Scale-Up for Heat Transfer

In Section 5.3.3, heat transfer was analyzed in a Newtonian fluid between two plates, 

It can be assumed that the thermal diffusivity (a) is constant. Considering that v = TtDN and the L/D ratio is usually constant, Eq. 8.182 can be written as  

If it can be assumed that the viscosity r, the thermal conductivity k, and the imposed temperature difference AT are constant, Eq. 8.184 becomes  

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Common scale-up Scale-up for heat transfer Scale-up for mixing... 

Steel, C. B. and P. F. Nolan, "Scale-up and Heat Transfer Data for Safe Reactor Operation" in Proceedings of the International Symposium on Runaway Reactions, p. 597, Center for Chemical Process Safety/AIChE, New York, NY (1989). 

Sample calculations in reports, 462 Saran, 437, 440-442 Sawing for equipment fabrication, 447 Scale formation in evaporators, 355-360 Scaling for equipment cost estimation, 169-171 Scaling factors for heat transfer, 586-587 Scale-up for equipment specifications, 36-39 Schedule number for pipe, 493 Screen, cost of 567 Self insurance, 264-265 Sensitivity of results for pipe sizing, 367-368 Separators, cost of 559-561 Sequential analysis, 771-772 Series compound-amount factor, 227... 

Steel, C.H. et al. 1989, Scale-up and heat transfer data for safe reactor operation, Int Symp on Runaway Reactions, 597-632 (CCPS. AIChE. USA). 

Similarly, oxidation reactions are also highly exothermic. If the reaction selectivity is affected by temperature, temperature control must be given due importance. Most gas-dispersed multiphase reactors yield fairly high heat transfer coefficients ( 400W/ m °C). However, as the reactor is scaled up, the heat transfer area may not be sufficient and additional heat transfer area must be provided. As an example, heat transfer area per unit volume for kettle-type reactors is given by (jacket heat transfer area/volume) = (4 X or (4/7). Most large stirred reactors face this problem... 

The difficulties and the risk of scaling up the heat-transfer coefficient from a small to a large reactor increase dramatically from the increased size of the reactor because the content of the reactor increases by a power of three, but the area for heat transmission grows (Mily by a power of two. 

Figure 5-41 indicates the mixing correlation exponent, X, as related to power per unit volume ratio for heat transfer scale-up. The exponent x is given in Table 5-6 for the systems shown, and is the exponent of the Reynolds number term, or the slope of the... 

The same concept of volumetric in situ heating by microwaves was also exploited by Larhed and coworkers in the context of scaling-up a biochemical process such as the polymerase chain reaction (PCR) [25], In PCR technology, strict control of temperature in the heating cycles is essential in order not to deactivate the enzymes involved. With classical heating of a milliliter-scale sample, the time required for heat transfer through the wall of the reaction tube and to obtain an even temperature in the whole sample is still substantial. In practice, the slow distribution of heat... 

It is important to add heat transfer scale-up considerations to the scale-up approach for liquid parenteral solutions as heat transfer applications may play a considerable role in preparation of these products. For heat transfer applications, constant horsepower per unit volume is used to achieve approximately similar heat transfer coefficients for the same type of impeller. This approach is a close approximation since the effect of horsepower on the heat transfer coefficient (ho) is relatively small ... 

In the case of exothermic or endothermic reactions, scale-up may impair conditions for heat input or removal because the ratio of the heat transfer surface area to the reactor volume is reduced. Identical conditions for heat transfer in both the model and full-scale plants may be achieved in exothermal reactions if both have the same thermal stability coefficient. This requirement is obtained by introducing external heat exchangers. Alternatively, a reactor with a strong exothermic reaction can be divided into several small size reactors. In this manner, the ratio of the external heat transfer surface area to the reactor volume is increased, thereby avoiding an excessive temperature rise in the reactor. 

He knows that he may not vary the temperature T0 and dp if he does not want to risk influencing the chemical course of the reaction. Consequently, as already mentioned, geometric similarity is inevitably violated during scale-up on account of dp/d Z idem. Damkohler is therefore prepared to waive adherence to L/d = idem as well. However, he points out that this will necessarily lead to consequences for heat transfer behaviour. In this case, he uses the hypothesis that thermal similarity is guaranteed if the ratio of IV to III (heat conduction through the tube wall to heat removal by convection) is kept equal ... 

Lacking knowledge of the larger scale reactor, it is tempting to simply assume that only the area for heat transfer varies upon scale-up. A natural parameter is the cooling time defined as... 

If only small amounts of heat need to be transferred, the tank wall is a satisfactory heat transfer surface, when appropriately jacketed (Fig. 1.2). The wall surface often is inadequate for heat transfer, particularly in the case of industrial tanks, because upon scale-up the liquid volume increases according to D whereas the surface area only increases according to D. Additional heat transfer surfaces have then to be installed in the form of differently designed pipe coils or pipe bundles (helical coils, meander coils (cooling basket) tube bundles see Fig. 1.3). 

In selecting metals and alloys as materials of construction, one must have knowledge of how materials fail, for example is, how they corrode, become brittle with low-temperature operation, or degrade as a result of operating at high temperatures. Corrosion, embrittlement, and other degradation mechanisms such as creep will be described in terms of their threshold values. Transient or upset operating conditions are common causes of failure. Examples include start-ups and shutdowns, loss of coolant, the formation of dew point water, and hot spots due to the formation of scale deposits on heat transfer surfaces. Identification and documentation of all anticipated upset and transient conditions are required. 

SOLUTION Now, AT = 107°C. Scaling with geometric similarity would force the temperature driving force to increase by = 1.9 as before, but the scaled up value for AT is now 201°C so that the coolant temperature would drop to —39°C, technically feasible but undesirable. Scahng with constant pressure forces an even lower coolant temperature. A scaleup using a sheU-and-tube reactor is feasible but scaling with constant heat transfer should be considered. 

The scale of operation often has an overriding importance on the selection of the equipment because of the means used for heat transfer. For very small-scale crystallization work it is common to use radiation. The capacity of such equipment varies from a few liters up to several hundreds of liters per day (of solution cooled). For operation on scales up to several thousand liters per day, it is possible to use tanks with water-cooled coils and an agitator. For large-scale applications where the quantity of solution is thousands of liters per day, it is almost universal practice to use vacuum evaporation to remove the solvent this is true whether the solution is cooled by adiabatic evaporation or in equipment where crystallization occurs because of isothermal evaporation. 

Heat transfer is proportional to stirring speed to the power 5/3 and also changes on scale-up. For example, for a tenfold increase in size of the crystallizer, the introduced stirring power must be increased by a factor of 10 (risk of crystal abrasion) to remove the heat of crystallization at the same driving force AT for heat exchange. 

Empirical correlations for heat transfer coefficients, pressure drop, penetration depth, residence time, scale-up rules as well as results of mathematical modeling and computer simulation that are necessary for process calculation and equipment design can be found elsewhere [3,54,55]. 

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