Multivariate linear regression of sonic logs on petrophysical logs for detailed reservoir characterization in producing fields

Abstract

Many development wells do not have sonic logs recorded, often because of mechanical issues with deviated wellbores or high cost. Consequently, tying development wells to the seismic data covering the field becomes difficult. This issue is magnified in fields where multiple heterogeneous thin sands form thick-stacked pay packages. Multivariate linear regression is a powerful tool to analyze the interdependence of data. Well data from three producing fields in the Balingian Province, offshore Sarawak, Malaysia, are used to calculate parameters relating the recorded sonic-log data to other recorded petrophysical log data. Those parameters are used next to estimate sonic logs from petrophysical log data alone. The petrophysical log data include depth, gamma ray, density, neutron porosity, and resistivity, thus reflecting the natural assumption that the formation velocity is dependent on compaction, lithology, density, pore space, and fluid content. Parameters are calculated separately for coals, gas-filled sands, and the normal shale and sand sequences, giving one set of parameters for each well. The regression is computed at log scale for every depth point. The coefficient of determination between recorded and estimated sonic logs for the same well is up to 0.96. Blind testing is applied to assess the actual reliability of the linear regression by using the parameters from each well in turn to estimate sonic logs for the other wells with only their petrophysical logs. The best set of parameters is obtained from composite wells with tens of thousands of depth points, where the data from several wells are combined. This ensures that there are multiple instances of coal layers and gas-filled sand layers at many depths, thus providing the most representative data set. Interpretation indicates that the synthetic seismic from estimated sonic logs leads to reliable observations regarding sands and coals and their seismic character.