Vogel's original equation assumes a perfectly undamaged well. In reality every well carries a skin — positive from damage or poor completion, negative from stimulation. Standing's modification lets you quantify exactly how much production you're losing to skin, and how much you'd gain by fixing it.
Topics 4.1 and 4.2 built the Vogel and composite IPR for wells with zero skin (Flow Efficiency = 1.0). This is rarely true. Formation damage during drilling and completion (filtrate invasion, fines migration, clay swelling), poor perforation design, scale and asphaltene deposition, or inadequate stimulation all impose a positive skin that throttles the well below its reservoir potential.
Conversely, acidising, hydraulic fracturing, or reperforation can create a negative skin that pushes production above the undamaged Darcy-Vogel baseline. The completion engineer's primary lever for improving production is to reduce this skin term — and Standing's extension quantifies exactly what that improvement is worth, in barrels per day, before a single dollar is spent on intervention.
Standing (1970) published a modification to Vogel's dimensionless IPR curve parameterised by Flow Efficiency (FE) — the ratio of actual well pressure drawdown to the ideal undamaged drawdown. This single parameter captures the entire skin contribution to IPR in a form directly usable for well performance prediction and workover economics.
▶
Lecture 4.3A: Why Skin Changes the Shape of the IPR — Not Just a Vertical Shift
19:45 · HD
Explains why skin doesn't simply translate the Vogel curve but fundamentally changes its shape and apparent qmax. Animated comparison of five IPR curves (FE = 0.5 to 2.0) showing how the FE family fans out. Includes a field case from the Middle East where pre-acid and post-acid IPRs confirmed a skin reduction from +18 to −2, increasing qmax by 340%. The lecture introduces Standing's flow efficiency modification and the visual interpretation of the FE correction chart.
LEARNING OBJECTIVES
After completing Topic 4.3, you will be able to:
1. Define Flow Efficiency (FE) in terms of skin factor S and the radial flow geometry, and explain what FE = 1.0, FE < 1.0, and FE > 1.0 mean physically.
2. Write and apply Standing's modified Vogel equation for any FE value, computing the corrected qo/qmax ratio at any pwf.
3. Calculate the skin-corrected qmax and show how it relates to the zero-skin (FE=1) qmax.
4. Construct the skin-corrected composite IPR (Standing + Darcy segment) for a damaged or stimulated well.
5. Quantify the production uplift from a workover or stimulation by comparing pre- and post-intervention FE values and IPR curves.
6. Apply Standing's curves graphically using the FE correction chart, and cross-check against the analytical formula.
7. Recognise the limitations of the FE correction and when a more rigorous approach (multirate test, pressure transient analysis) is needed.
PREREQUISITE
Required: Topic 4.1 (Vogel's equation and qmax), Topic 4.2 (composite IPR construction), Skin factor concept from Topic 2.1 (Darcy radial flow, Hawkins' formula). You must understand that S' = S + Dq and that J = kh / [141.2µB(ln(re/rw) − 0.75 + S')] before the FE definition becomes meaningful.
PBL CONNECTION — KARAMA FIELD PROBLEM
Pressure transient analysis of KA-07 indicates a total skin S' = +8 (a combination of formation damage S = +6 and completion-related skin). The reservoir engineer estimates that an acid job could reduce skin to S = +1 (FE improvement from 0.47 to 0.89). In this topic you will: (a) quantify how much production KA-07 is currently losing due to skin, (b) predict the post-acid IPR using Standing's method, and (c) determine whether stimulation alone — without an ESP — could achieve the field's 1,800 stb/d target rate. This analysis feeds directly into Module 04 Problem Set Task 7 (stimulation vs. artificial lift decision).
Topic Scope
Standing's FE correction to Vogel and composite IPR. Skin-to-FE conversion. Pre/post stimulation IPR comparison.
~110 min: 40 min reading, 20 min simulation, 30 min worked examples, 20 min quiz.
Section 1
Skin Factor and Its Effect on IPR
A review of the skin concept from a production engineering perspective — specifically, how positive and negative skin alter the IPR shape and apparent deliverability.
▶
Lecture 4.3B: From Hawkins' Equation to IPR Shift — How Skin Manifests in Deliverability
16:00 · HD
Derivation of the skin concept from Hawkins' equation. Shows the near-wellbore pressure "step" caused by positive skin and negative skin on a radial pressure profile animation. Explains how this step pressure drop directly reduces the effective drawdown available to drive fluid into the wellbore — reducing both the slope and the qmax of the IPR. Covers typical skin ranges for different well conditions.
Recap: Skin in the Radial Flow Equation
Skin factor S accounts for the deviation from ideal radial flow in the near-wellbore region. In the Darcy equation:
The skin S' appears additively in the denominator alongside the geometric term ln(0.472re/rw). For a typical onshore well, ln(0.472re/rw) ≈ 7. Therefore:
S = +7: doubles the denominator → halves the PI → halves the rate at any given drawdown
S = −3: reduces denominator to 4 → increases PI by 75% → significant stimulation benefit
S = 0: baseline (undamaged, normally completed) well
The additional pressure drop across the skin zone is:
Δpskin = 141.2 qo µo Bo S / (ko h) [psi]
This Δpskin is "wasted" pressure — it does not contribute to driving fluid through the bulk reservoir but is dissipated in the near-wellbore damage zone. The engineer's job is to minimise this waste through proper well design, good completion practice, and stimulation where needed.
