Batch process units size factor

In this section, an approach to solving the optimal control problem is introduced for reactor-separator processes. The approach involves the simultaneous determination of the batch times and size factors for both of the process units. Furthermore, the interplay between the two units involves trade-offs between them that are adjusted in the optimization. It should be noted that simpler models, than in normal practice, are used here to demonstrate the concept and, in the first example, provide an analytical solution that is obtained with relative ease. 

A batch plant for 7 products and 10 batch stages (equipment units) is to be designed. Products must be manufactured within H = 6200 hours. Tables 7.4-13 to 7.4-15 show processing times tij, size factors Sij, and yearly production requirements g for all products and stages. Cost coefficients for all... 

When designing a process unit to operate in batch mode, it is usually desired to detennim the batch time, t, and the size factor, S, which is usually expressed as the volume per uni mass of product, that maximize an objective like the amount of product. To accomplish this a dynamic model of the process unit is formulated and the degrees of freedom adjusted, as il lustrated in the examples that follow. As will be seen, there are many ways to formulate thn optimal control problem. To simplify the discussion, models are presented and studied f various input profiles, to see how they affect the objectives. Emphasis is not placed on tht formal methods of optimization. 

It is convenient to define the size factor, Sj, for task j, as the capacity required per unit of product. Commonly, it is defined as the volume required to produce a unit mass of product. For example, for the third cultivator in the tPA process of Sections 3.4 and 4.5, 4,000 L of medium yields 2.24 kg of tPA, which eventually yields 1.6 kg of final tPA product. Consequently, its size factor is 4,000 L/ 1.6 kg = 2,500 L/kg tPA product. Size factors can be computed for each task in a recipe. Normally, equipment vessel sizes are selected that exceed batch volume by 10 to 20%. Clearly, the batch factor in volume/mass produced is determined by the rate of processing the batch (e.g., kg/hr) multiplied by the batch time (hr) and divided by the density of the batch (kg/L) and the mass of product produced (kg). 

Analyte stability This factor can have a dramatic effect on the type of automated system used, or in the most extreme example, whether automated analysis can be used at all. Hence, it must be determined early in the method development and validation cycle. If a compound is temperature labile, then the use of cooled sample racks or trays may minimize this effect if degraded enzymatically an inhibitor may need to be added to prevent breakdown of the analyte pending analysis. Analyte stability can have a profound influence on the number of samples processed per unit time and hence the batch size. 

This delayed effect is influenced by the number of sterilisation units (objects) in one batch the load of the steriliser. It is hard to take all the contributing factors into account for the determination of the correct sterilisation time. Therefore, the temperature sensor that provides the input for the control of the sterilising process is placed inside a container in the coldest spot of the load. The coldest spot is to be identified by validation studies in a standardised batch size and loading scheme. 

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