Experimental and Computational Studies of Gas Mixing in Conical Spouted Beds

Refereed Proceedins The 1th International Conference on Fluidization - New Horizons in Fluidization Enineerin Enineerin Conferences International Year 007 Experimental and Computational Studies of Gas Mixin in Conical Spouted Beds Zhiuo Wan C. Jim Lim Xiaotao T. Bi University of British Columbia The University of British Columbia, cjlim@chml.ubc.ca University of British Columbia, xbi@chml.ubc.ca This paper is posted at ECI Diital Archives. http://dc.enconfintl.or/fluidization xii/64

FLUIDIZATION XII 59 Wan et al.: Studies of Gas Mixin in Conical Spouted Beds EXPERIMENTAL AND COMPUTATIONAL STUDIES OF GAS MIXING IN CONICAL SPOUTED BEDS Zhiuo Wan, C. Jim Lim and Hsiaotao T. Bi Fluidization Research Centre, University of British Columbia, Vancouver, Canada ABSTRACT The residence time distribution data in a conical spouted bed, obtained both from the bed bottom and the bed surface at different radial positions, were analyzed to obtain the mean residence time and the clet number. In parallel, local flow structures of a bed with the same dimensions and operatin conditions as in the experiment were enerated from the computational fluid dynamics (CFD) simulation usin the FLUENT codes, and then were used for the simulation of as dispersion. The results show that CFD simulations aree reasonably well with experiments. The radial distribution of the clet number is quite complex, with a maximum value at r=0.135 m under three operatin conditions investiated. INTRODUCTION The as residence time distribution is of considerable importance in predictin the conversion and selectivity for various catalytic reactions, and backmixin is undesirable as it may lead to increased by-products. Both vertical and horizontal mixin/dispersion can be studied usin steady and unsteady state tracer techniques. In the steady state tracer experiment, a steady flow of tracer as is introduced into the spouted bed at a certain location, and the tracer concentration is measured either downstream or upstream of the injection point. Ideally, the injection rate should be adjusted to match the local as velocity in the bed to achieve an isokinetic injection ( (1). Based on the tracer concentration measured upstream of the injection point, axial backmixin coefficient can be derived (). On the other hand, the radial dispersion coefficient is obtained by analyzin radial profiles of tracer concentrations measured downstream of the injection point (1). The overall or effective axial dispersion coefficient over the entire bed could be derived usin the unsteady state tracer technique. For as-solid multiphase systems, there have been a lare number of researches on as backmixin and/or radial dispersion in bubblin fluidized beds, circulatin fluidized beds/risers and downers, (e.. 3-7). However, there have been only a few studies on as mixin in cylindrical spouted beds and conical spouted beds (e.. 8-13), and almost no reports on the residence time distribution (RTD) simulation based on computational fluid dynamics (CFD) for spouted beds. In this study, as dispersion in conical spouted beds was investiated both experimentally and analytically based on tracer techniques and CFD simulations, respectively. Published by ECI Diital Archives, 007 1

