Fuel 158 (2015) 263–269

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Fuel

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Establishment of kinetic parameters of particle reactionfrom a well-stirred fluidized bed reactor

http://dx.doi.org/10.1016/j.fuel.2015.05.0380016-2361/� 2015 Elsevier Ltd. All rights reserved.

⇑ Corresponding author. Tel.: +972 (0)3 640 6515.E-mail addresses: hermanh@post.tau.ac.il (H.D. Haustein), kreitzberg@

wsa.rwth-aachen.de (T. Kreitzberg), goevert@wsa.rwth-aachen.de (B. Gövert),massmeyer@wsa.rwth-aachen.de (A. Massmeyer), kneer@wsa.rwth-aachen.de(R. Kneer).

H.D. Haustein ⇑, T. Kreitzberg, B. Gövert, A. Massmeyer, R. KneerInstitute of Heat and Mass Transfer (WSA), RWTH Aachen University, Augustinerbach 6, 52056 Aachen, Germany

a r t i c l e i n f o a b s t r a c t

Article history:Received 13 January 2015Received in revised form 12 May 2015Accepted 18 May 2015Available online 28 May 2015

Keywords:Kinetic parametersReaction rateFluidized bedChar particlesBoudouardFTIR

A novel method is presented for experimental study of gas-particle reactions, based on realizing awell-stirred reactor as a small scale fluidized bed. This reactor is evaluated against the drop tube reactorand the thermo-gravimetric analyser. It shows to enable high heat up rates (�104 K/s), long timescaleobservation (up to several hours), operation with small fuel particles (�100 lm) and accurate controlof reaction conditions. Char reaction rates are established from real-time gas product analysis by FTIRspectroscopy, through a detailed data-analysis procedure. This procedure employs a particlesurface-evolution model and accounts for sampling system signal attenuation. The validity of thewell-stirred conditions is established, and the method is employed for char combustion and gasification.Highly consistent results for char gasification over a wide range of conditions (T = 800–1100 �C,CCO2 = 19–76%), are used to demonstrate the establishment of kinetic parameters for an n-th orderapproach. Activation energy and order of reaction are found and compare well with the literature.

� 2015 Elsevier Ltd. All rights reserved.

1. Introduction

A well-stirred reactor provides spatially homogenous, con-trolled conditions for process and reaction analysis. Therefore, itmight serve as a basis for model development and validation[1,2]. For example, it can be used to experimentally establish inher-ent reaction rates of char combustion, required for reliablereactive-flow CFD simulation [3]. However, practical realizationof such an ideal system is difficult. The present study attempts todo this using a small-scale Fluidized Bed Reactor (FBR), with focuson the establishment of kinetic parameters of gas-particle reaction,under controlled conditions.

An FBR is a commonly used type of reactor, though generallyoperated on a larger scale and in continuous-feed mode, for pro-cesses such as gasification, bio-oil production or coal and charcombustion (e.g., [4–6]). Here, this reactor type was chosen andadapted for kinetic studies, due to the possibility of conductinglong timescale measurements up to reaction completion.Additionally, it is shown that the significant mixing of the reactor,as well as its operation with small fuel batches, promotes

homogenous and controlled conditions for more reliable kineticmeasurements. This allows for the evaluation of the reaction overits entirety with well-defined conditions greatly simplifying theanalysis and generality of results. Nevertheless, the FBR also hassome short-comings, which are addressed a few paragraphsfurther down. Dedicating an FBR to chemical kinetic parametersstudy, places it among other well-known methods:thermo-gravimetric analyzer (TGA, [7]), drop tube reactor (DTR,[8]) or its variant – an entrained flow reactor (EFR, see Shaddixand co-workers [9,10]). By comparison, the present method hasseveral advantages as it combines high heat up rates and high tem-peratures (characteristic to the DTR) with the strong signal andability to observe long timescales (characteristic to the TGA).Furthermore, accurate control over gas composition and tempera-ture allows reactions to be conducted at well-defined, uniformconditions. These inherent characteristics also enable examinationof application-relevant conditions, e.g. high heat up rates, interme-diate residence times and small fuel particles.

