Standing's Flow Efficiency (FE) Integrating Skin into the IPR Curve
Topics 3.1–3.4 established that GK-22 has Sd = +14 (all treatable formation damage) and confirmed pseudo-skin contributions are negligible. Now we use Standing's Flow Efficiency to translate that skin number into a graphical IPR curve — the tool that directly predicts production rates before and after treatment under any operating condition.
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′ = Sd = +14
The skin factor S appears in the denominator of the Darcy radial flow equation, scaling the productivity index J. But for wells producing below the bubble point — where gas liberation reduces oil relative permeability and curves the IPR — simply adjusting J is insufficient. The IPR becomes non-linear, and skin affects both the slope and the curvature of the relationship between pwf and q.
Standing (1970) solved this problem by introducing the concept of Flow Efficiency (FE): the ratio of the actual well's productivity to the ideal productivity that the same reservoir would deliver if there were no skin. Flow Efficiency normalises the skin effect into a single dimensionless number that directly scales the Vogel IPR curve for any skin condition.
The power of FE is that it bridges the skin audit (Topics 3.1–3.4) directly to production forecasting. By calculating FEcurrent = 0.33 (GK-22 is performing at 33% of its damage-free potential) and FEpost-acid = 0.88 (after treatment), engineers can draw both IPR curves on the same chart and calculate the production uplift without repeating the full Vogel calculation from scratch.
▶
Lecture 3.5a: Flow Efficiency — From Skin Number to IPR Curve
14:30
Derives Standing's FE definition from the Darcy equation, explains the physical meaning of FE above and below 1.0, and shows how FE transforms the Vogel reference curve for damaged (FE < 1) and stimulated (FE > 1) wells. Demonstrates the FE concept on the GK-22 well: FE = 0.33 translates to producing at one-third of potential. Covers the Brown/Harrison extension of Standing's curves to FE values above 1.5.
▶
Lecture 3.5b: Constructing FE-Modified IPR Curves — Single-Phase and Two-Phase
13:10
Step-by-step construction of FE-modified IPR curves for both single-phase (above bubble point, linear IPR) and two-phase (Vogel, below bubble point, curved IPR) reservoirs. Shows the graphical technique using Standing's nomogram and the algebraic approach using the FE-modified Vogel equation. Full GK-22 before-and-after treatment example with production uplift calculation and nodal analysis intersection.
▶
Lecture 3.5c: Workover Economics — Using FE to Justify Treatment Investment
9:20
Demonstrates how to use FE change (FEpre to FEpost) to calculate production uplift, incremental NPV, and break-even analysis for acid treatments and workovers. Covers the sensitivity of economic justification to post-treatment FE uncertainty. Real example: GK-22 acid treatment economics. Connects to the Module 03 PBL final deliverable format.
LEARNING OBJECTIVES
After completing this topic, you will be able to:
1. Define Flow Efficiency (FE) and explain its physical meaning as the ratio of actual to ideal well deliverability. 2. Calculate FE from the skin factor S and reservoir geometry using the Standing formula FE = 7/(7 + S). 3. Construct a FE-modified Vogel IPR curve for a well producing below the bubble point, given FE and reservoir pressure. 4. Apply the FE-modified Vogel equation to calculate qmax(FE) and construct complete IPR curves for damaged and stimulated conditions. 5. Determine production uplift (before vs after treatment) from a change in FE, both graphically and algebraically. 6. Apply FE analysis to the GK-22 well to predict post-acid treatment production and compare to the pre-treatment state. 7. Use FE to construct the workover economic justification: incremental production × oil price vs treatment cost. 8. Explain the limitations of Standing's FE correction at high FE values (>1.5) and when the Brown/Harrison extension applies.
PBL CONNECTION — GK-22 TREATMENT ECONOMICS
The Module 03 PBL final deliverable requires a production forecast and economic justification for the recommended GK-22 acid treatment. Topic 3.5 provides the FE-based IPR framework to deliver this.
Key numbers for GK-22:
Pre-treatment: S = +14, FE = 7/(7+14) = 0.333 (well at 33.3% of damage-free potential)
Post-treatment: S = +1, FE = 7/(7+1) = 0.875 (well at 87.5% of damage-free potential)
This topic constructs both IPR curves, calculates the production uplift (782 → 2,053 stb/d), and sets up the NPV calculation for the acid treatment decision.
Section 1
The Flow Efficiency Concept — Measuring Well Performance Against Potential
Flow Efficiency is the most intuitive way to communicate well damage and stimulation impact to non-technical stakeholders. It translates the abstract skin number into a simple percentage: "this well is performing at 33% of its potential."
