Mathematical substantiation of pulsed electromagnetic soundings for new problems of petroleum geophysics

M. N. Nikitenko ; V. N. Glinskikh ; D. I. Gornostalev

Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 24 (2021) no. 2, pp. 179-192.

Résumé

This paper concerns the development of fundamental theoretical foundations and the creation of algorithms and software for pulsed electromagnetic soundings in relation to studying an unconventional source of hydrocarbons with hard-to-recover reserves — the Bazhenov formation. We carry out the mathematical substantiation of a new geophysical technology for the localization of oil-prospective zones, using a spatially distributed system of highly deviated wells. For the fast mathematical simulation, we obtained a solution to the problem of pulsed electromagnetic soundings in layered homogeneous models of media for an arbitrary current pulse in the electromagnetic source, which allows deep parallelization. Based on the created computational algorithm, a parallel one was developed, as well as a fast computer program for numerical simulation of the signals of the new system on multiprocessor devices of the Siberian Supercomputer Center, SB RAS. We carried out a large-scale numerical simulation and analysis of the signals in realistic geoelectric models of the Bazhenov formation to estimate an applicable scope of the new pulsed electromagnetic sounding installation. The calculations show that determining spatial locations of the formation boundaries is possible when logging the wells over a wide range of the sonde spacings. We analyzed the applicability of the diagonal and off-diagonal field components to ensure high sensitivity for mapping the reservoir boundaries and evaluating its internal heterogeneities. The results obtained form a basis for the further design of the optimal configuration of the new electromagnetic sounding system.

Bibliographie

[1] Braduchan Yu.V., Bulynnikova S.P., Vyachkileva N.P., Gol'bert A.V., Gurari F.G. i dr., “Bazhenovskii gorizont Zapadnoi Sibiri. Stratigrafiya, paleogeografiya, ekosistema, neftenosnost'”, Tr. IGiG SO AN SSSR, 649, ed. V.S. Vyshemirskii, Nauka, Sib. otd-nie, Novosibirsk, 1986

[2] Gurari F.G., “O poiskakh nefti i gaza v mezozoe Zapadno-Sibirskoi nizmennosti”, Tr. SNIIGGiMS, 17, Gostoptekhizdat, L., 1961, 81–92

[3] Kontorovich A.E., Berman E.L., Bogorodskaya L.I. i dr., Geokhimiya yurskikh i nizhnemelovykh otlozhenii Zapadno-Sibirskoi nizmennosti, Tr. SNIIGGiMS. Ser. Neftyanaya geologiya, 36, Nedra, M., 1971

[4] Epov M.I., Glinskikh V.N., Petrov A.M. i dr., “Chastotnaya dispersiya elektrofizicheskikh kharakteristik i elektricheskaya anizotropiya porod bazhenovskoi svity po dannym elektrokarotazha”, Neftyanoe khozyaistvo, 2019, no. 9, 62–64

[5] Epov M.I., Shurina E.P., Arkhipov D.A., “Parallel'nye konechnoelementnye vychislitel'nye skhemy v zadachakh geoelektriki”, Vychislitel'nye tekhnologii, 18:2 (2013), 95–112

[6] Glinskii B.M., Kostin V.I., Kuchin N.V., Solov'ev C.A., Cheverda V.A., “Organizaciya parallel'nykh vychislenii dlya resheniya uravneniya Gel'mgol'ca pryamym metodom s ispol'zovaniem malorangovoi approksimacii i HSS-formata”, Vychislitel'nye metody i programmirovanie, 16:4 (2015), 607–616

[7] Kostin V.I., Reshetova G.V., Cheverda V.A., “Chislennoe modelirovanie trekhmernogo akusticheskogo karotazha s ispol'zovaniem mnogoprocessornykh vychislitel'nykh sistem”, Matematicheskoe modelirovanie, 20:9 (2008), 51–67

[8] Belonosov M. A., Kostov C., Reshetova G. V., et al., “Parallel numerical simulation of seismic waves propagation with Intel Math Kernel Library”, Applied Parallel and Scientific Computing, Lecture Notes in Computer Science, 7782, 2013, 153–167 | DOI

[9] Puzyrev V., Koric S., Wilkin S., “Evaluation of parallel direct sparse linear solvers in electromagnetic geophysical problems”, Computers Geosciences, 89 (2016), 79–87 | DOI

[10] Urev M.V., “Skhodimost' diskretnoi skhemy v metode regulyarizacii kvazistacionarnoi sistemy Maksvella v neodnorodnoi provodyashchei srede”, Sib. zhurn. vychisl. matematiki, 14:3 (2011), 319–332 | MR | Zbl

[11] Tabarovskii L.A., Primenenie metoda integral'nykh uravnenii v zadachakh geoelektriki, Nauka, Sib. otd-nie, Novosibirsk, 1975

[12] Kaufman A.A., Morozova G.M., Teoreticheskie osnovy metoda zondirovanii stanovleniem polya v blizhnei zone, Nauka, Novosibirsk, 1970

[13] Il'in V.P., “O chislennom reshenii pryamykh i obratnykh zadach elektromagnitnoi georazvedki”, Sib. zhurn. vychisl. matematiki, 6:4 (2003), 381–394 | MR | Zbl

[14] Kabanikhin S., Inverse and ill-posed Problems: Theory and Applications, Inverse and Ill-Posed Problems Series, 55, De Gruyter, Berlin, 2011 | DOI | MR

[15] Vladimirov V.C., Uravneniya matematicheskoi fiziki, Nauka, M., 1981 | MR

[16] Kaufman A.A., Sokolov V.P., Teoriya indukcionnogo karotazha metodom perekhodnykh processov, Nedra, Novosibirsk, 1972

[17] Svetov B.S., Elektrodinamicheskie osnovy kvazistacionarnoi geoelektriki, IZMIRAN, M., 1984

[18] Mogilatov V.S., Potapov V.V., “Universal'noe matematicheskoe obespechenie dlya indukcionnogo karotazha”, Karotazhnik, 246:12 (2014), 76–90

[19] Lavrent'ev M.A., Shabat B.V., Metody teorii funkcii kompleksnogo peremennogo, Nedra, M., 1973 | MR

[20] Nikitenko M., Itskovich G., Seryakov A., “Fast electromagnetic modeling in cylindrically layered media excited by eccentred magnetic dipole”, Radio Science, 51:6 (2016), 573–588 | DOI