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A pulse-decay method for low permeability analyses of granular porous media: Mathematical solutions and experimental methodologies
  • Tao Zhang,
  • Qinhong Hu
Tao Zhang
University of Texas at Arlington
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Qinhong Hu
University of Texas at Arlington

Corresponding Author:[email protected]

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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.