Particle shape and Stefan flow effects on the burning rate of torrefied biomass

Fuel 210 (2017) 107–120

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Full Length Article

Particle shape and Stefan flow effects on the burning rate of torrefied biomass

MARK

⁎

Nikita Vorobieva, , Anna Beckera, Harald Kruggel-Emdenb, Aidin Panahic, Yiannis A. Levendisc, Martin Schiemanna a b c

Department of Energy Plant Technology, Ruhr-University, Bochum, Germany Technical University Berlin, Germany Mechanical and Industrial Engineering Northeastern University, Boston, USA

A R T I C L E I N F O

A B S T R A C T

Keywords: Particle shape Biomass Torrefaction Char combustion Reaction kinetics Stefan flow

Experiments and subsequent analysis were conducted to gain insight into combustion phenomena of raw and torrefied biomass chars, and to describe the char combustion phase with respect to their frequently discussed non-spherical particle shape. Torrefied beech wood and miscanthus were burned in a laminar flow reactor at high heating rates (104–105 K/s). A stereoscopic imaging pyrometry system was used to measure particle temperatures, sizes and shapes of sub-mm particles in-flight. Additionally, partially reacted samples were collected and analyzed by means of scanning electron and digital microscopy. A good agreement was found between collected and in situ measured particle sizes and aspect ratios. The initially high aspect ratio of the aspherical biomass particles was observed to decrease during the burnout progress. Reaction rates were derived by conducting an energy balance around a burning particle, accounting for the effects of both the particle shape and Stefan flow. The char burnout rate was found to decrease with torrefaction intensity of beech wood; beech wood showed a slightly higher reaction rate than torrefied miscanthus being treated with the same thermal parameters. The effect of Stefan flow was found to be of minor relevance during combustion in air; neglecting it, in the case of small particles and/or particles with high aspect ratios, particularly those burning in elevated oxygen atmospheres, leads to underprediction of particle temperatures and hence, burnout times.

1. Introduction As biomass, in either raw or thermally pre-treated form, becomes increasingly important in energy production, growing interest for combustion modelling of biomass particles motivates comprehensive experimental characterization of effects associated to their specific combustion behavior. Furthermore, improved properties (e.g. heating value, grindability) of torrefied biomass provide high co-firing rates in large pulverized fuel (pf) boilers without major modifications [1]. Despite the higher volatile matter in biomass, char burnout is still important for its complete energy utilization and low carbon-in-ash content upon burnout. Precise prediction of char burnout is essential in commercial CFD (computational fluid dynamics) solvers, which are thestate-of-the-art tool for engineering of firing facilities. Presently the assumption of spherical char particles in CFD-simulations is well-established, as this approach is sufficiently accurate for coal chars, however it mismatches broadly the particle shape of the fibrous biomass particles. This has motivated prior research to investigate the

⁎

Corresponding author. E-mail address: [email protected] (N. Vorobiev).

http://dx.doi.org/10.1016/j.fuel.2017.08.037 Received 20 October 2016; Received in revised form 8 June 2017; Accepted 8 August 2017 0016-2361/ © 2017 Elsevier Ltd. All rights reserved.

effect of particle shape on char burnout. Particularly, the influence of convective transport by variation of particle aspect ratio for cylinders and prolate ellipsoids, compared to spheres, was discussed in [2] and showed a non-negligible effect of particle shape on the calculation of the char burnout rate. The extension of char burnout kinetics for spheroids was theoretically treated by several authors [3,4]. The average combustion rate of ellipsoids was found to be slightly higher than that for a spherical particle shape having the same surface area and not uniform with major semi-axis as preferred direction. However, those studies concentrated on diffusion limited combustion, Regime III, for which case the conservation equations were reformulated with ellipsoidal coordinates [5]. Similar issues were also investigated in conjunction to mass transfer on different spheroidal particles. Mou et al. [6] reported the diffusion field around a prolate spheroid as a function of position on particle surface. Also a Sherwood number correlation for mass transfer throughout ellipsoidal cells in ceramic foams was investigated by Incera Garrido et al. [7,8]. Studies on experimental determination of combustion parameters of

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Nomenclature

Greek letters

Latin letters

γ ε η ϑ κ λ ν ρ ρapp σ ψ

A cp C d D EA ECD F∗ h j jp jCp k L n p P q̇ R R S T v Vp w z

pre-exponential factor [kmol/(m2·s·atm)] heat capacity [J/(kg·K)] concentration [mol/m3] minor axis [m] diffusion coefficient [m2/s] activation energy [J/mol] equivalent circular diameter [m] shape coefficient heat of reaction [J/mol] molar flow [mol/s] molecular flux on particle surface [mol/(m2·s)] specific reaction rate [mol C/(m2·s)] calibration constant [1/K] characteristic length [m] major axis [m] reaction order partial pressure [Pa] total pressure [Pa] heat flow [W] ideal gas constant [J/(K·mol)] intensity ratio outer surface [m2] temperature [K] velocity [m/s] volume [m3] mass fraction [%] distance [m]

volume change in boundary layer emissivity normal direction dimensionless temperature Péclet number thermal conductivity [W/(m·K)] stoichiometric coefficient density [kg/m3] char apparent density [kg/m3] Stefan-Boltzmann constant [W/(m2·K4)] fraction of carbon that becomes CO2

