Module 03 PBL Hub — Gashaka GK-22 · Well Productivity Programme

Module 03 · PBL Overview

What You Will Do in This PBL

This problem-based learning exercise consolidates all six topics of Module 03 — Skin Factor Concept, Total Skin and Non-Darcy Flow, Formation Damage and Hawkins' Formula, Pseudo-Skin, Flow Efficiency and IPR, and Sand Control Skin — through a single authentic Niger Delta well scenario. The Gashaka GK-22 well was drilled through clay-sensitive Agbada Formation sands with water-based mud, completed overbalanced, and returned a pressure build-up skin of S′ = +14 on DST. Your job is to decompose that number into treatable and non-treatable components, design the correct intervention, and justify it economically and operationally.

Why PBL? Why GK-22?

Problem-Based Learning places the engineering scenario first and the theory second. You encounter the real numbers, a well producing at 33% of its potential, before you know exactly why. That discomfort is deliberate. It is what motivates genuine engagement with the underlying physics. GK-22 is chosen because it is pedagogically clean (one dominant damage mechanism, negligible pseudo-skins) yet operationally authentic (Niger Delta Agbada sands, WBM drilling, clay-sensitivity, sand control requirement). Every calculation you perform is traceable to a real engineering decision.

Learning Objectives

State the total skin decomposition S′ = S_d + S_c + S_c″ + D·q and assign numerical GK-22 values to every component.
Demonstrate that GK-22's non-Darcy skin Dq is negligible at the DST rate and justify the conclusion through the D-coefficient calculation.
Apply Hawkins' formula (forward and inverse) using corrected core flood data to determine the damage anatomy: k_s/k = 0.145, r_s = 3.76 ft single-zone; two-zone model with Zone 1 (solids, S_d1 = +6.20) and Zone 2 (filtrate, S_d2 = +7.80).
Use Brons–Marting and Cinco-Ley correlations to confirm S_c = 0 (b = 1.0) and S_c″ ≈ −0.005 (near-vertical), validating S_d = S′ = +14.
Calculate FE pre- and post-treatment (0.333 and 0.875), construct dual IPR curves, and quantify production uplift.
Perform a sand production risk assessment (critical drawdown pressure, CDP = 62 psi vs 1,700 psi drawdown), apply Saucier sizing to select 12/20 mesh gravel, and calculate ICHGP skin S_g = 0.12.
Compile the complete post-treatment skin audit (S′ = +1.12), calculate FE = 0.862, q = 2,022 stb/d, and produce an NPV-positive economic justification.
Write a Final Report: 2-page engineering recommendation memo with skin audit table, treatment specification, production forecast, economic justification, and risk register.

PBL Design Principle

Each sub-problem maps 1:1 to a Module 03 topic. SP-1 through SP-4 build the skin audit. SP-5 translates the audit into a production forecast. SP-6 closes the loop with sand control and the final deliverable. You must complete sub-problems in order — each one contributes locked numerical inputs to the next.

Learnings from Module 02 — What You Already Know

GK-22 IPR Baseline & Handover to Module 03

The Module 02 PBL (Single-Phase Inflow Performance) established the theoretical deliverability of a under undamaged conditions. Applying the same principles for the GK-22 well would result in the following key results. These are the starting point for Module 03. You do not need to re-derive the Darcy equation, those numbers are locked.

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Final Report — GK-22 Deliverability Summary

Transferred to Module 03 as locked inputs · Do not recalculate

Engineering Brief

You received the Gashaka GK-22 DST package and were asked: "What should this well produce if there were no skin?" The task was to apply the Darcy radial-flow equation in pseudo-steady-state form, evaluate the correct PVT properties at average reservoir pressure, and calculate the undamaged PI as the baseline for all subsequent Module 03 work.

Applying Module 02 — Key Results

J_ideal (S = 0)

1.380

stb/d/psi · undamaged PI

J_measured (DST)

0.460

stb/d/psi · actual PI

S′ (Horner PTA)

+14

total skin · all treatable?

