Optimization of Computations for Modeling and Inversion in NMR T2 Relaxometry

  • L. MuravyevEmail author
  • S. Zhakov
  • D. Byzov
Conference paper
Part of the Springer Proceedings in Earth and Environmental Sciences book series (SPEES)


Great success is achieved currently in the using of NMR relaxometry for detecting and distinguishing of reservoir fluids, for example, free and bound water, oil. NMR data enable petrophysicists, specialists in the development of deposits and geologists to study the types of fluids and their distribution in a reservoir that has been opened by a well. NMR allows identifying the intervals in which hydrocarbons are present and predict their recoverability. The investigations carried out in this work are aimed at the optimizing of calculating time for the integrals arising in the NMR forward and inversion problems, while preserving the predetermined error. The method of the Legendre polynomial expansion application for the solution of the problem of modeling relaxation curves in the NMR method is described. This tool makes it possible to reduce significantly the computational complexity of the relaxation curve calculation, and hence the calculation time in comparison with numerical integration methods. In addition, numerical methods do not allow to pre-select the parameters for partitioning a segment to achieve a given error. Since the method described in this paper uses an analytic expression for the integral, the calculation accuracy depends only on the integration error. The given approximation error is achieved due to the choice of the maximum degree of the polynomial at the stage of calculating the coefficients of the series of the Legendre polynomials.


NMR Petrophysics Relaxation time CPMG 



The authors are grateful to Corresponding Member of RAS, prof P.S.Martyshko for general guidance and VA.Vavilin and V.M.Mursakayev for a valuable discussion.


  1. Borgia, G. C., Brown, R. J. S., Fantazzini P. (1998). Uniform-Penalty Inversion of Multiexponential Decay Data. Journal of magnetic resonance 132, p. 65–77.CrossRefGoogle Scholar
  2. Coates, G.R., Xiao Lizhi, Prammer, M.G. (2000). NMR Logging. Principles & applications. Hulliburton Energy Services Publishing, Houston (USA). 234 p.Google Scholar
  3. Farrer, T. C., Becker, E. D. (1971). Pulse and Fourier Transform NMR: Introduction to Theory and Methods. New York and London, Academic Press. 118 p.Google Scholar
  4. Gang Yu, Zhizhan Wang, K. Mirotchnik, Lifa Li (2006). Application of Magnetic Resonance Mud Logging for Rapid Reservoir Evaluation. Poster presentation at AAPG Annual Convention, Houston, Texas, April 9–12.Google Scholar
  5. Himmelblau, D. (1972). Applied nonlinear programming. McGraw-Hill. 498 p.Google Scholar
  6. Mirotchnik, K., Kryuchkov, S., Strack, K. (2004). A Novel Method to Determine NMR Petrophysical Parameters From Drill Cuttings. SPWLA 45th Annual Logging Symposium. Pare MM.Google Scholar
  7. Muravyev, L.A., Zhakov, S.V. (2016). Methodical issues of investigations with laboratory NMR relaxometer. Geoinformatics 2016: XVth International Conference on Geoinformatics - Theoretical and Applied Aspects. Ukraine.
  8. Lawson, C.L., Hanson, R.J. (1974). Solving Least Squares Problems, Prentice-Hall.Google Scholar
  9. Provencher, S.W. (1982). CONTIN: A general purpose constrained regularization program for inverting noisy linear algebraic and integral equations. Comput. Phys. Commun. 27, 229.CrossRefGoogle Scholar
  10. Rafael Salaezar-Tio, Bogin Sun (2010). Monte Carlo optimazation-inversion methods for NMR. Petrophysics, vol.51, no.3,. pp. 208–218.Google Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Ural Federal UniversityEkaterinburgRussia
  2. 2.Institute of Metal Physics of Ural Branch of Russian Academy of SciencesEkaterinburgRussia
  3. 3.Institute of Geophysics Ural Branch of RASEkaterinburgRussia

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