Numerical and Analytical Study of Drilling Mud Flow through the Annulus with Cross non-Newtonian Model

In this work, the changes of drilling mud viscosity have been studied and Cross and Bingham plastic model parameters were determined based on some reported experimental data. For the non-Newtonian behavior of drilling mud, Cross model has a better prediction than the other models. Moreover, an analytical solution was derived for fluid with Cross model and a 2D numerical code was developed to solve momentum and continuity equations with a finite volume method. For the validation of the code, the velocity profiles and friction coefficient of Newtonian and non-Newtonian fluids in pipes and annulus were calculated and compared with the results of theoretical relations and analytical solutions. The results show good agreement and the friction factor error for Cross model is 5%, while, for Bingham model, it is 12%. Additionally, the flow field for Cross non-Newtonian fluid through the annulus was simulated and the results were presented in dimensionless terms. The friction factor in fully developed region and the entrance length was calculated and for the prediction of these two quantities, two new correlations were presented as a function of Reynolds number.