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This paper presents a multi-compartment population balance model for wet granulation coupled with DEM (Discrete Element Method) simulations. Methodologies are developed to extract relevant data from the DEM simulations to inform the population balance model. First, compartmental residence times are calculated for the population balance model from DEM. Then, a suitable collision kernel is chosen for the population balance model based on particle-particle collision frequencies extracted from DEM. It is found that the population balance model is able to predict the trends exhibited by the experimental size and porosity distributions by utilising the information provided by the DEM simulations.

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Model guided application (MGA) combining physico-chemical internal combustion engine simulation with advanced analytics offers a robust framework to develop and test particle number (PN) emissions reduction strategies. The digital engineering workflow presented in this paper integrates the kinetics & SRM Engine Suite with parameter estimation techniques applicable to the simulation of particle formation and dynamics in gasoline direct injection (GDI) spark ignition (SI) engines. The evolution of the particle population characteristics at engine-out and through the sampling system is investigated. The particle population balance model is extended beyond soot to include sulphates and soluble organic fractions (SOF). This particle model is coupled with the gas phase chemistry precursors and is solved using a sectional method. The combustion chamber is divided into a wall zone and a bulk zone and the fuel impingement on the cylinder wall is simulated. The wall zone is responsible for resolving the distribution of equivalence ratios near the wall, a factor that is essential to account for the formation of soot in GDI SI engines. In this work, a stochastic reactor model (SRM) is calibrated to a single-cylinder test engine operated at 12 steady state load-speed operating points. First, the flame propagation model is calibrated using the experimental in-cylinder pressure profiles. Then, the population balance model parameters are calibrated based on the experimental data for particle size distributions from the same operating conditions. Good agreement was obtained for the incylinder pressure profiles and gas phase emissions such as NOx. The MGA also employs a reactor network approach to align with the particle sampling measurements procedure, and the influence of dilution ratios and temperature on the PN measurement is investigated. Lastly, the MGA and the measurements procedure are applied to size-resolved chemical characterisation of the emitted particles.

In this work we present a novel four-dimensional, stochastic population balance model for twin-screw granulation. The model uses a compartmental framework to reflect changes in mechanistic rates between different screw element geometries. This allows us to capture the evolution of the material along the barrel length. The predictive power of the model is assessed across a range of liquid-solid feed ratios through comparison with experimental particle size distributions. The model results show a qualitative agreement with experimental trends and a number of areas for model improvement are discussed. A sensitivity analysis is carried out to assess the effect of key operating variables and model parameters on the simulated product particle size distribution. The stochastic treatment of the model allows the particle description to be readily extended to track more complex particle properties and their transformations. product size/porosity distribution and Saleh et al. [17] investigated the effect of binder delivery method on the TSG system. Though the number of experimental investigations is extensive, the large operating window of TSG systems often limits the applicability of these results to local regions of the operating space.The comprehensive review of the experimental TSG literature by Seem et al. 50[18] shows a complex interplay between the role of each screw element type, the overall screw configuration, feed formulation and liquid flowrates on the observed experimental trends. This emphasises the need for a particle-scale model of TSG that can accurately predict the physical properties of the bulk granular 3 product. Ultimately, the inversion of such a model could then be carried out 55 and coupled with process control systems to allow specification and control of product specification in TSG systems.Granular systems are generally modelled using population balance models (PBM) [19,20,21,2, 22,23,24,25,26,27]. TSG specific PBMs have been developed, ranging from one [28] to three dimensional particle models [29,30]. 60A lumped parameter method is typically used to estimate additional particle properties beyond those explicitly tracked by the model [29]. Flow information and collision data have been incorporated into TSG models through couplings with alternative modelling frameworks such as the discrete element method (DEM) [29] and experimental near-infrared chemical tracing [31,28]. Many 65 of these TSG PBM studies have shown results in qualitative agreement with the experimental studies; however, quantitative predictions have proven to be much more challenging. One reason for this could be over-simplification of the system within the models. All of the existing TSG PBM models are numerically solved using variations of the sectional method [32]. Such a numerical approach 70