Fraunhofer Institute for Industrial Mathematics ITWM
Fraunhofer Institute for Industrial Mathematics ITWM
Bergbau
© iStopckphoto
Eisenerz, Eisen, Gießerei, Bergbau, Rio Tinto Group

© iStopckphoto

Simulation of Mixing Processes for Granular Material

Blending beds are used for the homogenization and mixing of large quantities of different granular materials, for example in the cement industry. We develop dedicated software for the control and simulation of such blending beds.

The figure below shows the scheme of a modern blending bed. Different materials are transported from separate storage units onto a common conveyor belt, crushed, analyzed online with respect to their chemical composition, and finally piled up on the blending bed by the stacker. The mixing effect results from reclaiming the material in slices orthogonal to the stacked layers.

The objective is to control the feeding of material from the storage units such that the composition of the reclaimed slices meets specified requirements, for example remaining within narrow limits around target values for the lime saturation factor (LSF) and silicate module. In addition, the simulation of the blending bed determines how the premixed material is distributed across the stockpile and, ultimately, within the reclaimed slices. Therefore, simulation must be an integral part of a successful control strategy.

Schema Regelung und Mischbettsimulation
© Fraunhofer ITWM
Schema Regelung und Mischbettsimulation.

Mathematical and Algorithmic Basis

Based on our conducted research projects we have established the mathematical and algorithmic foundations for control and simulation of blending beds.

Premixing control has two essential aspects. From the measured composition of the premixed material, the composition of the materials in the storage units can be inferred using a Kalman filter. The feeding of material from the storage units must then be controlled such that certain modules reach optimal values, which leads to a quadratic optimization problem with linear constraints.

Our blending bed simulation is based on an internally developed, fast solver for a known variational inequality. This inequality describes the distribution of granular material in the case of weak feeding. The central idea of the solution method is to divide the feed into portions and drop each portion at a specific location. The resulting stockpile shape is obtained by stacking cones of appropriate height. The discretization error can be estimated exactly. 

The control and simulation algorithms were implemented numerically in MATLAB and, for time-critical cases, in C. The software includes a simple graphical user interface and can be used not only in the control room of a plant, but also for optimizing stacking and reclaiming processes, for joint plant planning with customers, and for computing guaranteed mixing grades. Compared with products currently available on the market, our software is characterized by high accuracy and short computation times.

Flow Simulation for Granular Materials

The software described here focuses on the storage of granular materials in large stockpiles. For flow simulation of granular materials in production processes and more complex storage conditions, such as silos, we are developing our software GRAIN.

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