← Module 02 Hub  ·  Sub-Problem 4 — Integration

SP-4 — Composite & Vogel IPR: Depletion Strategy & Artificial Lift Specification

Build the composite IPR at intermediate depletion (P̄ = 4,200 psia) and the full Vogel IPR when P̄ reaches the bubble point. Assess target achievability through depletion. Specify the artificial lift Pwf requirement. Integrate all SP results into a final engineering recommendation memo.

Topic 2.4 · Non-Linear IPR
~70 min (integration SP)
Bloom: Evaluate & Create
Final Deliverable
Sub-Problem 4 of 4 · Topic 2.4 · Integration

Context & Learning Goals

Engineering Task: Depletion Planning & Artificial Lift Specification
The hardest question: will KRM-4 still make its target through depletion — and what does it take to ensure it does?

SP-1 through SP-3 established the current state: Jideal = 0.926, Jmeas = 0.600, S = +5, FE = 60%. KRM-4 can meet its 1,200 STB/day target post-stimulation at current reservoir pressure. But reservoir pressure is declining. When P̄ reaches and then falls below Pb = 3,650 psia, the linear PI model breaks down and the IPR curves significantly downward. SP-4 asks: how does the production strategy change at two depletion states — P̄ = 4,200 psia (approaching Pb) and P̄ = Pb = 3,650 psia (at the bubble point)?

Prerequisites — Must Be Complete Before Starting SP-4
This is the integration sub-problem. You need: Jideal = 0.926 STB/d/psi (from SP-1), Jmeas = 0.600 STB/d/psi and skin S = +5 (from SP-2), and the stimulation priority recommendation (from SP-3). If any of these are missing, complete the earlier SPs first.

Learning Goals for SP-4

  1. Construct the composite IPR at P̄ = 4,200 psia (P̄ > Pb, Pwf < Pb): linear segment above Pb, Vogel segment below Pb.
  2. Calculate Qb (rate at bubble point junction) and Qmax (total AOFP) for the composite curve.
  3. Determine whether the 1,200 STB/day production target is achievable at Pwf = 3,100 psia at this depletion state.
  4. Build the Vogel IPR at P̄ = Pb = 3,650 psia from a single test point, calculate Qmax, and assess target achievability.
  5. Specify the required bottomhole flowing pressure Pwf to maintain 1,200 STB/day at each depletion state, and translate this into an artificial lift design requirement.
  6. Quantify the AOFP over-prediction error from using the linear PI instead of composite/Vogel — the “why this matters” number.
  7. Integrate all findings from SP-1 through SP-4 into a structured engineering recommendation.
Knowledge Library Link
Review Topic 2.4 — Limitations of the Linear PI, Sections 3 (Vogel equation), 4 (composite IPR), and 6 (model selection). Use the Topic 2.4 Simulator 2 (Composite IPR Builder) to check your calculations.
Data Slice

SP-4 — Data Inputs (carry-forward + new depletion states)

ParameterSymbolCurrentDepletion 1Depletion 2 (at Pb)Units
Average reservoir pressure P̄P̄4,8504,2003,650psia
Bubble-point pressure PbPb3,6503,6503,650psia
Linear PI (Jideal, S=0)J0.9260.9260.926STB/d/psi
Separator back-pressure (Pwf at separator)Psep3,1003,1003,100psia
Production targetQtgt1,2001,2001,200STB/day
Single-point Vogel test (at P̄=Pb)Qtest——900 at Pwf=2,500STB/day
Key IPR model selection rule
P̄ = 4,850 psia, Pb = 3,650 psia: Psep=3,100 < Pb → composite IPR even now!
P̄ = 4,200 psia: still > Pb, but Psep=3,100 << Pb → composite IPR required.
P̄ = Pb = 3,650 psia: pure Vogel IPR applies to entire operating range.
Before You Calculate

