Particle velocities and their residence time distribution in the riser of a CFB

Powder Technology 203 (2010) 187–197

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Powder Technology j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / p ow t e c

Particle velocities and their residence time distribution in the riser of a CFB Chian W. Chan a,⁎, Jonathan P.K. Seville a, David J. Parker b, Jan Baeyens a a b

University of Warwick, School of Engineering, Coventry CV4 7AL, UK University of Birmingham, School of Physics and Astronomy, Birmingham B15 2TT, UK

a r t i c l e

i n f o

Article history: Received 16 March 2010 Received in revised form 30 April 2010 Accepted 5 May 2010 Available online 19 May 2010 Keywords: Circulating fluidised bed Positron Emission Particle Tracking (PEPT) Residence Time Distribution (RTD) Solids hydrodynamics Riser operating modes

a b s t r a c t The riser of a Circulating Fluidised Bed (CFB) is the key-component where gas–solid or gas–catalytic reactions occur. Both types of reactions require different conditions of operating velocities (U), solids circulation fluxes (G), overall hydrodynamics and residence times of solids and gas. The solids hydrodynamics and their residence time distribution in the riser are the focal points of this paper. The riser of a CFB can operate in different hydrodynamic regimes, each with a pronounced impact on the solids motion. These regimes are firstly reviewed to define their distinct characteristics as a function of the combined parameters, U and G. Experiments were carried out, using Positron Emission Particle Tracking of single radio-actively labelled tracer particles. Results on the particle velocity are assessed for operation in the different regimes. Design equations are proposed. The particle velocities and overall solids mixing are closely linked. The solid mixing has been previously studied by mostly tracer response techniques, and different approaches have been proposed. None of the previous approaches unambiguously fits the mixing patterns throughout the different operating regimes of the riser. The measured average particle velocity and the velocity distribution offer an alternative approach to determine the solids residence time distribution (RTD) for a given riser geometry. Findings are transformed into design equations. The overall approach is finally illustrated for a riser of known geometry and operating within the different hydrodynamic regimes. © 2010 Elsevier B.V. All rights reserved.

1. Introduction and objectives of the paper Despite its early development [1] and subsequent widespread industrial application [2,3], the hydrodynamics of the CFB are still not fully understood as far as the relationship between operating conditions and solids/gas motion are concerned. There is controversy among researchers with regards to the distinction between the different regimes of dilute transport, fast fluidisation (core-annulus flow), and dense suspension upflow (DSU). These controversies centre on the axial profile of solids hold-up in the riser. (i) Some studies observed a bed at the riser bottom and a dilute phase or moderately dense phase (core-annulus) at the top [4– 9]: the axial solids hold-up profile has an inflection point and is referred to as the S-profile. Under increasingly higher solid flux at constant gas the depth of the bed increases [10–13]. (ii) Other studies indicate that an exponential solids hold-up profile exists with no dense bed but with an acceleration zone at the bottom of the riser, characteristic of other regimes ⁎ Corresponding author. Tel.: +44 7865076612; fax: +44 247618922. E-mail address: [email protected] (C. W. Chan). 0032-5910/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.powtec.2010.05.008

such as core-annulus flow without bed, dilute transport and/or dense suspension upflow [14–19]. Based on literature data and own results, the authors of the present paper believe that both S-profile and exponential profile occur in a riser, the typical S-profile being a transition from dilute transport to fully developed dense suspension upflow (DSU). The height of a riser is said to also have a significant impact on the flow regime transitions [20]. A CFB is able to operate in a dilute flow mode, in DSU and in the transition mode as further quantified in terms of operating velocity and solids circulation flux, and illustrated in Fig. 1, including the acceleration zone, the dense bed and the dilute/core-annulus/dense phase higher up the riser. The zone number refers to Fig. 3 of Section 2. Depending on the mode of operation, a riser may experience one or two acceleration regions: a riser without a bed at the bottom will only experience one acceleration region, whereas a riser with a bed at the bottom will display two acceleration regions, one below the bottom dense phase and the other where solids move to the upper phase [21]. If a CFB is to be applied in the various industrial applications, each with specific purposes and operating conditions governed by the type of chemical reactions, major design parameters include: (i) the hydrodynamic regime in the reactor (the riser) controlled by U and G, itself a function of the solids recirculation loop, i.e. the cyclone, the standpipe

