141.2 derivation

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:

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

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

$k$ = 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