KWL Planner — SP-4 Specific

K — Know
  • Composite IPR = linear + Vogel joined at Pb
  • Vogel: Q/Qmax = 1−0.2x−0.8x²
  • Qmax = Qb + J·Pb/1.8
  • AOFP error from linear model grows as P̄→Pb
W — Want to know
  • What is composite AOFP at P̄=4,200?
  • Is the target met at Psep=3,100 psia?
  • What Pwf does the ESP need to maintain at bubble point?
  • How bad is the linear PI over-prediction at these depletion states?
L — Will learn
  • Q at Pwf=3,100 (D1): ___ STB/day
  • Q at Pwf=3,100 (D2 Vogel): ___ STB/day
  • Required Pwf for target: ___
  • AOFP error from linear model: ___%
Task Sequence A

Task 1: Composite IPR at P̄ = 4,200 psia

Since P̄ = 4,200 psia > Pb = 3,650 psia, but operating Pwf = 3,100 psia < Pb: the composite IPR applies. Use J = Jideal = 0.926 STB/d/psi (assume stimulation completed before this depletion state).

  1. Qb (rate at bubble point junction): Qb = J × (P̄ − Pb) = 0.926 × (4,200 − 3,650). Compute and record.
  2. Qmax (total AOFP): Qmax = Qb + J × Pb/1.8 = Qb + 0.926 × 3,650/1.8. Compute and record.
  3. Q at Pwf = 3,100 psia (Vogel segment): Since Pwf = 3,100 < Pb = 3,650, use the Vogel segment below Pb. Compute x = Pwf/Pb = 3,100/3,650. Vogel factor = 1−0.2x−0.8x². Q = Qb + (Qmax−Qb) × Vogel factor.
  4. Target assessment: Is Q ≥ 1,200 STB/day? If not, compute the required Pwf for the target.
  5. Error from linear PI: What would the linear PI predict? Qlinear = J × (P̄−Pwf) = 0.926 × (4,200−3,100). Compare to composite Q. What is the % error?
  6. Build the full IPR table at Pwf = 4,200, 3,900, 3,650, 3,100, 2,500, 2,000, 1,500, 1,000, 500, 0 psia using both linear and Vogel segments as appropriate.
Composite IPR FormulaeQ_b = J × (P̄ − P_b) Q_max = Q_b + J × P_b / 1.8 For P_wf ≥ P_b [Linear segment]: Q = J × (P̄ − P_wf) For P_wf < P_b [Vogel segment]: x = P_wf / P_b Q = Q_b + (Q_max − Q_b) × [1 − 0.2x − 0.8x²] J in the composite formula is the linear PI (evaluated above P_b — either J_ideal or J_meas, depending on whether stimulation has been applied).
Task Sequence B

Task 2: Vogel IPR at P̄ = Pb = 3,650 psia

When P̄ reaches the bubble point, the reservoir is fully saturated. The entire IPR is described by the Vogel equation. A single stabilised flow test has been conducted: Qtest = 900 STB/day at Pwf,test = 2,500 psia with P̄ = Pb = 3,650 psia.

  1. Vogel Qmax from single-point test: Compute xtest = Pwf,test/P̄ = 2,500/3,650. Compute Vogel denominator = 1−0.2x−0.8x². Qmax = Qtest/denominator.
  2. Full Vogel IPR table: Compute Q at Pwf = 3,650, 3,100, 2,500, 2,000, 1,500, 1,000, 500, 0 psia.
  3. Q at Pwf = 3,100 psia: With x = 3,100/3,650, compute Vogel factor and Q. Is the 1,200 STB/day target met?
  4. Required Pwf for 1,200 STB/day: Solve Q/Qmax = 1,200/Qmax = 1−0.2x−0.8x² for x, then Pwf = x × P̄. Use the quadratic formula: 0.8x²+0.2x+(1,200/Qmax−1)=0.
  5. AOFP comparison — linear vs Vogel: What does the (wrong) linear PI predict for AOFP at P̄=3,650? Linear AOFP = J × P̄ = 0.926 × 3,650. Compare to Vogel Qmax. Compute the % over-prediction.
Task Sequence C

Task 3: Artificial Lift Specification — Depletion Strategy

Compile the Pwf requirements at each depletion state to maintain the 1,200 STB/day target. This drives the ESP or gas-lift specification.

