Modelling the flow structure of upward-flowing gas-solids suspensions

Powder

Technology,

60 (1990)

27

27

- 38

Modelling the Flow Structure of Upward-Flowing

Gas-Solids

Suspensions

M. J. RHODES Department (Received

of Chemical September

Engineering,

8, 1988;

University

of Bradford,

in revised form January

SUMMARY

A simple sampling probe is developed and tested and found to be successful in measuring radial solids flux profiles in the riser of a cold model circulating fluidized bed. Radial profiles measured at different axial positions and different conditions of gas velocity and imposed solids flux are presented. These profiles have a parabolic form and exhibit a strong downward solids flow near to the riser wall. A core-annulus flow model is proposed for the refluxing dilute-phase transport regime found typically in the circulating fluidized beds, riser reactors, vertical pneumatic conveying and the freeboards of bubbling fluidized beds. The predictions of the model are tested against the experimental results presented here and compared with the findings of other workers. Agreement between predictions and experiment is encouraging.

INTRODUCTION

Wherever the upward flow of particulate solids in a gas has been studied, researchers have reported radial non-uniformities in the flow or concentration of solids. At very low solids concentrations, any radial non-uniformities appear to be either non-existent or not detectable. This regime has been termed “co-current dilute-phase transport” by Rhodes [ 11. At higher solids concentrations, marked radial non-uniformities in concentration and solids motion appear. This regime, characterised by a dilute rapidly rising core and a downflow of solids adjacent to the walls of the pipe or riser, is termed the “refluxing dilute-phase transport regime” by Rhodes

[Il.

Many workers have reported observing this regime. Van Breugel and co-workers [Z], studying solids fluxes in an upward-moving 0032-5910/90/$3.50

Bradford

BD7

1DP (U.K.)

24, 1989)

gas-solids stream, reported a parabolic flux profile with a downward flux in the wall region. They showed that the presence of the solids significantly affected the gas velocity profile, with the result that most of the gas was chanelled through the centre of the riser. Bier1 and co-workers [3] attempted to emulate the fast fluidization conditions described by Yerushalmi et al. [4] and found strong radial flux variations in the riser of their circulating fluidized bed. Weinstein [ 51, using X ray photography, Brereton and Stromberg [6], using a capacitance probe, Rhodes [7] and Hartge et al. [S], using light probes, demonstrated that the flow regime in the circular riser of a circulating fluidized bed (CFB) was characterised by a dilute core and dense annulus. Horio and co-workers [9] used light probes to measure particle concentration and particle velocity in the 50-mm riser of a CFB and concluded that the flow was annular with downward-moving particles in the wall region. Monceaux et al. [lo] used a sampling probe in the 144-mm riser of a CFB and detected a region of downward-flowing solids in the wall region. Bolton and Davidson [ll], using a solids sampling technique in the 150mm riser of a CFB, detected a downward flux of solids near to the wall and showed that this downward flux decreased with increasing height above the solids feed point. This phenomenon is not restricted to the risers of CFBs and catalytic crackers. It has been observed in vertical pneumatic conveying, where gas velocities are much higher and pipe diameters much smaller [ 12, 131. It has been observed in the freeboard of bubbling fluidized beds, where gas velocities are far lower [14 - 161. Clearly, the phenomenon of solids downflow in the wall region occurs wherever gas-solids suspensions are transported upwards. This seems to be a surface or ‘wall’ effect, and so, one would expect to observe a downward flux of solids on any @

