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SP-5: Flow Efficiency, IPR Curves & Workover Economics

Use Standing's Flow Efficiency to convert Spre = +14 and Spost = +1.0 into production rates. Construct dual IPR curves, calculate Δq ≈ 1,271 stb/d (+162%), payback ≈ 5.1 days, and 24-month NPV ≈ $4.4M at $75/bbl. Run the post-treatment skin sensitivity table and include the correct NPV calculation with full working.

Module 03 · SP-5
Topic 3.5 — FE & IPR
Gashaka GK-22
~60 min
SP-5 · Topic 3.5 · Flow Efficiency & IPR

SP-5: Production Forecast & Workover Economic Justification

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Engineering Question for SP-5
Module 03 PBL · Gashaka GK-22

SP-1 through SP-4 have completed the pre-treatment skin audit: S′ = +14, confirmed as formation damage, with post-acid target Sd = +1.0. Now you answer the question every stakeholder is actually asking: how much oil will the well produce after treatment, and is the investment worth making?

Standing's Flow Efficiency translates the skin numbers into production rates through a single elegant formula. FE = 7/(7+S) gives the ratio of actual to ideal deliverability. By computing FE before and after treatment, then scaling the ideal PI, you obtain both IPR curves and all economic inputs. The dual IPR chart and NPV calculation produced in SP-5 form the core of the Final Report.

⚠ Calculation Transparency Required
Several earlier circulation versions of the GK-22 economics contained an error in the NPV calculation. The correct incremental production is ~1,271 stb/d at fixed pwf = 2,500 psia, yielding a daily net revenue gain of ~$88,970/day. The resulting NPV over a 24-month benefit period at 10% discount is approximately $4.4M for acid treatment alone (programme monthly-annuity convention: monthly CF × annuity factor ÷ 12 − cost). Show all calculation steps explicitly so any error can be independently verified.
Data & Locked Inputs for SP-5
These Inputs Are Locked — Derived From SP-1 Through SP-4
Jideal (S=0) = 1.380 stb/d/psi  |  Spre = +14.0  |  Spost = +1.0
ParameterSymbolValueUnitsNotes
Jideal (S = 0)Jideal1.380stb/d/psiSP-1 locked
Pre-treatment skinSpre+14.0—SP-2 locked
Post-treatment skin (acid only)Spost+1.0—SP-3 locked
Average reservoir pressurep̄R4,200psiaHub Data Pack
Operating pwfpwf2,500psiaHub Data Pack
Oil price (gross)—75$/bblBase case economics
Lifting + operating cost—5$/bblNet = $70/bbl
Acid treatment cost—450,000USDCoil-tubing acid, Niger Delta estimate
Benefit duration (conservative)—24monthsAgbada analogue well data
Discount rater10%/yrCompany hurdle rate
KWL Table
K — Know
  • FE = Jactual/Jideal = 7/(7+S)
  • q = J × (p̄R − pwf)
  • NPV = PV(monthly revenues) − treatment cost
  • Payback = cost / daily revenue gain
W — Want to Know
  • FE at S=+14 and at S=+1?
  • qpost at pwf = 2,500 psia?
  • How many days payback on $450K?
  • 24-month NPV at $75/bbl?
  • Break-even oil price?
L — Learned
  • FEpre = ________ | qpre = ________ stb/d
  • FEpost = ________ | qpost = ________ stb/d
  • Δq = ________ stb/d
  • Payback = ________ days
  • NPV (24 mo) = $________
Just-in-Time Resources

Just-in-Time Resources

Pull these up as you work SP-5. Each maps to the Module 03 topic behind this sub-problem: read the topic page, watch the matching lectures, then reproduce your numbers with the verified calculator.

Study
Topic 3.5 — Flow Efficiency & IPR — converting FE into an IPR shift and using it to justify the workover economically.
Topic 3.5 — Flow Efficiency & IPR
Watch
Lecture 3.5a — Flow Efficiency: From Skin Number to IPR Curve
Lecture 3.5b — Constructing FE-Modified IPR Curves: Single-Phase and Two-Phase
Lecture 3.5c — Workover Economics: Using FE to Justify Treatment Investment
Produced lectures
Self-check
flow_efficiency.py — FE-modified IPR, Δq, payback and 24-month NPV. This toolkit encodes the ÷12 NPV convention used on this page.
Verified calculator — reproduce your numbers
Tasks & Requirements

SP-5 Calculation Tasks

  1. Calculate FEpre and FEpost — two methods
    Method A (7-approximation): FE = 7/(7+S) for S = +14 and S = +1
    Method B (exact log): FE = ln(0.472·re/rw) / [ln(0.472·re/rw) + S] using ln(0.472×1650/0.35) = 7.707
    Tabulate both results and note the percentage difference.
    Expected (7-approx): FEpre = 0.3333, FEpost = 0.8750. Expected (exact log): FEpre = 0.3551, FEpost = 0.8851.
  2. Calculate J and q for both conditions at pwf = 2,500 psia
    Jpre = FEpre × Jideal → qpre = Jpre × 1,700
    Jpost = FEpost × Jideal → qpost = Jpost × 1,700
    Verify qpre ≈ 782 stb/d (confirms internal consistency of skin audit chain from SP-1 through SP-4).
    Expected: Jpre = 0.460 stb/d/psi, qpre = 782 stb/d ✓. Jpost = 1.208 stb/d/psi, qpost ≈ 2,053 stb/d. Δq ≈ 1,271 stb/d.
  3. 5-point dual IPR table and annotated chart
    For pwf = 4,200 / 3,500 / 2,500 / 1,500 / 0 psia: calculate qpre, qpost, qideal (S=0).
    Draw all three curves on the same axes. Label: current operating point (782 stb/d), post-acid operating point (~2,053 stb/d), AOF for each curve, shaded gain between pre- and post-acid curves.
  4. Economic calculation — payback and NPV
    Payback: Daily net revenue = Δq × ($75 − $5) = 1,271 × $70 = ?/day. Payback = $450,000 / daily revenue.

