Buildup Near Sealing Fault — Boundary Detection

Pressure buildup interpretation near a linear sealing fault. Demonstrates the classic derivative doubling signature: early IARF yields the correct permeability, then the Bourdet derivative doubles as the pressure signal reaches the fault and reflects back. Compares fault model against infinite reservoir to highlight the boundary effect.

Derivative doubling is the hallmark of a sealing fault. A single linear no-flow boundary causes the late-time semilog slope to exactly double. If the derivative drops to zero instead, the boundary is a constant-pressure source (aquifer) — use PO.PTA.Pw.VW.LinConP to model that case.

Early IARF must be flagged carefully. Only flag points between end of WBS and boundary arrival. For the default case (L=800 ft), the boundary effect appears around Δt ≈ 36h. The IARF window is Δt ≈ 4–12h.

Boundary distance estimation uses the radius of investigation at the departure time: L ≈ √(k·t/(948·φ·μ·ct)). This gives an approximate distance — the exact value depends on the rate history and WBS effects.

For real data use. Replace column D (Pws) with measured gauge pressures. Clear columns B–C (models). Identify the derivative doubling visually and enter the departure time in row 45.

IARF flag column (G) uses 1/0 numeric values. Same convention as all PTA blueprints.

Reference: Earlougher, R.C. (1977). "Advances in Well Test Analysis." SPE Monograph Series, Vol. 5.

• Interpretation Inputs (rows 3–12): Same as Horner — tp, q, Bo, μ, φ, ct, rw, h, Pwf, L (Bourdet smoothing).
• Forward Model (rows 15–22): k, S, Pi, C plus fault distance Lfault. Rate schedule defines constant-rate drawdown followed by shut-in.
• Data Table (rows 24–35): Column B = Pws from fault model (LinSealF). Column C = Pws from infinite model (VW, for comparison). Column D = measured Pws (defaults to fault case). Columns E–F = Horner time. Column G = IARF flag (early IARF only, before boundary). Column H = Bourdet derivative.
• Derivative Doubling: Compare columns B and C. Before boundary arrival, both models give the same Pws and derivative. After boundary arrival, the fault derivative doubles from |m| to 2|m| while the infinite case stays flat. This is the diagnostic signature of a sealing fault.
• Early IARF Interpretation (rows 38–42): Flag only the pre-boundary IARF window (G=1). The slope m, P*, k, and S are computed from this early window — same as standard Horner analysis.
• Boundary Analysis (rows 44–46): Enter the observed departure Δt (where the derivative starts increasing). The fault distance is estimated via _PO.PTA.Rinv as the radius of investigation at that time.
• Validation (rows 48–52): Round-trip validation of k, S, P*, and boundary distance L.