530 WANG, LIM, BI EXPERIMENTS The 1th International Conference on Fluidization - New Horizons in Fluidization Enineerin, Art. 64 [007] The conical spouted bed (full column) used in this study is made of Plexilas with an included anle γ of 45 o. The diameter at the conical base D i is 38 m, the diameter of the nozzle D 0 is 19 m, and the diameter of the upper cylindrical section D c is 5 m. For more details, please see Wan et al. (14). Glass beads of 1.16 mm in mean diameter with a narrow size distribution were used as the bed material, compressed air at the ambient temperature was used as the spoutin as. The static bed heiht employed in the experiment is 0 m, and spoutin velocities of 3.5 and 17.0 m/s based on the bottom inlet were used in the experiment with the hiher one for stable spoutin and the lower one for internal/partial spoutin. Durin experiments, helium was used as the as tracer. For RTD measurements, the tracer was introduced as a step function into the spoutin air far away from the bottom of the conical spouted bed by a solenoid valve, and the unsteady state response was measured by a thermal conductivity detection (TCD) system. Two samplin probes of 1 mm ID were connected separately to two TCDs to measure the tracer concentration, with one located just below the as inlet and the other just above the bed surface, with a separation distance of m. Both probes can be radially traversed to measure the tracer concentration at different radial positions. Output sinals from TCDs were amplified and collected via a data acquisition system. ESTIMATION OF THE GAS MIXING BEHAVIOUR For a neative step input function, the response curve from each samplin probe can be converted to the cumulative distribution function F(t) by V ( t) F( t) = 1 V (1) V 0 V where V 0 is the averae voltae sinal correspondin to C He =C 0, V is the averae value correspondin to C He =0, and V(t) is the transient value. To convert the cumulative distribution function into RTD function, the cumulative distribution function F(t) was fitted first by usin Levenber-Marquardt method, and the RTD function E(t) was obtained by differentiatin the fitted F(t) curve. df( t) E( t) = () dt For the two-probe measurement system, the mean residence time and the dispersion clet number of the dense section can be derived from the difference between measured RTD functions below the as inlet and above the bed surface by assumin that spouted bed behaves like a linear system, as shown in Fiure 1. For an open-closed system, the axial clet number can be related to the variance for a flow system with small backmixin by (15) 1 σ = 3( ) + (3) http://dc.enconfintl.or/fluidization_xii/64

FLUIDIZATION XII 531 where = σ t ( t Wan ˆ) et al.: Studies of Gas Mixin in Conical Spouted Beds σ is the variance, is the clet number, u L / D =, u is the interstitial as velocity, L is the distance between two samplin points, D is the dispersion coefficient. EXPERIMENTAL RESULTS AND DISCUSSIONS Fiure shows some experimental raw sinal V, calculated F functions and E functions at the inlet as well as at the bed surface based on neative step tracer experiments with response time las included. It can be seen from Fiure that the response at the as inlet was not a perfect step function, which could mean either that there exists as backmixin between the tracer injection point and TCD 1 or that the tracer injection was not a perfect step function. H 0 1 σ t,1 Helium ( t, ) t ( t, σ ) ( t p, ) Probe 1 Air σ t,p Probe ( t p1, σ t,p1) Injection point TCD TCD 1 Fi. 1. Definition of the mean residence time and correspondin variance for different sections. Fi.. Experimental raw data V, calculated F functions and E functions at the inlet ( ) and the bed surface ( ) with the probe located at the axis. (Stable spoutin, U i =3.5 m/s, full column) V (V) F(t) E(t) 4.0 3.0.0 1.0-1.0 1. 1.0 0.8 0.6 0. 3.0.0 1.0 4.0 4.5 5.0 5.5 6.0 6.5 7.0 Fiures 3 to 4 show the radial distribution of the mean residence time and the clet number at different operatin velocities or states, one in stable spoutin state and other two at partial spoutin states in the as velocity ascendin and descendin processes, respectively. Fiure 3(a) shows that the mean residence time increases with increasin radial distance from the centre of the column toward the wall, meanin that as velocity inside the conical spouted bed has a radial distribution, hiher in the centre and lower near the wall. Fiure 3(b) shows that the radial distribution of the clet number is quite complex, with a maximum value at r=0.135 m. This trend is commonly observed at different operatin velocities or states as shown in Fiure 4. Meanwhile, the radial distribution of as velocity in the ascendin process is different from that in the descendin process, so is the as mixin behaviour, even thouh operatin velocities are almost the same. Published by ECI Diital Archives, 007 3

