Multi-objective robust optimization of profit for a naphtha cracking furnace considering uncertainties in the feed composition

Abstract

A cracking furnace is the primary unit of a naphtha cracking center (NCC) to produce ethylene (EL) and propylene (PL); the yields of EL and PL depend on the naphtha composition of the NCC feedstock. However, the naphtha composition typically fluctuates depending on the feedstock suppliers, and the consequent uncertainties in the composition causes investment risks associated with the net profit. However, owing to the high dimensional uncertainties of the naphtha, conventional sampling (e.g. Monte Carlo method) based robust optimization is infeasible option due to high computational cost. In this study, we adopt the polynomial chaos expansion (PCE) to surrogate the system considering the uncertainty. Owing to the orthogonality of the PCE, the statistical moment of the PCE can be directly calculated without uncertainty sampling and iterative simulation. In this study, the PCE-based profit optimization model of the NCC furnace is developed as follows: Initially, we infer probability density functions (PDF) using industrial data to consider the uncertainty in the naphtha composition. Using the inferred PDF, we extract training dataset samples with coil outlet temperature (COT), product price, feed composition, and the net profit. Subsequently, using the training dataset, we develop a polynomial chaos expansion (PCE)-based surrogate model to predict the moments of the net profit, namely, the mean, variance, and skewness. Owing to the orthogonality of the model, the moments can be parameterized with only decision variables instead of computing the uncertainty. Finally, we incorporate the developed PCE-based model into a genetic algorithm to simultaneously optimize two conflicting objectives: maximizing the mean profit and minimizing the variance. The optimization results reveal the trade-off relationship between the mean profit and investment risk (variance and skewness) of the NCC process under feed uncertainty. Owing to the orthogonality, the optimal decision point can be provided with low computation time and high prediction accuracy compared with the sampling based optimization method. Considering the application of the proposed optimization model, we conduct case studies for two different scenarios of the product price. The optimal COTs for maximum mean profit with minimum variance of profit in the first and second scenarios range from 723 to 833 and 734 to 898 ℃, respectively. Therefore, the proposed model can quantitatively predict the mean profit with investment risk and help decision-makers select optimal operating conditions considering both the investment tendency and uncertainty in the naphtha composition.