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The '''Fowler–Yang equations'''<ref>Fowler A. C. and Yang X. S., Pressure solution and viscous compaction in sedimentary basins, J. Geophys. Res., B104, 12898–12997 (1999).</ref> for [[pressure solution]]<ref>Angevine C. L. and Turcotte D. L., Porosity reduction by pressure solution: a theoretical model for quartz arenites, Geol. Soc. Am. Bull., vol. 94, 1129–1134 (1983)</ref> and viscous compaction in [[sedimentary basins]] can be written as:
 
: <math> \frac{\partial \phi}{\partial t} = \frac{\partial }{\partial z}[(1-\phi) u], </math>
:<math> u=\lambda \phi^m \left[\frac{\partial^2 u}{\partial z^2}-(1-\phi)\right],</math>
 
where ''u'' is the [[Darcy's law|Darcy velocity]] and <math>\phi</math> is the [[porosity]] of the porous media. In addition, 0&nbsp;<&nbsp;&lambda;&nbsp;<&nbsp;10<sup>5</sup> is a constant, and while ''m''&nbsp;=&nbsp;8. This system is highly nonlinear, which can explain the transition from one behaviour to another in pressure solution.
 
==References==
{{Reflist}}
 
{{DEFAULTSORT:Fowler-Yang equations}}
[[Category:Mathematical modeling]]
[[Category:Sedimentary basins]]

Revision as of 08:03, 17 October 2013

The Fowler–Yang equations[1] for pressure solution[2] and viscous compaction in sedimentary basins can be written as:

ϕt=z[(1ϕ)u],
u=λϕm[2uz2(1ϕ)],

where u is the Darcy velocity and ϕ is the porosity of the porous media. In addition, 0 < λ < 105 is a constant, and while m = 8. This system is highly nonlinear, which can explain the transition from one behaviour to another in pressure solution.

References

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  1. Fowler A. C. and Yang X. S., Pressure solution and viscous compaction in sedimentary basins, J. Geophys. Res., B104, 12898–12997 (1999).
  2. Angevine C. L. and Turcotte D. L., Porosity reduction by pressure solution: a theoretical model for quartz arenites, Geol. Soc. Am. Bull., vol. 94, 1129–1134 (1983)