Difference between revisions of "18.41 derivation"

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:<math> C_{RF} =  \frac{C_{LF}}{2\pi} = \frac{115.7407407}{2\pi} = 18.42 </math>
 
:<math> C_{RF} =  \frac{C_{LF}}{2\pi} = \frac{115.7407407}{2\pi} = 18.42 </math>
  
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==See Also==
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Note that the published<ref name=DW/> and commonly used constant in '''18.41'''.
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[[Darcy's law]]<BR/>
 
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[[141.2 derivation]]<BR/>
 
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[[18.41 derivation]]
 
  
 
== Nomenclature  ==
 
== Nomenclature  ==
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:<math> \mu </math> = [[Darcy's law]] oil viscosity, cp
 
:<math> \mu </math> = [[Darcy's law]] oil viscosity, cp
 
:<math> \mu_o </math> = oil viscosity, cp
 
:<math> \mu_o </math> = oil viscosity, cp
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==See Also==
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[[Darcy's law]]<BR/>
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[[141.2 derivation]]<BR/>
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[[18.41 derivation]]
  
 
==References==
 
==References==
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|description=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.
 
|description=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.
 
}}
 
}}
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<div style='text-align: right;'>By Mikhail Tuzovskiy on {{REVISIONTIMESTAMP}}</div>

Latest revision as of 12:32, 12 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

Note that the published[1] and commonly used constant in 18.41.

Nomenclature

A = Darcy's law cross-sectional area, cm2
B_o = oil formation volume factor, m^3/m^3
C_{LF} = linear flow units conversion constant
C_{RF} = radial flow units conversion constant
h = effective feet of oil pay, m
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, atm
q = Darcy's law flow rate, cm3/sec
q_o = oil flow rate, m^3/d

Greek symbols

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

See Also

Darcy's law
141.2 derivation
18.41 derivation

References

  1. ↑ 1.0 1.1 Wolcott, Don (2009). Applied Waterflood Field DevelopmentPaid subscription required. Houston: Energy Tribune Publishing Inc. 
By Mikhail Tuzovskiy on 20230712123245
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