Hydrodynamic Model of Stationary Drilling Fluid Flow in a Cylindrical Pipeline

The stationary axisymmetric flow of drilling mud under the action of a constant pressure drop created by a drill pump in a horizontal pipeline is investigated. The relevance of the proposed work is determined by the fact that the quality of drilling mud is one of the most important components of the technological process of drilling oil wells. In this regard, there is a need to develop a formulation of a dispersed system, which is a drilling mud, which allows for effective cooling of the rock-destroying tool, high-quality removal of sludge to the surface in compliance with the requirements for solutions, with minimal material costs. The purpose of this work is: to establish a relationship between structural parameters and hydraulic resistance of the fluid flow within the framework of the Ostwald-de Waele rheological model; to study the stress–strain state of the model medium in a stationary, axisymmetric flow; to establish a relationship between the average flow hydrodynamic characteristics with its viscosity parameters. Analytical dependences of the distribution of effective viscosity and axial velocity of the medium flow are obtained. The dependence of the flow rate of the model medium on the magnitude of the pressure drop, as well as the distribution of the dynamic shear stress along the pipeline section, are determined.