53 WANG, LIM, BI 1.0 The 1th International Conference on Fluidization - New Horizons in Fluidization Enineerin, Art. 64 [007] 100 0.8 80 0.6 60 40 0. 0 0 4 8 0.1 0.16 0.0 0 0 4 8 0.1 0.16 0.0 (a) (b) Fi. 3. Radial distribution of the mean residence time and the clet number. (Full column, stable spoutin, U i =3.5 m/s) 0.6 0.5 Ascendin Descendin 60 50 Ascendin Descendin 0.3 0. 40 30 0 0.1 10 0 4 8 0.1 0.16 0.0 0 0 4 8 0.1 0.16 0.0 (a) (b) Fi. 4. Radial distribution of the mean residence time and the clet number. (Full column, partial spoutin, U i,d =17.05 m/s, Z d =0.16 m or U i,a =16.95 m/s, Z a =0.131 m) SIMULATION OF GAS MIXING IN A CONICAL SPOUTED BED General as mixin model From the analysis of a small control volume in the vertical direction with the assumptions that (a) the dispersion coefficient is constant within the bed and (b) as density remains constant within the bed, the followin expression can be derived: d( ε ρ X a) d( ε ρ v, z X a) d (4) dt + dz d ( X ε ρ D dz dz a ) = 0 In X and Y directions, similar expressions can be obtained, and the eneral threedimensional equation in Cartesian coordinates can be written as ( ε ρ X a) (5) t + ( ε ρ v X a ) [ ε ( ρ D) ( X a )] = 0 Because the flow rate of the tracer is very small with a maximum helium volume fraction of 0.3 % durin experiments, the volume fraction of the helium is assumed to http://dc.enconfintl.or/fluidization_xii/64 4 be proportional to the mass fraction of the helium.

ρ ρ FLUIDIZATION XII 533 X a = C He He Wan et al.: Studies of Gas Mixin in Conical Spouted Beds (6) where C He is the volume fraction of helium, ρ He is the density of helium. As discussed before, usin the neative step tracer input, the cumulative distribution function F(t) can be written as Equation (1). Considerin the linear characteristics of Equations (1) and (6), as well as the assumed linear characteristics of the samplin probes, for convenience, a pseudo positive step function curve derived from experiments was used as the tracer input in the current simulation with followin boundary conditions: When t-t i <0, X a =0; When t-t i 0, X a =F(t-t i ) at the tracer inlet (Pseudo positive step function) X a at the wall X a = 0 at the outlet, and = 0 z r In order to simulate as mixin behaviour in a conical spouted bed, as velocity field as well as the distribution of the voidae need to be calculated first. Thus, a conical spouted bed with the same eometrical dimensions and operatin conditions as those in the current experiment was simulated first usin the FLUENT simulation software, with details iven in Wan et al. (14). In the simulation, once stable spoutin has been reached and the averae as velocity field and voidae distribution were calculated, a DEFINE_ON_DEMAND function was activated to pass the averaed as velocity field and the voidae distribution to three User Defined Memories (UDMs) for further simulation on as mixin behaviour. At the same time, the current time t i was obtained. After chanin t i to the exact value just obtained, the User Defined Function was activated aain. To achieve the positive step injection, the whole column should be patched with for the User Defined Scalar (UDS) φ after it had been defined (includin definin UDS and the correspondin dispersion coefficient), and correspondin boundary conditions should be defined too. To simulate as mixin at the stable spoutin state and to save computation time, all equations were turned off except the newly defined UDS equation. Fiures 5 and 6 show the comparison between experimental results and CFD simulation results on the mean residence time and clet number. It can be seen that the dispersion coefficient affects simulation results sinificantly, with better areement between experimental and simulated results at D=00 m /s for the central spout reion. Near the wall, simulation results underestimate the clet number reatly and overestimate the mean residence time sinificantly for all values of the dispersion coefficient investiated. With a small dispersion coefficient, CFD simulation ives a similar radial distribution curve on the clet number as that from the experiment. The existence of a peak clet number in the radial profile can thus be attributed to the compromise of the decreasin as velocity and the increasin as streamline lenth as the radial location chanes from the centre to the wall. Fiure 6 suests that the difference between the CFD simulation and the experiment still cannot be resolved even usin different values of the dispersion coefficient for the spout and the annulus. Moreover, nelectin the dispersion (D=), Published by the ECI difference Diital Archives, between 007 the CFD simulation and the experiment near the 5