Elsevier

Sequoia/Printed

in The Netherlands

28

vertical surface in contact with an upwardflowing gas-solids suspension. Attempts to model the upward flow of gas-solid suspensions in terms of a dilute, rapidly rising core and dense, slowly falling annulus have been few. Morooka et al. [ 151 proposed this type of model for the flow in the freeboard of a bubbling fluidized bed on the basis of their measurements of radial variations in particle velocity and voidage using optical fibre and thermal probes. Nakamura and Capes [12] proposed an annular flow model for vertical upward conveying of coarse particles at gas velocities near to their terminal velocities. This model qualitatively predicts trends in variation in solids concentration and internal recirculation of solids within the vertical conveying line, but is restricted to coarse particles because of the assumptions involved. Bolton and Davidson [ 111, in their work on the riser of a CFB, modelled the measured decrease in downward flux of particles in the annulus with height in terms of a mass transfer coefficient governing transfer of solids from a turbulent, dilute core. In this paper, measurements of radial and axial variations in solids flux in the riser of a CFB are presented and compared with the results of others. A new model is proposed to account for the shape of the radial flux profiles and the change in flux profile with axial position in the riser of the CFB. Solids fluxes were measured using a “non-isokinetic sampling probe” similar to that described by Bier1 et al. [3]. These authors found that, under certain conditions, it was not necessary to use isokinetic sampling, since the measured flux varied little with suction rate applied to the probe. In the work reported here, a sampling probe based on that of Bier1 and co-workers was developed and after confirming the observation that suction rate was not critical, the probe was used to measure radial and axial solids flux variation within the riser of a CFB.

EXPERIMENTAL

Equipment The CFB experimental rig is shown in schematic form in Fig. 1 and is described in detail elsewhere [7, 171. The powder used

RobeA

103m

-

f=TobeB

103m

073m -

Prdxc 053m

t O33rn 033m x3m preszue

tapPIngs

Fig. 1. Diagram of the experimental circulating fluidized bed facility showing the location of sampling probes.

was an alumina of mean particle size 64 pm and particle density 1800 kg/m3. The size distribution of the powder is given in Table 1. The particle density of the powder was measured by the comparison method recommended by Abrahamsen and Geldart [18] for porous powders. The arrangement for sampling solids fluxes in the riser is shown in Fig. 2. The two 3-way valves enable the probe to be purged until sampling starts, and allow the suction rate to be set before the start of the sampling period. The first type of probe to be used was that shown in Fig. 3. This was found to be unsatisfactory for two reasons. Firstly, the horizontal arm of the probe affected the flow of solids in the riser when measurements were being made close to the nearside wall of the riser. This was detected from the obvious asymmetry of the radial flux profile. Secondly, the tip of the probe was in different axial positions when in the upward-pointing (measuring downward flux) and downward-pointing (measuring upward flux) positions. In order to overcome

29

TABLE 1 Size distribution of 9G aluminaa Particle size

312

233

173

129

96

71.4

53.1

39.5

29.4

Percentage undersize (by volume)

100

99.5

98.5

95.4

82.5

48.2

15.9

5.7

1.9

a Mean size = -

= 64 pm

(pm)

To

Vacuum

To

PUI ‘P

Atxno Isphere

air

Riser /

Sample

Collector

I

Fig. 2. Schematic diagram of the sampling system. 4mm mntaml d#an#w /

Fig. 3. First sampling probe.

these problems, the probe shown in Fig. 4 was constructed, and was found to give superior results. Effect

of suction

rate variation

Extensive tests were carried out to determine the effect of suction rate on the measured solids flux. With superficial gas velocity fixed at 4 m/s, mean solids circulation flux varied in the range 20 - 70 kg/(m’ s) and with the probe in different radial positions, the effect of varying the suction velocity at the

probe tip between 1.7 and 6.5 m/s was investigated. The results of these tests are presented in Fig. 5 and may be summarised by the following statements. In the dilute, upward-moving core of the riser, the suction velocity has practically no effect on the measured local upward and downward fluxes. In the region nearer to the riser walls where there is considerable solids downflow, both upward- and downward-measured local fluxes increase with increasing suction velocity. However, it can be seen from Fig. 5 that the local net solids flux (local upward flux - local downward flux) is virtually unaffected by the suction velocity at the probe tip over the range of velocities considered. This confirms the observations of Bier1 et al. [3] that isokinetic sampling is not necessary under these conditions of relatively high-concentration dilute-phase flow. Radial flux profiles

Using probes of the improved design (Fig. 4) installed in the riser at positions A,

4mm mternd / dmme'er

60mm

Fig. 4. Improved

‘;:

sampling

probe

ensuring

location

-I

of probe

tip is conserved

when probe

is inverted.