1.1 The Physical Meaning of Flow Efficiency
Consider two identical wells drawing from the same reservoir under the same drawdown — same p̄R, same pwf, same k, h, and fluid properties. The only difference is that Well A has S = 0 (perfectly undamaged) while Well B has S = +14 (GK-22's actual state). The flow efficiency is simply the ratio of their production rates at the same drawdown:
FE = qactual / qideal(S=0) (at the same pwf)
For a single-phase reservoir above the bubble point where IPR is linear (q = J × Δp):
FE = Jactual / Jideal = qactual / qideal
This ratio is always ≤ 1.0 for damaged wells and can exceed 1.0 for stimulated wells (where the near-wellbore permeability enhancement makes the well outperform the ideal Darcy model). The FE spectrum:
FE = 0 No flow
FE < 0.5 Extreme damage
FE 0.5–0.8 Moderate damage
FE 0.8–1.0 Mild/no damage
FE = 1.0 Ideal
FE > 1.0 Stimulated
KEY CONCEPT — FE IS A NORMALISED SKIN
FE and S contain the same information but expressed differently:
• S is additive: Stotal = S1 + S2 + S3
• FE is multiplicative on production: qactual = FE × qideal (only for linear IPR)
The advantage of FE is that it directly multiplies onto the Vogel IPR curve (which is normalised to qmax), making it the preferred tool for two-phase below-bubble-point wells where simple J scaling fails. Engineers use S for the skin audit (Topics 3.1–3.4) and FE for production forecasting (Topic 3.5).
1.2 FE and the Undamaged Flowing Pressure
An equivalent physical interpretation of FE comes from comparing the undamaged flowing pressure (what pwf would be if S = 0 at the same rate) with the actual pwf:
Figure 1.2.1 — IPR curves for GK-22 at three skin conditions (S=0 ideal, S=+14 current, S=+1 post-acid). All share the same p̄R = 4,200 psi intercept. At pwf = 2,500 psi, FE = 0.33 means the damaged well delivers only 782 stb/d vs 2,346 stb/d ideal. Post-acid (FE = 0.875), production rises to 2,056 stb/d. The “undamaged flowing pressure” p'wf = 3,538 psi is the BHP the ideal well would have while producing 782 stb/d — the damage consumes 1,038 psi of available drawdown.
1.3 FE from the Pressure Perspective
An alternative definition of FE uses the undamaged equivalent flowing pressure:
FE = (p̄R − p'wf) / (p̄R − pwf)
where p'wf is the flowing wellbore pressure that the well would have at the same flow rate if there were no skin. This can be read directly off the ideal IPR curve. Both FE definitions are equivalent; the rate-ratio form is more common in practice.
Section 2
The FE Formula — Connecting Skin to Flow Efficiency
The algebraic relationship between FE and skin factor S is derived directly from the Darcy radial flow equation. This gives a precise, testable connection between the skin audit and the production forecast.
2.1 Deriving FE from the Darcy Equation
For a single-phase (above bubble point) reservoir, the productivity index is:
J = 0.00708 koh / [μoBo(ln(0.472re/rw) + S)]
The ideal PI with S = 0:
Jideal = 0.00708 koh / [μoBo × ln(0.472re/rw)]
Using the standard approximation ln(0.472re/rw) ≈ 7 (valid for typical drainage areas 40–640 acres):
FE = Jactual/Jideal = 7 / (7 + S)
FE — Flow Efficiency
Dimensionless (0 to ∞)
Ratio of actual to ideal PI. FE < 1: damaged. FE = 1: ideal (S=0). FE > 1: stimulated (S < 0). GK-22 current: FE = 7/(7+14) = 0.333.
7 — Logarithm Approximation
ln(0.472 re/rw) ≈ 7
Valid for 40–640 acre drainage, rw = 0.33–0.5 ft. For non-standard geometry use the full logarithm. GK-22: ln(0.472×1650/0.35) = 7.71 (close to 7).
S — Total Skin
Dimensionless
The complete skin factor from the well test or skin audit. For GK-22: S = Sd = +14. After treatment: S = +1. For stimulated well: S = −3 (acid), S = −5 (fracture).