Indices

C f g i isoth O2 p s SF sol vol w ∞

carbon film gas any species isothermal oxygen related to particle outer surface on particle surface Stefan flow solid volatile wall bulk phase

miscanthus (miscanthus × giganteus) as a representative of herbaceous energy crops. Three different torrefaction programs with increasing holding temperature and time were tested for the beech wood sample. As reference, Rhenish lignite was chosen. Based on the literature study, the following questions were formulated:

solid fuels are comprehensively represented in the literature, to keep certain compactness only a small excerpt of literature, focusing closely to the given work, will be presented here. Two measurement techniques for char reactivity are prevalent. Thermogravimetric analysis (TGA) allows easier sample handling and continuous burnout progress monitoring, however the heating rates are only in the order of ≤102 K/min. The typical heating rates in commercial pf-applications are in the range of 104–105 K/s and can be replicated in a drop-tube reactors (DTR) with electrically heated walls or in gas flame driven laminar flow reactors. In several TGA-studies the reactivity of treated and raw biomass was compared with coal chars, as references, and also the differences between various biomass samples were investigated [9,10]. In the studies of Tilghman et al. [11] and McNamee et al. [12] the chars were produced at high heating rates in DTR and the char burnout was subsequently examined in a TGA. The combustion history of single biomass particles was investigated in [13,14] in a DTR in air and in different oxy-fuel conditions by means of high speed cinematography. Ref. [13] includes three raw and one torrefied residue biomass. Biomass char burnout increased with O2 concentration, and it was faster than burnout of coal chars. Mason et al. [15] investigated the ignition delay, volatile flame and char burnout duration as a function of moisture content and particle density on rather large single particles (up to 4 mm) of biomass in the post flame region of a Méker type burner with residual oxygen; they reported a tendency of an increased char particle aspect ratio towards a shorter volatile burning phase. In a DTR-study Pohlmann et al. [16] reported that the impact of preparation temperature on char texture, especially microporosity and mesoporosity, is relatively low. They also reported a decreasing reactivity with higher pre-treatment temperature and higher burnouts in oxy-fuel. In the present work two biomass types were used: torrefied and raw beech wood as a representative of woody biomass and torrefied

• How is the particle shape changing during the char burnout phase? • How strong is the influence of particle shape on the pyrometrically deduced char burnout rate considering the effect of Stefan flow? • What is the effect of different degrees of torrefaction on char temperature and burnout rate?

To answer these questions, experiments in a laminar flow reactor were carried out, in which the fuel samples were burned in an atmosphere with high oxygen content (29.3 vol%) to prevent boundarydiffusion limited combustion. Optical measurement of char particle temperature by pyrometry is a widely accepted method for non-invasive characterization of combustion behavior of solid materials [17–24]. A particular feature of this work is the use of a stereoscopic imaging pyrometer to measure not only the temperature, but also the size and shape of burning particles in-flight, these data were used to derive apparent char burning kinetics parameters. Particle samples were collected at various degree of burnout and used for further investigation of the particle structure in order to prove the validity of the imaging pyrometry technique. A previously derived shape dependent kinetic model for char burning rate determinations, presented in Ref. [2], was enhanced to include the effect of Stefan flow. The new model was discussed and subsequently applied to the measured data.

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2. Experimental details

further shape reconstruction, only particles that are in focus of both camera branches are selected. Therefore a focus range is defined in both image fields which is equivalent to the depth of field of the particular opposite camera system (red boxes in Fig. 1). The laminar flow reactor used in present work provides high heating rate which are typical for pulverized fuel combustion and the particle reacting region is fully accessible by optical measurement techniques. Similar experiment designs were reported in the literature [18,37–39]. The quartz-glass chimney with square cross-section (50 × 50 mm) supplies a distortion-free access to the interior which is highly necessary for sufficient precision of particle size measurements as well as 3d-reconstruction. The hot gas atmosphere is generated by a matrix of 99 small non-premixed flames (3–4 mm height) on the bottom of the reactor. A schematic of reactor design is given in [40]. The reactor is driven by a fuel-lean methane flame and char particles react with remaining oxygen in nitrogen dominated combustion atmosphere. The reaction atmosphere contents 29.3 vol% O2, 50 vol% N2, 13.8 vol% H2O and 6.9 vol% CO2, the total flow amounts 51.3 L/min at STP. The gas and wall temperature in the particle reacting zone was measured with a Type S (30 µm) thermocouple and are on average 1550 (+/ −19) K and 840 (+/−48) K respectively. Radiation correction was applied according to [41]. The test rig is equipped with a particle sampling probe (PSP) [21]. The burning char particles are quenched upon entering the PSP by a cold nitrogen flow. In that manner the sucked gas flow is immediately cooled down below 750 K after entering the PSP and further as the walls of PSP are water-cooled. The oxygen concentration is reduced to 5 vol% O2. The particle loaded quench gas flow is drawn through a coalescing filter (PTFE), where the sample is separated and stored while the complete collecting run. The temperature in the filter never exceeds 400 K and in the water jacket it is always below 320 K. Under such conditions the char combustion reaction can be considered to be frozen. A statistically relevant amount of samples (at least 600 particles) collected at different axial distances from the furnace inlet were analyzed with digital light microscope (Zeiss Axiophot); these samples are labelled with “MS” in the following. A qualitative observation of particle groups regarding their shape, size and visible surface structure was performed with a scanning electron microscope (Zeiss Gemini SEM).

