Thermal effects can be the key concern in reactor scaleup. The generation of heat is proportional to the volume of the reactor. Note the factor of V in Equation (5.32). For a scaleup that maintains geometric similarity, the surface area increases only as V2=3: Sooner or later, temperature can no longer be controlled,
Heat
generated
or
removed
Outlet temperature
and the reactor will approach adiabatic operation. There are relatively few reactions where the full adiabatic temperature change can be tolerated. Endothermic reactions will have poor yields. Exothermic reactions will have thermal runaways giving undesired by-products. It is the reactor designer’s job to avoid limitations of scale or at least to understand them so that a desired product will result. There are many options. The best process and the best equip- ment at the laboratory scale are rarely the best for scaleup. Put another way, a process that is less than perfect at a small scale may be the best for scaleup, precisely because it is scalable.
5.3.1 Avoiding Scaleup Problems
Scaleup problems are sometimes avoidable. A few simple possibilities are: 1. Use enough diluents so that the adiabatic temperature change is acceptable. 2. Scale in parallel; e.g., shell-and-tube designs.
3. Depart from geometric similarity so that V and Aextboth increase in direct proportion to the throughput scaling factor S. Scaling a tubular reactor by adding length is a possibility for an incompressible fluid.
4. Use temperature-control techniques that inherently scale as S; e.g., cold feed to a CSTR, or autorefrigeration.
5. Intentionally degrade the performance of the small unit so that the same performance and product quality can be achieved upon scaleup.
Use Diluents. In a gas system, inerts such as nitrogen, carbon dioxide, or steam can be used to mitigate the reaction exotherm. In a liquid system, a solvent can be used. Another possibility is to introduce a second liquid phase that has the function of absorbing and transferring heat; i.e., water in an emulsion or suspen- sion polymerization. Adding an extraneous material will increase cost, but the increase may be acceptable if it allows scaleup. Solvents have a deservedly bad name in open, unconfined applications; but these applications are largely eliminated. In a closed environment, solvent losses are small and the cost of con- fining the solvent is often borne by the necessary cost of confining the reactants.
Scale in Parallel. This common scaling technique was discussed in Section 3.2.1. Subject to possible tube-to-tube distribution problems, it is an inexpensive way of gaining capacity in what is otherwise a single-train plant.
Depart from Geometric Similarity. Adding length to a tubular reactor while keeping the diameter constant allows both volume and external area to scale as S if the liquid is incompressible. Scaling in this manner gives poor results for gas-phase reactions. The quantitative aspects of such scaleups are discussed
in Section 5.3.3. Another possibility is to add stirred tanks, or, indeed, any type of reactor in series. Two reactors in series give twice the volume, have twice the external surface area, and give a closer approach to piston flow than a single, geometrically similar reactor that has twice the volume but only 1.59 times the surface area of the smaller reactor. Designs with several reactors in series are quite common. Multiple pumps are sometimes used to avoid high pressures. The apparent cost disadvantage of using many small reactors rather than one large one can be partially offset by standardizing the design of the small reactors.
If a single, large CSTR is desired, internal heating coils or an external, pump- around loop can be added. This is another way of departing from geometric similarity and is discussed in Section 5.3.2.
Use Scalable Heat Transfer. The feed flow rate scales as S and a cold feed stream removes heat from the reaction in direct proportion to the flow rate. If the energy needed to heat the feed from Tin to Tout can absorb the reaction exotherm, the heat balance for the reactor can be scaled indefinitely. Cooling costs may be an issue, but there are large-volume industrial processes that have Tin 408C and Tout 2008C: Obviously, cold feed to a PFR will not work since the reaction will not start at low temperatures. Injection of cold reac- tants at intermediate points along the reactor is a possibility. In the limiting case of many injections, this will degrade reactor performance toward that of a CSTR. See Section 3.3 on transpired-wall reactors.
Autorefrigeration or boiling is another example of heat transfer that scales as S.The chemist calls it refluxing and routinely uses it as a method of temperature control. Laboratory glassware is usually operated at atmospheric pressure so the temperature is set by the normal boiling point of the reactants. Chemists some- times choose solvents that have a desired boiling point. Process equipment can operate at a regulated pressure so the boiling point can be adjusted. On the basis of boiling point, toluene at about 0.4 atm can replace benzene. The elevation of boiling point with pressure does impose a scaleup limitation. A tall reactor will have a temperature difference between top and bottom due to the liquid head.
