Selective Salt Recovery from Reverse Osmosis Brine - University of ...

action equation including activities. The activities in the solution phase were estimated
using the Bromley [21] method and resin phase activities were estimated using the
Wilson model [22]. The column was divided into equally sized elements in which a mass
balance equation including bed density, interstitial velocity, axial dispersion mass transfer
coefficient, total voidage, time and space was included. The equation also included mass
transfer terms for the external liquid film and the inside of a particle of resin. Mass
transfer was modeled as having two distinct parts, 1) the movement of ions from the bulk
phase through liquid film and 2) the diffusion of ions into the micro-pores of the resin.
The exchange reaction itself was considered to be instantaneous. The finite volume
method was used to solve the mass balance equations. His results matched well to
experimental data of ion exchange columns in which zinc was exchanged for sodium. He
concluded that the initial stage of mass transfer is controlled mainly by film resistance but
the overall mass transfer process is inter-particle resistance.
Nakamura [23] modeled a column containing a hydrogen-sodium-ammonia system.
He defined selectivity in terms of molarity and divided the column in equal volume
segments. In his model, total resin capacity and selectivity were determined as fitting
parameters, and he found that the exchange rate depended on the overall liquid phase
mass transfer coefficient and the surface area of particle. Film diffusion resistance was
found to control the overall rate of mass transfer.
Another application of the mass action law to model of ion exchange in a fixed bed
column was put forth by Borba et et [24]. This model considered thermodynamic
equilibrium at the liquid-solid interface, the external mass transfer resistance and internal
diffusion resistance (in series), and the concentration profile within pores described by
linear driving force (LDF) to predict ion exchange capacity. The column was divided
into equal volume segments and the following calculations were completed for each
segment using the finite volume method: liquid phase mass balance, external film mass
transfer, liquid phase charge balance, diffusion of species within particles, resin phase
charge balance, and mass balance between external mass transfer and diffusion mass
transfer. The Langmuir and the mass action law of equilibrium were compared to see
which fit the data better, and both were found to fit the data well. A column model
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