Powder Technology 279 (2015) 113–122

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Positron emission particle tracking in fluidized beds with secondarygas injection

Timo Hensler a,1, Martin Tupy b,1, Timo Strer a, Thorsten Pöschel b, Karl-Ernst Wirth a,⁎a Institute of Particle Technology, University of Erlangen-Nuremberg, Cauerstraße 4, D-91058 Erlangen, Germanyb Institute for Multiscale Simulation, University of Erlangen-Nuremberg, Nägelsbachstraße 49b, D-91052 Erlangen, Germany

⁎ Corresponding author. Tel.: +49 9131 8529403; fax:E-mail addresses: timo.hensler@fau.de (T. Hensler), m

(M. Tupy), T.Strer@web.de (T. Strer), thorsten.poeschel@fkarl-ernst.wirth@fau.de (K.-E. Wirth).

1 T. Hensler and M. Tupy contributed equally.

http://dx.doi.org/10.1016/j.powtec.2015.04.0050032-5910/© 2015 Elsevier B.V. All rights reserved.

a b s t r a c t

a r t i c l e i n f o

Article history:Received 16 January 2015Received in revised form 30 March 2015Accepted 4 April 2015Available online 16 April 2015

Keywords:Positron emission particle trackingFluidized bedSecondary gas injectionResidence timeDispersion coefficientMeasurement technology

Weapply positron emission particle tracking (PEPT) to a gas–solid fluidized bedwith injection of a secondary gasthrough a centrally arranged nozzle and present amethod to compute stationary fluid-dynamic characteristics ofthe system from the trajectories of a test particle. In order to evaluate this non-invasivemethod we compare thefield of density obtained by PEPT with the density obtained by a traditional, well-established and approved, yetinvasive,measurement technique tofindgood agreement. Besides the penetration depth of the jet region and theopening angle of the jet which are inferred from the density field, we use PEPT to measure quantities whosemeasurement using traditional methods is rather sophisticated, including the residence time of particles in thejet region and the suspended phase, the coefficients of axial and radial dispersion and the material flux acrossthe jet boundaries. We conclude that PEPT is a reliable and at the same time versatile technique to measurestationary fluid-dynamic properties of dynamical particle systems at spatial resolution only limited by theduration of the measurement.

© 2015 Elsevier B.V. All rights reserved.

1. Introduction

Fluidized bedswith secondary gas injection enjoy great popularity inmiscellaneous fields of process engineering. Their characteristic proper-ties, such as intense mixing of solids, excellent heat and mass transferconditions as well as easy solids handling, make them attractive for ap-plication in mixing and drying processes. Moreover they are imple-mented in power plant technology, but also as chemical reactors forheterogeneous catalysis or chemical vapor deposition [1,2].

The fundamental setup of a fluidized bed with secondary gas injec-tion is composed of two subsystems. The first one consists of the actualfluidized bed, in which particles are fluidized at moderate superficialfluid velocities by feeding the primary process fluid through a distribu-tor plate at the bottom of the plant. Apart from bubble formation,whichis commonly observed in gas–solid fluidized beds, solids are distributedhomogeneously in the first subsystem and particle motion therein isbased on random. Hence the first zone is in many cases considered anideally mixed system, which provides gradient-free conditions with re-spect to heat and material distribution. The second subsystem is in-duced by the injection of a secondary fluid, which is fed through theorifice of a nozzle. Depending on the velocity of the injected secondary

+49 9131 8529402.artin.tupy@cbi.uni-erlangen.deau.de (T. Pöschel),

fluid, a region with reduced solids concentration is formed at the top ofthe nozzle orifice. According toMerry [3] this region is termed the jet re-gion. In contrast to the statistical particle motion observed in the sus-pension phase of the fluidized bed, the jet region is characterized byan oriented flow field.

Several studies have been undertaken in the past to describe the in-teraction of the jet region with particles of the suspended phase and toderive correlations and design criteria for the description of fluidizedbeds with secondary fluid injection [3–6]. A large number of the con-ducted studies aimed at the investigation of the physical dimensionsof the jet region, namely its penetration depth into the fluidized bedand the jet opening angle, in dependence of the prevailing operatingconditions [7–9]. For that purpose invasive measurement techniqueswere often applied. As alternative, two-dimensional replicas of the sys-tems were constructed, which facilitate visual observation of the bedand the jet region. However, a drawback of previously applied proce-dures consists in their invasive nature. By changing the geometry ofthe bed or penetrating the bed with probes, the flow field is influenced,which has a detrimental effect on the significance of the obtained mea-surement data.

More recent studies focused on the effect of secondary gas injectionon the bubble size and behavior in gas–solidfluidized beds. Using a frac-tal injector system, Kleijn vanWillingen et al. found that the injection ofsecondary gas leads to a reduction of the average bubble size within thesuspension phase of the bed, which leads to an improved gas–solidcontact [10]. With regard to the implementation as a chemical reactorsystem the residence time behavior of the injected fluid was

114 T. Hensler et al. / Powder Technology 279 (2015) 113–122

investigated and allowed to draw conclusions on the dispersion of thefluid within the bed [11,12].

