Joint inversion of conventional well logs for evaluation of double-porosity carbonate formations

In this paper we propose a new approach of well log data interpretation for determining lithological and petrophysical characteristics of double-porosity carbonate formations containing shales. This approach is based on the theoretical calculation of rock physical properties and joint simultaneous inversion of the following conventional logs: P- and S-wave transit times, resistivity, density, neutron porosity, and gamma ray. The inversion procedure consists in minimizing a cost function that includes the sum of weighted square differences between the measured and calculated logs, and the regularization functional containing additional information (initial model parameters and ranges of their variations). The petrophysical parameters determined by the inversion are a shale volume, dolomite volume, matrix porosity, secondary porosity and secondary porosity type (aspect ratios of spheroids approximating secondary pores).To calculate the theoretical logs we use the formation model that corresponds to a transversely isotropic medium composed of intercalated layers of carbonates with secondary porosity of different types and shales. The carbonate rocks are treated as a composite material that consists of a homogeneous isotropic matrix (solid skeleton and matrix pore system) where the secondary pores represented by spheroids are embedded. The matrix physical properties are calculated taking into account the mineral composition of solid components. For computing the effective properties we apply the symmetrical self-consistent method of the effective medium approximation. The shale properties as well mineral and fluid characteristics can be considered as known and they are adjusted by the posterior analysis of error distributions for each log.The results of joint inversion obtained for various boreholes from vuggy and fractured carbonate reservoirs of the South Zone of Mexico show a good correspondence with core data, image log, and geological descriptions. Based on the experimental data we demonstrate that the output inversion parameters can be used to improve the classification of carbonate lithotypes and assessment of the secondary pore interconnections required for the permeability prediction.