Topics 3.1–3.3 confirmed that GK-22's total skin of +14 is entirely formation damage. But in other wells, and as a verification step for GK-22, we must quantify the geometric and mechanical contributions to skin that are independent of damage — the pseudo-skin components. These cannot be treated by acid. Understanding them is essential for correctly attributing skin and for optimising perforation and completion design.
GK-22 skin-audit case — canonical data (locked for all Module 03 topics):
ko = 85 md · h = 42 ft · μo = 1.8 cp · Bo = 1.32 rb/stb ·
p̄R = 4,200 psi · pwf = 2,500 psi · rw = 0.35 ft ·
re = 1,650 ft · q = 782 stb/d · S′ = +14
The total skin measured in a well test is the sum of all components, both treatable and non-treatable:
S′ = Sd + Sp + Sc + Sc″ + Ss + D·q
Topics 3.1–3.3 identified and quantified Sd (formation damage skin, Hawkins' formula) as the dominant contribution to GK-22's S′ = +14. This topic addresses the geometric pseudo-skin components:
Sc (partial completion skin): When only a fraction of the net pay (hp/h < 1) is perforated, radial flow must converge to enter the limited open interval. This flow geometry requires extra pressure drop — a positive pseudo-skin that persists regardless of damage. Unlike damage skin, it can only be remedied by additional perforations, not by acid.
Sc″ (deviation skin): When a well is deviated from vertical, the wellbore intersects more pay over any given vertical interval, and the effective wellbore area exposed to the formation is larger than assumed by the vertical Darcy model. This generally produces a negative pseudo-skin (a beneficial effect). For wells deviated >15°, this correction can be significant.
For GK-22 (vertical well, fully perforated across the 42 ft pay), both Sc and Sc″ are expected to be small. This topic verifies that conclusion and equips you to calculate these components for wells where they are significant.
▶
Lecture 3.4a: Pseudo-Skin — What Cannot Be Treated by Acid
13:15
Defines pseudo-skin as skin of geometric or mechanical origin. Distinguishes true formation damage (Sd, treatable) from partial penetration (Sc), deviation (Sc″), turbulence (Dq), and multiphase effects. Covers the physical flow convergence mechanism that creates positive Sc in partially-completed wells and why perforating more of the pay is more effective than acid for partially-completed wells.
▶
Lecture 3.4b: Calculating Sc and Sc″ — Brons–Marting and Cinco-Ley Methods
14:50
Derives the Brons–Marting partial penetration correlation and the Cinco-Ley deviation skin formula. Step-by-step worked examples for three scenarios: (a) GK-22 vertical, fully perforated; (b) a deviated well at 45° partially perforated; (c) a horizontal well. Shows how Sc and Sc″ are combined and how the Jones–Watts h/hp multiplier modifies formation damage in a partially-completed well.
LEARNING OBJECTIVES
After completing this topic, you will be able to:
1. Define pseudo-skin and explain why geometric skin components cannot be reduced by matrix acid treatment. 2. Explain the physical mechanism that creates positive partial completion skin Sc when hp/h < 1. 3. Calculate partial completion skin Sc using the Brons–Marting correlation for a vertical well. 4. Explain why well deviation creates a negative deviation skin Sc″ and calculate it using the Cinco-Ley formula. 5. Apply the Jones–Watts h/hp multiplier to correctly account for the interaction between partial penetration and formation damage skin. 6. Calculate the combined completion skin Sc = S′c + S″c for a specified well geometry. 7. Verify that GK-22's pseudo-skin contributions are negligible, confirming Sd ≈ S′ = +14. 8. Use the skin audit framework to identify whether additional perforations or a change in well trajectory would be more beneficial than acid treatment for a given well.
PBL CONNECTION — COMPLETING THE GK-22 SKIN AUDIT
This topic completes the skin audit for GK-22 by verifying the pseudo-skin contributions. Key facts from the GK-22 completion record:
Well inclination: Vertical (<5° deviation from vertical in the pay zone) Perforated interval: 42 ft (full pay interval, hp/h = 42/42 = 1.0) Shot density: 4 spf, 0° phasing
With full penetration and near-vertical trajectory, both Sc and Sc″ are expected to be negligible. This topic provides the rigorous calculation to confirm this, completing the skin audit: S′ = Sd(+14) + Sc(~0) + Sc″(~0) + Dq(~0) = +14. The entire skin is treatable formation damage.
Section 1
The Pseudo-Skin Concept, Geometric Contributions to S′
Not all skin is damage. Geometric constraints imposed by the completion geometry — how much pay is perforated and at what angle — create pressure drops that appear as skin but cannot be removed by any chemical treatment.