0.8

0.8 ? 2

2

1

3

SUCTION VELOCITY

4

5

AT PROBE

-

E 2

0.6

-

5

0.5

-

E

0.4

-

r8

0.3

-

:: J $

0.2

-

0.1

-

I

0

0.7

0

6

*

gas

radial

velocity

position:

0

1

= 4.0 to

Solids at

wall

Probe

(b)

5

0 0 AT PROBE

= 41.9

velocity

position:

I_

I

'

2

/I

Mean Probe

kg/&s = 4.0

2.5cm

m/s from

wall

Superficial

(cl Fig. 5. Effect

Probe

radial

gas

velocity

position:

of probe suction

= 4.0 5.5cm

velocity

at

wall

on solids collection

B and C shown in Fig. 1, radial solids flux profiles at these levels were built up. Sampling times were of the order of 2 to 3 min and measurements at each radial and axial posi-

(d) at different

Probe

radial

radial probe

1

AT PROBE

flux

level

Superficial

m/s from

downword I .i

solids

.

TIP (m/s)

-1

SUCTION VELOCITY

TIP (m/s)

.

6

Kj G.2 1 z 0.1 -

SUCTION VELOCITY

u$d

C

gas

radial

4

AT PROBE

Flux

level

Superficial

m/s riser

l

I

3

1

SUCTION VELOCITY

TIP (m/s)

next

.

l

downword

Probe Superficial

I

c

Mean

Probe

.

=41.9

5

6

TIP (m/s)

kg/&s

A

gas

velocity

position:

=4.0 centre

m/s of riser

locations.

tion were repeated in order to test reprodubility. Each radial profile was built up from a total of 30 measurements with the probe at 11 different radial positions.

i

31

Radial solids flux profiles were measured at positions A, B and C for the following mean conditions: U = 3.95 m/s, G = 42 kg/(m’ s) U = 3.96 m/s, G = 63 kg/(m’ s) U = 2.76 m/s, G = 42 kg/(m2 s) During each experiment, both the gas velocity and the mean solids circulation flux were checked periodically to ensure that they were reasonably constant. The mean solids circulation flux was measured by diverting solids into the primary measuring bed (see Fig. 1) for a known time. By fluidizing these diverted solids and measuring the pressure drop across them, the mass of solids, and hence the circulation flux were calculated. Further details of this method are presented elsewhere [ 171. Results The solids flux profiles resulting from these measurements are presented in Figs. 6, 7and8. Each flux profile was integrated over the cross-sectional area of the riser to yield an integrated mean flux which was compared with the externally measured mean flux. A simple mass balance tells us that the integrated mean fluxes measured at axial positions A, B and C should be equal to each

. * L-l n

PROBE PROBB

B 0 PROBB C

Fig. 7. Measured radial solids flux profiles at levels A, B and C in the 152-mm diameter riser at U = 3.96 m s-l; G = 63.4 kg mS2 s-l.

\fean solids Superficial

flux

= 42.4

gas velocity

kg/m’s = 2.76

m/s

Fig. 8. Measured radial solids flux profiles at levels A, B and C in the 152-mm diameter riser at U = 2.76 m s-l; G = 42.4 kg mP2 s-r; powder: see Table 1.

Fig. 6. Measured radial solids flux profile at level C in the 152-mm diameter riser at U = 3.95 m s-l; G = 41.2 kg mP2 s-r.

other and equal to the externally measured mean flux. In practice, the integrated mean fluxes measured at the three levels exhibit a

32

maximum deviation of 11.6% from their mean, but are always considerably lower than the externally measured mean flux (see Table 2). Possible causes of this rather poor agreement between internally measured and externally measured mean fluxes are: (i) difficulty in making accurate flux measurements very close to the riser wall where small errors have a large effect on the integrated mean flux; (ii) inaccuracies caused by the uneven inner wall of the riser -the riser is made up of sections of QVF glass tubing which itself has an uneven surface and probe measurements were made through plastic rings inserted at the joints between the glass sections. Further work is under way in which the glass riser has been replaced by a steel one with smooth walls; (iii) the assumption that the radial profile is constant with angular position in the riser may not be valid: some recent work by the present author using denser, larger particles revealed marked variations in radial profile with angular position. This work is reported elsewhere [ 191. TABLE

