Difference between revisions of "Vogel's IPR"

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(→‎2. Calculate the flowing rates, qo:)
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:<math> 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 ) } </math><ref name=KermitBrown1984 /> , productivity index for test below the bubble point pressure.
 
:<math> 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 ) } </math><ref name=KermitBrown1984 /> , productivity index for test below the bubble point pressure.
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==Discussion ==
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Why [[Vogel's IPR]]?
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{{Quote| text = Vogel's IPR solution has been found to be very good and is widely used in prediction of IPR curves. | source = Kermit Brown et al<ref name=KermitBrown1984 />}}
  
 
==[[Vogel's IPR]] calculation workflow==
 
==[[Vogel's IPR]] calculation workflow==
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:2.3 Calculate oil rate at given flowing bottomhole pressure, P<sub>wf</sub>:
 
:2.3 Calculate oil rate at given flowing bottomhole pressure, P<sub>wf</sub>:
 
::<math> 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 )</math>
 
::<math> 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 )</math>
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== Why [[Vogel's IPR]]?  ==
 
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{{Quote| text = Vogel's IPR solution has been found to be very good and is widely used in prediction of IPR curves. | source = Kermit Brown et al<ref name=KermitBrown1984 />}}
 
  
 
== Nomenclature  ==
 
== Nomenclature  ==

Revision as of 09:18, 10 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 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

Combination Constant PI and Vogel's IPR[2]

q_{ob} = J (\bar{P} - P_b) [2] , oil flow rate at the bubble point.
q_{o_{max}} = q_{ob} + \frac{J P_b}{1.8} [3] , maximum oil rate or absolute open flow (AOF).
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 )[2] , oil rate at given flowing bottomhole pressure.
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 ) } [2] , productivity index for test below the bubble point pressure.

Discussion

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]

Vogel's IPR calculation workflow

1. Calculate Productivity Index, J:

1.1 J from the flow test:
  • Test is above the bubble point:
J=\frac{q_{o_{test}}}{\bar{P}-P_{wf}}
  • Test is below the bubble point:
J = \frac{q_{o_{test}}}{\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 J from kh and JD:
J = \frac{kh\ J_D}{141.2 B \mu}
1.3 J from kh and skin:
J = \frac{kh\ \frac{1}{1 / 0.13 + s}}{141.2 B \mu}

2. Calculate the flowing rates, qo:

For each Pwf from \bar{P} to 0:

2.1 Calculate oil flow rate at the bubble point:
q_{ob} = J (\bar{P} - P_b)
2.2 Calculate maximum oil rate:
q_{o_{max}} = q_{ob} + \frac{J P_b}{1.8}
2.3 Calculate oil rate at given flowing bottomhole pressure, Pwf:
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 )

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 2.2 2.3 2.4 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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