Purpose of the study. Optimization of the parameters of high speed fan units of air coolers, the combination of which achieves the highest economic efficiency of fan units and, accordingly, the most rational range of specific speed values for the modes of maximum efficiency of fan units in combination with the relative diameter of the sleeve. Development of a mathematical model for determining the local values of the parameters of the efficiency of highspeed fan installations. Sustainable development of territories with active subsoil use is closely related to solving the problems of improving industrial safety and the efficiency of cooling the compressed gas at compressor stations of main gas pipelines, which actualizes the problem of mathematical modeling of energy conversion processes in the impellers of fan units of gas air coolers (AVO) to increase the competitiveness of the oil and gas complex RF in the context of globalization. Research methods. To optimize and determine the limiting combination of calculated parameters, the mathematical method of searching for the area of local maxima of a multiparameter problem in this part was performed in two stages: a mathematical model was built for determining the local values of the parameters that ensure the highest efficiency of fan installations with high speed; the most rational limiting combination of design parameters was determined, at which the highest economic efficiency of fan installations is achieved. Research results. The possibility of increasing the economic efficiency of axial fan units of high speed, made according to aerodynamic schemes with one impeller for gas air cooling devices, has been established. Using the mathematical analysis of the basic laws of axial turbomachines, equations for the efficiency of a fan unit and a fan are obtained, depending on the specific speed. Formulas are obtained for the maximum values of the efficiency of the fan and the fan unit of various specific speed depending on the coefficient of the consumpconsumption speed and on the relative diameter of the impeller sleeve. A method is proposed for constructing aerodynamic schemes of axial fan units for air-cooled gas coolers of the "K" type with maximum maximum values of efficiency for given values of specific speed, relative diameter of the impeller sleeve, aerodynamic quality of the impeller profiles, coefficient of aerodynamic resistance of the flow path of the coefficient of flow velocity. The possibility of creating a fan installation with a speed of ny ≥ 400 with an efficiency of at least ηy=0,86. Application area. Enterprises of the oil and gas complex of the Russian Federation for cooling compressed gas using AVO compressor stations of main gas pipelines.