Constant-Rate Drawdown Analysis

Constant-rate drawdown test interpretation using MDH (Miller-Dyes-Hutchinson) semilog analysis with Bourdet derivative for IARF identification. The most fundamental well test — a single rate from initial conditions. Includes forward model for synthetic data generation and round-trip validation.

No SORT required for Bourdet. Unlike the Horner blueprint where log₁₀(HT) is naturally descending, the drawdown log₁₀(t) axis is ascending — matching the Bourdet function requirement directly.

IARF flag column (F) uses 1/0 numeric values, not TRUE/FALSE. Avoids AVERAGEIF #DIV/0! from text-interpreted booleans.

For the default synthetic case (k=50 mD, S=5, C=0.001 bbl/psi), the unit-slope WBS ends at ~0.17h and IARF begins at approximately t ≥ 4h. Adjust Bourdet L between 0.1 and 0.5 to control smoothing.

MDH vs Horner. This blueprint analyzes drawdown (flowing) data. For buildup (shut-in) data, see po.pta.horner.pstar. Both methods yield the same k and S for the same reservoir — they just use different test configurations.

For real data use. Replace column C (Pwf) with measured gauge pressures. Clear or ignore the forward model block.

LAMBDA functions defined here (_PO.PTA.*) represent common PTA calculations not yet available as native PO functions.

Reference: Miller, C.C., Dyes, A.B., and Hutchinson, C.A. (1950). "The Estimation of Permeability and Reservoir Pressure from Bottom-Hole Pressure Build-Up Characteristics." JPT.

• Interpretation Inputs (rows 3–11): Reservoir and fluid properties — q, Bo, μ, φ, ct, rw, h, Pi, and Bourdet smoothing L. Initial pressure Pi is assumed known from pre-test surveys.
• Forward Model (rows 14–16): Optional validation block. Enter known k, S, C to generate synthetic Pwf via PO.PTA.Pw.VW at constant rate q.
• Data Table (rows 18–29): Column A = time t. Column B = Pwf from forward model. Column C = measured Pwf (defaults to =B for self-validation; replace with gauge data). Column D = pressure drop ΔP = Pi − Pwf. Column E = log₁₀(t). Column F = IARF flag (1/0). Column G = Bourdet derivative dΔP/dlog₁₀(t).
• Flow Regime Identification: On a log-log plot of ΔP and Bourdet derivative vs time: (1) unit-slope line during WBS — ΔP increases linearly with t; (2) transition hump; (3) flat derivative = IARF. Set F = 1 where derivative is approximately constant.
• Slope, m (row 31): AVERAGEIF of Bourdet values in IARF. This is the semilog slope dΔP/dlog₁₀(t) in psi/cycle — positive for drawdown.
• ΔP at t=1hr (row 32): Intercept of IARF line at log₁₀(t) = 0 (t = 1hr). Computed from mean ΔP and mean log₁₀(t) of IARF-flagged points.
• Permeability (row 33): Computed via _PO.PTA.PermFromSlope — k = 162.6 × q × Bo × μ / (|m| × h).
• Skin (row 34): Computed via _PO.PTA.SkinFromDp1hr — S = 1.151 × [ΔP₁ₕᵣ/|m| − log₁₀(k/(φμctrw²)) + 3.23].
• End of WBS (row 37): Computed via _PO.PTA.EndWBS. Useful for planning test duration — data before tWBS is dominated by wellbore storage and cannot be interpreted.
• Validation (rows 40–41): Compares forward model k, S against interpretation results. Expected: k < 1%, S < 2% on clean synthetic data.