Difference between revisions of "Darcy's law"

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The basic form of [[Darcy's law]] is very similar to in form to other physical laws. For example '''Fourier's law''' for heat conduction and '''Ohm's law''' for flow of electricity <ref name=DW/>.
 
The basic form of [[Darcy's law]] is very similar to in form to other physical laws. For example '''Fourier's law''' for heat conduction and '''Ohm's law''' for flow of electricity <ref name=DW/>.
  
 +
[[Darcy's law]] formula:
 
:<math>q=\frac{kA}{\mu} \frac{\Delta P}{L}</math>
 
:<math>q=\frac{kA}{\mu} \frac{\Delta P}{L}</math>
  
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The new constant '''k''' has therefore been isolated as being solely dependent on the nature of sand and is described as the '''permeability'''<ref name=DakeF/>.
 
The new constant '''k''' has therefore been isolated as being solely dependent on the nature of sand and is described as the '''permeability'''<ref name=DakeF/>.
  
== Darcy's law equation in differential form ==
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== Darcy's law equation ==
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===Differential form ===
 
If distance is measured positive in the direction of flow, then the pressure gradient must be negative in the same direction since fluids move from high to low pressure<ref name=DakeF/>. Therefore, Darcy's law is:
 
If distance is measured positive in the direction of flow, then the pressure gradient must be negative in the same direction since fluids move from high to low pressure<ref name=DakeF/>. Therefore, Darcy's law is:
  
 
:<math> q = -\frac{kA}{\mu} \frac{dP}{dL}</math>
 
:<math> q = -\frac{kA}{\mu} \frac{dP}{dL}</math>
 +
===Linear form===
 +
 +
===Radial form===
  
 
=== Conditions  ===
 
=== Conditions  ===

Revision as of 15:05, 22 July 2019

Darcy's law

Darcy's law. Equation and notations

Darcy's law is the fundamental law of fluid motion in porous media published by Henry Darcy in 1856 [1].

Darcy's law has been successfully applied to determine the flow through permeable media since the early days of Petroleum Engineering.

The basic form of Darcy's law is very similar to in form to other physical laws. For example Fourier's law for heat conduction and Ohm's law for flow of electricity [2].

Darcy's law formula:

q=\frac{kA}{\mu} \frac{\Delta P}{L}

Darcy's law History

Darcy's experimental equipment

Henry Darcy worked on the design of a filter large enough to process the Dijon towns daily water requirement [3].

Les Fontaines Publiques de la Ville de Dijon.png

By flowing water through the sand pack Darcy established that, for any flow rate, the velocity of the flow was directly proportional to the difference in manometric heights[3]:

u=K\frac{h1-h2}{L}

All the experiments were carried out with water changing the type of sand pack. The effects of fluid density and viscosity on the flow was not investigated[3].

Subsequently, others experiments performed with a variety of different liquids revealed the dependence of fluid flow on fluid density and viscosity.

The new constant k has therefore been isolated as being solely dependent on the nature of sand and is described as the permeability[3].

Darcy's law equation

Differential form

If distance is measured positive in the direction of flow, then the pressure gradient must be negative in the same direction since fluids move from high to low pressure[3]. Therefore, Darcy's law is:

 q = -\frac{kA}{\mu} \frac{dP}{dL}

Linear form

Radial form

Conditions

  • Single fluid
  • Steady stay flow
  • Constant fluid compressibility
  • Constant temperature

Darcy's law equation example

The permeability of 1 Darcy defined as permeability which allows fluid with viscosity of 1 centipoise flow with velocity of 1 cc/sec through the crossectional area of 1 cm2 with the pressure gradient of 1 atm.

Inflow Equations Derivation

Derivation of the Linear and Radial Inflow Equations Darcy's Law mtuz.png

Nomenclature

 A = cross-sectional area, cm2
 k = permeability, d
 L = length, cm
 P = pressure, atm
 q = flow rate, cm3/sec

Greek symbols

 \mu = Darcy's law fluid viscosity, cp

See Also

References

  1. Darcy, Henry (1856). "Les Fontaines Publiques de la Ville de Dijon". Paris: Victor Dalmont. 
  2. Wolcott, Don (2009). Applied Waterflood Field DevelopmentPaid subscription required. Houston: Energy Tribune Publishing Inc. 
  3. 3.0 3.1 3.2 3.3 3.4 Dake, L.P. (1978). Fundamentals of Reservoir Engineering. Amsterdam, Hetherlands: Elsevier Science. ISBN 0-444-41830-X.