Two wells in the same field, both with J = 2.0 STB/day/psi, are not equally productive if one drains 200 ft of pay and the other only 50 ft. The Specific Productivity Index normalises J by net pay thickness to reveal true reservoir quality, enabling honest well-to-well comparison, drilling decisions, and completion design.
▶
Lecture 2.3: The Specific Productivity Index — Normalisation, Comparison, and Field Development Application
14:20
Derives SPI from J and net pay thickness, shows why raw J comparisons across wells with different h are misleading, demonstrates SPI-based well ranking on a five-well Karama Field dataset, works through partial perforation correction, and applies SPI to predict J for an undrilled location. Includes a live field analogy from a North Sea chalk programme where SPI successfully identified a sweet spot missed by J alone.
In Topic 2.2 you mastered the Productivity Index J, the slope of the IPR straight line. J is a complete, measurable well performance descriptor and it drives rate prediction, artificial lift timing, and stimulation screening. But J has one limitation that becomes critical the moment you try to compare two wells with different reservoir thicknesses: J is not thickness-normalised.
Consider two Karama Field wells drilled into the same reservoir: KRM-3 has h = 130 ft and J = 1.75 STB/day/psi; KRM-4 has h = 95 ft and J = 0.60 STB/day/psi. Which well has better reservoir quality? You cannot tell from J alone. KRM-3’s higher J could be entirely explained by its extra 35 ft of pay, or it could reflect genuinely superior permeability. The Specific Productivity Index J/h (also written Js or SPI) divides J by net pay to extract the permeability signal and reveal which well is truly in the better rock.
SPI is the primary metric used in field development planning to map reservoir quality across a field, rank new drill locations, evaluate the effectiveness of individual completions, and design multi-zone commingled producers. This topic derives SPI from the radial inflow equation, explains when it is and is not a valid comparison tool, and works through the key field applications.
LEARNING OBJECTIVES
After completing this topic, you will be able to:
1. Define the Specific Productivity Index (SPI) as J/h and state its units (STB/day/psi/ft). 2. Derive SPI from the PSS radial inflow equation and identify which variables it isolates vs which it still conflates. 3. Explain why comparing raw J values between wells of different pay thickness is misleading, and how SPI corrects this. 4. Demonstrate three situations where SPI remains misleading despite the h-normalisation (varying μ, varying S, varying geometry). 5. Calculate SPI from well test data (J and h) and from reservoir parameters (k, μ, B). 6. Apply SPI to rank wells in a field, identify outliers indicating damage or naturally superior permeability, and predict J for undrilled locations given estimated h. 7. Use SPI with a partial perforation correction to assess how much productivity is being sacrificed by perforating only a fraction of the available pay. 8. Interpret SPI on a field map to identify permeability sweet spots and guide well placement recommendations.
PREREQUISITE
Topics 2.1 and 2.2 are direct prerequisites. SPI is defined as J/h, so fluency with J, the PSS radial inflow equation, and skin S is assumed throughout. Topic 2.2 Flow Efficiency (FE) is also referenced, make sure you can calculate FE from J_ideal and J_measured before proceeding.
PBL CONNECTION — KRM-4 PROBLEM SET
Sub-Problem 3 of the Karama Field KRM-4 problem set extends the PI analysis from Sub-Problem 2 by asking you to: (a) calculate SPI for all five KRM wells and rank them; (b) identify which wells have anomalously low SPI (damage) vs anomalously high SPI (superior reservoir quality or stimulation); (c) use the SPI trend across the field to predict J for a proposed sixth well KRM-6 at a location where net pay is estimated at 115 ft from seismic. This topic provides all the tools needed.
Section 1 of 7
Defining the Specific Productivity Index
SPI emerges naturally when you divide both sides of J by net pay thickness h, collapsing rock, fluid, and geometry terms into a single thickness-independent descriptor of reservoir quality.
1.1 Deriving SPI from the Radial Inflow Equation
Start from the Productivity Index derived in Topic 2.2:
J = 0.00708 · k · h / [μ · B · (ln(rₑ/rₗ) − 0.75 + S)]
Dividing both sides by net pay thickness h:
SPECIFIC PRODUCTIVITY INDEX DEFINITION
SPI = J / h = 0.00708 · k / [μ · B · (ln(rₑ/rₗ) − 0.75 + S)]SPI = Specific Productivity Index (STB/day/psi/ft)
J = Productivity Index from well test or calculation (STB/day/psi)
h = net pay thickness perforated and contributing to flow (ft)
k = effective permeability to oil at reservoir conditions (mD)
μ = oil viscosity at reservoir conditions (cp)
B_o = oil formation volume factor (RB/STB)
ln(rₑ/rₗ) = natural log of drainage-to-wellbore radius ratio (dimensionless)
S = skin factor (dimensionless; includes damage and stimulation)
Also expressed from measurements as:
SPI = J / h = Q / [h · (P̄ − Pwf)]Measurement form. Requires stabilised Q, known P̄, measured P_wf, and measured or estimated h (from petrophysical log interpretation).
1.2 Physical Meaning of SPI
SPI is the additional STB/day produced per foot of net pay for every additional psi of drawdown. Whereas J measures total well deliverability (which increases with more pay even if rock quality is identical), SPI isolates the quality of the rock itself, specifically, how efficiently each foot of pay contributes to production.
A high-SPI well is in genuinely good rock: high permeability, low viscosity oil, or both. A low-SPI well, even one with a high absolute J from a thick formation, may have inferior rock that will disappoint when production from a thinner zone is attempted. Conversely, a well with low J but high SPI is sitting in excellent rock but has limited pay thickness; additional perforations or wellbore deepening could dramatically improve it.
