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Solution of the inverse problem of self-polarization logging in a pack of layers with a penetration zone (terrigenous section)

UDK: 550.832.77
DOI: 10.24887/0028-2448-2019-10-38-41
Key words: direct and inverse problem, potential of spontaneous polarization, static potential, electrical resistivity, penetration zone, coefficient of oil and gas saturation
Authors: O.B. Kuzmichev (RN BashNIPIneft LLC, RF, Ufa), A.V. Zhonin (RN BashNIPIneft LLC, RF, Ufa), Yu.V. Martynova (RN BashNIPIneft LLC, RF, Ufa), S.A. Kolomasova (RN BashNIPIneft LLC, RF, Ufa)

In layers of limited thickness and high resistance, the amplitude of the spontaneous potential (SP) logs differs significantly from the amplitude corresponding to the layer of unlimited thickness. For a more accurate determination of reservoir properties by the SP method it is necessary to move from the apparent values of the curve to the static potential of the reservoir, that is, to solve the inverse problem.

The article presents an analytical solution for a direct problem of the SP method in case of rocks in a well crossing an electrically inhomogeneous layer of limited thickness with a zone of drilling mud penetration. The analytical solution of a similar problem proposed by Schlumberger-Doll Research (M.R. Taherian, at al.) for an impenetrable formation in the absence of penetration zone is discussed. It is shown Schlumberger’s solution is a subcase of the analytical solution regarded in present article. On the basis of the analytical solution of the direct problem the inverse problem of the SP method was solved taking into account the potentials of rock matrix. Solving the inverse problem in conjunction with the electric logging data is shown on the example of middle Cretaceous reservoirs (Achimov deposits) in Western Siberia. For this purpose we used algorithms of numerical solution of the direct problem in case of well crossing an electrically inhomogeneous layer of limited thickness with a zone of drilling mud penetration by the integro-interpolation method, and the analytical solution of the direct problem for a layer of limited thickness with regard to the potential of rock matrix. The results of numerical and analytical solutions of the inverse problem are almost identical. Proposed algorithms are intended to use in the Rosneft corporate software for petrophysical modeling.

References

1. Nosal E.A., Spontaneous potential log response expressed as convolution, Geophysics, 1982, V. 47, no. 9, pp. 1335–1337.

2. Doll H.G., Selective SP logging, AIME Trans., 1950, V. 189, pp. 129–141.

3. Kashik A.S., Informative adequacy-of measurements in applied geophysics (In Russ.), Geofizika, 2007, no. 4, pp. 7–14.

4. Shpikalov Yu.A., Solving the inverse problem of the method of self-polarization potentials in the well using mathematical filtering (In Russ.), Neftegazovaya geologiya i geofizika, 1980, no. 6, pp. 37–40.

5. Abrikosov A.I., The direct problem of the distribution of the field of potentials of intrinsic polarization in the well in inhomogeneous media (In Russ.), Neftegazovaya geologiya i geofizika, 1978, no. 6, pp. 24–27.

6. Taherian M.R. et al., Spontaneous potential: Laboratory experiments

and modeling results, The Log Analyst, 1995, V. 36, no. 5, pp. 34–48.

7. Vendel'shteyn B.Yu., Issledovanie razrezov neftyanykh i gazovykh skvazhin metodom sobstvennykh potentsialov (Research of sections of oil and gas wells by the method of intrinsic potentials), Moscow: Nedra Publ., 1966, 206 p.

8. Kuz'michev O.B., Issledovanie estestvennykh elektricheskikh poley v neftegazorazvedochnykh skvazhinakh (teoriya, apparatura, metodika, skvazhinnye ispytaniya) (The study of natural electric fields in the oil and gas exploration wells (theory, apparatus, method, well tested)), St. Petersburg, Nedra Publ., 2006, 252 p.

9. Kuz'michev O.B., Theoretical grounds of spontaneous polarization in oil and gas prospecting wells: from homogeneous to heterogeneous according to medium resistance (In Russ.), Geologiya, geofizika i razrabotka neftyanykh i gazovykh mestorozhdeniy, 2013, no. 9, pp. 37–42.

10. Ingerman V.G., Avtomatizirovannaya interpretatsiya rezul'tatov geofizicheskikh issledovaniy skvazhin (Automated interpretation of results of geophysical well survey), Moscow: Nedra Publ., 1981, – 224 s.

11. Metodicheskie ukazaniya po kompleksnoy interpretatsii dannykh BKZ, BK, IK (Guidelines for the comprehensive interpretation of data lateral logging sounding, lateral logging, induction log), Kalinin: Publ. of NPO Soyuzpromgeofizika, 1990, 85 p.

12. Levchenko A.A., Pantyukhin V.A., Chaadaev E.V., Opredelenie prodol'nykh udel'nykh elektricheskikh soprotivleniy sloistykh plastov-kollektorov po dannym metodov karotazha soprotivleniy (Determination of longitudinal specific electrical resistances of layered reservoirs according to resistance logging methods), Collected papers “Novye razrabotki v tekhnologii geofizicheskikh issledovaniy neftegazorazvedochnykh skvazhin” (New developments in the technology of geophysical exploration of oil and gas exploration wells), Tver': Publ of NPGP GERS, VNIGIK, 1992, pp. 119–124.

13. Potapov A.P., Kneller L.E., Determination of resistivity of reservoirs according to high frequency induction logging data in a thin-layered section (In Russ.), Karotazhnik, 1998, V. 52, pp. 62–67.

14. Patent no. RU2675187C1, Method for determining saturation of low-permeability reservoirs, Inventors: Kolonskikh A.V., Zhonin A.V., Mikhaylov S.P., Fedorov A.I., Murtazin R.R.

