What You Will Do in This PBL
This PBL consolidates all six topics of Module 04: Two-Phase Flow & Vogel's IPR, Composite IPR, Standing's Flow Efficiency, Gas Well Deliverability, Fetkovich's Deliverability Equation, and Predicting Future IPRs, by applying them to the Karama Field development scenario. Rather than one monolithic problem, you will solve six discrete sub-problems, each its own self-contained learning unit, before integrating everything into a Leadership Forum report in SP-6.
Learning Objectives
By the end of this PBL you will be able to:
- Construct Vogel's two-phase IPR from a single stabilised test point and read off AOFP and rate at any flowing BHP.
- Build a composite (Darcy + Vogel) IPR for a well where p̄ > pb, correctly computing the Darcy anchor rate qb at bubble-point.
- Calculate Flow Efficiency from skin and apply Standing's modified Vogel to predict pre-acid and post-acid IPRs, with economic payback of the stimulation.
- Perform LIT analysis on modified isochronal test data using pseudo-pressure m(p) to determine gas well deliverability coefficients A and B, and calculate AOFP at separator back-pressure.
- Fit the Fetkovich two-parameter deliverability equation (C, n) from a log–log multi-rate test plot and compare AOFP with the Vogel result.
- Predict future IPRs at multiple depletion stages using both Standing's J* mobility scaling and Fetkovich's depletion method, and design the artificial-lift escalation schedule.
- Synthesise all deliverability analyses into a defensible FDP recommendation covering stimulation sequencing, ESP sizing, compression timing, and infill-drilling trigger.
Why Six Sub-Problems?
The Karama scenario is genuinely ill-structured: it involves two reservoir fluids (oil and gas), multiple well states (damaged, stimulated, depleted), two deliverability frameworks (Vogel/composite vs. Fetkovich), and a 10-year production horizon. Solving all of this simultaneously obscures which concept is causing difficulty when answers diverge. By splitting into six focused sub-problems, each mapped to one or two topics, each concept is isolated, applied, and checked before moving on. SP-6 re-assembles everything into the integrated field recommendation.
Operations Memo — Karama Field
The Karama Field Development Plan (FDP) gate is in 72 hours. The facilities team cannot finalise the separator capacity (oil train), ESP specification, or compression design until they have a complete well deliverability picture. KA-07 (oil producer) is currently flowing on natural flow well below target. KA-G2 (gas cap producer) has been isochronal tested but AOFP has not been confirmed against contract requirements. Please provide:
- Current composite IPR for KA-07 at p̄ = 5,100 psia with pb = 4,500 psia.
- Quantification of the skin damage (S' = +8) and economic case for the proposed matrix acid job (target S = +1).
- KA-G2 gas deliverability coefficients and AOFP from the modified isochronal test data using LIT / m(p) analysis.
- Fetkovich deliverability fit for KA-07 — compare with Vogel AOF and explain any discrepancy.
- Life-of-field IPR prediction at p̄ = 3,200 / 2,600 / 2,000 psia using Standing's J* scaling and Fetkovich's depletion method.
- Integrated FDP recommendation — stimulation sequence, ESP stage sizing, gas compression onset, infill-drilling trigger.
The Engineering Workflow
Each step maps to one sub-problem. Complete in order. Later SPs depend on earlier outputs.
- SP-1 · IPRComposite Vogel IPR for KA-07
- SP-2 · FESkin + acid job economics
- SP-3 · GASLIT analysis — KA-G2 AOFP
- SP-4 · FETKFetkovich fit vs. Vogel
- SP-5 · DEPLFuture IPR family + lift design
- SP-6 · FDPIntegrated report + recommendation
Karama Field: Master Data Pack
The following data is the single source of truth for all six sub-problems. Each SP will highlight the specific subset it uses. Do not invent or estimate values not listed here unless explicitly instructed.
