Biomass Char Nitrogen Oxidation—Single Particle Model - Energy

Article pubs.acs.org/EF

Biomass Char Nitrogen OxidationSingle Particle Model Oskar Karlström,* Anders Brink, and Mikko Hupa Process Chemistry Centre, Åbo Akademi University, Biskopsgatan 8, 20500 Turku, Finland ABSTRACT: In this study, the release of NO during the combustion of single char particles of spruce bark was investigated. Modeled NO release rates were compared to experimentally determined NO rates from a single particle reactor of quartz glass. The operating conditions were between 1073 and 1323 K with 3−19 vol % O2 and with 0% NO in the surrounding gas. The NO release rates from the single particles were determined from measured molar fractions of NO at the outlet from the reactor system. In the model, the char-N is assumed to be oxidized proportionally to the char-C oxidation rate, which is measured. The formed NO is assumed to be reduced as a function of the local NO concentration inside the particle. The NO concentration profile inside the char particle is numerically calculated by taking into account the transport of NO inside and outside the particle and the reduction rates of NO inside the char particle. The modeled NO release rates were in good agreement with the measurements. The results show that the fractional conversion of char-N to NO increases as functions of decreasing particle size and conversion. The most likely explanation for this is that the formed NO diffuses away at an increasing rate as the particle decreases in size. Further, a suggested analytical model for the fractional conversion of char-N to NO is tested.

1. INTRODUCTION During the combustion of a solid char particle, the oxidation of carbon and nitrogen is frequently assumed to be nonselective,1−5 with a few exceptions.6,7 By assuming this nonselectivity, the rate of char-N oxidation is obtained from the rate of carbon oxidation and the N/C ratio in the char.2,4 For coal char particles, the conversion of char-N to HCN and N2O plays an important role.8 During the combustion of char particles of both coal and biomass, the main reaction product can be assumed, however, to be NO.8−10 The NO resulting from the char-N oxidation is partly reduced inside the char particle. The most important reduction routes are by NO char reactions or surface-catalyzed NO−CO reactions as the NO diffuses inside the particle.1 The fractional conversion of char-N to NO increases as functions of char conversion and decreasing particle size.5,11 In experiments carried out to investigate the reduction of NO inside char particles, char particles are generally introduced to a gas with a known background level of NO.8,12,13 In such experiments, the reduction rate of NO is generally related to the concentration of NO in the gas bulk phase and to the instantaneous mass of the char or to the internal surface area of the char.1,13 Such approaches are useful in the assessment of the reactivity of the NO reduction of various chars. Such analyses cannot, however, provide information regarding the fractional conversion of char-N to NO under combustion conditions. To predict the fractional conversion of char-N to NO, the concentration profile of NO inside the particle should be known. Modeling studies taking into account concentration profiles of NO are available for both fluidized-bed11,14−16 and pulverized fuel combustion conditions17 for coal char particles. In these studies, the differential equations for the NO concentration inside the fuel particles are solved by numerical methods, and it is not attractive to incorporate such models as submodels into computational fluid dynamics (CFD) codes. Yue et al.18 managed from the governing equations of oxygen, CO, and NO inside the char particle to derive an analytical © 2013 American Chemical Society

solution for the fractional conversion of char-N to NO. With their model, they successfully predicted the fractional conversion of char-N to NO from combustion experiments of single coal char particles in a laboratory-scale fluidized bed. Because the model is analytical, it is possible to incorporate the model as a submodel into a CFD code. For biomass particles, several studies report on the reduction of NO inside char particles at combustion conditions.5,9,12,19−25 Few studies are available on the fractional conversion of char-N to NO during combustion of biomass, however. Saastamoinen et al.24,25 modeled the NO formation and reduction inside an entire bed of biomass char particles under grate-fired conditions. They used a NO reduction model based on the concentration gradients of NO inside the entire bed of particles. In a previous study, we developed an engineering model to predict the formation and reduction rates of NO during combustion of single biomass char particles.5 In that model, the NO reduction rate is related to the external surface area of the particle, so that an increased external surface area gives a higher reduction rate of NO and vice versa. In this study, the NO release during the combustion of single biomass char particles is modeled by taking into account the NO concentration profiles inside and outside the particle. Modeled NO release rates are compared to experimental NO release rates obtained from a single particle reactor operated between 3 and 19 vol % O2 and at 1073−1323 K. Moreover, the analytical model by Yue et al.18 is tested for the investigated conditions. In the analytical model, one of the boundary conditions for the governing equation of NO inside the char particle is simplified: the concentration of NO is assumed to be zero at the external surface of the particle. This simplification is reasonable for combustion experiments of coal char particles in fluidized beds,18 but it is unclear whether it is valid for a single Received: November 27, 2012 Revised: February 21, 2013 Published: February 21, 2013 1410