2.2 The FE–Skin Relationship Table
The following table gives the FE corresponding to common skin values, and the equivalent effective wellbore radius r'w:
Skin S
FE = 7/(7+S)
J/Jideal
Description
r'w = rwe−S
+20
0.259
25.9% of ideal
Severe damage
0.35×e−20 ≈ 0
+14
0.333
33.3% of ideal
GK-22 current state
very small
+7
0.500
50.0% of ideal
Significant damage
negligible
+3
0.700
70.0% of ideal
Moderate damage
0.35×e−3 = 0.017 ft
+1
0.875
87.5% of ideal
GK-22 post-acid target
0.35×e−1 = 0.129 ft
0
1.000
100.0% = ideal
Undamaged (baseline)
0.35 ft (actual rw)
−2
1.400
140% of ideal
Light stimulation (acid)
0.35×e2 = 2.58 ft
−4
2.273
227% of ideal
Natural fractures / small frac
0.35×e4 = 19.3 ft
−6
5.250
525% of ideal
Large hydraulic fracture
0.35×e6 = 141 ft
GK-22 FE CALCULATION
Current state (S = +14):
FE_current = 7 / (7 + 14) = 7/21 = 0.333
Using full log (more precise):
FE_current = ln(0.472x1650/0.35) / (ln(0.472x1650/0.35) + 14)
= 7.71 / (7.71 + 14) = 7.71/21.71 = 0.355
Post-acid state (S = +1):
FE_post = 7 / (7 + 1) = 7/8 = 0.875
Using full log:
FE_post = 7.71 / (7.71 + 1) = 7.71/8.71 = 0.885
Production ratio pre to post:
q_post / q_pre = FE_post / FE_current = 0.875/0.333 = 2.628x
(using full log: 0.885/0.355 = 2.493x)
At current drawdown (1700 psi):
q_post = 782 x 2.628 = 2,055 stb/d (approximate formula)
q_post = 782 x 2.493 = 1,949 stb/d (full log formula)
Note: The 7-approximation gives a slightly higher FE and J ratio than the full logarithm. For GK-22 (re = 1,650 ft, rw = 0.35 ft), ln(0.472×1650/0.35) = 7.71 vs the approximation of 7. For all Module 03 calculations, both methods are acceptable; the 7-approximation is used for quick screening and the full log for final deliverables.
2.3 FE from Well Test Data — Field Measurement
In the field, FE is often measured directly from well test data without needing to know the individual skin components. From the measured PI (Jactual) and the theoretical undamaged PI:
This is the most direct field measurement of FE: just take the DST-measured PI and divide by the theoretical PI from reservoir parameters. No need to calculate S first — though S can then be back-calculated from S = 7(1/FE − 1).
The logarithm term ln(0.472 re/rw) has a remarkably narrow range for typical petroleum engineering parameters:
Drainage Area
re (ft)
rw = 0.33 ft
rw = 0.50 ft
40 acres
660
6.9
6.5
160 acres
1,320
7.5
7.1
640 acres
2,640
8.2
7.8
GK-22 (varies)
1,650
7.71
7.38
The approximation gives ln ≈ 7 to within ±15% for typical conditions. This is acceptable for screening and economics but may introduce 5–10% error in production forecasts for small drainage areas (re < 800 ft) or large wellbores (rw > 0.5 ft). Always use the full expression for final deliverables.
Section 3
Vogel IPR & Standing's FE Extension
The Vogel (1968) IPR equation describes two-phase flow below the bubble point as a dimensionless curve. Standing (1970) extended this framework to damaged and stimulated wells using Flow Efficiency — creating the most widely used method for constructing IPR curves in two-phase reservoirs.
3.1 Vogel's Reference Curve
Vogel's dimensionless IPR equation (for a well with FE = 1.0, no skin):
q/qmax = 1 − 0.2(pwf/p̄R) − 0.8(pwf/p̄R)²
The key parameter is qmax — the maximum flow rate at pwf = 0 (Absolute Open Flow, AOF). For pseudo-steady-state flow above the bubble point, qmax relates to the productivity index J* via:
qmax = J* × p̄R / 1.8
3.2 Standing's FE Extension — The Key Modification
Standing (1970) showed that a damaged or stimulated well's IPR can be obtained by replacing pwf in the Vogel equation with a “flow efficiency corrected” pressure. The FE-modified Vogel equation is:
Maximum flow rate at pwf=0 for a well with flow efficiency FE. qmax(FE) = FE × (J* × p̄R / 1.8) × correction factor. See Section 4 for derivation.
FE × pwf/p̄R
Dimensionless
The FE multiplier acts on the dimensionless pressure ratio, shifting the effective operating point on the Vogel reference curve. Damaged wells (FE < 1) see a lower “effective” pressure ratio, shifting production left.
