Green functions of mass diffusion waves in porous media

Abstract

A formulism of frequency-domain mass diffusion-waves in porous media is derived by means of Fourier transform. In analogy to conventional thermal-wave fields, internally consistent Green functions in Cartesian coordinates for linear mass diffusion-waves is also presented for infinite, semiinfinite and finite-size domains in three-dimensional spaces. The Green functions are utilized to analyze the response of a particular type of mass diffusion physical system to any arbitrary tracer source distributions. This method allows the introduction of frequency-dependent physically intrinsic properties of porous media. The Green functions presented in this letter may significantly advance understanding in linear mass diffusion-wave physics in porous media, and can be applied to retrieve spatial-temporal diffusive-wave fields from ambient mass fluctuations in geological reservoirs.

Characteristics of Carbon Dioxide Emissions from a Seismically Active Fault

“…After initial compaction followed by dilation, partial or complete fluid-path blockage suddenly reopen, causing a sudden permeability rise and leading to a flow jet (Levy et al, 1996;Min et al, 2004) and shock waves (Liepman et al, 1957;Talwani and Acree, 1985) propagating through the fluid path. Mass waves (Yang, 2018), obeyed by the advection-diffusion law, of carbon dioxide are simultaneously produced and accelerated due to the shock wave. In the following section, we discuss the mechanical effect of shock…”

“…is the effective diffusivity of mass (Yang, 2018) in the porous media, C(X, t) stands for the concentration, and D m is the molecular diffusivity. The first contribution, C(X, t)U(X, t), describes advection driven by velocity shockwaves, and the second,…”