The mathematical modeling of hydrodynamic pressure on the walls of the well when lowering the drill string when drilling oil and gas wells is considered. An analytical solution to the problem is obtained. Using numerical experiments, the influence of the viscoelastic properties of the flushing fluid on the hydrodynamic pressure on the well walls was studied. It has been shown that the relaxation properties of drilling fluids have a significant impact on the technological operations of lowering the drill string.
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