3.3 The qmax(FE) Expression
Setting pwf = 0 in the FE-modified Vogel equation (and using the fact that for linear flow above bubble point qmax,FE=1 = J*×p̄R/1.8):
A simpler form valid for FE values between 0.5 and 1.5:
qmax(FE) ≈ qmax,FE=1 × FE × (1 + 0.8(FE − 1))
3.4 Graphical Method — Standing's Nomogram
The original Standing (1970) graphical method uses the Vogel reference curve and the FE to shift the operating point. The procedure:
1
Calculate FE
Using FE = 7/(7+S) or from well test PI ratio. For GK-22 pre-acid: FE = 0.333. Post-acid: FE = 0.875.
2
Determine qmax,FE=1
From the undamaged J*: qmax,FE=1 = J* × p̄R / 1.8. GK-22: qmax,FE=1 = 1.376 × 4200/1.8 = 3,211 stb/d.
3
Enter Vogel Chart at FE
For each pwf value, compute FE × (pwf/p̄R) and read the corresponding q/qmax from the Vogel reference curve.
4
Scale to Actual q
Multiply q/qmax from Vogel curve by qmax(FE) to get actual rate. Plot pwf vs q to construct the complete FE-modified IPR.
IMPORTANT LIMITATION — ABOVE-BUBBLE-POINT WELLS
Standing's FE extension was originally derived for two-phase reservoirs below the bubble point (Vogel IPR). For GK-22 (p̄R = 4,200 psi, bubble point not specified but likely below p̄R for a Niger Delta crude), the single-phase approximation is used when pwf > pb.
For the Module 03 calculations, GK-22 is treated as a single-phase (above bubble point) reservoir for simplicity. The FE = J/Jideal relationship is exact for linear IPR. The Vogel-FE extension applies if the bubble point is known and pwf drops below it during production.
Rule: If pwf > pb throughout the operating range: use linear FE formula (FE = J/Jideal). If pwf < pb during production: use Vogel-FE extension.
Standing's original FE curves were shown by Brown and Harrison (based on unpublished work) to be incorrect for FE values above 1.5. The issue is that at very high FE (achieved by large hydraulic fractures with S < −5), the Vogel reference curve correction becomes non-physical — predicting production rates that exceed what the reservoir can actually deliver.
The Brown/Harrison extension provides a revised set of curves for FE = 1.5 to FE = 2.5 that correctly account for the reservoir-side deliverability limit. In practical engineering for the Module 03 scope (GK-22 acid treatment targeting S = +1, FE = 0.875), this correction is not needed.
When is it needed? For wells with large hydraulic fractures (S = −5 to −7, FE = 5 to 7), the standard Vogel-FE extension significantly overestimates production. Use the Harrison curves or the more rigorous Forchheimer-fracture models for these cases.
The FE-modified IPR curve is the primary deliverable of the skin audit. It predicts actual production at any wellbore pressure for a well at any skin condition, enabling before-and-after treatment comparison on a single graph.
4.1 Single-Phase IPR with FE (Above Bubble Point)
For GK-22 (treated as single-phase above bubble point), the IPR is linear and FE scales the slope directly:
q = FE × Jideal × (p̄R − pwf)
WORKED EXAMPLEGK-22 IPR Construction — Before and After Acid
WORKED EXAMPLETwo-Phase Extension — GK-22 at Different FE Values
If GK-22's bubble point pb = 2,200 psi (hypothetical), the Vogel extension applies below this pressure. Using J* = Jideal = 1.380 stb/d/psi:
q_max(FE=1) = J* x p_R / 1.8 = 1.380 x 4200 / 1.8 = 3,220 stb/d
FE = 0.333 (pre-acid, S=+14):
q_max(FE=0.333) = 3220 x 0.333 x [1 + 0.2x0.333 + 0.8x0.333^2] / 2
= 3220 x 0.333 x [1 + 0.0667 + 0.0889] / 2
= 3220 x 0.333 x 1.1556 / 2
= 3220 x 0.1924
= 620 stb/d (AOF at p_wf=0)
At p_wf = 2000 (below p_b = 2200):
q = 620 x [1 - 0.2x(0.333x2000/4200) - 0.8x(0.333x2000/4200)^2]
= 620 x [1 - 0.2x0.1586 - 0.8x0.1586^2]
= 620 x [1 - 0.0317 - 0.02013]
= 620 x 0.9482 = 588 stb/d
FE = 0.875 (post-acid, S=+1):
q_max(FE=0.875) = 3220 x 0.875 x [1 + 0.2x0.875 + 0.8x0.875^2] / 2
= 3220 x 0.875 x [1 + 0.175 + 0.6125] / 2
= 3220 x 0.875 x 1.7875 / 2
= 3220 x 0.7820
= 2518 stb/d (AOF at p_wf=0)
At p_wf = 2000:
q = 2518 x [1 - 0.2x(0.875x2000/4200) - 0.8x(0.875x2000/4200)^2]
= 2518 x [1 - 0.2x0.4167 - 0.8x0.4167^2]
= 2518 x [1 - 0.0833 - 0.1389]
= 2518 x 0.7778 = 1,958 stb/d
Key insight: Below the bubble point, the FE effect is amplified because gas liberation near the wellbore further reduces kro for damaged wells. The FE-Vogel approach correctly captures this compound effect.