High SPI
High k, low μ, low S per foot of pay. Every foot of perforated zone is working hard. Drilling more wells in this zone, or perforating additional pay, will deliver strong returns.
Moderate SPI
Typical production from moderate-quality reservoir. SPI is the expected value for this rock type and fluid system. Damage is not excessive. Good baseline for comparison.
Low SPI
Suggests either poor rock, high viscosity, or significant damage relative to the field average. Warrants investigation before committing to additional wells in this area or zone.
1.3 Units and Typical Values
SPI is measured in STB/day/psi/ft (oilfield units). In SI units it would be m³/(s·Pa·m). The range of SPI values in practice spans several orders of magnitude:
Reservoir Type
k (mD)
μ (cp)
Typical SPI (STB/d/psi/ft)
Notes
Tight chalk (Ekofisk)
1–10
0.5–1.0
0.003–0.02
Fracturing critical
Moderate chalk (Valhall)
5–30
0.5–1.0
0.01–0.06
Compaction-assisted
N. Sea sandstone (Brent)
50–500
0.5–1.5
0.05–0.3
Good producers
GoM turbidite
200–2000
0.3–1.0
0.2–2.0
Excellent reservoirs
Karama Field (KRM avg)
18
1.4
0.008–0.015
Moderate chalk
Heavy oil sandstone
500–5000
50–500
0.002–0.04
Viscosity dominates
1.4 SPI vs J — What Each Tells You
J and SPI convey different and complementary information. A completions engineer needs both:
J tells you…
The total deliverability of this well right now, at its current h, k, S, and fluid properties. Use J to predict actual production rates, set artificial lift timing, and calculate AOFP. J is what the well does.
SPI tells you…
The quality of the reservoir rock per unit thickness at this location, adjusted for fluid and geometry. Use SPI to compare wells, predict J at new locations, and identify whether a well is underperforming its rock. SPI is what the rock is.
Key relationship: J = SPI × h. To improve J, you can either improve SPI (by stimulation, which reduces S and effectively raises the numerator k by restoring near-wellbore kdamaged → kreservoir) or increase effective h (by perforating additional pay, opening new zones, or drilling a longer wellbore). SPI tells you which lever is stronger for a given well.
1.5 Worked Derivation — Calculating SPI for KRM-4
WORKED EXAMPLE 1SPI Calculation — KRM-4 Measured and Theoretical
Well data: k = 18 mD, h = 95 ft, μ = 1.4 cp, Bo = 1.25 RB/STB, re/rw = 3,729, S = +5 (from well test interpretation), Jmeasured = 0.60 STB/day/psi.
Interpretation: The rock SPI of 0.00974 is good for a chalk reservoir. The operational SPI of 0.00632 reflects damage. Acid stimulation targeting S → 0 would recover the full 0.00974 SPI and produce J = 0.926 STB/day/psi.
In SI units, SPI = k / [μ · denom_factor] in m³/(Pa·s·m). The oilfield SPI in STB/day/psi/ft converts to SI via:
SPI_SI = SPI_oilfield × 6.328 × 10⁻³ m³/(Pa·s·m)
In practice, SPIs are always reported in STB/day/psi/ft within oilfield operations. The dimensionless normalisation means that SPI comparisons between wells are scale-invariant, a Brent sandstone SPI of 0.15 STB/d/psi/ft at 200 mD is directly comparable to a chalk SPI of 0.01 STB/d/psi/ft at 15 mD, confirming the sandstone has 15× better reservoir quality per unit thickness.
Section 2 of 7
Why SPI? The Problem with Comparing Raw J Values
Comparing J across wells with different pay thicknesses gives misleading rankings. SPI removes the pay-thickness effect, but three important confounders remain that the engineer must account for.
2.1 The Pay-Thickness Confound — A Critical Illustration
Suppose a field development team ranks three wells by their measured J values:
Figure 2.3.1 — J Ranking vs SPI Ranking: Very Different Stories
This example illustrates why SPI is essential for field development decisions. Well A looks like the best producer (highest J), but it only achieves that rate because it has five times more pay. Per unit of reservoir, Wells B and C are in equal and superior rock. If the field team were planning where to drill the next well, using J rankings would steer them toward the Well A area (thick, mediocre rock) and away from the Well B/C area (thin but excellent rock). The SPI ranking correctly identifies the best reservoir quality zone.
2.2 Three Situations Where SPI is Still Misleading
SPI corrects the pay-thickness confound, but three other systematic differences between wells can still make raw SPI comparisons misleading:
1
Different fluid viscosities (μ): SPI = 0.00708k / [μ·B·denom]. If Well A has light oil (μ = 0.8 cp) and Well B has heavier oil (μ = 3.2 cp), a 4× viscosity difference will produce a 4× SPI difference even if both wells have identical k. To compare rock quality fairly, both wells must be producing from the same or similar fluid. In commingled multi-zone fields where fluid properties vary by zone, a viscosity correction should be applied before SPI comparison. The viscosity-corrected SPI is: SPI×μ×B = 0.00708k/denom, which is purely a function of k and geometry.
2
Different skin factors (S): SPI includes skin in its denominator. A damaged well (high S) will have a low SPI even if the rock is excellent. An acid-stimulated well (low or negative S) will have a high SPI even if the rock is only average. When SPI is used for reservoir characterisation (mapping k across the field), it must be corrected to S=0 by computing the ideal SPI: SPIideal = Jideal/h = 0.00708k/[μ·B·(ln(re/rw)−0.75)]. This requires knowing k and S separately from a well test interpretation, not just the measured J.