FE_current

0.333

well at 33% of potential

Calculation Chain (For Reference)

Darcy Radial Flow — Pseudo-Steady State (Module 02 result)J_ideal = 0.00708 × k_o × h / [μ_o × B_o × (ln(0.472·r_e/r_w) + S)] With S = 0 (no damage): Numerator = 0.00708 × 85 × 42 = 25.27 mD·ft Denominator = 1.8 × 1.32 × ln(0.472 × 1650/0.35) = 2.376 × ln(2,223) = 2.376 × 7.707 = 18.32 cp·rb/stb J_ideal = 25.27 / 18.32 = 1.380 stb/d/psi ✓ q_ideal at Δp = 1700 psi: 1.380 × 1700 = 2,346 stb/d q_measured at Δp = 1700 psi: 782 stb/d Production shortfall: 2,346 - 782 = 1,564 stb/d Annual revenue loss at $70/bbl: ~$40M/yr

Module 02 confirmed GK-22 is above bubble point at p̄_R = 4,200 psia (linear IPR is correct). The undamaged PI = 1.380 stb/d/psi is used as the fixed reference for all Module 03 FE and IPR calculations.

What Was Left Unanswered

The content of Module 02 measured the problem (S′ = +14; FE = 0.333; production shortfall of 1,564 stb/d). It did not explain what is causing the skin, how deep the damage extends, whether any of it is not treatable by acid, or what the well will produce after intervention. Those are exactly the questions Module 03 answers — one sub-problem at a time.

Critical Question for Module 03

S′ = +14 from the Horner plot is the total skin. It could, in principle, include: formation damage (S_d), partial completion skin (S_c), deviation skin (S_c″), and rate-dependent turbulence (Dq). Module 03 SP-1 through SP-4 systematically determine the contribution of each component. Only after that decomposition is complete can you design the correct treatment and predict the correct post-treatment production.

The Problem

Engineering Brief: GK-22 Workover Decision Memo

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FROM: Field Development Manager · TO: Well Productivity Team

RE: GK-22 Workover — Skin Audit, Treatment Design & Economic Approval

Gashaka GK-22 (Agbada Formation, depth 8,240 ft TVD) has been on production for 14 months at 782 stb/d. Pressure build-up analysis returns S′ = +14. The undamaged PI establishes we are at 33% of theoretical deliverability. The workover budget has been conditionally approved; however, fund release requires delivery of the following package within five working days:

Complete skin decomposition: Quantify all components of S′ = S_d + S_c + S_c″ + Dq. Identify what is and is not treatable.
Damage anatomy: Using Hawkins' formula and the attached core flood data (corrected), calculate k_s/k and r_s for the single-zone equivalent. Build the two-zone composite model (mud solids + filtrate). Specify what drove each zone.
Treatment design: Specify acid chemistry (HCl preflush → HCl/HF mud acid → KCl overflush), volumes in gal/ft and total bbl, placement strategy, and the reason HF must not contact gravel pack material. Include TCP reperforation specification (shot density, underbalance).
Post-treatment production forecast: FE pre- and post-acid. J and q at the current operating drawdown. IPR curves for both states on the same chart.
Sand control decision: CDP analysis vs current and projected drawdown. ICHGP recommendation including gravel sizing (Saucier rule), S_g calculation, and updated post-treatment total skin.
Economic justification: Treatment cost, payback period (days), 24-month NPV at $75/bbl, break-even oil price, and sensitivity to post-treatment skin achievement.

Engineering Workflow — Six Sub-Problems

SP-1 · Topic 3.1
Skin concept & PI baseline
SP-2 · Topic 3.2
Total skin: is any Dq?
SP-3 · Topic 3.3
Hawkins & damage anatomy
SP-4 · Topic 3.4
Pseudo-skin verification
SP-5 · Topic 3.5
FE, IPR & economics
SP-6 · Topic 3.6
Sand control & final audit

GK-22 Well Data Pack — Single Source of Truth

Reservoir, Fluid & Completion Data

All six sub-problems draw exclusively from this data pack. The specific subset required for each SP is highlighted within the individual SP file. Do not use values from any other source unless explicitly instructed.

