Numerical analysis of solids mixing in pressurized fluidized beds

In the production and processing of granular matter, mixing of solids plays an important role. Granular materials such as sand, polymeric particles, and fertilizers are processed in different apparatuses such as fluidized beds, rotary kilns, and spouted beds. In the operation of these apparatuses, proper mixing is essential, as it helps to prevent the formation of hot spots, off-specification products, and undesired agglomerates. In this article, we discuss various methods that are available to give quantitative information on the solids mixing state in granular systems based on a discrete description of the solids phase. We apply the different methods to two-fluid model simulations. It is found that some of these methods are grid-dependent; not reproducible; sensitive to macroscopic flow patterns; and/or able to calculate only overall mixing indices, rather than indices for each direction. We compare some methods described in the literature, and in addition, we propose two new methods that do not suffer from the disadvantages mentioned above. Simulations are performed for seven different operating pressures. It is found that mixing improves with operating pressure as a result of increased porosity in the dense phase.