Scaleup models

Possible explanations for this shortcoming are faulty equilibrium data (relative volatility different from design), nse of an improper stage model, wrong material balance (e.g., trace impurities), an erroneous scaleup model, or column internals being less efficient than anticipated. 

A variety of scaleup models for trickle beds are presented in the literature. All the models assume that even distribution of the fluid over the entire top catalyst bed surface will be achieved with the proper design of inlet distributor hardware. 

Partial Wetting/Mass Transfer/Catalyst Effectiveness Scaleup Model... 

For interpolation models it is important that the space of X is well covered. For design and scaleup models this is im-... 

Correlations of nucleation rates with crystallizer variables have been developed for a variety of systems. Although the correlations are empirical, a mechanistic hypothesis regarding nucleation can be helpful in selecting operating variables for inclusion in the model. Two examples are (/) the effect of slurry circulation rate on nucleation has been used to develop a correlation for nucleation rate based on the tip speed of the impeller (16) and (2) the scaleup of nucleation kinetics for sodium chloride crystalliza tion provided an analysis of the role of mixing and mixer characteristics in contact nucleation (17). Pubhshed kinetic correlations have been reviewed through about 1979 (18). In a later section on population balances, simple power-law expressions are used to correlate nucleation rate data and describe the effect of nucleation on crystal size distribution. 

Another way to examine scaleup of hydrodynamics is to build a cold or hot scale model of the commercial design. Validated scaling criteria have been developed and are particularly effec tive for group B and D materials [Gheksmau, Hyre and Woloshuu, Powder Tech., 177-199 (1993)]. 

This section has based scaleups on pressure drops and temperature driving forces. Any consideration of mixing, and particularly the closeness of approach to piston flow, has been ignored. Scaleup factors for the extent of mixing in a tubular reactor are discussed in Chapters 8 and 9. If the flow is turbulent and if the Reynolds number increases upon scaleup (as is normal), and if the length-to-diameter ratio does not decrease upon scaleup, then the reactor will approach piston flow more closely upon scaleup. Substantiation for this statement can be found by applying the axial dispersion model discussed in Section 9.3. All the scaleups discussed in Examples 5.10-5.13 should be reasonable from a mixing viewpoint since the scaled-up reactors will approach piston flow more closely. 

Chapter 3 introduced the basic concepts of scaleup for tubular reactors. The theory developed in this chapter allows scaleup of laminar flow reactors on a more substantive basis. Model-based scaleup supposes that the reactor is reasonably well understood at the pilot scale and that a model of the proposed plant-scale reactor predicts performance that is acceptable, although possibly worse than that achieved in the pilot reactor. So be it. If you trust the model, go for it. The alternative is blind scaleup, where the pilot reactor produces good product and where the scaleup is based on general principles and high hopes. There are situations where blind scaleup is the best choice based on business considerations but given your druthers, go for model-based scaleup. 

Consider the scaleup of a small, tubular reactor in which diffusion of both mass and heat is important. As a practical matter, the same fluid, the same inlet temperature, and the same mean residence time will be used in the small and large reactors. Substitute fluids and cold-flow models are sometimes used to study the fluid mechanics of a reactor, but not the kinetics of the reaction. 

The temperature counterpart of Q>aVR ccj-F/R and if ccj-F/R is low enough, then the reactor will be adiabatic. Since aj 3>a, the situation of an adiabatic, laminar flow reactor is rare. Should it occur, then T i, will be the same in the small and large reactors, and blind scaleup is possible. More commonly, ari/R wiU be so large that radial diffusion of heat will be significant in the small reactor. The extent of radial diffusion will lessen upon scaleup, leading to the possibility of thermal runaway. If model-based scaleup predicts a reasonable outcome, go for it. Otherwise, consider scaling in series or parallel. 

Previous chapters have discussed how isothermal or adiabatic reactors can be scaled up. Nonisothermal reactors are more difficult. They can be scaled by maintaining the same tube diameter or by the modeling approach. The challenge is to increase tube diameter upon scaleup. This is rarely possible and when it is possible, scaleup must be based on the modeling approach. If the predictions are satisfactory, and if you have confidence in the model, proceed with scaleup. 

What models should be used, either for scaleup or to correlate pilot-plant data Section 9.1 gives the preferred models for nonisothermal reactions in packed beds. These models have a reasonable experimental basis even though... 

When two or more phases are present, it is rarely possible to design a reactor on a strictly first-principles basis. Rather than starting with the mass, energy, and momentum transport equations, as was done for the laminar flow systems in Chapter 8, we tend to use simplified flow models with empirical correlations for mass transfer coefficients and interfacial areas. The approach is conceptually similar to that used for friction factors and heat transfer coefficients in turbulent flow systems. It usually provides an adequate basis for design and scaleup, although extra care must be taken that the correlations are appropriate. 

Himmelblau, D.M. (1985) Mathematical Modelling. In Bisio, E. and Kabel, R. L. (Eds.) Scaleup of Chemical Processes, Wiley. 

Testing includes screening (e.g., literature research, mixing calorimetiy, thermodynamic calculations, estimation of heats of reaction, DSC, flash point calculations), quantitative assessment (e g., accelerated rate calorimetry, specialized calorimetry), and scaleup (vent size packaging [VSP], modeling, reaction calorimetry). 

The sizing of pipelines for non-Newtonian liquids may be based on scaleup of tests made under the conditions at which the proposed line is to operate, without prior determination and correlation of rheological properties. A body of theory and some correlations are available for design with four mathematical models ... 

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