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Nomenclature D dp g G H HBTFB rv (rv)0.16 (rv)0.5 (rv)0.84 rt F (rt)0.16 (rt)0.5 (rt)0.84 S(rt) S(rv) t t̄ ta tb ts U Uslip Ut UTR vp, up vp, down − − vp vp X, Y, Z ε εb μg ρg ρp φ ΔPBTFB

Diameter of riser, [m] Diameter of particle, [m] Gravitational acceleration, [9.81 m s− 2] Solids circulation flux, [kg m− 2 s− 1] Height of riser, [m] Height of
BTFB,  [m] vp Ratio of P , [−] vp Value of rv at F(rv) = 0.16, [−] Value of rv at F(rv) = 0.50, [−] Value of
rv at  F(rv) = 0.84, [−] t Ratio of P , [−] t Cummulative distribution, [−] Value of rv at F(rt) = 0.16, [−] Value of rv at F(rt) = 0.50, [−] Value of rv at F(rt) = 0.84, [−] ðrt Þ0:84 −ðrt Þ0:16 Residence time span, , [−] ðrt Þ0:5 ðrv Þ0:84 −ðrv Þ0:16 Velocity span, , [−] ðrv Þ0:5 Residence time of solids, [s] Average residence time of solids, [s] Overall residence time of air in the riser, [s] Residence time of solids in the BTFB, [s] Overall residence time of solids in the riser, [s] Superficial air velocity through the riser [m s− 1] Slip velocity, [m s− 1] Terminal velocity of particle, [m s− 1] Transport velocity, [m s− 1] Average upward velocity of particle, [m s− 1] Average downward velocity of particle, [m s− 1] Average net upward velocity of particle, [m s− 1] Instantaneous net upward velocity of particle, [m s− 1] 3D-position of the tracer as viewed by PEPT [m] Voidage in riser, [−] Voidage of the bottom bed, [−] Viscosity of air, [kg m− 1 s− 1] Density of air, [kg m− 3] Density of solids, [kg m− 3] U , [−] Slip factor, φ = εvZ p Pressure drop across the BTFB, [Pa]

therefore offers a possibility to calculate the riser pressure drop per unit riser height, since equal to ρp (1 − ε). Earlier studies [22,23], mostly carried out by tracer response, have demonstrated that the solids flow mode and its RTD range from plug flow to back-mixing, and have shown that none of the traditional RTD models [24,25] fit the experimental results over the broad range of U and G. No precise conclusions or design recommendations could be drawn from these studies. The present research uses a real-time PEPT-approach, to measure particle velocities and their velocity distribution. The principles of PEPT have been explained by various authors [26–29]. Typical CFB research using PEPT is reported by Chan et al. [30–33] and Van de Velden et al. [22,23]. As far as the operating gas velocity (U) is concerned, stable CFBoperation is only possible at velocities in excess of the transport velocity (UTR), above which stable CFB operation can be maintained, provided that solids recirculation is applied externally. Van de Velden et al. [23] have demonstrated that the equation derived by Bi and Grace, as assessed in reference [23] provides a fair albeit safe prediction of the transport velocity for a wide variety of powders. It is however recommended to operate the riser at a velocity in excess of the calculated UTR, since empirical correlations are expected to be within a 10% accuracy for different powder systems. 2. The different hydrodynamic modes in the riser 2.1. The (U, G) distinction of the hydrodynamic modes Earlier CFB studies [2,4,21,30] defined different solids hydrodynamic regimes in the riser of CFB, as depicted in Fig. 3. Over 100 PEPTdata points and more than 300 literature data in risers of different geometry were used but not specifically indicated in Fig. 3 to simplify the presentation. UTR is the transport velocity. The particle movement and mixing will alter significantly according to the operating mode. 2.2. Particle velocities The average particle velocity and the velocity distribution are essential parameters in the definition of the average particle residence time in the riser and its residence time distribution. The average particle residence time is determined as the ratio of the riser height and the average net upward particle velocity. t=