KA-07 Oil Well: Reservoir & Completion Data
| Parameter | Symbol | Value | Units | Source |
|---|---|---|---|---|
| Average reservoir pressure | p̄ | 5,100 | psia | Pressure build-up (PBU) — Horner plot |
| Bubble-point pressure | pb | 4,500 | psia | PVT CCE experiment |
| Reservoir temperature | TR | 200 | °F | Wireline MDT survey |
| Net pay thickness | h | 68 | ft | Petrophysical log interpretation |
| Effective oil permeability (from PBU) | ko | 42 | md | Pressure-transient analysis (PTA) |
| Drainage radius | re | 1,320 | ft | Well spacing — 160-acre pattern |
| Wellbore radius | rw | 0.354 | ft | Caliper log — 8½″ open hole |
| Total skin (PBU Horner) | S' | +8 | — | Skin from transient analysis |
| Post-acid target skin | Spost | +1 | — | Completion analogue wells |
| Ideal PI (S = 0, Darcy eq.) | J* | 0.72 | stb/d/psi | Calculated from k, h, μ, Bo, geometry |
KA-07 PVT Data at Reservoir Conditions
| Parameter | Symbol | Value | Units | Note |
|---|---|---|---|---|
| Oil viscosity at p̄ | μo(p̄) | 0.95 | cp | PVT standing-cell measurement |
| Oil FVF at p̄ | Bo(p̄) | 1.38 | res bbl/stb | PVT differential liberation |
| Oil API gravity | °API | 36 | °API | Medium crude |
KA-07 Multi-Rate Production Test Results
| Test ID | qo (stb/d) | pwf (psia) | Stabilised? | Notes |
|---|---|---|---|---|
| T1 — Stabilised (below pb) | 820 | 1,800 | Yes — 72 hr | Used for Vogel & Fetkovich calibration |
| T2 — Stabilised (below pb) | 640 | 2,400 | Yes — 72 hr | Used for Fetkovich two-point fit |
| T3 — Above bubble point | 432 | 4,650 | Yes — 48 hr | Darcy segment only — do NOT use for Vogel |
| Natural flow (current) | ~642 | ~4,200 | Approximate | BHFP estimated from flowing gradient survey |
KA-07 Depletion PVT Mobility Table (for Future IPR Prediction)
| Future p̄ (psia) | kro | μo (cp) | Bo (res bbl/stb) | [kro/(μo·Bo)] | J* ratio vs. current |
|---|---|---|---|---|---|
| 5,100 (current) | 0.815 | 0.950 | 1.380 | 0.6232 | 1.000 |
| 3,200 (Stage 2) | 0.685 | 1.140 | 1.310 | 0.4589 | 0.737 |
| 2,600 (Stage 3) | 0.540 | 1.380 | 1.255 | 0.3116 | 0.500 |
| 2,000 (Stage 4) | 0.380 | 1.680 | 1.195 | 0.1893 | 0.304 |
KA-G2 Gas Well: Modified Isochronal Test Data
Reservoir pressure p̄ = 3,800 psia · Reservoir temperature T = 660°R (200°F) · Separator back-pressure = 800 psia
| Flow Period | Shut-in pws,i (psia) | qg,i (Mscf/d) | Flowing pwf,i (psia) | Type |
|---|---|---|---|---|
| Period 1 | 3,780 | 4,000 | 3,250 | Isochronal (8-hour equal periods) |
| Period 2 | 3,760 | 8,000 | 2,600 | Isochronal |
| Period 3 | 3,750 | 12,000 | 1,850 | Isochronal |
| Period 4 | 3,735 | 16,000 | 980 | Isochronal |
| Extended flow (stabilised) | p̄ = 3,800 | 10,000 | 2,200 | Stabilised point — use for LIT anchor |
KA-G2 Pseudo-Pressure Table m(p) × 10⁶ psia²/cp
| p (psia) | μg (cp) | Z | m(p) × 10⁶ | Reference point |
|---|---|---|---|---|
| 0 | — | — | 0.000 | Base |
| 800 | 0.0139 | 0.882 | 52.66 | Separator back-pressure |
| 980 | 0.0151 | 0.868 | 79.20 | Period 4 pwf |
| 1,850 | 0.0185 | 0.815 | 246.00 | Period 3 pwf |
| 2,200 | 0.0198 | 0.790 | 332.00 | Extended pwf |
| 2,600 | 0.0215 | 0.774 | 446.00 | Period 2 pwf |
| 3,250 | 0.0235 | 0.785 | 680.00 | Period 1 pwf |
| 3,735 | 0.0250 | 0.825 | 895.00 | Period 4 pws |
| 3,750 | 0.0251 | 0.826 | 903.00 | Period 3 pws |
| 3,760 | 0.0252 | 0.827 | 908.00 | Period 2 pws |
| 3,780 | 0.0253 | 0.828 | 918.00 | Period 1 pws |
| 3,800 | 0.0254 | 0.829 | 928.00 | Reservoir pressure p̄ |
Economic & Facilities Parameters
| Parameter | Value | Units | Note |
|---|---|---|---|
| Oil netback (price – lifting cost) | 58 | $/stb | Current realisation |
| Acid job cost — KA-07 | 450 | $K | Matrix acidise + workover rig |
| ESP Stage 1 installation cost | 1,200 | $K | 200-hp unit + installation |
| ESP operating cost | 800 | $/d | Power + maintenance |
| Gas sales price | 3.80 | $/Mscf | Contract price |
| Field oil production target | 1,800 | stb/d | FDP plateau rate |
| Gas sales contract | 18,000 | Mscf/d | Three-well total — 10-year term |
KWL Planner — Activate Prior Learning
Before opening the sub-problems, spend 8–10 minutes filling in the KWL table. This is the most productive 10 minutes of any PBL: forcing explicit articulation of what you know, what you want to know, and what you will learn reveals knowledge gaps before you start calculating and aligns the team on what matters most.