Typical Skin Values and Their Sources
Well Condition
Typical Skin S
FE Range
Source
Treatment
Ideal undamaged, open hole
0
1.00
Reference condition
—
Good initial cased/perforated
+1 to −1
0.88–1.13
Perforation geometry
Reperforation
Minor filtrate damage
+2 to +5
0.58–0.78
Drilling/completion
Acid wash / soak
Moderate damage
+5 to +15
0.32–0.58
Poor mud loss control
Matrix acidise
Severe damage
+15 to +50
0.12–0.32
Lost circulation, scale
Acid + re-completion
Lightly acidised
0 to −2
1.00–1.29
Stimulation
—
Propped frac / deviated
−3 to −5
1.29–1.56
Stimulation/geometry
—
Large frac, low-k formation
−5 to −7
1.56–2.00
Hydraulic fracturing
—
How Skin Changes the IPR — Not Just a PI Shift
For the single-phase (Darcy) IPR above the bubble point, skin simply scales the PI: Jactual = Jideal × (ln(re/rw) − 0.75) / (ln(re/rw) − 0.75 + S). The IPR remains a straight line, just with a different slope.
For the two-phase (Vogel) IPR below the bubble point, the effect is more complex. The skin doesn't just scale the curve — it fundamentally changes both the slope and the apparent qmax in a non-linear way. This is why Vogel's original equation (which assumes S = 0) gives wrong answers for damaged or stimulated wells, and why Standing's extension is needed.
CRITICAL ENGINEERING INSIGHT
A well with S = +10 and pR = 3,600 psi doesn't just produce less — it produces at a rate that is non-linearly less than the undamaged case. If you apply Vogel's unmodified equation and then separately apply a skin correction to the answer, you will overestimate the benefit of skin removal by ignoring the curvature effect. Standing's extension correctly handles both the scale and the shape of the correction simultaneously.
Total skin S' = Sd + Sp + Sgeo + Sfrac + Dq where:
Sd (damage skin): Formation damage from drilling filtrate, completion fluids, fines migration, clay swelling, scale, asphaltene. Always positive. Reduced by acidising.
Sp (perforation skin): Determined by perforation density (shots per foot), phase angle, penetration, and compaction damage. Can be positive (inadequate perforations) or near-zero (through-tubing gun, optimal density).
Sgeo (geometric skin): From partial penetration, deviated well in anisotropic formation, or limited entry. Usually positive for partially penetrated wells, negative for deviated wells in thick formations.
Sfrac (fracture skin): Negative contribution from hydraulically induced or natural fractures. The larger and more conductive the fracture, the more negative Sfrac.
Dq (non-Darcy / turbulence skin): Rate-dependent, always positive, significant in high-rate gas wells. For oil wells usually small unless very high GOR.
Standing's FE approach treats S' as a lumped parameter — it does not distinguish between these components. However, if the objective of a stimulation is to address only Sd, the engineer must be careful not to credit the FE improvement to components that stimulation won't change (e.g., Sgeo).
Section 2
Flow Efficiency — Definition, Calculation, and Interpretation
Flow Efficiency (FE) is the single number that captures the skin's effect on IPR in a form directly usable with Vogel's dimensionless framework.
Definition of Flow Efficiency
Standing (1970) defined Flow Efficiency as the ratio of the actual flowing bottomhole pressure drawdown to the ideal undamaged drawdown that would be needed to produce the same rate. Equivalently, it is the ratio of the ideal to actual pressure difference between reservoir pressure and wellbore pressure:
FLOW EFFICIENCY — Definition
FE = (pR − p'wf) / (pR − pwf) = Ideal drawdown / Actual drawdown
where:
pwf = actual measured BHFP (psi) — includes skin pressure drop
p'wf = equivalent BHFP if there were no skin (psi)
pR = average reservoir pressure (psi)
The approximation ln(0.472 re/rw) ≈ 7 is used for typical oilfield drainage geometries.
Interpretation of FE Values
FE = 0.2 S≈+28
FE = 0.4 S≈+10
FE = 0.6 S≈+5
FE = 0.8 S≈+2
FE = 1.0 S=0
FE = 1.2 S≈−1
FE = 1.5 S≈−2
FE = 2.0 S≈−3.5
FE < 1.0 — Damaged Well
The actual drawdown (pR − pwf) is larger than it needs to be for the given rate. Skin is consuming productive drawdown. A portion of the total pressure drop is wasted across the damage zone. Well underperforming relative to reservoir potential.
FE = 1.0 — Ideal Well
Actual and ideal drawdowns are equal. No skin — Darcy and Vogel equations apply exactly as derived. This is the reference condition for both Vogel's original curve and the composite IPR from Topic 4.2.
FE > 1.0 — Stimulated Well
Negative skin creates an effectively larger wellbore — the pressure profile is enhanced near the wellbore. The ideal drawdown would be larger than the actual drawdown for the same rate. Well outperforms the undamaged reference. Acidising or fracturing can achieve FE up to 2.0–2.5.
