Validation of gas flow experiments for porous media by means of computer simulations

Abstract

A profound understanding of gas flow in porous media is of great interest for various technological and scientific fields. Its investigation by laboratory measurements, however, poses several challenges. In particular, the determination of macroscopic flow parameters from pressure and gas flow measurements is prone to various error influences, some of which are very difficult to analyze experimentally. Computer simulations are a solution in this context as they facilitate modifications of the underlying geometry and boundary conditions in a flexible way. Here we present a simulation framework for the analysis of a recent experiment for determining the Knudsen diffusion coefficient and viscous permeability of various porous granular materials. By combining the finite element method with analytical models and other numerical methods, we were able to identify previously neglected physical effects that increase the uncertainty of the measurements. In particular, the porosity increase due to finite sample dimensions, in a layer of about a grain diameter thickness near the container wall, creates a deviation of the measured pressure gradient. This deviation amounts to ca. 5% for a sample width of about 100 grains and a porosity of 0.5, and is indirectly proportional to the porosity. The second most prominent error source, the sample support sieve, causes a slight constriction of the flow volume. Simulations of this effect show an error around 4-7%, dependent on the grain size. Based on these findings we recommend an overall sample dimension of 100 grains or larger. As an example of failures of the sample homogeneity, we elaborate how channels through the sample influence the flow properties. Respective suggestions for keeping all discussed effects negligible are discussed in detail. Our methodology demonstrates how the combination of finite element computations with analytical representations of the involved macroscopic parameters can assess the validity and accuracy of laboratory experiments.

Simulation and experiment of gas diffusion in a granular bed

“…The dashed lines show the same analysis but the porosity is averaged in planes (left) or cylinder shells (right) of one sphere diameter thickness. This is quantitatively comparable to the analysis of Laddha et al (2023) and expected to be the same as in experimental samples. The consequence of these boundary effects will be further discussed in Sect.…”

“…Boundary effects from the reduced porosity at container walls affect the experimental measurements and most probably also those by Schweighart et al (2021) and Asaeda et al (1974). Additional boundary effects influencing the experimental measurements are described by Laddha et al (2023). Most of these are avoided in the presented work, by paying special attention to the measurement setup and by a careful sample selection and preparation.…”

“…Experimental work on the rarefied gas flow through granular beds, aiming to represent cometary surface layers, was recently performed by Schweighart et al (2021), supported by numerical simulations by Laddha et al (2023). That work is focused on the transition regime between viscous and Knudsen flow.…”

Transmission probability of gas molecules through porous layers at Knudsen diffusion

“…In many applications it is advantageous to use T to describe the gas molecules throughput through a layer [12,13]. In other circumstances, in particular when the flux as it develops throughout the medium is of interest, the Knudsen diffusion coefficient D K is sought [10,14,16]. It represents the molecular flux per number density gradient in the porous medium.…”

Cometary dust collected by MIDAS on board Rosetta

“…Furthermore, the flow properties of bulk materials (e.g., flowability) are influenced by particle shape and particle size, amongst others (Mellmann et al 2013). Thus, the investigation of unaltered and thus more realistic particles could open up new possibilities for unraveling unresolved questions in space science, particularly in gas flow experiments in cometary environments (Laddha et al 2023). The importance of shape descriptors of the non-spherical MIDAS particles (Bentley et al 2016b;Kim et al 2023) is further enhanced as traditional models using purely spherical particles might not be sufficient to significantly improve gas flow models further.…”