Optimal design of a solar-grade silicon refinery incorporating a fairness approach

The present work aims to obtain an optimal design of a multi-product solar grade silicon refinery under a systematic approach, considering different equity schemes and always seeking to maximize the profit of the facility. The proposed refinery is intensified to satisfy the demands with the use of minimum resources. Our motivation is to include a fairness approach in the design and optimization process which will help to diversify production at a lower cost and with a larger profit. Evaluation under equity approaches of intensified schemes is needed to identify how convenient it is to retain conventional schemes compared to intensified ones. Products of interest to be evaluated include solar grade silicon, tetraethoxysilane at various purities (98.5%, 99.0% and 99.5% mol), silane, dichlorosilane, and monochlorosilane. The optimal profit allocation among these products is analyzed by evaluating different equity schemes (Social Welfare, Rawlsian Welfare and Nash approaches). Results show different income allocations under the equity schemes. These allocations are compared to the optimal design without equity schemes. Results show that the Nash scheme can provide fair trade-offs between the products (such as TEOS, SiH₄, SiH₂Cl₂ and SiH₃Cl) demanded by the market and the refinery's profit.