Economic-Based Performance Objective Functions

Optimization of chemical processes is based on tiie objective of maximizing the profit of the entire process. For processes involving chemical reactions, we can write the objective function as 

For convenience, the operating expenses are divided into different categories  

The revenue portion of Eq. 10.1.1 depends on the composition of the reactor outlet. A higher purity product is more valuable, and the economics of the process depends on whether unconverted reactants and undesirable by-products are separated from the final product. When species are separated, the separation cost should be incorporated into the analysis of the reactor operation. To maximize the profit of the process, an engineer can adjust the design and several operating parameters  

The profit objective function (Eq. 10.1.1) is then expressed in terms of these (and other) operating parameters, and we determine the optimal values of the parameters by solving the following equations  

For most operations with single chemical reactions, the profit function is expressed in terms of relatively simple functions of these parameters, and Eq. 10.1.3 can be solved analytically. For operations with multiple chemical reactions, we have to determine the optimal parameters numerically. 

---

In the multi-objective optimisation environment, each objective function, i.e. economical and environmental objectives, is normalised so that their values are of approximately the same magnitude and the same direction of optimisation. The range of each new formulated objective function is [0, 1 ] where 0 represents the best achievable value and 1 represents the worst achievable value respectively. Eq. (13) shows the normalisation process of the economical objective based on the calculated operating profit while Eq. (14) shows the normalised environmental objective based on the GWP performance, where the maximum and minimum values of each objective function is calculated based on single objective optimisation, minimisation and maximisation, within the selected decision variable. 

---