Accurate measurement of micro gas flow rates for comprehensive evaluation of polymeric membranes applicable in gaseous separations

ABSTRACT

The time-lag method is the most useful technique to determine gas permeability, diffusivity, and solubility. However, it is difficult to evaluate the transport properties of the membrane accurately because gas permeability depends on the technique used to assess gas flow. The significance of the present study is to design an economic isochoric apparatus to accurately measure micro-range gas flow rates ranging from 10⁻⁶ to 10 cm³(STP) s⁻¹. A strategic procedure is demonstrated to eliminate possible artifacts while conducting the gas permeation experiments, including utilizing downstream pressure rise profiles to identify nanoscale defects as well as transient and steady-state permeation. An indigenous apparatus was developed to estimate the polymeric intrinsic properties of the dense and thin-film composite membranes. The device has been successfully used to measure the gas permeation flow rate ranging from 1 × 10⁻⁵ to 1 × 10⁻¹cm³ (STP) s⁻¹, which indicates the broad applicability and reproducibility of the data suggesting the reliability of the designed apparatus. Permeation flow rates of binary mixtures of CO₂/CH₄ through the defect-free membranes were compared with the numerical estimations to validate the measured transport properties.

KEYWORDS:

• Gas separation
• membrane solubility
• isochoric apparatus
• asymptote fitting
• surface defects

Acknowledgments

This paper is of IICT manuscript communication number IICT/Pubs.2020/253. The first author Shiva Prasad Nandala is grateful to the Council of Scientific and Industrial Research (CSIR), New Delhi, India. and RMIT, Australia, for funding his research program. The instrumentation Division and Engineering workshop cluster of CEPT Division who rendered their support are also thankfully acknowledged. The corresponding author would like to thank GAP-789 project for granting the funds necessary for developing the Isochoric apparatus.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Consent to participate

This article is done by us together.

Consent for publication

All authors are willing to publish this work.

Terminology

Permeation rate (Q): The rate at which a gas permeates through the membrane matrix; the units for this quantity are given as cm³(STP)s⁻¹.

$\mathit{Q}=\frac{d{V}_p}{\mathit{dt}}$

Flux (J): The quantity of a given gas passing through a unit area of the membrane per unit time. The unit of this quantity is given as cm³(STP)s⁻¹cm⁻².

$\mathit{J}=\frac{Q}{A}=\frac{1}{A}\frac{\mathit{dv}}{\mathit{dt}}$

Permeance ($\tilde{P}$): The ratio of the gas permeation flux to the transmembrane pressure difference. The commonly used unit of permeance is GPU (10⁻⁶$\frac{c{m}^3\left(\mathit{STP}\right)}{\mathit{c}{m}^2\mathit{scmHg}}$) which is a thickness normalized permeation coefficient. This quantity is for non-homogeneous (Asymmetric membranes) such as thin-film composites or multi-layered membranes.

$\tilde{P}=\frac{J}{\mathrm{\Delta }\mathit{P}}=\frac{1}{\mathit{A}\Delta \mathit{P}}\frac{\mathit{dv}}{\mathit{dt}}$

Permeability (P): Permeability is a fundamental characteristic property of a gas-permeable membrane and is calculated by multiplying permeance and the thickness of the membrane. Barrer (10⁻¹⁰$\frac{c{m}^3\left(\mathit{STP}\right)\mathit{cm}}{\mathit{c}{m}^2\mathit{scmHg}}$) is the worldwide accepted unit for permeability. This quantity is meaningful only for homogeneous materials, in which the bulk characteristic properties remain unchanged as far as thickness is concerned. Hence, this quantity denotes the permeation coefficient for monolayered non-porous membranes.

$\mathit{P}=\tilde{P}\ast \mathit{l}=\frac{l}{\mathit{A}\Delta \mathit{P}}\frac{\mathit{dv}}{\mathit{dt}}$

Stage cut

Ratio of permeate flow rate to feed flow rate (Q_P/Q_F).

Supplementary material

Supplemental data for this article can be accessed online at https://doi.org/10.1080/01496395.2024.2346753

Nomenclature

Q	=	Permeation rate, cm3s−1
P	=	Permeability coefficient, Barrer (10−10$\frac{c{m}^3\left(\mathit{STP}\right)\mathit{cm}}{\mathit{c}{m}^2\mathit{scmHg}}$)
D	=	Diffusivity coefficient, cm2s−1
S	=	Solubility, cm3(STP) cm−3s−1
$\tilde{P}$	=	Permeance, GPU (10−6$\frac{c{m}^3\left(\mathit{STP}\right)}{\mathit{c}{m}^2\mathit{scmHg}}$)
l	=	Thickness of the specimen, cm
A	=	Area of the specimen, cm2
$\frac{\mathit{dp}}{\mathit{dt}}$	=	Rate of pressure change, cmHgs−1
V	=	Receiver volume, cm3
Vf	=	Upstream volume, cm3
∆P	=	Transmembrane pressure (TMP), cmHg
T	=	Temperature of the receiver, ℃
ϴ	=	Time-lag, s
xf	=	Mole fraction in the feed
xr	=	Mole fraction in the reject
y	=	Mole fraction in the permeate