Scale-up ratios

Table 6. Laboratory Unit, Pilot-Plant, and Commercial Scale-Up Ratios...

Determine die scale-up ratio R, assuming dial die original vessel... 

Volume entrained into circular jet from propeller mixer, cu ft/sec Flow, gal/min Scale-up ratio... 

The power per unit volume is constant. From power consumptions in a bench-scale bioreactor, the necessary agitation rate is calculated for the scale up ratio, using Equation (13.2.1). The choice of criterion is dependent on what type of fermentation process has been studied. The following equation expresses relations for the impeller size and agitation rate in small and large bioreactors. 

The scale-up ratio is defined as the relationship between productivities of large-scale and small-scale equipment items, i.e. 

Typical scale-up ratios for the incremental approach are shown in Table 5.3-4. It is not surprising that single-phase systems are easier to scale up than multi-phase systems. The reason is that the contact between phases changes with scale. In particular, the presence of solids complicates scale-up. 

Many factors act together to determine the optimum scale of a process. These include the demand for the product, competitors share of the market, any technical limitations on the size of operation and also economies of scale effects. There is an approximate logarithmic relationship between the unit production costs for a product and the volume of production, whereby considerable economies of scale can be achieved. If the costs of a process of one size (C ) is known then the costs of larger or smaller factories (C ) can be approximately obtained from the relationship C = Cx (or n° ), where n is the scale-up ratio, i.e. n=l for a plant that is twice as big. Alternatively, a graph of log capital costs vs. log of plant capacity gives a straight line with a slope equal to the scale-up factor (n). The power term varies from case to case, but is invariably less than one. This scale effect is one reason why unit production costs are inversely proportional to the scale of manufacture. For example, most amino acids are expensive and can only be used in... 

Known scale-up correlations thus may allow scale-up even when laboratory or pilot plant experience is minimal. The fundamental approach to process scaling involves mathematical modeling of the manufacturing process and experimental validation of the model at different scale-up ratios. In a paper on fluid dynamics in bubble column reactors, Lubbert and coworkers (54) noted ... 

The limit of the scale-up ratio is 3 in one dimension, that is, 27 times in volume under the condition that ESD is maintained constant. However, in the case of a stirred vessel, the rule NDy2 = constant has reliability under a limited condition. (Since almost all the curves overlap at the lower wave number range, this fact shows that this scale-up rule has reliability when the lower wave number range is significant for the observed phenomena.)... 

Determine the scale-up ratio R, assuming that the original vessel is a standard cylinder with DX1 = HThe volume V, is... 

Type of equipment Is pilot plant usually lieces- sary Major variables for operational design (other than flow rate) Major variables characterizing size or capacity Maximum scale-up ratio based on indicated characterizing variable Approximate recommended safety or over-design factor, %... 

Carlsmith and Johnson (C2) have reviewed the research and development of the FCC process. Drawing on their data, Ikeda (14) has recalculated scale-up ratio and operating results, as shown in Table II. The feed rate of oil is roughly proportional to the cross-sectional area of the reactor. Thus a large superficial velocity was chosen for the small-scale reactors, and scale-up was conducted under a constant superficial velocity. 

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