surrounding reducing giveaway losses invariably pivot around the octane number. Reducing octane number giveaway Efforts to mitigate octane number giveaway losses are thus at the forefront of practical discourse within the industry, as refineries seek to optimise their blending processes and minimise financial losses while ensuring compliance with regulatory standards and meeting consumer demand for high-quality gasoline products. By addressing the octane number giveaway issue, refineries stand to enhance their competitive edge and bolster their bottom line in a dynamic and fiercely competitive market landscape. The giveaway reduction requires improving confidence in the expected blend properties at the batch planning and execution steps. Finding the optimal recipe (the ratios of the involved components) is equivalent to solving a constrained optimisation problem. The total cost of the involved blended components is minimised under several constraints. The component costs are most often the subjective shadow prices of the components determined by the refinery. The constraints include the desired blend volume, the allowed specification ranges of blend properties, the avail - able amounts of the blending components, and the quantity and the property of the blend remaining from the previous blending batch (the heel). Perhaps the most challenging constraint to satisfy is the dependencies between the properties of the blended streams and the blend. This dependency is the blend model. Its fidelity is crucial to ensure that the blended gasoline’s actual measured properties coincide with its properties according to the model. The dependency between the octane numbers of the blending components and the blended gasoline is non- linear. There is no analytic formula fully describing this dependency. Over time, various approaches to approxi- mating this dependency have been developed. One of the developed approaches is a polynomic approximation:
gasoline blends. To mitigate this issue, refineries commonly adopt a practice of individually regressing the DuPont coef- ficients, tailoring them to their blend components’ specific composition and properties. This customisation allows refineries to better capture the nuanced distribution of component properties and ratios characteristic to their typ- ical blend formulations, thereby enhancing the accuracy of blend modelling outcomes. Despite its shortcomings in predictive accuracy, the DuPont model offers a redeeming quality in its interpreta- bility. This attribute refers to the model’s capacity to provide clear and understandable insights into the relationships between blend components and the resulting gasoline characteristics. The interpretability of the DuPont method facilitates a deeper understanding of how different factors influence blend outcomes, empowering refineries to make informed decisions regarding blend optimisation and qual- ity control. By leveraging the interpretive capabilities of the DuPont model, refineries can navigate gasoline blending complex - ities with greater confidence and precision, effectively bal - ancing the trade-offs between accuracy and practical utility in blend modelling. A typical practical way to deal with the limitations of the DuPont model and other simplified ana - lytic approximations of the blend model is the notion of bias: the difference between the predicted properties of the blend according to its recipe and the laboratory result of the actual mixture. If consistent, the bias measured for the few recent blends may be added to the regressed model prediction, assuming the following few recipes will involve components with sim- ilar properties. Hence, it can benefit from adding the same bias value. The concept of bias as a constant can be further refined if a dedicated model for bias estimation based on the properties of the blend components’ properties, their ratios, and model regression coefficients could be created using machine-learning (ML) tools. The resulting model is, in essence, a hybrid model, combining the prediction of two models: an analytic one, using the interpretable interaction coefficients obtained through regression, and an ML model, accounting for the residual of the first one. Hybrid model and ML methods A first principles model, also known as a physics-based model or mechanistic model, is a mathematical representa- tion of a system or phenomenon derived from fundamen- tal physical principles and laws. Unlike empirical models, which are based solely on observed data and correlations, first principles models are grounded in the underlying phys - ics, chemistry, or mechanics governing the behaviour of the system. These models typically involve differential equations or other mathematical expressions that describe the relation- ships between the various components and parameters of the system. They aim to capture the cause-and-effect relationships within the system and provide insights into its behaviour under different conditions. First principles models are widely used in science and engineering disciplines, including physics, chemistry,
Where: x i is the concentration of the i-th blend component. O i is the octane number of the i-th blend component. a i,j and a i,j,k are interaction coefficients. Its second-degree version has become a commonly used approximation method introduced by the DuPont Company in 1975.
Limitations Inherent limitations in the DuPont model’s precision high - light its inability to ensure accurate predictions across diverse ranges of component properties and ratios. Consequently, relying solely on the DuPont coefficients may result in discrepancies in estimating the characteristics of
36
PTQ Q3 2024
www.digitalrefining.com
Powered by FlippingBook