A General Semi-Mechanistic and the Bees Algorithm-Based Optimization Framework for Two-Roll Chocolate Refining: Target-Band Particle Size Control and Experimental Validation
摘要
Particle size distribution (PSD) is a key process descriptor in chocolate refining because it affects rheology, texture development, and downstream processability. In industrial practice, however, two-roll refining conditions are still often adjusted empirically, which makes it difficult to consistently transform a broad inlet PSD into a controlled intermediate product band suitable for downstream refining. This study proposed a general semi-mechanistic and optimization-based framework for two-roll chocolate pre-refining, developed to predict and control the redistribution of particle volume from a coarse inlet range toward a prescribed outlet interval. The model integrated roll-gap-governed stressing, a population-balance-based redistribution structure, a daughter-distribution kernel, and a closed-circuit recycle representation within a unified computational framework. Rather than claiming direct observation of each internal mechanism, the framework was used to predict the outlet PSD response and its dependence on operating variables under a consistent engineering representation of compression–shear action, effective redistribution, and recycle-assisted coarse-particle control. The operating conditions are optimized using The Bees Algorithm (BA), enabling selective target-band formation rather than indiscriminate particle size reduction. Although the modelling framework is formulated in general form, its practical applicability is demonstrated through an industrial fixed-geometry case study based on a production-scale system with a roll diameter of 400 mm and a roll width of 1300 mm. In the application considered, the inlet particle population lies in the 150–800 μm range and the desired outlet product is concentrated in the 120–150 μm band. In this study, the two-roll unit was treated as an upstream pre-refining and pre-size-control stage in the chocolate paste preparation line, located before the downstream five-roll refining operation. Accordingly, the 120–150 μm band was not interpreted as the final sensory target of finished chocolate, but as an intermediate engineering target used to narrow and stabilize the coarse feed before subsequent fine refining. The optimized solution is evaluated in terms of characteristic particle sizes, on-spec fraction, residual undersize and oversize fractions, specific energy consumption, thermal response, and cross-width uniformity. Experimental trials performed at MEMAK are used to compare numerical and measured cumulative and differential volumetric PSDs. The results show that the proposed framework captures the main redistribution behavior of the industrial process with good accuracy and successfully identifies an operating regime that concentrates most of the product volume within the desired target band. The study therefore provides both a general modelling framework for two-roll chocolate pre-refining and a practically validated basis for process optimization, operating-window identification, and future digital-twin-assisted industrial process control.