A model problem of the permeability field identification for a three-dimensional reservoir opened by a large number of wells in the conditions of stationary single-phase fluid filtration is considered. The permeability field is determined in the process of solving the inverse coefficient problem by on known values of bottomhole pressure. The solving problem algorithm is constructed so that the proportionality coefficients of the layers permeability on wells obtained from the results of geophysical well survey are preserved. The influence of various types of errors on the identification results is studied.
Inverse problem, permeability identification, spline-function
- Ashkenazy V.O. (2003). Spline Surfaces: Fundamentals of Theory and Computational Algorithms. Tver: Tverskoi gos. un-t., 82 p. (In Russ.)
- Aziz Kh., Settari E. (1982). Petroleum Reservoir Simulation. Moscow: Nedra, 407 p. (In Russ.)
- Bulygin D.V., Bulygin V.Ya. (1996). Geology and simulation of oil reservoir development. Moscow: Nedra, 382 p. (In Russ.)
- Carrera J., Newman Sh.P. (1986). Estimation of Aquifer Parameters Under Transient and Steady State Conditions: 3. Application to Synthetic and Field Data. Water Resour. Res., 22(2), pp. 228–242.
- Dakhnov V.N. (1985). Geophysical methods for determining reservoir properties and oil and gas saturation of rocks. Moscow: Nedra, 310 p. (In Russ.)
- Dennis J.E., Shnabel R. (1988). Numerical Methods for Unconstrained Optimization and Nonlinear Equations. Moscow: Mir, 440 p. (In Russ.)
- Elesin A.V., Kadyrova A.Sh. (2017). The Levenberg-Marquartd Method in the Problem of Identifying the Absolute Penetrability Coefficient of a Bed Under Conditions of Two-Phase Filtration. Journal of Engineering Physics and Thermophysics, 90(6), pp. 1362–1368.
- Elesin A.V., Kadyrova A.Sh., Mazuro P.A. (2009). The two-step Levenberg-Marquardt methods in hydraulic conductivity identification task. Georesursy = Georesources, 4(32), pp. 40–42. (In Russ.)
- Elesin A.V., Kadyrova A.Sh., Nikiforov A.I. (2018). Definition of the reservoir permeability field according to pressure measurements on wells with the use of spline function. Georesursy = Georesources, 20(2), pp. 102–107. https://doi.org/10.18599/grs.2018.2.102-107
- Golub G.H., Van Loan Ch. (1999). Matrix Computations. Moscow: Mir. 548 p. (In Russ.)
- Golubev G.V., Danilaev P.G., Tumashev G.G. (1978). Determination of hydraulic conductivity of heterogeneous oil reservoirs by non-local methods. Kazan: Kazan University, 168 p. (In Russ.)
- Larabi A., De Smedt F. (1994). Solving three-dimensional hexahedral finite element groundwater models by preconditioned conjugate gradient methods. Water Resour. Res., 30(2), pp. 509–521.
- Oliver D.S., Reynolds A.C., Liu N. (2008). Inverse Theory for Petroleum Reservoir Characterization and History Matching. New York: Cambridge University Press, 394 p.
- Panarina E.P., Mel’nikov S.I., Kremenetskii M.I. (2016). Individual assessment of parameters of jointly operated formations based on dynamic analysis of geophysical and hydrodynamic studies. Karotazhnik, 2(260), pp. 45–56. (In Russ.)
- Peaceman D.W. (1978). Interpretation of well block pressures in numerical reservoir simulation. Soc. Petrol. Eng. Journal, 18(3), pp. 183–194.
- Romm E.S. (1985). Structural models of the pore space of rocks. Leningrad: Nedra, 240 p. (In Russ.)
- Shiryaev I.M., Zakirov E.S., Indrupskiy I.M. (2019). Study of geologically consistent history matching peculiarities by means of gradient-free optimization methods. IOP Journal of Physics: Conference Series, 1391, 012146.
- Shvidler M.I. (1985). Statistical hydrodynamics of porous media. Moscow: Nedra, 288 p. (In Russ.)
- Stepanov S.V. (2005). History matching of a hydrodynamics model of an oil bed on the basis of a variational problem solution. Matematicheskoe modelirovanie, 17(12), pp. 110–118. (In Russ.)
- Sun N.-Z. (1994). Inverse Problems in Groundwater Modeling. Kluwer Acad., Dordrecht, Netherlands, 337 p.
- Tikhonov A.P., Arsenin V.Ya. (1979). Methods for solving ill-posed problems. Moscow: Nauka, 288 p. (In Russ.)
- Yeh W.W-G. (1986). Review of parameter identification procedures in groundwater hydrology: The inverse problem. Water Resour. Res., 22(2), pp. 95–108.
- Zakirov E.S. (2001). Three-dimensional multiphase problems of forecasting, analyzing and regulating the development of oil and gas fields. Moscow: Graal, 303 p. (In Russ.)
- Zakirov E.S., Indrupskiy I.M., Liubimova O.V. et al. (2017). Geostatistically consistent history matching of 3D oil-and-gas reservoir models. Doklady Earth Sciences, 476(2), pp. 1120–1124.
- Zinoviev N.P. (1984). Identification of hydraulic conductivity in the case of an elastic filtration regime in an oil reservoir. Issled. po prikl. matem., 11, part 2, pp. 78–84. (In Russ.)
-
Andrey V. Elesin
Institute of Mechanics and Engineering, FRC Kazan Scientific Center of the Russian Academy of Sciences
2/31, Lobachevsky st., Kazan, 420111, Russian Federation
e-mail: elesin@imm.knc.ru
Alfiya Sh. Kadyrova
Institute of Mechanics and Engineering, FRC Kazan Scientific Center of the Russian Academy of Sciences
2/31, Lobachevsky st., Kazan, 420111, Russian Federation
Anatoly I. Nikiforov
Institute of Mechanics and Engineering, FRC Kazan Scientific Center of the Russian Academy of Sciences
2/31, Lobachevsky st., Kazan, 420111, Russian Federation
Elesin A.V., Kadyrova A.Sh., Nikiforov A.I. (2021). Identification of the permeability field for three-dimensional reservoir using the results of geophysical well survey. Georesursy = Georesources, 23(1), pp. 106–111. DOI: https://doi.org/10.18599/grs.2021.1.11