Problem solution analysis on finding the velocity distribution for laminar flow of a non-linear viscous flushing fluid in the annular space of a well

Modern drilling fluids are non-linear viscous media with an initial shear stress. In classical scientific works on hydromechanical modeling of motion in pipes and annular channels the Shvedov – Bingham approximation Ostwald de Waale power-law model were used, which did not fully account for behavior technological a wide range rates. This article presents numerical solution mathematical fluid three-parameter Herschel Bulkley rheological space well. The equation takes into presence stress tendency viscosity to change rate, distinguishes it from models. target function solving is velocity distribution radial direction upward flow flushing fluid. analysis obtained based theory profile influence quality cuttings removal during wellbore cleaning. Due peculiarities statement task, supposes necessity differential solution, Wolfram Mathematica computational software has been used as calculation tool. allowed draw conclusions about possibility its application evaluation when moves modified excess coefficient relative quantitative parameter uniformity was substantiated.