Mathematical modeling problems connected with pulsed neutron-gamma logging



The work is devoted to direct and inverse problems of the transport equation in the context of a nuclear geophysical technology based on pulsed neutron-gamma logging of inelastic scattering (PNGL-IS). In the first part of the paper we analyze the distribution of fast neutrons from a pulsed source of 14.1 MeV and study distributions of gamma-quanta of inelastic scattering. The particle distributions are computed by the Monte Carlo methods. In the second part of the paper we consider the problem of evaluating the elemental composition of the rock from the PNGL-IS measurement data. In its solution we use the method of successive approximations over characteristic interactions, which can be classified as a simple iteration; at each iteration step we solve the corresponding direct problem for the system of neutron and gamma-quantum transport equations. The main aspects of the employed method and the results of the numerical experiments that prove the convergence to the exact solution are presented.


transport equation pulsed neutron-gamma log of inelastic scattering direct and inverse problems Monte Carlo methods successive approximations by the characteristic interactions 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    E. M. Filippov, Nuclear Geophysics (Nauka, Novosibirsk, 1973) [in Russian].Google Scholar
  2. 2.
    R. A. Rezvanov, Radioactive and Other Non-Electrical Methods for Well Survey (Nedra, Moscow, 1982) [in Russian].Google Scholar
  3. 3.
    G. Goertzel and M. H. Kalos, “Monte Carlo methods in transport problems” in Progress in Nuclear Energy, ed. by D. J. Hughes, J. E. Sanders, and J. Horowitz (Pergamon Press, New York, 1958), Vol. 1, Ser. 2.Google Scholar
  4. 4.
    J. Spanier and E. M. Celbard, Monte Carlo Principles and Neutron Transport Problems, (Addison-Wesley, Reading, Ma, 1969).MATHGoogle Scholar
  5. 5.
    Monte Carlo Method in the Problem of Radiation Transfer ed. by G. I. Marchuk (Atomizdat, Moscow, 1967) [in Russian].Google Scholar
  6. 6.
    A. I. Khisamutdinov, V. N. Starikov, and A. A. Morozov, Monte Carlo Algorithms in Nuclear Geophysics (Nauka, Novosibirsk, 1985) [in Russian].MATHGoogle Scholar
  7. 7.
    D. A. Kozhevnikov, Neutron Characteristics of Rocks and their Use in Oil and Gas Geology (Nedra, Moscow, 1982) [in Russian].Google Scholar
  8. 8.
    D. C. McKeon and H. D. Scott, “SNUPAR-a nuclear parameter code for nuclear geophysics applications,” Nucl. Sci. 36(1), 1215–1219, (1989).CrossRefGoogle Scholar
  9. 9.
    W. A. Gilchrist, E. Prati, R. Pemper, M. W. Mickael, D. Trcka, “Introduction of a new through-tubing multifunction pulsed neutron instrument,” in Trans. of SPE Annual Technical Conf. and Exhibition (SPE, Houston, 1999).Google Scholar
  10. 10.
    M. W. Michael, W. A. Gilchrist, R. J. Mirzwinski, G. N. Salaita, and R. T. Rajasingam, “Interpretation of the response of s new throw-tubing carbon/oxygen instrument using numerical modeling techniques,” at SPWLA 38th Annual Logging Symposium (SPWLA, Houston, 1997).Google Scholar
  11. 11.
    M. W. Michael, D. Trcka, and R. Pemper, “Dynamic multi-parameter interpretation of dual-detector carbon/oxygen measurements,” Trans. of SPE Annual Technical Conf. and Exhibition (SPE, Houston, 1999).Google Scholar
  12. 12.
    R. C. Hertzog, “Laboratory and Field Evaluation of An Inelastic Neutron Scattering and Capture Gamma Ray Spectroscopy Tool,” Sos. Petr. Eng. J. 20, 327–340 (1980).CrossRefGoogle Scholar