2

Comparison of integrated mean net solids flux with externally measured mean solids flux Integrated mean net solids flux

Externally measured mean solids

(kg/(m2

(hg/(m’

s))

Superficial gas velocity (m/s)

~11

Figure 6 Probe C

34.3

41.2

3.95

Figure 7 Probe A Probe B Probe C

47.4 55.8 57.6

63.4 63.4 63.4

3.96 3.96 3.96

Figure 8 Probe A Probe B Probe C

34.4 29.8 32.8

42.4 42.4 42.4

2.76 2.76 2.76

ANALYSIS

OF RESULTS

The solids flux profiles presented here are all representative of what the author terms “the refluxing dilute-phase transport regime”. The regime, which is characterised by a

rapidly rising dilute core surrounded by an annulus of slowly falling denser suspension, is exhibited wherever particulate solids are carried upwards in a pipe, duct or riser by a gas. A model is proposed for the refluxing transport regime based on the following assumptions : (i) The flow structure consists of a core region of solids rising in dilute-phase, surrounded by an annulus of solids falling in dense-phase suspension. (ii) All the gas passes through the core, giving no net flow of gas in the annulus (Bader et al. [20] give experimental evidence to support this assumption). (iii) At any axial position, there is a net rate of transfer of solids from the core to the annulus. This rate of transfer is directly proportional to the product of the concentration of solids in the core and the interfacial area between the core and annulus regions. This assumption expresses the envisaged mechanism for particle transfer from the core to the annulus: viz., solids presenting themselves at the core/annulus interface will transfer to the slow-moving annulus. Thus, the rate of transfer increases with increasing concentration of solids in the core and increasing interfacial area. If there exists an equilibrium core solids concentration at which there is no propensity for solids to transfer from the core, then for the purposes of this model, this concentration is assumed to be negligible in comparison with the actual core solids concentration under the conditions considered. (iv) The solids in the core behave as individual particles such that the relative velocity or slip velocity between gas and particles is equal to the single particle terminal velocity. (v) The superficial gas velocity is much greater than the single particle terminal velocity. (vi) The voidage in the core does not vary with radial positions within the core. There is evidence for this in the results of Bader et al. [20], Morooka et al. [15] and Rhodes

[71. (vii) The downflow velocity of solids in the annulus region is determined largely by the balance between gravitational forces and wall friction forces and is thus constant for a given combination of powder properties and wall material.

33

(viii) The voidage of the downward-flowing suspension in the annulus is independent of axial position in the riser. These assumptions given rise to the following equations governing the flow of solids and gas within the riser: Mass flowrate in the core

(with assumption (iv)) Incorporating assumption (v) and rearranging, core voidage

(2)

Based on assumption (iii), _dG, =dz

4&W

M2

(10)

MI-M,

- e1)

(3)

(for the derivation of eqn. (3), please refer to the Appendix) or using the finite increment of height AZ,

(9)

The results shown in Fig. 8 were analysed using the model. These flux profiles were first integrated in order to determine M, , M, and (x at each axial position A, B and C. The proportion of cross-section occupied by the core, CY,was taken to be determined by the radial position at which the measured local net solids flux is zero. The values of M, , M, and (Y thus found for the lowest axial position, position C, were then used as initial values in the model in order to predict the variation of M, , M,, el, E and (Ywith axial position, z. The core and annulus mass flow rates M, and M, are combined in the more useful solids recirculation ratio k, as used by Nakamura and Capes [12] and defined in eqn. (10): kc

DO!

*G=_4PPK(1--l)

1 -E = (1- e&2 + (1- EZ)(l - a2)

The value of the solids transfer coefficient K of eqn. (4) was adjusted to give the best fit between predicted and measured values of recirculation ratio, k (Fig. 9). A value of K = 0.011 m s-l was found to give best agreement with measured k-values. This gave rise to a

AZ

DO!

