(430g) A Novel Membrane Flux And Separation Factor Calculation Combined To Modified Unifac Model And Percolation-Fractal Theory | AIChE

# (430g) A Novel Membrane Flux And Separation Factor Calculation Combined To Modified Unifac Model And Percolation-Fractal Theory

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Tsinghua University
Membrane Technology & Engineering Research Center, Tsinghua University
Membrane Technology & Engineering Research Center

AICHE 2007 ABSTRACT

The study discusses the mass transfer models within membrane, which emphasizes particularly on the consideration to the transfer mechanism within membrane and membrane flux calculation. Solution-diffusion model was broadly applied in the separation mechanism of dense membrane, which includes solution (sorption) process, diffusion process and desorption process. It is generally suggested that the solution (sorption) process or diffusion process is the velocity-determined step. This solution process was more complex because of the plastication of components (membrane swelling) to polymer and the coupling effect between components.

Sorption models included UNIQUAC model, UNIFAC model, ASOG-FV model, Flory-Huggins theory, Entropic-FV model, Modified NRTL model and ENSIC model, etc. These models are related to statistic thermodynamics and physical chemistry. Among these models UNIFAC model is semi-empirical and needs less experimental data. Therefore UNIFAC model is often applied if experimental data is not enough.

Diffusion models included empirical models, dual sorption model and free volume theory. Because empirical models need too many parameters to apply in the complex (multi-component) system, the membrane flux can be calculated by the fitting and regression of mathematical methods. Dual sorption model might nevertheless be used as a foundation to understand the transfer process of high concentrations of liquids and vapors because it seems to be applicable to vapor permeation at low pressures. The essence of free volume model is that the small molecules transfer in the free volume to permeate from the membrane at last. The free volume can be described as temporary hollow spaces in the polymer structure as a result of density deviations of the polymer. The membrane flux can be obtained by reason of a set of complete calculation method in the free volume theory. However it is not excellent for these above-mentioned models to interpret the abnormal diffusion phenomenon within membrane.

The abnormal diffusion phenomenon is a kind of diffusion phenomena that does not conform to the Fick's law or are named as the non-Fick diffusion phenomena. In uniform Euclidean systems, the mean-square displacement of a random walker,, is proportional to the time t, , for any number of spatial dimensions d (Fick's Law). However, in disordered systems, this law is not valid in general. Rather, the diffusion law becomes anomalous, with, this indicates the slowing down of the diffusion. The slowing down of the diffusion is caused by the delay of the diffusing particles in the dangling ends, bottlenecks and backbends existing in the disordered structure. It is usually proposed that polymer membrane belongs to the disordered media system. Therefore the diffusion within membrane is a kind of abnormal diffusion. Very many researches deal with the abnormal diffusion phenomena, in which satisfactory interpretation can not be obtained.

Tiangang Shang and Cuixian Chen et al. put forward percolation-fractal model, in which anomalous diffusion phenomenon of small molecules transferring within membrane were systemically investigated. It is considered that the transfer process of small molecules is a random walk process in 'transfer path' within membrane. According to percolation theory, fractal geometry and random walk theory, the probability density expression of small molecules was deduced in the 'transfer path' of fractal region. It is not enough to consider the complex interaction among polymer molecules, among small molecules and between polymer molecules and small molecules in the percolation-fractal model.

According to the above-mentioned transfer mechanism within membrane, we suggested that it is necessary to sufficiently consider the various interactions among different components and between different components and membrane polymers. Firstly, sorption activities of small molecules can be calculated in feed and permeating side as the boundary values of the probability density expression in accordance with the modified UNIFAC model. The fractal dimension  and the abnormal diffusion exponent  can be determined by the renormalization and numerical calculation. The undetermined coefficients b and c in the probability density expression can be calculated adopting the boundary values from the modified UNIFAC model. Consequently the membrane flux and separation factor can be calculated adopting the probability density expression according to the integral transfer equation.

A novel membrane flux and separation factor calculation is proposed considering the interaction among polymer molecules, between polymer molecules and small permeating molecules, among small permeating molecules and probability density expression of small permeating molecules within membrane characteristic of stochastic fractal deducing from abnormal diffusion phenomenon within membrane. The continuous macroscopic membrane flux and separation factor can be calculated combined to the interaction between varied components in the system and the probability density that is microscopic discontinuous quantity.

It is concluded from the comparing and analyzing of theoretical flux and experimental flux, calculation separation factor and experimental separation factor that the errors are usually below the permissible error 20%. This indicates that the membrane flux and separation factor calculation is appropriate to application.

We described the mass transfer behavior of small permeating molecules within PVA composite membrane and analysed the interaction among polymer molecules, between polymer molecules and small permeating molecules, among small permeating molecules. It is determined of the key factor to the mass transfer behavior of small permeating molecules. The substituting degree, feed and permeating concentration effect on membrane flux and separation factor were determined by the calculation method.

The authors made a thorough research on the probability density expression of small molecules in the mass transfer within membrane. The fractal dimension and abnormal diffusion exponent were determined by numerical calculation, series expansion and renormalization. The flux and separation factor were calculated adopting UNIFAC model and probability density expression of small molecules, which results in the application of this membrane flux and separation factor calculation.

In accordance with the thorough research on the transfer mechanism, the calculation was obtained to predict membrane flux and separation factor which are comparatively consistent with experimental. According to the comparing and analyzing of the above calculation and experimental, the various key factors to determine membrane flux and separation factor were obtained to be able to make a direction to membrane material choice, membrane preparation conditions and feed treatment conditions.