The objective of the present article consists in the non-invasive in-vestigation of a three-dimensional gas–solid fluidized bed with second-ary gas injection through a single, centrally arranged nozzle. Apart fromthe determination of the jet characteristics an investigation of the be-havior of single particles is aimed at for the first time. For that purposea particle is randomly selected from the fluidized bulk material and la-beled radioactively. By means of positron emission particle tracking(PEPT) the motion of the particle is analyzed with high temporal andspatial resolution. A method for PEPT-data evaluation is presented, bymeans of which the local solids hold-up in the bed can be inferred.The derived solids concentrations are juxtaposed to those measuredinvasively, using capacitance probes. In addition to that, the residencetime behavior of the labeled particle in the jet region and in thesuspended phase is analyzed. With regard to the flow characteristicsof single particles in jetted fluidized beds the flux of particles acrossthe boundaries of the jet region is determined and dispersion coeffi-cients are derived.

2. Experimental setup

In the following sections the applied materials are introduced andthe experimental setupof thefluidized bedwith secondary gas injectionis presented. Besides that, information on the operating conditions ad-justed in the course of themeasurements is given. Subsequently the ap-plied measurement techniques are introduced and, in this regard, themeasuring procedure is explained.

2.1. Setup of the fluidized bed with vertical injector nozzle and appliedoperating conditions

The fundamental setup of the applied fluidized bed with secondarygas injection is depicted in Fig. 1.

Fig. 1. Bubbling fluidized bed with secondary gas injection through a vertically arrangedinjector nozzle.

The section, in which the bubbling fluidized bed is located, is com-prised by a hollow 1.4301 steel cylinder with an inner diameter of0.190m and its length amounts to 1.90 m. Prior to the start of an exper-iment a total mass of 30 kg of the bulkmaterial to be fluidized is provid-ed in this section. The primary process gas is supplied via a sinteredmetal distributor plate, which is located at the bottom of the plant.Due to its thickness of 0.010 m and an average pore diameter of20 μm, the sintered metal base plate is presumed to distribute the pri-mary process gas uniformly over the entire cross section of the plant.In the center of the distributor plate a nozzle is installed for the injectionof a secondary process gas in vertical upward direction. The nozzle ge-ometry consists of a cylindrical section with an outer diameter of0.035 m at the bottom and a truncated conical section at the top. Thenozzle orifice is located at an axial distance of 0.115m above the distrib-utor plate and the diameter of the orifice amounts to 0.010 m.

On passing thefluidized bed the process gas is conducted into a free-board, in which entrained particles are separated from the gas andreturned to the bed. After leaving the plant the process gas is lead to afilter.

In the course of all measurements presented in this work, the volu-metric flowrate of the primary process gas was 47.6 Nm3 h−1, resultingin a superficial gas velocity of 0.5m s−1. The secondary gas was injectedthrough the nozzle orifice at a flow rate of 15.8 Nm3 h−1 and a velocityof 60 m s−1, respectively.

2.2. Materials

The experimentswere carried out at room temperature and ambientpressure conditions. Air was used as the primary and secondary processfluid. The fluidized bulkmaterial consisted of glass beads with a densityof 2480 kg m−3 and a Sauter mean diameter of 732 μm. The point ofminimum fluidization was determined on the basis of the pressuredrop behavior of the bed in defluidization experiments, conducted atambient conditions. Hence minimum fluidization occurs at a superficialgas velocity of 0.31 m s−1.

For particle tracking purposes single particles are randomly selectedfrom the bulk of the glass beads. The diameter of the particle selected forthe measurement series presented in this article was determined to be700 μm.

2.3. Measurement techniques

The background of the applied measurement techniques is present-ed in the following. Themain focus of the present article is on the inves-tigation of the motion of single particles in a fluidized bed withsecondary gas injection bymeans of position emission particle tracking.In order to verify the validity of the derived data, solids concentrationsderived by PEPT are compared to those obtained from invasive mea-surements using capacitance probes.

2.3.1. Positron emission particle trackingThe essential principle, on which the PEPT-technique is based, con-

sists in labeling the particle to be tracked with a radioactive marker.The radiation arising from the nuclear decay of the marker is used tospot the position of the labeled particle within the investigated system.According to Fan et al. [13,14] three different labeling techniquesare distinguished, viz. direct activation, ion exchange and surfacemodification.

In this work, a single glass bead was selected from the bulk and la-beled according to the direct activation method. For this purpose theparticle was placed as a target in a Scanditronix MC40 cyclotron andbombarded by accelerated helium ions of the isotope 3He at 33 MeV.Herein 18O-oxygen isotopes contained in the tracer particle are convert-ed to radioactive fluorine isotopes 18F, with a half-life of 109.8min [15].The final activity of the particle was in the range of 20–40 MBq.

115T. Hensler et al. / Powder Technology 279 (2015) 113–122

The radioactive β+-decay of 18F-isotopes is accompanied by theemission of positrons, which annihilate instantaneously with electronsin the close surroundings of the labeled particle. Each annihilationevent leads to the emission of two collinear back-to-back γ-rays,which are detected by ADAC-Forte γ-ray cameras with an active areaof 0.5 m by 0.4 m. These cameras are equipped with NaI-single crystaldetectors and allow for detecting γ-ray signals with a maximum sam-pling frequency of 100 kHz [16]. The location of the particle is inferredby triangulation of the signals caused by the detected pairs of γ-rays[17]. In this study consecutive data points are obtained with a meantemporal distance of 146.7 ms. Due to the high sampling frequency ofthe γ-ray cameras one can state that the applied measuring systemallows for locating the position of the particle with high temporalresolution.

