Permeability testing
The two reservoirs connected to the sample end-faces have volumes
V1=58.725 ml and V2=162.53 ml, and at
the beginning of the test, we connected the reservoirs to a
high-pressure helium gas bottle to raise their internal pressures to two
different values P1i > P2i.
While P1i is greater than P2i, helium
flows through the sample until pressure equilibrium is reached. Two
digital manometers (Keller LEO3) connected to a computer and a Matlab
code record P1 and P2 over time (t). The two manometers also measure
temperature (T). Permeability is then calculated as:
\(\kappa=-\frac{\text{β\ η\ L}}{\left(\frac{1}{V_{1}}+\frac{1}{V_{2}}\right)\text{\ K\ A}}\ \),
eq. S1
Where η and K are Helium viscosity and bulk modulus, respectively; L and
A are the lengths and cross-section area of the sample; \(\beta\) is the
exponent of the pressure decay:
\(P_{1}={(P}_{1i}-{P_{2i})\ e}^{\text{β\ t}}+P_{f}\), eq. S2
Where \(P_{f}\) is the equilibrium pressure, i.e., P1and P2 at time infinite. We assume helium properties as
a function of pressure and temperature from the national institute for
standards and technology (NIST) fluid thermophysical properties (Arp et
al., 1998; Ortiz-Vega et al., 2020). \(P_{f}\) and \(\beta\) were
estimated by means of a non-linear least absolute residuals fit
implemented in Matlab.