Permeability

Permeability

I. Introduction: Measurement Principle

II. Darcy's law for compressible media

III. Darcy's law for incompressible media

IV. Error propagation and Standard Deviation

V. Conclusion

VI. References

I. Introduction: Measurement Principle

Two different methods were applied to determine the permeability:

The absolute permeability (kabs, [m², Darcy]) of gas was determined by a single-phase experiment with a sandstone as dry sample (LxBxH) shown in figure 1. With this steady state method a constant confining pressure of 4 bar was induced. At the upstream side a gas (air) pressure up to 1.5 bar was created.

The gas volume was measured at the downstream side with the soap bubbles: The velocities of the rising bubbles were measured in the brine. Out of this the “bubble” volume the gas flow can be determined.

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and the Klinkenberg correction

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The absolute permeability can be calculated. The temperature is supposed to be constant by about 25°C.

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Fig. 1: Photo of the apparatus with description.

The effective (or absolute) permeability of water is measured with a second apparatus. Here the dry sample is put into a dense glass cube surrounded by water with a confining pressure of 2 bar. The sample itself is sealed from the water. Now another water source with an upstream volume respectively to a height of a water column of 1.55 m is used to saturate the sample with water. On the downstream side the out coming volume of water with time is measured with a burette of 10 ml. The single-phase and steady state apparatus is shown in figure 2. Here is Darcy’s law for incompressible media applied:

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A Klinkenberg correction can’t be done here, because the used medium is water and not gas.

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Fig. 2: Schematic picture of used apparatus.

II. Darcy's law for compressible media

The absolute permeabality can be calculated out of the measurement results which were getting of the first descripte apparatus. The used sample 47-3 has a radius of 0.018 m, an area of 0.001121 m² and a length of 0.0371 m, the other sample 26-3 has a radius of 0.0189875 m, an area of 0.0011326 m² and a length of 0.024225. With the known atmospheric pressure (P2) of 101325 Pa, a gas viscosity of 0.000018 Pa/s and the measurement results for the relative pressure, shown in table 1 and 2, the absolute pressure (P1) can be calculated. The Pmean values, respectively , necessary for the Klinkengerg correction can be calculated with the artihemic mean ( and is shown in table 1 and 2, too.

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Tab. 1: Measured values for the relative pressure [Pa] and calculated values for P1, Pmean and 1/Pmean for both samples 26-3 and 47-3.

The measured volumes of gas over time are shown in table 2. Out of these results the flow rate [m³/s] and the flux [m/s] using the value for the area can be calculated. The permeability coefficient (k) is determined by using Darcy’s law for compressible media and is also shown in table 2.

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