Optimal distillation column diabatic configuration

Example 5.13 Optimal distillation column Diabatic configuration Consider a distillation column made of N distinct elements. The heat and mass transfer area can be defined separately. Defining an investment cost Q for element i as a linear function of the size. 1,. we have 

In the diabatic distillation column, each element is small enough that equipartition of entropy production may be approximately achieved by adjusting the heat flows and thus the liquid and vapor flow rates. We assume that each element performs a specified duty of Ji0. The total cost function Ct for all N elements is 

The derivative with respect to Aj yields a system of independent equations 

Since r is a constant depending only on economic conditions, the right of Eq. (5.136) must be independent of the element /. and thus an invariant throughout the process. The product fjOtAj is the annual cost related to irreversible energy waste in terms of exergy loss. These two quantities should be equal in ary element. 

We may conclude that under these assumptions, the optimal size distribution of the elements requires the equipartition of the ratio jTqPIoA on all the elements, and the cost of exergy loss is equal to the amortized proportional investment cost in that element. 

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Example 5.8 Optimal distillation column—Diabatic configuration... 

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