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biomass particle. In the figure, the flame is visible during the devolatilization. In the sixth snapshot, the flame has disappeared and the char oxidation starts. The outlet gas of the reactor system was analyzed with commercial analyzers for the measurement of CO, CO2, and NO. The residence time distribution of the reactor system was taken into account by deconvolving the measured signals. The measured release curves are deconvolved by the derivatives of the residence time distribution for the gas analyzers. The deconvolution routine from Matlab 2012 is used. Figure 2 shows an example of deconvolved raw data from the analyzers. The initial peak in the figure corresponds to the devolatilization, and the remaining tail corresponds to the char oxidation. The figure shows that the devolatilization finishes around 3 s earlier based on the deconvolved CO2 curve than based on the NO curve. This difference can be considered very small and is within the accuracy of the deconvolution. The local minimum of the deconvolved NO curve, immediately after the peak, is taken as the starting point for the char oxidation. The experiments were performed at 1073, 1173, and 1323 K and with 10 vol % O2. At 1173 K, experiments were also performed with 3 and 19 vol % O2. At these temperatures, the average gas velocity in the reactor is between 0.14 and 0.17 m/s. The Reynolds numbers are around 40. In an entirely laminar flow, the gas velocity in the center of a tubular reactor can be assumed to be twice the average velocity. However, because the gas flow in the reactor system is slightly disturbed by small flows of nitrogen from the sides of the reactor, the average gas velocity is taken as the slip velocity in the analysis. This may underestimate the slip velocity, but that is considered in the sensitivity analysis of the study. The NO and C release rates can be calculated from molar fractions of CO, CO2, and NO measured at the analyzers

char particle burning in a stream of gas. Finally, the fractional conversion of char-N to NO is predicted as functions of the temperature and particle size for the investigated biomass.

2. EXPERIMENTAL SECTION The biomass investigated in this study was spruce bark. Parent fuel was pelletized to cylinders with a diameter of 8 mm and a mass of 0.2 g. The length of the initial cylinder was around 4 mm. The experimental tests investigated in this study were also investigated in a previous study.5 Table 1 shows proximate analysis, ultimate analysis, density of

Table 1. Density of Parent Fuel and Char, Elemental Analyses spruce bark moisture (%)a fixed carbon (%, db)a volatile matter (%, db)a ash (%, db)a C (%)b

5 21.2 76 4.8 51.2

Cc (%)b N (%)b Nc (%)b ρ (kg/m3)c ρc (kg/m3)c

75.8 0.38 0.39 1004 248

Moisture, fixed carbon, volatile matter, and ash content (db = dry basis). bCarbon and nitrogen contents of parent fuel and char (db). c Densities of parent fuel and char. a

the parent fuel pellet, and density of the char. The experiments were conducted in the Åbo Akademi single particle reactor (SPR) shown schematically in Figure 1. The SPR consists of a quartz tube inserted in an electrically heated ceramic furnace.26 The inner diameter of the reactor is 443 mm. Gas mixtures of synthetic air and nitrogen were introduced to the reactor from the bottom of the reactor system. A small flow of nitrogen was also introduced from the side of the reactor. The sample was inserted with a manually movable probe. The probe was inserted from a cold environment into the hot reactor within a fraction of a second. The sample holder on the probe consisted of a thin net on which the single pellets were placed. The net inevitably influenced the heat transfer and diffusion to and from the particle. The change in the particle temperature and diffusion because of the net is not believed to play a significant role, however, because of the large mesh size and because only a small part of the net is in contact with the particle. A digital camera was used to record the experiments. Figure 1 shows snapshots from devolatilization and char oxidation of a

