Difference between revisions of "18.41 derivation"

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:<math> A </math> = [[Darcy's law]] cross-sectional area, cm<sup>2</sup>
 
:<math> A </math> = [[Darcy's law]] cross-sectional area, cm<sup>2</sup>
−
:<math> B_o </math> = oil formation volume factor, bbl/stb
+
:<math> B_o </math> = oil formation volume factor, m^3/m^3
 
:<math> C_{LF} </math> = linear flow units conversion constant  
 
:<math> C_{LF} </math> = linear flow units conversion constant  
 
:<math> C_{RF} </math> = radial flow units conversion constant
 
:<math> C_{RF} </math> = radial flow units conversion constant
−
:<math> h</math> = effective feet of oil pay, ft
+
:<math> h</math> = effective feet of oil pay, m
 
:<math> J_D </math> = dimensionless productivity index, dimensionless
 
:<math> J_D </math> = dimensionless productivity index, dimensionless
 
:<math> k</math> = [[Darcy's law]] permeability, d
 
:<math> k</math> = [[Darcy's law]] permeability, d
Line 57: Line 57:
 
:<math> L </math> = [[Darcy's law]] length, cm
 
:<math> L </math> = [[Darcy's law]] length, cm
 
:<math> P </math> = [[Darcy's law]] pressure, atm
 
:<math> P </math> = [[Darcy's law]] pressure, atm
−
:<math> \Delta P </math> = drawdown, psia
+
:<math> \Delta P </math> = drawdown, atm
 
:<math> q </math> = [[Darcy's law]] flow rate, cm<sup>3</sup>/sec
 
:<math> q </math> = [[Darcy's law]] flow rate, cm<sup>3</sup>/sec
−
:<math> q_o </math> = oil flow rate, stb/d
+
:<math> q_o </math> = oil flow rate, m^3/d
  
 
===Greek symbols===
 
===Greek symbols===

Revision as of 13:38, 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, 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

References

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