Reservoir & Fluid Properties

Parameter	Symbol	Value	Units	Source
Formation	—	Agbada Fm, Niger Delta (Miocene)	—	Geology report
Depth TVD	TVD	8,240	ft	Drilling report
Average reservoir pressure (static)	p̄_R	4,200	psia	DST Horner plot
Flowing wellbore pressure (DST test)	p_wf	2,500	psia	DST bottomhole gauge
Drawdown (p̄_R − p_wf)	Δp	1,700	psi	Calculated
Reservoir temperature	T_R	120	°F	DST gauge
Effective oil permeability (kh from PTA)	k_o	85	md	Horner build-up kh/h
Net pay thickness	h	42	ft	Petrophysical log interpretation
Oil viscosity at p̄_R	μ_o	1.8	cp	PVT report (live oil)
Oil FVF at p̄_R	B_o	1.32	rb/stb	PVT report
Wellbore radius	r_w	0.35	ft	Bit size / casing ID
Drainage radius	r_e	1,650	ft	Well spacing (218 ac equiv.)
ln(0.472 r_e/r_w)	—	7.707	dimensionless	Calculated
Oil porosity	φ	0.218	fraction	Core plug analysis
Oil API gravity	°API	35	—	PVT report
Oil specific gravity	γ_o	0.85	dimensionless	Derived from API

DST Production & Skin Summary

Parameter	Symbol	Value	Units	Note
DST production rate (controlled flow period)	q	782	stb/d	Surface metering
Total skin — Horner pressure build-up	S′	+14	dimensionless	PTA Horner method
Ideal PI (S = 0, Module 02 result)	J_ideal	1.380	stb/d/psi	Locked Module 02 input
Measured PI	J_meas	0.460	stb/d/psi	q / Δp = 782/1700
Flow Efficiency (current)	FE	0.333	dimensionless	J_meas/J_ideal = 0.460/1.380
Δp_skin (pressure wasted to skin)	Δp_s	~1,038	psi	141.2 q μ B S / (k h)

Well Completion & Geometry

Parameter	Symbol	Value	Units	Significance
Perforated interval	h_p	42	ft	= h, full pay penetration
Penetration ratio	b = h_p/h	1.00	dimensionless	S_c = 0 (Brons–Marting)
Well deviation in pay	θ	<5	degrees from vertical	S_c″ ≈ −0.005 (negligible)
Shot density (initial completion)	spf	4	shots/ft	Upgraded to 8 spf in workover
Perforating mode	—	Overbalanced (+500 psi)	—	Contributed to damage
k_v/k_h (assumed)	—	0.5	dimensionless	Laminated Agbada sand

Drilling History — Damage Drivers

Parameter	Value	Damage Significance
Mud system	Water-based mud (WBM), KCl-inhibited	Primary filtrate damage source in clay-bearing Agbada sand
Mud weight (in pay zone)	12.0 ppg	~0.9 ppg overbalance drives filtrate invasion
API fluid loss	6 mL/30 min	Moderate; filtrate invasion estimated 6–12 ft radius in 85 md sand
Cumulative days drilling through pay	18 days	Extended WBM exposure; deep filtrate invasion zone confirmed
Clay mineralogy (XRD, core)	Kaolinite 8–12%, smectite 3–5%, illite 2%	Kaolinite migration + smectite swelling: primary damage mechanisms
Unconfined compressive strength (UCS)	0.8 MPa	Unconsolidated; CDP = 62 psi — sand control mandatory
D₅₀ formation sand grain size	215 μm	Gravel sizing: target 12/20 mesh (Saucier rule: D_50,g = 5×215 = 1,075 μm)

Core Flood Laboratory Report — GK-22 (Verified & Corrected)

Sidewall Core Analysis: Permeability Damage & Acid Response

⚠ Data Correction Notice — Use These Values Only

The values below supersede all draft versions of this data that appeared in earlier learning materials. Core flood conditions: 5,000 psi net confining stress, 175°F, simulated formation brine (NaCl/KCl), and WBM filtrate composition matched to field mud report. Any discrepancy between these values and values cited elsewhere in the programme should be resolved in favour of this table for the purposes of completing this PBL.