and the L-valve; (ii) the required contact-time for the reaction, varying from short in most of the gas–catalytic, to long in gas–solid reactions. Reactions involving the gas phase are typically very fast, where a single pass through the riser is sufficient to convert gaseous reactants to gaseous products, independent of the solids residence time. The residence time distribution of the gas phase in a CFB has been reported by Mahmoudi et al. [3]. The overall design strategy of a CFB combines the previous prerequisites and relies upon the flow chart of Fig. 2. Within the flow chart of Fig. 2, the present paper will be limited to the study of the solids hydrodynamics from the respective particle velocity and residence time distribution (RTD) through Positron Emission Particle Tracking (PEPT). The average residence time and the residence time distribution (RTD) are essential for the design of the CFB reactors since solids and/or gas conversions proceed with time. Typical operating conditions for gas–solid and gas–catalytic reactions in the riser have been previously summarised with specific (U, G)combinations recommended for both reaction types [2,3]. The paper will also devote a major part of its assessment to predicting the riser voidage for the different hydrodynamic regimes in the riser. It

H vp

ð1Þ

In dilute flow, the particle velocity is nearly constant and close to the superficial gas velocity. This is no longer the case when the solids concentration increases especially in core-annulus flow. Referring to the regimes of Fig. 3, the following distinction with respect to particle velocities can be made: Regime II In dilute systems, [34–36] the particle velocity is related to the gas velocity by: vp =

U −Uslip ε

ð2Þ

According to Geldart [36], the slip velocity in dilute flow is close to Ut, thus reducing Eq. (2) to vp =

U −Ut ε

ð3Þ

Operating in a dilute riser (ε ∼ 1) at U = 5 m/s with a particle of Ut = 0.8 m s− 1, yields an average velocity, vp ∼ 4.2 m s− 1.

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189

Fig. 1. The different operation modes of a CFB riser, where IAZ is the initial acceleration zone where a BTFB is formed, while AZ is the acceleration zone in other cases.

Regime III Within a restricted range of (U,G)-combinations, a core-annulus flow mode is observed, where particle movement is mostly upward in the core and downward in the annulus, as discussed

by Van de Velden et al. [22], and illustrated in Fig. 6 of Section 4.1. below. The mechanisms underlying the origin and evolution of the coreannulus flow pattern have not been completely elucidated. Some propose that the core-annulus structure results from wall effects,

Fig. 2. Flow chart of the design strategy.

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was between 10–20 s [21], as function of U and G. If the pressure drop of the bottom bed is measured (ΔPBTFB), the height is defined by: HBTFB =

ΔPBTFB ρp ð1−εb Þ

ð6Þ

And tb is then tb =

ρp ð1−εb ÞHBTFB G

ð7Þ

For ash particles (ρp = 2200 kg m− 3) at G = 65 kg m− 2 s− 1 and 4.5 m s− 1, εb = 0.85 [Eq. (5)]. At tb of 20 s, the height of BTFB will be approximately 3.9 m for a pressure drop of 130 mbar. These values are in agreement with the recorded values of the industrial 58 MW CFB combustor of reference [4]. Regime V In a DSU flow mode, the solids velocity is determined by the solids flow rate imposed on the riser, hence Fig. 3. Modes of operation of a CFB riser, expressed as G vs. U – UTR defining. Zone I: transition zone and/or inaccuracy in UTR prediction. Zone II: dilute riser flow (DF). Zone III: core-annulus flow (CAF) only. Zone IV: core-annulus flow (CAF) with BTFB at the bottom. Zone V: dense suspension up-flow (DSU).

which slow down the gas phase, allowing particles to cluster. There is however evidence that non-ideal particle–particle collisions cause formation of particle agglomerates which form the core-annulus flow structure [37,38]. In core-annulus flow, the average velocity of the particles accounts for cluster formation: the interaction between the respective extent of downward and upward particles is expressed in a slip factor, φ, typically 2 especially for an industrial CFB [39], and determined from experimental results in Section 4.5. vp =

