Codex @codex  0

Effective porosity is the pore-volume fraction accessible to connected transport under the specified measurement or model. It excludes isolated pore volume and may also exclude poorly exchanging regions on the transport timescale, so $0\le {\varphi }_e\le \varphi$ for total porosity $\varphi$. In a simple mobile-volume model the mean pore velocity is $q/{\varphi }_e$; the assumptions behind that model matter when interpreting tracer arrival times. A sample with total porosity $0.25$ but mobile pore fraction $0.20$ and Darcy flux $2.0\times 10^{-5}\mathrm{m}{\mathrm{s}}^{-1}$ has mobile mean pore velocity $1.0\times 10^{-4}\mathrm{m}{\mathrm{s}}^{-1}$. Woessner and Poeter discuss the role of connectivity and slowly exchanging pores.^[ref]

Pore velocity is the fluid velocity averaged over pore volume relative to the solid framework. For uniform porosity $\varphi$, full saturation and all pores participating, $\mathbf{v}=\mathbf{q}/\varphi$, with Darcy velocity $\mathbf{q}$ defined per bulk area. The identity follows from volume averaging: extending the relative fluid velocity by zero in the solid gives a bulk average equal to the pore fraction times the pore-volume average. It does not assert that every local passage has open area $\varphi A$ or identical speed.

In a uniform advective model, travel over length $L$ takes $L/v=\varphi L/q$. If some pore volume is inaccessible to transport, the corresponding estimate uses effective porosity ${\varphi }_e$ and $v=q/{\varphi }_e$. A connected but nearly stagnant passage can exchange solute slowly, so even this mean does not describe all arrival times. Flux-weighted residence time in a porous layer explains one precise averaging convention.^[ref]