A porous medium is modelled with a bundle of capillary tubes. The porous medium has a fixed cross-sectional area A = s² and length L. The capillary tubes have a diameter of Dc length Le. Le is greater than L. The fluid flowing through the tubes has a viscosity u. The porous medium is subjected to a pressure differential, AP at the outlet and inlet of the tubes. An n x n array of N tubes fit into and approximate its flow characteristics.
a. Calculate the permeability and porosity.
b. What is the relationship between the permeability and specific surface area per unit pore volume (Svp)?
Hint:
Svp = Wetted Surface Area of the Pore/Volume of Pore
Svg = Wetted Surface Area of the Pore/Volume of Grain
c. What's the relationship of permeability to tortuosity (T)?
d. If we fit small tubes in between the existing tubes, how do the permeability and porosity change?