Inorganic Microporous Membranes for Gas Separation in Fossil Fuel ...

2 Theoretical background
wall interaction is often referred as transition flow and is presented in equation (11). The
first term in equation (11) originates from the viscous flow and the second from the
Knudsen diffusion equation. Both contributions can be identified from experimental data
(12).
N = −
2 ( Ar P + Br)
ε dP
τ dz
⎛ 1 ⎞ 2 8
A = ⎜ ⎟ B =
(12)
⎝ 8ηRT
⎠ 3 πMRT
The α-Al2O3 support with γ-Al2O3 intermediate layer show gas transport predominantly
by Knudsen diffusion as reported by Benes et al. 91
Micropore diffusion
Several research groups 45,91,122,124 have studied the gas transport in microporous media
such as the well-defined pore size MFI zeolite type membranes and amorphous sol-gel
derived silica membranes. The transport mechanisms in microporous membranes are a
function of the pore size, (condensable) properties of the transported species, activity of
the pore wall, applied temperature, texture and microstructure of the microporous layer
such as the connectivity of the pores, the porosity, the concentration and the connectivity
of the defects, and the thickness of the layers.
The single gas flux in microporous membranes is based on diffusion where the gas
molecule pore wall interaction is more frequent than the gas molecules interaction. The
diffusion flux (N in mol/m 2 s) is determined by the concentration of the gas and the
mobility of the gas to hop from one void (hereafter referred as the pore) to the
neighbouring pore. This theory of irreversible thermodynamics, where the flux of single
gas ‘i' is proportional to the gradient in its chemical potential for microporous
membranes, is thoroughly outlined by Benes. 122 The mass transport in microporous
membranes follows the Henry regime at high temperatures with relatively low pressure
and results in the following equation (13):
~
D
N = ∆
L
( T ) K(
T )
P
∆P represents the pressure difference over the membrane. L is the thickness of the
membrane layer. D ( T )
~
35
(11)
(13)
is the concentration independent single component chemical
diffusion coefficient and is related to the mobility of the gas component. K(T) is the
Henry coefficient. The diffusion flux is a thermally activated process described by an