Difference between revisions of "141.2 derivation"

Revision as of 05:55, 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.

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.

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.
-For example Darcy's law for the single-phase flow is as follows:
+For example Darcy's law for the single-phase flow is as follows<ref name=KermitBrown/>:
 :<math> 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</math>
@@ Line 49: / Line 49: @@
 .41 derivation
-Kermit E. Brown "The Technology of Artificial Lift Methods" Vol. 4 Production Optimization of Oil and Gas Wells by Nodal System Analysis, p. 30, section 2.227.1
+<references>
+<ref name=KermitBrown>{{cite book
+ |last1=Brown|first1= Kermit
+ |title=The Technology of Artificial Lift Methods.  Volume 4. Production Optimization of Oil and Gas Wells by Nodal System Analysis
+ |publisher=PennWellBooks
+ |volume=2
+ |date=1984
+ |place=Tulsa, Oklahoma
+}}</ref>
+</references>
 [[Category:Technology]]