Difference between revisions of "18.41 derivation"

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where  
 
where  
  
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:<math> C_{LF} = \frac{1000 \times 100}{10000} \frac{1000000}{86400} = \frac{1000\ 14.695950253959\ 30.48^2\ 5.61458333}{86400} = 887.2201322</math>
+
:<math> C_{LF} = \frac{1000 \times 100}{10000} \frac{1000000}{86400} = \frac{10000000}{86400} = 115.7407407</math>
  
 
For the radial flow:
 
For the radial flow:
  
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:<math> C_{RF} =  \frac{C_{LF}}{2\pi} = \frac{887.2201322}{2\pi} = 141.20546964</math>
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:<math> C_{RF} =  \frac{C_{LF}}{2\pi} = \frac{115.7407407}{2\pi} = 18.42 </math>
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One can be familiar with the inverse of the '''141.2''' constant:
 
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:<math> \frac{1}{C_{RF}} =  \frac{1}{141.20546964} = 7.08E-03 </math>
 
  
 
==See Also==
 
==See Also==

Revision as of 13:36, 9 July 2023

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[1]:

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

The derivation of the 18.41 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 metric units:

\frac{[cm^3] \frac{[m^3]}{[1000000 cm^3]}}{[sec] \frac{[day]}{[86400 sec]}} = - \frac{[D] \frac{[1000 mD]}{[D]}[cm^2] \frac{[m^2]}{[10000 cm^2]}}{[cP]} \frac{[atm]}{[cm] \frac{[m]}{[100 cm]}}

So:

\frac{[m^3]}{[day]} \frac{86400}{1000000} = - \frac{[mD][m^2]}{[cP]} \frac{[atm]}{[m]} \frac{1000 \times 100}{10000}

And:

\frac{[m^3]}{[day]} = - C_{LF} \frac{[mD][m^2]}{[cP]} \frac{[atm]}{[m]}

where

C_{LF} = \frac{1000 \times 100}{10000} \frac{1000000}{86400} = \frac{10000000}{86400} = 115.7407407

For the radial flow:

C_{RF} = \frac{C_{LF}}{2\pi} = \frac{115.7407407}{2\pi} = 18.42

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

References

  1. ↑ Wolcott, Don (2009). Applied Waterflood Field DevelopmentPaid subscription required. Houston: Energy Tribune Publishing Inc. 
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