ṁ NO,expt = ṁ C,expt =

V∞̇ p MNO(x NO(t )) RT

V∞̇ p MC(xCO2(t ) + xCO(t )) RT

(1)

(2)

where ṁ is the mass release from the char particle, V̇ ∞ is the volume flow of gas, p is the pressure, M is the molar mass, R is the universal gas constant, T is the temperature, and x is the molar fraction. Only a fraction of the outlet gas is analyzed. To test whether the gas is sufficiently mixed at the top of the reactor system, the following tests have been conducted: samples with known carbon contents have been

Figure 1. Åbo Akademi SPR and snapshots from a biomass particle during devolatilization and char oxidation. 1411

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Figure 2. Measured and deconvolved signal of molar fractions of CO2 and NO in product gases from the biomass particle burning at 1173 K and 19 vol % O2. oxidized, and carbon contents have been determined using the gas analyzers and integrating eq 2. Typically, a carbon balance closure of 90% was obtained. The nitrogen content was determined for chars prepared in the SPR at 1173 K in nitrogen, although some studies indicate that the char-N content may change as a function of the char preparation temperature.6

m pc p

MNO YN ṁ C,expt MN YC

(3)

(4)

where YN and YC are fractions of nitrogen and carbon on a mass basis in the char and ṁ C,expt is the experimental carbon release rate according to eq 2. Thus, the char-N is oxidized at the same rate proportionally to the char-C. The formation rate of NO, ṁ NO,f, is directly taken from the experiments to minimize uncertainties when modeling ṁ NO in eq 3. The NO reduction reactions can be simplified with the following mechanism: NO + CO → 1/2N2 + CO2

(R1)

NO + C → 1/2N2 + CO

(R2)

dm p dt

Hreac + Spεp (5)

where cp is the heat capacity of the char particle assumed to be 2300 J kg−1 K−1, h is the convective heat-transfer coefficient, εp is the emissivity of the particle surface and assumed to be 0.6 following Chen and Kojima,27 σ is the Stefan−Boltzmann constant, θR is the radiation temperature, f h is the fraction of heat that the particle absorbs from the char oxidation reactions (chosen to be 1), and Hreac is the heat released by the surface reactions. In the oxidation of the char, both CO and CO2 are formed as reaction products. According to camera pyrometer measurements (not shown here), the char particle surface temperature is close to the temperature obtained from the assumption that CO2 is the sole reaction product. Therefore, Hreac is calculated by assuming that the reaction product is CO2. The parent fuel particle is cylindrical, but after the devolatilization, i.e., as the char oxidation starts, the particle shape has been changed and corresponds to something between a cylinder with an aspect ratio of around 1 and a sphere. Therefore, Sp is calculated from the external surface area of a spherical particle. The initial value of the external char particle diameter is taken from the video, and the development of dc is modeled assuming the particle to be shrinking with a constant density. Thus, dc is initially equal to dp, but as the conversion proceeds, an ash layer is formed around the particle and dc is smaller, therefore, than dp. Because the investigated char particles are large and reactive, the char-C oxidation is limited by external mass transfer. Under such conditions, the char-C oxidation reactions take place very close to the external surface of the particle; i.e., the penetration depth of oxygen is very small compared to the particle size. As a result, it is justified to model the development of dc assuming the particle to be shrinking with a constant density. Inside the particle, the governing equation for NO is

where z denotes the fractional conversion of char-N to NO. Thus, if z equals 1, none of the formed NO is reduced, and if z equals 0, the entire formed NO is reduced and, therefore, NO is not released from the particle. The formation rate of NO is calculated here as ṁ NO,f =

dt

= hSp(T∞ − Tp) − fh σ(θR 4 − Tp 4)