5

r

Also, AM, = AG,Aa2

(5)

(if CYis considered to be constant over the small section of column of height, AZ). Mass balance of solids over AZ gives AM,=AM,

(6)

In the annulus, M, = ppA(l - ar2)(l - e2)uBZ

(7)

rearranging,

1 l/2

M2

PPup,(l - e,)A

(8)

Equations (2), (4), (5), (6) and (8) may be solved in sequence for a given increment in height AZ, using initial values for M, , M,, U and CV.Thus, since M, and M, determine the value of the net solids flux G in the riser, the model will predict variations in M, , M,, E1 and (x with height. Incorporating eqn. (9), the variation in mean voidage with height may also be predicted.

0: 0

0.1

0.2

0.3

Reclrcuhtlon

0.4

0.5

0.6

0.7

ratio. k

Fig. 9. Predicted variation in recirculation ratio k with axial position in the riser compared with experimental measurements at U = 2.76 m s-l; G = 42.4 kg ,-2 s-l; powder: see Table 1. Experimental points shown thus: 0. K = 0.011 m s-l.

34

rather poor agreement between measured and predicted values of (II(Fig. lo), but more promising correspondence in the case of the mean solids concentration, (1 - e), (Fig. 11). The model requires the introduction of a value of up,, the velocity of the downflowing suspension in the annulus. A value of up, = 0.2 m/s, determined by visual observation through the glass wall of the riser, was used in the predictions of (1 - E) in Fig. 11. The findings of Bolton and Davidson [ 111 were analysed in the same way and the results are shows in Fig. 12. These authors used a simple method to determine the change in downward solids flux with height in the riser, and did not measure values of CLIn the analysis here, a value of (Y= 1 was used. This value is reasonable in view of the very low net solids flux used in the experiments of Bolton and Davidson (G = 3.5 kg m-’ s-l). A value of solids transfer coefficient, K = 0.03 m s-l, gives the most favourable agreement between predicted and reported values of solids recirculation ratio, k in this case. Bolton and Davidson [ 111 reported a value of K (called the deposition coefficient by these authors) of around 0.04 m s- i, based on an analysis in

.

’

0

0

1.0

0.9 d

Fig. 10. Predicted variation in (Y with axial position in the riser compared with experimental measurements at U = 2.76 m s-r; G = 42.4 kg rnd2 s-l; powder: see Table 1. Experimental points shown thus: 0.

0.1

0.05 1-E

Fig. 11. Predicted axial solids concentration (1 - E) profile compared with experimental measurements at U = 2.76 m s-r; G = 42.4 kg mm2 s-l, with I+,, = 0.2 m s-l; powder: see Table 1. Experimental points shown thus: l.

0

0.8

.4. 1

2

3

4

Fig. 12. Predicted axial variation in solid recirculation ratio Iz compared with experimental measurements of Bolton and Davidson [ 111. Conditions: riser diameter, 150 mm; U= 2.2 m s-r; G = 3.5 kg rnh2 s-l; d, = 200 pm, pp = 384 kg m-‘. K = 0.03 m s-l, a=

1.

35

which the rate of particle transfer from core to annulus was governed by the difference between the actual concentration of solids in the core and an equilibrium concentration at which the net rate of particle transfer is zero. The model presented here, where particle transfer is governed by eqn. (3), is thought to be more appropriate for the analysis of higher gas velocity situations such as vertical conveying, circulating fluidized beds and riser reactors. It is likely that the approach of Bolton and Davidson is more suited to analysis of the freeboard of bubbling fluidized beds, where gas velocities are lower. Although the model proposed in the present work does not predict a priori value of recirculation ratio h for given conditions of gas velocity and imposed net solids flux, it does predict trends in k, (II and (1 - E) with an axial position in the refluxing transport regime as shown above and predicts the influ-

TABLE

ence of gas velocity and riser diameter on these trends. For example, the model predicts that increase in gas velocity or riser diameter will result in a lower rate of change of h, (Yand (1 - e) with height above the solids inlet. This predicted influence of increased gas velocity is demonstrated in comparing the results of Fig. 8 with the results of Fig. 7 where at a gas velocity of 4 m s-l, only change in flux profile with height is beyond the resolution of the experimental technique. The predicted effect of increasing gas velocity on the solids concentration profile is in agreement with the findings of many workers [8,17,21]. It is interesting to look at a summary of available measured values of recirculation ratio h and cr. These are presented in Table 3. In the case of Bolton and Davidson [ 111, no values of CYare available and in the case of Van Swaaij et al. [ 221, the degree of recirculation of solids is expressed as a ratio of

3

Summary of experimental suspensions Powder

Alumina (see Table 1)

data on the degree of recirculation

D

G

u

of solids in the vertical

upward

flow of gas-solids

k

a!

