The study is devoted to the mathematical description of the process of oil outflow in places of leakage of the tubing string, which allows a computer to locate a leakage in the tubing.
The authors propose methodology for identifying defects in the tubing and determining the location of the leak. The uniqueness of this methodology lies in quick determination of the place of leakage without the use of specialists, sophisticated and specialized equipment.
Mathematical modeling of oil flow in the tubing requires the apparatus of continuum mechanics. It is a general belief that the movement of oil in the pipe flows at low speeds due to its outflow from the hole. Using the general equations of mass and energy balance, the authors have obtained differential equations of fluid motion in a vertical pipe in the process of its outflow from the tubing and in the process of injection. Analytical expressions are the solution to these equations, as they can help in estimating the degree of damage and its location, as well as the feasibility of its eliminating.
The results show that an increase in the leakage and injection times leads to improving accuracy of locating damage. Thus, when conducting various geological and technical measures (GTM) at the well, it is possible to assess the presence of leakage and its intensity when deciding on the repair of tubing.
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