3
Different drainage geometry (re/rw, well spacing): The denominator ln(re/rw)−0.75 changes if wells are on different spacing patterns. A well on 160-acre spacing (re ≈ 1,490 ft) has a different geometry factor than one on 40-acre spacing (re ≈ 745 ft). The difference is small (ln(1490/0.35)−0.75 = 7.96 vs ln(745/0.35)−0.75 = 7.27, only 10%) but should be noted in frontier-field comparisons where spacing patterns vary substantially.
Best practice: When using SPI to compare reservoir quality across a field, always first check: (1) Are μ and B similar for all wells being compared? (2) Has skin been accounted for, are you using measured J or ideal J? (3) Are drainage radii approximately equal? If any of these differ substantially, apply corrections before drawing conclusions about which area has the best rock quality.
2.3 The SPI Diagnostic Chart — J vs h Cross-Plot
A powerful field tool is the J vs h cross-plot: plot J on the y-axis and h on the x-axis for all wells. Lines of constant SPI are straight lines through the origin with slope SPI. Wells on the same SPI line have the same reservoir quality. Wells above a reference SPI line are in better-than-average rock (or less damaged). Wells below the line are in poorer rock or are more severely damaged.
Figure 2.3.2 — J vs h Cross-Plot: Identifying Reservoir Quality Zones
On this cross-plot, KRM-3 plots above the average SPI line (superior reservoir quality or negative skin), while KRM-2 and KRM-5 both plot well below the line (damaged or poor reservoir). KRM-4 also plots below the line, consistent with its measured skin S≈+5. This chart immediately identifies where stimulation will be most effective (below-the-line wells with nearby above-the-line wells in the same reservoir unit) and where the best drilling targets are (areas where the few wells drilled plot well above the average SPI line).
Section 3 of 7
SPI Analysis for Vertical Wells — Field Ranking and Prediction
With a field dataset of J and h measurements from multiple wells, SPI analysis enables systematic ranking, outlier identification, and forward prediction of J for undrilled locations.
▶
Case Study: SPI-Based Well Ranking and New Well J Prediction — Karama Field
10:45
Works through the complete KRM field dataset (KRM-1 through KRM-5), calculates SPI for each well, constructs the J vs h cross-plot, identifies damaged and naturally high-quality wells, applies the SPI trend to predict J for proposed KRM-6 location (h = 115 ft from seismic), and discusses the uncertainty range on that prediction.
3.1 Step-by-Step SPI Field Ranking Procedure
1
Collect data for each well: Jmeasured from well test (two-rate PI test or single-point), h from petrophysical log interpretation (net pay criterion: porosity > φcutoff, Vsh < Vsh,cutoff, Sw < Sw,cutoff). Apply consistent petrophysical cutoffs across all wells.
2
Calculate SPI for each well: SPI = J/h. If J is measured at conditions including damage, this is the operational SPI. If you want to compare rock quality (reservoir-characterisation SPI), also compute Jideal/h using S=0 with reservoir parameters from well test analysis.
3
Calculate field-average SPI: Weight by h (or take the arithmetic mean of SPI values). Identify wells more than one standard deviation above (potential sweet spot, or negative skin) and below (damage or poor rock).
4
Investigate outliers: For wells with anomalously low SPI, check skin from well test analysis. If skin is high, stimulation will recover performance. If skin is near zero but SPI is still low, the rock itself is inferior at that location. For wells with anomalously high SPI, check for natural fractures, superior depositional quality, or stimulation (negative skin).
5
Predict J for new wells: Given a seismic-derived h estimate at an undrilled location, apply the field-average SPI (or a location-specific SPI from kriged reservoir quality maps) to predict J_predicted = SPI_avg × h_seismic. Apply uncertainty bounds reflecting the spread in SPI observed across existing wells.
3.2 Karama Field Full SPI Analysis — Worked Example
WORKED EXAMPLE 2KRM Field — Full SPI Ranking and KRM-6 Prediction
All five wells produce single-phase oil. μ = 1.4 cp, B = 1.25 RB/STB, re/rw ratio similar for all wells (ln(re/rw) ≈ 8.22).
Well
h (ft)
k (mD)
S (from test)
J_measured (STB/d/psi)
SPI_measured = J/h
J_ideal (S=0)
SPI_ideal
FE
KRM-1
110
22
+2
1.18
0.01073
1.35
0.01227
0.87
KRM-2
95
18
+14
0.41
0.00432
0.926
0.00975
0.44
KRM-3
130
25
−1
1.75
0.01346
1.68
0.01292
1.04
KRM-4
95
18
+5
0.60
0.00632
0.926
0.00975
0.65
KRM-5
75
12
+9
0.18
0.00240
0.575
0.00767
0.31
Field average SPI (ideal, unweighted) = (0.01227+0.00975+0.01292+0.00975+0.00767)/5 = 0.01047 STB/d/psi/ft
SPI Ranking by rock quality (SPI_ideal):
1st: KRM-3 SPI=0.01292 (best rock; k=25 mD, slight − skin)
2nd: KRM-1 SPI=0.01227 (good rock; k=22 mD, minor damage S=+2)
3rd: KRM-4 SPI=0.00975 (average rock; k=18 mD, field norm)
= KRM-2 SPI=0.00975 (same reservoir quality as KRM-4; S=+14 is damage not rock)
5th: KRM-5 SPI=0.00767 (below average rock; k=12 mD, structurally lower?)
SPI Ranking by measured performance (SPI_measured), includes damage effect:
1st: KRM-3 SPI=0.01346 (best performer — marginal stimulation + best rock)
2nd: KRM-1 SPI=0.01073 (good performer — mild damage)
3rd: KRM-4 SPI=0.00632 (moderate damage dragging it below avg)
4th: KRM-2 SPI=0.00432 (heavy damage — same rock as KRM-4 but S=+14)
5th: KRM-5 SPI=0.00240 (worst performer: poor rock + heavy damage)
KRM-2 insight: Measured SPI makes KRM-2 look like poor rock.