At the beginning of the measurement the tracer particle was addedto the fluidized bed illustrated in Fig. 1. Subsequently the γ-ray signalwas recorded for 122 min.

It needs to be emphasized that neither thefluid-dynamic behavior ofthe particle nor its surface properties are altered by labeling the selectedparticle according to the above described direct activation procedure.Therefore the conducted PEPT-measurements may be presumed to benon-invasive.

2.3.2. Solids concentration measurement by capacitance probesIn order to check the validity of the PEPT-measurements described

in Section 2.3.1, solids concentration measurements are performed forcomparison by means of capacitance probes [18–20].

The applied probes consist of cylindrical capacitors with an outer di-ameter of 3 mm. The outer cylindrical electrode creates the measuringvolume together with a central electrode, protruding 5 mm at the topof the probe. The diameter of the central electrode amounts to0.5 mm. By choosing short geometric dimensions of the probe, its influ-ence on the flow pattern of the fluidized bed is tried to be kept at aminimum.

Mounted on traversing units (Fig. 1), the probes are inserted into thefluidized bed at 5 different axial positions above the distributor plateconsecutively. On each level the probe is incrementally directed to var-ious radial positions between the inner wall of the plant and the centerin 5 mm-steps. At each position 125 × 103 signals are recorded with asampling rate of 5 kHz.

3. PEPT-data analysis

PEPT-measurements yield a data set containing the spatial coordi-nates of the tracer particle position as a function of time [17]. In the fol-lowing sections the procedures are explained, according to whichseveral process-relevant properties of the investigated system can bederived from the PEPT-raw data set.

Fig. 2. Evaluation of PEPT raw data; a) signal sensitivity in dependence of the position of th

3.1. Numerical evaluation of PEPT raw data

Due to the fact that the localization of the tracer particle requires tri-angulation of the signals obtained from simultaneously detected γ-raypairs, the sensitivity of PEPT data acquisition varies with the positionof the particle between the detectors. As shown in Fig. 2a, a source oftype 1 that is located close to the center of the space between the twocameras leads to a large fraction of the detector area, which is availablefor aligning γ-ray pairs. In this case a large number of γ-ray pairs can beused for triangulation. However, if the sourcemoves towards an edge ofthe detectors (Fig. 2a, type 2), the area fraction for aligning γ-ray pairsshrinks and thus leads to a reduced response.

In order to compensate this influence a piecewise linear interpola-tion is applied to the set of raw data, leading to a new set of particle co-ordinates with equal time intervals. In the following the measuredpositions of the tracer particle's center of mass are denoted by pi(t),where t represents time and i the index of the individual data points.For n data points a new set of data points qi(p,t) is obtained in thefollowing way:

qi p; tð Þ ¼ pi þpiþ1−pitiþ1−ti

t−tið Þ ð1Þ

Eq. 1 is valid for ti b t b ti + 1. For evaluation of the data presented inthis study, on average five interpolated data points are generated foreach experimental data point.

In addition to that, the properties of the investigated system are pre-sumed to be rotationally symmetric. Thus the properties of the field areevaluated along a vertical plane, which is rotated around the axis ofsymmetry obtained from the averaged particle position in the x and ydirections. As shown in Fig. 2b the results can be averaged by collectingdata at different orientations of the plane.

3.2. Derivation of the solids concentration

As described by Goldhirsch [21] continuous fields can be derivedfrom discrete particle positions by coarse graining. In order to deriveinformation on the solids holdup (1 − ε) in the investigated system,firstly the mass density ρm is deduced from the data set obtained ac-cording to Eq. 1. The density is inferred by use of the coarse grainingfunction of space, ϕ:

ρm q; tð Þ ¼X

imiϕ q−qið Þ ð2Þ

Herein ϕ is represented by a Gaussian of full width at half maximumω, which specifies the coarse graining scale or spatial resolution [21].Whereas the integral of the Gaussian is unity, its width ω may varyand defines the size of the circumcircle in which a regarded signal is

e tracer particle; b) evaluation of field properties along a vertical cut through the bed.

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valid. In case thatω approaches zero, the Gaussian becomes identical tothe Dirac delta function. Since the number of measurement signals is fi-nite, the obtained field will consist of spatially separated points in thiscase. For larger values of ω the result becomes smoother and yields acontinuous field. It is important to consider that gradients, which in-volve a scale smaller than ω, cannot be projected [21]. In this studysmooth fields were obtained with ω = 3.75 mm.

The mass of the tracer particle is represented by mi and does notchange in the course of the measurement. Therefore mi is regarded tobe constant in the following considerations. Since the obtained dataset is still time-dependent, the mass densities obtained for the individ-ual time stepsΔti are integrated over the total duration ofmeasurementttotal.

ρm qð Þ ¼mX

iϕ q−qið ÞΔtittotal

ð3Þ

Eventually the solids concentration at the observed position is in-ferred by correlating themass densitywith the density of the tracer par-ticle ρs:

1−εð Þ ¼ ρm

ρsð4Þ

3.3. Derivation of the relative residence time density

For the investigation of the residence time behavior of the labeledparticle, the bed is subdivided into annular sections with a height andwidth of 2.5 mm (see Fig. 3a). When regarding a certain volume ele-ment ΔVj, the labeled particle can enter several times k during thetotal duration of the measurement. Thus the relative residence timecan be determined by referring the cumulative residence time ∑

kΔt j; k

in the regarded volume element to the total duration of the measure-ment. Due to the fact that the volumes of the individual volume ele-ments vary with their radial position, the volume fraction ΔVj/Vtotal ofthe regarded volume element needs to be considered. Eventually therelative residence time density Ej

' is obtained as shown in Eq. 5.

