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Butterfly Chart in Resistivity Log Invasion Correction: Step-Profile Invasion Model, Rt Determination from Three-Depth Resistivity Measurements, and Application to WCSB Cardium and Montney Formation Evaluation

Butterfly chart in formation evaluation and petrophysics is a graphical interpretation aid for correcting deep, medium, and shallow resistivity log measurements for the effect of mud filtrate invasion, producing the true formation resistivity Rt required for water saturation calculation from the Archie equation. The chart plots dimensionless ratios of the three resistivity readings (Rd/Rm or Rild/Rim and Rs/Rm or Rills/Rim, where Rd is the deep resistivity, Rs is the shallow or medium resistivity, and Rm is the mud resistivity) on a set of overlapping curves representing different values of Rt/Rm (the ratio of true formation resistivity to mud resistivity) and di (the invasion diameter), allowing the log analyst to enter two of the three log readings on the chart's x- and y-axes and read off the corrected Rt/Rm and the invasion diameter simultaneously. The "butterfly" shape of the chart derives from the symmetry of the plotted grid: when both resistive invasion (Rxo greater than Rt, occurring when mud filtrate is more resistive than formation water) and conductive invasion (Rxo less than Rt, occurring when mud filtrate is less saline than formation water) cases are plotted on the same axes, the resulting pair of curved grid families opens outward from the center in mirror-image shapes that together resemble a butterfly's wings, distinguishing the butterfly chart from the related tornado chart (which shows only the resistive invasion family, the more common case in WCSB wells drilled with fresh-water-based mud into saline formation water bearing zones). The practical WCSB application of the butterfly chart centers on evaluating resistivity logs in zones of suspected water-bearing or intermediate-saturation character where the direction of invasion (resistive or conductive) is not obvious from the log alone: in WCSB Cardium sandstone reservoirs with 20,000-60,000 mg/L formation water salinity and fresh-water WBM filtrate, invasion is resistive (Rxo greater than Rt) and the standard tornado chart applies; in WCSB Montney siltstone reservoirs where connate formation water salinity ranges from 50,000 to 200,000 mg/L (denser brine causes very low Rt in water-wet zones) and KCl-polymer mud filtrate at 10,000-30,000 mg/L is much fresher than formation water, the invasion is always resistive and the tornado chart applies without needing the conductive wing of the butterfly; but in WCSB Viking or Mannville heavy oil zones where in-situ formation water may be relatively fresh (TDS 5,000-15,000 mg/L) and the heavy oil itself reduces the apparent deep resistivity by conduction through the aqueous phase, the butterfly chart is needed to distinguish between formation water conduction and conductive invasion when the log shows deeper reading lower than the shallow reading.

