Copula-based approximation of particle breakage as link between DEM and PBM

- Population balance modeling (PBM) is an important tool in process engineering.
- Particle breakage in processes can be described by a machine and material function.
- We give a mathematical formulation of these functions and a method to obtain them.
- This method is based on copula-based probability distributions, which are fitted to DEM data.
- The proposed approach provides a flexible interface that links PBM to DEM.

In process engineering, the breakage behavior of particles is needed for the modeling and optimization of comminution processes. A popular tool to describe (dynamic) processes is population balance modeling (PBM), which captures the statistical distribution of particle properties and their evolution over time. It has been suggested previously to split up the description of breakage into a machine function (modeling of loading conditions) and a material function (modeling of particle response to mechanical stress). Based on this idea, we present a mathematical formulation of machine and material functions and a general approach to compute them. Both functions are modeled using multivariate probability distributions, where in particular so-called copulas are helpful. These can be fitted to data obtained by the discrete element method (DEM). In this paper, we describe the proposed copula-based breakage model, and we construct such a model for an artificial dataset that allows to evaluate the prediction quality.

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