  13. 13.
    J. A. Grau and J. S. Schweitzer, “Elemental concentrations from thermal neutron capture gamma-ray spectra in geological formations,” Nucl. Geophys. 3(1), 1–9 (1989).Google Scholar
  14. 14.
    M. H. DeGroot, Optimal Statistical Decisions (McGraw-Hill, NewYork, 1970).MATHGoogle Scholar
  15. 15.
    A. N. Tikhonov and V.Ya. Arsenin, Methods for Solution of Ill-Posed Problems (Nauka, Moscow, 1986) [in Russian].Google Scholar
  16. 16.
    V. K. Ivanov, V. V. Vasin, and V. P. Tanana, Theory of Linear Ill-Posed Problems and its Applications (Nauka, Moscow, 1978) [in Russian].MATHGoogle Scholar
  17. 17.
    M. M. Lavrent’ev, V. G. Romanov, and S. P. Shishatskii, Ill-Posed Problems of Mathematical Physics and Analysis (Nauka, Moscow, 1980) [in Russian].MATHGoogle Scholar
  18. 18.
    G. I. Marchuk, Methods of Computational Mathematics (Nauka, Moscow, 1989) [in Russian].Google Scholar
  19. 19.
    V. F. Turchin, V. P. Kozlov, and M. S. Malkevich, “Using methods of mathematical statistics for solving ill-posed problems,” Usp. Fiz. Nauk 102(3), 33–55 (1970).Google Scholar
  20. 20.
    N. J. McCormick, “Inverse radiative transfer problems: as review,” Nucl. Sci. Eng. 112(3), 185–198 (1992).Google Scholar
  21. 21.
    T. A. Germogenova, “On inverse problems of atmospheric optics,” Dokl. Akad. Nauk SSSR 285(5), 1091–1096 (1985).MathSciNetGoogle Scholar
  22. 22.
    R. Sanchez and N. J. McCormick, “On the Inverse Source Problem for Linear Particle Transport,” in The 20th International Conference on Transport Theory. Book of Abstracts. Ed. by V. Ginkin and O. Ginkina (Obninsk, Russia, 2007).Google Scholar
  23. 23.
    G. I. Marchuk, “On the formulation of some inverse problems,” Dokl. Akad. Nauk SSSR 156(3), 503–506 (1964).MathSciNetGoogle Scholar
  24. 24.
    G. I. Marchuk, G. A., Mikhailov, and M. A. Nazaraliev, Monte Carlo Method in Atmospheric Optics, ed. By G. I. Marchuk (Nauka, Novosibirsk, 1976) [in Russian].Google Scholar
  25. 25.
    A. I. Khisamutdinov and E. B. Blankov, “Activation logging for oxygen, silicon, and aluminum, and the restoration of the fluid in the quartz-feldspar collectors,” Dokl. Akad. Nauk SSSR 309(3), 587–590 (1989).Google Scholar
  26. 26.
    A. I. Khisamutdinov and M. T. Minbaev, “Mathematical model and numerical method for identification of parameters of oil-and water-saturated layers based on the data of neutron activation logging,” Geol. Geofiz. 36(7), 73–85 (1995).Google Scholar
  27. 27.
    A. I. Khisamutdinov, “Numerical method of identifying parameters of oil-water saturation by nuclear logging,” Appl. Radiat. Isot., 50(3), 615–625 (1999).CrossRefGoogle Scholar
  28. 28.
    A. I. Khisamutdinov and M. A. Fedorin, “A numerical method for restoration of rock composition based on X-ray fluorescence data,” Dokl. Earth Sci. 392(7), 973–978 (2003).Google Scholar
  29. 29.
    A. I. Khisamutdinov, “On an approach to solving a few inverse problems of nuclear geophysics,” in Proceedings of the 19th ICTT (Budapest, 2005).Google Scholar
  30. 30.
    A. I. Khisamutdinov and A. I. Phedorin, “Numerical method of evaluating elemental content of oil-water saturated formations based on pulsed neutron-gamma inelastic log data,” SPE J SPE J. 14(1), 51–53 (2009).Google Scholar
  31. 31.
    A. I. Khisamutdinov, Characteristic Interaction and Successive Approximations in two problems for the Restoration of the Coefficients for the Equations of Transfer (and Composition of the Medium) (Geo, Novosibirsk, 2009) [in Russian].Google Scholar
  32. 32.
