SP-2 · Topic 3.2 · Total Skin S′ = S + Dq
SP-2: Is Any of GK-22's Skin Rate-Dependent?
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Engineering Question for SP-2
Module 03 PBL · Gashaka GK-22
SP-1 confirmed that S′ = +14 and Jactual = 0.460 stb/d/psi. But S′ is the total skin — it may contain both a rate-independent component S (formation damage, geometric effects, treatable by acid) and a rate-dependent component Dq (turbulence, non-Darcy inertia, not treatable by acid). Designing an acid treatment to remove a skin that is 50% turbulence-driven would waste the workover budget. You must quantify Dq before any treatment is specified.
For GK-22, an oil well at 782 stb/d in an 85 md formation, the answer is anticipated to be Dq ≈ 0. But engineering requires proof, not intuition. This sub-problem calculates D from first principles using two independent β correlations (Katz and Dake), computes Dq at the test rate, and extends the analysis to the projected post-acid rate (~2,000 stb/d) to confirm Dq remains negligible even at higher production.
Data for SP-2
GK-22 SP-2 Data Subset
Locked Input from SP-1
S′ = +14 (total skin from Horner PTA). All of this skin is to be decomposed: S′ = S + Dq. Your task is to determine the magnitude of Dq.| Parameter | Symbol | Value | Units | Used in |
|---|---|---|---|---|
| Effective oil permeability | ko | 85 | md | Both β correlations |
| Net pay / perforated interval | h = hp | 42 | ft | D formula denominator |
| Wellbore radius | rw | 0.35 | ft | D formula |
| Oil viscosity | μo | 1.8 | cp | D formula |
| Oil specific gravity | γo | 0.85 | dimensionless | D formula (35°API crude) |
| DST production rate | q | 782 | stb/d | Dq = D × q at test rate |
| Projected post-acid rate (from SP-5) | qpost | ~2,050 | stb/d | Dq sensitivity at high rate |
KWL Table
K — Know
- S′ = S + Dq: D is rate-independent component of skin per unit rate
- D-coefficient has units of (stb/d)−¹ for oil wells
- Non-Darcy flow is significant in high-rate gas wells; usually small for oil
- β = turbulence coefficient; inversely related to permeability
W — Want to Know
- What β value does GK-22's 85 md permeability give?
- How does D compare to the magnitude of S′ = +14?
- At what rate would Dq become significant (>1 skin unit)?
- Does Dq change the treatment decision?
L — Learned
- βKatz = ________ ft−¹
- D = ________ (stb/d)−¹
- Dq at 782 stb/d = ________
- Dq as % of S′ = _____% → treatment decision: ________
Just-in-Time Resources
Just-in-Time Resources
Pull these up as you work SP-2. Each maps to the Module 03 topic behind this sub-problem: read the topic page, watch the matching lectures, then reproduce your numbers with the verified calculator.
Study
Topic 3.2 — Total Skin & Non-Darcy Flow — decomposing S′ = S + Dq and back-calculating the rate-dependent term.
Topic 3.2 — Total Skin & Non-Darcy
Watch
Lecture 3.2a — Total Skin: Breaking the Well Test Number Apart
Lecture 3.2b — Calculating D: Theory, Correlations, and Field Practice
Produced lectures
Lecture 3.2b — Calculating D: Theory, Correlations, and Field Practice
Self-check
nondarcy.py — the non-Darcy coefficient D and Dq split (includes the FK-7 gas-well case where Dq dominates).