Use Diplomatic Scaleup. This possibility is called diplomatic scaleup because it may require careful negotiations to implement. The idea is that thermal effects are likely to change the distribution of by-products or the product properties upon scaleup. The economics of the scaled process may be perfectly good and the product may be completely satisfactory, but it will be different than what the chemist could achieve in glassware. Setting appropriate and scalable expec- tations for product properties can avoid surprises and the cost of requalifying the good but somewhat different product that is made in the larger reactor. Diplomacy may be needed to convince the chemist to change the glassware to lower its performance with respect to heat transfer. A recycle loop reactor is one way of doing this in a controlled fashion.
5.3.2 Scaling Up Stirred Tanks
This section is concerned with the UAextðT TextÞ term in the energy balance for a stirred tank. The usual and simplest case is heat transfer from a jacket. Then Aext refers to the inside surface area of the tank that is jacketed on the outside and in contact with the fluid on the inside. The temperature difference, T– Text, is between the bulk fluid in the tank and the heat transfer medium in the jacket. The overall heat transfer coefficient includes the usual contributions from wall resistance and jacket-side coefficient, but the inside coefficient is normally limiting. A correlation applicable to turbine, paddle, and propeller agitators is Nu ¼hDI ¼ Ch D2INI 2=3 wall 0:14 ð5:34Þ whereNu is the Nusselt number and is the thermal conductivity. The value for Chis needed for detailed design calculations but factors out in a scaling analysis; Ch 0:5 for turbines and propellers. For a scaleup that maintains constant fluid properties, ðhDIÞlarge ðhDIÞsmall ¼ ðD2INIÞlarge ðD2 INIÞsmall " #2=3
Assuming geometric similarity and recalling that DIscales as S1/3gives
hlarge hsmall¼ ðDIN2IÞlarge ðDINI2Þsmall " #1=3 ¼ S1=9N2=3
For a scaleup with constant power per unit volume, Example 4.7 showed that NI must scale as D2=3I : Thus,
hlarge hsmall ¼ ðDIÞlarge ðDIÞsmall 1=9 ¼ S1=27
and h decreases slightly upon scaleup. Assuming h controls the overall coefficient,
ðUAextÞlarge ðUAextÞsmall
¼ S1=27D2 I ¼ S
17=27
If we want UAextðT TextÞ to scale as S, the driving force for heat transfer must be increased:
ðT TextÞlarge ðT TextÞsmall
These results are summarized in the last four rows of Table 4.1. Scaling the volume by a factor of 512 causes a large loss in hAext per unit volume. An increase in the temperature driving force (e.g., by reducing Text) by a factor of 10 could compensate, but such a large increase is unlikely to be possible. Also, with cooling at the walls, the viscosity correction term in Equation (5.34) will become important and will decrease hAextstill more.
This analysis has been carried out for a batch reactor, but it applies equally well to a CSTR. The heat transfer coefficient is the same because the agitator dominates the flow inside the vessel, with little contribution from the net throughput. The analysis also applies to heat transfer using internal coils or baffles. The equations for the heat transfer coefficients are similar in form to Equation (5.34). Experimental results for the exponent on the impeller Reynolds number vary from 0.62 to 0.67 and are thus close to the semitheore- tical value of 2/3 used in Equation (5.34). The results in Table 4.1 are generally restricted to turbulent flow. The heat transfer coefficient in laminar flow systems scales with impeller Reynolds number to the 0.5 power. This causes an even greater loss in heat transfer capability upon scaleup than in a turbulent system, although a transition to turbulence will occur if S is large enough. Close-clearance impellers such as anchors and helical ribbons are frequently used in laminar systems. So are pitched-blade turbines with large ratios of the impeller to tank diameter. This improves the absolute values for h but has a minor effect on the scaling relationships. Several correlations forNu in laminar flow show a dependence onRe to the 0.5 power rather than the 0.67 power.
