← Module 03 PBL Hub

SP-1: Skin Factor Concept & GK-22 PI Baseline

Convert S′ = +14 into physical and economic meaning. Calculate Jideal and Jactual by two independent methods, quantify the production shortfall and wasted drawdown pressure, and construct the 5-point dual IPR table that serves as the foundation for all subsequent Module 03 sub-problems.

Module 03 · SP-1
Topic 3.1 — Skin Concept
Gashaka GK-22
~45 min
SP-1 · Topic 3.1 · Skin Factor Concept

SP-1: Skin Concept & GK-22 PI Baseline

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Engineering Question for SP-1
Module 03 PBL · Gashaka GK-22 · Niger Delta

The data pack handed you one number: S′ = +14. Before you can treat anything, you must understand what that number means physically, economically, and operationally. What is the production shortfall in stb/d and $/year? How much of the available drawdown is being consumed by the skin rather than driving flow? How does this translate into the Flow Efficiency metric that management and facilities teams can act on?

SP-1 is the foundation that every subsequent sub-problem builds upon. The numbers you derive here — Jideal, Jactual, Δpskin, and the dual IPR table — are carried forward as locked inputs to SP-2 through SP-6. Get them right, and verify them independently before proceeding.

Data for SP-1

GK-22 SP-1 Data Subset

Data Source
All values below are from the Module 03 Hub Data Pack. Do not substitute values from any other source.
ParameterSymbolValueUnitsNotes
Effective oil permeability (kh / h from PTA)ko85mdDST Horner build-up
Net pay thicknessh42ftPetrophysical interpretation
Oil viscosity at p̄Rμo1.8cpPVT report — live oil
Oil FVF at p̄RBo1.32rb/stbPVT report
Average reservoir pressurep̄R4,200psiaHorner static BHP
Flowing wellbore pressure (DST)pwf2,500psiaBH gauge reading
Wellbore radiusrw0.35ftCasing/bit geometry
Drainage radiusre1,650ftWell spacing
Total skin (Horner build-up)S′+14dimensionlessPressure transient analysis
DST production rate (controlled flow)q782stb/dSurface metering
Before You Calculate

KWL Table — SP-1

Complete the K and W columns before opening Topic 3.1. Fill the L column only after completing all tasks in this sub-problem.

K — Know

What you bring from Module 02 and pre-reading

  • J = q / (p̄R − pwf): PI from rate and drawdown
  • Darcy equation links J to k, h, μ, B, geometry, and S
  • S > 0 reduces J; S = 0 is the undamaged reference
  • Jideal = 1.380 stb/d/psi (locked from Module 02)
  • Jmeas = 0.460 stb/d/psi (q/Δp = 782/1700)
W — Want to Know

Specific open questions for SP-1

  • What is the annual revenue loss from S′ = +14?
  • How much drawdown (in psi) is consumed by the skin?
  • What is the FE, and what does 0.333 mean operationally?
  • What would the well produce if S were reduced to +1?
  • What does the dual IPR chart look like?
L — Learned (fill after tasks)

Complete after all SP-1 tasks are done

  • Jideal = ________ stb/d/psi
  • Jactual = ________ stb/d/psi
  • Annual shortfall = ________ stb/yr ≈ $________/yr
  • Δpskin = ________ psi (___% of Δp)
  • FE = ________ (well at ___% of potential)
Just-in-Time Resources

Just-in-Time Resources

Pull these up as you work SP-1. Each maps to the Module 03 topic behind this sub-problem: read the topic page, watch the matching lecture, then reproduce your numbers with the verified calculator.

Study
Topic 3.1 — Skin Concept — what S′ means physically, Jideal vs Jactual, and the link to Flow Efficiency.
Topic 3.1 — Skin Concept
Watch
Lecture 3.1 — Skin Factor: From Physics to Equation
Produced lecture
Self-check
skin_basics.py — Jideal/Jactual, FE = 7/(7+S), and Δpskin.
Verified calculator — reproduce your numbers
Tasks & Requirements

SP-1 Calculation Tasks

Complete all five tasks in order. Show all working steps. Carry at least four significant figures through intermediate calculations. Every result you obtain here will be referenced by SP-2 through SP-6 — accuracy matters.

