Scaleup and Modeling Considerations

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 

tlain = 0.02. There is a safety concern about the premixing step. One proposal is to feed A and B separately. Component A would be fed into the base of the bed using a central tube with diameter 0.212m and component B would be fed to the annulus between the central tube and the reactor wall. The two streams would mix and react only after they had entered the bed. The concentrations of the entering components would be increased by a factor of 2, but the bed-average concentrations and Us would be unchanged. Determine the fraction unreacted that would result from the proposed modification. 

Phthalic anhydride will, in the presence of the V2O5 catalyst of Example 9.1, undergo complete oxidation with A772 = — 760kcal/mol. Suppose the complete oxidation is pseudo-first-order in phthalic anhydride concentration and that ln( k//) = 12.300—10,000/T. 

An alternative route to phthalic anhydride is the partial oxidation of naphthalene. The heat of reaction is — 430 kcal/mol. This reaction can be performed using a promoted V2O5 catalyst on silica, much like that considered in Example 9.1. Suppose In(fik) = 31.6800—19,100/T for the naphthalene oxidation reaction and that the subsequent, complete oxidation of phthalic anhydride follows the kinetics of Problem 9.3. Suppose it is desired to use the same reactor as in Example 9.1 but with a, , = 53g/ m. Determine values for and T aii that maximize the output of phthalic anhydride from naphthalene. 

Example 9.1 on the partial oxidation of o-xylene used a pseudo-first-order kinetic scheme. For this to be justified, the oxygen concentration must be approximately constant, which in turn requires low oxygen consumption and a low pressure drop. Are these assumptions reasonable for the reactor in Example 9.1 Specifically, estimate the total change in oxygen concentration given atmospheric discharge pressure and aout = 21 g/m3. Assume = 0.4. 

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 they use empirical parameters D, hr, and Kr to account for the packing and the complexity of the flow field. For laminar flow in open tubes, use the methods in Chapter 8. For highly turbulent flows in open tubes (with reasonably large L/dt ratios) use the axial dispersion model in both the isothermal and nonisothermal cases. The assumption D = E will usually be safe, but do calculate how a PFR would perform. If there is a substantial difference between the PFR model and the axial dispersion model, understand the reason. For transitional flows, it is usually conservative to use the methods of Chapter 8 to calculate yields and selectivities but to assume turbulence for pressure drop calculations. 

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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. 

At the conditions reported in this paper where the total pressure is closer to 1000 psig and the feed gas to the FDP reactor is an approximately equimolar mixture of hydrogen and methane, the total carbon conversions are closer to the fraction of carbon that instantaneously reacts and kinetic interpretation is even more difficult. Therefore the kinetic analysis is not yet complete. However for the purposes of FDP reactor simulation, a mathematical model was used that assumed all the carbon reacts at a rate dictated by Equation 1 rather than assuming a portion of this carbon reacts instantaneously. This assumption is felt to be conservative because it does not allow for the fraction of carbon that may react at a considerably faster rate than the final amount of carbon conversion which was used to evaluate the rate constant k. The temperature dependency of k used for our initial reactor simulation studies (11) has been reported (I). While the more detailed kinetic analysis may result in a modified rate equation, the results of our simulation study (11) indicate that radiant heat transfer plays a dominant role in small FDP reactors such as the one used in this study. Because the effect of radiant heat transfer from the reactor walls diminishes as the diameter of the reactor increases, temperature profiles in commercial reactors will be considerably different from those existing in our present 3-inch id FDP reactor this indicates the necessity of using larger diameter pilot plants to obtain reliable scaleup data. 

I would like to add here another, less known, example - the design of a catalytic fluid bed reactor At low flow velocities such reactors are hard to scaleup Large bubbles are formed and the exact behavior of the bed is hard to predict (28, 39) This is well illustrated by the available data In Fig 5 conversion is plotted for a first order reaction as a function of bubble size for a specific case (40). It is very sensitive to bubble size In that sense bubble models are learning models and not predictive models, inasmuch as we cannot predict bubble size that accurately At higher velocities bubbles become less distinct and gas solid contact improves considerably (, 42) The risk of scaleup decreases ... 

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