Scaling with Constant Pressure Drop

Constant-Pressure Scaleups for Laminar Flow in a Tube 

As shown in the previous section, scaling with geometric similarity, Sr = Sl = gives constant pressure drop when the flow is laminar and remains laminar upon scaleup. This is true for both liquids and gases. The Reynolds number and the external area increase as. Piston flow is a poor assumption for laminar flow in anyfhing but small tubes. Conversion and selectivity of the reaction is likely to worsen upon scaleup unless the pilot reactor is already so large that molecular and thermal diffusion are negligible on the pilot scale. Ways to avoid unpleasant surprises are discussed in Chapter 8 

There are two equations and two unknowns. Simultaneous solution gives 

The reactor volume scales as S, and the aspect ratio of the tube decreases upon scaleup. The external surface area scales as SrSl = compared to for the case with geometric similarity. The Reynolds number also scales as 

This section considers how single tubes can be scaled up to achieve higher capacity at the same residence time and pressure drop. In marked contrast to the previous section, these scaleups are usually feasible, particularly for gas-phase reactions, although they have the common failing of losing heat transfer area relative to throughput. 

Constant-Pressure Scaleups for Laminar Flows in Tubes. As shown in the previous section, scaling with geometric similarity, Sr = SR = S1/3, gives 

Constant-Pressure Scaleups for Turbulent Flows in Tubes. Equation (3.34) gives the pressure drop ratio for large and small reactors when density is constant. Set AP2 = APi to obtain 1 = S,L75 S, S 4 75. Equation (3.31) gives the inventory relationship when density is constant. Set Stubes = 1 t° obtain S = SlSr-Simultaneous solution gives 

The same results are obtained from Equations (3.38) and (3.39), which apply to the turbulent flow of ideal gases. Thus, tube radius and length scale in the same way for turbulent liquids and gases when the pressure drop is constant. For the gas case, it is further supposed that the large and small reactors have the same discharge pressure. 

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Solution Now, Ar=107°C. Scaling with geometric similarity would force the temperature driving force to increase by S = 1.9, as before, but the scaled-up value is now 201°C. The coolant temperature would drop to —39°C, which is technically feasible but undesirable. Scaling with constant pressure forces an even lower coolant temperature. A scaleup with constant heat transfer becomes attractive. 

Increase the tube diameter, either to maintain a constant pressure drop or to scale with geometric similarity. Geometric similarity for a tube means keeping the same length-to-diameter ratio L/dt upon scaleup. Scaling with a constant pressure drop will lower the length-to-diameter ratio if the flow is turbulent. 

Determine the reactor length, diameter, Reynolds number, and scaling factor for pressure drop for the scaleup with constant heat transfer in Example 5.12. 

Pilot-scale particle collection efficiency has been found to be similar to the cold and dry experiments over 300 hours filtration time, Figure 12 presents a relatively constant pressure drop over time for the hot and dry experiments conducted on the pilot-scale filter under a gas flowrate of 20 Nm /h (80 Nm /hr/m ), with a particle load of 3000 mg/Nm and using Ottawa sand as the filtering media. Deep holes on Figure 12 are air pulses to back-flush the solids plugging the exits. 

The analysis of elution chromatography with a liquid eluent that was presented earlier was based on a constant eluent velocity, v. Unlike simple fixed-bed adsorption processes with low pressure drops, analytical-scale chromatographic techniques for a mobile gas phase employ long packed columns, where the gas undergoes a considerable pressure drop. As a result, the gas velocity changes with column location. But the gas velocity is proportional to the molar gas volume at every location. Therefore, by Boyle s law, the gas pressure P and velocity Vz at any location are related to those at the inlet (subscript, in) and outlet (subscript, out) by... 

A sample of the slurry was filtered at a constant rate of 0.00015 m3/s through a leaf filter covered with a similar filter cloth but of one-tenth the area of the full scale unit and after 625 s the pressure drop across the filter was 360 m of liquid. After a further 480 s the pressure drop was 600 m of liquid. 

C. Large-scale oxidation protocol. The large-scale oxidations reactions were carried out in a 300mL Parr autoclave equipped with an injection port, a thermocouple port, a septa sealed addition port and port connected to the volumetric measurement and gas supply module. The module consists of a forward pressure regulator and a calibrated ballast reservoir. The pressure in the reactor and in the ballast reservoir is monitored constantly and the pressure drop in the ballast reservoir is constantly converted into moles of oxygen uptake recorded vs. the time. 

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