GdG

Reference + Notes This work, position C

0.152

63

3.96

0.12

0.925

0.83

0.152 0.152

41 41

3.95 2.76

0.104 0.52

0.90 0.855

0.55 1.93

2.2

l-4.2

-

-

[ill

4.6

0.25

0.873

1.05

t201

Rhodes, unpublished

Vermiculite (200 I*m 384 kg/m3)

0.15

3.5

FCC (76 pm 17 14 kg/m3)

0.305

147

Alumina

0.305

44

2.93

0.19

0.86

0.73

(50 pm 1020 kg/m3)

0.305

24

2.95

0.12

0.89

0.58

0.18 0.18 0.18 0.18

133 141 206 344

4.7 4.3 6.0 5.7

-

-

3.2 1.2 2.4 1.5

FCC

0.18 0.18 0.18 0.18 0.18

236 385 432 284 514

8.5 7.6 8.5 9.4 11.0

-

-

0.32 0.66 0.89 0.17 0.46

1221

Alumina (50% at 40 pm)

0.30

300

6.0

0.28

0.87

1.2

121

36

downward flux G, in the annulus to net upward flux G. The relationship between k and G,/G is given in eqn. (11).

(11) The general trends indicated in Table 3 are that the degree of recirculation of solids in the refluxing transport regime increases with increasing imposed net solids flux and decreases with increasing superficial gas velocity. The effect of riser diameter on degree of recirculation is unclear in Table 2, but is the subject of investigation by the author. The results may be compared with the trends predicted by the “annular flow” model of Nakamura and Capes [12]. This model predicts the correct trend for the variation of k and (x with G and TJ and also predicts the same trends for the variation in k and cxwith equipment diameter D as predicted by the currently proposed model. However, whereas the Nakamura and Capes model does not envisage a net transfer of particles from core to annulus and so predicts no change in radial profile with axial position, it does allow prediction a priori of k. When compared with the k-values of Table 3, however, the Nakamura and Capes predictions are generally about an order of magnitude lower. The reason for the discrepancy is likely to lie in the simplifying assumption made by these authors in attempting to arrive at a tractable analysis of the problem. The most important of these is the mathematical approximation m = 1 + x/2, which is applicable only when the superficial gas velocity is less than 2~~. In the cases quoted in Table 3, the superficial gas velocities are far in excess of this value. The authors’ assumption that frictional losses are negligible compared with gravitational losses for the solids is only approximately true at gas velocities near to UT. This simplifying aSSUn@On iS invalid at the U/VTratios typiCa of the conditions found in Table 3. In short, the Nakamura and Capes model was formulated for coarse particles (typically >500 pm) and should not be expected to predict realistic values of k and CYfor Geldart [23] Group A powders at gas velocities greater than around 1 .O m s-l. Incorporating two further assumptions into the proposed model allows us to model the radial flux profile. Assumptions (ix) and (x)

are given below: (ix) The gas passing through the core exhibits a laminar velocity profile. (x) The downward solids flow in the annulus is evenly distributed over the annulus area. The model so far gives us, for a particular axial position, the upward mass flow rate in the core, M, , the core voidage el, which is independent of radial position, and the fraction of the cross-sectional area occupied by the core, oz. Assumption (ix) gives us gas velocity as a function of radial position: v,=2u

l-[

r2

1

(12)

R2CV2

The local particle velocity in the core is then calculated as a function of r by incorporating assumption (iv) (eqn. (13)). r 1-L

