Difference between revisions of "Darcy's law"

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*Constant fluid compressibility
 
*Constant fluid compressibility
 
*Constant temperature
 
*Constant temperature
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==Darcy's law equation examples==
  
 
== Inflow Equations Derivation ==
 
== Inflow Equations Derivation ==

Revision as of 14:56, 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].

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 in 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}

Conditions

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

Darcy's law equation examples

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.