534 WANG, LIM, BI wall (r=0.180 The 1th International m) still Conference exists, on suestin Fluidization - New that Horizons as in convection Fluidization Enineerin, may be Art. the 64 [007] dominant factor near the wall. On the other hand, that the simulated as velocity is lower near the wall (or hiher in the spout) than from the experiment suest that the mismatch between the simulated and measured may result from the mismatch of the simulated and measured radial velocity profiles. 1. 0.8 Experimental data D (m /s) 00 01 05 100 80 60 40 0 Experimental data D (m /s) 00 01 05 0 4 8 0.1 0.16 0.0 0 0 4 8 0.1 0.16 0.0 Fi. 5. Comparison between the experiments (symbols) and CFD simulations (lines). (Full column, stable spoutin, U i =3.5 m/s.) 1. 0.8 Experimental data D (m /s) Spout Annulus 01 01 01 01 100 80 60 40 0 Experimental data D (m /s) Spout Annulus 01 01 01 01 0 4 8 0.1 0.16 0.0 0 0 4 8 0.1 0.16 0.0 Fi. 6. Comparison between the experiments (symbols) and CFD simulations (lines). (Full column, stable spoutin, U i =3.5 m/s.) CONCLUSIONS Helium tracer experiments clearly show that there are radial distributions of the as velocity inside a conical spouted bed with hiher velocity in the centre and lower near the wall. There exists a maximum value of clet number at r=0.135 m, resultin from the balance of decreasin as velocity and increasin as streamline lenth with increasin the radial distance from the center to the wall. Meanwhile, the as mixin in the ascendin process is different from that in the descendin process, implyin that the radial distribution of as velocity is different too, even thouh operatin velocities are identical. The as mixin was also simulated usin a CFD model. It was found that, with a small dispersion coefficient, CFD simulation ives a similar radial distribution curve on the clet number as that from the experiment. The difference between the CFD simulation and the experiment cannot be eliminated usin different values of the dispersion coefficient for the spout and the http://dc.enconfintl.or/fluidization_xii/64 6

FLUIDIZATION XII 535 annulus, likely due to Wan the et al.: mismatch Studies of Gas of Mixin simulated in Conical Spouted and measured Beds radial velocity profiles. ACKNOWLEDGEMENTS This work is supported by the Natural Sciences and Enineerin Research Council of Canada (NSERC) under the Discovery Grant proram. NOTATION C 0 C He Initial volume fraction of helium in air, (%v/v) Volume fraction of helium in air, (%v/v) D Dispersion coefficient, (m /s) D 0 Gas inlet diameter, (m) D c Diameter of the cylindrical section, (m) D i Diameter of the bed bottom, (m) E(t) RTD function F(t) Cumulative distribution function H 0 Static bed heiht, (m) L Distance between two samplin points, (m) clet number, =(u L)/D, (-) r Radial coordinate, (m) t Time, (s) t i Time startin the injection of tracer as, (s) Mean residence time between the tracer injection point and the tip of tˆ1 tˆ p 1 the probe 1, (s) Mean residence time for the electric sinal from probe 1, (s) tˆ p Mean residence time for the electric sinal from probe, (s) u Interstitial as velocities, (m/s) U i Superficial as velocity based on D i, (m/s) U i,a Superficial as velocity based on D i durin ascendin process, (m/s) U i,d Superficial as velocity based on D i durin descendin process, (m/s) v Velocity vector of the as phase, (m/s) v,z Local axial interstitial as velocity, (m/s) V Manitude of the measured electrical sinal, (V) V 0 Averae value of the electrical sinal correspondin to C He =C 0, (V) V Averae value of the electrical sinal correspondin to C He =0, (V) X a Mass fraction of the tracer as, (-) Z Axial coordinate, (m) Z a Heiht of the internal spout in the ascendin process, (m) Heiht of the internal spout in the descendin process, (m) Z d Greek letters tˆ σ Mean residence time inside the conical spouted bed, (s) t Variance corresponds to tˆ, (s ) ε Voidae, (-) Published by ECI Diital Archives, 007 7

