We present an automatic inversion for petrophysical interpretation of data acquired in a vertical well by the array sonic, array induction, and density logging tools. The inversion is especially suited for challenging interpretation scenarios where the formation is drilled with oil-based mud and has complex mineralogy consisting of multiple minerals and pore types. The inversion accounts for the simultaneous effects on all the tool sensors from filtrate invasion, gas phase, complex mineralogy and mechanical damage. The resulting interpretation is robust, accurate, and honors the multiple radial investigation depths of the different tools.

The inversion estimates formation porosity and radial distributions of pore shape, oil, gas, and water saturation extending several feet from the wellbore. Radial changes in fluid saturation and pore shape are caused by filtrate invasion and mechanical damage respectively. Sonic and electromagnetic forward solvers are used to simulate data for different tools. The solvers are linked to formation properties through a saturation transform and an effective-medium rock physics model. Properties of the formation are estimated by the inversion such that the simulated data match the measured data at each log depth. For the first time, sonic data for both dipole flexural-wave and monopole compressional-headwave are included in the inversion. These data are sensitive to porosity and pore-shape effects, and the compressional-headwave additionally provides sensitivity to gas saturation in soft formations.

We tested the inversion on synthetic data and two field datasets for a gas-bearing formation drilled with oil-based mud. The results are visualized as 2D images with radial distribution of properties at each log depth. The images characterize depth of filtrate invasion and mechanic damage for guiding completion and production decisions. The images also provide far-field fluid saturation and porosity for reserves calculations. The far-field properties are in overall good agreement with core data and traditional interpretation, with differences from traditional interpretation of saturation and porosity in key intervals. Quality controls are included to check the validity of approximations underlying the inversion. The results demonstrate an efficient inversion framework for guiding reserves, production, and completions decisions in challenging scenarios.

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