U εφ

vp =

G ρp ð1−εÞ

ð8Þ

Empirical equations have however linked vp to a slip velocity, following Eq. (2), but with Uslip ≠ Ut. The riser voidage will also be lower than in dilute flow as concluded by Grace [42]. For particles with density 2260 kg m− 3, circulated at 200 kg m− 2 s− 1 at ε ∼ 0.975, the average particle velocity, vp = 3.5 m s− 1. 2.2.1. Acceleration zone All of the previous regimes (II–V) have acceleration zones where solid particles accelerate from zero velocity in the vertical direction to a constant upward velocity. The acceleration time is the time it takes for a particle to reach the constant velocity from the moment it starts accelerating. The acceleration zone precedes the hydrodynamically developed zone as shown in Fig. 1. The acceleration zone has been

ð4Þ

In core-annulus flow mode, with U = 5 m s− 1, ε ∼ 0.98 and φ = 2, the average particle velocity is reduced to 2.6 m s− 1 (against 4.2 m s− 1 in dilute flow). Regime IV It was earlier demonstrated [4,21] that under certain (U,G)conditions, a turbulent fluidised bed can be formed at the bottom of the riser, while the upper flow is of core-annulus nature. The characteristic core-annulus flow in Regime IV is similar to Regime III, and the same approach applies to this part of the riser flow. To estimate the characteristics of this bottom bed (pressure drop, height), the knowledge of the voidage is imperative. Ouyang and Potter [40] compiled a list of voidage results and the majority of the data fall within the range of 0.8 to 0.9. Chan et al. [2] concluded that the equation by King [41] is the simplest and most accurate approach to predict this voidage, εb:

εb =

U+1 U+2

ð5Þ

Operating at U = 6 m s− 1, corresponds to εb = 0.875, within the range of experimental data of Ouyang and Potter [40]. It was moreover found that the residence time of the solids in the BTFB, tb,

Fig. 4. Experimental set-up: 1) CFB-riser, 2) detectors, 3) high-efficiency cyclone, 4) downcomer and L-valve, 5) vent, to filter and atmosphere, 6) tracer.

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Fig. 5. Illustration of the axial (vertical) component of the tracer particle movement at U = 4.6 m s− 1and G = 21 kg m− 2 s− 1 within the geometric limits of the detectors. I is the time interval for the tracer circulation throughout the CFB, including the cyclone and the return loop.

studied in detail by Chan et al. [21], showing that it covers a length of 0.2 to 0.4 m only, irrespective of operating gas velocity and/or solids circulation flux and insignificant if compared to a typical industrial riser height of 15–20 m.

solids circulation rate from the tracer velocity in the downcomer so that it could be adjusted to the desired value. 4. Results 4.1. General PEPT-image characteristics

3. Experimental set-up Positron Emission Particle Tracking (PEPT) was applied in the experimental set-up of Fig. 4 at ambient conditions. Different risers were used, all with sharp (T) exit, and of dimensions 0.046, 0.09 and 0.16 m I.D. The bulk bed material used is rounded sand with a mean diameter of 120 μm and a particle density of 2260 kg m−³. A single particle of size ∼120 μm was labelled with radioactive 18F using anion-substitution surface adsorption [28,29]. The positrons emitted by the tracer annihilate with electrons to produce 2 co-linear gamma rays, detected by a pair of gamma ray cameras with surface area of 0.59 × 0.47 m². The particle positions were determined in real-time (∼1 location every 4–10 ms). A list of consecutive locations in three dimensions (X, Y and Z co-ordinates) was obtained. The U and G operating values were varied between 1 and 10 m s− 1 and between 5 and 622 kg m− 2 s− 1 respectively. Geiger counters are used to check whether the particles are circulating and to estimate the

The result of each experiment is a long list of X-, Y- and Zcoordinates as a function of time. Fig. 5 illustrates a typical recording of the motion of the tracer particle in the riser. Between each successive point, the distance travelled (ΔY) within a given time interval (Δt) can be calculated. The blanks between successive recordings correspond to the time interval spent by the particle in the rest of the riser (outside the camera view) and in the external recycle loop (where it was followed by Geiger counter only). It is also clearly seen that the tracer sometimes moves upwards and downwards (7th, 9th and last recording), whereas recordings 1, 3, 6 and 8 clearly illustrate how the particle continuously moves upwards. Fig. 6 fully illustrates these observations in greater detail showing the riser cross-sectional flow structure. At the given value of G, the operating mode is shown to shift from core-annulus at U = 2 m s− 1, to DSU at 5.1 m s− 1. The annulus thickness at U = 2 m s− 1 is approximately 20% of the riser radius

Fig. 6. Cross-sectional view of the riser with top: downwards moving particles and bottom: upwards moving particles; at solids circulation rate of 260 kg m−²s− 1 [23].

