Separators split-fraction model

The first three constraints represent orthogonal collocation applied to the differential equations at the collocation points. The next three equations represent mass balances at the separation point. The discretized RTD function and the expression for the mean residence time are given in the final constraints. As la —> 0, this model is equivalent to the original reaction-separation model (PI2). The main difference is that we allow separation only at the end of each element within each element no separation occurs. Although the model appears nonlinear, the nonlinearities are actually reduced when one considers the rates in terms of the mass fractions. The solution to this model then gives us the optimal separation split fractions as a function of time along the reactor. 

If the split fractions 7a = 7b = 7c. we have only a splitting operation without any separation. Otherwise, there is a relative separation between two adjacent components in the mixture and we define Ita 7bI as a measure of the intensity of separation between these two components. When 7a 7b = 7b 7c 0. we have only a splitting operation among these components, and the cost of separation is identically zero however, if 7a 7b = I, we have a sharp split between components A and B. Any intermediate degree of separation could then be modeled by complete sharp split separation followed by mixing in order to achieve the desired composition. 

Revise the process modeled in Problem 5.1 using split fractions of 99 and 1 percent instead of 99.9 and 0.1 percent in all the separators. How do the total flows change Would the equipment have to be larger Would it cost more Does the separation cost less Answer these questions qualitatively now when you finish your chemical engineering studies you will be able to answer them quantitatively. 

We can perform approximate material balance calculations to see what happens to the process if we were to recycle the distillate and process it with the feed. We model each separator as a set of constant split factors for each species. For example, we see that 97.94% of the pentane, 35.00% of the acetone, and none of the methanol leave in the top stream from the extractor. Water enters as the extraction agent and also as a small part of the feed 0.63% of the total water entering leaves with this top stream. We capture these results in the first three rows of numbers in Table X. We denote molar flow for species k in stream j leaving unit i by and the fraction of the flow of species k in the feed to unit / leaving in stream / by... 

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