Course 01 · Module 02 · Introduction

Single-Phase Inflow Performance: the Karama KRM-4 deliverability crisis

Karama Field Well KRM-4 is producing 35% below its pre-drill forecast and reservoir pressure is tracking toward the bubble point within 18 months. Your team has been engaged to diagnose the underperformance, benchmark the well against its field peers, and design a production strategy that maintains the 1,200 STB/day target through depletion. Four sub-problems must be solved before the final engineering recommendation can be assembled.

Karama Field · KRM-4 · Chalk reservoir 18 mD · 95 ft pay · 4,850 psia 4 sub-problems · 4 concept areas

The KRM-4 investigation

The Karama Field is a chalk oil reservoir producing from the Lower Cretaceous Karama Formation. Five wells (KRM-1 through KRM-5) have been producing for between 8 and 26 months. KRM-4, the subject of this engineering investigation, was drilled to a total depth of 11,840 ft TVD and completed across 95 ft of net chalk pay. It is perforated across the full pay interval and has not been stimulated.

A routine production review comparing KRM-4’s performance against its pre-drill PI forecast identified a 35% shortfall in production rate. The pre-drill forecast was based on analogous core data from KRM-1. A two-rate PI test was conducted and returned a stabilised measured PI of 0.600 STB/day/psi against a theoretical ideal of 0.926 STB/day/psi — confirming that a wellbore skin of S = +5 is responsible for the underperformance.

The Field Production Manager has requested a complete deliverability assessment covering: (1) verification of the theoretical productivity baseline; (2) diagnosis and quantification of the underperformance cause; (3) benchmarking of all five KRM wells by reservoir quality and stimulation priority; and (4) a production strategy that maintains the 1,200 STB/day field target through the anticipated depletion from P̄ = 4,850 psia to Pb = 3,650 psia over the next 18 months.

The investigation must culminate in a formal Engineering Recommendation Memo covering stimulation priorities, artificial-lift specification, and the KRM-6 drilling decision, with quantified analysis supporting each recommendation.

Learning integrationHow the four topics map to the four sub-problems
Each sub-problem is anchored to one Module 02 topic. Complete the topic before attempting its sub-problem. The sub-problems build sequentially, each answer feeds the next, with all four required for the integration deliverable in SP-4.
2.1 Darcy/PSS → SP-1: Theoretical baseline 2.2 PI test → SP-2: Skin & FE 2.3 SPI → SP-3: Field benchmarking 2.4 Non-linear IPR → SP-4: Depletion & memo
Your learning path
1
Topic 2.1 · Darcy Radial Flow & PSS · → SP-1

Establishing the undamaged baseline

What could KRM-4 deliver if there were no skin?
You have the KRM-4 characterisation data: k = 18 mD, h = 95 ft from log interpretation and core flood, confirmed by pressure build-up. Before any performance assessment, establish the undamaged productivity potential — assemble the PSS radial inflow equation term by term and calculate Jideal, the ceiling value that a successful acid stimulation could recover.
Jideal = 0.00708 × k × h / [μo × Bo × (ln(re/rw) − 0.75)] KRM-4: 0.00708 × 18 × 95 / [1.4 × 1.25 × (ln(1,320/0.354) − 0.75)] = 12.10 / [1.75 × 7.47] = 0.926 STB/day/psi
Tasks: (a) numerator 0.00708·k·h and the meaning of flow capacity k·h; (b) ln(re/rw) and the PSS denominator at S = 0 (expect 7.4–8.0 for 160-acre spacing); (c) assemble Jideal to 3 dp; (d) Qmax at Pwf = 3,100 psia — can the undamaged reservoir meet 1,200 STB/day? (e) sensitivity at k = 12.6 (P10) and 23.4 mD (P90).
PSS radial inflow equation0.00708 field-unit constantGeometric factor ln(re/rw)Flow capacity k·hSensitivity analysis
Open Topic 2.1 →SP-1 problem set
2
Topic 2.2 · Productivity Index · → SP-2

