Multiphase chemical reactors with characteristic multiscale structures are intrinsically discrete at the elemental scale. However, due to the lack of multiscale models and the limitation of computational capability, such reactors are traditionally treated as continua through straightforward averaging in engineering simulations or as completely discrete systems in theoretical studies. The continuum approach is advantageous in terms of the scale and speed of computation but does not always give good predictions, which is, in many cases, the strength of the discrete approach. On the other hand, however, the discrete approach is too computationally expensive for engineering applications. Developments in computing science and technologies and encouraging progress in multiscale modeling have enabled discrete simulations to be extended to engineering systems and represent a promising approach to virtual process engineering (VPE, or virtual reality in process engineering). In this review, we analyze this emerging trend and emphasize that multiscale discrete simulations (MSDS), that is, considering multiscale structures in discrete simulation through rational coarse-graining and coupling between discrete and continuum methods with the effect of mesoscale structures accounted in both cases, is an effective way forward, which can be complementary to the continuum approach that is being improved by multiscale modeling also. For this purpose, our review is not meant to be a complete summary to the literature on discrete simulation, but rather a demonstration of its feasibility for engineering applications. We therefore discuss the enabling methods and technologies for MSDS, taking granular and particle-fluid flows as typical examples in chemical engineering. We cover the spectrum of modeling, numerical methods, algorithms, software implementation and even hardware-software codesign. The structural consistency among these aspects is shown to be the pivot for the success of MSDS. We conclude that with these developments, MSDS could soon become, among others, a mainstream simulation approach in chemical engineering which enables VPE.

Discrete simulation of granular and particle-fluid flows: from fundamental study to engineering application

Processes involving particles, are known to exhibit extremely unpredictable behaviour, mainly due to the mesoscopic nature of granular media. Understanding particulate processes, not only for intellectual satisfaction, but also for process design and operation, basically requires a systems approach in modelling. Because they combine simplicity and flexibility, the stochastic models based on the Markov chain theory are very valuable mathematical tools to this respect. However, they are still largely ignored by the whole core of chemical engineering researchers. This motivates the existence of this review paper, in which we examine the three traditional issues: mixing and transport, separation and transformation.

Applications of Markov Chains in Particulate Process Engineering: A Review

Grinding of clinker is the last and most energy-consuming stage of the cement
manufacturing process, drawing on average 40% of the total energy required to produce
one ton of cement. During this stage, the clinker particles are substantially reduced in
size to generate a certain level of fineness as it has a direct influence on such
performance characteristics of the final product as rate of hydration, water demand,
strength development, and other. The grinding objectives tying together the energy and
fineness requirements were formulated based on a review of the state of the art of clinker
grinding and numerical simulation employing the Markov chain theory.
The literature survey revealed that not only the specific surface of the final
product, but also the shape of its particle size distribution (PSD) is responsible for the
cement performance characteristics. While it is feasible to engineer the desired PSD in
the laboratory, the process-specific recommendations on how to generate the desired
PSD in the industrial mill are not available.
Based on a population balance principle and stochastic representation of the
particle movement within the grinding system, the Markov chain model for the circuit
consisting of a tube ball mill and a high efficiency separator was introduced through the
matrices of grinding and classification. The grinding matrix was calculated using the
selection and breakage functions, whereas the classification matrix was defined from the
Tromp curve of the separator. The results of field experiments carried out at a pilot
cement plant were used to identify the model's parameters. The retrospective process data pertaining to the operation of the pilot grinding circuit was employed to validate the
model and define the process constraints.
Through numerical simulation, the relationships between the controlled (fresh
feed rate; separator cut size) and observed (fineness characteristics of cement;
production rate; specific energy consumption) parameters of the circuit were defined.
The analysis of the simulation results allowed formulation of the process control
procedures with the objectives of decreasing the specific energy consumption of the mill,
maintaining the targeted specific surface area of the final product, and governing the
shape of its PSD.

Improved cement quality and grinding efficiency by means of closed mill circuit modeling

Modeling of the mixing of monodisperse particles using a stationary DEM-based Markov process

Mathematical modeling of fluid energy milling based on a stochastic approach

Application of the theory of Markov chains to model different processes in particle technology

Raw materials are used in many industrial technologies. The raw material frequently has to be prepared as an intermediate with an appropriate particle size distribution, which requires the use of grinding. In grinding processes, energy consumption is a very important profitability criterion for the applied particular size reduction technology. The paper describes the comminution process that takes place in the jet mill using a modified form of the thermodynamic theory of grinding. In this theory, new material characteristics have been added: the surface and volumetric density of grinding energy. The thermodynamic theory is a combination of the classical Kick’s theory and the modified form of Rittinger’s theory. The tested physical magnitudes are a measure of the energy consumption of the grinding process. They describe the energy that must be provided in the grinding process to overcome interactions between particles related to the volume and surface of the material. Knowledge of these magnitudes is necessary to model thermomechanical phenomena in the solid state. The paper presents the results of research on comminution in a jet mill, on the basis of which the values of the tested material magnitudes were determined. It is graphically shown how the values of the tested magnitudes depend on the grain size of the ground samples.

Research on the Grinding Energy Density in a Jet Mill.

A model of the grinding and classification processes in the fluidized bed opposed jet mill based on the Markov chains approach was proposed. The methodology of modelling was elaborated and experimental research of the combined processes of grinding and classification was carried out.

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Vladimir P. Zhukov

Papers

Application of the theory of Markov chains to model different processes in particle technology

Research on the Grinding Energy Density in a Jet Mill.

Research and modeling of processes in the fluidized bed opposed jet mill

Optimal Positioning of the Circulating Load Input along the Tube Mill Length

Algorithme de construction de modèles markoviens multidimensionnels pour le mélange des poudres