Differences between Optimum Flow Sheet Solutions Obtained by Different Economic Objective Functions

Abstract

This paper discusses the shapes of cash flow functions obtained by modelling chemical processes at different levels of complexity, and the influence of these shapes on optimal solutions obtained by different economic objective functions. Cash flow functions can be unimodal (with maximum) or monotonically increasing (concave) with respect to capital investment. This depends on the quality of major trade-offs established in the model. Unimodal shape is common for modelling with simple and aggregated models, where increasing the investment above certain level causes loss to a project, which indicates improper or insufficient trade-offs in the model. Monotonically increasing concave cash flow functions are usually obtained by using more detailed models. This implies better trade-offs in the model as increasing the investment always brings some benefit (higher or lower). Example of methanol process synthesis presented in the paper indicate that models with monotonic cash flow functions produce significantly different optimal solutions when optimizing different economic criteria, e. g. the net present value, the profit and the internal rate of return. On the other side, the optimal solutions of models with unimodal functions are similar. These results suggest that models should be formulated at the level of complexity which produces monotonically increasing cash flow functions.