% =2u

r2

1

R2CY2J

-

UT

(13)

t1

Hence, local solids flux G, is given by

G,=

[“:“-5) -v$_~~( (14)

Equation (14) is used to calculate the radial solids flux profile in the core (i.e., between r = 0 and r = aR) and the solids flux in the annulus is calculated following assumption (x) from eqn. (15): G,=

A(1

M2 - a’)

(15)

This approach was used to model the profiles for the conditions depicted in Fig. 8. The result is shown in Fig. 13. By comparison of Figs. 8 and 13, it can be seen that the form and trends in the core flux profile is reasonably well modelled. In Fig. 14, the experimental conditions depicted in Fig. ‘7 are modelled and the measured local net fluxes are reproduced in order to aid comparison. As a first approximation, the simple approach gives encouraging results, although it is clear that in order to correctly model the flux profile near to the riser wall, account must be taken of the effect which the friction between core and annulus has in shaping the flux profile in this region.

37

Radial

Position,

r/R

Fig. 13. Predicted radial solids flux profiles at axial positions A (z = 4.3 m); B (z = 3.3 m) and C (z = 1.53 m) for a 152-mm diameter riser at U = 2.76 m s-l; G = 42.4 kg rnp2 s-l; powder: see Table 1.

Fig. 14. Comparison of predicted radial solids flux profile at position C for a 152-mm diameter riser at U = 3.95 m s-l; G = 41.2 kg me2 s-l; powder: see Table 1.

CONCLUSIONS

The main conclusions of this work are as follows: Conclusions regarding the experimental technique and results:

(1) The “non-isokinetic probe” or “bent tube probe” proposed by Bier1 and co-workers [ 31 has been developed and tested and shown to be successful in measuring local solids fluxes within a riser under refluxing dilute-phase transport conditions. (2) The radial solids flux profile under these conditions was found to be parabolic with a strong downward flux in the region near to the riser wall, indicating a coreannulus flow structure. (3) Under certain conditions, a change in radial flux profile with height in the riser was detected. A decrease in both net upward flux in the core and net downward flux in the annulus was detected under low-velocity conditions. This indicates a net rate of transfer of solids from core to annulus at any axial position in the riser. (4) Recirculation ratios k of the order of 0.1 - 0.5 were measured. The value of k was found to increase with decreasing gas velocity and with increased imposed solids flux. (5) The annular region of downwardflowing solids was found to occupy up to 15% of the riser diameter. The proportion of the diameter occupied by the downward-flowing solids, (1 - a), increases with decreasing gas velocity and increasing imposed solids flux. (6) k decreases with increasing height above the solids inlet. (7) (1 - CY)decreases with increasing height above the solids inlet. (8) The rate of change of k and (1- a) with vertical height in the riser decreases with increasing gas velocity. Conclusions regarding the proposed model: (9) The proposed core-annulus flow model, which envisages a rapidly-rising, dilute core surrounded by a slowly-falling, dense annulus, with a net transfer of solids from core to annulus at any given axial position, successfully predicts the observed trends listed above (conclusions (2) to (8)) and permits prediction of the form of the radial solids flux profile and of the development of this profile with changing axial position. (10) Quantitative a priori prediction of recirculation ratios and radial solids flux profiles from a knowledge of gas and particle properties, gas velocity, solids circulation rate and system geometry is still some way off. However, the proposed model should provide a useful basis from which, with additional

38

experimental data and a further insight into the interaction between core and annulus, a better understanding of the hydrodynamics of this flow regime may be developed. (11) Comparisons between the findings of other workers and the model are encouraging.

El

E2

pp

REFERENCES M. J. Rhodes, Chem.

