Scaleup pressure

Chapter 2 developed a methodology for treating multiple and complex reactions in batch reactors. The methodology is now applied to piston flow reactors. Chapter 3 also generalizes the design equations for piston flow beyond the simple case of constant density and constant velocity. The key assumption of piston flow remains intact there must be complete mixing in the direction perpendicular to flow and no mixing in the direction of flow. The fluid density and reactor cross section are allowed to vary. The pressure drop in the reactor is calculated. Transpiration is briefly considered. Scaleup and scaledown techniques for tubular reactors are developed in some detail. 

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. 

This chapter assumes isothermal operation. The scaleup methods presented here treat relatively simple issues such as pressure drop and in-process inventory. The methods of this chapter are usually adequate if the heat of reaction is negligible or if the pilot unit operates adiabatically. Although included in the examples that follow, laminar flow, even isothermal laminar flow, presents special scaleup problems that are treated in more detail in Chapter 8. The problem of controlling a reaction exotherm upon scaleup is discussed in Chapter 5... 

Equation (3.31) is satisfied with Sr = Sl=. Equation (3.32) is satisfied the same way, but with the added provision that the inlet and outlet pressures are the same in the large and small units. Scaling in parallel automatically keeps the same value for t. The scaleup should be an exact duplication of the pilot plant results but at S times the flow rate. 

For a series scaleup, Sr=, so that Re increases as S. This result ignores possible changes in physical properties. The factor p/p will usually increase with pressure, so Re will increase even faster than S. 

A factor of 2 scaleup at constant t increases both u and L by a factor of 2, but the pressure drop increases by a factor of 2 - = 6.73. A factor of 100 scaleup increases the pressure drop by a factor of 316,000 The external area of the reactor, IttRL, increases as S, apace with the heat generated by the reaction. The Reynolds number also increases as S and the inside heat transfer coefficient increases by 5 (see Chapter 5). There should be no problem with heat transfer if you can tolerate the pressure drop. 

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

Table 3.1 suggests that scaling in series could make sense for an adiabatic, gas-phase reaction with no change in the number of moles upon reaction. It would also make sense when the number of moles decreases upon reaction, since the high pressures caused by this form of scaleup will favor the forward reaction. Chapter 5 gives the design equations for nonisothermal reactions and discusses the thermal aspects of scaleup. 

Solution The approach is similar to that in Example 3.7. The unknowns are Sl and (Em)2. Set (Poudi = (Pout) - Equation (3.40) is used to calculate iPm)2 nd Equation (3.41) is used to calculate Sl- Results are given in Table 3.2. The results are qualitatively similar to those for the turbulent flow of a gas, but the scaled reactors are longer and the pressure drops are lower. In both cases, the reader should recall that the ideal gas law was assumed. This may become unrealistic for higher pressures. In Table 3.2 we make the additional assumption of laminar flow in both the large and small reactors. This assumption will be violated if the scaleup factor is large. 

Geometrically Similar Scaleups for Laminar Flows in Tubes. The pressure drop for this method of scaleup is found using the integrated form of the Poiseuille equation ... 

The same result is obtained when the fluid is compressible, as may be seen by substituting Sr = Si = S into Equations (3.40) and (3.41). Thus, using geometric similarity to scale isothermal, laminar flows gives constant pressure drop provided the flow remains laminar upon scaleup. The large and small reactors will have the same inlet pressure if they are operated at the same outlet pressure. The inventory and volume both scale as S. 

In laminar flow, the pressure drop is constant when scaleup is carried out by geometric similarity. In turbulent flow, it increases as the square root of throughput. There is extra pumping energy per unit volume of throughput, which gives... 

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 = 5 /, 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... 

Constant-Pressure Scaleups for Packed Beds. A scaleup with constant pressure drop can be achieved in a packed bed just by increasing the diameter to keep a constant gas velocity m. This gives... 

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... 

Flow regime General scaleup factors Series scaleup Geometric similarity Constant pressure scaleup... 

Example 5.10 A liquid-phase, pilot-plant reactor uses a 12-ft tube with a 1.049-in i.d. The working fluid has a density of 860 kg/m, the residence time in the reactor is 10.2 s, and the Reynolds number is 8500. The pressure drop in the pilot plant has not been accurately measured, but is known to be less than 1 psi. The entering feed is preheated and premixed. The inlet temperature is 60°C and the outlet temperature is 64°C. Tempered water at 55°C is used for cooling. Management loves the product and wants you to design a plant that is a factor of 128 scaleup over the pilot plant. Propose scaleup alternatives and explore their thermal consequences. 

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. 

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. 

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. 

The pressure drop was not measured in the pilot plant in Example 5.10, but the viscosity must be known since the Reynolds number is given. Use it to calculate the pressure drop. Does your answer change the feasibility of any of the scaleups in Examples 5.10-5.13 ... 

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

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