Petrophysical evaluation of clastic formations in boreholes with incomplete well log dataset by using joint inversion technique and machine learning algorithms

A succesful petrophysical evaluation of shaly-sand formations requieres: 1) the availability of high quality well log data and, 2) a petrophysical model that successfully represents the geological conditions of the rocks. Unfortunately, it is not always possible to fulfill these conditions, and in many cases the set of well logs is incomplete. To determine petrophysical parameters (i.e., volumes of laminar, structural and disperse shale) in clastic rocks from incomplete well log data we followed three approaches which are based on a hierarchical model, and on a joint inversion technique: 1) Available well log data (excluding the incomplete well log) are used to train machine learning algorithms to generate a predictive model; 2) the first step of the second approach machine learning algorithms are used to generate the missing data which are subsequently included a joint inversion; 3) in the third approach, machine learning process is used to estimate the missing data which are subsequently included in the prediction of the petrophysical properties. The supervised learning paradigm we used was in a joint based on different regression models (linear, decision trees, and kernel). A performance analysis of the three approaches is conducted with synthetic data (representing real conditions of clastic formations from an oil field in southern Mexico). We simulated gamma ray, deep resistivity, P-wave travel time, bulk density and neutron porosity logs by means of a hierarchical petrophysical model for clastic rock to accomplish a controlled analysis. The three different approaches were applied without P-wave travel time data to analyze the impact of the missing information. In general, the results indicate an adequate petrophysical parameter determination in each of the approaches. Metric evaluations indicate that the best performance was obtained by the second approach followed by approaches one and three. The correct estimation of the volumes of shale distribution could not be correctly resolved by any of the three applied methods but the total shale content could accurately be predicted which suggests that there is a non-uniqueness problem.