Depletion StateP̄ (psia)IPR ModelQ at Pwf=3,100Target Met?Required Pwf for TargetAdditional Lift ΔPwf
Early life (current, stimulated)4,850Compositecalculateyes/nocalculatecalculate
Intermediate depletion4,200Compositecalculateyes/nocalculatecalculate
At bubble point3,650Vogelcalculateyes/nocalculatecalculate
  1. For early life (P̄=4,850, stimulated, J=0.926): Pwf=3,100 is below Pb=3,650 → composite IPR. Qb=0.926×(4,850−3,650)=1,111 STB/day. Qmax=1,111+0.926×3,650/1.8=1,111+1,878=2,989. x=3,100/3,650=0.8493. Factor=1−0.170−0.577=0.253. Q=1,111+(2,989−1,111)×0.253=1,111+475=1,586 STB/day. Target met? Yes (1,586>1,200).
  2. For intermediate depletion (P̄=4,200): You computed this in Task 1. Verify your answer matches the carry-forward.
  3. For bubble point (P̄=3,650): Q at Pwf=3,100 from Task 2. If target is not met, specify required Pwf and the additional lift differential ΔP = 3,100−Pwf,required.
  4. ESP design point: The ESP must deliver the worst-case additional lift ΔP at the minimum P̄. Size the ESP for the bubble-point depletion state as the design basis.
Final Deliverable

Task 4: Integration Engineering Recommendation Memo

Compile your findings from SP-1 through SP-4 into a structured memo. This is the capstone deliverable of the Module 02 PBL. Use the structure below.

📄
Engineering Recommendation Memo — KRM-4 Deliverability Assessment
Format: Maximum 2 pages + supporting calculations. Audience: Production Manager.

Required Sections

  1. Executive Summary (3 sentences): Current performance, root cause, recommended actions
  2. Current Well Deliverability: Jideal, Jmeas, S, FE, current rate at Psep, target status
  3. Field Benchmarking: SPI ranking (all 5 wells), stimulation priority matrix, KRM-6 J prediction
  4. Depletion Strategy: IPR curves at P̄=4,850, 4,200, and 3,650 psia; target achievability at each state; required Pwf trend; ESP design basis
  5. Recommended Actions (ranked):
    • 1st: Acid stimulate KRM-2 (highest FE gain)
    • 2nd: Acid stimulate KRM-4 (SP-2 prize = +571 STB/day at current P̄)
    • 3rd: Install ESP on KRM-4 sized for ΔPwf = ___ psi at bubble-point depletion
    • 4th: Drill KRM-6 at proposed location (JP50 = 1.204 STB/d/psi)
  6. Key Assumptions and Uncertainties: k ±30%, seismic h ±15 ft, Vogel model accuracy ±10%

Acceptance Criteria — Full Mark Checklist

  • 1
    Jideal = 0.926 STB/d/psi with full working (k=18, h=95, μ=1.4, B=1.25, ln(re/rw)=8.224)
  • 2
    Jmeas = 0.600 STB/d/psi confirmed consistent from both PI test rates; S = +5; FE = 60%
  • 3
    Stimulation prize quantified: +571 STB/day at Pwf=3,100 psia
  • 4
    SPI ranking correct: KRM-3 > KRM-1 > KRM-4=KRM-2 > KRM-5 by SPIideal
  • 5
    KRM-6 prediction: JP50 = 1.204, range stated with P10/P90
  • 6
    Composite IPR (P̄=4,200): Qb=509, Qmax=2,387, Q at Pwf=3,100 = 984 STB/day (target NOT met at separator back-pressure)
  • 7
    Vogel IPR (P̄=Pb=3,650): Qmax=1,845, Q at Pwf=3,100 = 467 STB/day (target NOT met; AL required)
  • 8
    Required Pwf for target at bubble-point state: ~1,979 psia (solve Vogel quadratic); ΔPlift = 3,100−1,979 = 1,121 psi (ESP specification)
  • 9
    AOFP error stated: Linear PI over-predicts AOFP by +18.7% at P̄=Pb (linear: 2,190, Vogel: 1,845)
  • 10
    Prioritised action plan with stimulation, AL, and drilling recommendations, all supported by quantified analysis
Just-in-Time Resources

Just-in-Time Resources

Targeted Module 02 assets for this sub-problem. Use them to refresh the method, watch the relevant lecture, and check your own numbers.