Ideal SPI reveals it has IDENTICAL rock quality to KRM-4 (SPI_ideal = 0.00975).
All of KRM-2's underperformance is damage (S=+14). Acid stimulation should recover it.
KRM-5 insight: Even at ideal (S=0), SPI_ideal=0.00767 is below field average.
This suggests genuinely inferior rock at the KRM-5 location (k=12 mD vs 18 mD avg).
Stimulation will help but cannot make KRM-5 equal to KRM-3 or KRM-4.
KRM-6 PREDICTION (h_seismic = 115 ft from interpretation):
Using field-average SPI_ideal = 0.01047 STB/d/psi/ft:
J_predicted = SPI_avg × h = 0.01047 × 115 = 1.204 STB/d/psi
P10 (using 1-sigma low SPI = 0.00767): J_P10 = 0.00767 × 115 = 0.882 STB/d/psi
P90 (using 1-sigma high SPI = 0.01292): J_P90 = 0.01292 × 115 = 1.486 STB/d/psi
Expected plateau rate at P_wf=3,100 psia (P̄=4,850 psia):
Q_expected = 1.204 × (4,850−3,100) = 1.204 × 1,750 = 2,107 STB/day
Q_P10 = 0.882 × 1,750 = 1,544 STB/day
Q_P90 = 1.486 × 1,750 = 2,601 STB/day
Drilling recommendation: KRM-6 at the proposed location is expected to produce 1,544–2,601 STB/day, well above the 1,200 STB/day field production target. The SPI analysis supports drilling KRM-6, with the observation that seismic h uncertainty (±15 ft) is the dominant source of J prediction uncertainty, not SPI itself.
3.3 The SPI-Based Stimulation Priority Matrix
Combining SPI analysis with Flow Efficiency creates a two-axis decision matrix that simultaneously ranks stimulation candidates by both magnitude of potential gain and confidence that the gain is achievable:
Well
SPI_ideal (rock quality)
FE (damage fraction)
Stimulation Value
Action
KRM-2
0.00975 (avg)
0.44 (severe damage)
Very High — same rock as KRM-4 but half the performance
Priority 1: Acid stimulate immediately
KRM-5
0.00767 (below avg)
0.31 (very severe damage)
High — but rock ceiling is lower than KRM-2
Priority 2: Acid stimulate; manage expectations
KRM-4
0.00975 (avg)
0.65 (moderate damage)
Moderate — addressed in problem set
Priority 3: Acid stimulate when KRM-2 complete
KRM-1
0.01227 (above avg)
0.87 (mild damage)
Low — near-undamaged already
Monitor; consider light acid wash
KRM-3
0.01292 (best rock)
1.04 (slightly stimulated)
None — already outperforming
Model well; target nearby locations
Section 4 of 7
Partial Perforation, Net Pay Selection, and SPI Corrections
The h in SPI must be the pay thickness actually contributing to flow, not the gross reservoir interval. Partial perforation, multi-zone completions, and pay cut-off selection all affect how h is defined and measured, and incorrect h gives a meaningless SPI.
4.1 What h Means in SPI — A Precise Definition
Net pay h is not simply the gross reservoir interval. It is the thickness of reservoir rock that meets specific petrophysical quality criteria AND is perforated and contributing to production. Three h concepts must be kept distinct:
Gross Reservoir (H)
Total reservoir interval from top to base, including poor-quality rock, shales, and tight streaks. H is read from the well trajectory between reservoir top and base picks.
Net Pay (h)
Subset of H meeting petrophysical cut-offs for porosity (φ), shale volume (Vsh), and water saturation (Sw). Net-to-gross NTG = h/H. This is the h in the Darcy radial inflow equation.
Perforated Pay (hperf)
The subset of net pay that has been perforated. If only 60% of net pay is shot, hperf = 0.6h. The effective producing interval is hperf, not h. Using h instead of hperf under-estimates SPI.
Common error: Engineers sometimes use gross reservoir thickness H (e.g., from a formation tops report) instead of net pay h in SPI calculations. In a reservoir with NTG = 0.7, this gives SPI values that are 30% too low. Always use the net pay h from petrophysical interpretation, with clearly documented cut-off criteria, for SPI calculation.
4.2 Partial Perforation Effect on J and SPI
When only a fraction of the net pay is perforated, two things happen: (1) the directly contributing thickness is reduced (fewer STB/day per psi), and (2) there is an additional skin-like effect called partial penetration skin Spp arising from the 3D convergence of flow from the unperforation intervals into the perforated zone. This is treated in more depth in Topic 3.1 (Skin Components); here we focus on the SPI implications.
The simplest approximation for the effect of partial perforation on J is:
Jpartial ≈ (hperf/h) × Jfull × CFh_perf = perforated interval (ft) | h = total net pay (ft) | J_full = J if entire net pay were perforated
CF = correction factor for 3D flow geometry convergence (CF < 1.0; typically 0.75–0.95 for partial perforations spanning >50% of pay; requires Cinco-Ley or Saidikowski correlation for more accuracy)
The SPI calculated from a partial perforation therefore under-estimates the true reservoir SPI. To get the correct SPI for reservoir characterisation, you must either: (a) perforate the full net pay and measure Jfull, or (b) correct Jpartial using the partial penetration factor before dividing by total h.
