A typical gamma-gamma density tool used for making borehole geophysical measurements has a source and two in-line detectors at different distances from the source which results in each having unique effective penetration lengths (EPLs). Gamma-gamma tools typically have internal shielding so that the measurement is primarily influenced by the formation directly in front of the detectors. In high angle and horizontal wells, the difference in EPL creates an offset in measured depth (MD) between the two measurements when crossing a boundary between two layers having a density contrast. In a wellbore drilling down-section with the logging tool oriented toward the bottom of the wellbore, the detector with the deeper EPL senses the boundary at a shallower measured depth while the shallower-sensing one senses the boundary at a deeper measured depth. For a wellbore drilling up-section, the detection order and measured depths are reversed. This effect has been verified using Monte-Carlo N-Particle (MCNP) modeling code (Radtke 2006).
This offset in measured depth is a function of the relative difference in EPL, the azimuthal orientation/relative bearing of the detectors with respect to top of hole, and the relative angle between the wellbore and the formation boundary. By knowing the respective tool EPL's and the relative bearing of the detectors, and measuring/determining the offset in measured depth where the detectors have responsed to the bed boundaries, the incident angle or angle of attack can be calculated. The depth shifts can be calucaled by auto-correlation techniques or manually. The incident angle can be combined with the trajectory inclination to compute the apparent formation dip in the azimuth of the wellbore.
The incident angle gives us the indication of whether we are drilling up-section or down-section and how quickly we are cutting through the beds. These are a critical factors when determining the position of the wellbore relative to the geological layers while geosteering or when doing post drill look backs (correlation studies) and attempting to determine where the well was placed. A sinusoid fitting technique is typically used with azimuthal image data to determine formation dip and azimuth. The advantage of the new method is that sinusoids are not required. Only two or more single, oriented nonrotating measurements are needed. The method is validated with a full azimuthal density data set and then demonstrated in a second well with a commercial density logging tool that is conveyed through-the-bit. These tools are designed such that the density pad faces downward toward the bottom of the hole during logging operations and is not rotated azimuthally. Since azimuthal data is not acquired, one limitation of the technique is that the azimuth of the formation boundary cannot be computed.
