Difference between revisions of "Vogel's IPR"

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Revision as of 09:05, 5 April 2019

Vogel's Inflow Performance Relationship

Vogel's IPR[1]

Vogel's IPR is an empirical two-phase (oil + gas) inflow performance relationship correlation published in 1968 [1].

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 for the oil wells performance in the PQplot.

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 and Vogel's IPR[2] Combination Constant PI and Vogel's IPR

q_{ob} = J (\bar{P} - P_b)
q_{o_{max}} = q_{ob} + \frac{J P_b}{1.8} [3]
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[2]

IPR calculation workflow

Nomenclature

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

References

  1. ↑ 1.0 1.1 Vogel, J. V. (1968). "Inflow Performance Relationships for Solution-Gas Drive Wells". Journal of Petroleum Technology. 20 (SPE-1476-PA). 
  2. ↑ 2.0 2.1 Brown, Kermit (1984). The Technology of Artificial Lift Methods. Volume 4. Production Optimization of Oil and Gas Wells by Nodal System Analysis. Tulsa, Oklahoma: PennWellBookss. 
  3. ↑ Neely, A.B. (1976). Use of IPR Curves. Houston, Texas: Shell Oil Co. 

See also

IPR
141.2 derivation
Darcy's law
JD
Production Potential
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