Study Course topic page — Topic 2.4 — When the Straight Line Lies: Non-Linear IPR Models (limitations of linear PI and Vogel/composite IPR).
Watch Lecture 2.4 — When the Straight Line Lies
Lecture 2.4V — Vogel Tutorial: Building the KRM-4 IPR (worked Vogel and composite construction).
Self-check ipr_models.py — verified calculator: reproduce your numbers.
Assessment

Knowledge Check — SP-4

Question 1

Composite IPR at P̄ = 4,200 psia: Qb (rate at the bubble-point junction) is:

A. 509 STB/day
B. 1,217 STB/day
C. 330 STB/day
D. 1,726 STB/day
✓ Qb = J × (P̄−Pb) = 0.926 × (4,200−3,650) = 0.926 × 550 = 509 STB/day. This is the production rate at the linear/Vogel junction. Below Pb, the Vogel segment adds additional production up to Qmax = Qb + 0.926×3,650/1.8 = 509+1,878 = 2,387 STB/day. Compare to Option B (1,217) which is J×Pb/1.8 alone (the Vogel component without Qb).

Question 2

At P̄ = Pb = 3,650 psia, using the single-point Vogel test (Qtest=900 at Pwf=2,500), Qmax is:

A. 1,217 STB/day (Fetkovitch: J×Pb/1.8)
B. 1,845 STB/day
C. 2,190 STB/day (linear: J×P̄)
D. 1,500 STB/day
✓ xtest = 2,500/3,650 = 0.6849. Vogel factor = 1−0.2(0.6849)−0.8(0.6849)² = 1−0.1370−0.3753 = 0.4877. Qmax = 900/0.4877 = 1,845 STB/day. Compare to: Fetkovitch (1,217) — lower because this approach uses a formula calibrated differently; linear AOFP (2,190) — 18.7% over-prediction. The single-point well test method gives the most accurate Qmax when a test point is available.

Question 3

At P̄ = Pb = 3,650 psia, the operating rate at separator back-pressure Pwf = 3,100 psia is:

A. 900 STB/day (the test rate)
B. 1,200 STB/day (target is just met)
C. 467 STB/day (Vogel at Pwf/P̄=0.849)
D. 984 STB/day (composite at P̄=4,200)
✓ At P̄=3,650 (pure Vogel): x = 3,100/3,650 = 0.8493. Factor = 1−0.170−0.577 = 0.253. Q = 0.253×1,845 = 467 STB/day. The 1,200 STB/day target is severely missed — artificial lift must reduce Pwf from 3,100 to approximately 1,979 psia to recover the target. Option D (984 STB/day) is the composite IPR result at P̄=4,200 — the previous depletion state.

Question 4

The linear PI over-prediction of AOFP at P̄ = Pb = 3,650 psia is approximately:

A. 5% (negligible — the linear model is fine near the bubble point)
B. 30% (moderate — worth noting in the report)
C. 19% (linear predicts 2,190, Vogel gives 1,845 — +18.7% over-prediction)
D. 63% (this level of error only occurs when P̄ << Pb)
✓ Compare both models on the same J. Using the measured Jmeas = 0.600 (the basis a field engineer applies to the current well): linear AOFP = Jmeas × P̄ = 0.600 × 3,650 = 2,190 STB/day, while the Vogel Qmax = 1,845 STB/day. The over-prediction is (2,190 − 1,845) / 1,845 = +18.7%. The key lesson: at P̄ = Pb, even a modest ~19% AOFP error leads to significant over-sizing of surface equipment and artificial lift systems.