Key Takeaways

  • Step-profile invasion model assumed by the butterfly chart and its validity for WCSB sandstone and siltstone formation invasion profiles: The butterfly chart is derived from the step-profile invasion model, which assumes that the formation consists of two concentric cylindrical zones: a fully flushed zone (Rxo, extending from the borehole wall to the invasion diameter di) in which all mobile formation water has been displaced by mud filtrate, and an undisturbed zone (Rt, extending from di to the reservoir boundary) in which the original formation fluids are present. This two-zone step model is a simplification of the actual transition zone that exists between the flushed and undisturbed zones, where the fluid composition transitions gradually from mud filtrate to formation fluid. For WCSB Cardium sandstone (permeability 5-50 mD, porosity 12-18%), the invasion profile after 24-48 hours of mud exposure is reasonably well represented by the step model with di typically in the range of 600-1,200 mm from the borehole center, within the read-depth range of medium and shallow resistivity tools. For WCSB Montney tight siltstone (permeability 0.001-0.01 mD, porosity 5-9%), invasion is very shallow (di less than 150-300 mm after 72 hours of mud exposure), and all three resistivity tools read essentially the undisturbed formation (Rd = Rs = Rt to within measurement error), making the butterfly chart invasion correction essentially zero and rendering the invasion correction step unnecessary for Montney formation evaluation.
  • Dual induction log (DIL) and dual laterolog (DLL) resistivity measurement systems and their respective butterfly chart families for WCSB formation evaluation: Two different resistivity tool types generate three-depth measurements suitable for butterfly chart analysis, and each has its own set of charts: the dual induction log (ILD deep, ILM medium, MSFL shallow, used in low-to-moderate salinity WCSB WBM drilling environments) and the dual laterolog (LLD deep, LLS shallow, MSFL shallow, used in high-salinity OBM or conductive formation environments). Butterfly charts for induction tools (Schlumberger chart Rint-3 or equivalent) use ILD/MSFL and ILM/MSFL ratios as axes; butterfly charts for laterolog tools (Schlumberger chart Rla-3 or equivalent) use LLD/MSFL and LLS/MSFL ratios. For WCSB Cardium horizontal wells drilled with fresh WBM, the ILD/ILM/MSFL dual-induction system is standard; the chart entry uses ILD/ILM ratio versus ILM/MSFL ratio to read Rt/ILM and di simultaneously. A WCSB Cardium reservoir at 15% porosity, 60% water saturation, 25,000 mg/L formation water might show ILD = 8 ohm-m, ILM = 5 ohm-m, MSFL = 3 ohm-m in an invaded zone; the butterfly chart corrects the 5-ohm-m ILD apparent Rt to Rt = 9.5 ohm-m after removing the invasion effect of the 800-mm di invasion diameter, which changes the water saturation calculation from Sw = (F × Rw / ILD)^0.5 = (100 × 0.03 / 8)^0.5 = 0.61 to Sw = (100 × 0.03 / 9.5)^0.5 = 0.56, a difference of 5 saturation units that is significant for pay cutoff decisions in WCSB Cardium completions.
  • Invasion correction workflow using the butterfly chart for WCSB Cardium and Viking oil pay zone identification in wells with resistive invasion: The practical butterfly chart correction workflow for a WCSB Cardium oil pay zone proceeds as follows: (1) identify a zone of interest where ILD is elevated (greater than 10 ohm-m in a WCSB Cardium oil zone) and ILD greater than ILM greater than MSFL (classic resistive invasion profile with deeper tools reading higher resistivity than shallower tools because the oil-bearing undisturbed zone is more resistive than the freshwater-invaded zone); (2) compute ILD/ILM and ILM/MSFL ratios for each 0.15-m sample point in the zone; (3) enter the butterfly chart (tornado chart for resistive case) at these ratios and read off Rt/MSFL and di; (4) compute Rt = (Rt/MSFL) × MSFL; (5) use the corrected Rt in the Archie water saturation calculation: Sw = ((F × Rw) / Rt)^0.5 for cementation factor m = 2 and saturation exponent n = 2. For a WCSB Viking oil zone where ILD = 15, ILM = 10, MSFL = 4 ohm-m, formation water Rw = 0.04 ohm-m at formation temperature, and porosity = 22% (F = 0.62/0.22^2 = 12.8): uncorrected Sw = (12.8 × 0.04 / 15)^0.5 = 0.184; tornado chart-corrected Rt = 19 ohm-m; corrected Sw = (12.8 × 0.04 / 19)^0.5 = 0.164. The 1.6% improvement in Sw is modest here, but in thin pay zones at the pay/water cutoff Sw threshold of 0.40-0.60 used in WCSB Cardium and Viking pay recognition, a 5-10% invasion correction can shift a zone from above to below the pay cutoff.
  • Limitations of the butterfly chart for WCSB horizontal well invasion correction and the alternative of numerical inversion software: The butterfly chart was developed for vertical well logging where the invasion profile is approximately cylindrical around the borehole. In WCSB horizontal wells where the tool logs parallel to the formation bedding, the invasion geometry is no longer cylindrical (invasion penetrates perpendicular to the borehole, which in a horizontal well is also perpendicular to the formation beds), and the tool's position relative to the flushed and undisturbed zones changes continuously as the borehole approaches or departs from formation boundaries. The butterfly chart correction, which assumes a cylindrical invasion profile, is invalid for this geometry and will produce erroneous Rt values if applied to WCSB horizontal well resistivity logs without geometric correction. Modern WCSB formation evaluation for horizontal wells replaces the butterfly chart with 1D or 2D numerical inversion that accounts for horizontal well geometry, resistivity anisotropy in laminated WCSB Montney siltstone, and bed boundary positions from LWD gamma-ray and resistivity boundary detection algorithms used in real-time geosteering.
  • Butterfly chart versus production log analysis for confirming WCSB Cardium well invasion correction: post-production validation of Sw predictions: The accuracy of the butterfly chart invasion correction for WCSB Cardium oil zone water saturation prediction is ultimately validated by comparing the chart-corrected Sw values against the water cut observed in early production from the well. A WCSB Cardium horizontal completion where the butterfly chart-corrected Sw averages 0.35 over the 35-m net pay interval (within the pay cutoff of Sw below 0.45 for WCSB Cardium), but where the initial production water cut is 45% instead of the expected 20% for Sw = 0.35, suggests that the actual Rt in the formation is lower than the chart-corrected value, which can occur if: (1) the invasion profile deviates from the step model (e.g., a transition zone wider than the tool separation distorts the chart inputs); (2) the formation is laminated with alternating oil-bearing and water-bearing layers below vertical resolution of the tool, making the apparent Rt a mixture of both; or (3) the cementation factor m or saturation exponent n in the Archie equation is wrong for the specific WCSB Cardium lithofacies. These discrepancies between butterfly-chart-corrected Sw and production water cut are documented in WCSB Cardium field studies and used to calibrate regional Archie parameters and to set locally adjusted pay cutoff values for subsequent well evaluations.