    NPV (24-month benefit period, 10%/yr discount):
    Monthly CF = Δq × 30.4 days × $70/bbl
    Annuity factor A = (1 − (1+0.10/12)−24) / (0.10/12)
    PV(revenues) = Monthly CF × A ÷ 12  (programme monthly-annuity convention)
    NPV = PV(revenues) − $450,000

    Report NPV to the nearest $100K. Also calculate NPV at $50/bbl and $100/bbl.
    Expected: daily gain ≈ $88,970/day. Payback ≈ 5.1 days. Monthly CF ≈ $2,705K. Annuity factor ≈ 21.67. PV ≈ $4.88M (Monthly CF × 21.67 ÷ 12). NPV ≈ $4.4M. This is a high-value treatment — 1,271 stb/d incremental production over 2 years at $70/bbl net. The treatment cost ($450K) is small vs the production value.
  5. Sensitivity table — post-treatment skin vs economics
    For Spost = 0, +1, +3, +5, +8, +14 (ideal to no benefit): compute FEpost, qpost, Δq, monthly CF, and 24-month NPV at $75/bbl. State: at what post-treatment skin does the NPV fall below the treatment cost ($450K)? (It will be very high Spost — near +14.)
  6. Nodal analysis note (qualitative)
    Explain why a full nodal analysis (IPR + tubing performance curve intersection) would give a higher Δq than the fixed pwf = 2,500 psia calculation. In which direction does this change the NPV? Does this affect the investment decision?
    The improved post-acid IPR intersects the TPC at a lower pwf, accessing additional drawdown that was unavailable pre-treatment. This increases Δq beyond the 1,271 stb/d estimated here. The fixed-pwf approach is therefore conservative — the true economic upside is larger than the NPV calculated above.
Theory Reference
Flow Efficiency and IPR — GK-22 Verified CalculationsFE = 7/(7+S) [7-approximation, valid for typical drainage geometry] S_pre = +14.0: FE_pre = 7/21 = 0.3333 S_post = +1.0: FE_post = 7/8 = 0.8750 J_pre = 0.3333 × 1.380 = 0.4600 stb/d/psi J_post = 0.8750 × 1.380 = 1.2075 stb/d/psi q_pre = 0.4600 × 1700 = 782 stb/d ✓ (matches DST measurement) q_post = 1.2075 × 1700 = 2,053 stb/d Δq (fixed p_wf = 2500 psia) = 2,053 - 782 = 1,271 stb/d (+162%) Workover Economics — Correct CalculationNet oil value per barrel: $75 - $5 = $70/bbl Daily incremental revenue: 1,271 stb/d × $70/bbl = $88,970/day Treatment cost: $450,000 Simple payback = $450,000 / $88,970/day = 5.06 days Monthly incremental CF = 1,271 × 30.4 × $70 = $2,704,688/month NPV (24 months, 10%/yr) — programme monthly-annuity convention (÷ 12): Monthly discount rate: r = 10%/12 = 0.8333%/month Annuity factor: A = (1-(1.008333)^-24) / 0.008333 = 21.67 PV(revenues) = $2,704,688 × 21.67 ÷ 12 = $4,884,408 NPV = $4,884,408 - $450,000 = +$4,434,408 ≈ $4.4M NPV at different oil prices (24 months): recalculate as: CF_mo × A ÷ 12 - $450K $50 gross ($45 net): 1271×30.4×45 = $1,739K/mo → NPV ≈ $2.69M $60 gross ($55 net): 1271×30.4×55 = $2,124K/mo → NPV ≈ $3.39M $75 gross ($70 net): 1271×30.4×70 = $2,705K/mo → NPV ≈ $4.43M $100 gross ($95 net): 1271×30.4×95 = $3,671K/mo → NPV ≈ $6.18M Break-even analysis: At what Δq does NPV = treatment cost? PV = $450K → Monthly CF = $450K × 12 / 21.67 = $249,183/month Daily: $249,183 / 30.4 = $8,196/day → Δq = $8,196 / $70 = 117 stb/d The treatment delivers positive NPV if Δq > ~117 stb/d — readily met (expected Δq ≈ 1,271 stb/d).
The treatment is economically robust: at the expected S_post = +1 the NPV (~$4.4M, programme ÷12 convention) exceeds the $450K treatment cost by roughly 10×. Break-even requires only ~117 stb/d of incremental production against an expected ~1,271 stb/d.
Deliverable

✅ SP-5 Checklist

  • FE table: FEpre and FEpost by both methods. J and q for each.
  • Verification: qpre (FE method) = 782 stb/d matches SP-1 DST ✓.
  • 5-point IPR table: qpre, qpost, qideal at five pwf values.
  • IPR chart: Annotated with operating points, AOF values, shaded gain area.
  • Economics: Payback ~5.1 days; 24-month NPV ≈ $4.4M at $75/bbl. Calculations shown in full.
  • Sensitivity table: Spost = 0 / +1 / +3 / +5 / +8 vs NPV.
  • Nodal analysis note: Fixed pwf method is conservative; actual Δq and NPV higher.
Locked Outputs for SP-6 Final Skin Audit
FEpre = 0.333  |  FEpost,acid-only = 0.875  |  qpost,acid-only = ~2,053 stb/d  |  Payback ≈ 5.1 days  |  NPV (24 mo, $75/bbl) ≈ $4.4M