E0

j ¼X

kΔt j;k

ttotal

Vtotal

ΔV jð5Þ

In ideally mixed systems themotion of particles is based on randomand thus the probability to detect the tracer particle at a certainmomenttj is equal for every volume element of the system. From this follows thatthe relative residence time density is Ej, ideal' = 1.0 at every location. Thisbehavior is characteristic for the case of ideally mixed fluidized beds

Fig. 3.Processing of PEPT-data; a) sectioning of the bed geometry for derivation of the relative re

with negligible bubble formation. In real systems the relative residencetimewill have values in the range of 0≤ Ej,real

' ≤ 1 at positions, at whichthe probability of being detected is reduced. Those positions are identi-cal to positions with reduced residence time. At positions with largerresidence time of particles the relative residence time density will ob-tain values larger than one.

3.4. Derivation of the particle flux

Within the scope of PEPT-data evaluation the particle flux across theboundaries of the jet region shall be determined, which is of high rele-vance for the design of fluidized bed reactors with secondary gas injec-tion used in chemical reaction engineering. For that matter thecharacteristic dimensions of the jet region, e.g. the penetration depthand the jet opening angle, are derived from the solids concentrationprofile to specify the outline of the jet region. Subsequently the jet re-gion is approximated by an inverted cone as shown in Fig. 3b. Hereinthe surface of the cone is divided into two areas of investigation: thebase area and the lateral surface area. On each area the events are count-ed, at which the tracer particle either enters or leaves the jet region. En-trance and exit events can thus be treated separately. For the sake ofcomparability, the particle flux across the jet boundaries is presentedas a dimensionless quantity. Therefore the number of detected entriesNiin is referred to the total number of transfer events Ntotal. Since the

regarded areas of investigation differ in size, the area fraction ΔAj/Atotalalso needs to be considered. For a regarded area of investigation Aj thedimensionless solids flux Fj

in entering the jet region is thus determinedin the following way:

Finj ¼X

iNin

j;i

Ntotal

Atotal

ΔAjð6Þ

In analogy to Eq. 6 the dimensionless solids flux leaving the systemFjout is obtained by replacing the in-flux by the out-flux Nj,i

out.

3.5. Derivation of the axial and radial dispersion coefficients

Intensemixing of solids is one of the key properties of fluidized beds,whichmakes them attractive for operations in that gradient free condi-tions are desired. As described byWeinekötter [22] mixing of solids is aprocess that is based on an overlap of convection and dispersion.Whereas convection considers the movement of larger groups of parti-cles relative to each other [22], dispersion refers to the displacement ofsingle particles relative to those in their direct vicinity. Hence dispersiondescribes local mixing effects. Within a regarded system dispersion sig-nificantly influences the heat and mass transfer properties, which playsan important role in any kind of fluidized bed application.

sidence time density; b) boundaries of the jet region used for derivation of theparticleflux.

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Several studies were performed in the past to investigate dispersionusing PEPT. In the previous studies systems like rotating drums, severaltypes of mixers and bubbling fluidized beds were examined [16,23–25].A method developed by Lam Cheun U allows for the determination ofthe dispersion coefficient separately from the influence of convection[16]. In that a planar cut is applied to the system under investigationand the motion of the particle perpendicularly to the cut is tracked asa function of time. This delivers insight into the distance traveled bythe particle after different time steps. The variance of the mean squaredisplacementχ of the particle relative to the cut is represented by [16]:

Var χð Þ ¼ χ2−μ2 ð7Þ

In Eq. 7 μ represents displacement of particles due to convection. Thedispersion coefficient of solids δs is derived from the change in varianceof the mean square displacement with the length of the applied timestep. By applying vertical and horizontal cuts to the investigated system,the coefficients of axial and radial dispersion can be inferred at variouspositions within the system.

4. Results and discussion

The data obtained from particle tracking and evaluated according tothemethods described in the previous sections are presented in the fol-lowing. In order to validate the significance of the PEPT-measurementand the subsequent evaluation of raw data, PEPT-derived solids concen-trations are confronted with those obtained by invasive measurementsusing capacitance probes.

For better comparability of the presented data set to measurementsin similar systemswith different scales, all length-related properties arerepresented as dimensionless quantities. For that purpose axial and ra-dial positions are referred to the total diameter of the fluidized bed D.

4.1. Solids concentration

The radial solids concentration profiles measured invasively by useof capacitance probes inserted at several different levels above the noz-zle orifice are displayed in Fig. 4a. From the data measured at an axialdistance of Δh = 15 mm (Δh D−1 = 0.08) above the nozzle orifice itcan be seen that the solids concentration in the center of the plant isclose to zero, i.e. hardly any solids prevail directly above the nozzle ori-fice. When moving towards the wall, immediately a sharp increase ofthe solids concentration is observed. At a radial position of 2r D−1 =0.2 the solids concentration levels at a value of (1 − ε) = 0.60, whichis characteristic for the suspension phase fluidized slightly above thepoint of incipient fluidization. With increasing axial distance Δh fromthe nozzle orifice an increase of the solids concentration is noted inthe center of the plant. This indicates increasing intrusion of solidsinto the region above the nozzle orifice on the higher levels. Moreover,with growing axial distance from thepoint of secondary air injection the

Fig. 4.Radial distribution of the solids concentrationmeasured at different axial distances abovecapacitance probes; b) non-invasive measurement by PEPT; axial distance from nozzle: ■ Δh =

slope of the section between the center of the bed and the suspensionphase is reduced. Thus the regionwith reduced solids hold-up stretchesout to larger radii, leading to the conclusion that broadening of thejet region occurs. At axial distances larger than Δh = 165 mm (ΔhD−1 =0.87) above the nozzle orifice the solids concentration is distrib-uted evenly across the entire cross-section of the bed and thus hardlyany influence of the jet region is detected.

