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Afterflow

Afterflow is the continued influx of reservoir fluid from the formation into the wellbore during the period immediately after a well is shut in at the surface during a pressure transient test. When the surface valve closes, the wellbore does not instantly reach pressure equilibrium with the reservoir; instead, the compressible fluid column already in the wellbore expands, causing wellbore pressure to rise in response to stored wellbore energy rather than the reservoir response itself. The wellbore storage coefficient C, defined as C = Vwb × cwb where Vwb is the wellbore volume from sandface to gauge and cwb is the compressibility of the wellbore fluid column, quantifies the magnitude of the afterflow effect in units of bbl/psi (SI: m³/kPa). Values of C range from 0.001 bbl/psi for a small tubing string filled with single-phase oil to greater than 1.0 bbl/psi for a large-diameter casing packed with a gas-liquid mixture at high GOR. The dimensionless wellbore storage coefficient CD = 0.8936 × C / (φ × ct × h × rw²) controls how many log-decades of time the afterflow period dominates the buildup pressure derivative before radial flow from the reservoir emerges. Until afterflow subsides, the middle-time region (MTR) of the buildup, from which transmissibility kh/μ, skin, and average reservoir pressure are derived, cannot be identified or analysed. In Alberta and northeast British Columbia, afterflow duration in horizontal Montney and Duvernay wells commonly ranges from 6 to 48 hours, making downhole shut-in tools economically justified on wells where test quality directly informs multi-well pad development decisions worth hundreds of millions of dollars.

Key Takeaways

  • The wellbore storage coefficient C governs afterflow duration and must be estimated before designing any pressure transient test: The equation C = Vwb × cwb shows that both wellbore volume and fluid compressibility independently extend the afterflow period. A Montney horizontal well with a 2,500 m lateral and a gas-liquid mixture (cwb ≈ 150 × 10-6 psi-1) and a wellbore volume of 180 bbl gives C ≈ 0.27 bbl/psi, while a Viking vertical well with 80 bbl of single-phase oil (cwb ≈ 10 × 10-6 psi-1) gives C ≈ 0.0008 bbl/psi, a ratio of 337:1. This translates directly into proportionally longer afterflow on the horizontal well: at CD > 10,000, afterflow dominates the derivative for 12 to 36 hours, requiring a minimum buildup duration of two to three times the expected afterflow end time just to capture any MTR data at all.
  • The unit-slope diagnostic on the log-log pressure-derivative plot is the definitive afterflow identifier used by all modern well test analysts: During the afterflow-dominated period, the pressure change Δp and the Bourdet derivative d(Δp)/d(ln Δte) both plot as parallel lines with slope exactly equal to 1.0 on the log-log graph, because wellbore pressure rises linearly with time as stored fluid expands at a rate governed entirely by C. The transition away from unit slope marks the end of storage and the onset of the skin-dominated hump or, for wells with low positive skin, the direct emergence of the radial-flow plateau. On the Gringarten-Bourdet type curves, each curve is parameterised by CD e2s, and matching the shape of the transition hump allows simultaneous determination of C, skin s, and transmissibility kh/μ by regression against the radial-flow plateau level of 70.6 qμ/(kh) in field units.
  • Phase redistribution during afterflow creates anomalous pressure signals that are frequently mistaken for reservoir boundaries or natural fractures: In wells producing gas-condensate or high-GOR oil, shut-in allows gas to migrate upward and liquid to sink, changing the hydrostatic head of the wellbore fluid column over time. This generates a pressure hump superimposed on the wellbore storage signal, appearing on the derivative as an S-shaped deviation between the unit-slope region and the radial-flow plateau. Phase redistribution humps can mimic negative skin (suggesting fractures that do not exist), a dual-porosity fissure-matrix response, or a near-wellbore composite region. In deep Duvernay gas-condensate wells in the Fox Creek fairway of west-central Alberta, redistribution humps of 200 to 600 psi have been documented in surface shut-in tests with GOR above 6,000 scf/bbl, and their misinterpretation has caused fracture half-length overestimates of up to 300%.
  • The Agarwal equivalent time corrects the pressure buildup derivative for finite production time, preventing false boundary identification at long shut-in times: For a buildup test following a production period of duration tp, the Agarwal equivalent time is Δte = Δt × tp / (tp + Δt). Without this correction, the derivative appears to decline at shut-in times approaching tp, mimicking a closed reservoir boundary that does not exist. In Montney DST programmes where the pre-buildup clean-up flow period is only 4 to 8 hours, any shut-in extending beyond that duration will show significant derivative distortion unless Δte is used. Alberta Energy Regulator Directive 040 requires that all DST analysis submitted to the AER use Agarwal equivalent time or an equivalent Horner time ratio correction for proper MTR identification and the extraction of valid kh and skin values.
  • Downhole shut-in tools eliminate afterflow by closing at the sandface and reducing effective wellbore storage volume to near zero: Wireline-conveyed or tubing-conveyed downhole shut-in valves (Halliburton RTTS, Baker Hughes MFEV, Schlumberger RTV) close the flow path at or immediately above the perforations, setting Vwb effectively to zero in the storage equation and reducing C by 90 to 99%. With sandface shut-in, afterflow ends within seconds to minutes, and the pressure derivative reaches the radial-flow plateau within 30 to 90 minutes on most WCSB completions. On a Montney horizontal test, a downhole tool delivers clean MTR data within 4 to 8 hours versus 24 to 48 hours for surface shut-in, saving 1 to 2 rig-days at typical rates of CAD 26,000 to 35,000 per day. AER Directive 040 allows shortened minimum buildup periods when the operator documents that downhole shut-in was used and afterflow duration was confirmed to be less than 15 minutes.

