On the theory of solitons of fluid pressure and solute density in geologic porous media, with applications to shale, clay and sandstone

TL;DR

This paper introduces a non-linear wave model for pore pressure and solute density in porous rocks, suggesting solitons as a key transport mechanism in low permeability geological formations and exploring their implications for nuclear waste disposal and natural processes.

Contribution

It develops a novel non-linear wave model based on solitons for pore pressure and solute transport in porous media, linking theory with geological applications.

Findings

Evidence of solitons in shale and clay formations.

Implications for nuclear waste disposal and saline intrusion.

Potential presence of solitons in sandstone suggesting osmosis.

Abstract

In this paper we propose the application of a new model of transients of pore pressure p and solute density \r{ho} in geologic porous media. This model is rooted in the non-linear waves theory, the focus of which is advection and effect of large pressure jumps on strain (due to large p in a non-linear version of the Hooke law). It strictly relates p and \r{ho} evolving under the effect of a strong external stress. As a result, the presence of quick and sharp transients in low permeability rocks is unveiled, i.e. the non-linear Burgers solitons. We therefore propose that the actual transport process in porous rocks for large signals is not the linear diffusion, but could be governed by solitons. A test of an eventual presence of solitons in a rock is here proposed, and then applied to Pierre Shale, Bearpaw Shale, Boom Clay and Oznam-Mugu silt and clay. A quick analysis showing the presence of solitons for nuclear waste disposal and salty water intrusions is also analyzed. Finally, in a kind of "theoretical experiment" we show that solitons could also be present in Jordan and St. Peter sandstones, thus suggesting the occurrence of osmosis in these rocks.