15. Antonov Yu.N., Sokolov V.P., Tabarovskiy L.A., Obobshchenie teorii geometricheskogo faktora. Elektromagnitnye metody issledovaniya skvazhin (A generalization of the theory of geometric factor. Electromagnetic Well Research Methods), Novosibirsk: Nauka Publ., 1979, pp. 34–51.

In layers of limited thickness and high resistance, the amplitude of the spontaneous potential (SP) logs differs significantly from the amplitude corresponding to the layer of unlimited thickness. For a more accurate determination of reservoir properties by the SP method it is necessary to move from the apparent values of the curve to the static potential of the reservoir, that is, to solve the inverse problem.

The article presents an analytical solution for a direct problem of the SP method in case of rocks in a well crossing an electrically inhomogeneous layer of limited thickness with a zone of drilling mud penetration. The analytical solution of a similar problem proposed by Schlumberger-Doll Research (M.R. Taherian, at al.) for an impenetrable formation in the absence of penetration zone is discussed. It is shown Schlumberger’s solution is a subcase of the analytical solution regarded in present article. On the basis of the analytical solution of the direct problem the inverse problem of the SP method was solved taking into account the potentials of rock matrix. Solving the inverse problem in conjunction with the electric logging data is shown on the example of middle Cretaceous reservoirs (Achimov deposits) in Western Siberia. For this purpose we used algorithms of numerical solution of the direct problem in case of well crossing an electrically inhomogeneous layer of limited thickness with a zone of drilling mud penetration by the integro-interpolation method, and the analytical solution of the direct problem for a layer of limited thickness with regard to the potential of rock matrix. The results of numerical and analytical solutions of the inverse problem are almost identical. Proposed algorithms are intended to use in the Rosneft corporate software for petrophysical modeling.

References

1. Nosal E.A., Spontaneous potential log response expressed as convolution, Geophysics, 1982, V. 47, no. 9, pp. 1335–1337.

2. Doll H.G., Selective SP logging, AIME Trans., 1950, V. 189, pp. 129–141.

3. Kashik A.S., Informative adequacy-of measurements in applied geophysics (In Russ.), Geofizika, 2007, no. 4, pp. 7–14.

4. Shpikalov Yu.A., Solving the inverse problem of the method of self-polarization potentials in the well using mathematical filtering (In Russ.), Neftegazovaya geologiya i geofizika, 1980, no. 6, pp. 37–40.

5. Abrikosov A.I., The direct problem of the distribution of the field of potentials of intrinsic polarization in the well in inhomogeneous media (In Russ.), Neftegazovaya geologiya i geofizika, 1978, no. 6, pp. 24–27.

6. Taherian M.R. et al., Spontaneous potential: Laboratory experiments

and modeling results, The Log Analyst, 1995, V. 36, no. 5, pp. 34–48.

7. Vendel'shteyn B.Yu., Issledovanie razrezov neftyanykh i gazovykh skvazhin metodom sobstvennykh potentsialov (Research of sections of oil and gas wells by the method of intrinsic potentials), Moscow: Nedra Publ., 1966, 206 p.

8. Kuz'michev O.B., Issledovanie estestvennykh elektricheskikh poley v neftegazorazvedochnykh skvazhinakh (teoriya, apparatura, metodika, skvazhinnye ispytaniya) (The study of natural electric fields in the oil and gas exploration wells (theory, apparatus, method, well tested)), St. Petersburg, Nedra Publ., 2006, 252 p.

9. Kuz'michev O.B., Theoretical grounds of spontaneous polarization in oil and gas prospecting wells: from homogeneous to heterogeneous according to medium resistance (In Russ.), Geologiya, geofizika i razrabotka neftyanykh i gazovykh mestorozhdeniy, 2013, no. 9, pp. 37–42.

10. Ingerman V.G., Avtomatizirovannaya interpretatsiya rezul'tatov geofizicheskikh issledovaniy skvazhin (Automated interpretation of results of geophysical well survey), Moscow: Nedra Publ., 1981, – 224 s.

11. Metodicheskie ukazaniya po kompleksnoy interpretatsii dannykh BKZ, BK, IK (Guidelines for the comprehensive interpretation of data lateral logging sounding, lateral logging, induction log), Kalinin: Publ. of NPO Soyuzpromgeofizika, 1990, 85 p.

12. Levchenko A.A., Pantyukhin V.A., Chaadaev E.V., Opredelenie prodol'nykh udel'nykh elektricheskikh soprotivleniy sloistykh plastov-kollektorov po dannym metodov karotazha soprotivleniy (Determination of longitudinal specific electrical resistances of layered reservoirs according to resistance logging methods), Collected papers “Novye razrabotki v tekhnologii geofizicheskikh issledovaniy neftegazorazvedochnykh skvazhin” (New developments in the technology of geophysical exploration of oil and gas exploration wells), Tver': Publ of NPGP GERS, VNIGIK, 1992, pp. 119–124.

13. Potapov A.P., Kneller L.E., Determination of resistivity of reservoirs according to high frequency induction logging data in a thin-layered section (In Russ.), Karotazhnik, 1998, V. 52, pp. 62–67.

14. Patent no. RU2675187C1, Method for determining saturation of low-permeability reservoirs, Inventors: Kolonskikh A.V., Zhonin A.V., Mikhaylov S.P., Fedorov A.I., Murtazin R.R.

15. Antonov Yu.N., Sokolov V.P., Tabarovskiy L.A., Obobshchenie teorii geometricheskogo faktora. Elektromagnitnye metody issledovaniya skvazhin (A generalization of the theory of geometric factor. Electromagnetic Well Research Methods), Novosibirsk: Nauka Publ., 1979, pp. 34–51.



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