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The paper presents the results of an investigation into drilling mud flow with cuttings in a vertical well. The drilling mud rheology was described with the Herschel-Bulkley model. The axial Reynolds number was around 1000, the flow regime changing together with drill pipe RPM. The investigation covered the flow’s structures, integral parameters and cuttings transport in relation to drill pipe RPM and rate of penetration (ROP). In the laminar flow, most of the particles were localized in the quasi-solid region to move together with the last; the integral parameters had little dependence on drill pipe RPM increase. Increasing drill pipe RPM resulted in formation of the Görtler vortices near the channel’s external and internal walls, whose interaction led to the formation of smaller eddies converting the flow into a turbulent one. Due to the turbulence dispersion, the region taken by the particles widened. Particles suppress the vortex intensity near the channel’s external wall. Under the conditions described, increasing drill pipe RPM and ROP resulted in higher pressure drops and lower transport efficiency.

Transient three-dimensional flow simulations of power–law fluid in a long axisymmetric annular channel considering 0.5 diameter ratio were performed. An in–house CFD code considering URANS (Unsteady Reynolds Averaged Navier–Stokes), 2D RANS (steady-state axially uniform 2D RANS) and LES (Large Eddy Simulation) approaches were compared to perform the simulations. Flow structure was analyzed. Numerical experiments showed that rotation of the inner cylinder (drill pipe) leads to two effects: decrease of apparent viscosity in the region close to the rotating cylinder, thus decreasing viscous shear stresses; development of secondary vorticity structures increasing energy loss. First mechanism decreases pressure losses and dominates when Re < 300. At Re ∼ 300 the mechanisms compete with each other and pressure losses depends on power–law index n. At Re > 300 mechanism of second vortex structured dominates and increases pressure loss with rotation. Pressure losses for two-dimensional steady-state and three-dimensional transient problems were compared. Pressure losses using a two-dimensional approach can be underestimated by up to 30%.

To produce a well safely, the wellbore pressure during drilling must be in a range that prevents collapse yet avoids fracturing. This range is often called “the operating window”. Exceeding the limits of this range can trigger wellbore instability or initiate well control incidents. Pressure prediction requires an understanding of the hydrodynamics processes that occur in a borehole while drilling. Describing these processes is complicated by many factors: the mud rheology is usually non-Newtonian, the flow mode can be laminar or turbulent, and the drillstring can rotate and be positioned eccentrically. Known semi-analytical approaches cannot account for the full range of fluid flows that can arise during drilling. These techniques don’t take into account all factors. Accurate numerical simulation of the flow of drilling fluids is a means to describe the fluid behavior in detail. For numerical solutions of hydrodynamics equations a unique algorithm based on a finite-volume method and a new model of turbulence for non-Newtonian fluids was developed. The model considers string rotation and eccentricity of the drillstring. Newtonian and non-Newtonian fluids as described by the Herschel–Bulkley rheological model have been implemented. Data obtained via systematic parameter studies of the flow in a borehole are available for fast determination of parameters like pressure drop, velocity field, and stresses corresponding to any drilling condition. Applying the new model for the annulus flow and comparing the results to the parallel plate flow approximation enabled us to quantify the error made due to the approximated solution for non-Newtonian fluid rheology. The difference between the solutions grows as the annular gap increases. This situation is a function of the rheological parameters. Secondary flow effects can only be seen when applying the new solution method.