Fig. 4b shows the solids concentrations extracted from the PEPT-data set at axial positions equal to the levels at which the capacitanceprobes were inserted in the course of the invasive measurement series.The radial distribution atΔh=15mm(Δh D−1=0.08) shows that alsowhen using PEPT-derived data, the solids concentration in the center ofthe bed turns out to be close to zero. When moving from the center to-wards thewall, a sharp increase of the solids hold-up is found and at ra-dial positions larger than 2rD−1≥ 0.2 the solids hold-up varies between0.50 ≤ (1 − ε) ≤ 0.60. Also the increase of the solids concentration inthe center of the bed with increasing axial distance Δh from the nozzleorifice coincides with the observations made during the invasive mea-surements (Fig. 4a).

However, direct comparison of the concentration profiles displayedin Fig. 4a and b makes obvious that the PEPT-derived concentrationsare subject tomuch stronger variations than data obtained by the capac-itance probes. This is attributed to the uncertainty in averaging themea-sured data, originating from the number of available data points. Eachdata point obtained from a capacitance probe represents the averagevalue of 125 × 103 signals measured at the observed position withinthe bed. In comparison, the concentrations derived from particle track-ing represent a smaller number as they depend on the number of occur-rences, at which the tracer particle traveled to the regarded position inthe bed during the total duration of measurement. The observed varia-tions make clear that for evaluations with high spatial resolution a larg-er duration of measurement ought to be applied. For the presented dataseries, the duration of measurement was 122 min. A challenge, howev-er, is represented by the reduction of emitted radiation due to the half-life of the tracer. Therefore the starting activity of the tracer is to be en-hanced if an extended duration of measurement is desired [14]. An al-ternative consists in the use of several tracer particles at the sametime [26].

Besides its non-invasive character, particle tracking brings about theadvantage that themeasurement is not restricted to single spots withinthe bed. By means of PEPT, solids concentrations can be derived at anylocation, which can be reached by the particle. Fig. 5a shows the solidsconcentration map of the entire investigated system. At the bottom ofthe bed the outline of the nozzle becomes apparent, distinguishedfrom the fluidized bed by vanishingly small solids concentrations. Di-rectly above the nozzle orifice a short zone is detected, in which thesolids holdup is zero. This is in agreement with observations made inthe literature and termed as the jet according to Merry [3]. At thegiven operating conditions the length of the jet amounts to ljet =25 mm (ljet D−1 = 0.13).

the nozzle orifice; ug,bottom=0.5m s−1; ug,nozzle= 60m s−1; a) invasivemeasurement by15 mm, Δh = 45 mm, Δh = 105 mm, Δh = 165 mm, and Δh = 255 mm.

Fig. 5. Determination of the penetration depth and opening angle of the jet region; ug,bottom = 0.5 m s−1; ug,nozzle = 60 m s−1; a) solids concentration profile determined by PEPT;b) relative residence time density distribution.

118 T. Hensler et al. / Powder Technology 279 (2015) 113–122

The jet is surrounded by the so called jet region, in which the solidsconcentration increases until it reaches a final value of (1− ε) = 0.60,being characteristic for the suspension phase. Based on the reducedsolids holdup (1 − ε) ≤ 0.60, the jet region can be distinguished fromthe suspended phase. As shown in Fig. 5a the outline of the jet regioncan approximately be described by a conical shape. Thus a penetrationdepth of the jet region of ljet region = 275 mm (ljet region D−1 = 1.45) isobtained and the half jet opening angle is determined to be θjet=16.1°.

In Table 1 the experimentally obtained jet dimensions are comparedto those inferred from the correlations proposed byMerry [3]. It is foundthat the experimentally determined half jet angle deviates to −31.3%from the value suggested by the correlation of Merry [3]. Whereas thehalf jet opening angle is overestimated by the correlation, the penetra-tion depth is significantly underestimated. The experimentally deter-mined penetration depth of the jet exceeds the value calculated fromtheory about a factor of 2.5. A possible reason for the deviation mightbe found in the size distribution of the fluidized bulk material. For thecalculations according to Merry's correlation the Sauter mean diameterwasused as the representative size for the entirefluidized bulkmaterial.However, themeandiameter does not account for fines and coarser par-ticles. Another influence might arise from the invasive nature of themeasurement technique used for the establishment of the empiricalcorrelation by Merry, using a two-dimensional fluidized bed.

4.2. Relative residence time density

Apart from the solids concentrations shown in the previous section,PEPT also allows for the determination of the residence time behavior ofthe tracer particle in different sections of the bed. Fig. 5b shows the rel-ative residence time density inferred from the motion of the tracerparticle.

In the suspended phase of the fluidized bed relative residence timedensities are observed in a narrow range between E′j =0.8–1.2. Similar

Table 1Dimensions of the jet region—comparison between experiment and the correlationaccording to Merry [3].

