Difference between revisions of "141.2 derivation"

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(Brief)
(Brief)
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'''141.2''' is the well know constant which is used for converting from the Darcy's law units to the field units.
 
'''141.2''' is the well know constant which is used for converting from the Darcy's law units to the field units.
  
:<math> q = \frac{kh \Delta  P}{141.2B\mu} J_D</math>
+
:<math> q = \frac{1}{141.2} \frac{kh}{B\mu} \Delta  P\ J_D</math>
  
 
The derivation of the 141.2 constant is given below.
 
The derivation of the 141.2 constant is given below.

Revision as of 05:41, 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.

 q = \frac{1}{141.2} \frac{kh}{B\mu} \Delta  P\ 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