Residence Time Model

The dimensionless variance has been used extensively, perhaps excessively, to characterize mixing. For piston flow, = 0 for a CSTR, = 1. Most turbulent flow systems have dimensionless variances that lie between zero and 1, and can then be used to fit a variety of residence time models, as will be discussed in Section 15.2. The dimensionless variance is generally unsatisfactory for characterizing laminar flows where 1 is normal in liquid systems. 

The entire RTD can be made dimensionless. A normalized distribution has the residence time replaced by the dimensionless residence time, t = tjt. The first moment of anormalized distribution is 1, and all the moments are dimensionless. Normalized distributions allow flow systems to be compared in a manner that is independent of their volume and throughput. For example, all CSTRs have the same normalized RTD, W(r) = exp(—t). Similarly, allPFRs have /(t) = S(r — 1). 

This section opens the black box in order to derive residence time models for common flow systems. The box is closed again in Section 15.3 where the predictions can be based on either models or measurements. 

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I. Residence-Time Model for Total Mass Transfer with and without Chemical... 

Fig. 11. Change in concentration with the radius of the residence-time model for con-stant gas holdup and varying contact time and reaction rate [after Gal-Or and Resnick G2,G6)].

This section describes residence time models that are based on a hydrodynamic description of the process. The theory is simplified but the resulting models still have substantial utility as conceptual tools and for describing some real flow systems. 

Monosaccharides 1.8 h residence time Model river biofilm on High (59) Volk etal. (1997)... 

T. C. Thulasidas, R.L. Cerro. and M.A. Abraham, The Monolith Froth Reactor Residence Time Modelling and Analysis, Trans IChemE. 73 (part A) 3H (1995). 

Kim and White (2004) Polymerization of poly- s-caprolactone Engineering model linking residence-time-model, shear-effects model and reaction conversion during extrusion Reaction conversion and from extruder via correlating specific mechanical energy and Mw... 

The original residence time model [Reitema, 1961] was developed on the assumption that for 50% collection efficiency a particle must travel from the centre of the inlet pipe to the wall of the hydrocyclone, i.e. a distance of half of the inlet diamter, in the time that the particle is present within the hydrocyclone. The concept that only half of the uniformly suspended solids in the feed is processed giving the particle diameter at 50% collection efficiency was used in sigma analysis, see Section 8.2.2. 

Kan, K. M. and P. F. Greenfield. Residence-Time Model for Trickle-Flow Reactors Incorporating Incomplete Mixing in Stagnant Regions. AIChE Journal 29 (1983) 123. 

Jaffe, S. D. Hot Spot Simulation in Commercial Hydrogenation Processes. Ind. Eng. Process Des. Dev. 15 (1976) 410-416. Kan, K. M. and P. F, Greenfield. A Residence-Time Model for Trickle-Flow Reactors Incorporating Incomplete Mixing in Stagnant Regions. AICHE J. 29 (1) (1983) 123-132. 

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