SP-4: Pseudo-Skin Verification · GK-22

SP-4 · Topic 3.4 · Pseudo-Skin

SP-4: Verify That Geometric Pseudo-Skins Are Negligible

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Engineering Question for SP-4

Module 03 PBL · Gashaka GK-22

SP-1 through SP-3 have concluded that S_d = +14 (all formation damage, treatable by acid). But this conclusion carries an implicit assumption: that none of S′ = +14 comes from geometric pseudo-skins S_c from partial completion or S_c″ from wellbore deviation. Pseudo-skins are not treatable by acid; misattributing them to formation damage leads to a treatment that fails to deliver the predicted uplift.

For GK-22, a fully-perforated (b = 1.0), near-vertical well (θ <5°), both pseudo-skins should be negligible. SP-4 calculates them explicitly using the Brons–Marting (partial completion) and Cinco-Ley (deviation) correlations, confirming the conclusion that S_d = S′ = +14 with no geometric contribution. The SP also runs the Jones–Watts sensitivity: what would the total skin be if only 50% of pay had been perforated?

Data for SP-4

Parameter	Symbol	Value	Units	Used in
Net pay thickness	h	42	ft	Both correlations
Perforated interval	h_p	42	ft	Brons–Marting
Penetration ratio	b = h_p/h	1.00	dimensionless	b = 1 → S_c = 0
Well deviation in pay zone	θ	<5	degrees from vertical	Cinco-Ley
Wellbore radius	r_w	0.35	ft	h_D calculation
k_v/k_h (laminated Agbada sand)	k_v/k_h	0.5	dimensionless	Cinco-Ley anisotropy correction
Total skin to explain (from SP-1–3)	S′	+14.00	dimensionless	Residual = S_d

KWL Table

K — Know

S_c = 0 when b = h_p/h = 1.0 (full penetration)
S_c″ is a negative (beneficial) skin for deviated wells
Pseudo-skins are geometric — acid has no effect on them
Jones–Watts shows pseudo-skin amplifies S_d when b < 1

W — Want to Know

What exactly is S_c″ for θ = 4°, k_v/k_h = 0.5?
What would total skin be if b = 0.50 (50% of pay perforated)?
Does S_c″ materially change the skin audit conclusion?
What is h_D and why does it matter for S_c″?

L — Learned

S_c (b=1.0) = ________
θ′ = ________ degrees
h_D = ________
S_c″ (θ<5°) = ________
S_d = S′ − S_c − S_c″ − Dq = ________
S′ if b=0.50 would be: ________

Just-in-Time Resources

Pull these up as you work SP-4. 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 3.4 — Pseudo-Skin — the components of S′ that acid cannot treat: partial completion (S_c) and deviation (S_c″).

Topic 3.4 — Pseudo-Skin

Watch

Lecture 3.4a — Pseudo-Skin: What Cannot Be Treated by Acid
Lecture 3.4b — Calculating Sc and Sc″: Brons–Marting and Cinco-Ley Methods

Produced lectures

Self-check

pseudoskin.py — Brons–Marting S_c and Cinco-Ley S_c″, including the h_D convention behind the partial-completion skin.

Verified calculator — reproduce your numbers

Tasks & Requirements

SP-4 Calculation Tasks

Calculate partial-completion skin S_c using Brons–Marting
With b = h_p/h = 42/42 = 1.0: the term (1/b − 1) = 0, so S_c = 0 exactly for GK-22.

Sensitivity calculation: What would S_c be if GK-22 had been completed at b = 0.50 (21 ft of 42 ft pay perforated)?
Use the Brons–Marting approximation:
S_c ≈ (1/b − 1) × [ln(h_D/b) − G(b)], h_D = h/r_w = 120 (isotropic — anisotropy is not reapplied for partial-completion skin)
where G(0.5) ≈ 2.401 (tabulated value from Brons–Marting Figure 3).
Expected for b=0.50: S_c ≈ +3.08 (isotropic h_D = h/r_w = 120). Combined with Jones–Watts multiplier (Section 4 of Topic 3.4): if h/h_p = 2.0, the effective skin becomes S′ = (h/h_p) × S_d + S_c = 2.0 × 14 + 3.08 = +31.1. At S′ = +31.1, FE = 7/(7+31.1) = 0.184, and q at p_wf=2500 would be 0.184×1.380×1700 = 431 stb/d (vs 782 stb/d measured). This demonstrates why full perforation coverage is critical in damaged wells.
Calculate deviation skin S_c″ using Cinco-Ley (1975)
Step 1: Compute the anisotropy-corrected deviation angle:
θ′ = arctan[√(k_v/k_h) × tan(θ)] = arctan[√0.5 × tan(4°)]

Step 2: Compute the dimensionless thickness:
h_D = (h/r_w) × √(k_h/k_v)

Step 3: Apply Cinco-Ley correlation:
S_c″ = −(θ′/41)^2.06 − (θ′/56)^1.865 × log(h_D/100)