2.1. Sample preparation In the present work torrefaction was carried out in a lab-scale oven (HERATHERM OGH 60) which was inertized with nitrogen (15 L/min at STP). The reactor was charged with approximately 250 ml beech wood in form of wood chips (6 × 6 mm) or chopped miscanthus. A heating program was set to heat up the oven to 275 °C with the heating rate of approx. 8 °C/min (typical temperature as suggested in [25]). After achieving the target temperature, the sample was treated at constant conditions for 30 min, the bed temperature was recorded by a thermocouple and the oxygen concentration was continuously measured. Additional beech wood samples were torrefied at 250 °C for 20 min and 300 °C and 40 min. A more detailed description of the production process is given in [26]. The torrefied biomass and coal samples were ground and sieved to obtain particles in the size range of 90–125 μm. The results of ultimate and proximate analyses as well as low calorific value (LCV) are given in Table 1. The ultimate analysis was performed with CHN-analyzer LECO TruSpec according to [27] and the proximate analysis in thermogravimetric analyzer LECO TGA-601 according to [28–30] for biomass and [31–33] for coal. For the measurement of energy content an isoperibolic calorimeter IKA C200 was used [34]. 2.2. Pyrometry setup The imaging Stereoscopic Camera system for Optical Thermography (SCOT) enables a simultaneous measurement of surface temperature, size, shape and velocity of burning particles. A schematic of the measurement system and laminar flow reactor is depicted in Fig. 1. The optical axes of both subsystems are aligned perpendicularly and focused on the centerline of the reactor. The char particles are measured at several distances from the particle inlet which is equivalent to different burnout levels. In Fig. 2 a typical data set acquired at one certain height in reactor (80 mm from inlet) and one sample (B@275/30) is shown in the form of scatter plots. It contains temperature, projection area, expressed as equivalent circular diameter (ECD), length of major and minor axis of 424 single particles (black crosses). Additionally, the mean value (red dot) and onefold standard deviation in each direction (bars) of the particle population assuming Gaussian distribution are plotted. The temperature measurement is based on the principle of ratio pyrometry (wavelength peaks 785/650 nm). Temperature determination is based on the assumption that particles behave as grey body radiators (equal emissivity in both filter ranges), being typical for carbonaceous fuels [35,36]; detailed descriptions of the camera and filter specifications as well as the calibration procedure using a black body radiator and precision pinholes were reported in [22]. A simple 1Dversion of particle tracking velocimetry is realized by double exposure of the intensifier of cam 4 which happens simultaneously with the pyrometry measurement. The mean values of particle velocities were used to calculate particle residence times. Because of the imaging detectors, size measurement is trivial with known pixel resolution. For

2.3. Particle detection and data processing As the camera system records several images per second, only images with detectable particle content, judged by the minimum intensity in each image, were stored for further image processing. When the focus position of the particle in the image pair (Fig. 1) was proven, the particle was analyzed by a shape recognition routine. The maximal expansion in x and y direction (x-size (horizontal) and y-size (vertical)) as well as projected surface area served as input parameters for particle shape detection. A sketch of the image evaluation is shown in Fig. 3 left. Based on this information the projection of a real particle is approximated by an equivalent rectangle. This rectangle fulfills two conditions: it has the same area as a projection of the real particle and the corners touch the frame, which is defined by x-size and y-size. This evaluation was performed for both perspectives. The edge lengths of

Table 1 Proximate and ultimate analysis and low calorific value (LCV) of fuel samples. Sample

Label (sample@temeprature/time)

Moisture (an) wt%

Volatile (dry) wt%

Ash (dry) wt%

C (dry) wt%

H (dry) wt%

N (dry) wt%

LCV (dry) MJ/kg

beech wood torr. beech wood torr. beech wood torr. beech wood torr. miscanthus Rh. lignite

B@raw B@250/20 B@275/30 B@300/40 M@275/30 lignite

7.62 3.69 3.85 3.00 2.73 6.97

85.97 75.34 72.24 61.11 75.02 52.23

0.56 0.61 0.67 0.88 2.68 4.06

47.98 52.20 55.40 60.82 52.80 64.91

5.23 5.46 5.31 5.33 5.73 4.24

< 0.1 0.31 0.20 0.21 0.21 0.86

18.39 19.74 20.87 23.13 20.07 25.92

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Fig. 1. Schematic of Stereoscopic Camera system for Optical Thermography (SCOT), laminar flow reactor and sampling probe.

constants k1 and k2 :

equivalent rectangle were estimated by using scalar product, which is equal to zero in case of perpendicularity, and vector products for surface area calculation as well as symmetry properties. Note that the zcomponent of the projection and diameter d were always taken from that camera branch, in which the particle was closer to the ideal focus plane. This condition is fulfilled by comparing in which camera the particle is closer to the centerline of the image field, because the vertical axes of both image fields coincide, see Fig. 1. The length of a vector with components x, y and z was assumed to be the particle length L, whereby x was the projection of larger edge of equivalent rectangle on x-axis in camera 1 and y in camera 3, as depicted in Fig. 3 right. As an alternative, the equivalent circular diameter based only on the projection area was calculated. In the next step of evaluation, the length and diameter of the 3D-reconstructed particle was calculated by use of simple geometrical relations. The estimation of the char temperature T was based on Wien’s approximation of Planck’s radiation law and is subsequently a function of intensity ratio of both wavelengths R650/785 and of characteristic system

−

1 ε = k1·In ⎛R650/785· 785 ⎞ + k2· T ε650 ⎠ ⎝ ⎜

⎟

(1)

The ratio of the emissivities ε785/ ε650 was assumed to be unity, which is reasonable when the wavelengths are close together and graybody emission characteristics applies. To estimate both system constants one camera branch was calibrated at the PTB (Physikalisch Technische Bundesanstalt, German National Metrology Institute) at a blackbody source (ε = 0.999) [42]. Detailed information on the calibration procedure is given in [22]. 2.4. Measurement data The pyrometrically measured char particle surface temperatures, averaged over a large number of detected particles at different positions from the reactor inlet are shown in Fig. 4. The lignite sample exhibits the highest temperatures at the last measurement point, an effect which

Fig. 2. Scatter plots of a typical data set for one height in reactor, each black cross is a single particle, and corresponding mean value (red dot) with onefold standard deviation (B@275/ 30 at 36.2 ms).