Butterfly Chart Invasion Correction Identifying Bypassed WCSB Cardium Oil Pay in a Legacy Re-Entry Well

A legacy WCSB Cardium vertical well completed in 1978 has original log data showing ILD = 6 ohm-m, ILM = 4.5 ohm-m, MSFL = 3.2 ohm-m over a 4-m interval at 1,640-1,644 m. The well was completed below this interval and produced 85 m3/d oil initially from a different zone. Re-entry evaluation uses the butterfly chart for the 1,640-1,644 m interval: ILD/ILM = 1.33, ILM/MSFL = 1.41. Chart entry: Rt = 7.8 ohm-m (corrected from 6.0 apparent), di = 650 mm. Rw for Cardium at this field = 0.038 ohm-m at formation temperature. Porosity = 14% from neutron-density crossplot (uncorrected original log). F = 0.81/0.14^2 = 41.3. Corrected Sw = (41.3 × 0.038 / 7.8)^0.5 = 0.448. Uncorrected Sw = (41.3 × 0.038 / 6.0)^0.5 = 0.511. The corrected Sw of 0.45 places the interval exactly at the Cardium pay cutoff; the uncorrected Sw of 0.51 placed it in the transition zone and it was bypassed in 1978. Re-perforation of the 1,640-1,644 m interval: initial rate 22 m3/d oil at 18% water cut, confirming the corrected invasion analysis correctly identified the interval as productive. Accumulated recovery of the bypass pay in the 3 years following re-completion: 6,800 m3 oil.

Fast Facts

The tornado chart (resistive invasion only) and butterfly chart (both invasion types) were developed by Schlumberger and other logging service companies in the 1950s and 1960s alongside the commercialization of the dual induction log (DIL) and dual laterolog (DLL) tool systems, which for the first time provided three resistivity readings at different depths of investigation in a single logging run. WCSB formation evaluation adopted these charts immediately for Devonian carbonate and Cardium sandstone evaluation, where invasion correction could shift water saturation estimates by 5-15 saturation units in moderate-permeability zones, significantly affecting pay recognition decisions in fields where the pay cutoff was in the 0.40-0.60 Sw range.

The dual induction log (ILD, ILM, MSFL) and dual laterolog (LLD, LLS, MSFL) resistivity systems that produce the three depth-of-investigation readings used as inputs to the butterfly chart invasion correction, including the geometric factor theory governing depth of investigation and the sensitivity of the correction to the assumed invasion step profile, are described under resistivity log. The Archie water saturation equation that uses the butterfly-chart-corrected Rt to calculate Sw in WCSB reservoir evaluation, including cementation factor m and saturation exponent n calibration to WCSB Cardium and Montney core plug measurements, is described under Archie equation. The formation invasion process by which mud filtrate displaces mobile formation water from the near-wellbore zone in permeable WCSB sandstone and siltstone reservoirs, creating the depth-of-investigation contrast between flushed zone and undisturbed zone that the butterfly chart corrects, is described under invasion.

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