Question 6 of 12: Caliper Response and Spectral Gamma-Ray Isotopes
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Notes on this paper
National Exams, 98-Pet-B1, Well Logging and Formation Evaluation — May 2016, 3 hours, closed book (approved calculators permitted), 12 questions, all of them marked, values shown per question. neutron and density tools, SP, caliper, Archie, and log crossplots. There is no natural-gas-engineering content in the paper. All twelve questions are answered below.
Reference texts: Bassiouni, Theory, Measurement, and Interpretation of Well Logs (SPE Textbook Series Vol. 4); Asquith & Krygowski, Basic Well Log Analysis, 2nd ed. (AAPG Methods in Exploration 16); Ellis & Singer, Well Logging for Earth Scientists, 2nd ed.; Schlumberger, Log Interpretation Charts / Log Interpretation Principles and Applications.
The exam supplies a formula sheet (page 15) and four chart attachments: an SNP borehole-size correction chart and a nonideal-shale-membrane SP departure chart (page 16), SNP mud-weight and temperature/pressure correction charts (page 17), and a water-oil relative permeability ratio chart plus the Schlumberger Rw-equivalent conversion chart (page 18). Every chart reading below is quoted with the reading tolerance it deserves.
Question 6: Caliper Response and Spectral Gamma-Ray Isotopes (9 marks)
(a) Reading borehole shape from two independent caliper arms
Given. A caliper log (paper page 4) carrying two curves, each the reading of one independently sprung arm pair, plotted against a common hole-diameter scale that increases to the right. The bit size is the reference against which both are read.
Find. The cross-sectional shape of the hole at three or more depths where the two arms disagree, or where both depart from bit size.
Approach. Two independent arms measure two diameters roughly 90° apart. Compare each arm with bit size, then compare the arms with each other: agreement means a circular section, disagreement means an elliptical one, and the sign of the departure from bit size distinguishes washout from mudcake.
[Figure not reproduced: Two-arm caliper log as printed on exam page 4. See the official exam paper or the cited reference text.]
The two-arm caliper log reproduced from exam page 4: solid curve = arm 1, dashed curve = arm 2, hole diameter increasing to the right. The quiet stretches of the solid curve mark the in-gauge (bit-size) reference.
Zone A — upper interval: arm 2 far to the right, arm 1 near bit size. One diameter is greatly enlarged while the perpendicular diameter is unchanged, so the section is a strongly elongated ellipse (breakout), its long axis along the azimuth of arm 2. In a vertical hole this is the classic stress-induced borehole breakout, developing perpendicular to the maximum horizontal stress; in a deviated hole it can equally be a key seat cut by the drill string on the low side.
Zone B — second interval: dashed arm 2 swings well to the LEFT of bit size, solid arm 1 still near bit size. Drilling cannot leave a diameter smaller than the bit, so along arm 2 material has been added to the wall: most commonly a thick mudcake built on a permeable wall, or a squeezing/swelling formation creeping into the hole. The section is a flattened oval whose short axis lies along arm 2; if the cause is mudcake its thickness is $h_{mc} \approx \tfrac12(d_{bit} - d_{arm2})$ — and because mudcake forms only where filtrate can leave the borehole, such a zone is permeable. That is the single most useful qualitative statement a caliper makes.
Zone C — the sharp excursion about two-thirds of the way down, where the two arms swing in OPPOSITE directions. Over the same short depth the dashed arm 2 kicks far to the right (well above bit size) while the solid arm 1 swings far to the left (below bit size), just after a brief rightward flick. One diameter is enlarged and the perpendicular one reduced, so this is the most strongly elliptical section on the log: an elongated oval — breakout or key seat along arm 2 — whose short axis along arm 1 carries mudcake or a squeezed-in wall. Because both readings depart from bit size, pad-type logs (density, SNP, microlog) recorded across this interval should be treated as unreliable.
Zone D — the lower interval, where the two traces coincide (the dashed curve lies under the solid one) and wander only slightly about bit size, with a jagged, spiky character. The two diameters agree, so the section is round and essentially in gauge, but the high-frequency spikes show a rugose wall — small ledges and cavities rather than a smooth cylinder. Mandrel tools are little affected; pad tools will show spiky readings, so their trend rather than individual points should be used.
Depth interval
Caliper signature
Cross-sectional shape
Interpretation
A (upper)
arm 2 >> bit, arm 1 ≈ bit
elongated ellipse
stress breakout or key seat
B
arm 2 < bit, arm 1 ≈ bit
flattened oval, short axis along arm 2
mudcake on a permeable wall, or squeezing formation
C
arm 2 >> bit while arm 1 < bit (opposite swings)
strongly elongated oval
breakout / key seat with cake or squeeze on the short axis — pad logs unreliable
D (lower)
arms coincide near bit, spiky
round, in gauge, rugose
in-gauge but rugose hole; use pad-log trends
Check: the caliper curves are supplied on the exam page without a numbered diameter scale or a bit-size line, so the four zones above are read qualitatively from the relative positions of the two curves, taking the quiet stretches of the solid curve as bit size. The shapes and their causes are the graded content; no numerical diameter should be quoted from this figure.
(b) The three radioisotope families detected by a spectral gamma-ray tool
A total-count gamma-ray tool reports one number; a spectral (NGS) tool sorts the detected photons by energy and resolves the three naturally occurring radioactive series that account for essentially all gamma radiation from sedimentary rock:
Potassium-40 (40K) — identified by its single characteristic photopeak at 1.46 MeV. It is hosted in illite, glauconite, micas, feldspars and evaporitic sylvite (KCl); reported as weight per cent K.
Thorium-232 (232Th) series — identified through the 2.62 MeV photopeak of its daughter 208Tl. Thorium is chemically immobile and rides with the detrital clay and heavy-mineral fraction, so it is the best single indicator of true clay volume; reported in ppm.
Uranium-238 (238U) series — identified through the 1.76 MeV photopeak of its daughter 214Bi. Uranium is soluble and mobile, precipitating in organic-rich shale, in phosphates, and along fractures and stylolites, so a uranium spike need not mean clay at all; reported in ppm.
The practical value of the separation is precisely that: the computed uranium-free curve $\text{CGR} = \text{Th} + \text{K}$ gives a shale volume that is not fooled by a uranium-rich source rock or a mineralised fracture, which is the failure mode of a total gamma-ray curve. It also underlies the Th/K clay-typing crossplot used to distinguish kaolinite, illite, chlorite, montmorillonite and glauconite.