1.1 Total Skin Decomposition — All Six Components
The complete decomposition of total skin S′. The components are generally additive but their interactions must be carefully tracked:
S′ = Sd + Sp + Sc + Sc″ + Ss + D·qThis is what the well test measures
1.2 Why Pseudo-Skin Cannot Be Treated by Acid
The fundamental distinction is physical: acid removes permeability impairment from the rock matrix. Geometric pseudo-skin arises from the flow path geometry, not from any alteration of the rock. Even in a completely undamaged formation, a well that only penetrates 30% of the pay section will have positive pseudo-skin because the remaining 70% of the rock cannot directly feed the wellbore — fluid must flow vertically through the formation before converging into the perforations.
No amount of acid can change this geometry. The only engineering fixes for partial completion pseudo-skin are: (a) perforate more of the pay, or (b) accept the skin and quantify its contribution accurately so it is not attributed to treatable damage.
1.3 The Physical Origin of Partial Penetration Pseudo-Skin
The Darcy radial flow equation assumes that the entire pay thickness h contributes radially and uniformly to the wellbore. When only hp < h is perforated, the actual flow field must depart significantly from this ideal:
Figure 1.3.1 — Physical origin of partial completion pseudo-skin. Left: Full penetration (hp = h) produces ideal horizontal radial flow with Sc = 0. Right: Partial penetration (hp < h) forces fluid to flow vertically before converging into the open interval. The additional pressure drop from this non-radial flow geometry appears as a positive pseudo-skin Sc, regardless of formation damage.
KEY INSIGHT — INTERACTION WITH DAMAGE SKIN
Jones & Watts (Jones L, Watts J (1971) Estimating skin effect in a partially completed damaged well. J Petrol Technol 23(2):249–252.) showed that partial completion pseudo-skin and formation damage skin are not simply additive in the standard form. The correct total skin for a partially completed, damaged well is:
S = (h/hp) × Sp + Sc
The h/hp multiplier accounts for the fact that flow velocities are higher in the perforated interval (because only hp carries the flow), so the damage pressure drop is proportionally greater. This is critical: a partially completed well with formation damage is doubly penalised — both Sc and the amplified Sd increase total skin above simple addition.
Section 2
Partial Completion Skin Sc: The Brons–Marting Correlation
When only a fraction of the net pay is perforated, the additional pressure drop from non-radial flow convergence must be quantified. The Brons–Marting (1961) correlation provides the standard engineering method for vertical wells.
2.1 Dimensionless Parameters for Partial Completion
The Brons–Marting approach uses two dimensionless groups to characterise the completion geometry:
Penetration Ratio (hp/h)
b = hp / h
Fraction of the net pay section that is open to flow. b = 1.0 is full penetration (Sc = 0). b = 0.5 means 50% of pay is perforated. b < 0.3 generally produces Sc > 5, which is significant.
Dimensionless Pay Thickness (hD)
hD = (h/rw) × √(kh/kv)
Ratio of pay thickness to wellbore radius, corrected for permeability anisotropy. Captures how easily fluid can flow vertically to reach the perforations. High hD = more geometric restriction = higher Sc.
2.2 The Brons–Marting Partial Completion Formula
For a vertical well in an isotropic formation (kh/kv = 1, the simplest case), the partial completion pseudo-skin is:
Sc = (1/b − 1) × [ln(hD/b) − G(b)]
b — Penetration Ratio
hp/h (dimensionless)
hp = perforated length (ft); h = net pay (ft). GK-22: b = 42/42 = 1.0, so Sc = 0 exactly.
hD — Dimensionless Thickness
h/(rw×√(kh/kv))
For isotropic kh = kv: hD = h/rw. GK-22: hD = 42/0.35 = 120. Sc increases with hD.
G(b) — Geometric Function
1.35/[b0.825(1+b3.5/hD)]
Brons–Marting empirical correction. Accounts for flow field geometry near the perforated interval. G(b) reduces Sc slightly from the asymptotic value.
2.3 Approximate Forms for Quick Estimation
For hD > 20 (the usual case in reservoir engineering), the Brons–Marting formula simplifies to:
Sc ≈ (1/b − 1) × [ln(h/rw) − ln(1/b) − 0.75]
A further useful form derived by rearranging is:
Sc ≈ (1 − b)/b × [ln(h/(b×rw)) − 0.75]
2.4 Sensitivity of Sc to Penetration Ratio and Pay Thickness
The following table uses GK-22's geometry (h = 42 ft, rw = 0.35 ft, isotropic k) to show Sc across a range of perforation scenarios. This is the design table an engineer would use when deciding how much of the pay to perforate:
hp (ft)
Penetration b = hp/h
1/b − 1
hD = h/rw
Sc (approx)
J ratio vs full perf
Interpretation
42 (full)
1.00
0.00
120
0.0
1.00×
Ideal — no geometric skin
37
0.88
0.14
120
+0.6
0.96×
Negligible — minor zone excluded
29
0.70
0.43
120
+2.1
0.83×
Moderate — justifies perforation review
21
0.50
1.00
120
+3.1
0.69×
Significant — equivalent to moderate damage
13
0.30
2.33
120
+11.5
0.45×
Severe — dominates total skin
8
0.20
4.00
120
+19.6
0.35×
Extreme — well producing tiny fraction of potential
WORKED EXAMPLEPartial Penetration Scenario — Modified GK-22 (if only 50% perforated)
Hypothetical: suppose GK-22 had only been perforated across hp = 21 ft (the upper half of the 42 ft pay), with Sd = +14 still present. Calculate total skin and production rate.
