Like any other precipitation process, in supercritical water hydrothermal synthesis (SWHS), the need to improve product quality and minimize production cost requires understanding and optimization of Particle Size Distribution (PSD). In this work, using Population Balance Equation (PBE) containing nucleation and growth terms, the reactive precipitation of zirconia nanoparticles prepared by SWHS in the batch reactor was modeled. An optimization method using genetic algorithm function in MATLAB environment was developed to find simultaneously the kinetic parameters of nucleation and crystal growth rates, used for predicting PSD in PBE. The methodology developed evaluated kinetic parameters at comparable order of magnitudes to those presented in the literature, indicating a reasonable validation of the modeling method adopted. PSD results, however, showed a weak convergence of experimental and those predicted, suggesting that here, aggregation most likely played a considerable role in the PBE modeling of SWHS preparation of the zirconia nanoparticles.

This paper proposed a numerical model aiming at coupling the MUltiple-SIze-Group (MUSIG) with the semiempirical air entrainment model based on the Euler-Euler two-fluid framework to handle the bubble transport in hydraulic jump flows. The internal flow structure including the recirculation region, the shear layer region and the jet region was accurately predicted. The flow parameters such as the water velocity and void fraction distributions were examined and compared with the experimental data, validating the effectiveness of the numerical model. Prediction of the Sauter mean bubble diameter distributions by the Population Balance approach at different axial locations confirmed the dominance of breakage due to the high turbulent intensity in the shear layer region which led to the generation of small gas bubbles at high void fraction. Comparison between different cases indicates that high Froude number not only give rise to longer recirculation region and higher void fraction due to larger air entrainment rate, but also generate larger bubble number density and smaller bubble size because of the stronger turbulence intensity in the same axial position.

Operational variables of a mineral processing circuit are subjected to different variations. Steady-state simulation of processes provides an estimate of their ideal stable performance whereas their dynamic simulation predicts the effects of the variations on the processes or their subsequent processes. In this paper, a dynamic simulator containing some of the major equipment of mineral processing circuits (i.e. ball mill, cone crusher, screen, hydrocyclone, mechanical flotation cell, tank leaching and conveyor belt) was developed. The dynamic simulator of each mentioned unit was also developed according to Population Balance models with the help of MATLAB/Simulink environment and was verified against the data from the literature. Comminution and separation sections were linked using empirical models which correlate the separation and extraction kinetics to particle size. Applying the developed simulator, the dynamic behavior of a grinding-leaching circuit was analyzed and the results showed that such simulations are required for both designing and controlling the circuits.

A particular Population Balance model (PBM) which consists of hydrodynamic and electrostatic parts is developed for electrocoalescence of distributed water droplet in the continuous oil phase. The approach is the modification of a recognized PBM by adding the electrostatic effects on the overall coalescence rate including the number of times (frequency) occurring collision and the efficiency of coalescence. Moreover, the modified model has been being implemented in a CFD-PBM problem for a pilot plant electrocoalescer to predict the profile of water phase and size distribution of droplets. The results recognize the effect of local electric field intensity and local water content on electrocoalescence rate. Furthermore, the results demonstrate that separation for the very small droplets (<4μ m) is minor, for the medium sizes (8-32μ m) is more considerable, and for larger droplets (>64μ m) occurs completely. Ultimately, by making a comparison between the simulation results and the pilot data, the EHD PB model is validated.

In this work, the Markov Chain Monte Carlo is applied to estimate parameters that represent mechanisms that describe particles' dynamics in particulate systems from the literature's proposed models. Initially, the reduced sensitivity coefficient is evaluated to verify which parameters could be estimated simultaneously. The technique is then applied to estimate the models' parameters in different numerical scenarios to determine the rates that influence Population dynamics. After the analyzes are performed, the estimates show good precision, accuracy, and a good fit between the measured and estimated state variables. The results show that the Markov chain Monte Carlo can determine the rates of Population Balance phenomenon.