PI test interpretation — measuring the damage

What does KRM-4 actually produce, and how big is the stimulation prize?
SP-1 established what KRM-4 should produce; SP-2 establishes what it does produce and why. Interpret both test rates independently to extract Jmeasured, confirm linearity, then use Jideal from SP-1 to back-calculate skin S via the Hawkins–van Everdingen rearrangement, and quantify how many STB/day the skin is costing the asset.
S = (Jideal/Jmeas − 1) × (ln(re/rw) − 0.75) KRM-4: Jmeas = 0.600 → S = +5, FE = Jmeas/Jideal = 60% Stimulation prize: ΔQ ≈ +571 STB/day (+54%) at Pwf = 3,100 psia
Tasks: (a) Jmeas from Rate 1 (350 STB/d, ΔP 583 psi) and Rate 2 (620 STB/d, ΔP 1,033 psi), confirm ≤ 2% consistency; (b) back-calculate S (ratio and algebraic forms), verify against S = +5; (c) Flow Efficiency FE as %; (d) stimulation prize Qstim − Qcurrent; (e) repeat for KRM-2 (Jmeas = 0.41) and compare stimulation priority.
Two-rate PI test methodSkin back-calculationFlow Efficiency (FE)Stimulation prizeIPR linearity
Open Topic 2.2 →SP-2 problem set
3
Topic 2.3 · Specific Productivity Index · → SP-3

Field SPI benchmarking & the KRM-6 decision

How good is KRM-4’s rock compared with the rest of the field?
SP-2 confirmed underperformance is formation damage, not poor rock. Normalising PI by net pay (SPI = J/h) removes the thickness effect and exposes true rock quality for each well, driving two decisions: which wells to stimulate first, and whether to drill KRM-6 at the proposed seismic location.
SPI = J / h [STB/day/psi/ft] Field average SPIideal = 0.01047 → KRM-6 J(P50, h=115 ft) = 1.204 STB/d/psi Range: P10 = 0.882 — P90 = 1.486 STB/d/psi
Tasks: (a) SPImeas and SPIideal for all five KRM wells (complete the table); (b) rank by SPIideal (true rock quality, damage-independent); (c) stimulation priority matrix combining SPIideal and FE, with per-well rate gain after skin removal; (d) predict KRM-6 J at h = 115 ft with P10/P90 — is h or SPI the dominant uncertainty? (e) is QP10 at Pwf = 3,100 still above the 1,200 STB/day target?
SPI = J/h normalisationJ vs h cross-plotReservoir quality rankingStimulation priority matrixAnalogue J prediction
Open Topic 2.3 →SP-3 problem set
4
Topic 2.4 · Non-Linear IPR Models · Integration · → SP-4

Depletion strategy & final recommendation

How is the 1,200 STB/day target held as P̄ falls toward the bubble point?
The integration sub-problem. The linear PI model valid today breaks down as P̄ approaches Pb = 3,650 psia. Build the composite IPR (P̄ = 4,200 psia) and the full Vogel IPR (P̄ = Pb), assess target achievability at each depletion state, specify the artificial-lift requirement, and integrate all SP results into the recommendation memo.
Composite (P̄ > Pb): Qb = J(P̄ − Pb); Qmax = Qb + J·Pb/1.8 Vogel (P̄ = Pb = 3,650): Qmax = 1,845 STB/day → target missed at Pwf=3,100 ESP basis: required Pwf = 1,979 psia → ΔPwf = 1,121 psi
Tasks: (a) composite IPR at P̄ = 4,200, assess target, find required Pwf; (b) Vogel IPR at Pb from a single-point test (900 STB/d at 2,500 psia), solve the quadratic for Pwf,required; (c) ESP specification on the worst-case (bubble-point) state; (d) linear-PI AOFP error vs Vogel Qmax; (e) compile the 10-point recommendation memo from SP-1–SP-4.
Composite IPRVogel equationSingle-point QmaxVogel quadraticESP lift specificationLinear-PI error
Open Topic 2.4 →SP-4 problem set
★
PBL Hub · Integration deliverable

Launch the Module 02 PBL — Karama KRM-4 deliverability assessment

Once all four topics are complete, open the full problem set: data pack, KWL planner, four sub-problem launch cards, delivery map, and assessment criteria. The package culminates in the Engineering Recommendation Memo for the Field Production Manager — a go/no-go decision on the intervention programme supported by quantified analysis from every sub-problem.
Launch KRM-4 PBL →
Reference answer framework — KRM-4 key numbers

The table gives the key numerical answers your sub-problem solutions should converge on. If a calculation differs materially, review the relevant Topic before finalising your memo. All values use Jideal = 0.926 STB/d/psi as the undamaged baseline.

