle, m ṁ ″ = decomposition rate per unit surface area, kg/m2·s dx.doi.org/10.1021/ef3002235 | Energy Fuels 2012, 26, 3230−3243

Energy & Fuels

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q″ = heat flux, W/m2 q″net = net heat flux at particle surface, W/m2 T = temperature, K Tp = pyrolysis temperature, K Ts = surface temperature, K Ts,L = surface temperature at the time tL, K t = time, s tL = duration of thermal penetration movement from the front surface to the back face of particle, s tp,ini = time of commencement of pyrolysis at the surface of particle, s tp = conversion/pyrolysis time, s x = spatial coordinate xc = char depth, m xt = thermal penetration depth, m

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Greek Letters

α = thermal diffusivity, m2/s Δhp = specific enthalpy of pyrolysis, J/kg ε = emissivity ρ = density, kg/m3 σ = Stephen−Boltzmann coefficient Subscripts

0 = initial condition ∞ = surrounding condition B = biomass BC = boundary condition C = char ext = external r = reactor

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A Simplified Pyrolysis Model of a Biomass Particle Based on

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