  1. Calculate the ideal PI, Jideal, with S = 0
    Apply the Darcy radial-flow equation in pseudo-steady-state form:

    Jideal = 0.00708 × ko × h ÷ [μo × Bo × (ln(0.472 × re/rw) + 0)]

    Report Jideal to three decimal places in stb/d/psi.
    Verification check: You should obtain Jideal ≈ 1.380 stb/d/psi. If your answer differs by more than 1%, identify the error before proceeding. Common mistakes: using re/rw without the 0.472 PSS correction; omitting the 0.00708 field-unit constant; using Bo and μo at standard conditions instead of reservoir conditions.
  2. Calculate the actual PI, Jactual, two ways — and verify they agree
    Method A: Direct from DST data: Jactual = q / (p̄R − pwf) = 782 / 1,700
    Method B: Darcy equation with S′ = +14 in the denominator

    Both methods must return Jactual ≈ 0.460 stb/d/psi. If they disagree, the skin value or well test data contains an inconsistency — this is the fundamental sanity check for any skin analysis.
    Why two methods? Method A is empirical (what we measured). Method B is theoretical (what the model predicts given S = +14). Agreement validates that the measured S′ = +14 is physically consistent with the measured J = 0.460. Disagreement would indicate PTA error, multi-rate testing issues, or wellbore storage contamination of the build-up.
  3. Calculate the annual production shortfall and its revenue equivalent
    At the current operating drawdown Δp = 1,700 psi:
    qideal = Jideal × 1,700   |   qactual = 782 stb/d (measured)
    Shortfall = qideal − qactual [stb/d]
    Annual shortfall = Shortfall × 365 [stb/yr]
    Annual revenue loss = Annual shortfall × $70/bbl (net value after opex)

    State the result in a form suitable for a management summary slide.
  4. Calculate Δpskin — the pressure wasted across the damage zone
    Using the skin pressure drop formula:
    Δpskin = 141.2 × q × μo × Bo × S′ ÷ (ko × h)

    Use q = 782 stb/d and S′ = +14. Express in psi. Calculate what fraction of the available drawdown (1,700 psi) is consumed by the skin effect.
    Physical meaning: Δpskin is the pressure drop that occurs across the damage zone — pressure that is "wasted" as heat in the near-wellbore altered zone rather than driving productive flow. If you removed all damage (S → 0), this pressure would become available as additional drawdown, driving significantly more flow.
  5. Construct a 5-point dual IPR table and sketch both curves
    For pwf = 4,200 / 3,500 / 2,500 / 1,500 / 0 psia, calculate q [stb/d] for both:
      •  S = 0 (ideal, undamaged) using Jideal = 1.380 stb/d/psi
      •  S = +14 (current) using Jactual = 0.460 stb/d/psi

    Sketch both IPR curves on the same axes. Annotate: current operating point (pwf = 2,500 psi, q = 782 stb/d); AOF (Absolute Open Flow, pwf = 0) for each curve; and the shaded area representing the production gain available if S were eliminated.
Validation Checkpoint — Do This Before SP-2
Jactual from Method A (DST) = 782/1700 = 0.460 stb/d/psi. Your Method B (Darcy with S=+14) must match this within ±2%. If it does, proceed. If not, the most likely cause is a logarithm calculation error — double-check ln(0.472 × 1650/0.35) = ln(2,223) = 7.707.
Theory Reference