On the other hand, this method also has some limitations: First,it is not as suitable as the DTR for rapid reactions (time resolutionof ms), and it does not allow direct measurement of the fuel con-version in contrast to the TGA (mass-loss with resolution of lg).Secondly, the mixing bed does not permit fuel-particle quenchingand extraction, for examination of morphology and compositionevolution, as possible in an EFR or DTR. Finally, the modeling ofthe transport processes in an FBR for conversion of results to a

264 H.D. Haustein et al. / Fuel 158 (2015) 263–269

generalized/intrinsic form, is generally more complex than forother methods (Kunii and Levenspiel [11]). A concluding compar-ison of the FBR to these other methods will be conducted inSection 3.3.

The fluidized bed approach for performing char kinetic studieswas first explored by Fennel et al. [6]. That study was instrumentalfor the methods and the approach employed in the present study.Indeed, many similarities to that study exist here (similar particlesizes, sampling rates and relative flow rates – 10 times the mini-mum fluidization), though in order to extend the knowledgeobtained there key differences are introduced: (i) Bed diameter is8 times smaller resulting in a total reactor volume about 200 timessmaller which should increase reactor homogeneity. Larger fuelbatch sizes are used for increased signal to noise ratio and lowersample size uncertainty; (ii) an extensive fluidization and homo-geneity study is conducted here to validate the desired conditions;(iii) rather than the problematic, noise amplifying de-convolution(reverse) employed there, an iterative convolution (forward, noisereducing) and fitting process is used; (iv) by examining a slower,endothermic, gasification process errors related to sampling delayand sampling rate are reduced; (v) although changes in CO2 levelscould not be directly measured for carbon mass closure (whereasstoichiometry is assumed and only CO is measured here), due tothe advantages listed above the present study has much higherrepeatability and much lower uncertainty. Finally, the chars exam-ined there are of the traditional kind (lignite, bituminous), whilethe present study examines an alternative emerging source –woodchar (biogenic fuel).

The reaction process examined here is related to coal combus-tion and gasification. The complexity of this process can be reducedby splitting it in two: pyrolysis and char reaction, corresponding toshorter and longer timescales (see [12,13]). In the present study,only the slower process of char reaction is examined experimen-tally, which is characterized by three different regimes [14]:Regime (I) For smaller particles/low temperatures the reaction islimited only by the inherent chemical reaction rate (‘‘kineticallycontrolled’’) and takes place throughout the accessible particle sur-face; Regime (II) At increased temperatures (or particle size) it iscontrolled by both kinetics and intra-particle pore diffusion andtakes place closer to the outer surface of the particle; Regime(III) At high temperatures, pressures and particle sizes the reactionis limited by the transport of reactant-gas to it (‘‘diffusion con-trolled’’) and reaction takes places only on its outer surface.

In the current study, char reaction rates were established exper-imentally through real-time FTIR gas sampling and comprehensivedata analysis, under Regime I conditions. Since the presentedmethod is quite novel, the analysis method is described in detail.Furthermore, the first part of the results focuses on the validationof the desired operating conditions (well stirred). This is followedby a parametric study of char gasification reaction rates under var-ious conditions. The method and its validation are conducted forboth gasification and combustion, although the full parametricstudy and finding of kinetic parameters is done for gasificationalone in this work. In the light of these results, the method’s advan-tages and limitations are re-evaluated and discussed.

2. Experimental method

The experimental setup consists of a small-scale bed of inertparticles, which is fluidized by a rate and composition controlledgas-mixture. Into this, small batches of well-characterized fuelare introduced, while the products are continuously analyzed fromthe exhaust gas. The analysis procedure accounts for the evolutionof the char particle surface during the reaction and the dispersion

caused by the sampling system, to calculate a characteristic reac-tion rate from measurement data.

