18.41 derivation

Brief

18.41 is the well know constant which is used for converting from the Darcy's law units to the metric units in the well's inflow equations.

For example Darcy's law for the single-phase flow is as follows:

$q_o = \frac{1}{18.41} \times \frac{k_oh}{B_o\mu_o} \times \Delta P \times J_D$

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
141.2 derivation 18.41 derivation

Nomenclature

$A$ = Darcy's law cross-sectional area, cm²

$B_o$ = oil formation volume factor, bbl/stb

$C_{LF}$ = linear flow units conversion constant

$C_{RF}$ = radial flow units conversion constant

$h$ = 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

$\Delta P$ = drawdown, psia

$q$ = Darcy's law flow rate, cm³/sec

$q_o$ = oil flow rate, stb/d

Greek symbols

$\mu$ = Darcy's law oil viscosity, cp

$\mu_o$ = oil viscosity, cp