Online gasoline blending with EPA Complex Model for predicting emissions

The empirical Complex Model developed by the US Environmental Protection Agency (EPA) is used by refiners to predict the toxic emissions of reformulated gasoline with respect to gasoline properties. The difficulty in implementing this model in the blending process stems from the implicit definition of Complex Model through a series of disjunctions assembled by the EPA in the form of spreadsheets. A major breakthrough in the refinery-based Complex Model implementation occurred in 2008 and 2010 through the use of generalized disjunctive and mixed-integer nonlinear programming (MINLP). Nevertheless, the execution time of these MINLP models remains prohibitively long to control emissions with our online gasoline blender. The first objective of this study is to present a new model that decreases the execution time of our online controller. The second objective is to consider toxic thresholds as hard constraints to be verified and search for blends that verify them. Our approach introduces a new way to write the Complex Model without any binary or integer variables. Sigmoid functions are used herein to approximate step functions until the measurement precision for each blend property is reached. By knowing this level of precision, we are able to propose an extremely good and differentiable approximation of the Complex Model. Next, a differentiable objective function is introduced to penalize emission values higher than the threshold emissions. Our optimization module has been implemented and tested with real data. The execution time never exceeded 1 s, which allows the online regulation of emissions the same way as other traditional properties of blended gasoline.