Jet dimension Experimental Correlation [3] Deviation from theory/%

Half jet angle θjet/° 16.1 23.4 −31.3Length ljet region/mm 275 88 212.7

to the observationsmade during the evaluation of the solids concentra-tions (Fig. 5a), the nozzle can be distinguished from the fluidized bed bythe absence of particles, represented by E′nozzle = 0. Above the nozzleorifice a zone with reduced relative residence time density is observed.This zone can be subdivided into the jet and the jet region.Whereas therelative residence time density in the jet is zero, it increases throughoutthe jet region until it reaches the value of the suspension phase at theboundaries of the jet region.

When applying the boundaries of the jet region defined by the jetopening angle and the penetration depth of the jet region obtainedfrom the solids concentration profile (Fig. 5a), the mean relativeresidence time density of E′jet region = 0.699 is obtained for the tracerparticle in the jet region. Thismeans that the residence time of the tracerparticle within the jet region is 69.9% of that in an ideally mixed systemwith even solids distribution.

Moreover, regions with increased relative residence time densityE′j ≥ 1.0 are observed. This is for example the case directly above theprimary gas distributor at the bottom of the bed. Due to the broad par-ticle size distribution of the bed material it is likely that large particlessettle and accumulate at the bottom of the plant at the given superficialvelocity of the primary process gas. This goes along with reduced parti-cle mobility in the regarded section. Once the tracer particle enters thissection, it takes some time until it is released again, leading to an in-creased relative residence time density at the bottom of the bed.

In addition to that, increased relative residence time densities areobserved above the jet region at the top of the bed. It can also be seenthat the width of the jet region covers a large fraction of the cross sec-tion of the bed at a height ofΔh D−1=1.4. Due to the small plant diam-eter and the largewidth of the jet region the exchange of solids betweenthe upper section and the lower section of the bedmight be inhibited. Inthis respect it appears conclusive that individual particles float on top ofthe bed, leading to an increased residence time in the upper part of theplant.

4.3. Particle flux across the boundary of the jet region

In the previous section the residence time behavior of the tracerparticle in the jet region was investigated. However, the residencetimebehavior alone does not give insight into the orientation of the par-ticle flow. In order to investigate the flow direction of particles passingthe jet region, the jet dimensions derived in Section 4.1 are used to

Fig. 7. Net-flux of solids crossing the boundaries of the jet region; ug,bottom = 0.5 m s−1;ug,nozzle = 60 m s−1; Ntotal = 4442; Atotal = 1.027 × 105 mm2.

119T. Hensler et al. / Powder Technology 279 (2015) 113–122

approximate the jet by an inverted cone (Fig. 3b). The particle fluxescrossing the lateral surface area as well as the base area of that coneare depicted in Fig. 6.

In Fig. 6a the solids fluxes entering and leaving the jet region via thelateral surface area are displayed as a function of the axial position rela-tive to the point of secondary gas injection. It can be seen that the in-fluxof particles increases with increasing distance from the point of injec-tion and levels at a distance of Δh = 70 mm (Δh D−1 = 0.37). At dis-tances larger than Δh = 140 mm (Δh D−1 = 0.74) the in-fluxdecreases. In contrast to that the out-flux of particles remains at a lowlevel along the whole axis of the jet region, leading to a positive net-flux of particles on the lateral surface area. At an axial distance ofΔh=217mm (Δh D−1 =1.14) in- and out-fluxes reach similar values,thus the net-flux of zero is observed. At higher axial positions out-fluxoverweighs slightly. Generally, however, it can be concluded that in-flux of particles predominates on the lateral surface area of the jetregion.

The particle fluxes entering and leaving the jet region via the basearea are displayed in Fig. 6b as a function of the radial position. It isfound that in the center of the plant no in-flux of particles is detected.When moving towards the wall, a slightly increasing tendency of parti-cles to enter the jet region is observed. The out-flux of particles behavesin the opposite way: The maximum out-flux of particles is detected inthe center of the bed, followed by a decreasing tendency towards thewall. At the boundary of the jet region and the suspended phase at 2rD−1 ≈ 0.7 the in-flux and the out-flux compensate each other. Overall,negative values are obtained for the net-flux across the entire base areaof the investigated region. This leads to the conclusion that out-flux ofparticles dominates theflowbehavior at the upper area of the jet region.

The net-fluxes of particles entering and leaving the jet region, as ob-tained from Fig. 6, are depicted as vectors perpendicular to the regardedsurface in Fig. 7. The length of the individual vectors indicates the mag-nitude of the net-flux at a regarded position. Fig. 7 illustrates oncemorethat the particles preferentially enter the jet region via the lateral sur-face area and leave via the base area.Moreover, it shows that the largestsurface-weighed in-flux occurs directly above the jet at Δh = 68 mm(Δh D−1 = 0.37) above the nozzle orifice.

All in all one can state that themajority of particles enters the jet re-gion via the lateral surface area and escapes through the center at thetop.

4.4. Coefficients of axial and radial dispersion

For the determination of the dispersion coefficient with regard toparticles, vertical and horizontal planes were applied as cuts throughthe system separately. In this way, the dispersion coefficients alongthe reactor axis and across the reactor cross-section could be derived.