Converting Between Skin and FE
The approximate formula FE ≈ 7/(7 + S) assumes ln(re/rw) ≈ 7, which holds for typical drainage radii and wellbore sizes. For more precise work, substitute the actual geometric term. Below is a conversion table:
Skin S
7 + S
FE = 7/(7+S)
Jactual/Jideal
Description
+50
57
0.123
0.123
Severely damaged — near loss of production
+20
27
0.259
0.259
Very poorly completed well
+10
17
0.412
0.412
Significantly damaged
+7
14
0.500
0.500
Well produces at 50% of potential
+5
12
0.583
0.583
Moderate damage
+3
10
0.700
0.700
Minor to moderate damage
+1
8
0.875
0.875
Minor damage — good completion
0
7
1.000
1.000
Reference (undamaged)
−1
6
1.167
1.167
Light stimulation
−2
5
1.400
1.400
Good acidise result
−3
4
1.750
1.750
Propped frac or deviated well
−4
3
2.333
2.333
Effective hydraulic fracture
−5
2
3.500
3.500
Large frac, low-permeability well
IMPORTANT LIMITATION
The approximation FE ≈ 7/(7+S) is only valid for wells where ln(0.472 re/rw) ≈ 7. For wells with unusual drainage geometries (very small re in tight spacing, very large re in gas wells), use the full expression:
FE = [ln(re/rw) − 0.75] / [ln(re/rw) − 0.75 + S]
For example, a gas well with re = 2,640 ft and rw = 0.33 ft gives ln(re/rw) = ln(8,000) = 9.0, so FE ≈ 8.25/(8.25 + S), not 7/(7+S). The error from using the approximation on this well would be about 15% in the FE value.
p'wf is the "equivalent undamaged BHFP" — the bottomhole pressure that an ideal (zero-skin) well would need to achieve the same production rate as the actual damaged well. From the skin equation:
p'wf = pwf + Δpskin = pwf + 141.2 q µ B S / (kh)
Or alternatively, from the FE definition rearranged: p'wf = pR − FE × (pR − pwf)
When FE < 1: p'wf > pwf — the ideal well needs less drawdown (higher BHFP) for the same rate. This makes sense because the ideal well has no wasted pressure across a damage zone.
When FE > 1: p'wf < pwf — the stimulated well is producing more than an ideal undamaged well at the same actual BHFP. The negative skin "extends" the effective wellbore, making the pressure profile more favourable.
Section 3
Standing's Modified Vogel Equation
The complete mathematical formulation of Standing's FE-corrected IPR — deriving how FE enters Vogel's equation and changes qmax.
▶
Lecture 4.3C: Deriving Standing's Equation — Substitution and Mathematical Proof
22:30 · HD
Step-by-step derivation showing how Standing substituted the ideal pressure p'wf into Vogel's original equation to obtain the FE-corrected curve. Proves that the FE correction changes both the numerator ratio and the effective qmax. Compares Harrison's extension (for FE > 1.5) with Standing's original work (valid for FE 0.5–1.5). Shows the shape of the corrected curve for each FE value and explains why high FE (stimulation) produces a concave-up IPR while low FE (damage) produces a steeper curve that flattens rapidly.
Derivation of Standing's Equation
Vogel's original equation uses actual pwf/pR as the normalised flowing pressure. Standing's insight was that in a damaged or stimulated well, the ideal pressure ratio p'wf/pR should be used instead — because the Vogel curve describes two-phase flow behaviour in the bulk reservoir (away from the skin zone), which is driven by the ideal (skin-free) pressure.
Key result: qmax is the maximum rate for the undamaged (FE=1) condition. The actual maximum rate qmax,FE for the real well is found by setting pwf = 0:
qmax,FE = qmax × [1 − 0.2(1 − FE) − 0.8(1 − FE)²]
This is the AOF of the actual well at zero BHFP, accounting for skin.
Understanding qmax,FE — The Skin-Corrected AOF
qmax,FE is not a constant of the reservoir — it depends on skin. When skin is removed (S → 0, FE → 1), qmax,FE → qmax (the ideal Vogel AOF). When skin is large (FE << 1), qmax,FE can be dramatically less than qmax.
FE
S (approx.)
1 − FE
Vogel Factor at pwf=0
qmax,FE/qmax
Production as % of Potential
0.3
~+16
0.70
1−0.2(0.7)−0.8(0.49)=1−0.14−0.392
0.468
46.8%
0.5
~+7
0.50
1−0.2(0.5)−0.8(0.25)=1−0.10−0.200
0.700
70.0%
0.7
~+3
0.30
1−0.2(0.3)−0.8(0.09)=1−0.06−0.072
0.868
86.8%
1.0
0
0.00
1−0−0
1.000
100.0%
1.2
~−1
−0.20
1−0.2(−0.2)−0.8(0.04)=1+0.04−0.032
1.008
100.8%
1.5
~−2.3
−0.50
1−0.2(−0.5)−0.8(0.25)=1+0.10−0.200
0.900
~110% effective*
2.0
~−3.5
−1.00
1−0.2(−1)−0.8(1)=1+0.20−0.800
0.400
Requires Harrison†
*For FE > 1, qmax,FE must be computed differently — see the Harrison extension note below.
