Quantitative interpretation of pulsed neutron capture logs : fast numerical simulation and inversion in thinly-bedded formations
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Pulsed neutron capture (PNC) logs are commonly used for formation evaluation behind casing and to assess time-lapse variations of hydrocarbon pore volume. Because conventional interpretation methods for sigma logs assume homogeneous formations, errors may arise, especially in thinly-bedded formations, when appraising petrophysical properties of hydrocarbon-bearing beds. There exist no quantitative interpretation methods to account for shoulder-bed effects on sigma logs acquired in sand-shale laminated reservoirs. Because of diffusion effects between dissimilar beds, sigma logs acquired in such formations do not obey mixing laws between the sigma responses of pure-sand and pure-shale end members of the sedimentary sequence. We introduce a new numerical method to simulate rapidly and accurately PNC logs. The method makes use of late-time, thermal-neutron flux sensitivity functions (FSFs) to describe the contribution of multi-layer formations toward the measured capture cross section. It includes a correction procedure based on 1D neutron diffusion theory that adapts the transport-equation-derived, base-case FSF of a homogeneous formation to simulate the response of vertically heterogeneous formations. Benchmarking exercises indicate that our simulation method yields average differences smaller than 2 c.u. within seconds of CPU time with respect to PNC logs simulated with rigorous Monte Carlo methods for a wide range of geometrical, petrophysical, and fluid properties. We develop an inversion method to reduce shoulder-bed effects on pulsed neutron capture (PNC) logs in the estimation of layer-by-layer capture cross sections, Σ. The method is based on the previously developed rapid approximation of PNC logs. Tests performed on synthetic examples that include a variety of lithology, saturating-fluid, and bed-thickness configurations confirm the efficiency, reliability, and stability of the inversion procedure. Inversion consistently improves the vertical resolution and Σ definition of PNC logs across beds thinner than 45 cm. Our fast, iterative algorithm inverts sigma logs in seconds of CPU time, and is therefore suitable for joint petrophysical interpretation with other open- and cased-hole logs.