Departure Curve

Key Takeaways

• Resistivity departure curves for induction and laterolog tools account for the multiple borehole and invasion effects that cause the measured resistivity to differ from the true formation resistivity in predictable ways that depend on the tool's specific electrode or coil geometry: the induction log (ILD) shallow and medium correction charts (API/Schlumberger Chart Book Rint-1 through Rint-4) correct the measured induction log readings for borehole size (from 6 to 18 inches) and mud resistivity (from 0.01 to 100 ohm-m) by looking up the raw ILD reading and the borehole-corrected reading on a family of curves parameterized by Rm/Rxo (the ratio of mud resistivity to flushed zone resistivity) that characterizes the invasion contrast; the laterolog departure curve corrections (Chart Rlat-1 through Rlat-6) are applied sequentially: first a borehole correction for the mud-filled cylinder around the electrode array (which reduces the measured laterolog reading when the mud is much more conductive than the formation), then a shoulder effect correction for adjacent bed responses (when the bed being measured is thin relative to the tool's vertical resolution), then an invasion correction that uses the three-curve combination of deep laterolog (LLD), shallow laterolog (LLS), and micro-spherically focused log (MSFL) to determine both the true formation resistivity Rt and the invasion radius ri from a crossplot or chart; the sequential nature of the corrections and their interdependence (each correction assumes the others have been applied) requires that they be applied in the specified order to produce the properly corrected Rt value used in the Archie saturation equation.
• Density log departure curves are essential for obtaining accurate formation bulk density (and hence porosity) in wells where the density logging pad is not in full contact with the formation, because even small standoffs between the pad and the formation surface cause the pad to measure a density-weighted average of the formation and the intervening mud cake or borehole fluid: the compensated density log (typically run with a Pad-mounted source and two detector arrays at short and long spacings) uses the difference in count rate between the short and long detector arrays to compute a correction term (delta-rho or spine-and-rib correction) that partially corrects for the effect of standoff, mud cake, and borehole fluid invasion on the density measurement; the departure curve for the uncorrected density (the reading before delta-rho correction is applied) shows how the measured density deviates from the true formation density as a function of standoff in inches and mud cake density in g/cc, with positive standoff (pad floating above the formation) causing the apparent density to be biased toward the lower mud density; in highly rugose boreholes (where the density pad cannot maintain contact along the entire formation face) and in oil-based mud wells (where the pad may hydroplane on the oil film), the delta-rho correction term becomes large and the density measurement quality deteriorates, requiring that zones with large delta-rho values be excluded from quantitative porosity interpretation and that an alternative porosity source (neutron, NMR, or sonic) be used in these intervals.
• Departure curve application workflow in integrated log analysis requires the systematic application of borehole and environmental corrections to all relevant log curves before crossplotting or saturation calculation to ensure that the petrophysical analysis reflects the true formation properties rather than the borehole-distorted apparent measurements: the raw log data as recorded by the tool in the well (the field log) contains all borehole and environmental distortions, and the departure curve corrections convert the field log to the corrected log that is used in interpretation; service company chart books (Schlumberger Log Interpretation Charts, Halliburton Log Interpretation Charts, Baker Hughes formation evaluation reference) provide the departure curves for each tool type organized by tool model and borehole condition parameter; modern log interpretation software (Petrel Petrophysics, TechLog, IP Interactive Petrophysics) implements the departure curve corrections as automated algorithms that apply the charts computationally using the caliper log (to provide borehole diameter), the mud log (to provide mud weight and mud resistivity), and the depth record to apply the appropriate corrections at each depth level; the importance of proper departure curve corrections is greatest in wells with large borehole sizes (above 12 inches, where the borehole volume seen by the tool is a large fraction of the total tool response volume), high mud weights (above 15 ppg, where the dense mud has a significant effect on neutron and density readings), or large invasion (where the deep reading tool still sees a significant fraction of the invaded zone).
• Normal compaction trend departure curves in pore pressure prediction are a distinct application of the departure concept that shows how the observed formation compaction (measured by sonic velocity, resistivity, or density logs) departs from the expected normal compaction trend for the same depth in a normally pressured formation, with the magnitude of the departure providing a quantitative indicator of the degree of overpressure in the formation: Eaton's method (the most widely used pore pressure prediction method) uses the ratio of the observed log value (sonic transit time, resistivity, or density) to the normal compaction trend value at the same depth to calculate the formation pore pressure as a fraction of the overburden stress; in the sonic log departure curve for pore pressure prediction, a formation compacting normally (normally pressured) plots on or near the established normal compaction trend line (a straight line in a semi-log plot of sonic transit time versus depth, reflecting the increasing velocity with depth from compaction); an overpressured formation plots to the left of this trend line (higher sonic transit time, lower velocity, indicating undercompaction relative to the depth), with the horizontal departure from the trend line in log-linear space being proportional to the degree of overpressure; the selection of the normal compaction trend line (which must be calibrated against known normally pressured intervals in the well or offset wells) is the critical step in departure-based pore pressure prediction, and an incorrectly positioned trend line produces systematically biased pore pressure predictions throughout the overpressured section.
• Departure curve uncertainty and its impact on petrophysical results must be recognized when the corrected log value is used in saturation calculations that are highly sensitive to the resistivity input, because errors in the departure curve correction (from incorrect borehole parameters, wrong chart selection, or off-scale borehole conditions) propagate into the saturation calculation with amplification from the exponent n in the Archie equation (Sw = (F x Rw / Rt)^(1/n), where the exponent n is typically 1.8-2.2 for water-wet systems): a 10% error in the corrected Rt from an incorrectly applied departure curve produces approximately a 5-10% error in the calculated water saturation Sw (depending on the saturation level), which can shift a water-bearing interval into the oil-pay classification or vice versa in marginal cases; the uncertainty in departure curve corrections is particularly significant for laterolog tools in high-resistivity formations (above 200 ohm-m) where the correction factors become large and their uncertainty correspondingly large, and for induction logs in low-resistivity formations (below 2 ohm-m) where the borehole signal may dominate the formation signal and the correction factor may exceed the formation signal itself; quantifying the impact of departure curve uncertainty on the saturation calculation requires sensitivity analysis in which the borehole parameters (caliper, mud resistivity) are varied over their plausible ranges and the resulting range of Rt and Sw values is used to define the uncertainty bounds on the petrophysical interpretation.