Verified calculator — reproduce your numbers
Tasks & Requirements
SP-2 Calculation Tasks
- Calculate β using Katz (1959) correlation
βKatz = 4.11 × 1010 / ko1.33 [ft−¹]
With ko = 85 md, compute β to 3 significant figures.Expected result: βKatz ≈ 1.55 × 108 ft−¹. This extremely large number for permeability in ft−¹ is physically correct — turbulence effects at the pore scale create very large inertial coefficients. - Calculate β using Dake (1983) correlation and compare
βDake = 2.73 × 1010 / ko1.10 [ft−¹]
Compare to Katz result. Express the percentage difference. What does this tell you about uncertainty in β?Expected result: βDake ≈ 1.12 × 108 ft−¹. The ~28% difference between correlations is typical — β correlations are empirical fits to limited laboratory data. For screening purposes, either is acceptable. For a gas well (where Dq might be +5 or more) the choice matters; for GK-22 oil well it will not. - Calculate D — the non-Darcy rate coefficient
Doil = 2.22 × 10−15 × β × γo × ko × h ÷ (hp2 × rw × μo)
Calculate D using β from both Katz and Dake correlations. Report D in (stb/d)−¹.Expected: D ≈ 9.4 × 10^−7; (stb/d)−¹ (Katz β). Note the hp2 in the denominator: D is highly sensitive to the perforated interval. GK-22 with hp = h = 42 ft (full pay penetration) has maximum hp → minimum D. Partial completion (hp = 21 ft) would quadruple D. - Calculate Dq at the DST rate and at the projected post-acid rate
DqDST = D × 782 | Dqpost = D × 2,050
Express Dq as: (a) absolute skin units; (b) % of S′ = +14
State whether Dq is negligible at both rates. Define your threshold for "negligible" (e.g. Dq < 0.1, or Dq/S′ < 1%). - Write the diagnostic statement for the Module 03 Final Report
Two sentences (maximum): state the confirmed value of Dq at 782 stb/d and at 2,050 stb/d, and state the engineering conclusion for the skin decomposition. This statement is quoted verbatim in SP-6's Final Skin Audit table under the Dq row.Example format: "Non-Darcy skin Dq = [value] at the DST rate (782 stb/d), representing [x]% of the measured total skin. Dq remains negligible (<0.01 skin units) at the projected post-acid rate of 2,050 stb/d, confirming that S′ = +14 is entirely rate-independent. The Darcy skin S = S′ = +14."
Why This Matters — The Design Risk of Skipping SP-2
In a high-rate gas well with k = 85 md and q = 20 MMscf/d, Dq can exceed +10 skin units. If an engineer designed an acid treatment expecting post-acid S → 0 but half the skin was turbulence-driven (not treatable), the treatment would deliver only half the expected production uplift. For GK-22 at 782 stb/d oil, Dq is confirmed negligible — but this verification is essential. An untested assumption that "it's an oil well so Dq ≈ 0" is not engineering.
Theory Reference
D Coefficient — Full Derivation
Non-Darcy Coefficient D — Oil Well FormulaD_oil = (2.22 × 10⁻¹⁵ × β × γ_o × k_o × h) / (h_p² × r_w × μ_o)
GK-22 calculation using β_Katz = 1.55 × 10⁸ ft⁻¹:
Numerator: 2.22e-15 × 1.55e8 × 0.85 × 85 × 42
= 2.22e-15 × 1.55e8 × 3,034.5
= 2.22e-15 × 4.703e11
= 1.044e-3
Denominator: 42² × 0.35 × 1.8 = 1,764 × 0.63 = 1,111.3
D = 1.044e-3 / 1,111.3 = 9.39 × 10⁻⁷ (stb/d)⁻¹
Dq at q = 782 stb/d:
Dq = 9.39e-7 × 782 = 7.34 × 10⁻⁴ ≈ 0.001 skin units
As % of S' = 14: 0.001/14 = 0.007% — analytically negligible
Dq at q = 2,050 stb/d (post-acid target):
Dq = 9.39e-7 × 2,050 = 1.92 × 10⁻³ ≈ 0.002 skin units
Still negligible: 0.002/14 = 0.014%
Compare to a gas well: k = 50 md, q = 20 MMscf/d, h_p = 30 ft, μ_g = 0.02 cp, γ_g = 0.65. D ≈ 5 × 10⁻⁴ (Mscf/d)⁻¹. Dq at 20 MMscf/d = 5e-4 × 20,000 = 10 skin units! For gas, Dq regularly exceeds S_d. This is why SP-2 is essential — the method is the same; the magnitude is context-dependent.
Deliverable
✅ SP-2 Checklist
- β table: βKatz and βDake with full working. % difference noted and discussed.
- D calculation: Full formula applied with both β values. Units confirmed as (stb/d)−¹.
- Dq at 782 stb/d: Absolute skin units and as % of S′ = +14.
- Dq at 2,050 stb/d: Same as above — confirms Dq negligible at post-acid rate.
- Diagnostic statement: Two-sentence engineering conclusion for the Final Report (ready to be quoted verbatim in SP-6 skin audit table).
- Implication: One sentence on what this result means for the treatment design — does it change anything vs the assumption that all S′ = Sd?
Locked Output for SP-3 through SP-6
Sd = S′ = +14.0 (confirmed, all rate-independent) |
Dq ≈ 0.001 (negligible, <0.01% of S′) |
All of S′ = +14 is treatable formation damage.