Section 5 — PBL Core Task
GK-22 Flow Efficiency — Full Before/After Treatment Analysis
Applying the complete FE framework to GK-22: calculating FE values, constructing both IPR curves, quantifying the production uplift, and comparing to nodal analysis results.
GK-22 Canonical Data:
ko = 85 md · h = 42 ft · μo = 1.8 cp · Bo = 1.32 rb/stb ·
p̄R = 4,200 psi · rw = 0.35 ft · re = 1,650 ft ·
Jideal = 1.380 stb/d/psi · Spre = +14 · Spost = +1
5.1 Complete FE Summary Table for GK-22
Parameter
Pre-Treatment (S = +14)
Post-Treatment (S = +1)
Ideal (S = 0)
Flow Efficiency FE
0.333
0.875
1.000
Productivity Index J (stb/d/psi)
0.460
1.208
1.380
Production at pwf = 2,500 psi
782 stb/d
2,056 stb/d
2,346 stb/d
Production at pwf = 1,500 psi
1,242 stb/d
3,265 stb/d
3,726 stb/d
AOF (pwf = 0)
1,932 stb/d
5,078 stb/d
5,796 stb/d
% of ideal deliverability
33.3%
87.5%
100%
Production uplift vs pre-treatment
—
+1,274 stb/d (+163%)
+1,564 stb/d (+200%)
5.2 GK-22 IPR Plot — Three Conditions
The canvas-based IPR plot in Section 8 (Interactive Simulator) shows all three curves. Key observations from Figure 3.5.2:
Pre-Acid (FE = 0.333)
Steep slope, low AOF (1,932 stb/d). At pwf = 2,500 psi: q = 782 stb/d. The well is severely under-producing. Even if pwf were reduced to atmospheric (maximum drawdown), only 1,932 stb/d would be achievable — confirming the well needs treatment before any artificial lift investment.
Post-Acid (FE = 0.875)
Shallower slope, higher AOF (5,078 stb/d). At pwf = 2,500 psi: q = 2,056 stb/d. 87.5% of the ideal well's deliverability. The small residual skin (S = +1) leaves 12.5% of potential untapped. This is the practical target for the Module 03 acid design.
Ideal (FE = 1.0)
Shallowest slope, highest AOF (5,796 stb/d). Theoretical upper limit for GK-22's reservoir. The difference between FE = 0.875 (post-acid) and FE = 1.0 (ideal) represents the 12.5% production that could only be recovered by perfect acid penetration and zero residual damage — rarely achieved in practice.
5.3 Nodal Analysis Integration
The IPR curves are only meaningful when combined with the Tubing Performance Curve (TPC) in a nodal analysis. The TPC defines what the tubing system can deliver at the wellhead. The intersection of IPR and TPC gives the operating point:
NODAL ANALYSIS — GK-22 OPERATING POINT PRE AND POST ACID
Assume the GK-22 tubing string produces at a fixed wellhead pressure of 250 psi through a 2.875-inch (73 mm OD) tubing string. From VLP correlation analysis:
TPC delivers approximately: p_wf = 250 + 1.5q (simplified linear TPC for illustration)
Pre-acid operating point: IPR = TPC
J_pre x (p_R - p_wf) = p_wf - 250 / 1.5 ... solving iteratively
0.460 x (4200 - p_wf) = (p_wf - 250) / 1.5
... p_wf ≈ 2,490 psi, q ≈ 790 stb/d (consistent with measured 782 stb/d ✓)
Post-acid operating point (same TPC):
1.208 x (4200 - p_wf) = (p_wf - 250) / 1.5
... p_wf ≈ 1,918 psi, q ≈ 2,760 stb/d
Note: The TPC allows q to increase above 2,056 stb/d (the value at fixed p_wf=2500)
because as q increases on the post-acid IPR, the new operating p_wf drops,
allowing the TPC to carry more flow at lower wellhead pressure.
