24-Pet-B1 Natural Gas Engineering · May 2016
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
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 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.
The Hingle plot solves Archie graphically by plotting a porosity-sensitive log reading against $R_t^{-1/m}$ on specially ruled paper, so that all 100 % water-bearing points fall on a straight line through the matrix point. Everything it can and cannot do follows from that construction, and four limitations are decisive.
1. It requires a single, known, constant matrix over the interval plotted. The vertical axis is a raw log reading — $\rho_b$, $\Delta t$ or $\phi_N$ — converted to porosity by a matrix value that is assumed fixed; the matrix point is the pivot the whole grid is built on. If limestone stringers, dolomite, or a changing sand–silt matrix are mixed into the same plot, the points scatter into a cloud rather than a line, and both the porosity scale and the derived $R_w$ are wrong.
2. It requires clean formations. Archie's law has no clay-conductivity term, so shaly points always plot at higher apparent porosity and lower apparent resistivity than the clean water line predicts. They fall below the water line, are indistinguishable from higher-porosity wet rock, and if they are used to fit the line they drag it round and produce an $R_w$ that is far too low. In shaly sand a Waxman–Smits or dual-water treatment is required instead.
3. It requires that some points in the interval be 100 % water bearing, and that $R_w$ be constant across them. The water line is the plot's only calibration: without a set of wet points there is nothing to anchor it to, and in a wholly hydrocarbon-bearing interval the technique cannot start. Equally, a transition from fresh to saline formation water over the interval, or a change of $R_w$ across a fault or a permeability barrier, splits what should be one water line into several and invalidates the fit.
4. It requires the cementation exponent $m$ (and the tortuosity factor $a$) to be assumed in advance. The horizontal axis is ruled as $R_t^{-1/m}$, so the grid paper itself is specific to one value of $m$ — commonly 2. If the true $m$ is 1.8 or 2.3, as it often is in carbonates or in vuggy or fractured rock, the "straight" water line is curved and the reading is biased. In this respect the Pickett plot is the more flexible tool, because it solves for $m$ from the slope instead of assuming it.
Two further practical restrictions are worth remembering: the method is graphical, so its precision is limited by the plotting and by the scatter of the points, and it needs a deep resistivity that is genuinely $R_t$ — thin beds, deep invasion, or an uncorrected shallow reading all displace the points horizontally.
