Scaleup ratio

Section 1.5 described one basic problem of scaling batch reactors namely, it is impossible to maintain a constant mixing time if the scaleup ratio is large. However, this is a problem for fed-batch reactors and does not pose a limitation if the reactants are premixed. A single-phase, isothermal (or adiabatic) reaction in batch can be scaled indefinitely if the reactants are premixed and preheated before being charged. The restriction to single-phase systems avoids mass... 

The existing information is available mainly on the laboratory scale, which would give very large scaleup ratios and hence lack confidence and certainty. 

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. 

Series Scaleup of Laminar Liquid Flows. The pressure drop is given by Equation (3.14). Taking ratios gives... 

Const ant-Pres sure 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 = Equation (3.31) gives the inventory... 

The reactor volume scales as S, and the aspect ratio of the tube decreases upon scaleup. The external surface area scales as SrSr = compared... 

An integral form of Equation (3.15) was used to derive the pressure ratio for scaleup in series of a turbulent liquid-phase reactor, Equation (3.34). The integration apparently requires ji to be constant. Consider the case where ii varies down the length of the reactor. Define an average viscosity... 

A volumetric scaleup by a factor of 512 is quite large, and the question arises as to whether the large vessel wiU behave as a CSTR. The concern is due to the factor of 4 increase in mixing time. Does it remain true that tmix h/i and tmix t If so, the assumption that the large vessel wiU behave as a CSTR is probably justified. The ratio of internal circulation to net throughput—which is the internal recycle ratio—scales as the inverse of the mixing time and will thus decrease by a factor of 4. The decrease may appear worrisome, but if the increase in mixing time can be tolerated, then it is likely that the decrease in internal recycle ratio is also acceptable. 

Applying these factors to the 5= 128 scaleup in Example 5.10 gives a tube that is nominally 125 = 101 ft long and 1.0495 = 4.1 inches in diameter. The length-to-diameter ratio increases to 298. The Reynolds number increases to 85005 = 278,000. The pressure drop would increase by a factor of 0.86 j jjg temperature driving force would remain constant at 7°C so that the jacket temperature would remain 55°C. 

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. 

Solution Ideally, the scaleup will maintain the same inlet concentrations for the two phases, the same relative flow rates and holdups for the two phases, and the same ratio of gas transferred to liquid throughput. It is also necessary to maintain a constant residence time in the liquid phase. It is simple to set the flow rates ... 

The reactor volume scales as S, and the aspect ratio of the tube decreases upon scaleup. The external surface area scales as SrSl = >S, 6 /27 compared with A2/3 for the case with geometric similarity. The Reynolds number also scales as S16/27. It increases upon scaleup in both cases, but less rapidly when the pressure drop is held constant than for geometric similarity. 

When the impeller tip speed is held constant, the same maximum shear rate is maintained. However, the average impeller shear rate related to impeller speed drops dramatically, and the power per unit volume drops inversely to the tank size ratio. In general, this is a very unconservative scaleup technique and can lead to insufficient process results on full scale. 

It is characteristic that this ratio F increases on scaleup, since if we maintain equal volumes of gas per volume of liquid per time on scaleup, which is necessary to provide the same stoichiometric percentage of gas absorbed from the gas phase, then the linear velocity increases directly proportional to the depth of the large tank. 

The objective of this phase was to determine whether the decreased surface-to-volume ratio in an industrial unit would reduce the partial pyrolysis of the fuel and result in lower PNA emissions than observed from the smaller laboratory boiler. A test of PNA emissions was, therefore, conducted at the Exxon U.S.A. terminal in Charleston, South Carolina. The boiler available at this site was a Cleaver Brooks Model DL-68 water tube unit rated at a maximum capacity of 50,000 lb/hr. of steam at 185 psig. This is roughly equivalent to 1425 hp, or a scaleup of approximately 30 from the laboratory boilers. The conventional fuel used in this unit was RSFO with a maximum feed rate of 24.6 > /min. or 22.7 kg/min. The boiler was installed in August, 1978, and is used to raise steam for the terminal operations with heavy fuel oil products. 

The HPLC separation previously made using 0.3-in. ID diameter columns was scaled up to 0.9-in. ID columns. The scaleup was straightforward and permitted 1.0 g to be injected on the 24 ft of 0.9-in. ID columns. The amount of sample injected was increased by the ratio of the cross-sectional areas of the two column systems. The flow rate was increased by the ratio of the cross-sectional areas of the 0.3- to 0.9-in. ID columns to 30 mL/min. The linear velocity and hence the separation time remained essentially the same. 

Note that the ratio of liquid level to tank diameter on the pilot scale is 16.4/18.0 or 0.91, whereas the ratio for the large-scale vessel is 166/120 or 1.38. For geometric similarity, all such length ratios should instead be equal. Since the ratios are not equal in this case, it is necessary to use nongeometric scaleup. 

These results are consistent with a scaleup from the pilot-scale operation. Although power per volume is reduced and impeller to tank diameter ratio is increased, torque per volume is about half and tip speed is the same. With any realistic scaleup, some factors unavoidably must change, while the important ones are held constant. In a different situation and process, a different variable, such as power per volume, might be held constant. Other variables, such as blend time, could be calculated, at each step in the scaleup. 

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