Accurate inversion of elemental concentrations from the pulsed neutron geochemical logging based on an active-set method

Since the mineral compositions can be obtained from the concentrations of the major elements in the formation, the accurate determination of the elemental concentration is very critical to the reservoir evaluation. However, it is always a challenge to accurately obtain the concentrations of major elements in the complex lithology or unconventional reservoirs (such as shale gas reservoirs) due to the complexity of lithology and the limitation of the current data processing method. The widely used weighted least squares (WLS) method, which is applied in the quantitative energy spectral processing for the pulsed neutron geochemical logging, suffers the absence of constraint condition of the solution variables and thus it is hardly to determine the elemental concentrations in a high precision and accuracy. In this paper, we introduced an active-set method (ASM) to improve the inversion accuracy after transforming the inversion problem into a quadratic programming problem with constraints. The ASM is capable of constraining the solution variables within reasonable boundary limits, and thus the high-precision elemental yields can be determined by the iterative processing. The conversion of elemental yields into elemental concentrations is accomplished via an oxide closure model and a pseudo-capture spectrum method. To verify the applicability, we numerically obtained the capture and inelastic spectra by the Monte Carlo simulation from three formation models with different porosities: simple formation, complex lithology formation, and unconventional formation models. Then the ASM and WLS methods are used to process both the capture and inelastic spectra in different models. The results comparison between the two methods shows that the elemental concentrations inverted by using the ASM are more accurate than those determined by using the WLS method. Finally, a field logging data set is processed by the ASM, and the results indicate the feasibility of the inversion result from the ASM from the pulsed neutron geochemical logging.