HARRISON'S EXTENSION FOR FE > 1.5
Standing's original family of curves (1970) covered FE values of 0.5 to 1.5. For stimulated wells with FE significantly greater than 1.5 (e.g., fractured wells with S = −4 to −6), Harrison et al. published an extension that provides additional curves. In practice, for the Karama Field problem set (where stimulation targets FE ≈ 0.47 → 0.89), Standing's original range is fully adequate. For fracture-stimulated wells, the Fetkovich approach (Topic 4.5) is often preferred as it can directly fit multirate test data from the stimulated well.
Check 1: At pwf = pR (shut-in):
p'wf/pR = 1 − FE(1 − 1) = 1. Vogel factor = 1−0.2(1)−0.8(1) = 0. Therefore qo/qmax = 0. ✓ (Zero production at reservoir pressure, regardless of FE.)
Check 2: At pwf = 0 (AOF condition):
p'wf/pR = 1 − FE(1 − 0) = 1 − FE. Vogel factor = 1 − 0.2(1−FE) − 0.8(1−FE)².
At FE = 1: factor = 1 − 0.2(0) − 0.8(0) = 1. So qo/qmax = 1. ✓
At FE = 0.5: factor = 1 − 0.2(0.5) − 0.8(0.25) = 0.70. So qo/qmax = 0.70 — meaning the damaged well can only reach 70% of the undamaged qmax, even at zero BHFP.
Check 3: FE effect on slope at pwf = pR:
dq/dpwf at shut-in ∝ −FE × 1.8 qmax/pR. A higher FE gives a steeper initial IPR slope — meaning stimulated wells respond more to initial drawdown. This is physically correct: the stimulated well has lower near-wellbore resistance so pressure changes propagate more effectively into production.
Section 4
The Family of FE Curves — Graphical Application
Understanding the visual pattern of Standing's FE correction curves and how to read the correction chart in the field.
▶
Lecture 4.3D: Reading the Standing FE Chart — Field Application Walkthrough
14:00 · HD
Step-by-step walkthrough of the Standing FE correction chart. Shows how to: (1) calculate FE from skin, (2) locate the FE curve on the chart, (3) read off the corrected qo/qmax at any pwf/pR, and (4) convert back to actual production rates. Includes a worked example comparing pre-acid (FE=0.5) and post-acid (FE=1.1) IPR curves on the same chart.
Reading the FE Chart — Three-Step Graphical Method
In field practice, Standing's chart is used graphically when analytical calculation isn't convenient. The three-step method:
GRAPHICAL METHOD — Standing's Chart
Step 1: Calculate FE from skin: FE = 7/(7+S)
Step 2: Calculate the BHFP ratio: pwf/pR
Step 3: Enter the chart at pwf/pR on the y-axis. Move horizontally to the appropriate FE curve. Read off qo/qmax on the x-axis.
Step 4: Multiply by qmax (the undamaged well's AOF at FE=1) to get actual rate.
Key Observations from the FE Family
Damaged Wells (FE < 1)
Curves are compressed to the left — they produce less at any given BHFP. The lower the FE, the more the curve is compressed. At very low FE (severe damage), the IPR curve becomes nearly vertical near zero rate — confirming almost no deliverability. The "useful" range of BHFP is greatly reduced.
Stimulated Wells (FE > 1)
Curves extend to the right of the FE=1 reference — more production at any given BHFP. The curve is less steep (more gradual) because the enhanced near-wellbore conductivity means small drawdown changes produce larger rate changes. The "diminishing returns" threshold of the Vogel curve is pushed to higher rates.
READING EXAMPLE — KA-07 Pre and Post Acid
KA-07 pre-acid: S = +8, FE = 7/15 = 0.467. At pwf/pR = 0.6 (BHFP = 3,060 psi with pR = 5,100 psi):
p'wf/pR = 1 − 0.467(1−0.6) = 1 − 0.467×0.4 = 1 − 0.187 = 0.813
Vogel factor = 1−0.2(0.813)−0.8(0.813²) = 1−0.163−0.529 = 0.308
→ Pre-acid produces 30.8% of undamaged qmax at this BHFP.
KA-07 post-acid: S = +1, FE = 7/8 = 0.875. At same pwf/pR = 0.6:
p'wf/pR = 1 − 0.875(0.4) = 1 − 0.350 = 0.650
Vogel factor = 1−0.2(0.650)−0.8(0.650²) = 1−0.130−0.338 = 0.532
→ Post-acid produces 53.2% of undamaged qmax at the same BHFP.
Result: The acid job increased the rate at this BHFP from 30.8% to 53.2% of qmax — a +73% production increase with no change in BHFP.
Section 5
Standing's Extension Applied to the Composite IPR
Combining Standing's FE correction with the two-segment (Darcy + Vogel) composite IPR to handle the most general real-world case: a well above bubble point with non-zero skin.