Step 1: Penetration ratio b = h_p/h = 21/42 = 0.50
Step 2: Dimensionless thickness h_D = h/r_w = 42/0.35 = 120
Step 3: Partial completion skin (approximate form)
S_c = (1/b - 1) x [ln(h_D/b) - G(b)]
= (2.0 - 1) x [ln(120/0.50) - G(0.5)]
G(0.5) = 1.35 / [0.5^0.825 x (1 + 0.5^3.5 / 120)]
= 1.35 / [0.562 x (1 + 0.0884/120)]
= 1.35 / [0.562 x 1.0007]
= 1.35 / 0.5624
= 2.401
S_c = 1.0 x [ln(240) - 2.401]
= 5.480 - 2.401
= +3.08
Step 4: Jones-Watts modified total skin (h/h_p multiplier on damage)
S_total = (h/h_p) x S_d + S_c
= (42/21) x 14 + 3.08
= 2.0 x 14 + 3.08
= 28.0 + 3.08
= +31.1
Step 5: Production rates
J_ideal = 0.00708 x 85 x 42 / (1.8 x 1.32 x 7) = 1.376 stb/d/psi
J_50pct = 0.00708 x 85 x 42 / (1.8 x 1.32 x (7.71+31.1)) = 0.214 stb/d/psi
q = 0.214 x (4200-2500) = 364 stb/d
Compare with GK-22 actual (S'=+14, full perf): 782 stb/d
Production loss from partial penetration alone: 418 stb/d additional
Conclusion: Partial penetration with damage creates a compounding effect. The 50% penetration scenario produces only 364 stb/d vs 782 stb/d for the actual full-penetration case — demonstrating why perforation coverage of the full pay section is critical before acid treatment.
2.5 Effect of Permeability Anisotropy (kh/kv)
In most real formations, vertical permeability kv is less than horizontal permeability kh due to lamination and shale barriers. This makes it harder for fluid to flow vertically to reach the perforations, increasing Sc:
hD,corrected = (h/rw) × √(kh/kv)
kv/kh ratio
√(kh/kv)
hD,corrected (h=42 ft, rw=0.35 ft)
Sc at b=0.5
Change from isotropic
1.0 (isotropic)
1.00
120
+3.1
—
0.3
1.83
220
+4.2
+1.1 units
0.1
3.16
380
+5.2
+2.1 units
0.01
10.0
1200
+7.8
+4.7 units
The Brons–Marting (1961) formula presented here is the most widely used for practical petroleum engineering. It gives reliable results for:
● Vertical wells · ● Penetration ratios b ≥ 0.1 · ● hD > 10 · ● Well not too close to boundary
The Brons–Dake formula is preferred for:
● Very thin pay zones (hD < 10) · ● Wells near no-flow boundaries · ● Stratified reservoirs where cross-flow is limited
For GK-22 (hD = 120, full penetration), neither formula is needed — Sc = 0 by definition. For deviated or horizontal wells, the Cinco-Ley correlation (Section 3 of this topic) replaces both Brons formulas.
Section 3
Deviation Skin Sc″ — The Cinco-Ley Formula
Well deviation generally creates a negative pseudo-skin — a productivity bonus. Understanding this effect is important both for correctly interpreting well test skins in deviated wells and for optimising well trajectory in development drilling decisions.
3.1 Why Deviation Creates Negative Skin
When a well is drilled at an angle θ from vertical, the wellbore intersects the pay zone over a longer distance than vertical. The apparent thickness penetrated is h/cos(θ), providing more formation face area in contact with the wellbore. This is equivalent to having a larger effective wellbore radius or a longer perforated interval — both of which appear as negative skin in the radial flow equation.
For moderate deviations (15°–60°), the deviation skin Sc″ ranges from −0.5 to −3, which is a useful but not transformational benefit. For high-angle wells (>75°), the concept transitions to horizontal well models (Joshi equation) that must replace the simple Cinco-Ley correction.
3.2 The Cinco-Ley Deviation Skin Formula
Derived by Cinco-Ley, Miller & Ramey (1975), the deviation skin for a fully penetrating deviated well is:
S″c = −(θ′/41)2.06 − (θ′/56)1.865 × log(hD/100)
θ′ — Effective Angle
degrees
θ′ = arctan[√(kv/kh) × tan(θ)]. For isotropic k, θ′ = θ. For kv/kh < 1, θ′ < θ (anisotropy reduces the deviation benefit).
hD — Dimensionless Thickness
h√(kh/kv) / rw
Same dimensionless group as partial completion. Higher hD (thicker pay or lower kv) slightly modifies the deviation skin via the log correction term.
