Three-layer nonstationary model of cuttings transport in oil wells

A model has been proposed for the original three-layer nonstationary liquid-solid mixture flow in the annulus of a well with an arbitrary geometry. One of the important features of the model is taking into account the bulldozer effect, when the removal of solid particles from the well occurs not only due to bed erosion and deposition, but due to the sliding of the upper layers of the bed relative to the stagnant bed layer. To select an efficient numerical scheme for solving the equations of motion, its characteristics were determined, which made it possible to use the explicit scheme of the Godunov method. This significantly reduced the running time in the computer implementation of the numerical scheme with accuracy satisfactory for the engineering practice. Another important goal of the work was to carry out a comparative analysis of the results of calculation of non-stationary processes and steady states with the experimental results of other works at different flowrates, fluid rheology, well inclinations, and pipe eccentricity. Based on the analysis results, principal model factors have been identified that can result in calculation errors. The code developed based on the proposed model enables determination of drilling parameters for complete well cleaning, time needed for the process and calculation of hydraulic losses with a reasonable degree of accuracy, etc.