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Fig. 3. Image evaluation and particle aspect ratio reconstruction. The left image refers to individual camera view, while the projection on the right is calculated from both camera branches.

has previously been observed by two other pyrometric experiments for a similar sample [43]. The temperature level of the lignite is continuously above the torrefied beech wood B@275/30, which in turn is about 100 K higher than that of M@275/30. The trend to slightly increasing particle temperature is visible for all samples in Fig. 4A. The bars on each data point represent one standard deviation for each particular particle population assuming Gaussian distribution of measurement data. Note, the spread covered by the bars is primarily due to inhomogeneity of the fuel particles and not to measurement uncertainties, which are far below the statistical spread observed here [22]. All three torrefied beech wood samples in Fig. 4B do not differ significantly in their temperature. The raw beech wood sample exhibits a temperature decrease towards the end of char burnout. Furthermore, it is remarkable that this sample appears to burnout much earlier than all other samples, which can be attributed to the higher volatile content of raw biomass compared to the torrefied samples. The photographs in Fig. 5 clearly demonstrate that the char burnout phase of the raw sample is shorter compared to torrefied samples, which is highlighted by the smaller streak length. The values for equivalent circular diameter (ECD) of lignite sample measured by SCOT show an already known behavior in Fig. 6A, where the average particle diameter achieves a maximum in the middle of the optically accessible combustion phase and decreases afterwards [18,44]. This development is caused by interaction of two phenomena: the first is the relation between particle size and ignition delay [38]; the second is the typical decrease of diameter of char particles burning

Fig. 5. DSLR images of particle streaks of raw and three differently torrefied beech wood samples at temperatures and times (see Table 1) listed on the top of the photograph (Canon EOS 50D, 1 s, F/20, ISO-400, 50 mm).

Fig. 4. Char particle temperature measured with SCOT over the residence time after entering the reactor in 29.3 vol% O2, 50 vol% N2, 13.8 vol% H2O, 6.9 vol% CO2 and gas temperature of 1550 (+/−19) K.

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Fig. 6. Average equivalent circular diameter (ECD) and corresponding standard deviation of particle population measured in situ by SCOT and microscopy (MS) of collected samples in 30% O2 atmosphere.

and would severely bias the diameter and temperature measurements to larger values. The differences between char burnout and volatile combustion events based on a temperature-diameter scatterplot and possible selection criteria were reported in [22]. In contrast, the PSP collects all particles and the particle population analyzed by MS includes both partially reacted and unignited particles or those which were excluded from SCOT size analyses as they were recorded in the volatile combustion phase. Obviously this separation of reacting and non-reacting particles is especially pronounced in the case of miscanthus but it applies to a lesser degree for all other samples. This consideration is also supported by SEM images of miscanthus and beech wood shown in Fig. 7, although the statistic relevance is limited because of little number of observed particles. The conversion of carbon was derived from the ash-tracer method [46] with known initial ash and carbon content of the respective sample. The small amount of collected sample limits the possibility of tests repetitions and, thus, it reduces the accuracy of the results. Hence, the C-conversion values given in Fig. 7 have to be understood as rough estimations. The initial torrefied samples of miscanthus show the typical fibrous structure of herbaceous biomass. The beech wood particles are also edgy and exhibit generally certain similarities to miscanthus. It should be noted that there are no marked differences in appearance between the SEM images of raw and torrefied samples, which is the reason for not including them in Fig. 7. Major differences emerge during burnout, for instance in the SEM image of M@275/30 at 26 ms some particles appear almost unreacted while others show advanced burnout. Obviously with progressing burnout there are significant changes in the surface structure and particle shape. Some smaller particles at 26 ms have indications of char burnout or at least finished pyrolysis, as their surface has become smoother and more pores are visible, whereas larger particles still have sharp edges like in initial state. Compared to miscanthus the visible impression of beech wood at 35 ms is more

under zone II or zone III conditions [45]. Smaller particles tend to ignite earlier than larger ones. Simultaneously the particle diameter shrinks during the combustion due to enhanced carbon consumption on the particle outer surface. Since the data in Fig. 6 are averaged over many particles, the overlap of both processes causes the observed maxima. While this effect was observed for lignite, it was not observed for the majority of biomass samples investigated here. The ECD-values either increase continuously as in case of miscanthus (M@275/30, Fig. 6B) or they stagnate after a short rise as in case of medium-torrefied beech wood sample (B@275/30, Fig. 6C). However the diameter development of the highly torrefied beech wood (B@300/40, Fig. 6D) resembles that of the lignite samples. Notably the average particle diameter of beech wood particles tends to increase with increasing torrefaction degree although all samples were classified to be in the same sieve fraction. The ECD of collected samples analyzed by microscopy agree with measurements with SCOT in most cases. Miscanthus sample is an exception, as only the last measurement point from MS matches the values of SCOT. As expected, the biomass particles deviate from the chosen sieve diameter as they appear significantly fibrous in structure. Additionally, the collected samples show a higher standard deviation for the ECD than the SCOT measurements. The differences between SCOT and MS-measurements in case of miscanthus may relate to the ignition behavior and rapid char burnout phase. Only burning events which produce a significant amount of radiation passing the narrow spectral filters are detectable by SCOT. Consequently, only particles, which undergo char burnout or have an envelope flame, are detected. Note that, the focus of present work lies exclusively on char burnout, thus presented results for particle temperature, size and aspect ratio refers only to char particles. Particles with envelope volatile flames are clearly distinguishable from burning char particles and were excluded from the data set in course of evaluation routine, since they are not relevant for char burnout kinetics 112

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Fig. 7. SEM images of torrefied miscanthus, torrefied beech wood and lignite at different burnout levels.