The actual production gain is from 790 → 2,760 stb/d (3.49x improvement).
Important: The gain calculated from FE at fixed pwf (2,056/782 = 2.63×) is less than the actual nodal gain (2,760/790 = 3.49×) because the TPC allows pwf to drop when IPR improves, accessing additional drawdown. Always use nodal analysis for final production forecasts; the fixed-pwf FE calculation gives a conservative (lower) estimate.
Section 6
Workover Economics — Using FE Change to Justify Treatment
The FE framework provides a direct, defensible economic justification for acid treatment. By converting the FE change to incremental production, and multiplying by oil price, the NPV of the treatment can be calculated and compared to the treatment cost.
6.1 The Economic Framework
The acid treatment economic justification requires three quantities:
1
Δq (incremental production)
Δq = qpost − qpre at the operating pwf = 2,056 − 782 = 1,274 stb/d from FE analysis. From nodal analysis: Δq ≈ 1,970 stb/d (larger due to pwf drop). Use nodal value for economics.
2
Treatment Duration Benefit
Acid treatments in similar Niger Delta Agbada sands have shown benefits lasting 18–36 months before progressive fines migration re-builds skin. Use 24 months conservative estimate for NPV.
INPUT PARAMETERS:
Oil price: $75/bbl
Operating cost: $5/bbl (lifting + processing)
Net oil value: $70/bbl
Treatment cost: $450,000 (coiled-tubing acid job, Niger Delta)
Incremental production: 1,274 stb/d (fixed p_wf) or 1,970 stb/d (nodal)
Treatment duration: 24 months (conservative), 36 months (base case)
Discount rate: 10% per annum
DAILY REVENUE (fixed p_wf basis):
Revenue = 1,274 stb/d x $70/bbl = $89,180/day
SIMPLE PAYBACK PERIOD:
Payback = $450,000 / $89,180/d = 5.0 days
NPV CALCULATION (24-month benefit, 10% discount, fixed p_wf):
Monthly incremental revenue = 1,274 x 30 x $70 = $2,675,400/month
Discount factor for 24 months at 10%/yr: (1-(1+0.1/12)^-24)/(0.1/12) = 21.67
NPV = $2,675,400 x 21.67 / 12 - $450,000
= $2,675,400 x 1.806 - $450,000
= $4,831,072 - $450,000
= +$4,381,072
NPV (36-month benefit):
NPV ≈ +$7,100,000 (approximately)
BREAK-EVEN ANALYSIS:
Break-even oil price: $450,000 / (1,274 x 24x30 x 21.67/12)
= $450,000 / $4,831,072 x $70 = $6.51/bbl
Well delivers positive NPV at any oil price above $6.51/bbl.
This treatment is economically robust in any realistic price environment.
Conclusion: The GK-22 acid treatment has a payback period of <1 week and delivers NPV > $4.3M (24-month) to $7.1M (36-month) at $75/bbl. The break-even price of $6.51/bbl confirms this is one of the highest-value, lowest-risk interventions in the field portfolio. This is the justification format required in the Module 03 PBL final deliverable.
Combined case (acid + ICHGP, the full PBL intervention, $1,050,000): The figures above are for the acid-only job ($450,000). The Module 03 PBL deliverable evaluates the combined acid + ICHGP programme, which carries the full uplift of Δq ≈ 1,240 stb/d (S′ → +1.12, FE 0.862) at fixed pwf. Combined-case payback = $1,050,000 / (1,240 stb/d × $70/bbl) = $1,050,000 / $86,800/d ≈ 12 days — still well inside two weeks, even though the cost is 2.3× the acid-only job. Use the acid-only payback (5 days) when justifying the stimulation step alone, and the combined 12-day payback when justifying the full sand-controlled completion.
6.2 Sensitivity Analysis on Post-Treatment FE
The economic value depends critically on achieving the target post-treatment skin S = +1 (FE = 0.875). If the acid underperforms:
Post-Treatment S
FEpost
qpost at pwf=2500 psi
Δq vs pre-treatment
24-month NPV (approx)
0 (ideal)
1.000
2,346 stb/d
+1,564 stb/d
$5.3M
+1 (target)
0.875
2,056 stb/d
+1,274 stb/d
$4.3M
+3 (partial)
0.700
1,656 stb/d
+874 stb/d
$2.9M
+5 (poor)
0.583
1,380 stb/d
+598 stb/d
$2.0M
+8 (fail)
0.467
1,104 stb/d
+322 stb/d
$1.1M
+14 (no change)
0.333
782 stb/d
0
−$0.45M
KEY RISK FACTOR
Even a “poor” result (post-treatment S = +5, FE = 0.583) still delivers NPV > $2.0M — more than 4× the treatment cost. The acid treatment remains economically positive unless the skin improvement is less than +3 units (S > +11 post-treatment). Given that core floods confirmed 76% permeability restoration, achieving S < +3 post-acid is highly probable. The treatment decision is robust to significant uncertainty in the post-treatment outcome.