Sidewall Core Location & Baseline Permeability

Sample	Depth (ft TVD)	Description	Porosity (%)	k_baseline (md) Clean brine, 5,000 psi stress
GK-1	8,240	Clean Agbada sand, low clay content	22.4	88
GK-2	8,255	Clay-rich lamina (kaolinite-dominant)	20.1	72
Pay average	—	Thickness-weighted (60% GK-1, 40% GK-2)	21.8	≈85 (matches DST kh ✓)

Damage Flood: WBM Filtrate (KCl 3,500 ppm, pH 9.2, 175°F, 18-day soak)

Sample	k_baseline (md)	k_s after WBM (md)	k_s/k_baseline	Dominant damage mechanism
GK-1 (clean sand)	88	18	0.205	Smectite swelling + minor kaolinite detachment
GK-2 (clay-rich lamina)	72	6	0.083	Kaolinite pore-bridging dominant; smectite swelling
Pay average (used in Hawkins)	—	12	0.145	Simple average of individual ratios: (0.205 + 0.083) / 2

How the pay-average k_s/k = 0.145 is derived

The Hawkins single-zone equivalent uses the arithmetic mean of the two individual sample ratios: (0.205 + 0.083) / 2 = 0.144 ≈ 0.145. This represents the average impedance to flow across the 42 ft perforated interval. The weighted permeability approach (by k × thickness fraction) gives 0.162 (slightly higher) but the arithmetic-mean method is the standard used for two-sample core programmes. Both are defensible; 0.145 is the design basis for all Module 03 calculations.

Acid Response Flood: 3% HCl / 2.5% HF Mud Acid (175°F, 24-hour soak)

Sample	k_s pre-acid (md)	k_acid post-acid (md)	k_acid / k_DST	Interpretation
GK-1	18	92	92/85 = 1.082 (108.2%)	Acid slightly over-etches; minor wormhole in clean sand
GK-2	6	38	38/85 = 0.447 (44.7%)	Partial clay dissolution; residual chlorite inhibits full recovery
Pay average (used in post-acid skin calc)	12	65	(92+38)/2/85 = 0.765 (76.5%)	Used for post-acid Hawkins forward calculation

Post-Acid Skin Prediction (Verified Calculation)

Post-acid k_s,new = 0.765 × 85 = 65.0 md. Hawkins forward: S_d,post = (85/65 − 1) × ln(3.76/0.35) = 0.3077 × 2.374 = +0.73 ≈ +1.0. Target post-treatment skin is therefore S′_post = +1.0 (from damage alone) + S_g (from gravel pack, calculated in SP-6). The post-acid skin of +1.0 is used in SP-5 and SP-6 as the locked treatment target.

Before You Start

KWL Planner — Activate Prior Knowledge

Spend 10–15 minutes completing the KWL table before opening any sub-problem file. This is the single most important step in any PBL exercise: forcing explicit articulation of what you already know, what you genuinely need to find out, and what you expect to learn exposes knowledge gaps before you start calculating. Superficial entries ("I know about skin") are far less useful than specific ones ("I know skin enters the PI denominator but I do not know how to decompose S′ into S_d + S_c + Dq").