silicon oxide, suggesting that the miscanthus sample contained quartz. The lignite char samples are homogeneously covered with ash beads and the asphericity is less pronounced in comparison to biomass, nevertheless the resulting particle shape of the coal chars is probably better described by an ellipsoid than an ideal sphere. The measured aspect ratios (L/ d ), obtained from both SCOT and MS techniques are depicted in Fig. 8 and show good agreement in general. The aspect ratio of lignite chars (Fig. 8A) starts at value of 1.5 and

homogeneous and also the gap between measured ECD-values with both techniques is significantly smaller (Fig. 6C). After a longer residence time both miscanthus and beech wood are strongly affected by burnout. Their pores are enlarged and in the case of miscanthus the shape is clearly shrunken and has become more spherical. The shape of beech wood particles seems to be more stable. The white looking structures in miscanthus SEMs were present at all measurement levels, they keep their shape and the EDX-analysis showed a high content of 113

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Fig. 8. Average aspect ratio L/ d and corresponding standard deviation of particle population measured in situ by SCOT and microscopy (MS) of collected samples.

species transport in the particle boundary layer (single-film model, no reactions in the boundary layer [50,51]) has to be taken into account. The integration of the influence of particle shape in the convection term is derived by adaptation of a methodology described in [52]. The heat conduction term in uniformed formulation over an isothermal surface element dSisoth is modelled by Fourier’s law. The temperature gradient in normal direction ∂T / ∂η can be replaced by the dimensionless temperature ϑ = (T −T1)/(T1−T2) , where T1 and T2 are isotherms.

exhibits a slight increase up to 1.7 at longer residence times. Both biomass samples in Fig. 8B and C undergo a strong reduction of L/ d with progressing burnout. The data points near to 0 ms residence time represent the initial aspect ratio before combustion, and as already has been indicated by the SEM images, the aspect ratio of both samples is quite similar and amounts to 2.9. After entering the reactor, the aspect ratio decreases significantly to a value of 2 and remains on this level. This effect is even more pronounced for raw beech wood, see Fig. 8D. A tendency of larger biomass particles to “spherodize” was also reported in [14,47]. The SCOT measurements for B@275/30 spread slightly around the MS-values and show a good agreement in general. The SCOT-results for M@275/30 mismatch the microscopy in a very similar way as already discussed for ECD. Again, the standard deviation in the miscanthus data is strikingly large. In Fig. 8D the influence of torrefaction degree on aspect ratio of beech wood particles is reported. The aspect ratio seems to increase with higher degree of torrefaction. High torrefied beech wood sample (B@300/40) sample exhibits additionally a tendency with decreasing L/ d after having achieved certain degree of burnout.

q ̇ = −λ (T1−T2)

q̇ =

ji hi−F ∗λdT

(4)

The molar enthalpy hi and heat capacity cg,i of each species, which is passing the boundary layer can be referred to stoichiometric coefficients of Eq. (2): h ̂ = ∑i νi hi and cĝ = ∑i νi cg,i . The formulation of dT can be now replaced by definition of thermal capacity dT = dh /̂ cĝ . The stoichiometric coefficients are related to carbon consumption νi = ji / jC . The modifications can now be set in Eq. (4) and the enthalpy is formal integrated from particle surface to bulk phase:

Typically at zone II conditions (pore diffusion control, which has been shown to fulfill stability conditions according to Semenov theory as deduced in [48]) both CO and CO2 are formed on the particle surface from oxidation of the carbonaceous fuel (Eq. (2)).

νO2

∑ i

3.1. Kinetics model

CO

(3)

Exclusively the integral term in Eq. (3) expresses the shape dependence and is further referred to as shape coefficient F ∗ = ∫F ∂ϑ/ ∂η dSisoth . Analytical solutions for several particle shapes already exist in the literature [53–55]. Shape coefficients for sphere, cylinder and prolate ellipsoid are listed in [2]. The derivation of heat transport including the effect of SF from [56] is revised by consequently addressing the shape coefficient concept, starting with formulation of heat transfer through an arbitrary surface.

3. Char burnout kinetic modelling and results

1 + ψ⎞ C (s ) + ⎛ O2 → ψ CO2 + (1−ψ) CO  2  ⎝  ⎠ ⏟2  νCO ν

∫F ∂∂ϑη dSisoth

̂ h∞

∫h ̂

(2)

j cĝ dh ̂ = C∗ q̇ ̂ F λ h− jC

Hence the impact of Stefan flow (SF) [49] on the energy balance and

(5)

In the next step the term on the right hand shall be extended to the 114

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definition of Péclet number Pe which expresses a decrease of the convective heat transfer caused by the non-equimolar heterogeneous reaction on char surface:

· l∗

v Pe = SF a

=

jpγ j∗

= κ,

q ̇p =

i

ji p hip +

κ ⎤ ⎡ 2λ ⎢ 2γ ⎥ (Tp−T∞). ∗ S p ⎥ ⎢ l − exp κ 1 γl∗F ∗ ⎥ ⎢ ⎦ ⎣

(

)

(9)

The second term on the right side includes as well the impact of SF as that of particle shape and is directly applied as convective term to the energy balance around the burning particle, see Eq. (10). A detailed explanation of other terms in energy balance is given in [2].

(6)

with a = λ /(C·cg ) the thermal diffusivity and vSF = j p ·γ / C the SF-velocity; γ = (ψ−1)/(ψ + 1) describes the volume change in the boundary layer (see Eq. (2)) and depends on the CO2 to CO production ratio CO2/ CO = 0.02exp(−3070/Tp) pO0.21 according to [57]. The adequate ac2,s curacy of this approach was evaluated in [58]. l∗ = (Nu·Sp)/ F ∗ is the characteristic length of the particle and was adopted from the solution of convective heat transport for spherical particle by using the shape factor F ∗ (see Ref. [2]):

Nu·λ F ∗·λ ΔT = ΔT . l∗ Sp

∑

κ

⎤ dTp Vp j Δh 2λ ⎡ 2γ ⎥ (Tp−Tg ) = C ρ cp vp εσ (Tp4−Tw4 ) + ∗ ⎢ + Sp    dz Sp Sp app l ⎢ exp(κ ∗ ∗ )−1 ⎥   γl F radiation ⎣ ⎦    reaction th . inertia convection

(10) As oxidation is assumed to be the dominated conversion mechanism in the N2-dominated atmosphere, the reaction rate modelled as onestep-Arrhenius approach is proportional to pO2,s , with A as pre-exponential factor, EA as activation energy and n as reaction order. Note, that expansion of the model for oxy-fuel conditions requires additional consideration of gasification reactions [50,59].