It is sometimes proposed to increase Aextby adding internal coils or increas- ing the number of coils upon scaleup. This is a departure from geometric simi- larity that will alter flow within the vessel and reduce the heat transfer coefficient for the jacket. It can be done within reason; but to be safe, the coil design should be tested on the small scale using dummy coils or by keeping a low value for TText. A better approach to maintaining good heat transfer upon scaleup is to use a heat exchanger in an external loop as shown in Figure 5.8. The illu- strated case is for a CSTR, but the concept can also be used for a batch reactor. The per-pass residence time in the loop should be small compared to the resi- dence time in the reactor as a whole. A rule-of-thumb for a CSTR is
ttloop¼
Volume of loop
Flow rate through loop< tt=10 ð5:35Þ Reaction occurs in the loop as well as in the stirred tank, and it is possible to eliminate the stirred tank so that the reactor volume consists of the heat exchan- ger and piping. This approach is used for very large reactors. In the limiting case where the loop becomes the CSTR without a separate agitated vessel, Equation (5.35) becomes q=Q > 10. This is similar to the rule-of-thumb discussed in Section 4.5.3 that a recycle loop reactor approximates a CSTR. The reader may wonder why the rule-of-thumb proposed a minimum recycle ratio of 8 in Chapter 4 but 10 here. Thumbs vary in size. More conservative designers have
proposed a minimum recycle ratio of 16, and designs with recycle ratios above 100 are known. The real issue is how much conversion per pass can be tolerated in the more-or-less piston flow environment of the heat exchanger. The same issue arises in the stirred tank reactor itself since the internal pumping rate is finite and intense mixing occurs only in the region of the impeller. In a loop reac- tor, the recirculation pump acts as the impeller and provides a local zone of intense mixing.
Example 5.9: This is a consultant’s war story. A company had a brand- name product for which they purchased a polymer additive. They decided to create their own proprietary additive, and assigned the task to a synthetic chemist who soon created a fine polymer in a 300-ml flask. Scaleup was assigned to engineers who translated the chemistry to a 10-gal steel reactor. The resulting polymer was almost as good as what the chemist had made. Enough polymer was made in the 10-gal reactor for expensive qualification trials. The trials were a success. Management was happy and told the engi- neers to design a 1000-gal vessel.
Now the story turns bad. The engineers were not rash enough to attempt a direct scaleup with S¼ 100, but first went to a 100-gal vessel for a test with S¼ 10. There they noted a significant exotherm and found that the poly- mer had a broader molecular-weight distribution than achieved on the small scale. The product was probably acceptable but was different from what had
← CSTR q Qout Qin Shell-and- tube heat exchanger
been so carefully tested. Looking back at the data from the 10-gal runs, yes there was a small exotherm but it had seemed insignificant. Looking ahead to a 1000-gal reactor and (finally) doing the necessary calculations, the exotherm would clearly become intolerable. A mixing problem had also emerged. One ingredient in the fed-batch recipe was reacting with itself rather than with the target molecule. Still, the engineers had designed a 2000-gal reactor that might have handled the heat load. The reactor volume was 2000 gal rather than 1000 gal to accommodate the great mass of cooling coils. Obviously, these coils would significantly change the flow in the vessel so that the standard correlation for heat transfer to internal coils could not be trusted. What to do?
Solution: There were several possibilities, but the easiest to design and implement with confidence was a shell-and-tube heat exchanger in an external loop. Switching the feed point for the troublesome ingredient to the loop also allowed its rapid and controlled dilution even though the overall mixing time in the vessel was not significantly changed by the loop.
There is one significant difference between batch and continuous-flow stirred tanks. The heat balance for a CSTR depends on the inlet temperature, and Tin can be adjusted to achieve a desired steady state. As discussed in Section 5.3.1, this can eliminate scaleup problems.
5.3.3 Scaling Up Tubular Reactors
Convective heat transfer to fluid inside circular tubes depends on three dimen- sionless groups: the Reynolds number, Re ¼ dtuu=, the Prandtl number, Pr ¼ CP= where is the thermal conductivity, and the length-to-diameter ratio, L=D. These groups can be combined into the Graetz number, Gz ¼ RePrdt=L. The most commonly used correlations for the inside heat transfer coefficient are
hdt= ¼ 3:66 þ 0:085Gz 1þ 0:047Gz2=3 bulk wall 0:14 ðDeep laminarÞ ð5:36Þ for laminar flow andGz < 75,
hdt= ¼ 1:86Gz1=3 bulk wall 0:14
ðLaminarÞ ð5:37Þ
for laminar flow andGz > 75 and hdt= ¼ 0:023Re0:8Pr1=3
bulk wall 0:14
forRe > 10,000, 0.7 < Pr < 700 and L/dt> 60. These equations apply to ordin- ary fluids (not liquid metals) and ignore radiative transfer. Equation (5.36) is rarely used. It applies to very lowRe or very long tubes. No correlation is avail- able for the transition region, but Equation (5.37) should provide a lower limit onNu in the transition region.
