Difference between revisions of "18.41 derivation"

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(Created page with "== 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...")
 
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'''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.
 
'''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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For example [[Darcy's law]] for the single-phase flow is as follows<ref name=KermitBrown/>:
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For example [[Darcy's law]] for the single-phase flow is as follows<ref name=DW/>:
  
 
:<math> q_o = \frac{1}{18.41} \times \frac{k_oh}{B_o\mu_o} \times \Delta P \times J_D</math>
 
:<math> q_o = \frac{1}{18.41} \times \frac{k_oh}{B_o\mu_o} \times \Delta P \times J_D</math>
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<ref name=KermitBrown>{{cite book
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{{cite book
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  |last1=Brown|first1= Kermit
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  |last1= Wolcott |first1=Don
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  |title=The Technology of Artificial Lift Methods. Volume 4. Production Optimization of Oil and Gas Wells by Nodal System Analysis
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  |title=Applied Waterflood Field Development
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  |publisher=PennWellBooks
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  |date=2009
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  |volume=4
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  |publisher=Energy Tribune Publishing Inc
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  |date=1984
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  |place=Houston
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  |place=Tulsa, Oklahoma
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  |url=https://www.amazon.com/Applied-Waterflood-Field-Development-Wolcott/dp/0578023946/ref=sr_1_1?ie=UTF8&qid=1481788841&sr=8-1&keywords=Don+wolcott
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Revision as of 13:25, 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 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

References

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