Full Papers Investigation of the Dynamics of a High-Flux CFB Riser Using Chaos Analysis of Pressure Fluctuations By Samwel V. Manyele, Roger E. Khayat, and Jesse (J.-X.) Zhu* The dynamics of a high-flux circulating fluidized bed riser (10 m high with i.d. of 76.2 mm) were studied using a chaos analysis technique with differential pressure signals sampled at 400 Hz. Spent FCC particles (d p =67 lm) were used as the solid phase. The solids flux ranged between 50±400 kg/m 2 s while the gas velocity was varied between 4.0±10.0 m/s. Using the measured signals,thecomplexityandpredictabilityofthegas-solidsflowwerecharacterizedusingcorrelationdimensionandKolmogorov entropy. The axial profiles of the dimension and entropy revealed a more complex and less predictable gas-solids flow in the transitionsectionoftheriser.Bothdimensionandentropydecreasedwithincreasingsolidsholdupandsolidsflux.Moreover,the correlation dimension increased exponentially with decreasing average absolute deviation (AAD), at a power of 0.3. On the other hand, the entropy was observed to decrease exponentially with increasing average cycle time (ACT) of the pressure fluctuations at a characteristic power ranging between 0.95 and 1.10. Also, a comparison was made between low- and high-flux conditions based on the dynamic properties of the riser. 1 Introduction Circulating fluidized beds (CFBs) are dynamic processes due to the mixed influence of several phenomena including particle aggregation; particle-particle, particle-wall, and particle-gas interactions. As a result, measured signals of differential pressure or solids concentration exhibit complex fluctuations. However, the sampled signals contain useful information about the dynamics of gas-solids flow inside the fluidized beds. Analysis of the sampled signals of pressure fluctuations provides important dynamic information on the gas-solid flow in the fluidized beds, and hence is widely used [1±3]. The techniques used to analyze pressure fluctuation signals include statistical, spectral and chaos analyses. Both statistical and spectral analyses reflect only univariate and linear structures in the signals representing gas-solids flow. Because of the nonlinear characteristics of the pressure fluctuations, nonlinear signal analysis techniques are recom- mended, e.g., chaos analysis [4±6]. The importance of studying the dynamics of the high-flux riser is based on the fact that industrial applications, like FCC reactors, are operated at high-flux (250±1400 kg/m 2 s) and high gas velocities ranging from 4±28 m/s [7±10]. Moreover, thecorrespondingsolidsholdupinthedeveloped-flowsection of a typical FCC riser is high, ranging between 1 and 12 % [10,11],whilestudiesreportedinliteratureonthedynamicsof the CFBs were conducted in dilute risers. Furthermore, most of the literature studies on chaos analysis of pressure fluctuations in CFBs were based on low-flux operating conditions,withrelativelylowsolidsholdup,whichisprobably due to the operational limitations imposed by lower blower capacities and lower solids inventory [9,12]. Studiesonthedynamicsofhigh-fluxandhigh-densityCFBs helpinunderstandingthefundamentals,improvingthedesign of new units, and operation of existing reactors such as FCC risers. Once the dynamics are known, other applications requiring even higher solids/gas feed ratios and higher solids concentrationintheriserscanbeimplemented.Thisstudywas made possible by the proper selection of the air blower, solids feeding system, and the overall CFB geometry to avoid the instabilities resulting from insufficient pressure head from the gas blower and downcomer [9,12]. To cover the gap between studiesreportedintheliteratureandindustrialapplicationsof CFBs,theoperatingconditionsinthisstudywererangedfrom lowertohighersolidscirculationrates(G s = 50±400 kg/m 2 s) 1). For a system undergoing chaotic motion, two nearby orbits in the state-space move exponentially rapidly apart in time. This exponential rapid separation of orbits in time (called sensitivity to initial conditions) is the precise manifestation of theinstabilityalloverthephase-space,whichleadstothenon- periodicity of the sampled signals. Chaos analysis of pressure fluctuations for example, unfolds the multidimensional structureofthegas-solidsflowviatheattractorreconstruction usingtheembeddingtechnique[13].Thisanalysisconvertsthe pressure fluctuations from the time-domain into space- Chem. Eng. Technol. 25 (2002) 8, Ó WILEY-VCH Verlag GmbH & Co. KG aA, Weinheim, 2002 0930-7516/02/0808-0801 $ 17.50+.50/0 801 ± [*] S. V. Manyeley, Department of Chemical and Biochemical Engineering, University of Western Ontario, London, Ontario, Canada, N6A 5B9; R. E. Khayat, Department of Mechanical and Materials Engineering, University of Western Ontario, London, Ontario, Canada, N6A 5B9; J. (J.±X.) Zhu, (corresponding author), Department of Chemical and Biochemical Engineering, University of Western Ontario, London, Ontario, Canada, N6A 5B9 (e-mail: zhu@uwo.ca). 0930-7516/02/0808-0801 $ 17.50+.50/0 ± 1) List of symbols at the end of the paper.