(376al) Combined Concentration Polarization and Pore-Flow Modeling to Predict the Performance of a Nano Filtration Membrane for NaCl Rejection

Abstract:

Membrane based filtration techniques
are gaining importance day by day for its effectiveness and simplicity [1]. Different pressure driven techniques are exercised for
membrane separation; nano filtration is one of them. Nano filtration membranes
stand handy for different applications because of their thermal, chemical and
mechanical stability [2]. High surface charge of these membranes help in
separation of charged species from a solution. This particular property can be
used to segregate any type of salt from water. Hence, it can be a useful
technique for desalination of water which is a challenge for present day's world
[3,4].

            Modeling and simulation
always provides useful lead to understand the underlying physical phenomenon
behind a real life system. It also proves to be useful in scaling up the system
and predict its performance in remote scenarios. Transport phenomena based
membrane modeling is not a new field of study; a number of works have been
reported till date which deals with it. Different studies have been done
starting from prediction of different fouling mechanism [5,6] of membranes to prediction of flux for different
processes [7,8]. In order to predict the flux and permeate
concentration across the membrane a number of theoretical models have been
proposed such as (a) osmotic pressure model [9–11]; (b) film theory [12–14]; (c) solution diffusion model; (d) Kedem-Katchalsky
equation etc. Each of these models has their advantages and limitations also.
In film theory the mass transfer boundary layer is assumed which under predicts
the permeate flux of the membranes. Prediction of exact relation between
osmotic pressure and solute concentration is very hard and often leads to
erroneous flux prediction. If these models are used in tandem with similarity
solution then gives further erroneous result. Similarity solution technique
uses the order of magnitude analysis method which is an approximation method to
club different coordinates into a uniform one. On the other hand integral
analysis gives much accurate result than its similarity counterpart. Pore flow
model on the other hand gives extremely satisfactory result in case of
transport of charged species through membranes which possesses effective
surface charge [15–17]. This model uses the Nernst-Planck equation within the
membrane pores to predict actual amount of species transport through a membrane
which other models fail to predict to that accuracy.         

            However, to the best of
the knowledge of the authors there is no attempt has been made where integral
method is coupled to the pore flow model in order to predict the flux and
amount of species transported across a membrane with realizable surface charge.
In this present work attempt has been made to bridge this gap. Here integral
method has been used to calculate the concentration within the mass transfer
boundary layer and on the membrane surface and then pore flow technique is used
to predict actual flux and concentration profile at permeate. Simulation data
are then compared with the experimental findings and it can be observed from
the results that they are in excellent agreement with each other. This study
will be extremely helpful in predicting the performance of nano filtration
membranes and also to scale up the process. 

Key words: Membrane; pore flow, nano
filtration,

Result:

Some results are given below which
shows the parity between experimentally determined permeate flux and
concentration (with respect to the transmembrane pressure) with that of the
theoretical one.  

Variation of non dimensional permeate concentration with
transmembrane pressure.

Variation
of permeate flux with transmembrane pressure.

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