# Features of Mathematical Modelling of Hydrodynamic Research of Oil Layers

V.P.Tanana, A.V. BokovThe oil field reserves estimation is carried out by experts of geological services in terms of hydrodynamic researches of oil layers. Existing techniques are aimed at determining the hydraulic conductivity of oil-bearing layer and well productivity according to their short-term operation. Different methods are used for processing the results of measurement, in particular those based on the numerical solution of direct and inverse filtering. In solving the problem of determining the coefficient of hydraulic conductivity using numerical methods we should take into account the features of underground fluid mechanics. These features should be considered when we work out a mathematical model of the process and during the development of algorithms for its numerical solution. A number of conditions can specify the problem of determining the coefficient of hydraulic conductivity as the inverse problem of nonlinear hydrodynamics. The essential part for solving this problem is to prove the uniqueness of the solution. In this paper, we state the conditions for the inverse filtering with mixed boundary conditions that guarantee the uniqueness of the solution.Full text

- Keywords
- hydrodynamic methods of research of wells, mathematical model, inverse problem of filtration, uniqueness of the solution of the inverse problem.
- References
- 1. Tanana V.P., Bokov A.V. About the Only Solution of Inverse Problems of Unsteady Filtration [O edinstvennosti resheniya obratnoy zadachi nestatsionarnoy fil'tratsii]. Rukopis' deponirovana v VINITI, 1996, no. 1290-В96.

2. Bokov, A.V. About the Only Solution of Inverse Problems of Unsteady Filtration [O edinstvennosti resheniya obratnoy zadachi nestatsionarnoy fil'tratsii]. Bulletin of the South Ural State University. Series "Computational Mathematics and Software Engineering", 2012, no. 47 (306), issue 2, pp. 12-21.

3. Stepanov V.V. Kurs differentsialnykh uravneniy [Course on Differential Equations]. Moscow, GTTI, 1938. 376 p.

4. Martynenko N.A., Pustyl'nikov L.M. Konechnye integral'nye preobrazovanija i ih primenenie k issledovaniju sistem s raspredelennymi parametrami [Finite Integral Transformations and their Application to the Study of Systems with Distributed Parameter]. Moscow, Nauka, 1986. 304 p.

5. Levitan, B.M., Sargosyan I.S. Vvedenie v spektral'nuyu teoriyu [Introduction to Spectral Theory]. Moscow, Nauka, 1970. 672 p.

6. Levinson, N. The Inverse Sturm-Liouville Problem. Math. Tidsskr. Ser. B.,1949, vol. 13, pp. 25-30.