Key Equations & Physical Interpretation

The Darcy PI Equation — Full Derivation Reference

Darcy Radial Flow — Pseudo-Steady State with Skin (Field Units)J = 0.00708 × k_o × h ───────────────────────────────────────────────────────── μ_o × B_o × [ln(0.472 × r_e/r_w) + S] Units: k [md], h [ft], μ [cp], B [rb/stb], r [ft] → J [stb/d/psi] The constant 0.00708 converts md·ft/(cp·rb/stb) to stb/d/psi GK-22 numerical evaluation (S = 0): Numerator: 0.00708 × 85 × 42 = 25.27 ln term: ln(0.472 × 1650/0.35) = ln(2,223) = 7.707 Denominator: 1.8 × 1.32 × (7.707 + 0) = 2.376 × 7.707 = 18.32 J_ideal = 25.27 / 18.32 = 1.380 stb/d/psi ✓ GK-22 numerical evaluation (S = +14): Denominator: 2.376 × (7.707 + 14) = 2.376 × 21.707 = 51.58 J_actual = 25.27 / 51.58 = 0.490 stb/d/psi (Darcy equation) Note: The DST-measured J = 782/1700 = 0.460 stb/d/psi is slightly lower. The small difference (6%) is within the uncertainty of r_e from well spacing. Both values are acceptable — use 0.460 (DST-measured) as the reference.
The 0.00708 constant applies to field units: mD, ft, cp, rb/stb, psia, stb/d. Never mix unit systems within this equation. A common error is to use k in Darcy (1 Darcy = 1000 mD) instead of millidarcy.

Skin Pressure Drop Formula

Pressure Drop Across the Skin ZoneΔp_skin = 141.2 × q × μ_o × B_o × S / (k_o × h) GK-22: Δp_skin = 141.2 × 782 × 1.8 × 1.32 × 14 / (85 × 42) = 141.2 × 782 × 1.8 × 1.32 × 14 / 3,570 = 3,706,340 / 3,570 ≈ 1,038 psi Fraction of available drawdown: 1,038 / 1,700 = 61% Interpretation: of the 1,700 psi drawdown available to drive production, only 662 psi (39%) is doing useful work moving fluid to surface. 1,038 psi (61%) is dissipated as additional pressure drop in the damage zone.

Flow Efficiency and Its Physical Meaning

Standing's Flow Efficiency — Derivation from Darcy EquationFE = J_actual / J_ideal = (ln(r_e/r_w)) / (ln(r_e/r_w) + S) ≈ 7 / (7 + S) [valid for typical well spacing: ln term ≈ 7] GK-22 pre-treatment: FE = 7 / (7 + 14) = 7/21 = 0.333 GK-22 post-acid (S=1): FE = 7 / (7 + 1) = 7/8 = 0.875 Interpretation of FE = 0.333: The GK-22 well is delivering only 33.3% of the oil it could produce from the same reservoir interval if there were no near-wellbore damage. Two-thirds of the well's productive potential is being destroyed by formation damage that is, in principle, removable by acid stimulation.
FE is the most intuitive way to communicate well damage to non-technical stakeholders. "The well is operating at 33% of its potential" conveys the problem immediately. "S = +14" does not.

Why the log term ≈ 7 approximation works

For GK-22: ln(0.472 × re/rw) = ln(0.472 × 1,650/0.35) = ln(2,223) = 7.707. The approximation (7 vs 7.707) introduces a 9% error in FE. Using the exact log term: FEpre = 7.707/(7.707+14) = 0.355; FEpost = 7.707/(7.707+1) = 0.885. Both methods are used in Module 03 — the 7-approximation for quick screening, the exact value for deliverables.

Deliverable

SP-1 Required Outputs

✅ SP-1 Checklist — Complete All Items Before Proceeding to SP-2

  • Jideal: Calculated by Darcy equation (S = 0). Report to 3 decimal points with full working shown.
  • Jactual — two methods: (A) DST direct (q/Δp); (B) Darcy equation with S = +14. Both methods shown. Agreement confirmed.
  • Annual production shortfall: In stb/yr and equivalent revenue at $70/bbl net value.
  • Δpskin: In psi, and as % of the total available drawdown (1,700 psi). Physical interpretation in one sentence.
  • 5-point dual IPR table: pwf (psia) | qideal (stb/d) | qactual (stb/d) for 5 pressure values. Verify qactual at pwf = 2,500 = 782 stb/d ✓.
  • IPR chart sketch: Both curves on the same axes, annotated with: current operating point, AOF for each curve, and a statement of FE = 0.333.
  • Management summary statement (1–2 sentences): In plain language, what does S′ = +14 mean for GK-22 production?
Numbers to Carry Forward — Locked Inputs for SP-2 through SP-6
Jideal = 1.380 stb/d/psi   |   Jactual = 0.460 stb/d/psi   |   FEcurrent = 0.333   |   Δpskin ≈ 1,038 psi   |   Shortfall ≈ 1,564 stb/d