A dimensionless modelling approach to axial dispersion in an automated single-screw reactor

Abstract

Viscous reaction systems offer clear sustainability advantages but pose significant challenges for continuous reactor operation due to poor macromixing and pronounced axial dispersion. Single-screw reactors equipped with tailored mixing elements represent a promising solution. However, although several modelling approaches for axial dispersion under viscous conditions have been proposed, their applicability remains limited, as they are largely empirical and strongly dependent on specific screw geometries and operating conditions. In this study, a semi-empirical, dimensionless modelling framework is developed to predict axial dispersion in an automated single-screw reactor. Axial dispersion was quantified using residence time distribution analysis and expressed as the dimensionless vessel dispersion number. Experiments were conducted over a wide operating window, including variations in screw rotational speed, volumetric flow rate, fluid viscosity (1-1000 mPa.s), and mixing element geometry. A fully automated reactor platform was implemented to generate a large, reliable dataset, in alpha tegrating closed-loop experiment execution, inline data acquisition, automated RTD processing, statistical validation, and adaptive experiment selection. Key dimensionless groups, including the drag-to-inertia ratio, Schmidt number, and geometric normalization parameters, were employed to capture the coupled effects of flow dynamics, fluid properties, and reactor geometry. A rational semi-empirical correlation was derived and optimized using a differential evolution algorithm, yielding strong agreement across all mixing element datasets. The model identifies an optimal drag-toinertia ratio at each Schmidt number for which back-mixing and axial dispersion are minimized, providing a scalable and physically interpretable framework for macromixing optimization in viscous single-screw reactor systems.