θ — Well Deviation
degrees from vertical
Measured from the vertical axis. θ = 0 is vertical (S″c = 0). Valid for 0° to 75°. Above 75° use horizontal well models.
3.3 Deviation Skin Values Across the Range
Using GK-22 geometry (h = 42 ft, rw = 0.35 ft, kh/kv = 1.0, hD = 120):
θ (from vertical)
θ′ (isotropic)
Sc″ (Cinco-Ley)
Effective rw′ multiplier
Practical impact
0° (vertical)
0°
0.0
1.00×
Baseline — GK-22 case
15°
15°
−0.3
1.35×
Negligible — not worth drilling directionally for this
30°
30°
−1.1
3.0×
Moderate benefit: J improves ≈ 12% vs equivalent vertical
45°
45°
−1.26
3.5×
Significant: J improves ≈ 19.5%; often justifies deviated trajectory
60°
60°
−3.2
24.5×
Substantial: J improves ≈ 34%; primary reason to drill deviated
75°
75°
−4.5
90.2×
Large benefit; approaching horizontal well territory — use Joshi model
WORKED EXAMPLE45° Deviated Well — Calculating Sc″
A hypothetical deviated version of GK-22 at 45° from vertical, fully penetrating the 42 ft pay, with kh/kv = 1.0 (isotropic):
Step 1: Effective angle (isotropic: theta' = theta)
theta' = arctan[sqrt(kv/kh) x tan(theta)]
= arctan[sqrt(1.0) x tan(45)]
= arctan[1.0 x 1.0]
= arctan(1.0) = 45.0 degrees
Step 2: Dimensionless thickness
h_D = h x sqrt(kh/kv) / r_w = 42 x 1.0 / 0.35 = 120
Step 3: Cinco-Ley deviation skin
S''_c = -(theta'/41)^2.06 - (theta'/56)^1.865 x log(h_D/100)
= -(45/41)^2.06 - (45/56)^1.865 x log(120/100)
= -(1.0976)^2.06 - (0.8036)^1.865 x log(1.20)
= -1.209 - (0.668 x 0.0792)
= -1.209 - 0.053
= -1.262
Rounding: S''_c ≈ -1.26
Step 4: Effect on PI
J_vertical (S''_c=0): uses ln term + 0 = 7.71
J_deviated (S''_c=-1.26): uses ln term - 1.26 = 7.71 - 1.26 = 6.45
J ratio = 7.71/6.45 = 1.195 -> deviated well produces 19.5% more than vertical
At GK-22 drawdown (1700 psi):
q_vertical = 0.490 x 1700 = 833 stb/d (S=0 well)
q_deviated = 0.490 x (7.71/6.45) x 1700 = 995 stb/d
This 19.5% production improvement from 45° deviation comes with no damage removal — it is purely geometric. In a well with S′ = +14 (like GK-22), the deviation bonus is masked by the large damage skin. But after acid treatment (Sd → +1), the deviation benefit becomes proportionally much more significant.
3.4 Effect of Permeability Anisotropy on Deviation Skin
When kv/kh < 1 (low vertical permeability, common in laminated sands), the effective deviation angle is reduced and the deviation skin is smaller in magnitude (less negative):
kv/kh
θ′ (for physical θ = 45°)
Sc″
J improvement vs vertical
1.0 (isotropic)
45.0°
−1.26
+19.5%
0.3
28.2°
−0.72
+10.2%
0.1
17.4°
−0.34
+4.7%
0.01
5.7°
−0.05
+0.7%
PRACTICAL LIMITS OF THE CINCO-LEY FORMULA
The Cinco-Ley formula is applicable only for θ ≤ 75° from vertical. For high-angle and horizontal wells:
θ = 75° to 88°: Use Joshi (1988) horizontal well equation with appropriate geometry. The deviation skin concept breaks down as the well approaches true horizontal flow geometry.
θ > 88° (near-horizontal): Joshi equation is the correct model. Horizontal well productivity can be 3–10× higher than vertical depending on anisotropy, reservoir thickness, and well length.
GK-22 verification: With θ < 5°, θ′ ≈ 5°, and Sc″ = −(5/41)2.06 − negligible log term ≈ −0.014 ≈ 0. This confirms the GK-22 deviation skin is zero within measurement precision.
Given GK-22's reservoir parameters (k = 85 md, h = 42 ft, isotropic), would deviating the well to 45° have been worthwhile?
Without stimulation (Sd = +14): Sc″ = −1.26. Effective total skin = 14 − 1.26 = +12.74. J ratio vs vertical: (7+14)/(7+12.74) = 21/19.74 = 1.064. Only 6.4% gain — the large damage skin dominates and almost completely masks the deviation benefit. Not worth the directional drilling cost.
After acid treatment (Sd → +1): Sc″ = −1.26. Effective total skin = 1 − 1.26 = −0.26. J ratio vs clean vertical: 8.0/7.74 = 1.034. Only 3.4% improvement — the gain is modest even after acid because k = 85 md is already quite good.
