One of the Absolute permeability models based on simulating the flow through the multi-pipe conduits or multi-grain pack:
|
|
where
| Flow Zone Indicator | pore surface area | ||||
| effective porosity | pore shape factor | pore volume | |||
| pore channel tortuosity |
The alternative form is derived from the correlation which is valid in some practical cases:
\frac{1}{\sqrt{F_S} \, S_{gV}} \approx 0.0037 \cdot d |
where
| average grain size |
so that Absolute permeability is going to be:
k = \frac{d^2}{72 \cdot \tau^2} \cdot \frac{(\phi -\phi_0)^3}{( 1 - \phi+\phi_0)^2} |
where
| absolute permeability | |
| effective formation porosity | |
| porosity cut-off | |
| grain size | |
| pore channel tortuosity |
This correlation was historical the first physical permeability model, based on the fluid flow in porous media with simplified structure consisted of a bunch of independent capillaries with various diameters.
Later on it's been upgraded to percolation through inter-grain porous space which specifies the Flow Zone Indicator as a function of grains size distribution, grain shape and packing.
The most popular correlation with a mean grain size is given as:
FZI = a \cdot D_g |
where coefficient is a function of grain shape, packing, inter-grain clay and, as a consequence, of inter-grain effective porosity
.
Petroleum Industry / Upstream / Subsurface E&P Disciplines / Petrophysics / Absolute permeability / Absolute permeability @model
J. Kozeny, "Ueber kapillare Leitung des Wassers im Boden." Sitzungsber Akad. Wiss., Wien, 136(2a): 271-306, 1927.