J = 0.00708 · k · h / [ μo · Bo · (ln(re/rw) − 0.75 + S) ] [STB/day/psi]
QuantitySymbolCurrent (damaged)Post-stim (S=0)At bubble point (Vogel)Source / SP
Skin factorS+500Two-rate PI test / SP-2
Flow efficiencyFE0.65 (65%)1.0001.000Jmeas/Jideal / SP-2 (0.600/0.926 = 0.648, rounds to 0.65)
Productivity index JSTB/d/psi0.6000.9260.926Darcy / SP-1 & SP-2
Q at Pwf = 3,100 psia (early life)STB/day1,0501,6211,586 (composite)J×ΔP / SP-1, 2, 4
Stimulation prize ΔQSTB/day—+571 (+54%)+571Qstim−Qcurrent / SP-2
Field-average SPIidealSTB/d/psi/ft0.01047All 5 wells / SP-3
KRM-6 J prediction (P50, h = 115 ft)STB/d/psi1.204  [P10: 0.882 — P90: 1.486]SPI×h / SP-3
Composite AOFP (P̄ = 4,200 psia)STB/day2,387 (Qb=509; QVogel=1,878)—Composite IPR / SP-4
Q at Pwf = 3,100 (P̄ = 4,200)STB/day638 — target missed—Vogel segment / SP-4
Vogel Qmax (P̄ = Pb = 3,650)STB/day——1,845Single-point test / SP-4
Q at Pwf = 3,100 (Vogel, P̄ = 3,650)STB/day——467 — target missedVogel equation / SP-4
Required Pwf for target (Vogel)psia——1,979Vogel quadratic / SP-4
ESP lift requirement ΔPwfpsi——1,121 (3,100−1,979)AL specification / SP-4
Linear AOFP over-prediction at P̄ = Pb%——+18.7% (linear 2,190 vs Vogel 1,845)Error analysis / SP-4
Final deliverable — Engineering Recommendation Memo

The Module 02 PBL culminates in a structured Engineering Recommendation Memo for KRM-4, integrating the outputs from all four sub-problems into a document that could be submitted directly to the Field Production Manager for a go/no-go decision on the intervention programme.

Section 1 — Executive summary

Current well state (Q, FE, J, % of ideal), root cause of underperformance, and recommended actions in priority order with headline numbers — three sentences.

Section 2 — Current deliverability (SP-1 & SP-2)

Jideal with full PSS calculation, Jmeas from the two-rate test, S = +5 derivation, FE = 65%, stimulation prize +571 STB/day at Pwf = 3,100 psia.

Section 3 — Field benchmarking (SP-3)

Complete SPI table for all five KRM wells, J vs h cross-plot coordinates, stimulation priority ranking, KRM-6 J prediction (P10/P50/P90) with uncertainty attribution.

Section 4 — Depletion strategy (SP-4)

Composite IPR at P̄ = 4,200 psia and Vogel IPR at P̄ = 3,650 psia, target achievability at each state, required Pwf trajectory, ESP design basis, linear-model AOFP error.

Section 5 — Prioritised action plan

1st acid-stimulate KRM-2 (S=+14, FE=44%); 2nd acid-stimulate KRM-4 (+571 STB/day); 3rd install ESP sized for ΔP = 1,121 psi at bubble-point depletion; 4th drill KRM-6 (JP50 = 1.204 STB/d/psi).

Section 6 — Assumptions & uncertainty

k ±30% (P10/P90 J range), seismic h ±15 ft (KRM-6 J uncertainty), Vogel accuracy ±10–20%, bubble-point arrival ±6 months, post-stimulation skin assumption.

Topic reference library

Topic 2.1 — Darcy Radial Flow & PSS Equation

PSS derivation, the 0.00708 field-unit constant, geometric factor ln(re/rw), PSS vs steady-state, worked examples. KRM-4: Jideal = 0.926, numerator = 12.10, denominator = 13.08.

Topic 2.2 — Productivity Index

PI definition, two-rate test, skin back-calculation, Flow Efficiency, Standing’s modified Vogel for damaged wells, stimulation prize. KRM-4: Jmeas = 0.600, S = +5, FE = 60%, prize = +571 STB/day.

Topic 2.3 — Specific Productivity Index

SPI = J/h normalisation, J vs h cross-plot with SPI isolines, field benchmarking, stimulation priority matrix, analogue J prediction with uncertainty. KRM field average SPIideal = 0.01047.

Topic 2.4 — Limitations of the Linear PI & Non-Linear IPR

Three IPR failure modes, Vogel equation, single-point Qmax, composite IPR construction, back-pressure gas IPR, model selection. KRM-4: composite Qmax = 2,387, Vogel Qmax = 1,845.

