What is the meaning of effective density in porous media? Is the density of air inside the pore space not same as density of free air? I am trying to understand the physical meaning of using effective density in porous media. Is it a fictitious value? Can't I use the density of solid and fluid as it is while modeling porous media?
 A: Density in a porous medium is not the same as the density of a pure substance.
Consider the general case when several phases are present in a porous medium. By definition, effective density is $$\rho_i = \lim_{\Delta V \to 0 } \frac{m_i}{\Delta V} \tag{1}\label{dens},$$ where $m_i$ - mass of $i$ phase (for example mass of oil or gas in considered porous medium volume), $\Delta V$ - volume of considered porous media.
By definition $m_i$ is $$m_i =\rho^0_i \cdot S_i \cdot \phi \cdot \Delta V ,\tag{2}\label{mass}$$ where $\rho^0_i$ - density of pure substance, $S_i$ - proportion of the pore space occupied by the phase, $\phi$ - porosity.
Substitute \eqref{mass} to \eqref{dens} and derive folowing relation $$\rho_i = \rho^0_i \cdot S_i \cdot \phi \tag{3}\label{relation}.$$
From \eqref{relation} It can be seen that the concepts of effective density and density of pure substances differ
A: The density inside a porous medium cannot be the same, in general, as the density outside. The simplest way to understand why, is to look at the system (pourous medium + air inside and air outside) as a two component system. Interactions inside the porous medium modify the chemical potential of air inside. Condition of equilibrium requires that the chemical potential of air inside and outside must be equal. Therefore, being temperature and pressure the same, concentration (density) of air inside and outside must be different.
From the experimental point of view, people do not use chemical potentials, since the relation with density is  unknown. Usually some estimation of the porous network volume is obtained with some adsorption experiments and the amount of air can be obtained by weighting the sample (or using Archimede's principle).
