Question 6 of 12: Caliper-Derived Borehole Shape and Spectral Gamma Ray
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 2014, 3 hours, closed book (calculators permitted), 12 questions, all marked, 100 marks total.
Reference texts: Bassiouni, Theory, Measurement, and Interpretation of Well Logs (SPE Textbook Series Vol. 4); Asquith & Krygowski, Basic Well Log Analysis, 2nd ed. (AAPG); Ellis & Singer, Well Logging for Earth Scientists, 2nd ed.; Schlumberger, Log Interpretation Charts / Log Interpretation Principles and Applications.
Question 6: Caliper-Derived Borehole Shape and Spectral Gamma Ray (7 marks)
(a) Borehole cross-sectional shape from the two-arm caliper
A two-independent-arm caliper measures hole diameter along two perpendicular (or near-perpendicular) axes; when the two traces track together the hole is round and near-gauge, and where they diverge the hole is elongated (elliptical or key-seated) along the axis of the larger-reading arm. Reading the supplied log from top to bottom against a nominal (bit) gauge:
[Figure not reproduced: The two-arm caliper log of Question 6 as printed on source page 4. See the official exam paper or the cited reference text.]
The Question 6 caliper log exactly as printed (source page 4). The two traces are the two independent arms (one solid, one dashed) and hole diameter increases to the right. Three irregular depths stand out, and they are of two physically different kinds: at the top two the arms move in OPPOSITE directions, at the third they move TOGETHER.
Interpreted borehole cross-sections at the three irregular depths. Two arms that disagree mean an elongated (oval) hole; two arms that move together mean a hole that is still round but off gauge.
Zone A — the top of the log (arms diverge; the DASHED arm reads the SMALLER diameter). The solid arm holds near its nominal reading while the dashed arm swings well to the left of it. A two-arm tool reading two different diameters is by definition in a non-circular hole, so the section is an ellipse whose short axis lies along the dashed-arm azimuth — the hole is under gauge on that side, the signature of a mudcake build-up or a ledge rather than of erosion.
Zone B — immediately below A (arms diverge again, but the DASHED arm now reads the LARGER diameter). The solid arm again stays near gauge while the dashed arm swings well to the right, by several inches and over a long, blocky interval. This is an elongated, washed-out oval whose long axis lies along the dashed-arm azimuth — a washout or key-seat. Note that the elongation azimuth has effectively rotated about 90° between A and B: the same arm is the short one in A and the long one in B.
Zone C — about mid-log (both arms move TOGETHER). Here the two traces stay superimposed while both swing sharply right and then broadly left: a narrow enlargement immediately followed by a longer under-gauge (tight) interval. Because the arms agree throughout, the hole stays essentially circular in this interval and only its diameter changes — a round washout over a round tight spot, not an oval.
Lower half of the log — the two traces track each other closely with only fine-scale wiggle: a near-circular, near-gauge, mildly rugose hole in competent rock.
The general rule the question is testing: where the two independent arms AGREE the hole is round (in gauge if they read bit size, washed out or tight if they do not); where they DISAGREE the hole is elongated, with the long axis along the azimuth of the larger-reading arm and the ellipticity set by the size of the separation.
(b) Radioisotopes detected by spectral gamma ray
A spectral (natural) gamma-ray tool resolves the total gamma count into its three naturally-occurring radioactive contributors by their characteristic energy windows:
Potassium-40 (K) — associated with feldspars, micas, and especially illitic/glauconitic clays;
Uranium (U, via the U-238 decay series) — often associated with organic-rich (source-rock) shales and phosphates, and can be present independent of clay content;
Thorium (Th, via the Th-232 decay series) — associated with heavy, resistant clay minerals (kaolinite, chlorite) and is the most reliable of the three for a pure clay-volume indicator, since it is least affected by adsorbed uranium in organic matter.