WORKED EXAMPLE 3Partial Perforation Correction — KRM-2 Completion Assessment
Context: KRM-2 has total net pay h = 95 ft (same reservoir quality as KRM-4). The original completion perforated only the top 55 ft (hperf = 55 ft, covering intervals of known better quality). Measured J from a well test = 0.41 STB/day/psi. CF = 0.88 (estimated from partial penetration correlation for hperf/h = 0.58).
Step 1: SPI calculated naively using h_perf:
SPI_naive = J / h_perf = 0.41 / 55 = 0.00745 STB/d/psi/ft
Step 2: SPI if we mistakenly used total h:
SPI_wrong = J / h = 0.41 / 95 = 0.00432 STB/d/psi/ft (too low — will appear as poor rock)
Step 3: Correct SPI for reservoir characterisation (must back out partial perforation effect):
J_full_estimate = J_partial / [(h_perf/h) × CF]
J_full_estimate = 0.41 / [(55/95) × 0.88]
J_full_estimate = 0.41 / [0.5789 × 0.88]
J_full_estimate = 0.41 / 0.5094 = 0.805 STB/d/psi (estimated J if 95 ft were perforated)
SPI_corrected = 0.805 / 95 = 0.008474 STB/d/psi/ft
Step 4: Predict J gain from perforating the remaining 40 ft:
J_additional = SPI_corrected × 40 = 0.008474 × 40 = 0.339 STB/d/psi
J_after_full_perf = J_partial + J_additional = 0.41 + 0.339 = 0.749 STB/d/psi
Rate gain at P_wf=3,100 psia: ΔQ = 0.339 × 1,750 = 593 STB/day additional
Recommendation: Perforate the remaining 40 ft of pay. Even with the partial perforation skin correction, the expected J gain of 0.339 STB/d/psi represents an additional 593 STB/day — substantial incremental production at minimal cost (reperforating vs drilling a new well).
4.3 Multi-Zone Commingled Wells — Additive J and SPI
When a well produces from multiple reservoir zones simultaneously (commingled production), the total well J is approximately the sum of the individual zone Js (assuming no cross-flow and similar P̄ in each zone):
Jtotal = Jzone1 + Jzone2 + … + JzoneN = Σ (SPIi × hi)Each zone contributes its own J_i = SPI_i × h_i to the total well deliverability.
SPI for each zone may differ if reservoir quality (k) differs by zone.
This additive property is used to design multi-zone completions: rank zones by SPI, perforate highest-SPI zones first, and compute expected total J before committing to completion design.
WORKED EXAMPLE 4Multi-Zone Completion Design — Additive SPI (Hypothetical Layered Well)
Note: This is a hypothetical completion-design exercise to illustrate additive SPI, not the KRM-6 forecast. The KRM-6 deliverability prediction is the single-interval estimate in Worked Example 2 (JP50 = 1.204 STB/d/psi at h = 115 ft). Here, consider an illustrative layered well that intersects three distinct reservoir zones (all zones: μ=1.4 cp, B=1.25 RB/STB, re/rw=3,729):
Zone
h (ft)
k (mD)
S (expected)
J_zone (STB/d/psi)
SPI_zone
A (upper)
45
28
+3
0.459
0.01020
B (middle)
35
15
+5
0.236
0.00674
C (lower)
35
8
+8
0.072
0.00206
Option 1 — Perforate all zones (commingled):
J_total = 0.459 + 0.236 + 0.072 = 0.767 STB/d/psi
Q at P_wf=3,100, P̄=4,850: 0.767 × 1,750 = 1,342 STB/day
Option 2 — Perforate Zone A only (high SPI):
J = 0.459 STB/d/psi; Q = 803 STB/day
But SPI analysis shows Zone C (SPI=0.00206) is pulling the completion's average SPI down.
Option 3 — Perforate Zones A and B only (selective):
J = 0.459 + 0.236 = 0.695 STB/d/psi; Q = 1,216 STB/day
Avoids Zone C's mediocre rock; cleaner completion; lower water risk if Zone C is wet.
Decision: Zone C adds only 0.072 STB/d/psi (= 126 STB/day). If Zone C has elevated S_w
risk or requires a separate stimulation treatment, the marginal gain may not justify the
cost. Zones A+B deliver 91% of the all-zone J with simpler completion.
The partial penetration skin Spp arises because flow must converge in 3D from the unperforated portions of the reservoir into the limited perforated interval, creating additional pressure drop beyond what the standard radial flow formula accounts for. Cinco-Ley et al. (1975) provided the most widely used correlation:
KRM-2 example: b = 55/95 = 0.578; h_D = 95/0.354 × sqrt(18/5) = 268 × 1.897 = 509; Spp = (1/0.578 − 1) × (ln(509) − G(0.578)) = 0.730 × (6.232 − 2.35) = 0.730 × 3.882 = 2.83. The partial penetration contributes about +2.8 skin units — significant, and worth evaluating if completion designers are considering reperforating the lower zone.
4.4 Net Pay Definition Consistency — A Critical QC Step
SPI comparisons across a field are only valid if the h values for all wells are computed using identical petrophysical cut-off criteria. If one well’s h was computed using φ > 8% and another using φ > 12%, their SPIs cannot be compared. This is a common but avoidable error in multi-well field studies. Best practice is to apply a common cut-off suite (φcut, Vsh,cut, Sw,cut) to all wells before computing SPI rankings.
Petrophysical Cut-off
Typical Value (Chalk)
Effect of Tightening
Effect of Loosening
Porosity φcut
φ > 10–15%
h decreases → SPI increases (fewer poor-quality ft in h)
h increases → SPI decreases (diluted by poorer rock)
Shale volume Vsh,cut
Vsh < 0.30–0.50
h decreases (excludes shaly intervals)
h increases (includes shaly intervals)
Water saturation Sw,cut
Sw < 0.60–0.75
h decreases (excludes wet zones)
h increases (includes wet zones)
Section 5 of 7
Field Applications of SPI
SPI is the bridge between petrophysical log analysis and production engineering. This section covers four high-value field applications: reservoir quality mapping, completion optimisation, drainage efficiency analysis, and field development planning under uncertainty.
