What You Will Do in This PBL
This PBL consolidates the four topics of Module 02: Darcy Radial Flow & PSS Equation, Productivity Index (PI), Specific Productivity Index (SPI), and Limitations of the Linear PI & Non-Linear IPR Models, by applying them to the Karama Field KRM-4 well. Rather than a single monolithic exercise, you will solve four discrete sub-problems, each mapped 1:1 to a topic, then integrating prior final debrief.
Learning Objectives
By the end of this PBL you will be able to:
- Apply the PSS radial inflow equation to calculate the theoretical Productivity Index J for a chalk oil well, correctly assembling all components (k, h, μ, B, re/rw, S).
- Interpret a two-rate PI test to extract measured J and skin S, and compare to the theoretical ideal to compute Flow Efficiency (FE).
- Calculate the Specific Productivity Index (SPI = J/h) for all five KRM wells and rank them by rock quality, distinguishing damaged wells from genuinely inferior reservoir.
- Use the SPI trend to predict J for a proposed new well KRM-6 with seismic-estimated net pay of 115 ft, and state the uncertainty range.
- Construct a composite IPR at an intermediate depletion state (P̄ = 4,200 psia, Pb = 3,650 psia) and determine whether the 1,200 STB/day production target can be achieved with the current back-pressure.
- Build a full Vogel IPR when P̄ reaches the bubble point and quantify the AOFP error from using the linear PI model.
- Recommend an intervention strategy (acid stimulation priority and artificial lift specification) supported by quantified analysis.
Why Four Sub-Problems?
The KRM-4 scenario is genuinely complex. It requires simultaneous reasoning about theoretical inflow, well test interpretation, field-wide reservoir characterisation, and future depletion behaviour. By splitting the problem into four focused sub-problems, each concept is isolated, applied, and checked before the next layer is added. Sub-Problem 4 is the integrating challenge: it requires outputs from SP-1, SP-2, and SP-3 to construct the correct non-linear IPR and make a production decision under depletion.
Karama Field Context
The Karama Field is a chalk oil reservoir producing from the Lower Cretaceous Karama Formation. Five wells have been drilled (KRM-1 through KRM-5); all produce single-phase oil above or near the bubble point. A sixth well location (KRM-6) has been proposed from a recent 3D seismic survey. KRM-4 has been selected for the deliverability assessment because it shows the largest discrepancy between predicted and actual production rate, the trigger for this engineering review.
Engineering Review Brief — Karama Field KRM-4
KRM-4 has been producing approximately 35% below its pre-drill rate forecast for the past six months. Additionally, reservoir pressure monitoring indicates P̄ is declining and is projected to reach the bubble point (Pb = 3,650 psia) within 18 months. Please provide a full deliverability assessment covering:
- Theoretical baseline: Assemble the PSS radial inflow equation and compute the theoretical (ideal, undamaged) PI for KRM-4.
- Well test interpretation: Interpret the two-rate PI test data (see Data Pack) to extract measured J and skin S. Compute Flow Efficiency and diagnose the underperformance cause.
- Field benchmarking: Calculate SPI for all five KRM wells. Rank them by reservoir quality. Identify stimulation priorities. Predict J for proposed KRM-6 (h = 115 ft from seismic).
- Depletion forecast: Construct composite IPR at P̄ = 4,200 psia and Vogel IPR at P̄ = Pb = 3,650 psia. Determine if the 1,200 STB/day target is achievable at current back-pressure. If not, specify the required artificial lift Pwf.
Deliverable: Engineering memo with calculations, IPR curves, stimulation priority matrix, and Artificial Lift (AL) specification.
Engineering Workflow
- SP-1 · TOPIC 2.1PSS equation & theoretical J
- SP-2 · TOPIC 2.2PI test → Jmeas, S, FE
- SP-3 · TOPIC 2.3SPI ranking & KRM-6 prediction
- SP-4 · TOPIC 2.4Composite & Vogel IPR
KRM-4 — Full Data Pack
The following data has been consolidated from the petrophysical log interpretation, core analysis, DST pressure data, two-rate PI test, and PVT laboratory report. This is the single source of truth for all four sub-problems. Relevant data subsets are highlighted within each sub-problem file.