From Topics 4.1–4.6, what can you already do?
- Vogel: q/qmax = 1 − 0.2(pwf/p̄) − 0.8(pwf/p̄)²
- Composite IPR joins Darcy (above pb) with Vogel (below)
- FE = Jactual/J* = f(skin)
- LIT gas analysis: Δm(p)/q = A + Bq
- Fetkovich: q = C(p̄² − pwf²)n
- Future J* scales with kro/(μoBo) mobility ratio
What do you still need to determine?
- Can KA-07 meet 1,800 stb/d without an ESP?
- Is the acid job payback fast enough to justify before ESP?
- Which Fetkovich exponent n is correct — 0.77 or something else?
- How much will AOFP drop by Year 5?
- Can three gas wells sustain 18,000 Mscf/d gas contract?
- At what reservoir pressure must the first ESP upgrade happen?
What each sub-problem resolves
- SP-1: Current IPR — AOF, qb, natural-flow ceiling
- SP-2: Skin penalty in $/day; acid job simple payback
- SP-3: Gas well coefficients A, B; AOFP at back-pressure
- SP-4: Why Fetkovich n ≠ 0.77 matters for ESP sizing
- SP-5: Life-of-field IPR family; lift escalation schedule
- SP-6: How to frame all findings as an FDP recommendation
Sub-Problems — Launch Sequence
Each sub-problem is a self-contained learning unit with its own data slice, worked calculations, interactive knowledge check, and a key-output card to carry forward. Complete them in order. Later SPs reference outputs from earlier ones.
Apply Vogel's equation to stabilised test T1, then build the full composite (Darcy + Vogel) IPR at p̄ = 5,100 psia. Determine qb, qv,max, AOFP, and whether KA-07 can ever reach 1,800 stb/d on natural flow at any BHFP.
Calculate FE for S' = +8 and target S = +1. Apply Standing's modified Vogel to build pre-acid and post-acid IPRs. Compute the production uplift at BHFP = 2,000 psia and the simple payback on the $450K acid job. Decide: stimulate before or after ESP installation?
Use the modified isochronal test data and the m(p) table to perform LIT analysis. Plot Δm(p)/q vs. q to obtain coefficients A (Darcy) and B (non-Darcy). Calculate AOFP at separator back-pressure 800 psia, then assess whether three KA-G wells can sustain the 18,000 Mscf/d contract.
Apply the Fetkovich log–log two-point method to tests T1 and T2. Solve for exponent n and coefficient C. Calculate AOFP. Compare with SP-1's Vogel AOFP — quantify the discrepancy and explain its implication for ESP sizing. Is Vogel over-predicting?
Use Standing's J* mobility scaling (PVT table) to predict KA-07 IPR at p̄ = 3,200 / 2,600 / 2,000 psia. Compare with Fetkovich's depletion method. Build the life-of-field IPR family. Identify at which depletion stage rate at BHFP = 800 psia falls below 1,800 stb/d and design the ESP escalation schedule.
Compile all SP-1 through SP-5 findings into the Karama Field Well Performance Report. Make explicit recommendations on stimulation sequencing, ESP Stage 1 specification, gas compression onset, and infill-drilling trigger. Present to the Leadership Forum with a one-page executive summary.
Delivery Map & Assessment
The PBL is designed for a full-day workshop (~5.5 hours) or three self-paced online sessions with synchronous debriefs. SP-6 produces the graded deliverable.
| Stage | Mode | Duration | Assessment |
|---|---|---|---|
| Hub Overview + Problem Brief + Data Pack | Self-paced | 20 min | — |
| KWL Planner | Team (2–3 learners) | 10 min | KWL sheet submitted to facilitator |
| SP-1: Composite IPR | Individual then team | 35 min | 5 MCQ auto-marked |
| SP-2: Standing's FE & acid job | Individual then team | 35 min | 5 MCQ auto-marked |
| SP-3: Gas well LIT + AOFP | Individual then team | 40 min | 5 MCQ auto-marked |
| SP-4: Fetkovich two-point fit | Individual then team | 30 min | 5 MCQ auto-marked |
| SP-5: Future IPR family + lift design | Individual then team | 40 min | 5 MCQ auto-marked |
| SP-6: Integrated FDP report | Team submission | 60 min | Graded report — 50% of module mark |
| Facilitated Debrief — Leadership Forum simulation | Tutor-led group | 30 min | Participation + reflection log |
Primary Deliverable — Karama FDP Well Performance Report
The SP-6 submission must include: (a) KA-07 composite IPR — annotated plot with key values; (b) stimulation economics summary with payback calculation; (c) KA-G2 LIT deliverability curve and AOFP; (d) Fetkovich vs. Vogel comparison with ESP-sizing implication; (e) life-of-field IPR family with lift-escalation schedule; (f) one-page executive summary with six specific FDP recommendations. Maximum length: 2,500 words + supporting plots.