Modeling the impacts of feed spacer geometry on reverse osmosis and nanofiltration processes
Introduction
Optimizing momentum and mass transfer in spiral wound elements is crucial for designing effective and efficient nanofiltration (NF) and reverse osmosis (RO) membrane processes. For example, poor mass transfer in NF/RO elements exacerbates concentration polarization, which increases osmotic losses, solute passage, and surface fouling phenomena [1], [2], [3], [4], [5], [6]. Plastic mesh feed spacers are thought to improve mass transfer in spiral wound elements, but this improvement comes at the cost of increased hydraulic losses. Hence, efforts to understand the interplay between feed channel geometry, hydrodynamics, mass transfer, and pressure drop in NF/RO spiral wound elements comprised a significant component of membrane research for many years [7], [8], [9], [10], [11], [12].
In principle, a better understanding of microscopic mass and momentum transfer in spacer-filled channels can improve spiral wound element design, product water quality, and energy efficiency of NF/RO processes. Numerous empirical correlations are available to describe mass and momentum transfer in open and spacer-filled channels [13], [14]. These approximate analytical models provide channel-averaged descriptions that are easily leveraged in macroscopic models of full-scale NF/RO system performance [15]. An alternative modeling approach involves computational fluid dynamic (CFD) simulations, which rigorously describe microscopic transport phenomena [10], [16], [17], [18], [19], [20], [21], [22], [23], [24]; however, it is difficult to translate CFD results into full-scale performance models.
The aim of this work is to develop a multi-scale model that links microscopic and macroscopic transport phenomena enabling rigorous assessment of full-scale process performance as a function of feed spacer geometry (filament size, shape, and separation). Microscopic transport is evaluated using a previously developed finite element-based numerical model of momentum and mass transfer in spacer-filled membrane feed channels [10]. Next, we fit the numerical results with empirical correlations for mass and momentum transfer. Finally, we incorporate the empirical correlations into a macroscopic model describing full-scale NF/RO process performance. Full-scale simulations elucidate potential impacts of feed spacer geometry on mass transfer, hydraulic losses, product water quality, and energy consumption in four representative NF/RO-based water purification scenarios.
Section snippets
Full-scale NF/RO system performance
The macroscopic transport model outputs include global average product water quality in the form of system average permeate solute concentrations (Cp) and product water fluxes (), as well as total product water recovered (Y) and specific energy consumed (SEC). System average product water flux is determined fromwhere Qp is the total product water flow rate, Am is the total membrane area, is the local permeate velocity, x is the axial location, and L is the total system
Insights derived from the microscopic model
The microscopic transport model describes concentration, pressure, and velocity profiles in a short section of a spacer-filled channel. Concentration and pressure profiles (, u0 = 0.1 m s−1, and rs = 0.99) for an open channel (hc = 0.5 mm) and a spacer-filled channel (hc = 0.5 mm, df/hc = 0.5, and lf = 2.25 mm) are plotted in Fig. 4. There is a sharp decrease in concentration and increase in pressure near each spacer. For the scenario depicted, spacers decrease concentration polarization by a few
Conclusions
A new multi-scale modeling approach utilized finite element simulations of momentum and mass transfer in spacer-filled channels to develop mass transfer and friction factor correlations, which were then used in a macroscopic model of full-scale NF/RO process performance. Hence, the impacts of microscopic transport were translated into system level outcomes for the first time. From this model study, we conclude the following.
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Friction-related hydraulic losses are dramatically more sensitive to
Acknowledgements
Financial support for this work was provided by the UCLA Cota-Robles fund and graduate student opportunity award. We also thank Dr. Arun Subramani of MWH for valuable discussions regarding finite element-based CFD simulations.
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