The Complete General IPR Model
The most general inflow model combines all three elements:
Darcy segment above pb: Modified by skin (Jactual = Jideal × FE × 7/[ln(re/rw)−0.75] → simplifies to J × FE for normalised form)
Vogel segment below pb: Modified by Standing's FE correction on p'wf/pb
Join at pb: Must still be continuous in rate and slope
where p'wf/pb = 1 − FE(1 − pwf/pb) and qmax,FE = qb + qinc,FE
PRACTICAL SIMPLIFICATION — Most Common Field Approach
In the vast majority of field applications, the engineer has a measured (or calculated) Jactual from a well test — this already incorporates the skin. The composite IPR construction from Topic 4.2 then proceeds normally using Jactual (not Jideal), and the Standing FE correction is applied only to the Vogel segment below pb.
Practical workflow:
1. Use Jactual (from PI test with skin present) to compute qb normally
2. Compute FE from skin: FE = 7/(7+S)
3. Apply Standing's equation below pb with this FE
4. Total qmax,FE = qb + (Jactual×pb/1.8) × FE_factor
This is the method used in all worked examples and the simulator.
The Production Uplift Triangle
The area between the damaged and stimulated IPR curves (visible in Figure 5.1) represents the total producible uplift from a stimulation treatment — integrated across all possible operating BHFPs. This is the basis of stimulation economic evaluation: the larger this "uplift triangle," the greater the NPV of the workover investment.
At any given operating BHFP, the uplift in rate from stimulation is:
Δqstimulation = qo,FE_post − qo,FE_pre [stb/d]
This is calculated using the Standing equation at the same pwf with pre- and post-stimulation FE values.
Section 6
Workover & Stimulation Economics Using Standing's Method
Translating IPR improvements from FE into production uplift, incremental revenue, and simple payback calculations — the economic case for well intervention.
▶
Lecture 4.3E: From Skin Reduction to Dollars — Workover Economics Fundamentals
20:00 · HD
Full economics walkthrough from FE improvement to NPV calculation. Covers: production uplift calculation from pre/post FE curves, production profile (ramp-up, plateau, decline), opex vs. capex breakdown for acid jobs, ESP recompletions, and fracture stimulations, simple payback time, discounted cash flow at 10% discount rate, and the "minimum uplift needed" concept. Uses KA-07 acid job case study. Shows why a stimulation with a payback of less than 6 months is almost always sanctioned in the industry.
The Economics Framework: Four Numbers
A simple but effective stimulation economics evaluation requires only four numbers:
① Incremental Rate Δq (stb/d)
Rate after stimulation minus rate before, at the same operating BHFP. Calculated from Standing's equation with pre- and post-job FE values. This is the fundamental production benefit.
② Incremental Revenue ($/d)
Δq × (Oil price − Lifting cost) = Δq × netback price [$/stb]. Typical netback for an offshore well: $50–65/stb. For KA-07: Δq × $58/stb.
③ Stimulation Cost ($)
Matrix acid job: $200K–$800K depending on depth, acid volume, and whether a rig workover or coiled tubing is used. For a typical KA-07 scope: ~$450K.
④ Simple Payback (months)
Stimulation cost / Incremental daily revenue × (1/30). Any payback under 6 months is generally economically compelling. Under 3 months: almost always sanctioned.
FIELD EXAMPLE — KA-07 Acid Job Economics
Well data: pR = 5,100 psi, pb = 4,500 psi, current BHFP = 4,200 psi, Jideal = 0.72 stb/d/psi (at S=0, estimated from kh). Current state: S = +8 → Jactual = 0.72 × 7/15 = 0.336 stb/d/psi → FE = 0.467. Post-acid target: S = +1 → Jactual,post = 0.72 × 7/8 = 0.630 stb/d/psi → FE = 0.875.
This is an extremely compelling economic case for stimulation. The well should be acidised before considering any more expensive intervention.
Stimulation Type
Typical S Reduction
FE Improvement
Typical Cost
Best Suited For
Acid soak (bullhead)
−2 to −5
0.2–0.4 FE units
$80K–$200K
Carbonate scale, mild damage
Matrix acid job (CTU)
−5 to −15
0.3–0.7 FE units
$200K–$600K
Sandstone/carbonate damage
HCl + HF system
−8 to −20
0.5–0.9 FE units
$300K–$800K
Clay-plugged sandstones
Reperforation (TCP gun)
Variable
0.1–0.5 FE units
$150K–$500K
Poorly perforated intervals
Propped fracture
S → −3 to −6
FE → 1.75–3.5
$800K–$5M
Low-k reservoir, tight intervals
For a well like KA-07 with significant skin and below-bubble-point natural flow, the engineer faces three options:
Option A — Stimulate only: Reduces skin, increases FE, improves natural flow rate. Limited by: (a) residual skin after treatment, (b) well still above pb if natural TPC intersects Darcy segment. Best when natural flow can sustain economic rate after stimulation.
Option B — Lift only: Pulls BHFP below pb, accessing Vogel segment. But with high skin (low FE), the Vogel curve is compressed — lift delivers less incremental rate than it would on an undamaged well. The ESP is working harder than necessary to overcome both hydrostatic head and skin pressure drop.
Option C — Stimulate then lift: The optimal sequence. Stimulate first to remove skin, then install lift to capture the Vogel segment on the improved (high FE) IPR. This is typically the highest NPV option for wells with significant skin. The KA-07 analysis in the PBL problem set asks you to quantify and compare all three options.
Decision rule of thumb: If the stimulation payback is < 6 months, always stimulate before making any lift decision. The improved IPR will also change the optimal lift design (smaller pump, lower power requirement for the same target rate).
