# Simulation of Mixing Processes for Granular Material

Mix beds are used for the homogenization and mixing of large amounts of different granular materials, e. g., in cement industry. In cooperation with the department System Analysis, Prognosis and Control, there was developed software for the control and simulation of such mix beds was developed for the company MVT Mechanical and Process Engineering Bernhard Blatton Ltd.

The figure below shows the scheme of a modern mix bed. The different materials are transported from separate stocks onto a common transport belt, crushed in the crusher, examined online with respect to their chemical composition, and finally piled up on the mix bed by the stacker. The mixing effect results from the process of reclaiming the material in slices orthogonal to the stacked layers.

The objective is to control the feeding of material from the stocks in such a way that the composition of the reclaimed slices meets certain demands, e. g., remains within narrow limits around required values for time saturation factor and silicate module. Additionally, the simulation of the mix bed also determines how the premixed material is distributed across the stock and, finally, within the reclaimed slices. Hence, simulation must be included into control in order to solve the problem.

#### Mathematical and Algorithmic Basis

First, in the course of the project the mathematical and algorithmic foundations for the control and simulation of mix beds were laid at the ITWM.

The premixing control has two essential aspects: from the measured composition of the premixed material, it is possible to conclude the composition of the materials in the stocks, which is achieved by a Kalman filter. The feeding of material from the stocks must be controled in such a way that certain modules show optimum values, which leads to a quadratic optimization problem with linear constraints.

The mix bed simulation is based on a fast solver for a known variational inequality, developed at the ITWM. The inequality describes the distribution of a granular material in the case of weak feeding. The central idea of the solution method is to portion the feeding of the material and to drop each portion over a certain point. The new form of the stock then results from the stocking of cones of appropriate height. The discretization error can be estimated exactly.

The control and simulation algorithms were implemented numerically in MATLAB and, for critical cases with respect to time, in C. Apart from its application in the control room of an existing plant, the software, which includes a simple graphic user interface, can also be used for the optimization of stacking and reclaiming processes, for the planning of a new plant together with the customer, or for the computation of guaranteed mixing grades. Up to now, products which account for the structure of the stock in a similar way, are not available on the market yet.

Type of Project: Industry Project
Project Partner: MVT, Dillingen