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Fig. 7. PEPT view of the bottom of the riser, at U – UTR = 2.1 m/s, for G (kg m− 2 s− 1) = (a) 5.5; (b) 20.1 (c) 55.5 (d) 210.

which agrees with the overall literature finding on annulus thickness as discussed elsewhere [2]. To examine the extent of the acceleration zone and the possible occurrence of a dense bottom bed, the bottom section of the riser was separately viewed by Chan et al [21]. The solids movement differs completely with operating regimes, as depicted in Fig. 7. These regimes cover different operating regimes. At low G-values (b∼10 to 20 kg m−²s− 1) the tracer particle is seen to descend below

the solids entry point, i.e. the L-valve, where after it is accelerated and conveyed up the riser in a dilute flow mode; as G starts to increase, the a core-annulus flow mode and a bubbling/turbulent fluidized bed (BTFB) at the bottom of the riser appear. A further increase of G results in a dense suspension upflow mode. It is hence evident that the existence of a BTFB is limited to a specific range of U, G operating

Table 1 Measured upwards and downwards velocities of particles by PEPT. U (m s− 1)

G (kg m− 2 s− 1)

vp, up (m s− 1)

vp, down (m s− 1)

Flow mode of Fig. 3

3.2 3.6 5.5 7.5 3.2 4.9 5.2 5.3

52 55 57 67 305 208 260 347

2.2 2.4 3 4.8 2.2 4 4.3 4.5

0.81a 0.72a 0.52a 0.54a 0.13b 0.02b 0.03b 0.03b

Core-annulus Core-annulus Core-annulus Core-annulus DSU DSU DSU DSU

a b

Significant downward flow of particles. Predominantly dense core flow through out riser cross-section.

Fig. 8. The difference between PEPT-measured vp, up and predicted vp.

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values [21]. The different operating conditions can be exported onto the phase diagram of Fig. 3, where (a) corresponds to operation in Zone II; (b) is typical for Zone III; (c) is a zone IV operation and (d) is the DSU mode of zone V. 4.2. Distinction between upward and downward flowing particles

4.3. Slip velocity The PEPT study of the solids in the riser allows for comparison of the experimental particle velocities with the predicted particle velocity from Eq. (2). According to Fig. 8, core-annulus flow data do not correspond with the prediction of Eq. (3), which clearly represents the solids hydrodynamics that show a very dominant core flow, i.e., dilute flow or dense suspension upflow (DSU). The deviation of data in core-annulus flow is the result of cluster formation, with an effective terminal velocity in excess of the particle terminal velocity, Ut. A slip factor approach is then more appropriate, although PEPT results for core-annulus can be fitted as:
 U  Ut vp;up = 0:56 ε

ð9Þ

4.4. Voidage of regimes Since the voidage determines the particle velocity as shown in all the equations of Section 2.2, it is important to be able to accurately predict the voidage. Again, literature presents a wide range of values as reviewed in [2]. On a theoretical basis, the voidage is determined by ε=

volume of air volume of air + volume of solids

ð10Þ

Accounting for the respective residence times of the gas and solid phase, this is transformed into ε=

U × ta U × ta + ρG × ts

Eq. (13) corresponds with the empirical equation of Pugsley et al. [45]. Alternatively, the PEPT-velocities can be used to calculate the voidage from

ε = 1−

Particle velocities are defined by the increase or decrease in spatial co-ordinates for a given Δt. Representative results are shown in Table 1 for some of the experimental runs. When a typical core-annulus flow mode is observed, the downward velocity of solids in the annulus region is close to the terminal velocity (0.67 m s− 1) of the tracer particle (120 μm, 2260 kg m− 3). The experimental downward velocity in the annulus is within the range of literature findings [43,44].