Interactive Tools
Flow Efficiency & IPR Simulators
Three interactive tools: FE calculator from skin, live IPR canvas (before/after treatment), and a treatment economics calculator. GK-22 values pre-loaded.
GK-22 preloaded.
Try:
► Spre=+14, Spost=0: best case acid
► Spre=+14, Spost=+5: underperforming acid
► Spost=−2: over-stimulated (light frac)
► Change pwf: see production sensitivity
Live IPR Canvas — Before & After Treatment INTERACTIVE
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Treatment Economics Calculator INTERACTIVE
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GK-22 economics preloaded. Adjust oil price to test robustness. At what oil price does NPV turn negative?
Assessment
Knowledge Check — Standing's Flow Efficiency
Ten questions covering FE definition, calculation, IPR construction, and GK-22 application.
1. Flow Efficiency (FE) is defined as the ratio of:
B is correct. FE = Jactual/Jideal = (actual PI) / (PI the well would have with S=0 at the same p̄R, k, h, μ, B). This is equivalent to FE = qactual/qideal at the same drawdown (for linear IPR), or FE = (p̄R − p'wf) / (p̄R − pwf) using the undamaged equivalent flowing pressure concept. Option C confuses FE with production ratio between states; FE is a ratio at the same conditions not between different time points.
2. For GK-22 (k = 85 md, h = 42 ft, μ = 1.8 cp, B = 1.32, rw = 0.35 ft, re = 1,650 ft, S = +14), what is the Flow Efficiency using the approximation FE = 7/(7+S)?
B is correct. FE = 7/(7+S) = 7/(7+14) = 7/21 = 0.333. This means GK-22 is operating at only 33.3% of its damage-free potential — two-thirds of possible production is being destroyed by formation damage. Using the full logarithm: FE = ln(0.472×1650/0.35) / (ln(0.472×1650/0.35) + 14) = 7.71/21.71 = 0.355, slightly higher. The 7-approximation gives a slightly more conservative (pessimistic) FE value.
3. Using FE = 0.333 (pre-acid) and Jideal = 1.380 stb/d/psi for GK-22, what is the actual PI Jpre and the production rate at pwf = 2,500 psi (p̄R = 4,200 psi)?
C is correct. Jpre = FE × Jideal = 0.333 × 1.380 = 0.460 stb/d/psi. q = Jpre × (p̄R − pwf) = 0.460 × (4200 − 2500) = 0.460 × 1700 = 782 stb/d. This matches the GK-22 measured DST production rate — a critical verification that the FE framework is internally consistent with the established canonical data. The q = 1,932 stb/d in option D is the AOF (pwf = 0), not the rate at pwf = 2,500 psi.
4. A well has J* (ideal PI) = 2.5 stb/d/psi and p̄R = 3,500 psi. Using the Vogel equation for a two-phase reservoir, what is qmax(FE=1) and the Absolute Open Flow AOF?
B is correct. qmax(FE=1) = J* × p̄R / 1.8 = 2.5 × 3500 / 1.8 = 8750 / 1.8 = 4,861 stb/d. This is the Vogel AOF for an undamaged well. The factor 1.8 (Vogel denominator) is key — it means the AOF is 1/1.8 = 55.6% of what it would be if the Vogel IPR were linear (which it is not). Option A (8,750) incorrectly omits the 1.8 divisor. Option C (2,500) confuses J* with qmax. Option D uses 1.43 instead of 1.8.
5. After acid treatment, GK-22 achieves Spost = +1, giving FEpost = 0.875. What production rate is predicted at pwf = 2,500 psi using the linear IPR (Jideal = 1.380 stb/d/psi)?
C is correct. Jpost = FEpost × Jideal = 0.875 × 1.380 = 1.208 stb/d/psi. qpost = 1.208 × (4200 − 2500) = 1.208 × 1700 = 2,056 stb/d. This represents a production uplift of 2,056 − 782 = 1,274 stb/d (+163%) from the acid treatment. Note: this is the production at the same fixed pwf = 2,500 psi. With nodal analysis (TPC interaction), the actual uplift would be higher as pwf drops to a new, lower operating point.