536 WANG, LIM, BI φ The 1th International Arbitrary Conference scalar on in Fluidization the as - New phase, Horizons (-) in Fluidization Enineerin, Art. 64 [007] γ Cone anle, (º) ρ He Density of helium, (k/m 3 ) ρ Density of the as phase, (k/m 3 ) σ Variance, σ = σ / ( ˆ t ) (-) σ t, 1 Variance correspondin to (s tˆ1, ) σ t, p1 σ t, p REFERENCES Variance correspondin to tˆ (s ) p 1, Variance correspondin to tˆ, (s ) p 1. Bader R.; Findlay J.; Knowlton T. M. (1988). Gas/Solids Flow Patterns in a 30.5- cm-diameter Circulatin Fluidized Bed, in Circulatin Fluidized Bed Technoloy II: Proceedins of the nd International Conference on Circulatin Fluidized Beds, Basu, P. and Lare, J. F., ramon Press, Oxford, 13-137.. Kunii D. and Levenspiel O. (1991). Fluidization Enineerin, nd edition, Butterworth-Heinemann, Boston. 3. Sotudeh-Gharebaah, R. and Chaouki, J. (000). Gas mixin in a turbulent fluidized bed reactor, Canadian Journal of Chemical Enineerin, 78(1), 65-74. 4. Cao, C.-S. and Weinstein, H. (000). Gas dispersion in downflowin hih velocity fluidized beds, AIChE Journal, 46(3), 53-58. 5. Bi, X. T. (004). Gas and solid mixin in hih-density CFB risers, International Journal of Chemical Reactor Enineerin,, Article A1. 6. Bai, D.; Yi, J.; Jin, Y.; Yu, Z. (199). Residence time distributions of as and solids in a circulatin fluidized bed, in Fluidization VII: Proceedins of the Seventh Enineerin Foundation Conference on Fluidization, Enineerin Foundation, New York, 195-0. 7. Wan, Z.-G. and Wei, F. (1999). Study on as mixin in turbulent fluidized bed, Enineerin Chemistry & Metallury, 0(Supplement), 80-86. 8. Sun, S.-L.; Bao, X.-J.; Wei, W.-S. (005). Gas residence time distributions in a spouted bed, Chinese Journal of Chemical Enineerin, 13(3), 91-96. 9. Lim, C. J. and Mathur, K. B. (1974). Residence time distribution of as in spouted beds, Can. J. Chem. En., 5(Set ), 150-155. 10. Lim, C. J. and Mathur, K. B. (1976). A flow model for as movement in spouted beds, AIChE J., (4), 674-680. 11. San Jose, M. J.; Olazar, M.; nas, F. J.; Arandes, J. M.; Bilbao, J. (1995). Correlation for calculation of the as dispersion coefficient in conical spouted beds, Chem. En. Sci., 50(13), 161-17. 1. Olazar, M.; San Jose, M. J.; nas, F. J.; Auayo, A. T.; Arandes, J. M.; Bilbao, J. (1993). A model for as flow in jet spouted beds, Can. J. Chem. En., 71(), 189-194. 13. Olazar, M.; San Jose, M. J.; nas, F. J.; Auayo, A. T.; Arandes, J. M.; Bilbao, J. (1995). A simplified model for as flow in conical spouted beds, Chem. En. J. (Lausanne), 56(), 19-6. 14. Wan, Z. G.; Bi, H. T.; Lim, C. J. (006). Numerical Simulations of Hydrodynamic Behaviors in Conical Spouted Beds. China Particuoloy, 4(3-4), 194-03. 15. Levenspiel, O. (1979). The chemical reactor omnibook, Publisher: Corvallis, OR. http://dc.enconfintl.or/fluidization_xii/64 8