Vogel's IPR

Vogel's Inflow Performance Relationship

Vogel's IPR

Vogel's IPR is an empirical two-phase (oil + gas) inflow performance relationship correlation published in 1968 .

Vogel's IPR is based on computer simulations to several solution gas drive reservoirs for different fluid and reservoir relative permeability properties.

Vogel's IPR is the default IPR correlation to calculate oil wells performance in the PQplot nodal analysis software which is available online at petroleum engineering site www.pengtools.com.

Math and Physics

Vogel's IPR equation

$\frac{q_o}{q_{o_{max}}} = 1-0.2 \frac{P_{wf}}{\bar{P}} - 0.8 \left ( \frac{P_{wf}}{\bar{P}} \right )^2$

Single phase liquid and Vogel's IPR

Combination Constant PI (Darcy's law) and Vogel's IPR

$q_{ob} = J (\bar{P} - P_b)$

$q_{o_{max}} = q_{ob} + \frac{J P_b}{1.8}$

$q_o = q_{ob} + (q_{o_{max}} - q_{ob}) \left (1-0.2 \frac{P_{wf}}{\bar{P}} - 0.8 \left ( \frac{P_{wf}}{\bar{P}} \right )^2 \right )$

$J = \frac{q_o}{\bar{P}-P_b + \frac{P-b}{1.8} \left (1-0.2 \frac{P_{wf}}{\bar{P}} - 0.8 \left ( \frac{P_{wf}}{\bar{P}} \right )^2 \right ) }$

Why Vogel's IPR?

Vogel's IPR solution has been found to be very good and is widely used in prediction of IPR curves.

— Kermit Brown et al

Vogel's IPR calculation workflow

1. Calculate Productivity Index, J:

1.1 J from the flow test:

• Above the bubble point: $J=\frac{q_{o_{test}}}{\bar{P}-P_{wf}}$
• Below the bubble point: $J = \frac{q_o}{\bar{P}-P_b + \frac{P-b}{1.8} \left (1-0.2 \frac{P_{wf}}{\bar{P}} - 0.8 \left ( \frac{P_{wf}}{\bar{P}} \right )^2 \right ) } :1.2 kh and [[JD]] :1.3 kh and skin == Nomenclature == :<math> B$ = formation volume factor, bbl/stb

$J_D$ = dimensionless productivity index, dimensionless

$kh$ = permeability times thickness, md*ft

$\bar{P}$ = average reservoir pressure, psia

$P_{\bar{P}}$ = average reservoir pseudopressure, psia²/cP

$P_{wf}$ = well flowing pressure, psia

$P_{P_{wf}}$ = average well flowing pseudopressure, psia²/cP

$q$ = flowing rate, stb/d

$q_g$ = gas rate, MMscfd

$T$ = temperature, °R

Greek symbols

$\mu$ = viscosity, cp

See also

IPR

141.2 derivation

Darcy's law

JD

Production Potential