2.1. Experimental setup

The experimental system employed here is the same that haspreviously been used by the authors and is only briefly describedat this point [15,16]. The FBR is located inside a controlled electricoven, allowing temperatures up to 1280 �C to be imposed with highstability (e.g.: 1000 ± 2 �C). The desired composition of the gas mix-ture can be set from a base gas (air, CO2, N2 or Ar), which can beenriched with a reactant (O2 or CO2) by independenttemperature-corrected mass flow controllers (MFC), in order to setflow rate at reactor conditions. This gas mixture heats up as it flowsdown the annular gap to the gas distributor (sintered silica glass,pore diameter range 40–100 lm) which uniformly distributes theflow to fluidize an inert bed of round sand-like alumina (Al2O3 diam-eter dp = 112 ± 30 lm and sphericity /s = 0.80 ± 0.18, established bylaser diffraction analysis and microscopy). A small portion of this gasmixture is used to purge and mildly pressurize the char injection(fuel feed) system. For each run a small batch (<25 mg) of pulverizedfuel is dropped onto the bed, where it heats up and reacts with thefluidizing gas. The heating rate has been approximated analyticallytaking radiative and convective heat transfer into account. The emis-sivity of the bed has been calculated adapting the model of Palconok[17]. The approximation gives values on the order of 104 K/s similarto the values found by Yu et al. [18]. After complete reaction of thechar, the remaining ash becomes an inert part of the bed materialwhich is periodically exchanged. The pressure loss over the distrib-utor and fluidized bed is measured by differential pressure gauge,while the bed temperature is measured with an immersedceramic-shielded type S thermocouple. The bed has a diameter ofD = 34 mm, with a non-fluidized bed height of Hd = 30 mm, and atypical fluidized height fluctuating around Hf = 70 mm. The gaseousreaction products are captured just above the fluidized bed. Drivenby a slight reactor overpressure (typically 10 mbar) the exhaustgas is fed into the gas analyzer through a sampling line and a filter;afterwards it exits out to a safety venting system. The entire sam-pling system is heated to 180 �C to prevent unwanted tar condensa-tion. A Gasmet DX-2000 FTIR spectrometer, measuring in the mid-IRrange (wave numbers of 600–4200 cm�1) was employed forreal-time gas analysis, sampling at 0.5 Hz with an accuracy of 2%of the measurement range after initial calibration.

For additional validation experiments (Section 3.1), some of thetubes in the FBR were exchanged to measure the temperature andgas composition at various heights within the bed (details inFig. 1). An identically scaled, transparent cold fluidized bed wasused for observation of bed fluid-dynamics. Therein the pressuredrop across the distributor and bed height was measured as a func-tion of flow rate, under standard air conditions. This systemdemonstrated that the char particles are thoroughly mixed intothe bed in less than 2 s.

2.2. Data analysis

The char reactions examined here can be well-described by thecarbon conversion curve, or ‘‘burnout’’ (the mass fraction of solidcarbon that has reacted). While obtaining the curve from analysisof exhaust gas-analysis is straightforward, establishing a character-istic reaction rate for the entire conversion requires a more com-plex analysis procedure: In general, an appropriate char surfaceevolution model is used to generate a predicted curve and the reac-tion rate (control parameter) is found by iterative comparison tothe experimental one.

As the particle is consumed its surface is constantly changing,and eventually decreases towards complete burnout. By using a

Purging gasFuel feed

(1)Thermocouple(2) Sampled gas

SealingsFluidizing gas

Distributor

El. heating

(1) Sampled gas(2) closed

Fluidizedbed

Fig. 1. Interior of the fluidized bed reactor.

0 10 20 30 40 50 60 700

0.2

0.4

0.6

0.8

1

Car

bon

Con

vers

ion

X [

-]

0

0.02

0.04

0.06

0.08

0.1

Time t [s]

dX/d

t [1/

s]

X (URM)X (URM, conv.)XdX/dt

Fig. 2. Experimental rapid char reaction in air T = 800 �C, CO2 = 21%. Carbonconversion rate as calculated from Eq. (2) using FTIR measurements and corre-sponding carbon conversion and its comparison to URM prediction with andwithout convolution. Circles stand for the experimentally found carbon conversionrates dX/dt. Its integral over time, the carbon conversion, is represented by triangles.The dashed line gives the carbon conversion prediction of the uniform reactionmodel, whereas the continuous line expresses its convolution.

H.D. Haustein et al. / Fuel 158 (2015) 263–269 265

suitable model for particle surface evolution, a characteristic reac-tion rate covering the entire process can be determined. Severalsurface evolution models exist in literature: the uniform reactionmodel (URM), stated to be appropriate for Regime I/II conditionsand highly porous chars [11]; the shrinking core model (SCM),which has recently been shown to be suitable for high-ash/low-porosity char [19], its offspring the grain model for agglomer-ated char [20] or the more complex random-pore model [21]. Inthis work, due to examination of a highly-porous fuel the URMwas considered and tested for validity. This model (given in Eqs.(1)) represents a limiting case – reaction throughout the volumeof the particle with constant size).

