Calculation of drilling fluids velocity profile of the Herschel-Bulkley rheological model in the annular space of a well

Nikitin, V.I.; Zhivaeva, V.V.; Kazazyan, M.G.

doi:10.33285/0130-3872-2021-11(347)-22-25

COGWLS

2021

DOI: 10.33285/0130-3872-2021-11(347)-22-25

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Calculation of drilling fluids velocity profile of the Herschel-Bulkley rheological model in the annular space of a well

V.I. Nikitin¹,

V.V. Zhivaeva²,

M.G. Kazazyan³

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2022

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“…The mathematical formulation of the problem on finding the velocity distribution in laminar mode of Herschel -Bulkley fluid motion in the annular space of the well consists in solving the stationary modified Navier -Stokes differential equation of motion [34,35]…”

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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

Nikitin

2022

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

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confidence: 99%

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

Nikitin

2022

PMI

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Calculation of drilling fluids velocity profile of the Herschel-Bulkley rheological model in the annular space of a well

Cited by 1 publication

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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

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

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