Section 7 — Interactive Tool
Flow Efficiency & Standing's Correction Simulator
Compare pre- and post-stimulation IPR curves in real time. Adjust skin, reservoir conditions, and operating BHFP to quantify production uplift and workover economics.
Standing's FE IPR Simulator — Pre vs. Post Stimulation INTERACTIVE
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Scenarios to explore:
• KA-07 base: pR=5100, pb=4500, Jideal=0.72, Spre=+8, Spost=+1 → pwf=4200
• What skin would make stimulation + natural flow achieve 1,800 stb/d without ESP?
• Compare acid job (S: +8→+1) vs. fracture (S: +8→−3) at the same BHFP
• What's the minimum oil price at which the acid job is economic (payback < 12 months)?
• Set Spost = Spre (no improvement) — confirm zero uplift
Skin Sensitivity Table — q at Target BHFP vs. Skin INTERACTIVE
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Section 8
Worked Examples
Five fully worked problems covering all aspects of Standing's extension, from basic FE calculation through to complete pre/post-stimulation IPR comparison and economic evaluation.
WORKED EXAMPLE 4.3-ABasic FE Calculation and Skin-Corrected qmax
Given: A solution-gas drive reservoir (pR = pb = 3,200 psi — pure Vogel case). Well test gives qmax,undamaged = 1,800 stb/d (from a clean, undamaged reference well in the same field). Current well has skin S = +6.
Tasks: (a) Calculate FE. (b) Calculate actual qmax,FE. (c) What rate does the well produce at pwf = 1,280 psi (40% of pR)?
WORKED EXAMPLE 4.3-CFinding Required Skin for Target Rate
Given: Well with pR = pb = 3,600 psi (pure Vogel, depleted reservoir), J* = 0.85 stb/d/psi, current skin S = +9 (FE = 0.438). Management has set a well target rate of 1,200 stb/d at a natural flow BHFP of 1,800 psi. Current rate at this BHFP is only 380 stb/d.
Task: What maximum skin is permissible for the well to achieve 1,200 stb/d at pwf = 1,800 psi? Is acid alone sufficient, or is a frac needed?
SOLUTION 4.3-C
q_max,undamaged = J* × p_R / 1.8 = 0.85 × 3,600 / 1.8 = 1,700 stb/d
p_wf/p_R = 1,800/3,600 = 0.500
Standard Vogel factor at this ratio = 0.700 (undamaged rate = 1,700 × 0.700 = 1,190 stb/d)
Wait: undamaged rate at p_wf/p_R = 0.5 is only 1,190 stb/d — just below target!
So even with zero skin (FE=1.0), target of 1,200 stb/d is barely achievable.
Need slight stimulation (FE > 1.0) or nearly zero skin.
Let's find FE needed for q = 1,200 stb/d at p_wf/p_R = 0.500:
1,200 / 1,700 = 0.7059 = 1 - 0.2(p'_wf/p_R) - 0.8(p'_wf/p_R)²
Let x = p'_wf/p_R:
0.8x² + 0.2x - 0.2941 = 0
Quadratic: x = [-0.2 + √(0.04 + 4×0.8×0.2941)] / (2×0.8)
= [-0.2 + √(0.04 + 0.9412)] / 1.6
= [-0.2 + √0.9812] / 1.6
= [-0.2 + 0.9906] / 1.6
= 0.7906 / 1.6 = 0.4941
So p'_wf/p_R = 0.4941
Now: p'_wf/p_R = 1 - FE(1 - p_wf/p_R)
0.4941 = 1 - FE(1 - 0.500)
0.4941 = 1 - 0.5 FE
0.5 FE = 1 - 0.4941 = 0.5059
FE = 1.012
Required FE ≈ 1.0 (essentially zero skin)
Convert FE to skin:
FE = 7/(7+S) → 1.012 = 7/(7+S) → 7+S = 7/1.012 = 6.917 → S = -0.083
CONCLUSION: The target requires skin of approximately S = 0 (zero damage, undamaged well).
Current skin S = +9 needs to be reduced to S ≈ 0.
A good matrix acid job targeting S = 0 should be sufficient.
A propped frac (S → negative) would overshoot the target but
might be warranted if acid cannot achieve S = 0.
VERIFY at S = 0 (FE = 1.0), p_wf/p_R = 0.500:
q = 1,700 × 0.700 = 1,190 stb/d ≈ 1,200 stb/d ✓ (within engineering tolerance)
The acid job needs to achieve S ≤ 0 to meet target. A typical
good acid job in sandstone achieves S = +1 to 0 — right at the limit.
If the acid cannot achieve S ≤ 0, a propped frac would be recommended.
WORKED EXAMPLE 4.3-DPre/Post Acid IPR Comparison — Full Curve Construction
Task: Construct both composite IPRs (pre and post acid) and determine the rate at BHFP = 2,000 psi for each. Calculate production uplift and 12-month cumulative oil gain.
WORKED EXAMPLE 4.3-EBack-Calculating Skin from Two-Rate Test
Given: pR = pb = 4,000 psi (pure Vogel reservoir). A reference undamaged well in the same field has qmax,undamaged = 2,400 stb/d. The well under investigation was tested at two rates: Test 1: q₁ = 650 stb/d at pwf1 = 2,800 psi. Test 2: q₂ = 820 stb/d at pwf2 = 2,000 psi.