6. A stimulated well has S = −3 (post-fracture). What is FE, and what does FE > 1.0 physically mean?
D is correct. FE = 7/(7+(−3)) = 7/4 = 1.75. FE > 1.0 does not violate physics — it means the stimulated well outperforms the theoretical “ideal” vertical radial flow model because the fracture creates a dramatically more efficient flow path. The ideal Darcy model (S=0) is not actually the maximum possible production from a reservoir; it is merely the production from an undamaged vertical well. A fracture effectively increases the wellbore radius (r'w = rw×e3 = 7.0 ft for S=−3), enabling access to a much larger reservoir volume per unit time. Production at FE = 1.75 is 1.75× the ideal undamaged vertical well — entirely consistent with reservoir physics.
7. In the FE-modified Vogel equation q = qmax(FE) × [1 − 0.2(FE × pwf/p̄R) − 0.8(FE × pwf/p̄R)²], what is the effect of setting FE = 0 (complete wellbore plugging, S = ∞)?
A is correct. When FE = 0: qmax(FE) = 0 (from the qmax(FE) formula, which contains FE as a factor). The bracket term [1 − 0.2(0 × ...) − 0.8(0 × ...)²] = [1 − 0 − 0] = 1. But since qmax(FE=0) = 0, q = 0 × 1 = 0 for all pwf. This correctly represents a completely plugged wellbore with zero production regardless of drawdown — exactly what FE = 0 (S = ∞) means physically. The equation is well-defined at FE = 0 and gives the correct physical result.
8. Why does nodal analysis (TPC intersection) give a LARGER production uplift than the fixed-pwf FE calculation for the same skin improvement?
B is correct and captures the key physical mechanism. The fixed-pwf calculation holds pwf = 2,500 psi constant and shows q increasing from 782 to 2,056 stb/d. But the actual tubing system has a TPC: as production rate increases (IPR improves), the wellbore flowing pressure required by the tubing system also changes. For a typical well on natural flow, higher q means higher friction losses in the tubing, but the net effect is that pwf actually decreases as IPR improves (the reservoir can sustain higher rates at lower BHP). This lower pwf accesses more drawdown, producing even more oil than the fixed-pwf estimate. For GK-22: fixed pwf gives Δq = +1,274 stb/d; nodal gives Δq ≈ +1,970 stb/d.
9. GK-22's acid treatment costs $450,000. The incremental production (from FE analysis at fixed pwf) is 1,274 stb/d. At a net oil value of $70/bbl (price minus opex), what is the payback period in days?
A is correct. Payback period = Treatment cost / Daily revenue = $450,000 / (1,274 stb/d × $70/bbl) = $450,000 / $89,180 = 5.04 days ≈ 5 days. This is an extraordinary return: the entire treatment cost is recovered in 5 days of incremental production. Over a 24-month treatment benefit period, the NPV exceeds $4.3M. This rapid payback is why formation damage treatments on high-permeability, high-rate wells are among the most economically attractive interventions in the oil industry — especially when, as with GK-22, a large damage skin (+14) exists in a highly productive formation (85 md).
10. After completing Topics 3.1–3.5, what is the complete Module 03 conclusion for GK-22 in terms of FE?
C is the complete and correct Module 03 conclusion. It integrates all findings:
• Topic 3.1: S′ = +14, J = 33% of ideal (FE = 0.333), Δpskin = 1,038 psi wasted
• Topic 3.2: Dq ≈ 0.001 — all skin is rate-independent (S = S′ = +14)
• Topic 3.3: Sd = +14 confirmed; Hawkins ks/k = 0.145, rs = 3.77 ft; acid will achieve S → +1
• Topic 3.4: Sc = 0, Sc″ ≈ 0 — no geometric skin; Sd = S′ confirmed
• Topic 3.5: FEpre = 0.333 → FEpost = 0.875; qpost = 2,056 stb/d; payback 5 days; NPV $4.3M+
This is the Module 03 PBL final deliverable framework. Topic 3.6 (Gravel Pack and Sand Control Skin) will complete the full Module 03 scope.
NEXT STEPS
Topics 3.1–3.5 have established the complete skin audit and FE-based production forecast for GK-22. The acid treatment recommendation (S → +1, FE = 0.875, q = 2,056 stb/d) is fully justified economically.
Proceed to Topic 3.6: Gravel Pack and Sand Control Skin (SG) — which quantifies the additional pressure drop through gravel-filled perforations and screens, completing the Module 03 skin component library and providing the framework for sand control completion design in the GK-22 context.