Effective Diffusivities of Gases in a Reconstructed Porous Body
Advancing the chemical engineering fundamentals
Transport Phenomena in Porous/Granular Media - II (T2-7b)
Keywords: stochastic reconstruction, pore network, random walk, diffusivity
A method of the 3-D stochastic reconstruction based on statistical
information obtained from 2-D cuts through the porous body is exemplified
on a sample of $\alpha$--alumina with the total porosity $\phi = 0.404$.
A 3-D replica (image) of $\alpha$-alumina conforming to the measured and
simulated microstructural descriptors is generated by the simulated annealing
technique. Microstructural descriptors considered for this purpose include
the two-point probability function and the lineal-path function of the void
phase. The 3-D image of the pore space is analysed and transformed onto an
equivalent 3-D pore network of irregular topology. Since visual inspection
of the image reveals that the pore space is well represented by pores of
convergent-divergent shapes, a chamber-and-throat network with nodes arranged
on the simple cubic lattice is chosen for the transformation.
A simulator of steady diffusion flow in the pore network is used for prediction
of effective diffusivities of inert gases (isobaric counter-current diffusion
in binary mixtures involving H$_2$, He, N$_2$, and Ar).
For each network bond comprising a throat and halves of two adjacent chambers,
a general expression for the diffusion flow rate as the function of nodal mole
fractions, pore dimensions, and transport properties of gases (e.g. bulk binary
diffusivity, $D_{AB}$) is derived. These flow rates have to fulfil the mass
conservation law in all network nodes, which are located in the centres of
gravity of chambers. By imposing a macroscopic gradient of mole fractions
across the pore network, unknown values of the nodal mole fractions are
determined by solving the corresponding system of non-linear equations. Finally,
the total flow rate through the network boundary is computed and the effective
diffusivity is evaluated from the first Fick law. In addition to these network
calculations, the ratio of the bulk binary diffusivity to the effective diffusivity,
$F = D_{AB} / D_{AB}^{\mathit{eff}}$, in the 3-D replica is directly estimated
by exploiting random-walk simulation, which is based on calculation of the
mean-squared displacement versus time for a number of Brownian particles taking
discrete steps in the pore space. Both predicted values of the ratio $F$ (8.33
and 7.98 predicted by the network calculation and by random-walk simulation,
respectively) are in a good agreement with its experimental value of 8.1.
Note, that the ratio $F$, which is identical, in form, to the formation factor,
slightly deviates from Archie's law $F = \phi^{-2} = 6.13$ in our particular case.
See the full pdf manuscript of the abstract.
Presented Tuesday 18, 16:00 to 16:20, in session Transport Phenomena in Porous/Granular Media - II (T2-7b).