ð11Þ

193

G vp ⋅ρp

ð14Þ

If experimental PEPT values of vp are used at each combined (U, G) operation in Eq. (14), the experimental values of ε are accurately predicted by Eq. (12) in dilute and DSU modes (error of 0.47 to 2.19%) whereas core-annulus ε-predictions and experimental values all correspond to within 0.35% when using Eq. (13). The voidage for DSU as found by PEPT also contradicts the previous indications of Grace [42], clearly underestimating the value of ε, given as 0.75–0.93 only. Both Eqs. (12) and (13) will be used in the design recommendations of Section 5. 4.5. Slip factor in different regimes The particle velocities of the different regimes can be predicted by their respective and specific equations of Section 2.2. A more general approach would be the use of Eq. (4) throughout the regimes, thus defining the respective slip factor. Together with calculated values of ε, vp data were hence used to define the corresponding slip factor, φ, as depicted in Fig. 9. Contrary to the DSU-findings of Grace [42], the slip factors range from 1.2 to 1.5, with an average of 1.3, far smaller than 5 to 10 as indicated by Grace [42]. The average slip factor for DSU is only fractionally higher than the average slip factor for dilute flow of 1.2. The slip factor for the core-annulus regime is between 1.7 and 2.3, in agreement with the findings of Matsen (φ = 2) [39]. The values of φ in dilute flow correspond with findings of Hellinckx and Van Rompay [46], who determined a slip factor being close to 1 at very high superficial gas velocities (N20 m s− 1) and slightly higher as function of increasing Ut/U ratio, with e.g. φ = 1.1 for Ut/U ∼ 0.5. Clearly, in the transition between DF and CAF, slip factors are less well-defined. 4.6. The particle velocity distribution Due to its cluster flow nature, a core-annulus riser flow should exhibit more mixing than dilute flow or DSU. The velocity profile should therefore show a wider distribution of velocities, whilst dilute flow or DSU should exhibit a narrower range closely resembling plug flow behaviour at a more constant particle velocity. The span of the velocity distribution curve, S(rv), can help to define the deviation of real solids flow to that of ideal plug flow, being understood as the

p

In dilute and dense flow systems, solids/gas velocities and residence times are about equal. In core-annulus flow, the flux of downward annulus solids, calculated for the cross-sectional area of the annulus region and the average vp,down is of the same order of magnitude as the net solids circulation rate, thus increasing the effective solids circulation flux within the riser by a factor close to 2. Eq. (11) can be simplified to: ε=

U U+

ε=

U U+

G ρp

2G ρp

for dilute and DSU mode

ð12Þ

for core  annulus mode

ð13Þ Fig. 9. Slip factor for the different modes and their associated G values at 1 b U − UTR b 8.

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Fig. 10. a: Velocity distribution in the riser at constant G of 35 kg m− 2 s− 1 but increasing U from 2.4 m s− 1 to 5.4 m s− 1. b: Velocity distribution in the riser at constant G of 54 kg m− 2 s− 1 but increasing U from 3.2 m s− 1 to 6.7 m s− 1. c: Velocity distribution in the riser at constant U of 3.6 m s− 1 but increasing G from 35 kg m− 2 s− 1 to 316 kg m− 2 s− 1. d: Velocity distribution in the riser at constant U of 5.4 m s− 1 but increasing G from 35 kg m− 2 s− 1 to 260 kg m− 2 s− 1.

condition of constant velocity of all particles throughout the riser cross section and height. 
 vp is hereafter defined at some The velocity ratio, rv rv = vp critical points of the velocity distribution curve, F(rv): Sðrv Þ =