G

Gl

try, May 1978,

9

s-1 (32

G,

K k

M Ml J42

MT

R r u % % % V, vT z

mean downward solids flux in annulus, kg mP2 s-r local solids flux at a distance r from riser centre, kg mP2 s-l solids transfer coefficient, m s-l recirculation ratio (M,/M), net upwards mass flow rate of solids, kg s-l upward mass flow rate of solids in core, kg s-l downward mass flow rate of solids in annulus, kg s-r rate of solids transfer from core to annulus, kg s-l radius of riser or pipe, m radial distance from riser centre line, m superficial gas velocity, m s-l particle velocity in core, m s-l particle velocity in annulus, m s-l local particle velocity at a distance r from riser centre line, m s-l local gas velocity at a distance r from riser centre line, m s-l single particle terminal velocity, m s-l axial distance above solids feel point, m

Greek symbols a! fraction of riser or pipe diameter occu-

E

pied by core, mean voidage over riser or pipe crosssection, -

Des.,67

(1989)

J. W. van Breugel, J. J. M. Stein and R. J. Vries, Inst. Mech. Eng., 184 (1970) 18. T. W. Bierl, L. J. Gajdos, A. E. McIver and J. J. McGovern, D.O.E. Report No. EE2449-I 1 (1980). J. Yerushalmi, D. Turner and A. M. Squires, Znd. Eng. Chem. Proc. Des. Dev., 15 (1976) 47. H. Weinstein, AZChE Annual Meeting, San Francisco, (1984). K. C. Pratt and B. J. Byrne, Chemistry and Zndus-

LIST OF SYMBOLS

dP

Res.

Proc.

The author wishes to thank the Science and Engineering Research Council for its continued support for his work on circulating fluidized beds.

cross-sectional area of riser or pipes, m2 diameter of riser or pipe, m particle mean size, m imposed solids flux, kg me2 s-r mean upward solids flux in core, kg mP2

Eng.

30.

ACKNOWLEDGEMENTS

A D

voidage of the suspension in the core voidage of the suspension in the annulus particle density, kg me3

10

11

12 13 14 15 16

17 18 19

20

21

22 23

p. 343.

M. J. Rhodes, Ph.D. Thesis, Univ. Bradford (1986). E. U. Hartge, Y. Li and J. Werther, in P. Basu (ed.), Circulating Fluidized Bed Technology, Pergamon Press, Oxford, 1986, p. 153. M. Horio, K. Morishita, 0. Tachibana and N. Murata, in P. Basu and J. F. Large (eds.), Circulating Fluidized Bed Technology IZ, Pergamon Press, Oxford, 1988, p. 147. L. Monceaux, M. Azzi, Y. Molodtsof and J. F. Large, in P. Basu (ed.), Circulating Fluidized Bed Technology, Pergamon Press, Oxford, 1986, p. 185. L. W. Bolton and J. F. Davidson, in P. Basu and J. F. Large (eds.), Circulating FZuidized Bed Technology ZZ, Pergamon Press, Oxford, 1988, p. 139. K. Nakamura and C. E. Capes, Can. J. Chem. Eng., 51 (1973) 39. K. C. Pratt and B. J. Byrne, Chemistry and Zndustry, May (1978). S. T. Pemberton and J. F. Davidson, Chem. Eng. Sci., 41 (1986) 253. S. Morooka, K. Kawazuishi and Y. Kato, Powder Technol., 26 (1980) p. 75. M. Horio, A. Taki, Y. S. Hsieh and I. Muchi, in J. R. Grace and J. M. Matsen (eds.), Fluidizotion, Plenum Press, New York, 1980, p. 509. M. J. Rhodes and D. Geldart, Powder Technol., 53 (1987) 155. A. Abrahamson and D. Geldart, Powder Technol., 26 (1980) 35. M. J. Rhodes, T. Hirama, G. Cerutti and D. Geldart, in J. R. Grace, L. W. Shemilt and B. A. Bergounou (eds.), Fluidization VZ, Banff, Canada, May 1989, Engineering Foundation, New York, 1989, p. 73. R. Bader, J. Findlay and T. M. Knowlton, in P. Basu and J. F. Large (eds.), Circulating Fluidzzed Bed Technology ZZ, Pergamon Press, Oxford, 1988, p. 123. Y. Li and M. Kwauk, in J. R. Grace and J. M. Matsen (eds.), Fluidization, Plenum Press, New York, 1980, p. 537. W. P. M. van Swaaij, C. Buurman and J. W. van Breugel, Chem. Eng. Sci., 25 (1970) 1818. D. Geldart, Powder Technol., 7 (1973) 285.