How the depth of investigation changes with spacing: A computer model for carbon/oxygen logging

C/O tools using dual-spaced detectors have been developed by several companies. It is necessary to understand the depth of investigation of the two detectors for applying the tools to cased-hole reservoirs. How the depth of investigation changes with the detector spacing is simulated for a large-size C/O tool in a high-porosity formation, using a general-purpose Monte Carlo computer code for radiation transport. The computer model is structured in a 35 p.u. sandstone formation which is segregated into 8 concentric zones all with radial thickness of 7.5 cm. A 31/2-in (8.9 cm) outer diameter tool is eccentered in 51/2-in (14 cm) casing, which is centrally cemented in a 77/8-in (20 cm) borehole. As the water-saturated zones are progressively replaced by oil-saturated zones, C/O ratios from inelastic gamma spectra at different spacings are calculated. For certain spacings, the trend of C/O ratio increasing with oil-zone radial thickness may be regressed using a sigmoid function, and the depth of investigation can be obtained. Calculated results show that the relationship between the depth of investigation and spacing appears roughly linear, and the investigation depths of the dual-spaced detectors in a C/O tool are significantly different.