Logarithm-transform piecewise linearization method for the optimization of fasoline blending processes

Gasoline blending is a key process in a petroleum refinery, as it can yield 60%-70% of a typical refinery's total revenue. This process not only exhibits non-convex nonlinear blending behavior due to the complicated blend mechanism of various component feedstocks with different quality properties, but also involves global optimum searching among numerous blending recipes. Since blend products are required to meet a series of quality requirements and highly-sensitive to the proportion changes of blending feedstocks, global optimization methods for NLP problems are often difficult to be applied because of heavy computational burdens. Thus, piecewise linearization methods are naturally proposed to provide an approximate global optimum solution by adding binary variables into the models and converting the original NLP problems into MILP ones. In this paper, Logarithm-transform piecewise linearization (LTPL) method, an improved piecewise linearization, is proposed. In this method a logarithm transform is applied to convert multi-variable multi-degree constraints into a series of single-variable constraints. As a result, the number of 0-1 variables is greatly reduced. In the final part of this paper, an industrial case study is conducted to demonstrate the effectiveness of LTPL method. In principle, this method would be useful for blending problems with complicated empirical or theoretical models.