Conclusion: For the GK-22 well with 85 md permeability and 42 ft pay, the deviation benefit (Sc″ ≈ −1.3 at 45°) is economically marginal. Directional drilling is most valuable in low-permeability formations (k < 10 md) where the logarithmic denominator is small and any reduction in effective skin produces a large proportional J improvement.
Section 4
Combined Completion Skin Sc = S′c + S″c
In general wells, partial completion and deviation effects are both present and interact. The combined completion skin framework and the Cinco-Ley tables for simultaneous partial penetration and deviation.
4.1 The Combined Completion Skin Formula
For a deviated well with partial penetration, the combined completion skin Sc as:
Sc = S′c + S″c
where S′c is the partial completion skin (positive, from Brons–Marting) and S″c is the deviation skin (negative, from Cinco-Ley). The total skin then becomes:
S′ = (h/hp) × Sd + Sc + D·q
Note that when a well is deviated AND partially completed, the deviation actually increases the partial completion skin: Cinco-Ley showed that the partial penetration skin S′c increases with deviation angle, because the sealed-zone flow must travel even further to reach the perforated interval. This is why the combined Sc tables must be used for simultaneous deviation and partial penetration.
4.2 Important Special Case — The Along-Hole vs Vertical Perforation Length
For deviated wells, a commonly used simplification is available: since deviation effects are the converse of partial completion, it is often sufficient to use the measured along-hole perforation length hp,ah (which is longer than the vertical equivalent hp,v = hp,ah×cosθ) when calculating S′c, and then ignore the separate S″c term:
Simplified approach: use hp = hp,along-hole in Brons–Marting, and set S″c = 0 (unless hp > h)
KEY CONCEPT — WHICH APPROACH TO USE?
The choice depends on the level of precision needed:
Quick screening (pre-drill or early development): Use Brons–Marting with along-hole hp and ignore S″c separately. Error is typically <1 skin unit.
Well test interpretation (skin attribution): Use separate S′c and S″c from the Cinco-Ley tabulated values. This is necessary when you are trying to determine how much of the measured S′ is formation damage vs geometry.
4.3 Practical Impact Matrix — When Do Pseudo-Skins Matter?
The following matrix guides the engineer on when to perform rigorous pseudo-skin calculations vs when they can be safely neglected:
Well Type
Penetration b
Sc significant?
Deviation θ
Sc″ significant?
Recommended Action
Vertical, fully perforated
1.0
No (Sc=0)
0°
No
Skip calculation — GK-22 case
Vertical, partial perf (>70%)
0.7–1.0
Minor (<2)
0°
No
Quick estimate acceptable
Vertical, partial perf (50–70%)
0.5–0.7
Moderate (2–5)
0°
No
Rigorous Brons–Marting required
Vertical, partial perf (<50%)
<0.5
Large (>5)
0°
No
Full calculation; consider more perfs
Deviated (15°–45°), fully perforated
1.0
No
15°–45°
Moderate (−0.3 to −2.1)
Cinco-Ley required for test interpretation
Deviated (>45°), fully perforated
1.0
No
>45°
Significant (<−2)
Must include in skin decomposition
Deviated (>30°), partially perforated
<0.8
Large
>30°
Significant
Use Cinco-Ley combined tables
Near-horizontal (>75°)
1.0 (hL)
N/A
>75°
Model change needed
Use Joshi horizontal well model
Section 5 — PBL Verification Task
GK-22 Pseudo-Skin Audit — Completing the Skin Decomposition
Rigorous calculation of all pseudo-skin components for GK-22, confirming the Topics 3.1–3.3 conclusion that the entire S′ = +14 is attributable to treatable formation damage.