(7)

Term (j p γ )/ j∗ in Eq. (6) follows the aforementioned definition of Péclet number, with j∗ = λ /(cg ·l∗) as characteristic molar flux and j p as total molar flux related to particle surface. Eq. (5) is extended by Sp , , cg and γ to following expression: It has to be noted that according to Eq. (2) all stoichiometric coefficients are related to carbon consumption and following applies: ν j p = jCp · ∑i , whereby jCp is nothing else as the reaction rate. Furthermore, we assume that the thermal capacity of all species are approximately the same and one can write ∑ νi ≈ cĝ / cg . The Eq. 8 is solved for q̇ and the enthalpy h ̂ is divided in chemical enthalpy on particle surface and sensible heat h ̂ = hp̂ + cĝ (T −Tp) . We return to a reformulated Eq. (4) related to particle surface by reconverting all modifications on the enthalpy:

jC E = jCp = Aexp ⎛⎜− A ⎞⎟ pOn2,s Sp RT p⎠ ⎝

(11)

pO2,s is derived from Fick’s diffusion equation considering SF. The oxygen transport equation suggested in [49] is formulated including the shape coefficient F ∗.

jO2 = F ∗DO2 dCO2 + Sp vSF CO2 = Sp jOp2

(12)

Eq. (13) is obtained by substituting SF-velocity vSF related in this case to oxygen flux jOp2 and rearranging the previous equation.

Fig. 9. Effect of Stefan flow on predicted particle temperature and correction term for convective heat transport in dependence of reaction rate for different particle sizes and shapes (equal surface area to a sphere with given diameter; L/d = 2.5).

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dCO2 =

jO2 ⎛ RT ⎜1− γCO2⎞⎟ F ∗DO2 ⎝ p ⎠

consequence of the enhanced convective heat transfer of around nonspherical particles. For ellipsoids the curve of L/ d = 1 coincides with that of a sphere, whereas a cylindrical particle with the aspect ratio of unity provides a higher temperature holding the reaction rate constant than an equivalent sphere. Furthermore, the aspect ratio of cylinders affects the energy balance stronger as in case of elliptical particle shape, which can be seen by the large difference between the plots.

(13)

CO2 is further expressed according to the ideal gas law as partial pressure and the integration limits are set to particle surface pO2,s and bulk phase pO2,∞.

∫p

pO2,∞

O2,s

dpO2 1−

pO2 p

= γ

jO2 ·RT F ∗DO2

(14)

jOp2

3.3. Char burnout kinetics results

jCp ·νO2

= in terms After the evaluation of integral and converting of carbon consumption, we obtain an uniformal formulation of pO2,s , that depends on reaction rate of the particle. pO2,s =

p ψ−1 jC Sp RT ⎞ P P + ⎛⎜pO2,∞ − ⎞⎟ exp ⎛⎜ ⎟ ∗ γ γ⎠ ⎝ ⎝ 2 DO 2 F P ⎠

The choice of an appropriate particle shape for each fuel was made based on the SEM and MS analyses of collected samples. Based on the results of this analysis cylindrical particle shapes were selected for miscanthus and beech wood, whereas ellipsoidal shapes were selected for lignite (see Fig. 7). Reaction rate parameters were calculated for statistically relevant quantities of particles (at least 300, in most cases more than 500 for each position) as reported in Section 3.1 using some assumptions previously justified [43,44,50]. Furthermore, a particle emissivity ε of 0.7 was assumed. This value seems to be acceptable based on currently available literature [60–62]. The apparent char density ρapp (see Table 3) was calculated with solid density ρsol measured by means of pycnometry and volatile content in unburned sample ρapp = ρsol (1−wvol ) . For the specific thermal capacity of char a literature value of 2000 [J/kg K] [18] was used for all fuels. The thermal conductivity and diffusion coefficients were calculated according to the film temperature Tf and molar gas composition [63]. The temperaturedependent coefficients of thermal capacity of gas species was obtained from NIST [64]. The intrinsic activation energy EA of char oxidation was broadly investigated in the past and was estimated to be 160 kJ/ mol [65,66]. The apparent activation energy is defined as a half of intrinsic value [67] and is assumed to be constant in further calculations. Under the given reaction conditions (Section 2.2) it is reasonable to assume that oxidation is the dominant carbon consuming reaction and gasification with CO2 and H2O being negligible [68]. Based on the experimental data a best-fit global pre-exponential factor A which applies to a point cloud from one measurement point (note, that the data points in Fig. 4, Fig. 6 and Fig. 8 are average values of a Tp-ECD-dp-Lp data cloud for each residence time) is calculated. The energy balance is satisfied for a number of nodes (dp-Lp values covering the measured range). For spherical shapes it is sufficient to vary the particle diameter dp [43], whereas for aspherical particles both length Lp and diameter dp have to be treated as free parameters. The temperature of particles is calculated by interpolation between nodes and the optimal kinetics parameters are determined by the method of least squares. This method is chosen according to the standard procedure in commercial CFD-solvers, where the heterogeneous reaction rate is defined by two parameters of the Arrhenius approach ( A and EA ) and constant apparent reaction rate order, usually n = 1, which was also applied herein [19]. It has to be noted, that the assumption of n = 1 does not represent the reaction order which would result from detailed chemical analysis or application of Thiele analysis. Hurt et al. report that the reaction rate in different experiments begins at unity at low temperature, is reduced for medium temperature and raises with temperature when reaching values similar to those reported here [66]. Other authors focused on the determination of reaction orders, and found non-unity values as well [69–71]. However, for reactivity comparison and a first set of rate parameters, the approach using fixed n is justifiable mainly for numerical but chemical reasons [50]. The global pre-exponential coefficients A are plotted against the residence time in