K — What We Know

From Module 02 and Topics 3.1–3.6 pre-reading

Skin S modifies the Darcy PI denominator: J = 0.00708kh / [μB(ln(r_e/r_w) + S)]
Positive S reduces J; negative S (stimulation) increases J
S′ = S_d + S_c + S_c″ + Dq (total skin decomposition)
Hawkins' formula: S_d = (k/k_s − 1) × ln(r_s/r_w)
FE = 7/(7+S) relates skin to Flow Efficiency
GK-22 measured S′ = +14; J = 0.460 stb/d/psi; FE = 0.333
CDP = 62 psi; drawdown 1,700 psi → sand control needed

W — What We Want to Know

Open questions before we start

How large is Dq for GK-22 at 782 stb/d? (Is any skin rate-dependent?)
What k_s/k and r_s are consistent with S_d = +14?
Are S_c and S_c″ truly negligible for a full-pay, near-vertical well?
What production rate does acid treatment deliver?
How does gravel-pack skin S_g affect the post-treatment FE?
Is the combined workover NPV-positive at $75/bbl?
What is the break-even oil price for the treatment?

L — What We Learned

Complete this column after each sub-problem

SP-1: ________________________________
SP-2: ________________________________
SP-3: ________________________________
SP-4: ________________________________
SP-5: ________________________________
SP-6: ________________________________

Facilitator Guidance

Teams who complete the W column with specific, calculable questions ("what is D for an oil well at k = 85 md?") rather than generic ones ("what is non-Darcy flow?") consistently achieve better PBL outcomes. The W column items become your personal success criteria: by SP-6, every item in the W column should have a specific, numerical answer in the L column.

Launch

Sub-Problems — Complete in Sequence

Each sub-problem is a self-contained PBL unit with its own data slice, guided tasks, theory reference, and deliverable. SP-3 through SP-6 explicitly depend on numerical outputs from earlier sub-problems and attempting them out of sequence will produce incorrect answers. Expected times shown are for an engineer working at graduate level; experienced completions engineers may move faster.

SP-1

Topic 3.1 · Skin Factor Concept

Skin Concept & GK-22 PI Baseline

Convert S′ = +14 into physical and economic meaning. Calculate J_ideal, J_actual, annual production shortfall ($40M/yr), Δp_skin (1,038 psi = 61% of drawdown), and FE = 0.333. Construct the 5-point dual IPR table.

⏱ ~45 min Launch SP-1 →

SP-2

Topic 3.2 · Total Skin S′ = S + Dq

Is Any of the Skin Rate-Dependent?

Calculate D using Katz and Dake β correlations. Compute Dq at 782 stb/d ≈ 0.001 skin units (<0.01% of S′). Extend to post-acid 2,000 stb/d: still negligible. Write the diagnostic statement: all of S′ = +14 is rate-independent formation damage.

⏱ ~40 min Launch SP-2 →

SP-3

Topic 3.3 · Formation Damage & Hawkins

Damage Anatomy & Acid Treatment Design

Apply Hawkins inverse with k_s/k = 0.145 to get r_s = 3.76 ft. Build two-zone model (Zone 1 solids: S_d1 = +6.20; Zone 2 filtrate: S_d2 = +7.80, r_s2 = 8.08 ft). Predict post-acid S_d = +0.73 ≈ +1.0. Design full 4-step acid treatment.

⏱ ~60 min Launch SP-3 →

SP-4

Topic 3.4 · Pseudo-Skin S_c & S_c″

Verify Geometric Skins Are Negligible

Brons–Marting: S_c = 0.000 (b = 1.0 full penetration). Cinco-Ley: S_c″ = −0.005 (θ′ = 2.83°, h_D = 169.7). Confirm S_d = S′ = +14.00. Sensitivity: what would S′ be if only 50% of pay were perforated?

⏱ ~40 min Launch SP-4 →

SP-5

Topic 3.5 · Flow Efficiency & IPR

Production Forecast & Workover Economics

FE_pre = 0.333 → FE_post = 0.875. q_post = 2,053 stb/d at p_wf = 2,500 psi (+163%). Dual IPR curves with annotated operating points. Payback = 5.1 days at $70/bbl net. 24-month NPV ≈ +$4.3M. Sensitivity table: S_post = 0 to +8.