GK-22 Canonical Data:
ko = 85 md · h = 42 ft · μo = 1.8 cp · Bo = 1.32 rb/stb ·
p̄R = 4,200 psi · pwf = 2,500 psi · rw = 0.35 ft ·
re = 1,650 ft · q = 782 stb/d · S′ = +14 Completion record: hp = 42 ft (full pay) · θ = 4° (near-vertical) · kv/kh = 0.5 (assumed laminated sand)
FULL CALCULATIONGK-22 Complete Pseudo-Skin Audit
Step 1: Partial Completion Skin S'_c
b = h_p/h = 42/42 = 1.000 (full penetration)
Since b = 1.0 exactly:
S'_c = (1/b - 1) x [...] = (1/1 - 1) x [...] = 0 x [...] = 0.000
S'_c = 0.00 (verified: no partial penetration pseudo-skin)
Step 2: Deviation Skin S''_c
theta = 4 degrees from vertical (from directional survey in pay zone)
k_v/k_h = 0.5 (assumed; Agbada laminated sand)
Effective angle theta':
theta' = arctan[sqrt(k_v/k_h) x tan(theta)]
= arctan[sqrt(0.5) x tan(4 degrees)]
= arctan[0.7071 x 0.06993]
= arctan[0.04946]
= 2.83 degrees
Dimensionless thickness h_D:
h_D = h x sqrt(k_h/k_v) / r_w = 42 x sqrt(2.0) / 0.35
= 42 x 1.4142 / 0.35
= 59.40 / 0.35 = 169.7
Cinco-Ley deviation skin:
S''_c = -(theta'/41)^2.06 - (theta'/56)^1.865 x log(h_D/100)
= -(2.83/41)^2.06 - (2.83/56)^1.865 x log(169.7/100)
= -(0.0690)^2.06 - (0.0505)^1.865 x log(1.697)
= -0.00408 - (0.00267 x 0.2296)
= -0.00408 - 0.000613
= -0.00469 ≈ -0.005
S''_c = -0.005 (negligible: vertical well deviation is effectively zero)
Step 3: Non-Darcy skin Dq (confirmed in Topic 3.2)
Dq ≈ 0.001 (confirmed negligible at 782 stb/d, k=85 md)
Step 4: Complete skin audit summary
S' (measured, well test) = +14.0
S_c (partial penetration) = +0.0 (full penetration)
S''_c (deviation) = -0.005 ≈ 0.0
Dq (turbulence) = +0.001 ≈ 0.0
─────────────────────────────────────────────────
Implied S_d (formation damage) = 14.0 - 0.0 - 0.0 - 0.0
= +14.0
CONCLUSION: S_d = S' = +14.0 confirmed.
The ENTIRE measured skin is formation damage (treatable).
All pseudo-skin calculations confirm: GK-22's total skin of +14 is attributable to formation damage with negligible contribution from geometric or rate-dependent effects. The acid treatment designed in Topic 3.3 (targeting Sd → +1) remains the correct primary intervention.
For GK-22, perforation damage is not listed separately: the Topic 3.3 Hawkins audit derived Sd = +14 from the measured S′ with Sc = 0, S′c ≈ 0 and Dq ≈ 0, so the overbalanced-perforating contribution (4 spf, 0° phasing, 12g charges) is already absorbed into Sd. Sd = +14 includes perforation damage (Sc = 0). Quoting a separate Sp of +0.8 to +1.5 would double-count it, so it is folded into Sd and the treatment budget targets the full +14.
Section 6
Design Applications — Using Pseudo-Skin Analysis to Optimise Completions
Pseudo-skin analysis is not just a diagnostic tool — it directly guides completion design decisions: how much pay to perforate, what well trajectory to select, and when horizontal well technology is warranted.
6.1 Perforation Interval Selection
The most common application of Sc calculation is determining the minimum perforation coverage of the pay section to keep pseudo-skin below an acceptable threshold. The following design rules apply:
1
Target Sc < 2
For the pseudo-skin to be negligible (<15% of typical damage skins of +5 to +14), you need b > 0.65 for hD = 100. This means ≥65% of pay must be perforated in most wells.
2
Exclude Only Non-Pay Intervals
Shale stringers, tight streaks, and high-water-saturation zones should be excluded from perforations. But ensure the remaining perforations still cover ≥65% of net pay to avoid significant Sc.
3
Jones–Watts Multiplier in Damaged Wells
If formation damage is present, the effective skin in a partially perforated well is S = (h/hp) × Sd + Sc. Acid can reduce Sd, but if hp/h = 0.5, the amplification factor of 2× on Sd means even small residual damage is heavily penalised.
4
When to Add Perforations vs Acid
If Sc > Sd, add perforations first (cheaper than acid). If Sd > Sc, acid first. If both are significant, a perforation + acid combination workover is the most efficient sequence (perforations first to reduce the h/hp multiplier on damage).
6.2 Trajectory Selection — Vertical vs Deviated vs Horizontal
The three key performance metrics for trajectory selection are:
Parameter
Vertical Well
45° Deviated
Horizontal Well
Sc″ (deviation skin)
0
−1.3 to −2.5
See Joshi model
Best for low k (<5 md)
Poor
Moderate
Excellent (Joshi)
Best for high k (>50 md)
Adequate
Good (+10–25%)
Marginal extra gain
Best for thin pay (<20 ft)
Adequate
Good
Excellent
Best for thick pay (>100 ft)
Good
Very good
Less efficient
Damage skin treatment
Full acid access
Full acid access
Limited reach, coiled tubing
GK-22 (85 md, 42 ft)
Appropriate ✓
Minor benefit
Not warranted
6.3 The Interaction Between Pseudo-Skin and Stimulation
After a successful acid treatment reduces Sd to near zero, the relative importance of pseudo-skin components changes significantly. A skin component of Sc = +3 that was buried under Sd = +14 becomes the dominant skin after acid:
SCENARIO COMPARISONPre- and Post-Acid Skin Importance for a Partially Completed Well
Suppose a well had hp/h = 0.50 (50% penetration) with Sd = +10. Calculate J improvement from acid alone (Sd → 0) vs from adding perforations alone (b: 0.5 → 1.0):
Initial state: b = 0.50, S_d = +10, h_D = 120
S'_c = (1/0.5 - 1) x [ln(120/0.5) - G(0.5)] ≈ +3.1
Total skin S' = (h/h_p) x S_d + S_c = 2 x 10 + 3.1 = +23.1
J ratio vs ideal (S=0): 7/(7+23.1) = 0.233 (23.3% of ideal)
Option A: Acid only (S_d → 0, b unchanged)
S' = 2 x 0 + 3.1 = +3.1
J ratio: 7/(7+3.1) = 0.693 (69.3% of ideal)
J improvement: 0.693/0.233 = 2.97x
Option B: Add perforations only (b → 1.0, S_d unchanged)
S'_c,new = 0 (full penetration)
S' = 1.0 x 10 + 0 = +10.0 (no h/h_p amplifier, full perf)
J ratio: 7/(7+10) = 0.412 (41.2% of ideal)
J improvement: 0.412/0.233 = 1.77x
Option C: Add perforations then acid
S'_c,new = 0, S_d → 0
S' = 0 + 0 = 0
J ratio: 7/7 = 1.000 (100% of ideal)
J improvement: 1.000/0.233 = 4.29x
Verdict: Acid first (2.97x) > add perforations (1.77x)
Combined gives maximum (4.29x); but acid alone delivers most of the gain.