5.1 Reservoir Quality Mapping with SPI
When SPIideal (skin-corrected) is plotted spatially for each well in a field, it creates a reservoir quality map. Because SPIideal = 0.00708k/[μ·B·(ln(re/rw)−0.75)], and μ, B, and geometry are approximately constant across a field, this map is essentially a permeability map expressed in production engineering terms. High-SPI areas correspond to sweet spots, zones of elevated permeability driven by better depositional quality, diagenetic preservation, or natural fracturing.
Figure 2.3.3 — Schematic SPI Map of Karama Field: Identifying the Sweet Spot
On the Karama Field SPI map, the sweet spot (SPIideal > 0.013) is centred on the KRM-3 well location. The proposed KRM-6 location falls within the 0.011–0.013 SPI contour, supporting a J prediction above the field average. KRM-2 and KRM-5 fall in areas of lower rock quality, confirming that even after successful stimulation they will not match KRM-3’s performance.
5.2 Completion Efficiency — Measuring What Fraction of Reservoir Potential is Captured
A complementary metric derived from SPI is the Completion Efficiency (CE): the ratio of achieved J to the theoretically achievable J if the entire net pay were perforated at ideal (zero skin) conditions:
CE = Jmeasured / Jmax = (SPImeasured × hperf) / (SPIideal × h)CE = 1.0: perfect — entire pay is perforated, zero skin.
CE < 1.0: losses from partial perforation AND/OR damage AND/OR poor rock selection.
CE can be decomposed: CE = (h_perf/h) × FE × CF_pp (perforation fraction × Flow Efficiency × partial penetration correction)
WORKED EXAMPLE 5KRM-4 Completion Efficiency Decomposition
KRM-4: h = 95 ft total, hperf = 95 ft (fully perforated), S = +5 (damage only, no partial perf skin), Jmeasured = 0.60, Jideal = 0.926.
CE (simple) = J_measured / J_ideal = 0.60 / 0.926 = 0.648
Decomposition:
Perforation fraction = h_perf / h = 95/95 = 1.00 (fully perforated, no loss here)
Flow Efficiency FE = J_measured / J_ideal(S=0) = 0.60 / 0.926 = 0.648
Partial penetration correction CF = 1.00 (fully perforated)
CE = 1.00 × 0.648 × 1.00 = 0.648
Interpretation: KRM-4's 35.2% performance loss relative to maximum is ENTIRELY
due to formation damage (skin S=+5). The completion interval selection is fine.
Remedy: acid stimulate to restore skin S → 0, recovering CE → 1.0.
Expected J after stimulation: 0.926 STB/d/psi.
Expected rate gain at P_wf=3,100: +571 STB/day.
Compare KRM-2 (partial perf AND heavy damage):
h_perf = 55 ft, h = 95 ft, S = +14, J_measured = 0.41
J_ideal_full_pay = 0.926 STB/d/psi (same reservoir quality as KRM-4)
CE = 0.41/0.926 = 0.443
Decomposed: perf fraction = 55/95 = 0.579; FE_at_perf_zone = 0.44; CF ≈ 0.88
CE ≈ 0.579 × 0.44 × 0.88 ≈ 0.224 [note: multiplicative factors give rough estimate]
3 sources of loss: partial perf + heavy damage + 3D convergence penalty
5.3 Using SPI Under Reservoir Uncertainty
In early field development, before any well is drilled, SPI predictions depend on analogues. The pre-drill workflow:
1
Select analogue field(s): Similar depositional setting, same formation, comparable burial depth and diagenesis. Collect all published SPI or kh/h values from analogue wells.
2
Build an SPI distribution: P10/P50/P90 SPI from analogue data. For a chalk field analogous to Karama: P10 = 0.007, P50 = 0.010, P90 = 0.014 STB/d/psi/ft.
3
Estimate h from seismic: Apply formation thickness maps from seismic horizon interpretation. Include uncertainty (± 10–20 ft typical).
4
Generate J distribution: J = SPI × h. Monte Carlo sampling of SPI and h distributions gives a J probability distribution that feeds directly into economics and project sanctioning.
5
Update with first well data: After drilling and testing the first well, its SPI measurement collapses the analogue uncertainty. Use it to update the SPI distribution for all subsequent wells in the same reservoir unit.
FIELD CASENorth Sea Chalk Development — SPI as a J Predictor
In the development planning of a North Sea chalk field, seismic interpretation provided h estimates of 80–180 ft across six proposed well locations. Analogue SPI from the Ekofisk and Valhall fields gave P50 SPI = 0.012 STB/d/psi/ft. Predicted J range: 0.96–2.16 STB/d/psi (P50). The four wells drilled in Years 1–2 measured actual SPIs of 0.010, 0.013, 0.009, and 0.015 — all within 25% of the P50 analogue. This validated the SPI approach and narrowed the J prediction uncertainty for the remaining two well locations from ±56% (pre-drill) to ±18% (using field-calibrated SPI). The ±18% residual uncertainty was attributed entirely to seismic h estimation error, not reservoir quality variability.
Section 6 of 7 — Interactive
Interactive Simulators — SPI Analysis
Three tools: (1) an SPI Calculator that computes ideal and measured SPI from well parameters; (2) a Five-Well Field Ranking tool that reproduces the KRM cross-plot and ranks wells dynamically; (3) a New Well J Predictor using the field SPI trend. Use these before tackling Sub-Problem 3 of the KRM-4 problem set.