URM : XðtÞ ¼ 1� e�rt ð1Þ

These equations are based on the assumption of the initial conditionX(t = 0) = 0, where X is the carbon conversion, t is time and r is thecharacteristic reaction rate.

For the investigated conditions, reactions lasted from 15 s up toseveral hours. The progression of the reaction was found throughthe evolving gas concentrations, measured by the FTIR, from whichthe carbon conversion rate was then deduced. Based on a mass bal-ance and the dominant chemical reactions (2C(s) + O2 ? 2CO andC(s) + O2 ? CO2 or C(s) + CO2 ? 2CO when the CO2 to O2 ratio ishigh), the measured changes in the concentration of the carbonreaction products – CO and CO2 – relate to the carbon conversionrate, according to Eq. (2).

@X@t¼ MC

mC;0

_mi

Miþ

_mO2

MO2

� �� CCOðtÞ þ DCCO2 ðtÞ

1� CCOðtÞ=2ð2Þ

where M is the molecular weight, _m indicates the mass flow rate,and subscripts i and C represent the carrier gas (N2, CO2, etc.) andcarbon (char), respectively. Furthermore, subscript C,0 denotes theinitial carbon-fuel mass (found from the total carbon captured inthe exhaust by FTIR, as explained later). The Parameter C refers to

concentration, i.e. the molar fraction of a gas species instanta-neously measured by FTIR, and D indicates the difference betweenoutlet and inlet value.

As a mass balance based on the samples weight did usually notobtain closure – 50% to 80% of the introduced carbon was capturedin the exhaust gas – the data was normalized to obtain completeburnout (X = 1). This is equivalent to the assumption that a per-centage of the char does not undergo a reaction in the fluidizedbed. This ‘‘loss’’ may occur by particles sticking to the fuel feedsystem or by elutriation of fine particles in the early stages of thereaction. In any case, complete conversion of the char in the bedwas verified by continued measurement until recovery of steadylevels of CO2 and CO (<50 ppm). This procedure of normalizingthe calculated burnout curves to the detected carbon in theexhaust has been done by other research groups, (e.g. Lou et al.[4], who recovered similar fractions) and doesn’t affect the mea-sured reaction rate.

The analysis method is demonstrated for the case of a rapidreaction (combustion at 800 �C in air) in Fig. 2. This figure showsthe carbon conversion rate dX/dt, which is determined by meansof Eq. (2). The resulting carbon conversion X is obtained as the inte-gral over time thereof. Before fitting a chosen surface evolutionmodel (e.g. Eq. (1)) to this experimentally found carbon conversioncurve, it is necessary to take dispersion along the sampling lineinto account. These effects are related to the long piping (�2 m)and the fine filtration (<2 lm) required by the gas analyzer. Toallow for these issues the carbon conversion, predicted by the sur-face evolution model, is convoluted by a transfer function F(t) (Eq.(3)), which is derived from the Taylor–Aris convection–diffusiontransport equation. The procedure of (de)convoluting data isdescribed in detail by Abad et al. and is outlined briefly in the fol-lowing [22]:

FðtÞ ¼ 12

Erfca� 2bt

2ffiffitp

� �þ expð2abÞErfc

aþ 2bt2ffiffitp

� �� �ð3Þ

In Eq. (3) Erfc represents the complementary error-function andparameters a and b represent the sampling system specifics. Theirvalues, a = 4.60 and b = 0.376, were found within 10% by repeatedFTIR measurement of the system’s response to a stepwise inletinput. Fig. 3 shows the systems response to a sudden increase inCO2 concentration and the fitted convolution function for the deter-mination of a and b. The transfer function can be used to determine

0 10 20 30 40 50

0

0.2

0.4

0.6

0.8

1

Time t [s]

Nor

med

Con

cent

ratio

n [-

]

unit-stepstep-responsefitted step-response

Fig. 3. Response of the FBR-System to a sudden increase of CO2 concentration from0 to 20 Vol.-% in the feed-gas.

