Example:
You have just pressed a pellet (disk) of kaolinite to be used for a flow through experiment to study fluid-rock interactions. You need to know the porosity of the pellet. Here's one way to proceed.
Given:
Io = 10,000 counts per second (CPS). This is the intensity measurement with no sample in place.
I = 3,500 CPS Intensity of transmitted beam with sample in place.
Kaolinite
r = 2.6 g/cm3Kaolintite µ* = 30.8 cm2/g
x = 0.02 cm (thickness of pellet)
Assuming that air does not influence the absorption is not totally true. However, given the small value of
r for air ~ 0.0 g/cm3, we can simplify the calculation. The pellet is a mixture of air and kaolinite.I = Io exp(-µ*
r x) mixture3500 = 10000 exp(-µ*
r 0.02)0.35 = exp(-µ*
r 0.02)Find natural log of each side.
-1.0498 = - (µ*
r) 0.0252.49 = (µ*
r) mixture
The value of 52.49 represents kaolinite's absorption contribution to the thickness of the pellet.
If the pellet were 100% kaolinite, then (µ*
r) kaolinite = 80.0852.49 = (30.8) (2.6) (fraction of thickness)kaolinite
Thicknesskaolinite = 0.66
Therefore, the porosity = 34%