Difference between revisions of "141.2 derivation"

From wiki.pengtools.com
Jump to: navigation, search
(→‎Nomenclature)
(→‎Nomenclature)
Line 51: Line 51:
 
== Nomenclature  ==
 
== Nomenclature  ==
  
 +
:<math> q </math> = [[Darcy's law]] flow area, cm<sub>3</sub>/sec
 
:<math> B_{o}(P) </math> = oil formation volume factor as a function of pressure, bbl/stb
 
:<math> B_{o}(P) </math> = oil formation volume factor as a function of pressure, bbl/stb
 
:<math> h</math> = effective feet of oil pay, ft
 
:<math> h</math> = effective feet of oil pay, ft

Revision as of 06:02, 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

q = Darcy's law flow area, cm3/sec
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 = Darcy's law permeability, d
k_o = effective permeability to oil, md
L = Darcy's law length, cm
P = Darcy's law pressure, atm
\bar{P} = average reservoir pressure, psia
P_{wf} = well flowing pressure, psia
q = Darcy's law flow rate, cm3/sec
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. 
Retrieved from "https://wiki.pengtools.com/index.php?title=141.2_derivation&oldid=3652"