Fig. 8a shows the obtained distribution of the axial dispersion coeffi-cient along the reactor axis. It must be kept inmind that each data point

Fig. 6. Solids flux across the boundaries of the jet region; ug,bottom = 0.5 m s−1; ug,nozzle = 60 mb) solids flux across the base area of the jet region; in flux, out flux, and net flux.

represents the axial dispersion coefficient for particles at a certain axialposition, averaged over the entire cross-section of the plant. As refer-ence level the axial position of the nozzle orifice is used.

At the bottom and at the top of the bed low axial dispersion coef-ficients with a magnitude of δs,axial = 6 10−3 m2 s−1 are observed.These values are in good agreement with axial dispersion coeffi-cients obtained by Lam Cheun U [16], who fluidized sand and alumi-num oxide particles in a bubbling bed using air as process fluid. Thusthe low axial dispersion coefficients are attributed to the suspensionphase of the bubbling fluidized bed at the top and bottom of theplant. With increasing distance from the distributor plate at the bot-tom of the plant the axial dispersion coefficient reaches highervalues and achieves its maximum at 20 mm (Δh D−1 = 0.11)above the nozzle orifice. When applying the axial position of maxi-mum axial dispersion to the solids concentration profile (Fig. 5a) itturns out that this position is equal to the upper end of the jet,which is free of particles. At the top of the jet the injected air getsin first contact with particles.

Moving towards higher levels the axial dispersion coefficient de-creases linearly until it reaches the characteristic value of bubblingbeds at the upper section of the bed. It is to be noted that the positionof the section with linearly declining axial dispersion coefficient isequivalent to that of the jet region (Fig. 5a).

s−1; Ntotal = 4442; Atotal = 1.027∙105 mm2; a) solids flux across the lateral surface area;

Fig. 8. Dispersion coefficient for the solids phase; ug,bottom = 0.5 m s−1; ug,nozzle = 60 m s−1; a) axial dispersion; b) radial dispersion.

120 T. Hensler et al. / Powder Technology 279 (2015) 113–122

Interestingly, significantly increased axial dispersion coefficients aredetected at axial positions between−0.4≤Δh D−1≤ 0 below the pointof secondary gas injection. This leads to the conclusion that the injectionof secondary gas has remarkable influence on particles that are locatedbelow the nozzle orifice. Under consideration of the reduced solidsholdup and the lower residence time of particles in that section of thebed (Fig. 5a and b) it seems likely that the injection of secondary gas, ac-companied by solids circulation, induces a doughnut-shaped vortex thatsurrounds the nozzle.

The distribution of the radial dispersion coefficient over the cross-section of the plant is depicted in Fig. 8b. Here each data point repre-sents themean radial dispersion coefficient measured at a certain radialposition, averaged along the total height of the bed. Compared to theaxial dispersion coefficient, the values of the radial dispersion coeffi-cient are generally reduced. In consideration of themixing effect causedby thewake of bubbles rising vertically through the bed, it appears to beconclusive that axial dispersion exceeds radial dispersion. On closer ex-amination of the distribution of the radial dispersion coefficient it can beseen that a nearly constant value of δs,radial =1.75 × 10−4 m2 s−1 is ob-tained between 0.8 ≤ 2r D−1 ≤ 1.0, i.e. the region in proximity of thewall which is hardly affected by the injection of secondary gas. In con-trast to that the radial positions, which are affected by the jet region,show larger radial dispersion coefficients. The maximum is reached ata radial position of 2r D−1 ≈ 0.33. However, radial dispersion decreasesagain when approaching the center of the bed.

The previous investigations showed that both the axial and the radi-al dispersion coefficients show constant values outside the jet region(Fig. 8).They may be interpreted as the dispersion coefficients inthe suspension phase. By applying the geometric dimensions of the jetregion as determined experimentally (Table 1) the areas can be local-ized within the bed, which are influenced by the jet region. The meandispersion coefficient δs on an investigated planar cut (Fig. 8) may beinterpreted as the weighed arithmetic mean of the dispersion coeffi-cients in the jet region δs,jet region and in the suspension phase δs,suspension.

Fig. 9.Dispersion coefficient for solids in the jet region; ug,bottom=0.5m s−1; ug,nozzle= 60m s−

6.50 × 10−3 m2 s−1; b) radial dispersion in the jet region; δs,suspension = 1.79 × 10−4 m2 s−1.

The measure of weighing is the area fraction of the jet region Ajet region

and the suspension phase Asuspension compared to the total area of theplanar cut Atotal.

δs ¼Ajet region

Atotalδs;jet region þ

Atotal−Ajet region

Atotalδs; suspension ð8Þ

Eq. 8 can be applied individually for axial and radial dispersion. As-suming that the axial dispersion coefficient of the suspended phasehas a constant value of δs,suspension = 6.50 × 10−4 m2 s−1 throughoutthe whole suspension phase, the behavior of the axial dispersion coeffi-cient for solids within the jet region can be inferred as a function of theaxial position and is shown in Fig. 9a. In accordance with the curve pro-gression shown in Fig. 8a, the axial dispersion coefficient has its maxi-mum value closely above the nozzle orifice and decreases withincreasing axial distance from the nozzle. However, it is found that themaximum value of the axial dispersion coefficient of δs,jet region(max) =.27 m2 s−1 is several orders of magnitude larger than the cross-sectionaveraged value. This is due to the large area fraction of the suspensionphase at the level of the nozzle orifice. At the upper end of the jet atΔh D−1 = ljet D−1 = 1.45 the value of the axial dispersion coefficientconverges with that of the suspension phase.

