Fowler–Yang equations

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

$\frac{\partial \phi}{\partial t} = \frac{\partial }{\partial z}[(1-\phi) u],$

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

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.

References

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)