Correct estimation of permeability using experiment and simulation

Abstract

Estimation of permeability of porous media dates back to Henry Darcy [H. Darcy, Les Fontaines Publiques de la Ville de Dijon (Victor Dalmont, 1856)], and its knowledge is essential in many scientific and engineering endeavors. Despite apparent simplicity of permeability measurements, the literature data are scattered, and this scatter not always can be attributed to the precision of experiment or simulation or to sample variability. Here, we demonstrate an excellent agreement (<1%) between experiments and simulations, where experimental results are extensive and stable, while flow is simulated from first principles, directly on three-dimensional images of the sample, and without fitting parameters. Analyzing when experiments and simulations agree reveals a major flaw affecting many experimental measurements with the out-of-sample placement of pressure ports, including industry standards. The flaw originates from (1) incorrect calculation of the applied pressure gradient, (2) omitting virtual part of the measured system, and (3) pressure loss at the sample–tube contact. Contrary to common wisdom, the relative magnitude of (3) is defined by the sample–tube diameter ratio and is independent of the size of sample pores. Our findings are applicable to a wide range of permeability measurements, including geological-sample-type (Hassler cell) and membrane-type. The reported pressure loss (3) also affects two-phase flow measurements, such as capillary pressure estimation. Removing or taking the flaw into account advances the understanding and control of flow-related processes in complex geometries.