Regarding the small problem of asking for the number of theoretical boards in Pro2, please seek help from various experts.
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Does anyone know how the red dots in the picture are determined? The article describes it like this (The graphs of N and R were generated from the results of shortcut column simulation, and the optimum values of N and R were identified based on the slope, which was inclined sharply from its tipping point.), which roughly means to obtain a critical value with the largest slope change. But I don’t understand how to get it? thank you all
The red dot is the optimum Nand R.
Basically, the point where R continues to increase, but N does not change much, can be fitted to a curve and find the downward derivative.
The point you are talking about is the minimum number of theoretical boards. . Moreover, there is no way to fit a curve. I don't know what's wrong with the fitting. Anyway, excel can't fit it. Asking for advice
Do you know how to fit curves in excel? If R is large, the operating cost is high. If N is large, the one-time investment in equipment is high. When R increases, N decreases. It can be seen from the curve that when R reaches a certain size, continuing to increase has little effect on the decrease of N. That is, there is no need to continue to increase R desperately at this time, which is equivalent to asking you to find this inflection point.
It's the same as finding the theoretical version through diagramming in Principles of Chemical Engineering. Choose the best R based on how much R changes as N changes.
If the poster is not engaged in academic research, there is no need to worry too much about the value of R. Under the premise of certain feeding conditions and product purity, sensitivity analysis was performed to obtain the above-mentioned curve cluster. This curve cluster can well represent the changing trend of operating costs and equipment investment. In engineering design, as long as the approximate number of plates continues to increase and the reflux ratio (energy consumption) decreases very little, this point will be regarded as the optimal number of plates and reflux ratio. If the poster is engaged in academic research, it feels like connecting discontinuous points to make a smooth curve, and doing the second-order derivative (first-order deltRR/deltNt,, the second-order is the derivative of the first-order formula) to obtain this optimal point.
Please tell me how you made this picture?