    A. I. Khisamutdinov, “Characteristic interactions and successive approximations in problems on evaluating coefficients of transport equations and elemental content of a medium,” J. Inv. Ill-Posed Probl., No. 19, 189–222 (2011).Google Scholar
  33. 33.
    Version 5. X-5 Monte Carlo Team. Diagnostics Applications Group ( Los Alamos National Laboratory, 2003).Google Scholar
  34. 34.
    A. I. Khisamutdinov, “The GGDL program and its application to investigatigation into the possibilities of double-beam gamma-gamma density logging,” in Monte Carlo Methods in Physics and Geophysics (BGU, Ufa, 1973), [in Russian].Google Scholar
  35. 35.
    A. I. Khisamutdinov, “GGL (gamma-gamma logging) program,” in Alg. Progr. No.2 (1974).Google Scholar
  36. 36.
    A. A. Morozov and A. I. Khisamutdinov, “Monte Carlo calculation of the photoneutron distribution,” At. Energ. 29(6), 449–450 (1970).CrossRefGoogle Scholar
  37. 37.
    B. V. Banzarov and A. I. Khisamutdinov, Certificate of state registration of computer programs No. 615224 (2010).Google Scholar
  38. 38.
    F. A. Alekseev, I. V. Golovatskaya, Yu. A. Gulin et al., Nuclear Geophysics in the Study of Oil Fields (Nedra, Moscow, 1978) [in Russian].Google Scholar
  39. 39.
    E. R. Cohen, “A survey of neutron thermalization theory,” in Proceedings of the First United Nations International Conference on the Peaceful Uses of Atomic Energy (UN New York, 1956).Google Scholar
  40. 40.
    R. Woodhouse and S. A. Kerr, “The evaluation of oil saturation through casing using carbon/oxygen logs,” in Proceedings of International Meeting on Petroleum Engineering (Tianjin, China, 1988)Google Scholar
  41. 41.
    R. C. Odom, R. D. Wilson, and R. K. Ladtkow, “Log examples with a prototype three-detector pulsed-neutron system for measurement of cased-hole neutron and density porosities,” in Proeedings of SPE Rocky Mountain Petroleum Technology Conference, (Keystone, Colorado, 2001).Google Scholar
  42. 42.
    M. M. Herron, “Geochemical classification of terrigenous sands and shales from core or log data,” J. Sed. Petrol. 58(1), 820–829 (1988).MathSciNetGoogle Scholar
  43. 43.
    S. Agostinelli et al. “Geant4: a simulation toolkit,” NIM A 506(3), 250–303 (2003).CrossRefGoogle Scholar
  44. 44.
    A. I. Khisamutdinov, B. V. Banzarov, and M. A. Fedorin, “Mathematical modeling of non-stationary problems of particle transport in a pulsed neutron-gamma logging,” Preprint (A. Trofimuk Institute of Petroleum Geology and Geophysics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, 2008).Google Scholar
  45. 45.
    L. P. Abagyan, N. O. Bazazyants, I. I. Bondarenko, and M. N. Nikolaev, Group Constants for Calculations of Nuclear Reactors (Atomizdat, Moscow, 1964) [in Russian].Google Scholar
  46. 46.
    M. J. Berger, J. H. Hubbell, S. M. Seltzer, J. S. Coursey, D. S. Zucker.
  47. 47.
    A. I. Khisamutdinov and B. V. Banzarov, “Non-simulational evaluation and improving the methods of mathematical expectations for statistical modeling of particle transport,” Vych. Tekhnol. 17(2), 99–114 (2012).Google Scholar
  48. 48.
    A. I. Khisamutdinov, Unbiased Estimates in Monte Carlo Methods for Integral Equations (Computing Center, Siberian Branch of the USSR Academy of Sciences, Novosibirsk, 1986) [in Russian].Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2015

Authors and Affiliations

  1. 1.Trofimuk Institute of Petroleum Geology and Geophysics, Siberian Branchthe Russian Academy of SciencesNovosibirskRussia

Personalised recommendations