Approximate scaling behavior for incompressible fluids based on Equations (5.36)–(5.38) is given in Table 5.1. Scaling in parallel is not shown since all scaling factors would be 1. Scaleups with constant pressure drop give the same results for gases as for liquids. Scaleups with geometric similarity also give the same results if the flow is laminar. Other forms of gas-phase scaleup are rarely possible if significant amounts of heat must be transferred to or from the reactants. The reader is reminded of the usual caveat: detailed calcula- tions are needed to confirm any design. The scaling exponents are used for
TABLE 5.1 Scaleup Factors for Liquid-Phase Tubular Reactors.
Flow regime General scaleup factors Series scaleup Geometric similarity Constant pressure scaleup Deep laminar
Diameter scaling factor SR 1 S1=3 S1=3
Length scaling factor SL S S1=3 S1=3
Length-to-diameter ratio SLS1R S 1 1
Pressure scaling factor,P SSR4SL S 2
1 1
Heat transfer area, Aext SRSL S S2=3 S2=3
Inside coefficient, h S1R 1 S1=3 S1=3
Coefficient times area, hAext SL S S1=3 S1=3
Driving force,T SSL1 1 S2=3 S2=3
Laminar
Diameter scaling factor SR 1 S1=3 S1=3
Length scaling factor SL S S1=3 S1=3
Length-to-diameter ratio SLS1R S 1 1
Pressure scaling factor,P SSR4SL S 2
1 1
Heat transfer area, Aext SRSL S S2=3 S2=3
Inside coefficient, h S1=3S1RS1=2L 1 S1=9 S1=9 Coefficient times area, hAext S1=3S2=3L S S5=9 S5=9
Driving force,T S2=3S2=3L 1 S4=9 S4=9
Fully turbulent
Diameter scaling factor SR 1 S1=3 S11=27
Length scaling factor SL S S1=3 S5=27
Length-to-diameter ratio SLS1R S 1 S2=9
Pressure scaling factor,P S1:75SR4:75SL S2:75 S1=2 1
Heat transfer area, Aext SRSL S S2=3 S0:59
Inside coefficient, h S0:8S1:8R S0:8 S0:2 S0:07 Coefficient times area, hAext S0:8S0:8R SL S1:8 S0:87 S0:66 Driving force,T S0:2S0:8R S1L S0:8 S0:13 S0:34
conceptual studies and to focus attention on the most promising options for scaleup. Recall also that these scaleups maintain a constant value for Tout. The scaleup factors for the driving force, T, maintain a constant Toutand a constant rate of heat transfer per unit volume of fluid.
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/m3, 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 60C and the outlet temperature is 64C. Tempered water at 55C 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 alterna- tives and explore their thermal consequences.
Solution: Table 5.1 provides the scaling relationships. The desired throughput and volume scaling factor is S¼ 128:
Some alternatives for the large plant are as follows:
Parallel—put 128 identical tubes in parallel using a shell-and-tube design. The total length of tubes will be 1536 ft, but they are compactly packaged. All operating conditions are identical on a per-tube basis to those used in the pilot plant.
Series—build a reactor that is 1536 ft long. Use U-bends or coiling to make a
reasonable package. The length-to-diameter ratio increases to 137S¼ 17,600. The
Reynolds number increases to 8500S¼ 1:1 106, and the pressure drop will be
S2:75¼ 623,000 times greater than it was in the pilot plant. The temperature driv-
ing force changes by a factor of S0:8¼ 0:021 from 7C to 0.14C. The produc-
tion unit would have to restrict the water flow rate to hold this low a T:
Note that we used Equation (5.38) to scale the heat transfer coefficient even though the pilot plant was in the transitional region. Also, the driving force for
turbulent flow should be based on the log-mean T. The difference is minor,
and approximations can be justified in a scaling study. When a reasonable scaleup is found, more accurate estimates can be made. The current calculations are accu- rate enough to show that a series scaleup is unreasonable.
Geometric similarity—build a reactor that is nominally 12S1=3¼ 61 ft long and
1:049S1=3¼ 5:3 inches in diameter. Use U-bends to give a reasonable footprint.
Correct to a standard pipe size in the detailed design phase. The length-to-dia- meter ratio is unchanged in a geometrically similar scaleup. The Reynolds
number increases to 8500S2=3¼ 216,000 and the pressure drop increases by
factor of S1=2¼ 11:2: The temperature driving force will increase by a factor of
S0:13¼ 1:9 to about 13C so that the jacket temperature would be about 49C.
This design seems reasonable.
Constant pressure—build a reactor that is nominally 12S5=27¼ 29 ft long and
1:049S11=27¼ 7:6 in in diameter. The length-to-diameter ratio decreases by a