Module 04 PBL  ›  Sub-Problem 2 of 6

SP-2 · Acid Job — Quantify the Value of Stimulation

KA-07 has total skin S' = +8. Apply Standing's Flow Efficiency to compute pre-acid and post-acid IPRs. Calculate the production uplift, simple payback on the $450K acid job, and recommend whether to stimulate before or after ESP installation.

Topic 4.3 — Standing's FE ⏱ ~35 min 5 MCQ Requires SP-1 outputs
Sub-Problem 2 · Context

Your Task: Quantify Skin Loss and Acid Job Value

FROM: Karama Asset Manager  ·  TO: Production Engineering
RE: KA-07 Acid Job Decision — FDP Gate

Pressure transient analysis confirmed total skin S' = +8 on KA-07. The completion contractor has proposed a matrix acid job targeting S = +1 at a cost of $450K. The FDP team is debating whether to: (A) acid the well first, then install ESP, or (B) install the ESP without acid treatment and accept the skin damage. Using SP-1 outputs and Standing's Flow Efficiency method, compute the pre-acid and post-acid IPRs, the production uplift at operating BHFP = 2,000 psia, and the simple payback on the acid job investment.

SP-2 Data Slice (plus SP-1 outputs)

ParameterValueUnitsSource
J* (ideal PI, from SP-1)0.72stb/d/psiSP-1 output
qb at pb (from SP-1)432stb/dSP-1 output
Pre-acid skin Spre+8—PBU Horner analysis
Post-acid target skin Spost+1—Completion analogues
Operating BHFP (ESP target)2,000psiaESP design constraint
Oil netback58$/stbEconomics parameters
Acid job cost450$KCompletion contractor quote
p̄, pb5,100 / 4,500psiaMaster data pack
Theory & Equations

Standing's Flow Efficiency — Skin-Corrected Vogel

Flow Efficiency Definition

Flow Efficiency (FE) is the ratio of actual-to-ideal drawdown for the same rate, or equivalently the ratio of actual-to-ideal PI. For a well with skin S:

Flow Efficiency (Guo et al., Eq. 3.32)FE = J_actual / J* = (p̄ - p_wf - ΔP_skin) / (p̄ - p_wf) Approximation (valid for typical well geometry): FE ≈ 7 / (7 + S) Pre-acid (S = +8): FE_pre = 7 / (7 + 8) = 7/15 = 0.467 Post-acid (S = +1): FE_post = 7 / (7 + 1) = 7/8 = 0.875 J_actual = J* × FE

Standing's Modified Vogel — FE-Corrected IPR

Standing's modified Vogel (skin-corrected composite IPR)q_o = q_b,actual + q_v,actual × [1 - 0.2×(p'_wf/p_b) - 0.8×(p'_wf/p_b)²] where: q_b,actual = J_actual × (p̄ - p_b) q_v,actual = J_actual × p_b / 1.8 p'_wf / p_b = 1 - FE × (1 - p_wf/p_b) Note: p'_wf is the "effective" flowing pressure that accounts for the skin pressure drop. As FE decreases (more damage), p'_wf/p_b approaches 1 → Vogel factor → 0 → less production.

Production Uplift and Payback

Acid job economicsΔq = q_post_acid(p_wf = 2000) - q_pre_acid(p_wf = 2000) [stb/d] Daily revenue uplift = Δq × netback [$/d] Simple payback (days) = Acid cost / Daily revenue uplift
Guided Tasks

