Difference between revisions of "141.2 derivation"

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18.41 derivation
 
18.41 derivation
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== Nomenclature  ==
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:<math> B_{o}(P) </math> = oil formation volume factor as a function of pressure, bbl/stb
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:<math> h</math> = effective feet of oil pay, ft
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:<math> J_D </math> = dimensionless productivity index, dimensionless
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:<math> k_o</math> = effective permeability to oil, md
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:<math> P </math> = pressure, psia
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:<math> \bar{P} </math> = average reservoir pressure, psia
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:<math> P_{i} </math> = initial pressure, psia
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:<math> P_{wf} </math> = well flowing pressure, psia
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:<math> q_o </math> = oil flow rate, stb/d
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===Greek symbols===
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:<math> \mu_o(P) </math> = oil viscosity as a function of pressure, cp
  
 
==References==
 
==References==

Revision as of 05:58, 23 April 2018

Brief

141.2 is the well know constant which is used for converting from the Darcy's law units to the field units in the well's inflow equations.

For example Darcy's law for the single-phase flow is as follows[1]:

 q_o = \frac{1}{141.2} \times \frac{k_oh}{B_o\mu_o} \times \Delta P \times J_D = 7.08 \times 10^-3 \times \frac{k_oh}{B_o\mu_o} \times \Delta  P \times J_D

The derivation of the 141.2 constant is given below.

Math and Physics

Darcy's law:

 q = -\frac{kA}{\mu} \frac{dP}{dL}

In Darcy's units:


 \frac{[cm^3]}{[sec]} = - \frac{[D][cm^2]}{[cP]} \frac{[atm]}{[cm]}

Converting to the field units:

 \frac{[cm^3] \frac{[ft^3]}{[30.48^3 cm^3]} \frac{[bbl]}{[5.61458333 ft^3]} }{[sec] \frac{[day]}{[86400 sec]}} = - \frac{[D] \frac{[1000 mD]}{[D]}[cm^2] \frac{[ft^2]}{[30.48^2 cm]}}{[cP]} \frac{[atm] \frac{[14.695950253959 psia]}{[atm]}}{[cm] \frac{[ft]}{[30.48 cm]}}

So:

 \frac{[bbl]}{[day]} \frac{86400}{30.48^3\ 5.61458333} = - \frac{[mD][ft^2]}{[cP]} \frac{[psia]}{[ft]} \frac{1000\ 14.695950253959}{30.48}

And:

 \frac{[bbl]}{[day]} = - C_{LF} \frac{[mD][ft^2]}{[cP]} \frac{[psia]}{[ft]}

where

 C_{LF} = \frac{1000\ 14.695950253959}{30.48} \frac{30.48^3\ 5.61458333}{86400} = \frac{1000\ 14.695950253959\ 30.48^2\ 5.61458333}{86400} = 887.2201322

For the radial flow:

 C_{RF} =  \frac{C_{LF}}{2\pi} = \frac{887.2201322}{2\pi} = 141.20546964

One can be familiar with the inverse of the 141.2 constant:

 \frac{1}{C_{RF}} =  \frac{1}{141.20546964} = 7.08E-03

See Also

Darcy's law

18.41 derivation

Nomenclature

 B_{o}(P) = oil formation volume factor as a function of pressure, bbl/stb
 h = effective feet of oil pay, ft
 J_D = dimensionless productivity index, dimensionless
 k_o = effective permeability to oil, md
 P = pressure, psia
 \bar{P} = average reservoir pressure, psia
 P_{i} = initial pressure, psia
 P_{wf} = well flowing pressure, psia
 q_o = oil flow rate, stb/d

Greek symbols

 \mu_o(P) = oil viscosity as a function of pressure, cp

References

  1. Brown, Kermit (1984). The Technology of Artificial Lift Methods. Volume 4. Production Optimization of Oil and Gas Wells by Nodal System Analysis. 4. Tulsa, Oklahoma: PennWellBooks.