⏱ ~60 min Launch SP-5 →

SP-6

Topic 3.6 · Sand Control Skin S_g

Sand Control Decision & Module 03 Final Audit

CDP = 62 psi vs 1,700 psi drawdown (27×). ICHGP mandatory. Saucier: 12/20 mesh. S_g = 0.12. Final S′ = +1.12, FE = 0.862, q = 2,022 stb/d. Risk-adjusted NPV >$7M. Write Module 03 Final Report.

⏱ ~60 min + Final Report Launch SP-6 →

Recommended Flow

SP-1 and SP-2 answer "what is the problem?" (magnitude and type of skin). SP-3 and SP-4 answer "where does it come from?" (damage anatomy, not geometry). SP-5 answers "what does fixing it achieve?" (production and economics). SP-6 asks "what else must we manage?" (sand control) and delivers the complete engineering recommendation. The SP-6 Final Report is the capstone deliverable. It cannot be written until all six sub-problems are complete.

Logistics & Assessment

Delivery Map & Assessment Framework

Stage	Mode	Time	Assessment Mechanism
Hub overview + Module 02 handover + Data Pack + KWL	Team (2–3 engineers)	25 min	KWL table submitted
SP-1: Skin concept & PI baseline	Individual → team review	45 min	5-point IPR table + Δp_skin calculation
SP-2: Total skin & non-Darcy verification	Individual → team review	40 min	D calculation + diagnostic statement
SP-3: Hawkins, damage anatomy, acid design	Team workshop	60 min	Two-zone model + acid treatment spec
SP-4: Pseudo-skin verification	Individual	40 min	Brons–Marting + Cinco-Ley calcs + sensitivity
SP-5: FE, IPR curves, economics	Individual → team review	60 min	Dual IPR chart + NPV table + sensitivity
SP-6: Sand control, S_g, final skin audit + Final Report	Team synthesis	60 min + report	Final skin audit table + 2-page recommendation memo
Facilitated debrief	Tutor-led group	45 min	Reflection log + peer review

Module 03 Final Report — Mandatory Deliverable

Final Report — Submission Specification

Format: 2-page engineering recommendation memo (template in SP-6). All tables and the IPR chart count within the page limit.
Section 1 — Complete Skin Audit: Table with all components (S_d, S_g, S_c, S_c″, Dq) pre- and post-treatment. Every number must reference its SP and calculation.
Section 2 — Confirmed Diagnosis: Physical cause of damage (WBM filtrate + kaolinite/smectite), evidence from core flood (k_s/k = 0.145), and damage geometry (r_s = 3.76 ft single-zone; r_s2 = 8.08 ft filtrate zone).
Section 3 — Treatment Specification: TCP reperforation (8 spf, 1,000 psi UB) → 5% HCl preflush → 3% HCl/2.5% HF mud acid (volume in gal/ft and total bbl, justify depth) → KCl overflush → ICHGP (12/20 mesh, k_g = 800,000 md, 8 spf).
Section 4 — Production Forecast: S′_post = +1.12, FE = 0.862, J = 1.190 stb/d/psi, q = 2,022 stb/d at p_wf = 2,500 psi. Include annotated dual IPR chart.
Section 5 — Economic Justification: Total treatment cost ($1.05M), payback (~12 days), 24-month NPV at $75/bbl (~$4.1M acid-only, ~$4.0M with ICHGP), risk-adjusted NPV including sand protection (>$7M).
Section 6 — Risk Register: Minimum 2 risks with likelihood, consequence, and mitigation (e.g. acid underperformance; gravel pack degradation timeline; water breakthrough triggering CDP collapse).

Total estimated time: 5.5 hours plus 45-min facilitated debrief

Designed for a two-day workshop (Day 1: SP-1, SP-2, SP-3 + lunch KWL review; Day 2: SP-4, SP-5, SP-6, Final Report draft, Debrief) or four self-paced online sessions. The sub-problem architecture allows pause-and-resume without loss of context.

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