Mathematical and graphical approaches to improve the process of saturation of flushing fluid with air in the circulation system of a drilling rig unit

The object of research is the process of air saturation of the flushing fluid using a multi-nozzle foam generator in the circulation systems of drilling rigs. One of the most problematic areas in the known designs of foam generators is the insufficient efficiency of air saturation of the fluid, which is solved by the design proposed in the work. The design of a multi-nozzle foam generator is proposed by improving the mixing chamber. This design allowed to provide improved foam formation, more efficient air saturation of the flushing fluid, reduce the time of well development and increase the productivity of the device without changing the pressure and supply of fluid and air. During the study, computer mathematical modeling was used (in the Maple 9.5 software environment), a study of the dependence of air flow on pressure and fluid flow at nozzle diameters of 4 mm and 6 mm was performed. The studies considered graphical analysis to determine the optimal operating modes of the foam generator. An improved multi-nozzle foam generator with improved foaming efficiency, uniform saturation of the flushing fluid with air, reduced energy consumption and reduced well development time was obtained. This is due to the improvement of the design of the mixing chamber, which has a number of features. The proposed design provides intense turbulence, uniform mixing of the fluid with air, optimization of the geometric parameters of the nozzles and feed channels, as well as reduction of hydraulic losses in the foaming process. Thanks to this research, it is possible to obtain indicators that characterize the pattern of increasing air flow in proportion to increasing pressure. Compared with known analogues, the proposed foam generator, thanks to the variable geometric parameters of the mixing chamber and nozzles, allows to obtain foam mixtures with a wider range of properties. Such geometric changes provide better saturation of the fluid with air, create more intense turbulence, reduce hydraulic losses, and also increase the productivity and efficiency of well development.