(15)

The energy balance (Eq. (10)) and Eq. (15) form a coupled set of equations, which can be solved iteratively for every single particle. For statistically relevant data sets (meaning one specific fuel in one atmosphere at one position/residence time) the size-dependent particle temperature is fitted to the measured Tp-Lp-dp-point cloud and the bestfit kinetic parameters are determined by the least squares method, as has been demonstrated in [43,44] for spherical particles. 3.2. Effect of Stefan flow To visualize the effect of Stefan Flow (SF) it is appropriate to use the energy balance (Eq. (10)) to predict the particle temperature. In Fig. 9A and B the particle temperature is shown as a function of reaction rate jCp for three different particle sizes. The given particle size corresponds to a sphere with the same outer surface as the aspherical particle, for which the aspect ratio L/ d is held at 2.5. For instance the specification “100 µm” means in case of cylinder L = 144.34 µm and d = 57.74 µm and for ellipsoid L = 173.30 µm and d = 69.32 µm, but both particles have the same outer surface as a sphere with diameter of 100 µm. As reaction rate jCp refers to the outer surface, the results for different particle shapes are more comparable when being calculated in this manner. The calculation was performed with typical values of the experiment which are given in Table 2. For both particle shapes the consideration of SF-correction (term in square brackets in Eq. (10)) leads to an increase in particle temperature. This result makes sense, as the convective heat transfer coefficient between particle surface and gas layer is reduced, because of the nonequimolar reaction, which itself leads to a net gas flow moving away from the particle surface. The functional correlation between the SFcorrection term [(κ /(2γ ))/(exp(κSp/(γl∗F ∗))−1)] and the reaction rate jCp is depicted in Fig. 9C and D, the data without SF consideration for all particle sizes were merged to one black dashed line. As shown this value is always smaller than unity and decreases with higher reaction rate. Hence a higher particle temperature is needed to equilibrate the energy balance. The gap between both particle temperature predictions, with and without SF consideration, increases with increasing particle temperature and with higher reaction rate. Additionally, in Fig. 9A and B the impact of SF on particle temperature increases with decreasing particle size. The upper temperature limit and the lowest reached value of SF-correction term for larger particles is given at the condition pO2,s = 0 , as the transport limitation precludes a further increase in reaction rate and particle temperature. Fig. 9 emphasizes two tendencies: first (and well known) is that, larger particles are more affected by transport limitations, and second is that cylindrical particles reach this limitation at lower reaction rates than ellipsoids. The predicted influence of particle shape, particularly the aspect ratio L/ d , on the temperature is depicted exemplary in Fig. 10 for particles with a surface area equivalent to a sphere with 50 µm diameter. For a constant temperature the reaction rate increases with increasing aspect ratio regardless of the particle shape and is a

Table 2 Assumed values for the theoretical study.

116

dTp/ dz [K/m]

Tg [K]

Tw [K]

vp [m/s]

ρapp [kg/m3]

1000

1573

873

2.25

450

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Fig. 10. Effect of Stefan flow on predicted particle temperature in dependence of reaction rate for different aspect ratios and shapes (equal surface area to a sphere with a diameter of 50 µm).

measure for the reaction rate. Hence the apparent reaction rates undergo the same progression as A in Fig. 11A, after achieving a minimum it rises for the last measurement point. The reaction rates of beech wood samples with varying degree of torrefaction, are depicted in Fig. 12B. For reasons of clarity, the standard deviation is not depicted for miscanthus in Fig. 12A; it is approximately 14% at each data point in this case. The torrefaction intensity causes a decrease of reaction rate in case of beech wood. But the B@300/40 sample shows an alternating development, a kind of “reactivation” on later residence time which is similar to that of lignite. This kind of reactivation, especially for lignite, has been observed before by authors in Ref. [43]. This effect may have several reasons, e.g. opening of new pores or peripheral fragmentation, both effects would increase the number of accessible active sites. The reaction rate of raw beech wood drops deeper than those of low and high torrefied samples. Both effects are related to the development of particle size (see Fig. 6).

Table 3 Apparent density ρapp .

ρapp [kg/

B@250/ 20

B@275/ 30

B@300/ 40

B@raw

M@275/ 30

lignite

344

363

459

280

359

684

m3]

Fig. 11A. Since the global value applies for whole data set, there is no deviation bars given. The values of A for lignite are higher (approx. 20–27.5 kmol C/m2 s atm) than for all other investigated fuels. Additionally, it has a pronounced minimum around 40 ms, which has been previously observed for a similar sample in [43]; a similar behavior can be seen also in case of M@275/30. The oxygen partial pressure at the particle surface pO2,s is calculated with global A and apparent EA for every single particle (Fig. 11B). Herein we obtain for every single particle an individual pO2,s -value, thus the bars represent the standard deviation of population at each residence time. As pO2,s -values of all samples are sufficiently far away from oxygen deficiency (still being above 6 kPa), the char burnout took place in pore diffusion limited regime (zone II of combustion [67]). The assumed particle shape affects a change in reaction rate. The trend of the impact is similar for all samples and it is exemplarily presented for miscanthus in Fig. 12A. Thereby the assumption of elliptical particle shape leads to higher reaction rate jCp than that of spheres based on the ECD. Cylindrical particles have a lower reaction rate compared to a spherical shape. Using the one-step Arrhenius approach with fixed activation energy the pre-exponential coefficient is a

4. Overall discussion The effect of Stefan flow (SF) on reaction rate calculation is relatively small and lies in the range of 4–5 % for a typical particle size of 100 µm at 2300 K, which leads to a difference of 25–30 K in predicted temperature, marginally higher for cylindrical shape than for elliptical. In a theoretical study, Yu et al. [72] investigated the prediction of char burnout behavior considering Stefan flow and CO combustion in oxyfuel atmosphere; they reported that with increasing O2 concentration the effect of SF becomes more pronounced and the consideration of SF results in longer burnout times. This is consistent with the results of this work, since the lower reaction rate in case of SF consideration (see

Fig. 11. Global pre-exponential coefficient A and oxygen partial pressure on particle surface over the residence time in reactor.

