Difference between revisions of "141.2 derivation"

Revision as of 05:47, 23 April 2018

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:

q = \frac{1}{141.2} \frac{kh}{B\mu} \times \Delta P \times J_D = 7.08 \times 10^-3\ \frac{kh}{B\mu} \Delta P\ J_D

The derivation of the 141.2 constant is given below.

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

@@ Line 3: / Line 3: @@
 '''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:
-:<math> q = \frac{1}{141.2} \frac{kh}{B\mu} \Delta  P\ J_D = 7.08 \times 10^-3\ \frac{kh}{B\mu} \Delta  P\ J_D</math>
+:<math> q = \frac{1}{141.2} \frac{kh}{B\mu} \times \Delta P \times J_D = 7.08 \times 10^-3\ \frac{kh}{B\mu} \Delta  P\ J_D</math>
 The derivation of the 141.2 constant is given below.