SP-5 · Future IPR & Life-of-Field Depletion

Sub-Problem 5 · Context

Your Task: Life-of-Field IPR & Lift Escalation Schedule

FROM: Field Development Team · TO: Production Engineering

RE: 10-Year IPR Forecast for KA-07 — Facilities Basis

Before finalising the FDP, the facilities team needs a 10-year well deliverability forecast for KA-07. As the reservoir depletes, the IPR curve shifts and the ESP must work progressively harder to maintain target rate. Using the PVT mobility table in the Master Data Pack, apply Standing's J* scaling to predict IPR at p̄ = 3,200 / 2,600 / 2,000 psia. Apply Fetkovich's depletion method for comparison. Plot the life-of-field IPR family. Identify at which depletion stage an ESP upgrade is required to keep rate at BHFP = 800 psia above 1,800 stb/d.

SP-5 Data Slice — PVT Mobility Table (from Master Data Pack)

p̄ (psia)	k_ro	μ_o (cp)	B_o (res bbl/stb)	[k_ro/(μ_oB_o)]	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

Data Provenance

This depletion PVT/mobility table (anchored at p̄ = 5,100) and the current-state intake values μ_o ≈ 0.95 cp / B_o ≈ 1.38 res bbl/stb are an illustrative dataset for this exercise (not a published correlation). The rows are internally self-consistent and behave correctly as the well depletes, but the numbers are bespoke to this PBL and should not be cited as canonical KA-07 PVT.

Starting Point from SP-2

Use J*_post-acid = 0.630 stb/d/psi (post-acid, S = +1) as the current reference for Standing's method. This represents the well after stimulation — the FDP planning basis. If you use the undamaged J* = 0.720, you are predicting the ideally cleaned-up well's future — both are useful for P50/P90 planning.

Theory & Equations

Standing's J* Scaling & Fetkovich Depletion

Standing's J* mobility scaling (Guo et al. Eq. 3.37)J*_future / J*_present = [k_ro/(μ_o × B_o)]_future / [k_ro/(μ_o × B_o)]_present Using the ratio column directly from the PVT table: J*_future = J*_present × (J* ratio from PVT table) Future composite IPR: q_b,f = J*_f × (p̄_f − p_b,f) [Darcy segment] q_v,f = J*_f × p_b,f / 1.8 [Vogel increment] AOFP_f = q_b,f + q_v,f Note: p_b may also change with depletion (gas comes out of solution). For simplicity in this PBL, assume p_b remains at 4,500 psia.

Fetkovich depletion method (Guo et al. Eq. 3.61)J'_future = J'_initial × (p̄_future / p̄_initial) AOFP_future = J'_future × p̄²_future = J'_i × (p̄_f/p̄_i) × p̄²_f = J'_i × p̄_i × (p̄_f/p̄_i)³ ← AOFP scales as CUBE of pressure ratio J'_initial is calibrated from the current AOFP: J'_i = AOFP_i / p̄_i² (using current composite AOFP)

Guided Tasks

Work Through in Sequence

Determine current J* reference. Use J*_post-acid = 0.630 stb/d/psi from SP-2 as the present reference. Current AOFP (from composite IPR with J* = 0.630): q_b = 0.630 × 600 = 378, q_v = 0.630 × 4500/1.8 = 1,575, AOFP = 1,953 stb/d.
Apply Standing's J* ratio for each depletion stage. J*_future = J*_present × J*-ratio from PVT table. For Stage 2 (p̄ = 3,200): J* = 0.630 × 0.737 = ? stb/d/psi. Repeat for Stages 3 and 4.
Compute future AOFP at each stage (Standing). q_b,f = J*_f × (p̄_f − p_b), q_v,f = J*_f × p_b / 1.8, AOFP_f = q_b,f + q_v,f.
Compute rate at BHFP = 800 psia for each stage (Standing IPR). r = 800/p̄_f. If 800 ≥ p_b, use Darcy; else use composite Vogel. Determine at which stage q at 800 psia BHFP falls below 1,800 stb/d.
Apply Fetkovich depletion for comparison. J'_i = AOFP_i/p̄² = 1,953/(5,100²) = ? stb/d/psia². Scale: AOFP_f = J'_i × (p̄_f/p̄_i) × p̄²_f. Compare with Standing AOFP at each stage.
Design the lift escalation schedule. Based on the future IPR family, determine: (a) at what reservoir pressure does natural flow become inadequate; (b) when does ESP Stage 1 (BHFP = 2,000 psia) become inadequate; (c) when is ESP upgrade needed (BHFP = 800 psia); (d) when does KA-07 reach economic abandonment?