Assessment criteria
The Module 02 PBL is assessed on six criteria
  1. Theoretical baseline (SP-1) — Jideal correct to 3 dp with full working (numerator, geometric factor, denominator, assembled PI) and a complete sensitivity table.
  2. PI test interpretation (SP-2) — Jmeas from both rates and confirmed consistent; skin back-calculated by ratio and algebraic form; FE correctly expressed; stimulation prize quantified in STB/day.
  3. Field benchmarking (SP-3) — SPI table complete for all five wells; quality ranking correct (KRM-3 > KRM-1 > KRM-4 = KRM-2 > KRM-5 by SPIideal); KRM-6 prediction with P10/P50/P90 and dominant uncertainty identified.
  4. IPR model selection (SP-4) — composite IPR applied when Pwf < Pb; Vogel applied at P̄ = Pb; quadratic solved for required Pwf; linear-model error quantified.
  5. ESP specification (SP-4) — design basis chosen as worst-case (bubble-point) depletion; lift differential ΔP = 1,121 psi derived; consequence of using linear PI for sizing stated.
  6. Recommendation quality — memo is decision-ready: actions specific, sequenced, and each supported by a quantified number; no advice unsupported by the analysis.
Common mistakes to avoid
Watch for these
Using Bob = 1.28 instead of Bo(P̄) = 1.25 in the PSS equation. Bob is the FVF at bubble-point pressure; the PSS inflow equation requires properties at average reservoir pressure P̄. Using Bob introduces a 2.4% error in Jideal that propagates into every subsequent calculation.

Concluding that consistent J across two rates means S = 0. A constant J confirms the IPR is linear (no turbulence, no below-bubble-point curvature), not that the well is undamaged. Skin suppresses J uniformly across rates and is only detectable by comparing Jmeas to Jideal.

Applying Vogel when P̄ > Pb. Vogel requires P̄ ≤ Pb. When P̄ > Pb but Pwf < Pb, the correct model is the composite IPR (linear above Pb, Vogel below). Pure Vogel at P̄ = 4,200 psia gives the wrong Qb and Qmax.

Choosing the wrong J for the composite IPR linear segment — match it to the scenario. Two composite IPRs are built in SP-4. The current-well composite (damaged well, no stimulation yet) uses Jmeas = 0.600, giving Qb = 330 STB/day. The post-stimulation composite (skin removed, S = 0) uses Jideal = 0.926, giving Qb = 509 STB/day. Using Jideal for the current well overstates deliverability and the AL requirement; using Jmeas for the post-stimulation case understates the stimulation prize. State which scenario you are modelling before picking J.

Sizing the ESP for the current reservoir state. The ESP must be sized for the worst-case depletion (P̄ = Pb = 3,650 psia, Vogel regime). Sizing at the current 4,850 psia gives an under-specified pump that fails at depletion.

Ranking wells by absolute J rather than SPI. KRM-1 (h = 110 ft) and KRM-3 (h = 130 ft) differ in pay, so raw J misleads. By SPIideal, KRM-3 (0.01292) exceeds KRM-1 (0.01227). Always normalise for h before concluding on reservoir quality.
Reference
Reservoir & completion: k = 18 mD · h = 95 ft · μo = 1.4 cp · Bo = 1.25 RB/STB · P̄ = 4,850 psia (initial) · rw = 0.354 ft · re = 1,320 ft (160-acre spacing)
Fluid: Pb = 3,650 psia · Bob = 1.28 RB/STB · μob = 1.6 cp · Rs = 620 scf/STB · 32°API · undersaturated oil
Operations: Qtarget = 1,200 STB/day · Psep = 3,100 psia · Pwf,min (ESP) = 800 psia · KRM-6 proposed h = 115 ± 15 ft
Well-test results: Qmeas = 350 & 620 STB/day · Pwf = 4,267 & 3,817 psia · Smeasured = +5 · build-up k = 18 mD (confirmed)
Required
Module 01: the deliverability foundation — Darcy radial flow, the PSS equation, skin and the geometric factor are assumed from Module 01 before starting here.
Required
Mathematics: natural logarithm (ln), basic algebra and the quadratic formula (for the Vogel Pwf solution), and unit handling (psia, mD, cp, RB/STB).
Helpful
IPR familiarity: prior exposure to the Vogel inflow curve helps with SP-4, but the composite and Vogel models are developed from first principles in Topic 2.4.