Asymptotic method for finding the coefficient of hydraulic resistance in lifting of fluid on tubing

In this work the process of gas-lift in the oil production is considered. The process is described by partial differential equations of hyperbolic type. A small parameter is introduced, which is the inverse of the well depth. Gas-lift process is investigated behind the front of sound wave. The initial system of hyperbolic equations is reduced to the nonlinear ordinary differential equation (NODE) of the first order relatively to the gas volume and gas liquid (GLM), which depends on the coordinates of wells and hydraulic resistance coefficient (HRC). An asymptotic solution of NODE is obtained and this solution is calculated at the point. It is shown that for the determination of HRC statistical data of well is required (volume of injected gas at the wellhead of the annular space and GLM at the end of lift (debit)). Then on the basis of these results, by constituting the corresponding functional, which is the quadratic deviation of the statistics and calculated asymptotic solutions, the functional gradient is derived that allows one to calculate HRC in first approximation relative to small parameter. An example for the specific case from the practice shows that HRC in first approximation differs from the value on the order of 10