When regarding the behavior of the radial dispersion coefficient forsolidswithin the jet region, it is found that low values prevail in the cen-ter. With increasing radial distance from the central axis, the radial dis-persion coefficient increases in a linear way. At intermediate radialpositions nearly constant values are obtained. At the boundary of thejet region a sudden drop of the radial dispersion coefficient is observedand values characteristic of the suspension phase are reached. Generallyit is found that the dispersion coefficients within the jet region showlarger values than in the suspension phase, which is equivalent with in-tense mixing of particles in the jet region.

Combining the results obtained from the axial and radial dispersioncoefficients, it is found that strong mixing of solids in horizontal and

1; ljet region=270mm; θjet region=16.1°. a) Axial dispersion in the jet region; δs,suspension=

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vertical direction prevails in the lateral sector of the jet region. In thecenter of the jet region, however, strong axial mixing predominates.Moreover it turned out that mixing effects caused by the injection ofsecondary gas also affect particles in the region below the nozzle orifice.

5. Conclusions

The focal objective of the presented work consisted in the non-invasive investigation of the motion of single particles in a fluidizedbedwith secondary gas injection bymeans of positron emission particletracking (PEPT). For this purpose a particle was selected randomly fromthe bulk material and labeled radioactively for use in a gas–solid fluid-ized bedwith secondary gas injection through a vertically arrangednoz-zle. Subsequent tracking of the particle motion resulted in a data setproviding the coordinates of the particle within the system as a functionof time. For derivation of characteristic fluid-dynamic properties of theinvestigated system from particle tracking rawdata, an evaluation algo-rithm is presented.

To validate the significance of the obtained data, solids concentra-tions obtained from particle tracking are compared to concentrationsmeasured invasively using capacitance probes. Direct comparison re-vealed that both techniques yield the same trends with regard to thesolids concentration. However, it is found that particle tracking resultsin a reduced amount of data points at the individualmeasurement posi-tions compared to the invasive measurement technique. This leads tofluctuations in the solids concentrations if very high spatial resolutionis applied during evaluation of particle tracking data. In order to over-come this inconvenience, longermeasurement duration, increased trac-er activity or multiple-particle tracking, respectively, is recommended.

A significant advantage of PEPT over conventional techniques turnedout to be the fact that PEPT allows for non-invasive analysis of the be-havior of a single particle at any locationwithin the system of investiga-tion. Within the context of the evaluation of the solids concentrationprofile of the fluidized bed with secondary gas injection, the character-istic dimensions of the jet region could be determined. Thus the pene-tration depth of the jet region as well as the jet opening angle wasobtained. Moreover, the residence time behavior of the tracked particlewas analyzed. By applying the dimensions of the jet region, as obtainedfrom the solids concentration profile, the relative residence timedensityof a single particle within the jet region could be determined. Anothertarget property was the solids flux crossing the boundaries of the jet re-gion, which serves to give insight into the flow direction of particles en-tering and leaving the jet region. It was found that particles primarilyenter the jet region via its lateral surface area, whereas they escapethrough the center of the boundary area at the top of the jet region. Fur-ther studies revealed the dispersion coefficients for solids within the jetregion and the suspended phase.

Generally it can be concluded that PEPT allows for analysis of themotion behavior of individual particles. In combination with the pre-sented method of data evaluation, several fluid-dynamic properties ofthe investigated system could be inferred: Under consideration of thedispersion coefficients and the particle flux crossing the boundaries ofthe jet region, insight into local flow conditions could be gained.Furthermore, the obtained information on the relative residence timedensity bears high application-oriented value for the design and optimi-zation of fluidized beds systems with secondary gas injection.

It is important to note that the results discussed in this work refer toa single tracer particle with a defined diameter that corresponds to themean particle size of the used bulk material. The idea that tracking par-ticles of a different size fraction may result in different particle behaviorprovides an incentive for future investigations.

NotationA area, [m2]D inner plant diameter, [m]E′ relative residence time density, [−]

F dimensionless solids flux, [−]g gas, [−]h axial position, [m]i index of individual events, [−]j index of the space of investigation, [−]k index of time intervals, [−]l length, [m]m mass, [kg]n total number of data points, [−]N number of transfer events, [−]p measured position of the tracer particle, [m]PEPT positron emission particle tracking, [−]q particle position obtained by interpolation, [m]r radial position, [m]s solid, [−]t time, [s]u velocity, [m s−1]V volume, [m3]δ dispersion coefficient, [m2 s−1]ε void fraction, [−](1-ε) solids volume fraction, [−]θ angle, [°]μ convective displacement of the particle, [m]ρ density, [kg m−3]ρ time-averaged density, [kg m−3]ϕ coarse graining function of space [24], [m−3]χ axial displacement from starting plane, [m]ω spatial resolution, [m]

Acknowledgments

The authorswould like to thank the collaborators in the teamof Prof.David Parker at the School of Physics andAstronomyat theUniversity ofBirmingham for their great support in conducting the particle trackingexperiments. Moreover, the authors would like to express their grati-tude to Prof. Jonathan Seville for providing valuable incentives and hisreadiness for fruitful discussions. The financial support by the GermanResearch Foundation DFG (EXC315/2) in the framework of the Clusterof Excellence “Engineering of Advanced Materials and Processes” isgratefully acknowledged.

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