# Characterization of Porosity & Permeability

Porosity and permeability are closely related, so it is unsurprising that measuring the properties share common techniques that involve determining interconnected pore volume.

### Porosity

Porosity (n) is measured as the ratio of the volume of voids within a material to the total volume of the material. In a laboratory setting, this requires careful measurement of sample volume, and of pore volume. A right cylindrical core sample is extracted using a core drill press, rock saw, and surface grinder. X-ray CT scanners may be used to identify undamaged full-diameter sections for sampling. The dimensions of the sample – length (l) and diameter (d) – are measured using calipers. The volume (V ) of a right cylinder is then a simple calculation: Vtotal = πdl

Next, the sample is dried by baking it in an oven for 24 hours to ensure that no water remains in the pore space.

The pore space is filled with helium gas, which is both nonreactive (thus not altering the sample) and has a small nucleus to ensure the gas can quickly penetrate even small pore spaces provided the pores are interconnected and not isolated. The cylinder is placed in a helium pycnometer: a sample chamber and a reference chamber, both at a known volume and at a fixed temperature. The reference and sample chambers are pressurized with helium gas. Once the sample is inserted, the two chambers are connected, allowing the gas to flow out of the reference chamber into the sample chamber. The ratio of the initial and final pressures is used in conjunction with Boyle’s Law (P1V1 = P2V2) to calculate the solid volume of the sample: Vsolid = V2 = P1V1/P2

Finally, the pore volume is calculated as the difference of the total volume (determined by dimensional measurement) and the solid volume (determined by the helium pycnometer): Vpore = Vtotal − Vsolid

This technique is limited to materials with interconnected pore spaces. Isolated pores are not penetrated by the helium gas, and thus are not measured by this technique.

Alternately, liquid mercury can also be used following a similar process, where the size of infiltrated pores is proportional to the exerted pressure. The measured pore volume has the the same limitations, with the added risk of working with a neurotoxin. In the future, when helium resources have been bled away in party balloons, mercury will be the primary option, and careless graduate students will be the new mad hatters.

### Permeability

Permeability is measured as the hydraulic conductivity (k), which is the the ratio of flow velocity (v) to the hydraulic gradient (i): k = v (3.5) i

￼Hydraulic conductivity is measured in a laboratory setting by placing a sample under standard temperature conditions, then measuring the rate of discharge of water through a cross-sectional area of the medium. The water must be under laminar flow conditions so that turbulence does not complicate the flow rate. The hydraulic gradient and the cross-sectional area are coordinated to produce unit measurements. A typical example of the laboratory equipment are the Matest Hoek cells to measure the flow of water through a rock specimen of the specified diameter. A similar process can be followed using flowing air instead of water for dissolvable materials

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