The behaviour of low-viscosity, pressure-driven compressible pore fluid flows in viscously deformable porous media is studied here with specific application to gas flow in lava domes. The combined flow of gas and lava is shown to be governed by a two-equation set of nonlinear mixed hyperbolic–parabolic type partial differential equations describing the evolution of gas pore pressure and lava porosity. Steady state solution of this system is achieved when the gas pore pressure is magmastatic and the porosity profile accommodates the magmastatic pressure condition by increased compaction of the medium with depth. A one-dimensional (vertical) numerical linear stability analysis (LSA) is presented here. As a consequence of the pore-fluid compressibility and the presence of gravitation compaction, the gradients present in the steady-state solution cause variable coefficients in the linearized equations which generate instability in the LSA despite the diffusion-like and dissipative terms in the original system. The onset of this instability is shown to be strongly controlled by the thickness of the flow and the maximum porosity, itself a function of the mass flow rate of gas. Numerical solutions of the fully nonlinear system are also presented and exhibit nonlinear wave propagation features such as shock formation. As applied tomore »
Elastic Properties of Confined Fluids from Molecular Modeling to Ultrasonic Experiments on Porous Solids
Fluids confined in nanopores are ubiquitous in nature and technology. In recent years, the interest in confined fluids has grown, driven by research on unconventional hydrocarbon resources -- shale gas and shale oil, much of which are confined in nanopores. When fluids are confined in nanopores, many of their properties differ from those of the same fluid in the bulk. These properties include density, freezing point, transport coefficients, thermal expansion coefficient, and elastic properties. The elastic moduli of a fluid confined in the pores contribute to the overall elasticity of the fluid-saturated porous medium and determine the speed at which elastic waves traverse through the medium. Wave propagation in fluid-saturated porous media is pivotal for geophysics, as elastic waves are used for characterization of formations and rock samples. In this paper, we present a comprehensive review of experimental works on wave propagation in fluid-saturated nanoporous media, as well as theoretical works focused on calculation of compressibility of fluids in confinement. We discuss models that bridge the gap between experiments and theory, revealing a number of open questions that are both fundamental and applied in nature. While some results were demonstrated both experimentally and theoretically (e.g. the pressure dependence of compressibility more »
- Award ID(s):
- 1944495
- Publication Date:
- NSF-PAR ID:
- 10230277
- Journal Name:
- Applied physics reviews
- ISSN:
- 1931-9401
- Sponsoring Org:
- National Science Foundation
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