Scale‐dependent energy conservation and its connection to flow field instability in porous media

Abstract

AbstractIt has been known for decades that isothermal flow fields in porous media can become unstable, resulting in the growth of preferential flow paths and nonmonotonic moisture profiles. The standard approach to modeling isothermal fluid transport in a porous systems is to use Richards equation with equilibrium relationships for the driving potential and monotonic transport coefficients. However, it is well known that under these conditions, solutions to Richards' equation are unconditionally stable. This has left open the question of whether Richards' equation could predict the onset of flow field instability, and what is required to model it. Importantly, past work has shown that pore scale processes can actually cause nonequilibrium driving potentials to arise in unsaturated media. How these can lead to flow field instability can be understood using a form of spectral perturbation theory. Here the driving potential is represented using a Fourier expansion, which is then substituted into Richards equation. The result shows that the evolution of perturbations to the flow field are affected by the interaction between different wavelength components in the Fourier expansion. In particular, there are situations where nonequilibrium driving potentials can set up conditions that would allow the onset of instability in solutions to Richards' equation.