Optimization of Computations for Modeling and Inversion in NMR T2 Relaxometry

Abstract

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.