ðrv Þ0:84 −ðrv Þ0:16 ðrv Þ0:5

ð15Þ

The F-values at 84% and 16% represent the standard deviation in a Gaussian distribution. For ideal plug flow, S would be 0 since (rv)0.84 = (rv)0.16 = (rv)0.5. Larger values of S mean more mixing, deviating from ideal plug flow behaviour. Figs. 10 present data obtained via PEPT to exemplify the changes in the flow/mixing behaviour including calculated S values at both constant U and increasing G, and constant G and increasing U, thus representing the complete range of solids hydrodynamics of Fig. 2. If S(rv) exceeds 1, a more prominent downward flow of particles in the annulus occurs. It is also clear that there are various flow regimes under different values of U and G, otherwise S(rv) should remain relatively constant. 4.7. Span approach and use in RTD prediction A good approach to identify the degree of mixing can use the same span approach where velocity spans are transformed into time spans


 t – . The span of the residence time distribution (RTD) curve, S(rt), t can help to define the deviation of the real solids flow to
that  of ideal t plug flow. The residence time ratio, rt is defined as rt = – at critical t points of the residence time distribution curve, F(rt). For ideal plug flow, S would be 0 since (rt)0.84 = (rt)0.5 = (rt)0.16. Larger values of S mean more mixing. Figs. 11 present transformed PEPT data into a time scale, accounting for the height of the PEPT camera, travelled by the particle at velocity, vp. The span of the RTD curve, S(rt), can help to define the deviation of real solids flow to that of ideal plug flow. S is defined as: Sðrt Þ =

ðrt Þ0:84 −ðrt Þ0:16 ðrt Þ0:5

ð16Þ

Obviously, some particles spend a considerable shorter or longer time in the riser. This can be accounted for when developing a F(t) function based upon rt and S (rt). The degree of mixing as indicated by the S values in Fig. 11-c and d also confirms the different regimes of the phase diagram, repeated as Fig. 12, with indication of the data points with respective S-value. At U = 5.4 m s− 1 and G = 57 kg m− 2 s− 1, the S values for both velocity distributions and RTD are the largest since it is operating in the coreannulus regime with/without BTFB at the bottom. The particle reflux from top to bottom within the annulus and the particle exchange between core and annulus at different heights of the riser, explains the larger spread in RTD [47]. The velocity distribution is greater in

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195

Fig. 11. a: Solids RTD at constant G of 35 kg m− 2 s− 1 but increasing U from 2.4 m s− 1 to 5.4 m s− 1. b: Solids RTD at constant G of 54 kg m− 2 s− 1 but increasing U from 3.2 m s− 1 to 6.7 m s− 1. c: Solids RTD at constant U of 3.6 m s− 1 but increasing G from 35 kg m− 2 s− 1 to 316 kg m− 2 s− 1. d: Solids RTD at constant U of 5.4 kg m− 2 s− 1 but increasing U from 35 m s− 1 to 260 m s− 1.

core-annulus flow due the momentum transfer between upward flowing core and downward flowing annulus particles [47]. Fig. 12 will illustrate how phase transitions affect S(rt).

From Fig. 13, both S(rr) and S(rt) are fairly constant in dilute flow regime, being 0.33 and 0.40 respectively. For core-annulus flow, both S(rr) and S(rt) are larger but still constant, being 1.4 and 2.3 respectively. For DSU flow, the degree of mixing falls between dilute flow and core-annulus flow where the values of S(rr) although a linear relationship is proposed: Sðrv Þ = 0:15ðU−UTR Þ + 0:32

ð17Þ

Sðrt Þ = 0:3ðU−UTR Þ + 0:31

ð18Þ

It is no surprise that the mixing behavior in DSU flow is between dilute flow and core-annulus flow. DSU flow exhibits greater mixing than dilute flow due to the high concentration of solids with more intense particle–particle collisions resulting in higher mixing than experienced in the dilute flow. 4.8. Prediction of cumulative distribution curve Within the 84% and 16% span, it appears possible to linearise the F(rt) curve using the span S(rt) as fitting parameter. This results in:

Fig. 12. Modes of operation in the CFB-riser. For zone identification, see Fig. 3. S(rt) values are added between [brackets]. If plotting the S(r t ) and S(r v ) values against U− U TR , the data are represented in Fig. 13.

F ðrt Þ =

0:72 0:72 r + 0:5− ; valid for 0:16bF ðrt Þb0:84 Sðrt Þ t Sðrt Þ

ð19Þ

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Fig. 13. a: S(rv) as a function of U − UTR for various flow regimes. b: S(rt) as a function of U − UTR for various flow regimes.

