The dynamic transport of gas-solids in a riser leads to highly non-uniform and complex flow distributions in both axial and radial directions. This study presents a continuous modeling approach that simultaneously computes the axial and radial non-uniform distribution of gas and solid phase transport properties in the risers. The radial non-uniform distributions of transport properties of gas and solids are approximated by the 3rd order polynomials, which have been validated by available experimental data from literatures. The radial heterogeneity is due to a combined effect of riser wall boundary, the radial transport by the collision-induced diffusion, and the turbulent convection of solids. Some important transport properties, such as core-wall boundary and back-mixing ratio, are flow-coupled and solved by the proposed model. The model predictions have been validated against some published experiment data, including the distributions of solid concentration, velocity and pressure gradient along the risers.

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