A pulse-decay method for low permeability analyses of granular porous
media: Mathematical solutions and experimental methodologies
Abstract
There are lingering issues concerning gas permeability measurements at
nano-darcy levels for low-permeability media. This is due to the lack of
both well-documented mathematical solutions for interpreting gas flow
data in granular samples, as well as standardized experimental
methodologies needed to provide reproducible results. In this work, the
mathematical solutions by Cui et al. (2009) have been upgraded into a
detailed gas permeability technique (GPT), which provides a
re-derivation of three mathematical solutions (one not presented
previously), essential laboratory methodologies, and data processing
procedures, in the form of a pulse decay method for matrix permeability
measurements of tight granular media. Mathematically, this work provides
the 1) evaluation of the applicable conditions and error analyses for
these three solutions; 2) investigation and recommendations for the GPT,
both mathematical solutions and experimental procedures; and 3)
examination of the flow state of probing gases using the gas kinetic
theory. Experimentally, this work documents that 1) proper values of
(gas storage capacity) and (dimensionless time) need to be considered;
2) a stable temperature and unitary gas condition (e.g., helium) are
critical to maintain. The results show that a wide range of flow
regimes, from laminar flow to Fickian diffusion after slippage
correction, can be studied to derive the transport coefficient using the
GPT technique, which is a rapid, sensitive, and reproducible method for
the measurement of sub-nano-darcy level matrix permeabilities in
granular and crushed rock samples.