3. MODEL 3.1. Numerical Model. All char-N is assumed to be oxidized to NO, although for biomass, a small fraction of the char-N reacts to HCN, which further may react with NO to N2O.9,10 At the temperatures considered in this study, it is likely, however, that most of the char-N is oxidized to NO.9 The NO release from the char particle is modeled as ṁ NO = ṁ NO,f − ṁ NO,r = zṁ NO,f

dTp

The relative importance of R1 and R2 varies with the temperature and is not well-understood.1 In this study, therefore, the NO reduction rates are lumped together and expressed as kNOCNOγ, where kNO = ANOe−ENO/RTp is the kinetic rate constant and CNO is the concentration of NO (mol/m3). Here, ANO is the pre-exponential factor, ENO is the activation energy (kJ/mol), and γ is the reaction order for the NO reduction. At any degree of conversion, the char particle is assumed to be isothermal. The temperature of the char particle is calculated from

⎛ d2C 2 dC NO ⎞ NO ⎟ − kNOC NOγ + ζk O2CO2 = 0 D NO,c⎜ + 2 r dr ⎠ ⎝ dr (6)

where ζ is N/C if CO2 is the product and 2N/C if CO is the product. The O2 concentration in the char particle is calculated from 1412

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Energy & Fuels ⎛ d2C ⎞ 2 dCO2 ⎟ O2 + − k O2CO2 = 0 DO2,c⎜⎜ 2 r dr ⎟⎠ ⎝ dr

Article

When the number of layers is further increased, the results are not changed notably. 3.2. Analytical Model. The analytical model by Yue et al.18 has been successfully used under laboratory-scale fluidized-bed conditions. In this study, the model is tested for a single particle burning in a stream of gas. In the model, first-order kinetics is assumed for the NO reduction. The concentration of NO is obtained from

(7)

Here, DNO,c and DO2,c are diffusion coefficients of NO and O2 in N2 as determined for wood char: Di,c = 0.20Di.28 The concentrations outside the particle are obtained from ⎛ d2C 2 dCi ⎞ ⎟=0 Di⎜ 2i + r dr ⎠ ⎝ dr

⎛ d2C 2 dC NO ⎞ NO ⎟ − (k COCCO + kNO)C NO D NO,e⎜ + 2 r dr ⎠ ⎝ dr

(8)

In any time step, eqs 6 and 7 are solved inside the char core of the particle. Equation 8 is solved inside the ash layer of the particle and outside the ash layer of the particle. Equations 6 and 7 are solved using the boundary conditions at the center of the particle dCi =0 dr

+ ζk O2CO2 = 0

To solve this equation analytically, the boundary condition at the surface of the particle (r = R) is

C NO = 0 (9)

dC NO =0 dr

(10)

dCi = K i(Ci , ∞ − Ci) dr

z = ((ThO2 2)/(ThO2 2 − ThNO2))

(11)

((ThO2 cosh(ThO2) − ThNOsinh(ThO2)coth(ThO2))

where Ki is the external mass-transfer coefficient. Because the ash porosity is very high, the diffusion coefficient in the ash layer is assumed to be the same as in the gas phase. The external mass-transfer coefficient is calculated from ShDi Ki = dp

/(ThO2 cosh(ThO2) − sinh(ThO2)))

Re =

udc ν

ν Sc = Di

ThO2 =

(12)

dp

K O2

2

DO2,e

(21)

and ThNO is the Thiele modulus for the NO reduction reactions (R1 and R2).

(13)

ThNO =

(14)

dp

K COCCO,s + KNO

2

D NO,e

(22)

Because CCO,s is zero in the analytical model, KCOCCO,s + KNO is equal to KNO and, correspondingly, the Thiele modulus for NO required in eq 20 becomes

(15)

Here, Sh, Re, and Sc are the Sherwood number, the Reynolds number, and the Schmidt number, respectively. In the equations, u is the slip velocity (m/s) between the surrounding gas and the particle and ν is the kinematic viscosity (m2/s). In the bulk phase, the boundary conditions for eq 8 are the conditions in eq 11 and

Ci = Ci, ∞

(20)

Here, ThO2 is the Thiele modulus for the char-C oxidation

where Sh = 2 + 0.6Re 0.5Sc1/3

(19)

The boundary conditions in eqs 18 and 19 are simplifications required to obtain analytical solutions. If the particle would be surrounded by a very thin boundary layer, the NO concentration would rapidly decrease outside the particle. In such a case, the boundary conditions in eq 18 can be justified. When the concentrations of O2 and NO inside the particle are considered from analytical solutions, the fractional conversion of char-N to NO can be calculated from18