Work Through in Sequence

  1. Compute FE for pre-acid (S = +8) and post-acid (S = +1) conditions. FEpre = 7/(7+8) = ?   FEpost = 7/(7+1) = ?
  2. Compute Jactual pre-acid and post-acid. Jactual,pre = 0.72 × FEpre = ? stb/d/psi  ·  Jactual,post = 0.72 × FEpost = ?
  3. Compute qb,actual and qv,actual for each skin state. qb = Jactual × (5,100 − 4,500) and qv,max = Jactual × 4,500 / 1.8.
  4. Compute p'wf/pb at operating BHFP = 2,000 psia for each skin state. r = 2,000/4,500 = 0.4444  ·  p'wf/pb = 1 − FE × (1 − 0.4444).
  5. Compute q at BHFP = 2,000 psia for pre-acid and post-acid IPRs. Apply Standing's equation with the corrected p'wf/pb ratios.
  6. Compute Δq, daily revenue uplift, and acid job payback. Acid cost = $450K  ·  Netback = $58/stb.
  7. Make the recommendation. Should the operator acid first then install ESP, or install ESP immediately? Justify with numbers.

Worked Solution

Step-by-step solution — KA-07 SP-2Step 1 — Flow Efficiency: FE_pre = 7/(7+8) = 7/15 = 0.4667 FE_post = 7/(7+1) = 7/8 = 0.8750 Step 2 — Actual PI: J_pre = 0.72 × 0.4667 = 0.336 stb/d/psi J_post = 0.72 × 0.8750 = 0.630 stb/d/psi Step 3 — q_b and q_v,max: Pre-acid: q_b = 0.336 × 600 = 201.6 stb/d q_v,max = 0.336 × 4500/1.8 = 840 stb/d Post-acid: q_b = 0.630 × 600 = 378.0 stb/d q_v,max = 0.630 × 4500/1.8 = 1,575 stb/d Step 4 — p'_wf/p_b at BHFP = 2,000 psia (r = 0.4444): Pre-acid: p'/p_b = 1 - 0.4667×(1-0.4444) = 1 - 0.4667×0.5556 = 1 - 0.2593 = 0.7407 Post-acid: p'/p_b = 1 - 0.8750×(1-0.4444) = 1 - 0.8750×0.5556 = 1 - 0.4861 = 0.5139 Step 5 — Rate at BHFP = 2,000 psia: Pre-acid Vogel factor: 1 - 0.2×0.7407 - 0.8×0.7407² = 1-0.1481-0.4390 = 0.4129 q_pre = 201.6 + 840 × 0.4129 = 201.6 + 346.8 = 548.4 ≈ 548 stb/d Post-acid Vogel factor: 1 - 0.2×0.5139 - 0.8×0.5139² = 1-0.1028-0.2111 = 0.6861 q_post = 378.0 + 1575 × 0.6861 = 378.0 + 1080.6 = 1,458.6 ≈ 1,459 stb/d Step 6 — Economics: Δq = 1,459 - 548 = 911 stb/d Daily revenue uplift = 911 × $58 = $52,838/day Payback = $450,000 / $52,838 = 8.5 days ← outstanding ROI

Key Results

Pre-acid FE
0.467
S = +8 · 53% of potential lost
Post-acid FE
0.875
S = +1 · 87.5% of potential
Δq at 2,000 psia
+911
stb/d uplift from acid
Acid payback
8.5
days — exceptional ROI
Recommendation
An 8.5-day payback is one of the strongest economic cases in production engineering. The recommendation is unambiguous: stimulate first, then install ESP. Post-acid, the well produces 1,459 stb/d at 2,000 psia BHFP — far closer to the 1,800 stb/d target than the pre-acid 548 stb/d. Installing the ESP without acid treatment would mean the pump continuously fights skin-related pressure drop, wasting energy and reducing achievable rate.
Interactive Tool

Flow Efficiency IPR Simulator

Explore how skin and FE reshape the IPR. The blue curve is the ideal (S=0); the orange curve is the pre-acid IPR; the green curve is the post-acid IPR.