Reservoir & Completion Data
| Parameter | Symbol | Value | Units | Source |
|---|---|---|---|---|
| Average reservoir pressure (current) | P̄ | 4,850 | psia | Monthly BHP survey |
| Reservoir temperature | Tres | 210 | °F | DST gauge |
| Net pay thickness | h | 95 | ft | Log interpretation (φ>10%, Vsh<0.35) |
| Gross reservoir thickness | H | 138 | ft | Log interpretation |
| Net-to-gross ratio | NTG | 0.688 | fraction | h/H |
| Permeability (core plug, avg) | k | 18 | mD | Core flood (steady-state) |
| Porosity (log-derived) | φ | 0.22 | fraction | Density-neutron crossplot |
| Irreducible water saturation | Swi | 0.18 | fraction | Centrifuge Pc |
| Drainage radius | re | 1,320 | ft | 160-acre well spacing |
| Wellbore radius | rw | 0.354 | ft | 9⅝″ csg + 7″ liner |
| Skin factor (from PI test) | S | +5 | — | Two-rate PI test interpretation |
| Perforations | — | 95 | ft (full pay) | Completion report |
PVT Laboratory Data (at Reservoir Conditions)
| Parameter | Symbol | Value | Units | Note |
|---|---|---|---|---|
| Bubble-point pressure | Pb | 3,650 | psia | CCE experiment — P–V break |
| Oil FVF at P̄ = 4,850 psia | Bo(P̄) | 1.25 | RB/STB | Above bubble point (use this value) |
| Oil FVF at Pb | Bob | 1.28 | RB/STB | Peak FVF at bubble point |
| Oil viscosity at P̄ | μo(P̄) | 1.4 | cp | Live oil viscosity (use this value) |
| Oil viscosity at Pb | μob | 1.6 | cp | Increases below bubble point |
| Oil API gravity | °API | 32 | °API | Medium crude |
| Solution GOR at P̄ | Rs | 620 | scf/STB | Constant above Pb |
| Oil compressibility (above Pb) | co | 14.2×10−6 | psi−1 | PVT report |
Two-Rate PI Test Data
| Parameter | Rate 1 (Low) | Rate 2 (High) | Units |
|---|---|---|---|
| Stabilised flow rate Q | 350 | 620 | STB/day |
| Flowing BHP Pwf | 4,267 | 3,817 | psia |
| Static BHP P̄ (shut-in) | 4,850 | 4,850 | psia |
| ΔP = P̄ − Pwf | 583 | 1,033 | psi |
| J from this rate point | 350/583 = 0.600 | 620/1,033 = 0.600 | STB/d/psi |
Karama Field — All Five Wells Data
| Well | h (ft) | k (mD) | S (from test) | Jmeas (STB/d/psi) | Jideal (STB/d/psi) |
|---|---|---|---|---|---|
| KRM-1 | 110 | 22 | +2 | 1.18 | 1.35 |
| KRM-2 | 95 | 18 | +14 | 0.41 | 0.926 |
| KRM-4 (this well) | 95 | 18 | +5 | 0.60 | 0.926 |
| KRM-3 | 130 | 25 | −1 | 1.75 | 1.68 |
| KRM-5 | 75 | 12 | +9 | 0.18 | 0.575 |
Operating Constraints
| Parameter | Symbol | Value | Units | Rationale |
|---|---|---|---|---|
| Production target | Qtarget | 1,200 | STB/day | Field production plan |
| Separator back-pressure (current) | Psep | 3,100 | psia | Surface facility constraint |
| Min Pwf (ESP limit) | Pwf,min | 800 | psia | ESP operating range |
| Proposed KRM-6 location h (seismic) | hKRM-6 | 115 ± 15 | ft | 3D seismic horizon interpretation |
KWL Planner — Activate Prior Learning
Before opening the sub-problems, spend 5–10 minutes filling in the KWL table. This forces explicit articulation of what you know, what you want to know, and what you will learn — revealing real knowledge gaps before you start calculating. Teams that skip this step consistently make more errors in the sub-problems.
From Module 01 and pre-reading Topics 2.1–2.4, what do you already know?
- Darcy’s law governs radial laminar flow
- J = Q / (P̄ − Pwf) defines the PI
- Skin S is the dimensionless damage/stimulation indicator
- The IPR is linear only above the bubble point
- SPI = J/h normalises for pay thickness
What do you still need to determine?
- How large is KRM-4’s skin and what does it cost in rate?
- Is KRM-4 underperforming because of damage or poor rock?
- Which KRM well is in the best reservoir quality?
- Will 1,200 STB/day still be achievable once P̄ reaches Pb?
- How do we predict J for an undrilled location?
What the sub-problems will teach you
- SP-1: How to assemble and compute the PSS J
- SP-2: Two-rate PI test → skin → FE → stimulation value
- SP-3: SPI ranking, field benchmarking, KRM-6 prediction
- SP-4: Composite and Vogel IPR → AL specification
Sub-Problems: Launch Sequence
Each sub-problem is a self-contained learning unit with its own data slice, guided calculations, knowledge check, and carry-forward values. Complete them in order: SP-4 requires outputs from SP-1, SP-2, and SP-3.
Assemble every term of the PSS radial inflow equation (k, h, μ, B, re/rw) and compute Jideal at S = 0. This is the undamaged productivity potential of the reservoir — the ceiling that stimulation could recover.
Use the two-rate PI test data to compute Jmeasured and confirm consistency across rates. Back-calculate skin S from Jideal vs Jmeasured. Compute FE and quantify the STB/day cost of damage. Size the stimulation prize.
Calculate SPI for all five KRM wells using measured J and h. Build the J vs h cross-plot. Identify damaged wells vs genuinely inferior rock. Construct the stimulation priority matrix. Predict J for KRM-6 at h = 115 ft.
Build the composite IPR at P̄ = 4,200 psia and the Vogel IPR at P̄ = Pb. Assess target achievability. Specify the required artificial lift Pwf. Integrate all SP results into a final engineering recommendation memo.
Delivery Map & Assessment
The PBL is designed for either a one-day workshop or three self-paced online sessions with a synchronous debrief. Total effort is approximately 4.5 hours excluding the facilitated debrief.
| Stage | Mode | Duration | Assessment |
|---|---|---|---|
| Hub Overview + Problem Brief + Data Pack | Self-paced | 15 min | — |
| KWL Planner | Team (2–3 learners) | 10 min | KWL sheet submitted |
| SP-1: Darcy Radial Flow — Theoretical J | Individual then team | 35 min | 5 MCQ + carry-forward value |
| SP-2: PI Test — Skin & Flow Efficiency | Individual then team | 40 min | 5 MCQ + stimulation value memo |
| SP-3: SPI — Field Ranking & KRM-6 Prediction | Individual then team | 40 min | 5 MCQ + ranking table + prediction |
| SP-4: Non-Linear IPR — Depletion Strategy | Individual then team | 70 min | IPR curves + AL spec + recommendation memo |
| Facilitated Debrief (via SP-4 debrief page) | Tutor-led group | 30 min | Participation + reflection log |