A mathematical approach of the entropic index applied to chemical systems

This article deals with the mathematical efforts for developing an entropic performance index, taking into account both the different entropy concepts for establishing it, including Communication Theory, and its practical application. To illustrate the performance of the index developed, two different approaches were applied to a reactive system that consists of multiple generic reactions. The reactive system was optimized using the strategy of generating the minimum entropy rate and then the index was applied to check the progress of the process. The index increased from 0.2146 to 0.549, thus indicating a better result and, consequently, more favourable operating conditions. Additionally, a more refined procedure was carried out, which generated a maximum value for the index of 0.6174. To reveal the efficiency of this index, classic indicators based on trade-offs between conversion and yield were also used to optimize the reactive system, which resulted in an index value of 0.6129. A detailed comparative analysis showed a convergence of the optimal regions, given by the classical method and that established by the entropy index. However, the optimal operating points are different, which can be explained by the interactions between the components considered by the entropic index. The conclusion to be drawn is that the results based on the entropy index describe the real system more appropriately, and therefore its performance is superior.