Fowler–Yang equations
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],](../I/m/db9976f15c62ea44f3054bb23e011350.png)
![u=\lambda \phi^m \left[\frac{\partial^2 u}{\partial z^2}-(1-\phi)\right],](../I/m/61f972ab0fbece41b7a211b33dc9b29a.png)
where u is the Darcy velocity and 
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
- ↑ Fowler A. C. and Yang X. S., Pressure solution and viscous compaction in sedimentary basins, J. Geophys. Res., B104, 12898–12997 (1999).
- ↑ 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)