0

10

20

30

40

50

Bed

Hei

ght [

mm

]

No back pressure20 mbar back pressure

4

5

mba

r]

(a)

(b)

266 H.D. Haustein et al. / Fuel 158 (2015) 263–269

the temporal evolution of the systems response R(t) to a unit-stepperturbation S (Eq. (4)):

RðtÞ ¼ S � FðtÞ ð4Þ

Considering the predicted carbon conversion curve X(t) as a ser-ies of unit-step perturbations at discrete values of t, convolution ofthis curve can be carried out by using a linear combination of Eq.(4):

RðtkÞ ¼ Sðt1Þ � FðtkÞ þXk�1

i¼1

Sðtiþ1 � tiÞ � Fðtk � tiÞ ð5Þ

By substituting S in Eq. (5) with the predicted carbon conver-sion X, R(tk) gives its convolution at the specific time tk.

After the convolution has been performed, the resulting burn-out curve is iteratively fit with a least-square regression to themeasured data by changing the parameter r until convergencehas been achieved. The fitting was done to the 10–80% part ofthe carbon conversion curve, to avoid the influence of reactionstartup and delayed completion. Reaction rates found accordingto this procedure, are representative of the majority of the conver-sion, and not just of a single part of the reaction, as is often the casein kinetic studies.

The need for the above described convolution procedure isespecially apparent at short timescales – on the order of the typicalsystem delay. By including the convolution procedure, the workingrange of this method is extended.

Fig. 2 shows the different curves obtained by the abovedescribed analysis procedure.

2.3. Fuel characterization

For the detailed kinetic-parameter establishment it is impera-tive to characterize the fuel used. The fuel chosen was awell-pyrolyzed wood-based char (biomass). The pyrolyzation hasbeen carried out in the fluidized bed reactor under pure nitrogenatmosphere with a residence time of 30 min at 900 �C. Fuel parti-cles were ground and sieved to a typical diameter of

Table 1Fuel composition of wood char WC1173 (biomass pyrolyzed at 1173 K for 30 min).

Water Ash (dry) Volatiles (dry)

Proximate analysis (wt-%)0.10 3.88 3.70

C H N S O

Ultimate analysis (dry, wt-%)92.3 0.42 0.44 0.01 2.95

dp = 140 ± 20 lm (>80% mass) – a compromise betweenapplication-like smaller fuel particles and the lower limits of oper-ation in the current system (entrainment at minimal gas analysisflow-rate). This diameter was matched to the bed particles(Archimedes number matching) – to promote mixing and preventbuoyancy-driven separation. As the analysis in Table 1 shows, thechar consists mainly of carbon, with ash and volatiles accountingfor less than 8%.

3. Results

3.1. Validation of the method

To verify operation under well-stirred conditions the fluidiza-tion regimes of the bed must be identified, as well as homogeneityof temperature and composition inside the fluidized bed.

3.1.1. Qualification of the fluidization regimesTo examine the fluidization regimes, observations were con-

ducted in a transparent (cold) fluidized bed with identical dimen-sions. From analysis of high-speed video (HSV) and pressuremeasurements the regimes of fluidization were identified. Bedheight was deduced from time-averaged images, were it wasdefined arbitrarily as the location of a 50% decrease in brightness.Fig. 4a) shows the results. With the onset of flow there is a slightincrease in bed height, though no bubbling can be observed – justgas flow between the particles. The first bubbles appear �60 Nl/h,accompanied by a clear increase in bed height, after which bedheight increases almost linearly with flow (Fig. 4a) & leftmostinset).

An additional interesting observation made is the significantinfluence of system over pressure (due to back-pressure in thesampling line). This is represented by the curves in Fig. 4a. As thefigure shows, even a low backpressure of 20 mbar extends thepre-bubbling and bubbling range. Most importantly it shifts thetransition to full-fluidization to somewhat higher flow rates. Thisaspect must be considered when operating the bed under higherpressures.

0

1

2

3

0 100 200 300 400 500 600

Pres

sure

Dro

p [

Flow Rate [Nl/h]

TotalDistributorParticle Bed

Fig. 4. Fluid-dynamics of the fluidized bed (cold transparent system): (a) averageincrease in bed height; (b) pressure drop across each element.