At the outer layer of the char core, CO2,s is solved by iteration in such a way that the incoming flow of oxygen assuming Fick’s law equals the consumption of oxygen. Correspondingly, CNO is solved in such a way that the produced NO equals the NO that diffuses away from the particle. In the ash layer, eq 8 is solved using the boundary condition in eq 10 and at the external surface of the ash layer from Di

(18)

and at the center of the particle

and at the surface of the char core

Ci = Ci,s

(17)

ThNO =

dp 2

KNO D NO,e

(23)

3.3. Determination of Parameters. The kinetic parameters, ANO, ENO, AO2, EO2, and γ, are determined by minimizing the objective function

(16)

The bulk phase NO concentration is calculated from the NO release from the particle divided by the total molar flow of the reactor systems. The differential equations described in this section are solved by the difference method by discretizing both the particle and the region outside the particle into 50 layers.

fmin =

1 jmax

∑ fmin ,j 2 j

(24)

where 1413

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fmin , j = (∑ ṁ NO,expt (t ))−1 ∑ |ṁ NO,expt (t ) − ṁ NO(t )| t=0

activation energy is 71 kJ/mol and the reaction order is 0.59. Generally, reaction orders for NO reduction inside biomass chars have been reported to be below 1.19−23 In our previous study, we reported an apparent reaction order of 0.9 and an apparent activation energy of 41 kJ/mol for the same char and experimental conditions as investigated in this study.5 In that study, however, the NO reduction rate was related to the maximum concentration of NO inside the biomass particle. Because, in this study, the NO reduction is related to the true (calculated) concentration of NO inside the particle, it is expected that the true reaction order is lower than the apparent reaction order and that the true activation energy is higher than the apparent activation energy under regime II conditions.29 Figure 3 shows modeled and experimental NO release rates at 1173 K and 10 vol % O2 using the numerical model. In the figure, the NO release curves are in good agreement. Initially, the NO release rates are low and then increase as a function of the burnout. The measured NO release during the char oxidation is expected to be entirely from the char-N because NO was not present in the inlet gas to the reactor, the temperatures are too low for significant thermal NO formation,30 and the prompt NO formation is not expected to play an important role.10 In the figure, the modeled and experimentally based NO reduction degree (1 − z) as a function of the char oxidation time is also shown. Initially, the degree of NO reduction is close to 100% (z = 0), and therefore, the NO release is low. The degree of NO reduction then decreases as a function of conversion, and correspondingly, the fractional conversion of char-N to NO increases. To compare the concentrations of NO inside and outside the particle, two points are selected from Figure 3: A is at 50 s, and B is at 190 s. From Figure 3, it can be seen that the fractional conversion of char-N to NO is 20% at A and 60% at B. Figure 4 displays the concentration of NO at points A and B. It can be seen that the absolute values of the NO concentration are significantly higher at point B than at point A inside the particle. This may be expected, because the fractional conversion of char-N to NO is higher at A than at B: the higher the fractional conversion of char-N to NO, the lower the concentration of NO inside the particle. Goel et al.15 suggested the char-N conversion is dependent upon the outflowing NO in such a way that a steeper concentration gradient in the boundary layer favors NO diffusion from the particle, resulting in less reduction of NO. This is supported by the curves in Figure 4: the NO concentration gradient outside the particle is much steeper for the smaller particle size. Thus, as the particle decreases in size, the formed NO is more rapidly transported away from the

t=0

(25)

Here, t = 0 is the time for when the char combustion begins, and j is the number of the experiments, i.e., five in the current study. In the analytical model, A1 and E1 are constrained in such a way that ThO2 must be larger than 10 for the initial char particle radius at 1073 K and γ is fixed to 1. With this assumption, the char oxidation is always close to being masstransfer-controlled (except at the very final degrees of conversion because of very small particle sizes), because the particle temperature in all experiments is higher than 1073 K. For the numerical model, A1 and E1 are constrained so that ⎛ 10 ⎞2 ⎜ ⎟ DO2,e < k O2 ⎝ rc ⎠

(26)

It is not possible to determine A1 and E1 from the measurements directly because the conversion is nearly limited by external diffusion of oxygen, i.e., regime III conditions. Moreover, it is important to note that A1 and E1 are not used to model the carbon release rate; the carbon release rate in the model is taken directly from the measurements because the NO formation rate is proportional to the carbon release rate. However, A1 and E1 are used to obtain the position in the char particle where the carbon is consumed and NO is formed, i.e., close to the external surface of the particle. The parameter optimization problem is a non-convex optimization problem. Therefore, it is not possible to use conventional optimization methods for the optimization of the kinetic parameters. Here, the parameters are determined using a genetic algorithm based on differential evolution.