5. Design application of the findings Having determined the methods to calculate the average particle velocity (Section 2) and the associated parameters ε and φ (Section 4), the average residence time, t̄, in the riser of height H is also determined.

From the data transformation to its respective velocity span and RTD span, it is now also possible to approximate the RTD function as a t linear dependency of . t The design approach is illustrated for the different regimes of Fig. 3 when using 120 μm sand particles (2260 kg m− 3) with transport velocity UTR = 2.2 m s− 1 and Ut = 0.67 m s− 1, in a riser of 15 m operated at 5 m s− 1. Obviously, residence times are short in dilute and DSU operating modes, moderate in core-annulus mode and long for the operation of core-annulus mode with BTFB present. It is now obvious that very fast solid reactions, such as calcinations of fine limestone [48] will be achieved in a single pass, whereas slower solid reactions will need multiple passes in the CFB, or could benefit from the presence of a BTFB (as used in e.g. the combustion of biomass [4]). The range of operating U and G for the known commercial risers was reviewed by van de Velden et al. [22,23] with reported CAF operating in the range of U–UTR = 0.5 to 5 m s− 1 and G-values of 10 to about 80 kg m− 2 s− 1. CFB operations in DSU-mode are reported for U–UTR values in excess of about 8 m s− 1 and G-values between 150–1200 kg m− 2 s− 1. The target application thus determines the most appropriate operating mode, and Table 2 above then enables to estimate the respective average solids residence time in the specific riser mode for a single pass of the particles. If the particles are subject to multiple passes through the riser, their average residence time is expected to be a multiple of the single pass prediction, although the recycle loop (cyclone, downcomer and L-valve will certainly increase the residence time distribution curve. Under specific operating conditions, mainly around the regime transition (U, G)-values of Fig. 3, and especially in high risers, different regimes can co-exist along the riser height. Since it is at present impossible to determine the extent of each regime along the riser height, the prediction above will be indicative only but will set the extreme values of the solids residence time being the lowest if operating under a DF or DSU regime, and the highest for a CAF with BTFB regime. The real value will be between both extremes, but prediction from the presented data alone is yet impossible. 6. Conclusion The design of CFB-riser reactors requires the knowledge of the solids residence time, as determined by the particle movement within

Table 2 Design specifications for each flow regime in a typical CFB riser. Parameters

Flow mode

Voidage, ε

Zone II: dilute flow (DF) Eq. (12)

Zone III: core-annulus (CAF) Eq. (13)

Particle velocity, vp Slip factor, φ S(rv) S(rt) t̄ Overall F(rt)

Eq. (3) 1[36] 0.33 0.4 . t = H vp Eq. (19)

Eq. (4) ∼ 2[39] and present study 1.4 2.3 . t = H vp

Zone IV: core-annulus (CAF) with BTFB Eq. (13): CAF Eq. (5): BTFB Core-annulus: Eq. (4) ∼ 2[39] and present study 1.4 2.3 . t = H vp + tb ; tb = 10−20s [21]

Zone V: DSU Eq. (12) Eq. (3) 1.3 (present study) Eq. (17) Eq. (18) . t = H vp

Example: 120 μm sand with density of 2260 kg m− 3; UTR = 2.2 m s− 1; Ut = 0.67 m s− 1; and 15 m higher riser Operating conditions

U = 5 m s− 1, G = 10 kg m− 2 s− 1

U = 5 m s− 1, G = 55 kg m− 2 s− 1

U = 5 m s− 1, G = 70 kg m− 2 s− 1

U = 5 m s− 1, G = 300 kg m− 2 s− 1

ε

0.9991

0.988

0.974

φ vp S(rv) S(rt) t̄

1 4.33 m s− 1 0.33 0.4 3.1 s

2 2.53 m s− 1 1.4 2.3 5.8 s

BTFB: 0.85 CAF: 0.990 2 CAF: 2.52 m s− 1 1.4 2.3 Assuming tb ∼ 15 s 6.2 + 15 s = 21.2 s

1.3 5.1 m s− 1 0.725 1.12 2.9 s

C. W. Chan et al. / Powder Technology 203 (2010) 187–197

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