Modeling of gas extraction from rheologically complex media in the field of centrifugal forces in a hydrocyclone

Liquids processed in the oil industry, in particular drilling fluids, in many cases have nonlinear viscoplastic properties. Such liquids have a yield strength, and their effective viscosity decreases with an increase in the intensity of the deformation rates, which affects the hydrodynamics of the devices. In the published works, it is concluded that the rheological equation of state of a non-Newtonian fluid is applicable to multiphase heterogeneous systems, which is written in the form of the Herschel-Bulkley law for drilling mud purification processes. We believe that this law describes the properties of a nonlinear viscoplastic fluid. The mathematical model of separation of inhomogeneous liquid systems in the field of centrifugal forces is adapted to the process of degassing of viscoplastic liquids in a cylindrical hydrocyclone. The model takes into account the action of inertia, Coriolis forces and the attached mass of the liquid. The system of partial differential equations describing the degassing process is reduced to a system of ordinary differential equations and solved numerically. The system of ordinary differential equations was solved in projections on the coordinate axis using the Runge-Kutta method with a fixed step according to a program compiled in the Compaq Vizual Fortran language, applied to the geometry of the working space of a cylindrical hydrocyclone. Based on the results of modeling the fields of velocity and pressure components during the flow of a nonlinear viscoplastic fluid in a cylindrical hydrocyclone and subsequent approximation of the calculated data, a simulation of the degassing process of a nonlinear viscoplastic fluid in a hydrocyclone was performed, which consisted in the numerical solution of the obtained system of differential equations for various values of the determining similarity numbers and rheological constants of the dispersion medium when they change in a wide range. Based on the results of numerical modeling, the influence of the plasticity number at different values of the separation factor and the nonlinearity index of the flow curve on the degree of extraction of gas bubbles is analyzed. The physical justification of the obtained results is given. The obtained results can be used in the development of equipment for cleaning drilling fluids.

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