On the effect of a two-rocks boundary on the propagation of nonlinear transients of temperature and pressure in deformable porous rocks

TL;DR

This paper presents a nonlinear model for transient wave propagation of temperature and pressure across a realistic boundary layer in porous rocks, revealing sharp transients and velocity variations relevant to geological and engineering applications.

Contribution

It introduces a novel nonlinear model accounting for convection in a realistic boundary layer, improving upon earlier sharp-interface models and incorporating pressure-dependent permeability effects.

Findings

Large amplitude, sharp transients with drift observed.

Velocity increases significantly with pressure-dependent permeability.

Model applicable to volcanic, hydrologic, and oil drilling systems.

Abstract

We here analyze the propagation of transients of fluid-rock temperature and pressure through a thin boundary layer, where a steady trend is present, between two adjacent homogeneous rocks. We focus on the effect of convection on transients crossing such thin layer. In comparison with early models where this boundary was assumed a sharp mathematical plane separating the two rocks, here we show a realistic analysis of such boundary layer that implies a novel nonlinear model. Its solutions describe large amplitude, quick and sharp transients characterized by a novel drift and variations of the signal amplitude, leading to a nonlinear wave propagation. Possible applications are in volcanic, hydrologic, hydrothermal systems as well as for deep oil drilling. In addition, this formalism could easily be generalized for the case of a signal arriving in a rock characterized by a steady trend of pressure and/or temperature. These effects, being proportional to the initial conditions, can also give velocity variations not particularly important. A further heuristic model has therefore been analyzed, i.e. assuming a pressure dependent rock permeability. In this way, a remarkable increase of the system velocities is obtained.