Task: Back-calculate the FE and skin of this well.
SOLUTION 4.3-E — Back-Calculating FE from Two-Rate Test
From Standing's equation, at any test point:
q/q_max = 1 - 0.2(p'_wf/p_R) - 0.8(p'_wf/p_R)²
where p'_wf/p_R = 1 - FE(1 - p_wf/p_R)
For Test 1 (q₁ = 650, p_wf1 = 2,800, p_R = 4,000):
q₁/q_max = 650/2,400 = 0.2708
p_wf1/p_R = 2,800/4,000 = 0.700
Let x₁ = p'_wf1/p_R = 1 - FE(1 - 0.700) = 1 - 0.3FE
0.2708 = 1 - 0.2x₁ - 0.8x₁² ...(1)
For Test 2 (q₂ = 820, p_wf2 = 2,000, p_R = 4,000):
q₂/q_max = 820/2,400 = 0.3417
p_wf2/p_R = 2,000/4,000 = 0.500
Let x₂ = p'_wf2/p_R = 1 - FE(1 - 0.500) = 1 - 0.5FE
0.3417 = 1 - 0.2x₂ - 0.8x₂² ...(2)
From equation (1): 0.8x₁² + 0.2x₁ = 0.7292
From equation (2): 0.8x₂² + 0.2x₂ = 0.6583
Solve for x₁ from eq (1): x₁ = [-0.2 + √(0.04 + 4×0.8×0.7292)] / (2×0.8)
= [-0.2 + √(0.04 + 2.3334)] / 1.6
= [-0.2 + √2.3734] / 1.6
= [-0.2 + 1.5406] / 1.6 = 1.3406/1.6 = 0.8379
Since x₁ = 1 - 0.3FE → FE = (1 - 0.8379)/0.3 = 0.1621/0.3 = 0.5403
Verify with equation (2):
x₂ = 1 - 0.5×0.5403 = 1 - 0.2702 = 0.7298
Check: 0.8(0.7298²) + 0.2(0.7298) = 0.8(0.5326) + 0.1460
= 0.4261 + 0.1460 = 0.5721
q₂/q_max = 1 - 0.5721 = 0.4279 × 2,400 = 1,027 stb/d — doesn't match 820!
Discrepancy suggests slightly different FE from each test — iterate or average:
From Test 2 alone:
0.8x₂² + 0.2x₂ - 0.6583 = 0
x₂ = [-0.2 + √(0.04 + 4×0.8×0.6583)] / 1.6
= [-0.2 + √2.147] / 1.6 = [-0.2 + 1.465] / 1.6 = 0.791
FE₂ = (1 - 0.791)/0.5 = 0.418
Average FE = (0.540 + 0.418)/2 ≈ 0.479
FE ≈ 0.48 → S = 7/FE - 7 = 7/0.48 - 7 = 14.58 - 7 = 7.6
ANSWER: FE ≈ 0.48, S ≈ +8 (moderate to significant damage)
Note: Scatter between the two test points is typical of field data.
Use multiple test points and average, or use the Fetkovich approach (Topic 4.5)
for a more robust multirate analysis.
SELF-STUDY CHALLENGE 4.3-F
KA-07 post-acid (S=+1, FE=0.875): What additional production is gained by also installing an ESP to pull BHFP from natural flow (calculate natural flow BHFP by assuming TPC gives pwf = 3,800 psi post-acid) down to 2,000 psi? Compare: (a) pre-acid natural flow, (b) post-acid natural flow, (c) post-acid with ESP at 2,000 psi. Express each as a rate and as a % of qmax,ideal (the undamaged, skin-free AOF). This is the Module 04 PBL Problem Set Task 8.
Assessment · Topic 4.3
Knowledge Check — Standing's Extension
10 questions covering FE definition, Standing's equation, skin correction, stimulation economics, and composite IPR with skin. Target 80% before proceeding to Topic 4.4.
1. Flow Efficiency (FE) is defined as the ratio of:
Correct — B. FE = (pR − p'wf) / (pR − pwf). The ideal drawdown (numerator) is the drawdown that would be needed in an undamaged well to produce the same rate. The actual drawdown (denominator) is larger because skin wastes some of it. Equivalently, FE ≈ 7/(7+S) for typical drainage geometries.
2. A well has skin S = +7 in a reservoir where ln(0.472re/rw) ≈ 7. What is the Flow Efficiency?
Correct — C: FE = 0.500. FE = 7/(7+S) = 7/(7+7) = 7/14 = 0.500. This is an important reference case: when skin equals the geometric term (S = ln(re/rw) − 0.75 ≈ 7), the actual PI is exactly half the undamaged PI. The well is working at 50% efficiency — a very common field scenario for poorly stimulated or damaged wells.
3. In Standing's modified Vogel equation, the corrected pressure ratio p'wf/pR is calculated as:
Correct — D. From the FE definition: p'wf = pR − FE(pR − pwf). Dividing by pR: p'wf/pR = 1 − FE(1 − pwf/pR). This is the corrected normalised pressure that is substituted into Vogel's equation. When FE = 1: p'wf/pR = pwf/pR (no correction needed). When FE < 1: p'wf/pR > pwf/pR (effective pressure is higher, meaning less is available for production).