Key result: For this well, acid alone (Option A) delivers 2.97× production improvement vs the less efficient Option B (perforations alone, 1.77×). However, the combination delivers 4.29× — and critically, perforating first then acidising is better than acidising first then perforating, because clean perforations allow acid to penetrate further and more uniformly into the damage zone.
Interactive Tools
Pseudo-Skin Simulators
Three interactive tools: partial completion skin (Brons–Marting), deviation skin (Cinco-Ley), and a combined skin audit calculator. GK-22 values are pre-loaded.
GK-22 preloaded (h=hp=42 ft → Sc=0).
Try:
► hp = 21 ft (50%): see Sc and J-ratio
► hp = 13 ft (30%): severe Sc
► kh/kv = 10: anisotropy effect
► Vary Sd: see Jones–Watts amplification
Ten questions covering partial completion skin Sc, deviation skin Sc″, and the GK-22 audit.
1. The term "pseudo-skin" refers to skin components that are:
C is correct. Pseudo-skin components are of geometric or mechanical origin — they arise from how the well is completed (how much pay is perforated, at what angle) rather than from any alteration of the rock matrix. They cannot be removed by acid because acid addresses permeability impairment in the rock, not the geometry of flow convergence. Option D is wrong because deviation skin Sc″ is typically negative (beneficial). Option B is wrong because turbulence (Dq) is a separate rate-dependent skin component.
2. For the GK-22 well (h = 42 ft, hp = 42 ft, θ = 4°, kv/kh = 0.5), what are the partial completion skin Sc and deviation skin Sc″?
A is correct. S′c = (1/b − 1) × [...] = (1/1.0 − 1) × [...] = 0 × [...] = 0.00 exactly, because the well is fully perforated (b = hp/h = 42/42 = 1.0). For S″c: θ′ = arctan[√0.5 × tan(4°)] = arctan[0.707 × 0.0699] = arctan(0.0494) = 2.83°. S″c = −(2.83/41)2.06 − small log term ≈ −0.005. Both are negligible, confirming Sd = S′ = +14 for GK-22.
3. A well has h = 80 ft net pay but only hp = 32 ft (b = 0.4) is perforated, with kh/kv = 1.0 (isotropic) and rw = 0.35 ft. Calculate hD and use the approximate Brons–Marting formula to estimate Sc. (Use G(0.4) ≈ 2.8.)
B is correct. hD = (h/rw) × √(kh/kv) = (80/0.35) × 1.0 = 228.6 ≈ 229. Sc = (1/b − 1) × [ln(hD/b) − G(b)] = (1/0.4 − 1) × [ln(229/0.4) − 2.8] = (2.5 − 1) × [ln(572.5) − 2.8] = 1.5 × [6.35 − 2.8] = 1.5 × 3.55 = +5.33 (with G(0.4) = 2.8 as specified). This is a significant pseudo-skin that would require perforating more of the pay or accepting the skin as a permanent geometric constraint.
4. The Jones–Watts correction (S = (h/hp) × Sd + Sc) applies to a partially completed, damaged well. If h = 60 ft, hp = 20 ft, and Sd = +6, what is the total skin compared to a fully completed well with the same Sd? (Assume Sc = +5 for this partial penetration.)
D is correct. Fully completed (b=1): total skin = 1.0 × Sd + 0 = 1.0 × 6 + 0 = +6. Partially completed (b = 20/60 = 0.333): S = (h/hp) × Sd + Sc = (60/20) × 6 + 5 = 3 × 6 + 5 = 18 + 5 = +23. The Jones–Watts h/hp amplifier is crucial: the formation damage skin is multiplied by 3 because all flow must pass through the one-third of pay that is open. This dramatically shows why perforating more of the pay before acid treatment maximises the acid treatment's effectiveness — it reduces the multiplier on Sd.
