Fowler–Yang equations

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

 \frac{\partial \phi}{\partial t} = \frac{\partial }{\partial z}[(1-\phi) u],
 u=\lambda \phi^m \left[\frac{\partial^2 u}{\partial z^2}-(1-\phi)\right],

where u is the Darcy velocity and \phi 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.


  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)