# Self-similar distributions of fluid velocity and stress heterogeneity in a dissolving porous limestone

## TL;DR

This study investigates how fluid flow and stress distributions in dissolving porous limestone evolve in a self-similar manner, revealing universal scaling laws and heavy-tailed stress distributions that influence rock failure.

## Contribution

It demonstrates that during dissolution, stress heterogeneity follows self-similar scaling laws and fluid velocities follow stretched exponential distributions, providing a unified framework for microstructure evolution.

## Key findings

- Stress distributions evolve self-similarly with porosity increase
- Fluid velocity follows a stretched exponential distribution
- Stress invariants exhibit heavy tails indicating failure risk

## Abstract

In a porous rock, the spatial distribution of the pore space induces a strong heterogeneity in fluid flow rates and in the stress distribution in the rock mass. If the rock microstructure evolves through time, for example by dissolution, fluid flow and stress will evolve accordingly. Here, we consider a core sample of porous limestone that has undergone several steps of dissolution. Based on 3D X-ray tomography scans, we calculate numerically the coupled system of fluid flow in the pore space and stress in the solid. We determine how the flow field affects the stress distribution both at the pore wall surface and in the bulk of the solid matrix. We show that, during dissolution, the heterogeneous stress evolves in a self-similar manner as the porosity is increased. Conversely, the fluid velocity shows a stretched exponential distribution. The scalings of these common master distributions offer a unified description of the porosity evolution, pore flow, and the heterogeneity in stress for a rock with evolving microstructure. Moreover, the probability density functions of stress invariants (mechanical pressure or von Mises stress) display heavy tails towards large stresses. If these results can be extended to other kinds of rocks, they provide an additional explanation of the sensitivity to failure of porous rocks under slight changes of stress.