Simulator 1 — SPI Calculator (Theoretical and Measured) INTERACTIVE
Initialising…
Engineering experiments:
• Set k=18, h=95 (KRM-4 baseline) — observe SPI_ideal vs SPI_measured at S=+5
• Reduce S from +5 to 0 — SPI_measured rises to SPI_ideal (stimulation recovery)
• Double k from 18 to 36 mD — SPI doubles (linear proportionality)
• Increase μ from 1.4 to 7 cp (5×) — SPI drops by exactly 5× (confirming μ in denominator)
• Increase h while keeping k constant — J increases but SPI is UNCHANGED (the point of normalisation)
Simulator 2 — Five-Well Field SPI Ranking and J vs h Cross-Plot INTERACTIVE
Enter measured J and h for each well. Simulator computes SPI, ranks wells, and plots the J vs h cross-plot with SPI lines.
Initialising…
Try raising KRM-2's J slider to 0.90 (simulating a successful acid job) — observe KRM-2 jumping up to KRM-4's SPI level on the cross-plot, confirming identical rock quality once damage is removed.
Simulator 3 — New Well J Prediction from SPI Trend INTERACTIVE
Initialising…
Default values are KRM-6 prediction parameters from Worked Example 2. Explore how seismic h uncertainty (the h ± slider) compares to SPI uncertainty as a driver of J prediction risk.
PBL EXERCISE — SUB-PROBLEM 3 PREPARATION
Using Simulator 2, enter the KRM field data as given in Worked Example 2 (h values fixed, J values from your Sub-Problem 2 calculations). Record:
(a) SPI for each KRM well (measured);
(b) the SPI ranking order from #1 to #5;
(c) which wells fall below the field-average SPI line (and therefore have damage or poor rock);
(d) which wells fall above the field-average SPI line.
Then use Simulator 3 with hKRM-6 = 115 ft and your computed field-average SPI to predict JKRM-6 and the expected production rate range. These are the answers to Sub-Problem 3 parts (a) through (d).
Assessment — Section 7 of 7
Knowledge Check — Topic 2.3
Ten questions at problem-set difficulty. Covers SPI definition, calculation, field ranking, partial perforation correction, limitations, and new-well prediction. Full worked explanations provided for all questions.
1. Well A has J = 2.4 STB/day/psi and h = 160 ft. Well B has J = 1.1 STB/day/psi and h = 60 ft. Which well has the higher Specific Productivity Index (SPI), and what does that imply?
SPI_A = 2.4/160 = 0.0150 STB/d/psi/ft. SPI_B = 1.1/60 = 0.0183 STB/d/psi/ft. Well B has a higher SPI — meaning each foot of its reservoir contributes more productivity than each foot of Well A's reservoir. Well A's higher absolute J comes entirely from having 2.7 times more pay. For drilling decisions (where to drill the next well), the area near Well B has genuinely better reservoir quality per unit thickness. Option C is the common misconception that must be avoided: higher J does not imply higher SPI when h differs between wells.
2. Using the radial inflow equation, write the explicit expression for SPIideal (S=0) and identify which variables it is purely a function of, excluding fluid properties.
SPI = J/h = [0.00708kh/(μB·denom)] / h = 0.00708k/[μB·(ln(r_e/r_w)−0.75)] at S=0. Net pay h cancels out entirely — which is the whole point of the normalisation. What remains is purely a function of k (rock property), μ and B (fluid properties), and the drainage geometry. If μ, B, and geometry are similar across all wells in a field (same fluid, similar spacing), then SPI_ideal reduces to being proportional to k alone. This is why SPI is a proxy for permeability in production engineering terms.
3. A well has SPImeasured = 0.0045 STB/d/psi/ft and SPIideal (S=0) = 0.0120 STB/d/psi/ft. What is the Flow Efficiency and what is implied about the well?
FE = SPI_measured / SPI_ideal = 0.0045 / 0.0120 = 0.375. The well operates at 37.5% of its undamaged potential — 62.5% of productivity is lost to damage. This is a severe damage case (comparable to KRM-5 in the Karama field example). Option C is wrong because FE is derived from the ratio of measured to ideal SPI at the same location — the ideal SPI reflects the rock quality correctly. The measured SPI being low is because of skin S, not rock quality. Stimulation to remove the damage will recover FE toward 1.0 and SPI_measured toward SPI_ideal. A similar calculation on a well with genuinely poor rock would give a low SPI_ideal too, making SPI_measured/SPI_ideal potentially close to 1.0 (little damage, just poor rock) — a very different situation.
4. Four wells in a field have identical reservoir properties (same k, h, μ, B, r_e, r_w) but different skin values. Rank them by SPI from highest to lowest: Well P (S = −3), Well Q (S = 0), Well R (S = +5), Well S (S = +15).
SPI = 0.00708k/[μB(ln(r_e/r_w)−0.75+S)]. As S increases (more damage), the denominator increases and SPI decreases. As S decreases below 0 (stimulation), the denominator decreases and SPI increases. So: P (S=−3) has the smallest denominator (highest SPI); Q (S=0) is the undamaged baseline; R (S=+5) is moderately reduced; S (S=+15) has the largest denominator (lowest SPI). Ranking: P > Q > R > S. This demonstrates that measured SPI (which includes skin) should not be used directly as a rock quality indicator — the skin-corrected SPI_ideal should be used instead.
5. A well has net pay h = 120 ft but only 70 ft is perforated (hperf = 70 ft). The measured J = 0.78 STB/d/psi. A partial penetration correction factor CF = 0.90 applies. What is the estimated J if the full 120 ft were perforated?