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Fig. 12. Reaction rates of torrefied miscanthus sample considering different particle shapes, beech wood samples of various degrees of torrefaction.

range of 104 K/s order) as compared to chars of raw material.

Fig. 9) results in a longer burnout time. The enhanced reduction of heat transfer at increasing O2 concentrations upon taking SF into consideration has been reported by Gonzalo-Tirado et al. [73]. This supports the predicted lower particle temperatures herein when SF is not considered in the model. Both publications [72,73] emphasize that below approx. 20% O2 the effect of SF is not significant. A potential application with elevated O2 concentration in the combustion atmosphere is for example oxy-fuel combustion, where O2 acts as an adjustable process parameter. Relevant literature also included works of devolatilization and char burnout of biomass in oxy-fuel [74,75]. One should note, that in the application of biofuel-oxy combustion, which has been proposed as a carbon sink when carbon capture and storage is applied [76], the effect of Stefan flow becomes even more pronounced. Therefore, its inclusion in burning rate calculations for higher oxygen partial pressures is highly recommended. The differences between calculated reaction rates for different particle shapes in Fig. 12A corresponds to the theoretical considerations presented in Section 3.2. Furthermore, it was shown, that in case of cylinders an increased L/ d value is needed to reach the reaction rate of a sphere. Considering the measured L/ d the gap in Fig. 12B is becoming smaller at higher value of measured aspect ratio (36 ms, see also Fig. 8), but the aspect ratio is not high enough to exceed the reaction rate jCp of a sphere. For ellipsoidal particles a higher L/ d always means an increase of reaction rate, compared to that of a sphere. The improvement of prediction accuracy, when the cylindrical particle shape in biomass pf-simulations with commercial CFD-solvers is considered, has been reported in [77,78]. In both studies the prediction of carbon monoxide and nitrogen monoxide concentrations in flue gas, and in [77] also of the char burnout, were more accurate, although only the thermal gradient within the particle and trajectory has been adapted to cylindrical shape. Guo et al. [79] found similar aspect ratios as in present work between 2.5 and 2.9 for four raw biomass (herbaceous and woody) with particle size in range of 85–150 µm; again a similar tendency to higher aspect ratio for larger particles was found. As is evident from Fig. 12B, the main effect of stronger torrefaction is the reduction of the reaction rate, which automatically leads to a longer burnout time. Beyond our current study, the data base dealing with the impact of torrefaction intensity on biomass conversion rate is limited. In two TGA-investigations [12,80] the char burnout behaviors of differently torrefied biomass samples were investigated. McNamee et al. [12] provided intrinsic reaction rates for char burnout of raw and differently torrefied willow and eucalyptus (270 and 290 °C for either 30 or 60 min). The same tendency of reactivity reduction with rising torrefaction temperature or prolonging torrefaction time (both can be understood as increased torrefaction intensity) was found. The difference between raw and torrefied samples was more pronounced in case of eucalyptus. Also Fisher et al. [80] noticed a lower oxidation reactivity of torrefied willow chars produced at high heating rates (lower

5. Conclusions A comprehensive study of six fuels was conducted, including herbaceous and woody biomass at different degrees of torrefaction and lignite as reference coal. Thereby the focus was on the correct integration of particle shape and the influence of the torrefaction degree on the reaction rate. A theoretical approach from Ref. [2] has been extended to include the effect of Stefan flow and reaction kinetics parameters, normalized with oxygen partial pressure on particle surface, have been derived for all samples. The following findings are emphasized:

• Particle diameters and aspect ratios obtained from in situ mea-

• •

• • •

118

surement with SCOT and from digital microscopy of collected samples are in agreement for most samples. Discrepancies especially in case of miscanthus have been attributed to the broad temporal distribution of the ignition delay time and also to the fact that in the statistics of SCOT only the reacting particles were included. However, only this part of particle population is relevant for kinetics calculation. These findings have been supported by SEM images. The shape reconstruction technique was found to be sufficiently precise despite its very trivial approach. This has been verified by means of digital microscopy, where particles are aligned to the object plane and the determination of the aspect ratio is clearly identifiable. During combustion of moderately torrefied biomass samples a clear trend to “spherodization” has been found. The aspect ratio of particles reduces with progressing char burnout in the same order of magnitude for both samples, from 2.9 to 2.0. The aspect ratio of lignite remains relatively constant on a value of 1.5. Also the surface structure of biomass chars undergoes significant changes. The reduction of convective heat transfer by Stefan flow depends equally on particle size and on particle shape; small particles and particles with high L/ d ratio are affected the most. The reaction rate jCp depends strongly on the particle shape. This fact emphasizes the importance of knowledge of particle shape and corresponding external surface for the prediction of carbon conversion and particle temperature. The torrefaction intensity does not have a significant effect on the particle temperature and pre-exponential factor, but it appears to have some influence on particle size evolution and char burnout duration. This was exemplified by the case of the investigated beech wood sample with the highest degree of torrefaction which exhibited the same trend of decreasing ECD as the lignite coal. All torrefied samples deviated strongly from raw beech wood whose ECD and L/ d decrease dramatically after entering the reactor.

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