H.D. Haustein et al. / Fuel 158 (2015) 263–269 267

As the pressure readings show (Fig. 4b), subtraction of the dis-tributor pressure drop (measured without a bed) from the total(measured with a bed) gives the additional drop due to the bedparticles. This ‘‘bed flow resistance’’ shows a constant increase pastthe point of bubbling (60 Nl/h), with a clear drop-off from thistrend (saturation of the pressure drop) when full fluidization isattained (�100 Nl/h). The fully fluidized state can be seen in therightmost inset in Fig. 4a at an extreme flow-rate of 500 Nl/h). Atsuch high flow rates a large amount of particles can be carriedaway by the flow – obstructing the flow in the sampling line andleading to an intermittent type flow (periodic eruption).Therefore, optimal operation of a fluidized bed of these size parti-cles is in the lower fully fluidized range (well stirring) at �200–250 Nl/h, the range used in subsequent experiments. The rangesobtained from the cold flow observations were converted to themuch hotter bed conditions under the assumption that the densityfollows the ideal gas temperature dependence and viscosity’sdependence is described by the kinetic theory of gases.

3.1.2. Homogeneous bulk temperatureOnce fluid-dynamic operating conditions were established, the

FBR could be optimally operated at higher temperatures. In orderto verify that the conditions in the bed are known and controlled,the temperature of the inflow gas (heating up in the annulus andthen flowing through the distributor) was measured. This wasdone as follows: Initially, the flow was allowed to exit the reactorthrough the exhaust pipe at the top of the reactor. At a certaininstant the exhaust was closed and the flow was forced past thethermocouple, which is located in a pipe 30 mm above the distrib-utor. This procedure was repeated several times and in two differ-ent modes: under steady state conditions at 800 �C and during heatup (�500 �C at a heat up rate of 200 K/h). In the first case, no mea-sureable change in temperature was observed (the interior of thesystem is typically 3 K lower than the preset/oven temperature).While in the latter, a clear increase of the measured heat up ratewas observed indicating that the air flow was hotter than the innersystem (which typically trailed the oven temperature by �30 K).From these two observations it is safe to conclude that the currentsetup does indeed deliver the inflow gas at a temperature veryclose to the preset value. To further establish the existence of spa-tially homogeneous conditions in the hot bed, K-type thermocou-ple measurements were conducted at several heights above thedistributor (cf, Fig. 5).

Thereby, the fluidized bed operational height was typically70 mm (immersed thermocouple). As Fig. 5 shows, the tempera-ture over the height of the bed did not vary more than the typicaluncertainty of the measurement (�0.5%) even over a 24 h period.Thus, the bed can be claimed to be homogenous in temperature.

0 50 100 150 200 250 300 350 400800

850

900

950

1000

1050

1100

Height above Distributor [mm]

Tem

pera

ture

[K

]

T(t1)

T(t1+24 h)

Fig. 5. Temperature vs. height above distributor, measured in a continuous 24 hinterval.

3.1.3. Homogeneous bulk gas-compositionSimilar measurements were conducted to establish uniformity

of the gas composition: The FTIR pickup pipe was introduced intothe fluidized bed and raised from 30 mm to 80 mm in a 1 mminterval. At each height char particles (15.75 ± 2.05 mg) weredropped in and combusted with air (21% O2), while the gas wasextracted from the respective location. This procedure wasrepeated 2–3 times at each height. The real-time CO2 and CO con-centrations measured by FTIR were converted to a burnout form(integration of Eq. (2)), as shown in Fig. 6. As the figure indicates,no clear trend can be observed with height, i.e. the variation ofconcentration with height is not larger than the variations encoun-tered from run to run at a fixed height. This shows that the signal isthe same regardless of the height within the bed, suggesting thatthe gas composition in the bed is indeed closely homogenous.

Once the well-stirred conditions were experimentally validated,the establishment of reliable kinetic parameters was pursued.

3.2. Method application – kinetic parameters of char gasification

To demonstrate the applicability of the method for findingkinetic parameters a specific fuel was chosen – wood charpyrolyzed at 900 �C (see fuel details in Section 2.3). This fuel waschosen due to its high carbon/low ash & volatile content, whichis suitable for a pure gasification reaction (Boudouard reaction,Cs + CO2 ? 2CO). Gasification experiments were conducted in thetemperature range of To = 800–1100 �C and at concentrations ofCCO2 = 19–76% (rest: N2).

Trends of CO and CO2 concentrations for three consecutive gasi-fication experiments at 900 �C are presented in Fig. 7. The threepeaks in this diagram (CO) are typical for the gasification experi-ments in the fluidized bed reactor. Furthermore the figure revealsthat CO2 concentrations stay nearly constant throughout the com-plete reaction, which is favorable for the extraction of kinetic data.

