Applicability of Newton-based Optimization Method Merged with the Monte Carlo Approach to Log Interpretation

The determination of the main petrophysical parameters is normally based on the log data. During the log interpretation process suitable mathematical algorithms taking into account all the available data and information are applied in the attempt to reliably relate log measurements to mineralogy, porosity and water saturation. Uncertainty is always associated to the results of the interpretation due to possible errors in the measurements, in the selected petrophysical models, and/or in the input parameters required by the models. The possibility to estimate the reliability of the petrophysical characterization of the reservoir rocks has a strong impact on the evaluation of the hydrocarbon originally in place (HOIP) and, thus, on the technical and economical exploitation strategies. The evaluation of the uncertainties associated to the results of the well log interpretation process can be performed only by applying a methodology that couples a robust optimization process to a representative statistical approach. On the basis of previous studies and applications to real cases, a methodology for log inversion and uncertainty estimation was formulated. According to this methodology, log interpretation was performed using the iterative solution of the Lagrangian relaxed problem with the Gauss-Newton algorithm, in which the constrains were managed with the active set method; the Monte Carlo statistical approach was applied to the log interpretation routine in order to assess the associated uncertainty. The use of a fast iterative inversion method proved fully compatible with the use of the Monte Carlo approach to estimate the range of uncertainty associated to the reservoir characterization. The rigorous formulation of the methodology and a discussion of the applicability limits and convergence requirements of the inversion method are presented in this paper. Results of the analyses that were carried out in the study showed that the validity limits were perfectly consistent with the domain of the petrophysical interpretation. The results obtained by the application of the methodology to a real case, a deep-water exploration well data complicated by a poor characterization of the reservoir fluids, is also presented the paper.