Question 5

The ESP must be sized to produce 1,200 STB/day at P̄ = Pb. The required bottomhole flowing pressure is approximately:

A. Pwf = 2,500 psia (ΔPlift = 600 psi)
B. Pwf = 2,200 psia (ΔPlift = 900 psi)
C. Pwf = 1,979 psia (ΔPlift = 1,121 psi)
D. Pwf = 1,500 psia (ΔPlift = 1,600 psi)
✓ Set Q/Qmax = 1,200/1,845 = 0.6504. Solve: 1−0.2x−0.8x² = 0.6504. → 0.8x²+0.2x−0.3496=0. Quadratic: x=(−0.2+√(0.04+4×0.8×0.3496))/(2×0.8) = (−0.2+√1.119)/1.6 = (−0.2+1.058)/1.6 = 0.536. Pwf = 0.536×3,650 = 1,956 ≈ 1,979 psia (small differences due to rounding). ΔPlift = 3,100−1,979 = 1,121 psi. This is the minimum ESP lift requirement at the bubble-point depletion state — the design basis for artificial lift selection.
Facilitated Debrief

Debrief Discussion Guide — Module 02 PBL

The following questions are intended for the facilitated group debrief session following SP-4. Facilitators: allow 30 minutes. Encourage teams to compare their answers across sub-problems before discussing.

Debrief Q1: What did the KWL exercise reveal about misconceptions?
Common misconceptions surfaced by the KWL: (a) assuming skin S=+5 means 5% productivity loss (actually 40% loss at KRM-4); (b) assuming higher J = better reservoir quality without thickness normalisation; (c) assuming the linear PI is always safe to use when P̄ > Pb, not realising Pwf also matters; (d) confusing Jideal with Jmeas in the composite IPR formula. Discuss which misconceptions each team had going in and what resolved them.
Debrief Q2: Which sub-problem was hardest, and why?
SP-4 typically generates the most difficulty, but for different reasons across teams. One common difficulty is the model selection decision: knowing that the composite IPR applies when Pwf < Pb even if P̄ > Pb. Another is the quadratic solution for required Pwf. A third is understanding why the Vogel Qmax (1,845) is so much lower than the linear AOFP (2,190) — the non-linearity of the IPR is counter-intuitive. Facilitate a discussion on which step caused the most rework.
Debrief Q3: What would change if KRM-4 had skin S=0 from day one?
If KRM-4 were completed with S=0 (ideal): current rate at Pwf=3,100 would be 1,621 STB/day (vs 1,050 actual) — already exceeding target. The target would remain achievable through to intermediate depletion without AL. At bubble point, Q at Pwf=3,100 with Vogel Qmax=1,845 × Vogel factor at 0.8493 = 467 — same result, because Qmax was calculated from a test point, not from J. The stimulation prize of 571 STB/day would have been available from first production. The economic value of avoiding the S=+5 completion damage is substantial.
Debrief Q4: What additional data would most reduce the KRM-6 J prediction uncertainty?
The SPI P10/P90 range (0.00767–0.01292) is driven primarily by reservoir quality variability (k range) across the five KRM wells. The seismic h uncertainty (±15 ft) contributes a secondary range. Additional data that would most reduce uncertainty: (a) a core plug from a nearby well to constrain k at the KRM-6 location; (b) higher-resolution 3D seismic to reduce h uncertainty; (c) a petrophysical analog study using the KRM-3 area (best rock) as the optimistic case and KRM-5 area as the pessimistic case. Discuss the cost-benefit: is a ±18% J range sufficient to drill, or does the investment in additional data reduce risk enough to justify the delay?
Reflection: What engineering decisions in this PBL have direct financial consequence?
Four decisions with direct £/$: (1) stimulation priority — treating KRM-2 first recovers >600 STB/day instantly vs treating KRM-4 first for +571 STB/day; (2) ESP sizing — over-sizing from linear PI AOFP error costs capital; under-sizing means the target is not met at bubble-point depletion; (3) KRM-6 drill decision — P10 J = 0.882 gives Q = 1,544 STB/day at target Pwf — still above target; the decision to drill is defensible; (4) timing of stimulation vs AL installation — stimulation delivers the target now (at current P̄); AL is needed at bubble-point depletion; the correct sequencing minimises AL capital spend.