Worked Solution — Standing's Method

Future IPR by Standing's J* scaling — KA-07 post-acidReference (current, post-acid): J* = 0.630 stb/d/psi, p̄ = 5,100 psia q_b = 0.630 × 600 = 378 stb/d q_v = 0.630 × 4500/1.8 = 1,575 stb/d AOFP_current = 378 + 1575 = 1,953 stb/d Stage 2 — p̄ = 3,200 psia: J*_f = 0.630 × 0.737 = 0.464 stb/d/psi q_b,f = 0.464 × (3200 − 4500) → NEGATIVE → p̄_f < p_b → Reservoir is now BELOW bubble point at p̄ = 3,200 psia! → Darcy segment disappears; use Vogel only: q_v,f = 0.464 × 3200/1.8 = 825 stb/d AOFP_f (Stage 2) = 825 stb/d [pure Vogel since p̄_f < p_b] Stage 3 — p̄ = 2,600 psia: J*_f = 0.630 × 0.500 = 0.315 stb/d/psi q_v,f = 0.315 × 2600/1.8 = 455 stb/d AOFP_f (Stage 3) = 455 stb/d Stage 4 — p̄ = 2,000 psia: J*_f = 0.630 × 0.304 = 0.192 stb/d/psi q_v,f = 0.192 × 2000/1.8 = 213 stb/d AOFP_f (Stage 4) = 213 stb/d Rate at BHFP = 800 psia using Vogel q = q_v,f × [1 − 0.2r − 0.8r²]: Stage 2 (p̄=3200): r=800/3200=0.250, f=1−0.05−0.05=0.900 q(800psia) = 825 × 0.900 = 743 stb/d ← BELOW 1,800 target! Stage 3 (p̄=2600): r=800/2600=0.308, f=1−0.062−0.076=0.862 q(800psia) = 455 × 0.862 = 392 stb/d ← Well below target Stage 4 (p̄=2000): r=800/2000=0.400, f=0.792 q(800psia) = 213 × 0.792 = 169 stb/d ← Near abandonment CRITICAL FINDING: Even with the ESP at maximum drawdown (BHFP = 800 psia), KA-07 can sustain ~1,800 stb/d target only at current post-acid conditions (AOFP = 1,953, q at 800 psia ≈ 1,857 stb/d). This composite AOFP of 1,953 stb/d is the traceable ESP-sizing basis used throughout SP-5 and SP-6. Once reservoir pressure drops to 3,200 psia (Stage 2), even maximum drawdown gives only 743 stb/d — far below target. IMPLICATION: KA-07 alone cannot sustain the 1,800 stb/d target beyond early depletion. The FDP must rely on additional wells or pressure maintenance (waterflood) to sustain plateau.

Fetkovich Depletion Comparison

Fetkovich depletion — AOFP decline by stageJ'_i = AOFP_i / p̄_i² = 1,953 / (5,100²) = 1,953 / 26,010,000 = 7.508 × 10⁻⁵ stb/d/psia² AOFP_f = J'_i × (p̄_f/p̄_i) × p̄²_f = J'_i × p̄_f³/p̄_i Stage 2 (p̄=3200): AOFP = 7.508×10⁻⁵ × 3200³/5100 = 7.508×10⁻⁵ × 32,768,000,000/5100 = 7.508×10⁻⁵ × 6,426,275 = 482 stb/d Stage 3 (p̄=2600): AOFP = 7.508×10⁻⁵ × 2600³/5100 = 7.508×10⁻⁵ × 17,576,000,000/5100 = 259 stb/d Stage 4 (p̄=2000): AOFP = 7.508×10⁻⁵ × 8,000,000,000/5100 = 118 stb/d Fetkovich declines faster than Standing → more pessimistic forecast Use Fetkovich as P10 (downside) and Standing as P50 (base case)

Life-of-Field Summary Table

Stage	p̄ (psia)	J*_f	Standing AOFP	Fetkovich AOFP	q at 800 psia BHFP	vs. 1,800 target	Action
Current	5,100	0.630	1,953	1,953	~1,857	✓ At target	ESP Stage 1 active
Stage 2	3,200	0.464	825	482	743	−1,057 stb/d	ESP upgrade needed
Stage 3	2,600	0.315	455	259	392	−1,408 stb/d	Infill well trigger
Stage 4	2,000	0.192	213	118	169	−1,631 stb/d	Economic review

Current AOFP

1,953

stb/d post-acid, p̄=5,100

Stage 2 AOFP

825

stb/d at p̄=3,200 (Standing)

Target met until

p̄≈5,100

Stage 2 already below target

Infill trigger

Stage 2

p̄=3,200 psia — plan now

Life-of-Field IPR Family

KA-07 — IPR Family Plot (4 Depletion Stages)

Each curve represents the Vogel IPR at one depletion stage (post-acid J* scaled by Standing's mobility ratio). Red dashed = 1,800 stb/d target. Orange dashed = BHFP = 800 psia (maximum ESP drawdown). The intersection of each IPR with 800 psia gives the maximum achievable rate at that stage.

Just-in-Time Resources

Need a Refresher? Pull These at Point of Need

Each links straight to the Module-04 asset that builds the method behind this sub-problem — open one only if you are stuck.