Assuming the reaction is well described by an n-th order rateequation and temperature dependency can be expressed with helpof the Arrhenius equation, the following term can be derived forthe reaction rate:

r ¼ k0e�E

RTCnCO2

ð6Þ

where R represents the universal gas constant and T the tempera-ture. In this equation the pre-exponential factor k0, activationenergy E and reaction order n are the kinetic constants that haveto be determined.

First, the activation energy and pre-exponential factor are foundby variation of the temperature, at constant CO2 concentration.Next, the order of reaction is deduced by variation of thereactant-gas concentration at constant temperature, as shown inFigs. 8 and 9, accordingly. The applied reaction rate for the deter-mination of these parameters is the characteristic rate found by

0 50 100 150

Time t [s]

0

0.6

1.0

Car

bon

Con

vers

ion

X [

-]

0.2

0.4

0.8

30 mm 30 mm 30 mm40 mm 50 mm 50 mm50 mm 60 mm 60 mm70 mm 70 mm 80 mm80 mm

R = 0.039 s-1

R 0.006 s-1

Fig. 6. Carbon conversion vs. time in air (21% O2) at 800 �C. Different symbolsindicate gas-sampling at different heights above the distributor, and comparison toaverage URM prediction.

0 5 10 15 20 25 30 35 400

0.5

1

1.5

2

2.5

3

3.5 x 104

CO

[pp

m]

0

25

50

75

100

Time t [min]

CO

2 [V

ol. %

]

CO2CO

Fig. 7. Concentration profiles of CO and CO2 for a typical gasification experiment at900 �C and 73% CO2.

−2 −1.5 −1 −0.5 0−5

−4.5

−4

−3.6

ln(CCO2) [-]

ln(r

) [-

]

Fig. 9. Reaction rate vs. CO2 concentration, WC1173 at 1000 �C.

268 H.D. Haustein et al. / Fuel 158 (2015) 263–269

iterative fitting (to the 10–80% of the carbon conversion curve)using the Eq. (1), and the convolution procedure described byEqs. (3)–(5). For the kinetic study an averaged value of five repet-itive measurements is used.

The activation energy was found by varying the temperature ata fixed concentration of 22 ± 2% CO2 at four different temperaturesfrom 900 to 1100 �C (cf, Fig. 8). As the figure shows can be approx-imated by an exponential law. Using Eq. (6) the activation energyand pre-exponential factor are calculated to be 205.4 kJ/mol and6.88�106 s�1 bar�0.6 respectively.

In order to establish the order of reaction 4 measurements at1000 �C and different reactant gas concentrations were performed.As Fig. 9 shows, the distribution of repeated results was reasonable(see error bars). The order of reaction was found as n = 0.60, by fit-ting a straight line to four different CO2 concentrations. This valueis similar to the value found by Kajitani et al. [23] for the lowestvolatile sub-bituminous coal char they examined (n = 0.56), thoughthe activation energy there is somewhat higher (257 kJ/mol).Better agreement is found with the CO2 gasification literature ofwood-based biomass: Risnes et al. [24] obtained very similar valuesof n = 0.59, 205.6 kJ/mol and 5.81�106 s�1 bar�0.59 for activationenergy and pre-exponential factor, while Barrio gave values of215 kJ/mol and 3.10�106 s�1 bar�0.38 [25].

It is important to conduct the kinetic study under intrinsic reac-tion conditions (Regime I). To verify that these conditions existedin our experiments, they were conducted only up to a temperaturewhere a deviation from the low-temperature trend was observed(above 1100 �C). Furthermore, the Thiele modulus andEffectiveness Factor expressing the extent of pore-diffusion limita-tion on an nth-order reaction were evaluated, according to theform given from Levenspiel [26] (similar to the form used in [6]):

1/T [1/K] ×10-4

7.2 7.4 7.6 7.8 8 8.2 8.4 8.6

ln(r

) [-

]

-6.5

-6

-5.5

-5

-4.5

-4

-3.5

-3

Fig. 8. Dependence of reaction rate on temperature, WC1173 fuel at 20% CO2.

