Particuology 9 (2011) 121–129 Contents lists available at ScienceDirect Particuology journal homepage: www.elsevier.com/locate/partic Scaling laws for gas–solid riser flow through two-fluid model simulation P.R. Naren a,b,∗ , Vivek.V. Ranade a a CREST, National Chemical Laboratory, Pune 411008, India b Chemical Engineering Department, Institute of Chemical Technology, Mumbai 400019, India article info Article history: Received 15 January 2010 Received in revised form 7 September 2010 Accepted 8 September 2010 Keywords: Risers Scaling CFD Periodic boundary Two-fluid model Error bar abstract Scale up of gas–solid circulating fluidized bed (CFB) risers poses many challenges to researchers. In this paper, CFD investigation of hydrodynamic scaling laws for gas–solid riser flow was attempted on the basis of two-fluid model simulations, in particular, the recently developed empirical scaling law of Qi, Zhu, and Huang (2008). A 3D computational model with periodic boundaries was used to perform numerical experiments and to study the effect of various system and operating parameters in hydrodynamic scaling of riser flow. The Qi scaling ratio was found to ensure similarity in global parameters like overall cross- sectional average solid holdup or pressure drop gradient. However, similarity in local flow profiles was not observed for all the test cases. The present work also highlighted the significance of error bars in reporting experimental values. © 2010 Chinese Society of Particuology and Institute of Process Engineering, Chinese Academy of Sciences. Published by Elsevier B.V. All rights reserved. 1. Introduction Successful commercialization of a process relies on the ability to scale up the process from lab to the industrial scale. For gas–solid circulating fluidized bed (CFB) reactors that are widely used in fluid catalytic cracking (FCC), combustion, etc., the scale up often depends on empirically developed scaling laws. The hydrodynam- ics of large scale industrial CFBs can be different from laboratory scale CFB systems, and the effect of reactor scale on the prevail- ing flow structure has to be properly accounted for. Otherwise, this might lead to performance deterioration and plant failure as well. For instance, an industrial scale plant for partial oxidation of n-butane to maleic anhydride was unsuccessful owing to scaling issues (Dudukovic, 2010). Therefore, development of proper scale up criteria assumes significance. Following Anderson and Jackson (1967), the two-fluid model was used to simulate the gas–solid riser flow. The scaling param- eters for the hydrodynamic similarity are derived from the dimensionless form of the conservation equations (Knowlton, Reddy Karri, & Smith, 2007; van der Meer, Thorpe, & Davidson, 1999; Xu & Gao, 2003, etc.). Evaluation of scaling laws requires extensive experimentation. However, performing experiments under extreme operating conditions and at larger scales may not be feasible at all times. In this context, computational fluid dynam- ∗ Corresponding author. Present address: UCCS, UMR CNRS 8181, Ecole Centrale de Lille, Cité Scientifique 59651, France. Tel.: +33 320335438. E-mail address: prnaren@gmail.com (P.R. Naren). ics offers the advantage by facilitating evaluation of these scaling parameters with fewer requirements of extensive physical exper- iments. Recently Qi, Zhu, and Huang (2008) proposed an empirical scal- ing parameter (Eq. (1)) based on Froude number and flow rate ratio. Froude number used in the Qi scaling ratio was defined as the ratio of the inertial forces to the gravity force with riser diameter as the characteristic dimension (Eq. (2)). The proposed scaling parame- ter ensured both local and global hydrodynamic similarity in riser reactors. The parameter was tested with data from the literature and their own experiments. Qi scaling ratio: Fr –0.3 D G s  p u g , (1) where Fr D = u 2 g gD . (2) For the same Qi scaling ratio, solid concentration, particle veloc- ity and cluster voidage exhibited similar radial profile in the fully developed flow region. The average solid holdup was shown to vary linearly with respect to the scaling ratio Fr –0.3 D G s /( p u g ). The Qi scaling ratio looks like a promising single scaling param- eter ensuring hydrodynamic similitude in riser systems at both local and global levels. Nevertheless, this empirical parameter can- not guarantee hydrodynamic scaling in risers beyond the tested range without rigorous validation. This parameter was tested with most of the data sets obtained with air as fluid medium at ambient 1674-2001/$ – see front matter © 2010 Chinese Society of Particuology and Institute of Process Engineering, Chinese Academy of Sciences. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.partic.2010.09.010