Steady Flow of a Cement Slurry

Understanding the rheological behavior of cement slurries is important in cement and petroleum industries. In this paper, we study the fully developed flow of a cement slurry inside a wellbore. The slurry is modeled as a non-linear fluid, where a constitutive relation for the viscous stress tensor based on a modified form of the second grade (Rivlin–Ericksen) fluid is used;we also propose a diffusion flux vector for the concentration of particles. The one-dimensional forms of the governing equations and the boundary conditions are made dimensionless and solved numerically. A parametric study is performed to present the effect of various dimensionless numbers on the velocity and the volume fraction profiles.