4. RESULTS AND DISCUSSION 4.1. Results. The parameters determined for the numerical model are available in Table 2. For the NO reduction, the Table 2. Kinetic Parameters and Reaction Order spruce bark AO2 (1/s)

5.27 × 1014

EO2 (kJ/mol)

168

ANO (1/s(mol/m3)1−γ) ENO (kJ/mol) γ

2.38 × 104 71 0.59

Figure 3. Modeled and experimental NO release rates for char particles of spruce bark and degree of NO reduction inside the particle. The initial mass of the parent fuel particle is 0.2 g. 1414

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rate as a function of conversion. Because these factors are not taken into account in the model, this may be compensated for by a reduced value in the reaction order. Figure 6 shows modeled and experimental NO release rates at 1073 and 1323 K with 10 vol % O2 using the numerical

Figure 6. Modeled and experimental NO release rates for char particles of spruce bark.

model. In both cases, there is a deviation between the rates during the initial char oxidation. During the first seconds of the char oxidation, the NO release is close to zero, according to the experiments. This cannot be seen in the modeled NO release rates. Garijo et al.21 also observed this behavior during NO reduction experiments inside char particles of biomass. Their explanation is that the initially available NO is adsorbed onto the internal surface of the char, and after a few seconds, a steady state is reached between adsorption and desorption products. It is possible that this initial NO adsorption occurs in the experiments of this study. Nevertheless, because this has a small impact on the overall modeled NO release rates, it is not included in the model. Figure 7 shows modeled and

Figure 4. Modeled NO concentration profiles inside and outside a biomass char particle.

particle and, consequently, less NO is reduced. Figure 5 shows the dimensionless radius, external surface area, and volume of

Figure 5. Degree of NO reduction inside a char particle (z), normalized particle diameter, external surface area, and volume as a function of time.

the char core as functions of time at 1173 K and 10 vol % O2. In the figure, the NO reduction degree curve is also plotted. In general, there is a relatively good agreement between the changes in the radius and the changes in the degree of NO reduction. This is equivalent so that the relationship (the reduction of NO/the formation of NO) is approximately proportional to the diameter. It is likely that the NO concentration inside the particle increases as a function of conversion. Moreover, the reaction order is low, i.e., 0.59. One interesting point is that the lower the reaction order, the less the NO reduction rate is influenced by an increased concentration of NO inside the particle. Thus, if the reaction order would be, e.g., 1, the fractional conversion of char-N to NO would not increase as rapidly, as seen in Figure 3. Two possible explanations may motivate a higher reaction order than 0.59: (i) accumulation of nitrogen in the char6,31−33 and (ii) thermal annealing.13 (i) If nitrogen were retained in the char during the char oxidation, the formation rate of NO would be expected to increase and, moreover, the fractional conversion of char-N to NO would be expected to increase as a function of conversion. (ii) If thermal annealing occurs, the char reactivity for the NO reduction would be expected to decrease, resulting in a higher relative NO release

Figure 7. Modeled and experimentally measured amounts of NO released during char combustion of biomass particles. The numbers on the x axis refer to the temperature (K) and vol % O2 in the surrounding gas.

experimental amounts of nitrogen released from the char particle of NO. At 1073 K, around 40% of the char-N is released as NO, and at 1373 K, around 20% of the char-N is released as NO. In the analytical model, the reaction order for the NO reduction is 1, and therefore, the pre-exponential factor and the activation energy also differ34,35 and must be determined separately. The activation energy for the NO reduction is in this case 200 kJ/mol and higher than that for the numerical model 1415

