Question 3 of 11: Gamma-ray log — lithology zonation
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Notes on this paper
National Exams — December 2016. 98-Pet-B1, Well Logging and Formation Evaluation (every question is log-interpretation content, not gas-engineering material). 3-hour closed-book exam, 11 questions, all marked, calculators and attached graphs/formula sheet permitted.
Reference texts: Bassiouni, Theory, Measurement, and Interpretation of Well Logs (SPE Textbook Series Vol. 4); Asquith & Krygowski, Basic Well Log Analysis, 2nd ed.; Ellis & Singer, Well Logging for Earth Scientists, 2nd ed.; Schlumberger, Log Interpretation Charts.
Check: Q3, Q7, Q8, Q9(b), Q10 and Q11 are built on the paper's printed logs and attached charts. Values printed as annotations on the logs (Q11's SSP, PSP and GR labels) are used exactly as printed. Values read off a curve or a chart (Q9(b) and the Q8 chart check, Q10's track readings) are read from the printed figure and flagged inline with their precision. All arithmetic that follows is exact.
[Figure not reproduced: Fig. Q3 — The printed gamma-ray sketch redrawn to scale (ten beds, top to bottom), with each bed labelled by the zone number from the question. Dashed vertical line: the shale line set by the four beds that return to the same right-hand level. See the official exam paper.]
The sketch has ten beds but only seven lithologies, so the first step is to find the reference level. Four beds (the top one, the 3rd, the 5th and the bottom one) return to exactly the same right-hand deflection. A GR log returns to one repeatable level only in shale, so that level is the shale line, and every other bed is placed by how far it sits to the left (cleaner) or right (hotter) of it.
Beds 1, 3, 5 and 10, on the common right-hand level: 1, Shale. Clay minerals carry K, Th and U, and a thick shale gives the same reading every time it recurs.
Bed 7, the only kick to the right of the shale line: 7, Black marine shale. Organic-rich marine shale adds organically bound uranium on top of the clay-mineral radioactivity, so it reads hotter than ordinary shale.
Bed 4, just left of the shale line: 5, Sandy shale. It is mostly clay with a little sand, so the reading drops only slightly below the shale level.
Bed 9, about halfway between the clean beds and the shale line: 4, Shaly sand. This is a sand framework with dispersed or laminated clay. It reads above clean sand in proportion to its shale volume but well below shale.
Beds 2, 6 and 8, the three deep kicks to the left: the clean lithologies. Ranked by how far left each one goes: bed 2 is the lowest (6, Anhydrite, since evaporite minerals carry essentially no K, Th or U), bed 6 is next (3, Limestone, a clean carbonate) and bed 8 is the least deep of the three (2, Sandstone, where quartz is non-radioactive but traces of feldspar, mica and heavy minerals give clean sands a slightly higher reading than clean carbonates and evaporites).
The gaps between the three clean kicks are small on the sketch, so GR alone gives this order only as the usual ranking (anhydrite < limestone < sandstone). In practice you confirm it with a porosity log. Anhydrite reads $\rho_b\approx2.98\ \text{g/cm}^3$ with $\phi_N\approx0$. Clean limestone has a photoelectric factor near 5.1 and clean sandstone near 1.8. The four beds on the shale line, the single hot bed and the two intermediate beds are not ambiguous: their positions on the sketch fix them.
Q3 — Bed-by-bed zone assignment (beds numbered top to bottom on the printed log)
