A Method for Formation Elemental Concentration Determination Based on the Macroscopic Capture Cross-Section Constraint

Efficient and accurate formation elemental concentration and mineralogy measurement are indispensable for reservoir evaluation and geological understanding. Pulsed neutron logging based on neutron-induced gamma-ray measurement has been widely used to determine the formation compositions. The neutrons produced from the instrumental pulsed neutron generator (PNG) can interact with the surrounding formation nuclei by inelastic scattering and thermal-neutron capture. Then, the excited nuclei can emit elemental characteristic gamma rays, which are recorded as inelastic or capture spectroscopy by the scintillation detector. The spectrum measured downhole is a mixture of the characteristic spectra of all the formation elements. The measured spectrum can be decomposed by mathematical methods to obtain the elemental relative yield of each element, and the elemental concentrations can be determined using oxide closure or inelastic-capture closure combined with the elemental sensitivities. However, one of the challenging problems for elemental concentration determination is the multi-solution in the inversion. When employing an algorithm, such as linear least-squares, to solve multicomponent spectroscopy, small errors or noise can easily cause large oscillations in the result. As a typical discrete ill-posed problem, additional constraints are required to get the most appropriate solution. Fortunately, current pulsed neutron instruments can collect energy and time spectra in one measurement. In addition to the solved elemental relative yields, the macroscopic capture cross section (Sigma) extracted from the capture time spectrum is also an effective feature to reflect the elemental concentration of the formation. Therefore, a method for formation elemental concentration determination based on the macroscopic capture cross-section constraint was developed to overcome the multi-solution in the traditional inversion. In the proposed method, a swarm intelligent optimization algorithm is introduced to decompose the multicomponent spectroscopy by constructing an adequate objective function. This kind of algorithm can solve complex optimization problems due to the global search ability, robustness, and self- adaptability. The objective function of this problem represents the weighted sum of the spectral decomposition error and the Sigma conversion error relative to the measured Sigma, and the solution of the objective function is the relative yield of each formation element. In each iteration, the formation compositions can be obtained using the elemental characteristic spectra so that the formation Sigma can be converted from the determined formation compositions combined with the reservoir parameters such as saturation, salinity, and porosity to compare with the measured Sigma. In the optimization, the measured formation Sigma is a strong constraint. The objective function for solving the optimal formation elemental concentrations is to ensure that the obtained optimal elemental concentration can maintain the consistency between the converted Sigma and the measured Sigma on the basis of reasonable spectral decomposition error. The experiments show that the proposed method can effectively reduce the multi- solution in formation elemental concentration determination and improve the accuracy of the interpretation results. KEYWORDS Pulsed neutron logging; Formation elemental concentration; Spectral analysis; Intelligent algorithm 1.