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Licensed Unlicensed Requires Authentication Published by De Gruyter September 10, 2013

Study of Phase Distribution of a Liquid-Solid Circulating Fluidized Bed Reactor Using Abductive Network Modeling Approach

Shaikh A. Razzak


This communication deals with the Abductive Network modeling approach to investigate the phase holdup distributions of a liquid–solid circulating fluidized bed (LSCFB) system. The Abductive Network model is developed/trained using experimental data collected from a pilot scale LSCFB reactor involving 500-μm size glass beads and water as solid and liquid phases, respectively. The trained Abductive Network model successfully predicted experimental phase holdups of the LSCFB riser under different operating parameters. It is observed that the model predicted cross-sectional average of solids holdups in the axial directions and radial flow structure are well agreement with the experimental values. The statistical performance indicators including the mean absolute error (~4.67%) and the correlation coefficient (0.992) also show favorable indications of the suitability of Abductive Network modeling approach in predicting the solids holdup of the LSCFB system.


The author would like to acknowledge the support provided by King Abdulaziz City for Science and Technology (KACST) through the Science & Technology Unit at King Fahd University of Petroleum & Minerals (KFUPM) for funding this work through Project No. NSTIP # 11-ENV1644-04, as part of the National Science, Technology and Innovation Plan. The author also acknowledges Dr. Mohammad Mozahar Hossain and Dr. Syed Mashiur Rahman of KFUPM, for their comments and advices.

Notation list

ArArchimedes number
Acceleration, m/s2
Drag coefficient
CPMComplexity penalty multiplier
Particle diameter, m
Dimensionless particle diameter
KTotal number of coefficients used in the model
NTotal number of training data
PSEPredicted squared error
FSEFitting squared error
Weights obtained through training the network
Radial position, m
Radius of the riser, m
Reynolds number at terminal settling velocity
Time, s
Superficial liquid velocity, cm/s
Superficial solids velocity, cm/s
Auxiliary liquid velocity, cm/s
Terminal settling velocity, cm/s
Normalizing liquid velocity
Net superficial liquid velocity, cm/s
Dimensionless terminal settling velocity, cm/s
Velocity, m/s
Riser height, m

Greek letters

Density, kg/m3
Estimated true unknown model error variance
Viscosity, cP
Time lag, s


gGas phase
lLiquid phase
sSolid phase
bedFluidized bed


1. AttaA, RazzakSA, NigamKD, ZhuJ-X. (Gas)-liquid-solid circulating fluidized ed reactors: characteristics and applications. Ind Eng Chem Res2009;48:787692.10.1021/ie900163tSearch in Google Scholar

2. ZhengY, ZhuJ-X. Radial flow structure in a liquid-solid circulating fluidized bed. Chem Eng J2002;88:14150.10.1016/S1385-8947(01)00294-7Search in Google Scholar

3. RazzakSA, BarghiS, ZhuJ-X. Application of electrical resistance tomography on liquid–solid two-phase flow characterization in an LSCFB riser. Chem Eng Sci2009;64:28518.10.1016/j.ces.2009.02.049Search in Google Scholar

4. CuiY, NakhlaG, ZhuJ-X, PatelA. Simultaneous carbon and nitrogen removal in anoxic-aerobic circulating fluidized bed biological reactor (CFBBR). Environ Technol2004;25:699712.10.1080/09593330.2004.9619360Search in Google Scholar

5. LanQ, BassiA, ZhuJ-X, MargaritisA. Continuous protein recovery from whey using liquid-solid circulating fluidized bed ion-exchange extraction. Biotechnol Bioeng2002;78:15763.10.1002/bit.10171Search in Google Scholar

6. PatelA, ZhuJ-X, NakhlaG. Simultaneous carbon, nitrogen and phosphorus removal from municipal wastewater in a circulating fluidized bed bioreactor. Chemosphere2006;65:110312.10.1016/j.chemosphere.2006.04.047Search in Google Scholar

7. RazzakSA, RahmanSM, HossainMM, ZhuJ-X. Investigation of artificial neural network methodology for modeling of a liquid-solid circulating fluidized bed riser. Powder Technol2012;229:717.10.1016/j.powtec.2012.06.010Search in Google Scholar