Study Future IPR & Standing's depletion scaling: C01_M04_T6 — Future IPR Topic theory page

Watch Lecture 4.6D — Life-of-Field Lift Design: IPR Family to ESP Roadmap Produced lecture

Self-check ../../courses/c01/production/m04/topic-4-6-future-ipr/file-pack/future_ipr.py verified calculator — reproduce your numbers

Knowledge Check

SP-5 · 5 Questions

Future IPR Prediction — Knowledge Check

1. In Standing's J* scaling, J*_future = J*_present × [k_ro/(μ_oB_o)]_future / [k_ro/(μ_oB_o)]_present. Why does J* decline even if reservoir permeability k doesn't change?

Correct — C. This is the fundamental physics of solution-gas drive depletion. The J* ratio captures all three effects: k_ro decreasing (gas saturation builds), μ_o increasing (oil becomes heavier as it loses dissolved gas), and B_o decreasing (oil shrinks at surface). Together, these reduce the oil's ability to flow into the wellbore — even with the same reservoir pressure drawdown, less oil arrives at the wellbore per unit time. The PVT mobility table quantifies this trajectory.

2. At Stage 2 (p̄ = 3,200 psia), the Darcy segment of the composite IPR disappears — there is no q_b. Why?

Correct — B. The composite IPR has a Darcy segment only when p̄ > p_b. At Stage 2, p̄ = 3,200 psia < p_b = 4,500 psia — the average reservoir pressure has depleted below the bubble point. The entire reservoir is now undersaturated with gas saturation throughout. There is no pressure range above p_b to drive Darcy single-phase flow. The full IPR becomes q = q_v,max × Vogel(p_wf/p̄_f), where q_v,max = J*_f × p̄_f/1.8.

3. The Fetkovich depletion method gives lower future AOFP than Standing's method (482 vs. 825 stb/d at Stage 2). Which prediction should be used as the base case for FDP planning?

Correct — C. Standing's method is more rigorous because it uses measured PVT data (k_ro, μ_o, B_o) to track the fluid mobility change with pressure. Fetkovich's linear J' depletion assumption is a simplification that tends to over-predict the rate of PI decline. The correct approach is: Standing = P50 base case for engineering design; Fetkovich = P10 downside for stress-testing the design against pessimistic depletion. Reservoir simulation would be used for a major FDP sanction, but analytical methods suffice for early screening and pre-FID planning.

4. The life-of-field analysis shows KA-07 can barely meet the 1,800 stb/d target even at current conditions (AOFP = 1,953 stb/d with ESP at 800 psia BHFP). At Stage 2 (p̄ = 3,200 psia) the maximum rate drops to 743 stb/d. What does this mean for field development planning?

Correct — A. This is the most important strategic finding of the entire Module 04 PBL. KA-07's AOFP — even at maximum ESP drawdown — falls below the 1,800 stb/d target at Stage 2 pressure (3,200 psia). No amount of artificial lift investment can overcome an insufficient AOFP: the pump can only draw BHFP to zero, and AOFP is the physical ceiling on rate. The field development plan must incorporate infill wells and/or pressure maintenance before Stage 2 is reached. This is precisely the type of integrated finding that goes into SP-6.

5. An engineer claims: "We can extend the life of KA-07 by acidising it again at Stage 2 to remove further skin." Is this a valid strategy?

Correct — D. The Stage 2 J* decline from 0.630 to 0.464 stb/d/psi is driven by k_ro falling (from 0.815 to 0.685), μ_o rising (from 0.95 to 1.14 cp), and B_o falling — all fluid/rock property changes from depletion, not from skin damage. A matrix acid job only addresses near-wellbore damage (skin). If skin is already near zero (S = +1 post-acid), further stimulation has negligible benefit on J*. The AOFP decline at Stage 2 is irreversible without pressure maintenance or infill drilling to sustain reservoir pressure.

SP-5 Output

Record Before Moving to SP-6 — Final Integration

SP-5 Key Outputs — KA-07 Life-of-Field IPR Family

Current (p̄ = 5,100): J* = 0.630, AOFP = 1,953 stb/d, q at 800 psia = ~1,857 stb/d ✓

Stage 2 (p̄ = 3,200): J* = 0.464, AOFP = 825 stb/d, q at 800 psia = 743 stb/d ✗

Stage 3 (p̄ = 2,600): J* = 0.315, AOFP = 455 stb/d, q at 800 psia = 392 stb/d ✗

Stage 4 (p̄ = 2,000): J* = 0.192, AOFP = 213 stb/d, q at 800 psia = 169 stb/d ✗

Fetkovich depletion (P10 pessimistic): Stage 2 AOFP = 482 stb/d

Critical finding: KA-07 alone CANNOT sustain 1,800 stb/d beyond current conditions even at max ESP drawdown. Infill well and/or pressure maintenance required by Stage 2.

→ All five SP outputs now ready. Proceed to SP-6: Integrated FDP Report for the Karama Leadership Forum.