The gas-solid two-phase flow model based on the kinetic theory of granular flow (KTGF) has been widely used in the numerical simulation of multiphase flow behavior in petroleum engineering, chemical engineering, and power engineering. KTGF is particularly appropriate when the particle loading is relatively high. In KTGF, the isotropic fluctuating energy of particles is assumed. Recently, the experimental and simulation studies of gas-solids risers reveals an anisotropic fluctuation of particle velocity exists. Therefore, an anisotropic second-order moment of particles (SOM) is required and has been developed to predict the flow behavior of particulates in multiphase flow.

In industrial applications, the fluidizations of the mixture of particles with different diameters and densities are in highly concerned. Especially when the density or size of particles differs for the multi-type particles, segregation will be formed because of the interactions of particles in the gas-solids fluidized beds with multi-type particles. This will effect heat transfer and chemical reactions of particles. Based on kinetic theory of granular flow, the model of anisotropic fluctuating velocity of the multi-groups of particles is proposed to show the difference of the velocity and second order moment of fluctuation velocity among all groups with different diameters or/and densities.

The second-order moment model of multi-type particles (SOM) is applied to simulate the flow behavior of gas-solid flow with different size and density of particles in risers. The effects of gas-particle interaction and particle-particle interaction are investigated in terms of the particle distribution and turbulent characteristics. The mixing and segregation phenomena are analyzed accordingly. The distributions of velocity and volume fractions of binary mixture of particles are predicted in a riser, and compared to experiments. The high solids volume fraction with big particles is found in the bottom regime, and more small particles are found at the top along the height of the riser with binary mixture. More big particles are formed near the walls, and the high volume fraction of small particles is in the center along the radial direction of the riser. From simulations, it is found that the big particles have low second order moment of fluctuating velocity of particles, while the small particles in the binary mixture have large fluctuating velocity. The axial fluctuating velocities of big particles and small particles are larger than the lateral fluctuating velocity. With the decrease of gas velocity and the increase of solids volume fractions, the ratio of axial component and lateral component of fluctuating velocity is reduced. The axial and lateral second order moments of fluctuating velocity increase at the first, reach maximum, and then decrease with the increase of solids volume fractions in the riser with binary mixture. Simulated fluctuating velocities of big and small particles are in agreement with experiments measured in a riser with binary mixture.

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