8. RazzakSA. Hydrodynamics modeling of an LSCFB riser using ANFIS methodology: effects of particle shape and size. Chem Eng J2012;195:4961.10.1016/j.cej.2012.04.077Search in Google Scholar

9. LahiriSK, GhantaKC. Development of an artificial neural network correlation for prediction of hold-up of slurry transport in pipelines. Chem Eng Sci2008;63:1497509.10.1016/j.ces.2007.11.030Search in Google Scholar

10. NakajimaY, KikuchiR, TsutsumiA, OtawaraK. Nonlinear modeling of chaotic dynamics in a circulating fluidized bed by an artificial neural network. J Chem Eng Japan2001;34:10713.10.1252/jcej.34.107Search in Google Scholar

11. OtawaraK, FanLT, TsutsumiA, YashidaK. An artificial neural network as a model for chaotic behavior of a three-phase fluidized bed. Chaos Solutions Fractals2002;13:35362.10.1016/S0960-0779(00)00250-2Search in Google Scholar

12. HaykinS. Neural networks: a comprehensive foundation. New Jersey: Prentice-Hall, 1994.Search in Google Scholar

13. MusaviMT, ChanKH, KalantriK. On the generalization ability of neural network classifiers. IEEE Trans Pattern Anal Machine Intel1994;16:65963.10.1109/34.295911Search in Google Scholar

14. RahmanSM, KhondakerAN, Abdul-AalR. Self-organizing ozone model for Empty Quarter of Saudi Arabia: group method data handling based modeling approach. Atmos Environ2012;59:398407.10.1016/j.atmosenv.2012.05.008Search in Google Scholar

15. RahmanSM, RatroutN. Time series prediction of intersection traffic flow using group method of data handling (GMDH) based abductive network. In: First Saudi Graduate Student Conference Proceeding, March 1–4, Riyadh, Saudi Arabia, 2010.Search in Google Scholar

16. Abdel-AalRE. Hourly temperature forecasting using abductive networks. Eng Appl Artif Intel2004;17:54356.10.1016/j.engappai.2004.04.002Search in Google Scholar

17. Abdel-AalRE. Short-term hourly load forecasting using abductive networks. IEEE Trans Power Syst2004;19:16473.10.1109/TPWRS.2003.820695Search in Google Scholar

18. MohandesMA, RehmanS, RahmanSM. Spatial estimation of wind speed. Int J Energy Res2011;36:54552.10.1002/er.1774Search in Google Scholar

19. PeirceC. Abduction and induction. In: BucklerJ, editor. Philosophical writings of peirce. New York: Dover, 1955.Search in Google Scholar

20. BuckDS, NelsonDE. Applying the Abductory Induction Mechanism (AIM) to the extrapolation of chaotic time series. Aerospace and Electronics Conf., NAECO., In: Proceedings of the IEEE, Dayton, OH, 1992:91015.Search in Google Scholar

21. MontgomeryGJ, DrakeKC. Abductive reasoning networks. Neurocomputing1991;2:97104.10.1016/0925-2312(91)90055-GSearch in Google Scholar

22. BarronA. Predicted squared error: a criterion for automatic model selection. In: FarlowSJ, editor. Self-organization methods in modeling: GMDH type algorithms. New York: Marcel-Dekker, 1984:8793.Search in Google Scholar

23. Abdel-AalRE, ElhadidyMA, ShaahidSM. Modeling and forecasting the mean hourly wind speed time series using GMDH-based Abductive Networks. Renew Energy2009;34:16869.10.1016/j.renene.2009.01.001Search in Google Scholar

24. CliftR, GraceJR, WeberME. Bubbles, drops, and particles. New York: Academic Press, 1978.Search in Google Scholar

25. LiangW-G, LiangG, ZhangSL, ZhuJ-X, JinY, YuZQ, et al. Flow characteristics of the liquid-solid circulating fluidized bed. Powder Technol1997;90:95102.10.1016/S0032-5910(96)03198-1Search in Google Scholar

Published Online: 2013-09-10

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