Bubble Effect in Pressure Transient Analysis: Gas Liberation Near the Wellbore During Buildup Testing and Horner Plot Distortion in WCSB Oil Wells

Key Takeaways

• Near-wellbore two-phase zone geometry and relative permeability impairment during extended production below bubble point: When a WCSB Cardium or Devonian oil well flows at FBHP below the bubble point, the reservoir behaves as two concentric zones: an inner two-phase zone extending from the wellbore out to the radial distance where reservoir pressure equals the bubble point, and an outer single-phase undersaturated zone beyond that radius. The inner zone radius expands with cumulative production as average reservoir pressure depletes. Within the two-phase zone, gas saturation builds from the critical gas saturation (Sgc approximately 3-8% for typical WCSB sandstone) up to values of 10-25% depending on depletion severity and rock pore structure. At 15% gas saturation in a water-wet Cardium sand, oil relative permeability may be reduced to 0.65-0.75 of its single-phase endpoint value using typical Corey-type relative permeability functions, with the oil exponent n approximately 2-3 for WCSB sandstone. The effective permeability to oil in the near-wellbore zone is therefore measurably reduced, producing additional pressure drawdown that resembles a positive skin in a single-phase interpretation but has a thermodynamic rather than a mechanical cause and cannot be corrected by acid stimulation or other remedial treatment.
• Total compressibility discontinuity at bubble point and its mechanistic role in generating two Horner semilog slopes during pressure buildup: The slope of the Horner semilog straight line is proportional to 162.6 qBmu / (kh), and the apparent kh product is controlled through total system compressibility ct in the transient flow equations. Below bubble point, ct includes contributions from free gas compressibility (cg approximately 30-50 × 10-6 psi-1 at 3,000-5,000 psi WCSB reservoir conditions), oil compressibility (co approximately 10-15 × 10-6 psi-1), connate water compressibility (cw approximately 3-5 × 10-6 psi-1), and rock compressibility (cf approximately 3-6 × 10-6 psi-1); with even 10% free gas saturation, the cg × Sg term alone roughly doubles ct above its single-phase value. Above bubble point, ct drops to co + cw + cf, typically 17-26 × 10-6 psi-1 for WCSB Cardium conditions. Because pressure wave diffusivity equals k/(phi × mu × ct), the high-ct below-bubble-point period propagates pressure more slowly per unit of shut-in time, producing a steeper apparent Horner slope that gives an artificially elevated apparent kh if taken as the true formation mobility rather than the compressibility-elevated two-phase transient.
• Correct semilog straight line selection on the Horner plot and in-situ bubble point identification from the slope transition in WCSB well tests: Accurate interpretation of a WCSB buildup test affected by bubble effect requires identifying the later-time semilog straight line corresponding to fully single-phase undersaturated conditions above the bubble point, not the earlier steeper two-phase line. The shut-in pressure at which the slope change occurs on the Horner plot approximates the in-situ bubble point pressure at reservoir temperature and composition, providing a field-measured cross-check against the PVT-laboratory bubble point from recombination samples. This comparison is particularly valuable in WCSB Cardium and Devonian pools where PVT sample quality may be uncertain due to long production histories, evolved GOR in the tubing before sampling, or samples collected at separator conditions rather than downhole. The true formation permeability and skin are computed from the single-phase slope m2: permeability k = 162.6 qBmu / (m2 × h), and skin = 1.151 × [(P1hr - Pwf) / m2 - log(k / (phi × mu × ct × rw squared)) + 3.23], where ct is the single-phase undersaturated value and P1hr is read from the single-phase semilog line at one hour shut-in time.
• Skin and average reservoir pressure errors caused by bubble effect when the two-phase Horner slope is mistakenly selected for interpretation: If the interpreter selects the steeper two-phase slope m1 rather than the shallower single-phase slope m2, systematic errors in both permeability and skin calculations result. Apparent permeability computed from m1 is underestimated by the factor (m2/m1), which may be 1.3-2.0 for severely depleted wells with large two-phase zones extending 50-150 m radially. Computed skin using m1 is overestimated (more positive) because the artificially steep slope produces a lower apparent P1hr intercept on the extrapolated straight line, inflating the pressure deficit in the skin equation. A skin error of +5 to +15 units is plausible in heavily depleted WCSB Cardium wells, causing erroneous decisions to acid-stimulate or hydraulically fracture wells whose true mechanical skin is near-zero or mildly negative. Additionally, P* (initial reservoir pressure extrapolated from the Horner straight line) is overestimated when m1 is used, causing reserve estimates and reservoir simulation history-match targets to be calibrated to an erroneously high pressure baseline.
• Pressure derivative log-log plot as the definitive diagnostic for bubble effect versus wellbore storage and formation damage in WCSB well test interpretation: The pressure derivative plot (the derivative of delta-P with respect to the natural log of shut-in time, plotted against shut-in time on a log-log scale) provides the clearest diagnostic for distinguishing bubble effect from other pressure transient anomalies. True wellbore storage shows as a unit-slope log-log hump followed by a stabilized radial-flow plateau. True formation damage skin shows as a constant positive offset on both the pressure and derivative curves during the radial flow period without changing the derivative slope. Bubble effect, by contrast, produces an elevated derivative level during early shut-in (while pressure is below bubble point) that transitions to a lower plateau at later shut-in times (when pressure has rebuilt above bubble point and single-phase conditions are restored), with the derivative transition time and hump amplitude controlled by the two-phase zone radius and the compressibility ratio ct,below / ct,above. In WCSB Cardium wells, where wellbore storage coefficients are typically 0.01-0.1 bbl/psi and radial flow begins at 1-5 hours shut-in, the bubble effect derivative hump often overlaps the wellbore storage period, requiring numerical well test simulation with two-phase PVT properties to fully deconvolve the two effects.