J_full = J_partial / [(h_perf/h) × CF] = 0.78 / [(70/120) × 0.90] = 0.78 / [0.5833 × 0.90] = 0.78 / 0.525 = 1.486 ≈ 1.48 STB/d/psi. The additional 50 ft of unperforated pay plus the 3D flow convergence penalty (CF = 0.90) means the well is operating at only 52.5% of its full potential. Perforating the remaining 50 ft would add approximately J_additional ≈ 0.70 STB/d/psi — a substantial gain. This calculation is the basis for reperforating decisions in wells with known bypassed pay.
6. In which situation would comparing raw SPI values across two wells be MOST misleading without additional correction?
SPI = 0.00708k/[μB×denom]. A 5.6× viscosity difference (μ = 0.8 vs 4.5 cp) creates a 5.6× SPI difference even if both wells are in identical rock with identical permeability. Comparing their raw SPIs would incorrectly conclude that the light-oil well has 5.6× better reservoir quality. Options A and B describe conditions where SPI comparisons are valid. Option C (spacing difference) introduces a moderate ln(r_e/r_w) difference — typically 5–10% — which is much less distorting than a 5.6× viscosity difference. Option D is the most misleading scenario.
7. Field data gives five wells with SPI_ideal values (STB/d/psi/ft): 0.0080, 0.0120, 0.0095, 0.0135, 0.0070. A new well at a proposed location has seismic-estimated h = 90 ft. What is the expected J range (P10/P50/P90) using field SPI statistics?
Field SPI statistics: sorted values = 0.0070, 0.0080, 0.0095, 0.0120, 0.0135. Mean (P50) = (0.0070+0.0080+0.0095+0.0120+0.0135)/5 = 0.0500/5 = 0.0100. With 5 data points, the P10 SPI ≈ 0.0072 (below mean by ~1 std dev; std dev ≈ 0.0026) and P90 ≈ 0.0128. J_P50 = 0.0100 × 90 = 0.90. J_P10 = 0.0072 × 90 = 0.65. J_P90 = 0.0128 × 90 = 1.15. Option A is the closest match (P50=1.08 suggests slightly different averaging or weighting; Option C is nearest to the arithmetic mean calculation with P50=0.90). The key point is that SPI-based prediction provides a range — Option D is incorrect; SPI-based J prediction is standard practice and is how new wells are planned before drilling.
8. A well's measured SPI is 0.0060 STB/d/psi/ft. A neighbouring well in the same reservoir unit has SPI_ideal = 0.0115. The measured well has skin S = +7. Using the neighbouring well as a proxy for undamaged SPI, what is the implied Flow Efficiency of the measured well?
FE = SPI_measured / SPI_ideal = 0.0060 / 0.0115 = 0.522 ≈ 0.52. Using the neighbouring well's SPI_ideal as a proxy for the undamaged reservoir quality in this area is standard practice in field studies where not every well has been through a full transient well test with skin separation. An FE of 0.52 confirms significant damage (skin S=+7 is consistent with this FE level — check: with ln(r_e/r_w)≈8.2, FE = (8.2−0.75)/(8.2−0.75+7) = 7.45/14.45 = 0.52. ✓). Stimulation to S=0 would nearly double this well's J and SPI.
9. The petrophysical cut-off for net pay determination is changed from φ > 10% to φ > 15% for a field study. All else equal, what happens to the reported SPI values for all wells?
When the cut-off is tightened (φ threshold increased), lower-porosity intervals are excluded from the net pay count. This reduces h while J (from the well test) remains unchanged. Therefore SPI = J/h increases. This illustrates an important QC issue: SPI comparisons across wells or across studies are only valid if consistent petrophysical cut-offs are used. A field study that uses φ>10% for one set of wells and φ>15% for another will systematically over-estimate SPI for the second group, falsely suggesting better reservoir quality. Option D is wrong: the cut-off changes what we measure as h, not the actual rock permeability. Option B is wrong because while J is indeed measured independently, the h value used in SPI = J/h IS cut-off dependent.
10. A three-zone commingled completion has individual zone SPIs of 0.020, 0.012, and 0.005 STB/d/psi/ft, with net pays of 30, 50, and 60 ft respectively. What is the total well J, and what is the overall effective SPI of this completion?
Zone contributions: J_zone1 = 0.020 × 30 = 0.60; J_zone2 = 0.012 × 50 = 0.60; J_zone3 = 0.005 × 60 = 0.30. J_total = 0.60 + 0.60 + 0.30 = 1.50 STB/d/psi. Total h_total = 30+50+60 = 140 ft. Effective SPI = J_total / h_total = 1.50 / 140 = 0.01071 ≈ 0.0107 STB/d/psi/ft. Option A is correct. Note that Zone 3 (SPI=0.005, 60 ft of pay) contributes only 0.30 STB/d/psi (20% of total J) while representing 43% of the total pay thickness. If Zone 3 carries water risk, excluding it would sacrifice only 20% of J while avoiding a potentially wet completion — the kind of trade-off SPI analysis enables.
TOPIC COMPLETE — NEXT STEPS
You have completed Topic 2.3: Specific Productivity Index. You are ready to proceed to:
Topic 2.4 — Limitations of the Linear PI: Understand exactly when Q = J(P̄−Pwf) breaks down — below the bubble point (Vogel IPR), at high flow rates (non-Darcy effects), and for gas wells — and which replacement models to apply.
KRM-4 Problem Set Sub-Problem 3: Apply SPI analysis to the five KRM wells: calculate and rank SPIs, identify damaged vs genuinely poor rock, and predict J for the proposed KRM-6 well location using the field SPI trend.