Pressure Buildup: Horner Plot and Bourdet Derivative
Paste buildup data (shut-in time Δt in hours, pressure pws) and enter well and fluid properties to draw the Horner plot and the log-log plot with the Bourdet derivative, and compute k and skin from the semilog straight line.
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Educational tool for preliminary analysis. It is not a substitute for certified software or a qualified engineer’s review for major decisions.
Format: two columns, Δt (hr) then pws (psi). Leave the line limits empty to use the later half of the data (in log time).
Results
Calculation steps and intermediate values
Explanation and formulas
After producing at constant rate q for time tp, pressure rises when the well is shut in. During infinite-acting radial flow (IARF), pws plotted against log((tp + Δt)/Δt) is a straight line whose slope m (psi/cycle) gives permeability.
Skin s comes from the difference between the line pressure at Δt = 1 hr and the flowing pressure at shut-in. Extrapolating the line to (tp + Δt)/Δt = 1 gives p*, close to reservoir pressure for an infinite-acting system.
The Bourdet derivative is dΔp/d ln(Δte), with Agarwal equivalent time Δte = tp·Δt/(tp + Δt), computed with a smoothing window L. During IARF it is flat at m/2.303; an early unit slope indicates wellbore storage.
k = 162.6 · q · B · μ / (m · h) [md]
s = 1.151 · [ (p1hr − Pwf)/m − log10( k / (φ · μ · ct · rw²) ) + 3.23 ]
Δp_skin = 0.869 · m · s ; FE = (p* − Pwf − Δp_skin)/(p* − Pwf)
Δte = tp·Δt/(tp + Δt) ; Δp′ = dΔp / d ln(Δte) (Bourdet, window L) ; IARF: Δp′ = m/2.303
Validation
Published example (Earlougher, SPE Monograph 5, Example 5.1; also in Ahmed): q = 4900 STB/d, B = 1.55, μ = 0.20 cp, h = 482 ft, φ = 0.09, ct = 22.6×10⁻⁶ 1/psi, rw = 0.354 ft, tp = 310 hr, Pwf = 2761 psi, m = 40 psi/cycle, p1hr = 3266 psi. Book: k = 12.8 md, s = 8.6. Tool, on example data built from these values (same semilog line plus early wellbore storage; not the original table): m = 40.0, p1hr = 3266, k = 12.8 md, s = 8.6.
References
- Horner, D.R. (1951). Pressure Build-up in Wells. Proc. Third World Petroleum Congress, The Hague, Sec. II, 503–523.
- Earlougher, R.C. Jr. (1977). Advances in Well Test Analysis. SPE Monograph Vol. 5, Example 5.1.
- Bourdet, D., Ayoub, J.A. & Pirard, Y.M. (1989). Use of Pressure Derivative in Well-Test Interpretation. SPE Formation Evaluation 4(2): 293–302. SPE-12777-PA.
- Agarwal, R.G. (1980). A New Method to Account for Producing Time Effects When Drawdown Type Curves Are Used to Analyze Pressure Buildup and Other Test Data. SPE-9289-MS.
- Lee, J. (1982). Well Testing. SPE Textbook Series Vol. 1.