In this work, we aim to develop a numerical tool able to simulate viscous flows with large spherical suspensions at high concentration. Suspensions are described by their homogenized volumetric fraction. A two-phases formulation is used: the “suspension balance model” (SBM). This method introduces a particle stress to model the shear-induced migration and its effect on the flow equations. Concentration evolution is predicted by solving a new migration equation based on convection by flow and particle stress balancing. As particles interactions have a strong influence on the viscous flow, the new stress is also introduced into the Navier-Stokes equations. Its contribution is divided into a viscous stress, considered as a local viscosity increase, and a normal stress, considered as a volumetric force. The SBM model is then implemented into the Rem3D® injection simulation software. Migration and suspended flow equations benefit from the existing numerical stabilizations for 3D simulations. Migration accuracy is tested at each stage of its integration with simple validation cases. Finally, its robustness is proved with a more complex and three-dimensional industrial case, including moving free surface and complex flow as fluid-buckling.