4. A well with qmax,undamaged = 2,000 stb/d has FE = 0.5. What is qmax,FE (actual AOF at pwf = 0)?
Correct — D: 1,400 stb/d. At pwf = 0: p'wf/pR = 1 − FE(1−0) = 1 − 0.5 = 0.5. Standing factor = 1 − 0.2(0.5) − 0.8(0.5²) = 1 − 0.10 − 0.20 = 0.70. qmax,FE = 2,000 × 0.70 = 1,400 stb/d. Note: this is NOT simply FE × qmax (that would be 1,000) — Standing's equation gives a non-linear correction that accounts for the shape change, not just a linear scale.
5. Why is Standing's correction necessary for damaged wells, rather than simply applying Jactual = FE × Jideal to get a modified PI and then using Vogel normally?
Correct — C. Skin affects both the effective PI (through the denominator of the radial flow equation) and the shape of the Vogel curve by changing the effective normalised pressure p'wf/pR. Simply scaling the PI by FE and using the unmodified Vogel curve treats the two-phase region as if skin only linearly scales the rate — it doesn't capture how the FE correction distorts the curvature. Standing's substitution of p'wf correctly propagates the skin effect through the non-linear Vogel relationship.
6. An acid job reduces skin from S = +9 to S = +2. Using FE ≈ 7/(7+S), calculate the FE improvement.
Correct — A/B. Pre-acid: FE = 7/(7+9) = 7/16 = 0.4375. Post-acid: FE = 7/(7+2) = 7/9 = 0.7778. Improvement = 0.7778 − 0.4375 = 0.340 FE units. Note that a skin reduction from +9 to +2 (removing 7 skin units) produces a 77.6% relative improvement in FE — non-linearly larger than the 44% improvement one might naively expect from (9−2)/9 × 100%.
7. A stimulated well has FE = 1.5 and the reference undamaged well has qmax = 1,600 stb/d. What is the stimulated well's qmax,FE?
Correct — A: 1,440 stb/d. At pwf=0: p'wf/pR = 1 − 1.5(1−0) = 1 − 1.5 = −0.5. Standing factor = 1 − 0.2(−0.5) − 0.8(0.25) = 1 + 0.10 − 0.20 = 0.90. qmax,FE = 1,600 × 0.90 = 1,440 stb/d. Counterintuitively, a stimulated well (FE=1.5) may have a qmax,FE below qmax,undamaged! This is because Standing's equation is designed for FE 0.5–1.5 and the relationship becomes non-monotonic beyond FE=1. Harrison's extension handles FE>1.5 more accurately.
8. KA-07: Jactual = 0.336 stb/d/psi (pre-acid, S=+8), pR=5,100, pb=4,500 psi. What is qb (rate at bubble point)?
Correct — C: 202 stb/d. qb = Jactual × (pR − pb) = 0.336 × (5,100 − 4,500) = 0.336 × 600 = 201.6 ≈ 202 stb/d. Note this is much lower than the undamaged qb = 0.72 × 600 = 432 stb/d. The skin has reduced the Darcy segment anchor by 53% — the damage zone is severely throttling the well even above the bubble point.
9. Which of the following correctly describes the economic basis for matrix acidising in the context of Standing's extension?
Correct — D. Acidising specifically targets the near-wellbore damage zone, dissolving scale, fines, or damaged formation and reducing skin S. This increases FE from its pre-acid value toward 1.0 (or beyond for aggressive stimulation). The effect in Standing's framework is: higher FE → larger p'wf correction → more production at any given actual BHFP → the IPR curve moves right toward the undamaged reference. Neither pR, pb, nor far-field permeability changes from acidising.
10. What should an engineer do FIRST when confronted with a well producing well below its IPR potential, before deciding on artificial lift?
Correct — C. This is the core engineering judgment from Standing's extension. A well with high skin (low FE) will underperform dramatically regardless of how much BHFP is drawn down by artificial lift — the ESP is fighting both the hydrostatic head and the skin pressure drop simultaneously. The correct sequence is: (1) quantify skin via PTA, (2) calculate FE improvement from stimulation, (3) calculate payback, (4) if payback < ~6 months, stimulate first, THEN reassess whether lift is still needed and re-size accordingly. The post-stimulation IPR will often show that the lift requirement is smaller (or unnecessary), saving capital cost on the artificial lift system.
TOPIC 4.3 COMPLETE
Excellent — you have mastered Standing's extension! You can now: calculate FE from skin, apply Standing's FE correction to both pure Vogel and composite IPR, quantify production uplift from stimulation, and make an economically grounded stimulation vs. lift decision.
Next: Topic 4.4 — Gas Well Deliverability: real gas pseudo-pressure, non-Darcy turbulent flow, backpressure testing, and AOFP determination. A completely new set of equations governing a fundamentally different fluid system.
PBL Tasks 7–8: Complete the KA-07 stimulation vs. lift analysis in the Module 04 Problem Set using the simulator. Document your recommendation (stimulate only / lift only / stimulate then lift) with supporting IPR curves and economic payback calculations.