Pressure Buildup Test Analysis for WCSB Oil and Gas Wells: Horner Plot Method, Pressure Derivative Diagnostics, and Skin and Permeability Determination

Key Takeaways

• Wellbore storage effect identification and duration estimation in WCSB buildup tests and its role in masking early radial flow data: Wellbore storage (also called afterflow) is the continued flow of reservoir fluid into the wellbore after shut-in at the surface, driven by the compressibility of fluid in the wellbore volume between the shut-in point and the producing formation. During the wellbore storage period, the pressure derivative plot shows a unit-slope log-log trend (both pressure change and derivative increase proportionally with shut-in time), and the Horner plot has not yet developed the straight-line radial flow region. The wellbore storage coefficient C (bbl/psi) for a WCSB Cardium oil producer with 1,750 m of 2.875-inch tubing is approximately C = Vwb × cwb, where Vwb is the wellbore volume (approximately 4 m3 = 25 bbl for 1,750 m of 2.875-inch tubing) and cwb is the compressibility of the wellbore fluid (approximately 10-15 × 10-6 psi-1 for single-phase oil, higher if free gas is present). The end of wellbore storage and onset of radial flow is estimated to occur at shut-in time delta-t approximately equal to 170,000 × C / (kh/mu), and for a WCSB Cardium well with kh = 60 mD-ft and C = 0.06 bbl/psi this gives approximately 0.4 hours of wellbore storage before radial flow begins. Downhole shut-in tools (DSTs with bottomhole gauges, wireline-set bridge plugs, or surface-reading acoustic fluid-level monitors) reduce wellbore storage by orders of magnitude by eliminating the tubing volume from the wellbore compressibility, allowing radial flow data to be collected within minutes rather than hours of shut-in in tight WCSB formations.
• Pressure derivative log-log plot construction and flow regime identification for WCSB well test interpretation: The pressure derivative (dDeltaP/d ln(delta-t), where DeltaP = Pws - Pwf,initial) plotted against shut-in time on a log-log scale with the pressure change overlaid is the standard diagnostic plot for identifying flow regimes before selecting the correct straight line for parameter calculation. Key diagnostic signatures relevant to WCSB well testing: a horizontal pressure derivative plateau (derivative = constant = m/2.303) identifies radial flow, from which permeability is calculated; a half-slope log-log line (derivative proportional to delta-t^0.5) identifies linear flow, which occurs in hydraulically fractured WCSB Montney and Cardium wells where pressure transient propagates linearly along the hydraulic fracture face before radial flow develops; a V-shaped derivative minimum at intermediate shut-in time identifies dual-porosity (matrix-fracture) behavior in WCSB Devonian carbonates, where the initial decline in derivative as fractures deplete is followed by a recovery as matrix flow feeds the fractures; and a rising derivative at late shut-in time indicates a boundary effect (no-flow boundary from fault or reservoir limit), signaling that P* extrapolation from the Horner plot is unreliable and volumetric depletion methods should be used for average reservoir pressure instead.
• Horner time ratio selection and the pseudo-producing time correction for multi-rate WCSB production histories: The classical Horner buildup assumes the well has been producing at a constant rate q for a single producing time tp before shut-in. In WCSB practice, wells typically have a variable production history over months to years before a buildup test is run. The correct tp for the Horner analysis is the equivalent producing time: tp = Np / q_last (total cumulative production in STB divided by the last stable rate before shut-in, in STB/d), which gives the equivalent constant-rate time that would produce the same material balance as the actual variable-rate history. For a WCSB Cardium well with cumulative production Np = 120,000 STB and last stable rate q = 65 STB/d, tp = 120,000 / 65 = 1,846 days (5.1 years). The Horner ratio at early shut-in (delta-t = 1 hour) is (1,846 + 1/24) / (1/24) = 44,305, and at late shut-in (delta-t = 24 hours) is (1,846 + 1) / 1 = 1,847. The straight-line portion of the Horner plot used for permeability and skin calculation should be identified in the range of Horner ratios where the pressure derivative is flat (radial flow), typically at delta-t between 2 and 20 hours for most WCSB Cardium and Viking oil producers with k of 10-100 mD.
• Skin factor interpretation in WCSB well tests: distinguishing damage skin from geometric and turbulence sources in Cardium and Montney wells: The skin factor s calculated from a WCSB buildup test is a composite that may include: damage skin from mud filtrate invasion, fines migration, wettability alteration, or scale (always positive, typically s = +1 to +15 for WCSB Cardium wells before stimulation); partial penetration skin from casing perforation not spanning the full producing interval (positive, proportional to the fraction of net pay perforated); non-Darcy turbulence skin in high-rate WCSB gas wells (positive, rate-dependent, equals D × q where D is the non-Darcy coefficient and q is the flow rate); hydraulic fracture skin (negative for a well with an effective hydraulic fracture, typically s = -3 to -7 for a WCSB Cardium multistage frac with adequate propped fracture half-length); and natural fracture connectivity skin (negative if the wellbore intersects open natural fractures in a WCSB Devonian carbonate, providing apparent stimulation relative to the matrix-only radial flow expectation). Separating these skin components requires running tests at multiple flow rates (rate-dependent turbulence skin increases with rate, while damage and geometry skins are rate-independent) and comparing pre- and post-stimulation tests to isolate the fracture contribution.
• P* extrapolation and average reservoir pressure determination from WCSB Horner plot for material balance and reserve estimation: P*, the extrapolated static reservoir pressure from the Horner semilog straight line at infinite shut-in time (Horner ratio = 1), represents the average pressure in the drainage area of the tested well if no boundary effects have appeared during the test. For WCSB Cardium pool management, P* values from individual well buildup tests are plotted against cumulative production (the Havlena-Odeh material balance plot) to track reservoir energy and calibrate the geological model for reserve estimation and waterflood pressure maintenance design. A declining P* trend at a rate consistent with the single-phase compressibility × pore volume depletion rate confirms the pool is producing under undersaturated oil expansion (OOIP = N = cumulative production / (1 - P*/Pi) × Eo, where Eo is the undersaturated oil expansion term and Pi is the initial reservoir pressure), while a P* declining faster than expected signals active water influx or a smaller drainage volume than the geological model assumed. In WCSB tight reservoir testing (Montney, Duvernay), P* extrapolation is unreliable because the test duration (typically 24-72 hours) is insufficient to establish the Horner straight line for formations with permeability of 0.001-0.01 mD, and flowing material balance or rate-transient analysis is used instead to estimate average reservoir pressure from the multi-month production history.