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For simplicity, I consider the case of fluid injection at the origin in a medium with isotropic pressure diffusion, characterized by constant diffusivity.
Regarding this specification, Liang et al. applied the transient pulse decay to measure the permeability of tight rocks and synthetic materials using the pressure diffusion equation, in which due to dependent pressure of gas compressibility the diffusivity equation became non-linear (Liang et al. 1978).
For calcination, the effects of temperature, decomposition pressure, diffusion and pore efficiency were taken into account.
Recently, we proposed an original method allowing to model transient pressure diffusion in the fracture network only [1].
The differential form of single-phase seepage equation and the analytical solution for pressure diffusion equation are adopted to deduce the analytical solution for shape factors in transient pressure diffusion equation.
Model I includes only pressure diffusion effects, and Model II includes only thermodynamic effects at the solvent membrane interfaces.
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Carcione and Gei (2009) simulated fluid-pressure diffusion in inhomogeneous media by considering a single fluid.
Lai et al. (2013a) reported that the observed phase responses can be considered a measure of permeability in both the horizontal fluid flow model (Hsieh et al. 1987) and the vertical pore-pressure diffusion model (Roeloffs 1996).
For Sb in Si, using as input the measured effect of hydrostatic pressure on diffusion and the assumption of a pure vacancy mechanism, the measured effect of biaxial stress on diffusion can be predicted successfully with no free parameters.
For Sb in Si, using as input the results of ab initio calculations of effect of hydrostatic pressure on diffusion by the vacancy mechanism, the thermodynamic relationships successfully account for the measured effect biaxial stress on diffusion with no free parameters.
Down dip injection, capillary pressure and diffusion increase alpha factors.
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