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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 Standing's flow-efficiency IPR: C01_M04_T3 — Standing FE Topic theory page
Watch Lecture 4.3D — Reading the Standing FE Chart: Field Walkthrough Produced lecture
Self-check ../../courses/c01/production/m04/topic-4-3-standing-fe/file-pack/standing_fe.py verified calculator — reproduce your numbers
Knowledge Check

SP-2 · 5 Questions

Standing's Flow Efficiency — Knowledge Check

1. KA-07 has S' = +8. Using FE = 7/(7+S), what is FEpre?
Correct — C: 0.467. FEpre = 7/(7+8) = 7/15 = 0.4667. This means the damaged KA-07 is operating at only 46.7% of its undamaged potential. Each psi of drawdown delivers less than half the rate it should. The other 53.3% of potential is being wasted as skin pressure drop in the near-wellbore damage zone — a zone that can be removed by the matrix acid job.
2. After acidising to S = +1, FEpost = 7/8 = 0.875, giving Jactual,post = 0.72 × 0.875 = 0.630 stb/d/psi. What is qb,post at the bubble point (p̄ − pb = 600 psi)?
Correct — A: 378 stb/d. qb,post = Jactual,post × (p̄ − pb) = 0.630 × 600 = 378 stb/d. Compare with the pre-acid qb,pre = 0.336 × 600 = 201.6 stb/d — a 76% increase just at the bubble-point anchor rate. The improvement propagates through the entire Vogel segment below pb.
3. In Standing's modified Vogel, why is the corrected effective pressure p'wf/pb = 1 − FE×(1 − pwf/pb) used instead of the raw pwf/pb?
Correct — C. Skin damage (S > 0) creates an additional pressure drop ΔPskin in the near-wellbore region. This pressure is lost to friction through the damage zone — it is not available to drive Vogel-type two-phase flow from the reservoir. The effective p'wf is higher than the actual BHFP because skin has already "consumed" some of the potential drawdown. When FE < 1 (damaged), p'wf/pb is higher, reducing the Vogel factor, and therefore reducing the deliverable rate.
4. The production uplift from the KA-07 acid job at BHFP = 2,000 psia is Δq ≈ 911 stb/d and the acid costs $450K. At netback $58/stb, what is the simple payback period?
Correct — A: ~8.5 days. Daily uplift = 911 × $58 = $52,838/d. Payback = $450,000 / $52,838 = 8.52 days. This is an exceptional economic case. For reference, production engineers typically sanction stimulation with payback <90 days as "excellent"; <180 days as "good". At 8.5 days, this acid job is essentially free money — the only risk is that the achieved skin is worse than S = +1 (say S = +4 instead of +1), which would still give a payback under 20 days.
5. What is the best sequencing recommendation for KA-07 — acid then ESP, or ESP then acid?
Correct — A: Acid first. With an 8.5-day payback, there is essentially no economic argument for deferring the acid job. Additionally, if the ESP is installed first against a skin of +8, the pump must deliver far more head to achieve the same BHFP — meaning a larger, more expensive pump is required. After acid, skin drops to +1 and the ESP specification can be based on a much improved IPR, reducing both capital cost and energy consumption over the well's life. The correct sequence is: acid → ESP Stage 1 → ESP upgrade as reservoir depletes (SP-5).
SP-2 Output

Record Before Moving to SP-3

SP-2 Key Outputs — KA-07 Stimulation Analysis

FE pre-acid (S = +8): 0.467  ·  Jactual,pre = 0.336 stb/d/psi

FE post-acid (S = +1): 0.875  ·  Jactual,post = 0.630 stb/d/psi

q pre-acid at BHFP = 2,000 psia: 548 stb/d

q post-acid at BHFP = 2,000 psia: 1,459 stb/d

Δq from acid job: +911 stb/d  ·  Daily revenue uplift: $52,838/d

Simple payback on $450K acid job: 8.5 days — SANCTION IMMEDIATELY

Recommendation: Acid first → then ESP Stage 1 targeting BHFP = 2,000 psia

→ Carry Jactual,post = 0.630 stb/d/psi and post-acid IPR parameters to SP-5 and SP-6.