Well Productivity Index Calculator

IPR Darcy / Vogel / Fetkovich / Klinkenberg - VLP - Operating point - AOF

IPR CURVE

VLP CURVE

/// productivity index and linear IPR

Productivity Index (PI or J): Ratio of flow rate to drawdown pressure. Valid for oil above bubble point (Darcy linear flow). PI = Q / (Pr - Pwf) [bbl/d/psi or m3/d/bar]. Below bubble point, use Vogel or Fetkovich (Tab 2).

/// reservoir and well data

Static reservoir pressure Pr

bar

Bubble point pressure Pb

bar

Test flowing pressure Pwf_test

bar

Test flow rate Q_test

bbl/d

Water cut WC

GOR (solution)

scf/bbl

Reservoir permeability k

Net pay thickness h

Oil viscosity at reservoir T

Formation volume factor Bo

RB/STB

Drainage radius re

Wellbore radius rw

Skin factor S

Desired Pwf for production

bar

IPR curve (linear above Pb + Vogel below Pb)

/// Vogel and Fetkovich IPR - below bubble point

Vogel (1968): For solution-gas drive reservoirs below Pb. Qo/Qo_max = 1 - 0.2(Pwf/Pr) - 0.8(Pwf/Pr)². More accurate than linear PI below Pb. Fetkovich: Extends Vogel for high-rate wells where turbulence (non-Darcy flow) is significant: Q = C × (Pr² - Pwf²)^n, where n = 0.5-1.0.

Static reservoir pressure Pr

bar

AOF (Qo_max) from test

bbl/d

Desired Pwf

bar

Vogel IPR curve - inflow performance

/// gas well deliverability - Darcy and non-Darcy flow

Gas IPR: Uses pseudo-pressure m(p) or simplified pressure-squared approach. Darcy flow dominates at low rates; turbulence (non-Darcy / high-velocity) becomes significant at high rates. AOF = Absolute Open Flow potential (Pwf = 0 or atmospheric).

Reservoir pressure Pr

bar

Gas specific gravity γg

Reservoir temperature T

°C

Permeability k

Net pay h

Drainage radius re

Wellbore radius rw

Skin factor S

Desired Pwf

bar

Gas well IPR - pressure squared method

/// nodal analysis - IPR vs VLP (tubing performance)

Nodal Analysis: The operating point (natural flow rate) is found at the intersection of the Inflow Performance Relationship (IPR) and the Vertical Lift Performance (VLP / TPC). The VLP curve represents the minimum bottomhole pressure needed to lift a given flow rate to surface.

/// IPR parameters (Vogel model)

Reservoir pressure Pr

bar

AOF (Qmax at Pwf=0)

bbl/d

Bubble point Pb

bar

/// VLP / tubing performance parameters

Tubing head pressure (THP)

bar

Tubing depth (TVD)

Tubing inner diameter

Oil gradient (produced fluid)

bar/m

GOR (producing)

scf/bbl

Water cut

Nodal analysis: IPR (Vogel) vs VLP curves

/// skin factor and formation damage analysis

Skin factor S: Dimensionless measure of additional pressure drop near wellbore. S > 0: damage (drilling fluid, scale, clay); S < 0: stimulation (fracture, acid). Relates to extra pressure drop: ΔP_skin = 0.87 × S × m (m = slope of Horner plot in psi/cycle).

Skin factor S (measured/estimated)

dimensionless

Reservoir pressure Pr

bar

Undamaged PI (J*)

bbl/d/bar

Reservoir permeability k

Net pay h

Wellbore radius rw

Damage zone permeability kd

Damage radius rd

Current flowing Pwf

bar

/// key formulas - well deliverability

Productivity Index (PI): J = Q / (Pr - Pwf) [bbl/d/psi or m3/d/bar]
Darcy IPR: Q = J × (Pr - Pwf) [linear, valid above Pb]
AOF (linear): Qmax = J × Pr [at Pwf = 0]
Darcy steady-state (radial flow):
J_Darcy = 0.00708 × k × h / (μ_o × Bo × (ln(re/rw) - 0.75 + S)) [bbl/d/psi with k in mD, h in ft, viscosity in cP; convert the input thickness from m to ft]
Vogel IPR (1968): Q/Qmax = 1 - 0.2×(Pwf/Pr) - 0.8×(Pwf/Pr)²
Qmax (Vogel AOF at Pwf=0) = Q_test / [1 - 0.2×(Pwf_t/Pr) - 0.8×(Pwf_t/Pr)²]
Composite IPR (Pr > Pb):
- Above Pb: linear Q = J × (Pr - Pwf)
- Below Pb: Q = Qb + (Jb×Pb/1.8) × [1 - 0.2×(Pwf/Pb) - 0.8×(Pwf/Pb)²]
where Qb = J × (Pr - Pb), Jb = J
Fetkovich: Q = C × (Pr² - Pwf²)^n, n = 0.5-1.0
Gas Darcy IPR (simplified):
Q_g = kh × (Pr² - Pwf²) / (1422 × T_R × μ_g × Z × (ln(re/rw) - 0.75 + S)) [Mscf/d]
Skin from Hawkins formula: S = (k/kd - 1) × ln(rd/rw)
Damage ratio DR: DR = J_damaged / J_undamaged = (ln(re/rw) - 0.75) / (ln(re/rw) - 0.75 + S)
Flow efficiency FE: FE = (Pr - Pwf - ΔPskin) / (Pr - Pwf) = 1 - ΔPskin/(Pr-Pwf)
VLP / Gradient: Pwf_min = THP + gradient × depth + friction_loss
Operating point: Intersection of Q_IPR(Pwf) = Q_VLP(Pwf)

/// skin factor classification

Skin value S	Classification	Typical cause	Recommended action
< -5	Highly stimulated	Hydraulic fracture (long HF)	Monitor fracture closure
-5 to -2	Stimulated	Acid frac, short HF	Optimize artificial lift
-2 to 0	Slightly stimulated	Acid wash, good completion	Monitor production
0 to 3	Near ideal	Minor completion damage	No action needed
3 to 10	Moderate damage	Drill-in fluid, partial plug	Evaluate acid treatment
10 to 20	Significant damage	Clay swelling, scale, severe filtrate	Acid job / workover likely
> 20	Severe damage / near-wellbore plug	Formation fines, cement, bridging	Perforation optimization + acid

/// IPR model selection guide

Condition	Recommended IPR model	Notes
Pr > Pb (above bubble point)	Linear Darcy (PI method)	Most accurate, simple
Pr ≤ Pb (solution gas drive)	Vogel (1968)	Standard for solution-gas drive
Pr partially above Pb	Composite: Linear + Vogel	Most common real case
High-rate oil (turbulence)	Jones-Blount-Glaze	For gravel-packed wells
Gas wells (any)	Fetkovich / LIT / pseudo-pressure	Pressure-squared for P < 170 bar
Tight gas / unconventional	Modified Fetkovich + Klinkenberg	Slippage correction for low perm
Horizontal well	Joshi / Renard-Dupuy formula	Anisotropy correction needed

petrosmartacademy.com · Vogel 1968 / Fetkovich 1973 / Darcy Radial Flow / NACE Nodal Analysis · Educational tool only