Report S_c″ to 3 decimal places.
Expected: θ′ ≈ 2.83°, h_D ≈ 169.7, S_c″ ≈ −0.005. The negative sign is correct — deviation provides a slight production benefit (larger effective contact area between wellbore and formation). For θ < 15°, S_c″ is always a small negative number and never materially affects the skin audit for near-vertical wells.
Compile the complete pre-treatment skin audit (all components)
Fill in the table below:

S′ (total, measured) = +14.00 [source: PTA Horner]
− Dq (non-Darcy) = ________ [source: SP-2]
− S_c (partial completion) = ________ [source: Task 1 above]
− S_c″ (deviation) = ________ [source: Task 2 above]
= S_d (implied formation damage) = ________

Confirm S_d ≈ +14.00 to within rounding.
Sensitivity: Jones–Watts — what if only 50% of pay were perforated?
Using b = 0.50, S_c ≈ +3.08 (from Task 1), and the Jones–Watts skin amplification:
S′_total(b=0.5) = (h/h_p) × S_d + S_c
Calculate q at p_wf = 2,500 psi using this inflated skin. Compare to the measured 782 stb/d.
This illustrates why ensuring b = 1.0 (full perforation coverage) is critical before acid treatment.

Engineering Significance of SP-4

SP-4 is the final verification step before the treatment is designed. Its function is to eliminate alternative explanations for the high skin before committing to an acid programme. If GK-22 had b = 0.7 and θ = 35° (a moderately deviated, partially perforated well), the pseudo-skins could account for S_c = +2 and S_c″ = −1.5, reducing the inferred S_d from +14 to +13.5 — marginal in this case, but critical for wells where S′ = +8 and you need to know how much is treatable.

Theory Reference

Brons–Marting Partial Completion Skin (b = 1.0 Case)Sc = (1/b - 1) × [ln(h_D/b) - G(b)] where: b = h_p/h, h_D = (h/r_w) × sqrt(k_h/k_v) GK-22 (b = 1.0): (1/b - 1) = (1/1 - 1) = 0 Sc = 0 × [...] = 0.000 ✓ Sensitivity (b = 0.50): Use the ISOTROPIC dimensionless thickness h_D = h/r_w for partial-completion skin (anisotropy is not applied a second time here — Brons–Marting tabulated G(b) against h_D = h/r_w): h_D = 42/0.35 = 120 G(0.50) = 1.35 / [0.5^0.825 × (1 + 0.5^3.5/120)] = 2.401 (Brons–Marting tables) Sc = (1/0.5 - 1) × [ln(h_D/b) - G(0.5)] = 1.0 × [ln(120/0.5) - 2.401] = 1.0 × [ln(240) - 2.401] = 1.0 × [5.480 - 2.401] = +3.08 (isotropic basis; matches the +3.1 worked example and Jones–Watts cascade) Cinco-Ley Deviation SkinS''c = -(θ'/41)^2.06 - (θ'/56)^1.865 × log(h_D/100) GK-22: θ = 4°, k_v/k_h = 0.5 θ' = arctan[sqrt(0.5) × tan(4°)] = arctan[0.7071 × 0.06993] = arctan(0.04946) = 2.834° h_D = (42/0.35) × sqrt(2.0) = 120 × 1.414 = 169.7 S''c = -(2.834/41)^2.06 - (2.834/56)^1.865 × log(169.7/100) = -(0.06912)^2.06 - (0.05061)^1.865 × log(1.697) = -0.003977 - 0.002632 × 0.2296 = -0.003977 - 0.000604 = -0.00458 ≈ -0.005 ✓

The negative S''c confirms deviation is a slight benefit, not a penalty. For GK-22's θ < 5°, this -0.005 is analytically negligible — it has zero impact on the treatment decision or economic calculation. It is calculated here for completeness and to demonstrate the methodology.

Deliverable

✅ SP-4 Checklist

S_c (b=1.0): = 0.000 confirmed. Working shown (factor (1/b−1) = 0).
S_c″ (θ<5°): Full Cinco-Ley calculation with θ′, h_D, and formula. Result ≈ −0.005.
Complete pre-treatment skin audit table: S′ = +14.00, breakdown showing Dq ≈ 0.001, S_c = 0, S_c″ ≈ −0.005, implied S_d = +14.00.
Jones–Watts sensitivity: S′ at b = 0.50 (showing the amplification to +31.1 skin units) and resulting q = 431 stb/d — the counterfactual that makes the value of full perforation coverage quantitatively clear.
One-sentence confirmation: S_d = S′ = +14.00 — all pseudo-skin components are confirmed negligible. This statement locks the skin attribution for SP-5 and SP-6.

Module 03 Pre-Treatment Skin Audit — Confirmed Values for SP-5 & SP-6

S_d = +14.00 | S_c = 0.000 | S_c″ = −0.005 | Dq = 0.001 | S′ = +14.00 (all formation damage, all treatable by acid)

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