Equipartition principle in separation processes extraction

Example 5.5 Equipartition principle in separation processes Extraction Since the minimization of entropy production is not always an economic criterion, it is necessary to relate the overall entropy production and its distribution to the economy of the process. To do this, we may consider various processes with different operating configurations. For example, by modifying an existing design, we may attain an even distribution of forces and hence an even distribution of entropy production. 

Consider a simple mixer for extraction. In minimal entropy production, size I. time t. and duty J are specified and the average driving force is also fixed. We can also define the flow rate Q and the input concentration of the solute, and at steady state, output concentration is determined. The only unknown variables are the solvent flow rate and composition, and one of them is a decision variable specifying the flow rate will determine the solvent composition. Cocurrent and countercurrent flow configurations of the extractor can now be compared with the 

The specific entropy of a solvent increases with the solute concentration, and if the input solvent is the same, inequality (5.70) yields Ac1 Ac2, and hence Eq. (5.69) shows that Q Q2. This means that the solvent flow rate is smaller in the less dissipative operation, and the solvent at the outlet is more concentrated. That is, the operating conditions of solvent determine the less dissipative operation. Whether this optimum is an overall economic optimum will depend mainly on the cost of the technology. 

We can also compare the two processes with the same total entropy productions, the same size and duration, and the same phenomenological coefficients. Process 1 has only equipartitioned forces therefore, the duties of these processes will be different. The total entropy productions for the processes are expressed as 

Since Px = P2, combining Eqs. (5.71) and (5.72) yields Xavl Xav2, and hence Ji J2. That is, the flow rate for equipartitioned process 1 is larger than that of process 2 at a given size, duration, and entropy production. 

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