Wellbore Storage Physics and the Two Storage Mechanisms

Wellbore storage and the afterflow it generates arise from two physically distinct sources. The first is fluid compressibility storage: when the surface valve closes, the fluid column below the gauge expands to accommodate the incremental reservoir influx, and wellbore pressure rises as stored elastic energy is released. For single-phase oil at 3,000 psia, cwb ≈ 10 to 15 × 10-6 psi-1, giving C values of 0.001 to 0.05 bbl/psi for typical tubing volumes of 50 to 200 bbl. Gas has cwb ≈ 1/p in psi-1, so at 3,000 psia cwb = 333 × 10-6 psi-1, and even small gas volumes generate large C values and prolonged afterflow.

The second mechanism applies to wells without packers (open casing-tubing annulus): the rising liquid level in the annulus adds Cannulus = Aann / (144 × 0.4335 × γf) in bbl/psi (field units), where Aann is the annular cross-sectional area in in². For a 7-inch casing with 3.5-inch tubing, Aann ≈ 28 in² and Cannulus ≈ 0.013 bbl/psi for freshwater, which dominates the total C by one to two orders of magnitude compared to the compressibility term. The AER requires operators to account for the annular storage mechanism when sizing shut-in periods for wells tested without packers, since failing to do so systematically underestimates afterflow duration and results in buildup periods that are too short to capture the MTR.

Log-Log Diagnostic Plot and Gringarten-Bourdet Type Curves

The Bourdet pressure derivative method, published by Dominique Bourdet and co-authors in 1983, uses the logarithmic derivative of pressure change with respect to Agarwal equivalent time to separate superimposed flow regimes. The unit slope that characterises afterflow on the derivative is a mathematical consequence of linear pressure rise during storage: Δp = (q / 24C) × Δt in field units, so d(Δp)/d(ln Δte) = Δp exactly, placing both curves on the same unit-slope line. After the unit-slope period, the derivative passes through a transition hump parameterised by CD e2s. When CD e2s is large (above 103), the hump is pronounced and the derivative does not reach the radial-flow plateau until well after storage ends. When CD e2s is small (below 10), the hump is minimal and radial flow appears soon after storage subsides.

Kappa Engineering Saphir, the standard DST analysis package used by most Alberta operators, implements automated Gringarten-Bourdet type-curve matching with nonlinear least-squares regression to extract C, CD, skin, kh/μ, and average reservoir pressure simultaneously from the full diagnostic plot. IHS Harmony and Fekete F.A.S.T. WellTest also support the same type-curve library. All three platforms implement the Agarwal equivalent time transformation internally, so submission-ready diagnostic plots with correct time axes are produced automatically once the production history is loaded correctly.

Fast Facts

The wellbore storage and afterflow framework was formalised in petroleum engineering literature by Ramey and Agarwal in the early 1970s, and the dimensionless group CD e2s became standard after Gringarten et al. published their type-curve atlas in SPE Paper 4051 (1974). The Alberta Energy Regulator's Directive 040 (Well Testing Requirements) specifies minimum shut-in periods for drillstem tests based on estimated CD values and requires Bourdet derivative plots in all submitted DST reports filed with the AER. SPE Monograph Volume 5 by Earlougher (1977) remains a canonical reference for wellbore storage coefficient derivation and afterflow duration estimation. Canadian operators including Ovintiv, ConocoPhillips Canada, and ARC Resources routinely use Kappa Saphir for Montney and Duvernay transient analysis, submitting Gringarten-Bourdet type-curve matches as part of AER-required DST reports. Phase redistribution afterflow is most frequently documented in Duvernay condensate-rich wells in the Kaybob-Fox Creek corridor, where redistribution hump amplitudes up to 700 psi have been recorded in surface shut-in tests, and the CSEG Geoconvention proceedings include multiple case studies on phase redistribution identification techniques applicable to WCSB gas-condensate plays.

Afterflow is closely related to wellbore storage (the compressibility mechanism in the wellbore that causes afterflow; the two terms are often used interchangeably, though strictly afterflow refers to the fluid movement and wellbore storage refers to the physical capacity that drives it, defined by C = Vwb × cwb in bbl/psi), wellbore storage coefficient (the parameter C that quantifies how much fluid the wellbore stores per unit pressure increase, directly controlling afterflow duration and setting the CD value that determines which Gringarten-Bourdet type curve applies to a given test), pressure buildup test (the primary pressure transient test during which afterflow is most consequential because it masks the middle-time region from which transmissibility and skin are extracted, and for which AER Directive 040 specifies minimum shut-in duration requirements), wellbore unloading (the mirror-image phenomenon during a drawdown test where stored wellbore fluid is produced ahead of reservoir influx, distorting the early-time pressure drawdown derivative with a unit slope identical in shape to the afterflow unit slope on a buildup), and phase redistribution (the secondary wellbore phenomenon superimposed on afterflow when gas and liquid segregate in the shut-in wellbore column, adding anomalous pressure humps that can be mistaken for dual-porosity, negative skin, or outer boundary effects in incorrectly processed DST datasets).

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