/ ¼ dp

6

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffikoe�

ERT Cn�1

CO2

DCO2e2

sg ¼ 1

/1

tan hð3/Þ �1

3/

� �ð7Þ

Here / is the Thiele modulus, dp is the particle diameter, k0�e�E/RT isthe rate constant, CCO2 is the CO2 concentration, n is the order of reac-tion, DCO2 is the diffusivity constant of CO2 in N2 and e is the particlevoid fraction. In Eq. (7), the effective pore diffusivity was introducedas DCO2 � e2 following [6]. An estimate of the Effectiveness Factor – atthe maximal reaction rate found (r < 0.1 [1/s]) around 1100 �C (withCCO2 = 0.76 and DCO2 = 1.1 � 10�4 [m2/s] from [27]), together withorder of reaction found above and characteristic particle voidagee = 0.74 (found from Hg-porosimetry), gives a value of / = 1 � 10�3,resulting in g = 0.999, indicating that pore-diffusivity is not a limitingfactor to the reaction, and intrinsic kinetic conditions are maintained.

3.3. Comparison to other methods

(1) With the characteristics of the method clarified and vali-dated a more detailed comparison to other existing methods,beyond the obvious differences presented in the introduc-tion, is possible. As demonstrated in this paper the FBRdelivers spatially homogeneous conditions. In comparisonto that the TGA does not represent the individual particlewell or have homogenous conditions since particles are indirect contact with each other and the scale substrate.

(2) Currently, FBR results of gasification (a slower reaction) arewell-established, though combustion (a faster reaction)results are still not sufficiently reliable. Here the DTR hassome advantage over the FBR (and the TGA) – due to its abil-ity to resolve much shorter time scales.

(3) The present method (and the DTR) with high heat up ratesallows the study of an apparent reaction rate of high volatilecontent fuels whereas the TGA mode of operation (slow heatup) prevents the fuel from carrying almost any volatiles intothe reaction.

4. Discussion & conclusion

A method was presented for the experimental study ofgas-particle reactions. Spatially homogeneous conditions weredemonstrated by investigation of temperatures and gas concentra-tions at different heights in the fluidized bed. Measurementsshowed good uniformity, indicating homogenous conditions. Thiscan be understood to be partially due to intensive mixing and par-tially due to the small scale: Even strong reactions will not influ-ence the bulk temperature or gas composition, as fuel samplesare small compared to the bed. This homogeneity is further sup-ported by the consistency and repeatability of results over severalweeks (including system restarts).

H.D. Haustein et al. / Fuel 158 (2015) 263–269 269

With homogeneity and reliability established, kinetic parame-ters were obtained for char gasification with high certainty andin agreement with the literature. Char burnout rates were obtainedin batch-experiments by repeated FTIR spectroscopy of the productgas. Data analysis procedures and establishment of kinetic param-eters were exemplified by gasification of a pyrolyzed wood char.The presented method having well-controlled conditions andrepeatable results, delivers competitive performance that allowsthe development of a reaction kinetics database for support andvalidation of simulation. Based on the understanding and resultsgained from this study, the FBR can be evaluated as awell-stirred reactor and by comparison to the mentioned methods.

The presented method also entails shortcomings which are dis-cussed in the following.

The fuel delivery has uncertainty related to it as not all the car-bon delivered is recovered in the gas analyzer. Additionally longtimescale operation (>3 h) has proven to be problematic: Lowerfractions of carbon are recovered, possibly because of weak gasleakage, system noise or continuous particle elutriation from thebed. Dead volume, piping length in the sampling system and dis-persion of the signal limit reliable measurement of reactionsshorter than 15 s. Another limitation is the inherent coupling ofbed fluid-dynamics to reactant-gas delivery. At higher flow ratesexcessive entrainment occurs, yet sufficient reactant-gas may notbe available. This limit depends primarily on particle size, e.g. inthis study rates were limited to a reaction rate of about 0.07 s�1.

Acknowledgements

The authors would like to thank the Helmholtz association forfunding Dr. Herman Haustein and Thobias Kreitzberg within theframe-work of the Helmholtz Virtual Institute for GasificationTechnology (HVIGasTech). Therein, funding has been provided viathe Initiative and Networking Fund of Helmholtz Association.Also, the authors would like to express their gratitude to DFG forfunding Benjamin Gövert and Dr. Anna Massmeyer via theSFB/Transregio 129 ‘‘Oxyflame’’.

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