DOI: https://doi.org/10.24028/gzh.0203-3100.v37i2.2015.111299

A theory of hydrodynamic tomography

A.I. Kobrunov

Abstract


A problem of the forecast of spatial distribution of effective filtration resistance of permeable layer based on tomography principles is under consideration. Theoretical grounds of hydrodynamic tomography have been elaborated based on the data of hydrodynamic interception and analysis of dynamics of the fixed point on the curve of pressure renewal. Calculating schemes have been designed implementing the algorithm of solving a direct problem for calculation of interval travel time of the fixed point between the boreholes system for the specified distribution of piezoconductivity coefficient, as a problem of travel time minimization along the rays. Algorithm for solving the inverse problem based on the principle of algebraic tomography has been designed. Initial data for realization of hydrodynamic tomography algorithm can be synthesized in addition to direct experiment from the operation model of a deposit trained on its development history.


Keywords


filtration resistance; pizoconductivity coefficient; fixed point; interval time equation; hydrodynamic tomography; direct problem; algebraic tomography; regularization; operation model of a deposit; development history

References


Basniev K. S., Dmitriev N. M., Kanevskaya R. D., Maksimov V. M., 2006. Underground Hydromechanics. Moscow; Izhevsk: Institute of Computer Science Publ., 487 p. (in Russian).

Bogachov K. Yu., 2012. Effective solution of filtration of viscous compressible multiphase multicomponent mixtures on parallel computers: Dr. phys. and math. sci. diss. Moscow, 201 p. (in Russian).

Butkovskiy A. G., 1979. Characteristics of systems with distributed parameters. Moscow: Nauka, 219 p. (in Russian).

Goldin S. V., 1996. On the theory of radiation of seismic tomography. Part I: The Radon transform in the band and its treatment. Geologiya i geofizika 37(5), 3—18 (in Russian).

Gurvich I. I., Boganik G. N., 1980. Seismic exploration. Moscow: Nedra, 1680 p. (in Russian).

Ivanov V. K., Vasin V. V., Tanana V. P., 1978. Theory of linear ill-posed problems and its applications. Moscow: Nauka, 206 p. (in Russian).

Ipatov A. I., Kremenetskiy M. I., 2010. Geophysical and hydrodynamic control of the development of hydrocarbon deposits. Москва; Izhevsk: NITs «Regulyarnaya i haoticheskaya dinamika», 780 p. (in Russian).

Kanevskaya R. D., 2003. Mathematical modeling of hydrodynamic processes of development of hydrocarbon deposits. Moscow; Izhevsk: Institute of Computer Science Publ., 129 p. (in Russian).

Kobrunov A. I., 2013a. Kinematics of seepage flows and its applications for solving inverse problems Interference. Izvestiya Komi nauchnogo tsentra UrO RAN is. 4(16), 73—79 (in Russian).

Kobrunov A. I., 2012. Mathematical model tomography pressures in controlling the development of oil fields. Izvestiya Komi nauchnogo tsentra UrO RAN is. 4(12), 82—86 (in Russian).

Kobrunov A. I., 2013b. Mathematical models of systems analysis in applied geophysics. LAP LAMBERT. Saarbrcken, Deutchland: Academic Publ., 400 p. (in Russian).

Kobrunov A. I., Muhametdinov S. V., 2013. Mathematical models of evaluation of connectivity wells. Rassohinskie reading (Ukhta, 8—9 February 2013): Proc. of the Int. Seminar. Part 1. Ukhta: UGTU, P. 210—213 (in Russian).

Kobrunov A. I., Kudelin S. G., Drogobed A. N., 2013. Development of methods of hydrodynamic imaging. Rassohinskie reading (Ukhta, 8—9 February 2013): Proc. of the Int. Seminar. Part 1. Ukhta: UGTU, P. 221—224 (in Russian).

Krasnov V. A., Ivanov V. A., Khasanov M. M., 2012. Interference evaluation method according to the connectivity of the reservoir exploitation. SPE 1662053. Moscow. P. 1—6 (in Russian).

Marchuk G. I., Dymnikov V. P., Zalesny V. B., 1987. Mathematical models in geophysical fluid dynamics and numerical methods for their implementation. Leningrad: Gidrometeoizdat, 296 p. (in Russian).

Pat. 2092691 RF, IPC E21B047/00, 1997. A method for controlling seepage flows formed in the development of oil fields with layered strata. S. A. Kondarattsev, R. K. Muhamedshin, M. M. Khasanov, I. F. Hatmullin, N. I. Hisamutdinov, P. M. Galeev. № 95101668/03. Declared 10.02. 95. Published 10.10.97 (in Russian).

Pat. 2229020 RF, IPC E21V43/00, 2004. A method of detecting non-conductive elements of the oil reservoir at its operation. A. V. Shatskiy, V. V. Kolesov, I. M. Churinova, D. A. Shatskiy. № 2002129342/032002129342/03. Declared 05.11.2002. Published 20.05.2004 (in Russian).

Pat. 2298647 RF, IPC E21V47/10, 2005. Method study of oil reservoirs. A. V. Shatskiy, V. V. Kolesov, V. V. Denisov, D. A. Shatskiy, A. V. Bodryagin, S.V. Ivanov. № 2005111998/03. Declared 22.04.2005. Published 10.05.2007. Bull. № 13. 6 p. (in Russian).

Roslyak T. A., 2007. Development of oil and gas fields: study — method: posibie. Tomsk: TPU Publ., 66 p. (in Russian).

Tereshchenko S. A., 2004. Methods of computer tomography. Moscow: Fizmatlit, 319 p. (in Russian).

Tikhonov A. N., Arsenin V. Ya., 1974. Methods for solving ill-posed problems. Moscow: Nauka, 142 p. (in Russian).

Chodri A. N., 2011. Hydrodynamic studies of oil. Moscow: Ltd. «Premium Engineering», 687 p. (in Russian).

Shchelkachev V. N., 1995. Fundamentals and Applications of the theory of unsteady filtration. Part 1. Moscow: Neft i Gaz, 586 p. (in Russian).

Sheydegger A. E., 2008. Physicsoffluidflowsthroughporousmedia. Moscow; Izhevsk: Institute of Computer Science Publ., 249 p. (in Russian).

Kim J. S., Lake L. W., Edgar T. F., 2012. Integrated Capacitance — Resistance Model for Characterizing Water flooded Reservoirs. Proceedings of the 2012 IFAC Workshop on Automatic Control in Offshore Oil and Gas Production, Norwegian University of Scienceand Technology, Trondheim, Norway, May 31 — June 1, 2012, p. 19—24.