Question 3 of 12: Borehole-Diameter Effect on a 19½-in GNT Tool

Question 3: Borehole-Diameter Effect on a 19½-in GNT Tool (4 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given. A GNT (gamma ray–neutron, neutron–gamma) tool with 19½-in source-to-detector spacing; 10 lbm/gal barite-weighted mud; limestone formation of true porosity $\phi = 15$ p.u.; formation temperature 240 °F. GNT calibration curves are referenced to a 7⅞-in borehole.

Find. The direction and approximate magnitude of the apparent-porosity error introduced by a borehole diameter different from the calibration diameter.

Approach. Reason from the transport physics — how much of the neutron slowing-down and capture happens in the borehole rather than in the rock — then quantify with the tool's borehole-size departure curve.

The GNT is a mandrel (non-pad) neutron–gamma device: a source and a gamma detector 19½ in apart on a sonde that sits in the mud column, counting the capture gamma rays produced when the emitted neutrons are thermalised and absorbed. Because the mud is hydrogen-rich, every extra inch of hole diameter adds moderating and absorbing material between the source and the formation. Three consequences follow, and they all push the same way:

• More neutrons are slowed and captured in the borehole fluid, so fewer reach the formation and fewer capture gammas are generated in the rock;
• The capture gammas that are generated must traverse a thicker mud annulus to reach the detector, and barite (Ba, Z = 56) is a very efficient photoelectric absorber, so the surviving flux falls faster than it would in an unweighted mud;
• The mud itself is a low-density, high-hydrogen-index medium, so its response is equivalent to a very high porosity.

A GNT count rate that falls is interpreted by the calibration curve as a more hydrogenous, hence more porous, formation. The tool therefore reads too high in an enlarged hole and too low in an undergauge hole, and the error grows monotonically with the departure from the 7⅞-in calibration diameter. The 10 lbm/gal barite mud amplifies the effect relative to a fresh-water borehole. The 240 °F formation temperature works weakly in the opposite direction: hot borehole fluid is less dense, its hydrogen density is lower, and it moderates slightly less, which trims a few tenths of a porosity unit off the correction — a second-order term compared with hole size.

Applying representative departure values to the 15 p.u. limestone gives the apparent readings below. In a 12-in washout the tool would report about 18.4 p.u. against a true 15 p.u. — a 23 % relative error, which is why a caliper must be run with any GNT survey and the correction applied bed by bed.