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and values reported in the literature.19−23 Figure 3 shows modeled and experimental NO release rates from a single biomass char particle at 1173 K and 10 vol % O2 using the analytical model. It can be seen that the experimental NO release rate increases as a function of conversion, while the modeled NO release rate decreases as a function of conversion. Figure 3 also shows modeled and experimentally based curves for the degree of NO reduction as a function of the char oxidation time. It can be seen that two curves are not in good agreement. The modeled degree of NO reduction is relatively constant as a function of time from using the analytical model. In Figure 4, it can be seen that the NO concentration is at its maximum at the external surface of the particle. Consequently, it is clear that the assumption of the analytical model in which the concentration of NO is zero at the external surface area of the particle is insufficient for the experiments investigated in this study. 4.2. Model Validation. The kinetic parameters were determined from the experiments shown in Figures 3 and 5 and also from other experiments as described in the Experimental Section. To validate the numerical model, experiments were performed for larger particle sizes, i.e., initial mass of 0.5 g and diameter of 1 cm. Figure 8 shows modeled

in shape. In such a case, the maximum velocity at the center, where the particle is placed, is twice the average velocity in the reactor. Figure 9 shows modeled NO release rates with the slip velocity calculated from the (i) average gas velocity and (ii) peak velocity assuming a fully laminar flow, i.e., twice the average velocity. In both cases, the kinetic parameters in Table 2 are used. It can be seen that the NO release is higher as the slip velocity increases. This can be explained by the fact that as the Reynolds number increases so does the mass-transfer coefficient for the NO. Consequently, the formed NO is more rapidly transported away from the particle, and less NO can be reduced.15 In both cases, the NO release rates are relatively similar, and therefore, the kinetic parameters can be used for both slip velocities. In the model, the bulk concentration of NO is calculated from the NO released from the particle divided by the total gas flow. Although there is NO above the particle, NO release rates have also been modeled by assuming that the NO bulk concentration is zero, which corresponds to the inlet gas concentration of NO. In Figure 9, modeled NO release rates are plotted with a NO bulk concentration of zero. It can be seen that this assumption does not notably influence the modeled NO release rates. Figure 10 shows NO concentration

Figure 8. Modeled and experimental NO release rates for char particles of spruce bark. The initial mass of the parent fuel particle is 0.5 g.

Figure 10. Modeled NO concentration profiles inside and outside a char particle, using various slip velocities and assuming the bulk concentration of NO to be zero.

and experimental NO release rates for these larger particles using the kinetic parameters determined for the smaller particles (initial parent fuel mass = 0.2 g). These validation tests were performed at 1173 K with 10 and 19 vol % O2. At both conditions, the agreement between the curves is good and the model is thus successfully validated for these conditions. 4.3. Sensitivity Analysis. In the model, the slip velocity is calculated from the average gas velocity. By assuming that the flow is a laminar flow in a tube, the velocity is zero close to the walls and the velocity distribution at a cross-section is parabolic

profiles for the three different cases considered in this section. In all cases, the NO concentration profiles are almost identical inside the particle. In the figure, it can be seen that the NO concentration gradient in the bulk phase increases slightly for the increased slip velocity case and with a bulk NO concentration of zero. In the original case, the bulk concentration of NO is 6 ppm compared to the maximum NO concentration of around 70 ppm at the particle surface.

Figure 9. Modeled and experimental NO release rates for char particles of spruce bark, using various slip velocities and assuming the bulk concentration of NO to be zero. 1416

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particle decreases in size the relative diffusion rate of NO from the particle increases, the NO concentration at the external surface increases, and the NO release rate increases. Moreover, the model showed that less NO is released with an increased particle size and at an increased temperature.

This means that the transport of NO from the particle through the boundary layer is approximately 9% higher in this case compared to the case with 0% NO in the bulk phase. Nevertheless, as pointed out above and as seen in Figure 9, this has a small impact on the modeled NO release rates. 4.4. NO Reduction as Functions of the Particle Size and Temperature. Figure 11 shows modeled fractional

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AUTHOR INFORMATION

Corresponding Author

*Telephone: +3582153275. E-mail: oskar.karlstrom@abo.fi. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work has been partly carried out within the consortium FUSEC (2011−2014) with support from the National Technology Agency of Finland (Tekes), Andritz Oy, Metso Power Oy, Foster Wheeler Energia Oy, UPM-Kymmene Oyj, Clyde Bergemann GmbH, International Paper, Inc., and Top Analytica Oy Ab. Further, the work is part of the ERANETBioenergy Project SciToBiCom. The project SYMBIOSIS with financing from the Academy of Finland is gratefully acknowledged.