5. For the Cinco-Ley deviation skin formula, a well at 45° from vertical in an isotropic formation (θ′ = 45°) with hD = 120 gives Sc″ ≈ −1.26. If the same well has kv/kh = 0.1, what happens to Sc″?
C is correct. With kv/kh = 0.1: θ′ = arctan[√(kv/kh) × tan(45°)] = arctan[√0.1 × 1.0] = arctan(0.316) = 17.5°. Using Cinco-Ley at θ′ = 17.5° (instead of 45°): S″c ≈ −(17.5/41)2.06 − small term ≈ −0.18. This is much less negative than −1.26 at isotropic conditions. Low vertical permeability reduces the benefit of deviation because the geometric advantage of the larger wellbore contact area is undermined by the formation's difficulty in delivering flow vertically to the wellbore.
6. A well test gives S′ = +8. The well is 35° deviated (Sc″ = −0.9) and partially completed at 60% of pay (Sc = +2.1). Non-Darcy Dq = 0. What is the estimated formation damage skin Sd?
C is correct. From the total skin decomposition: S′ = Sd + Sc + Sc″ + Dq. Solving for Sd: Sd = S′ − Sc − Sc″ − Dq = 8 − 2.1 − (−0.9) − 0 = 8 − 2.1 + 0.9 = +6.8. Note that the deviation skin is subtracted (it is negative, so subtracting it adds back to Sd). The well appears to have S′ = +8, but +2.1 of that is from partial penetration (not treatable by acid) and −0.9 is the deviation credit. The treatable formation damage is +6.8, not +8. Designing acid for +8 would over-specify the acid volume.
B is correct. Partial completion skin arises because fluid must flow vertically to reach the perforated interval. Vertical permeability kv governs this vertical flow component. When kv is much less than kh (e.g. due to horizontal shale laminations), the vertical flow is severely restricted — a much larger pressure gradient is required to drive fluid up or down through the formation to reach the perforations. This additional pressure gradient manifests as higher Sc. Quantitatively, the effective dimensionless thickness hD = (h/rw) × √(kh/kv) increases when kv decreases, and higher hD gives higher Sc from the Brons–Marting formula.
8. For GK-22 after acid treatment (expected Sd = +1.0, Sc = 0, Sc″ = −0.005, Dq = 0.001), what will the post-treatment total skin S′ be?
A is correct. S′ = Sd + Sc + Sc″ + Dq = 1.0 + 0 + (−0.005) + 0.001 ≈ +1.0. The pseudo-skin components are all negligible for GK-22's vertical, fully-perforated geometry. Post-treatment J ratio vs the damaged state: (7 + 14) / (7 + 1.0) = 21/8 = 2.625×. Post-treatment production: 782 × 2.625 = 2,053 stb/d. This confirms the Module 03 treatment recommendation: acid targeting Sd → +1 is the primary intervention, yielding a 2.63× production improvement.
9. A completion engineer is designing the perforation programme for a new well in the same field as GK-22. The well will have h = 65 ft net pay. What minimum perforated interval hp (ft) is needed to keep Sc below +2.0? Assume hD = 186 (h=65 ft, rw=0.35 ft, isotropic) and use the approximate rule that Sc < 2 requires b > 0.65.
B is correct. Using the rule that Sc < 2 requires b > 0.65: minimum hp = 0.65 × h = 0.65 × 65 = 42.25 ft ≈ 42 ft. This means the completion engineer should target at least 42 ft of perforations across the 65 ft pay (64.6% coverage) to keep partial completion pseudo-skin below +2. If formation damage of Sd = +5 is also expected, the Jones–Watts amplification at b = 0.65 gives total damage contribution = (1/0.65) × 5 = +7.7, compared to +5 with full penetration — emphasising the value of maximising perforation coverage even before considering Sc itself.
10. Which of the following correctly ranks the pseudo-skin components for GK-22 from largest magnitude to smallest?
D is correct and captures the key conclusion of the GK-22 skin audit. All pseudo-skin components (Sc = 0, Sc″ = −0.005, Dq = +0.001) are negligible in magnitude — together they sum to less than 0.01 skin units, compared to Sd = +14. The GK-22 skin decomposition is complete: S′ = +14 is 99.9% formation damage, 0.1% geometric/turbulence effects. The acid treatment designed in Topic 3.3 remains the correct and only intervention needed. No additional perforations, no trajectory change, no rate management is indicated by the pseudo-skin analysis.
NEXT STEPS — MODULE 03 SKIN AUDIT COMPLETE
Topics 3.1–3.4 have completed the full GK-22 skin decomposition:
Proceed to Topic 3.5: Standing's Flow Efficiency (FE) — which integrates the skin factor into the IPR curve using the flow efficiency concept, enabling engineers to construct IPR curves for damaged (FE < 1) and stimulated (FE > 1) wells and predict production under any operating condition.