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Figure 11. Fractional conversion of char-N to NO as a function of the particle diameter and for various particle temperatures.

conversion of char-N to NO as a function of the particle size for various temperatures, with a slip velocity of 0.15 m/s and 10 vol % O2 in the gas. The figure illustrates that the fractional conversion of char-N to NO decreases as the temperature increases for a given particle size. This may be explained by the fact that the char-C oxidation is generally limited by external diffusion for the conditions considered in the figure, i.e., char particles larger than 2 mm and temperatures above 1100 K. Thus, the formation rate of NO is also a function of external diffusion of oxygen, and the NO formation rate is similar as the temperature increases. The NO reduction reactivity increases significantly, however, as a function of the temperature, and therefore, more NO is reduced as the temperature increases.

5. CONCLUSION The release of NO was investigated during char combustion of large biomass particles of spruce bark. Experimental rates were determined from a single particle reactor at 1073−1323 K and 3−19 vol % O2. A numerical model was used to solve the governing equations of NO inside and outside the char particle to model the fractional conversion of char-N to NO. Further, an analytical model developed for fluidized-bed conditions was tested. In the analytical model, the NO concentration is assumed to be zero at the external surface of the particle. Furthermore, the reaction order for the NO reduction is assumed to be 1. These restrictions were not mandatory for the numerical model. The following conclusions can be drawn: The experimental NO release rate increased as a function of conversion, although both the size and mass of the particle decreased as a function of conversion. Although the analytical model has previously been successfully used at fluidized-bed conditions, the simplified boundary conditions are not sufficient for a single particle burning in a stream of gas with a low slip velocity. The numerical model could successfully predict the experimental NO release rates. The model shows that as the 1417

NOMENCLATURE A = pre-exponential factor c = concentration (ppm or vol %) C = molar concentration (mol/m3) d = diameter (m) D = diffusion coefficient (m2/s) E = activation energy (kJ/mol) f h = fraction of heat particle adsorbs f min = objective function h = convective heat-transfer coefficient (Nu/kd) H = reaction enthalpy (J/kg) j = number of experiments k = kinetic rate constant K = mass-transfer coefficient (m/s) m = mass (kg) ṁ = mass flow (kg/s) M = molar mass (kg/mol) p = pressure (Pa) r = radius (m) R = universal gas constant (8.31 J mol−1 K−1) Re = Reynolds number S = external surface area (m2) Sc = Schmidt number Sh = Sherwoods number t = time (s) T = temperaure (K) Th = Thiele modulus u = slip velocity (m/s) ν = kinematic viscosity (m2/s) V̇ = volume flow (m3/s) x = molar fraction Y = mass fraction z = fractional conversion of char-N to NO γ = reaction order δ = boundary layer thickness (m) ε = emissivity ζ = constant θR = radiation temperature (K) ρ = density (kg/m3) dx.doi.org/10.1021/ef301932y | Energy Fuels 2013, 27, 1410−1418

Energy & Fuels

Article

σ = Stefan−Boltzmann constant (5.67 × 10−8 W m−2 K−4)

(32) Chambrion, P.; Orikasa, H.; Suzuki, T.; Kyotani, T.; Tomita, A. Fuel 1997, 76, 493−498. (33) Chambrion, P.; Kyotani, T.; Tomita, A. Energy Fuels 1998, 12, 416−421. (34) Young, B. C.; Smith, I. W. Symp. (Int.) Combust., [Proc.] 1981, 1249−1255. (35) Murphy, J. J.; Shaddix, C. R. Combust. Flame 2006, 144, 710− 729.

Subscripts

c = char particle expt = experimental f = formation i = NO and O2 p = particle R = reduction s = external surface ∞ = gas phase

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dx.doi.org/10.1021/ef301932y | Energy Fuels 2013, 27, 1410−1418