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In forward osmosis (FO), an osmotic pressure gradient generated across a semipermeable membrane is used to generate water transport from a dilute feed solution into a concentrated draw solution. This principle has shown great promise in the areas of water purification, wastewater treatment, seawater desalination and power generation. To ease optimization and increase understanding of membrane systems, it is desirable to have a comprehensive model that allows for easy investigation of all the major parameters in the separation process. Here we present experimental validation of a computational fluid dynamics (CFD) model developed to simulate FO experiments with asymmetric membranes. Simulations are compared with experimental results obtained from using two distinctly different complex threedimensional membrane chambers. It is found that the CFD model accurately describes the solute separation process and water permeation through membranes under various flow conditions. It is furthermore demonstrated how the CFD model can be used to optimize membrane geometry in such as way as to promote the mass transfer.
Symbol  Description  Unit 
water permeability  m (s Pa)^{−}^{1}  

solute permeability  m s^{−}^{1} 

solute concentration  kg m^{−}^{3} 
diffusion coefficient  m^{2} s^{−}^{1}  
g  gravitational acceleration  m s^{−}^{2} 
J_{s}  solute flux  kg (m^{2} s)^{−}^{1} 
J 
water flux  m s^{−}^{1} 
diffusion resistivity  s m^{−}^{1}  
mass transfer coefficient  s m^{−}^{1}  
solute mass fraction  kg kg^{−}^{1}  

surface normal vector  m 

surface normal direction  m 

viscosity of fluid  Pa s 

pressure  Pa 

osmotic pressure  Pa 
seperation coefficient    
Reynolds number    

fluid denisty  kg m^{−}^{3} 

structural parameter  m 
U  fluid velocity vector  ms^{}^{1} 
mean crossflow velocity  ms^{−}^{1}  
Index  Description  

drawside of membrane  

feedside of membrane  

between active layer and support  

at the membrane surface 
In recent years, forward osmosis (FO) has received increasing interest as an alternative to conventional hydrostatic pressuredriven membrane processes. Compared with pressuredriven systems, FO is an approach driven by an osmotic pressure gradient across a semipermeable membrane and requires no hydraulic pressure operation. As a consequence, FO is potentially more costeffective compared with, e.g., reverse osmosis (RO) [
Despite the unique advantages of FO, a number of technical barriers still impede industrial applications [
Membrane separation processes, especially in pressuredriven systems, have been extensively studied during the last 40 years and many different analytical or semianalytical models have been proposed for describing various features of the separation processes, e.g., effects such as concentration polarization [
Several CFD models dealing with pressuredriven membrane systems have been developed [
Here we present experimental validation for the CFD model in two different complex threedimensional membrane chambers and use simulated results from these chambers to demonstrate the strength of the CFD approach by discussing and analyzing the results with the goal of masstransfer optimization in mind.
The membranes used in all experiments were obtained from a SeaPack product (HTI, Albany OR, USA). FO experiments were performed using two different chamber geometries (see representations in
The computational meshes for the two flow chambers used in simulations. These represent the geometries of the chambers used in experiments. The membranes are modeled as planes in the middle of the chambers, lying in the symmetryplanes normal to the
The CFD model used in this work has been described in our previous work [
In the model the membranes are assumed to be smooth twodimensional planes over which the water permeation flux is given as follows, assuming that hydraulic pressure differences across the membrane can be ignored and that there is a linear relationship between solute concentration and osmotic pressure [
Assuming a linear relationship between the solute concentration and osmotic pressure,
The solute flux is in the opposite direction of the water flow,
In summary, Equation (4) provides a boundary condition for the velocity on either side of the membrane and Equation (6) provides a boundary condition for the solute mass fraction
Both investigated chambers have a plane of symmetry normal to the Yaxis (see
The chamber geometries used in all experiments and simulations are represented by their computational domains in
In order to obtain meaningful results it is essential that the computational grids are fine enough to capture any significant flow effects. For most simulations performed in this work, the computational grids consisted of approximately 500,000 cells. In both chambers the cells were graded such that the first grid points were located within 5 µm of the membrane, which was done to accurately capture ECP effects [
The CFD model allows the osmotic pressure, fluid viscosity, solution diffusion coefficient and fluid density to be functions of solute mass fraction. Empirical expressions for the physical properties of a NaCl solution at 25 °C were taken from Geraldes
The CFD model requires knowledge of three membrane characteristics, namely the pure water permeability coefficient
which is valid at concentrations up to 1.5 M [
In Equation (13)
The numerical procedure was the same as described in our previous work [
Steadystate solutions in which the water flux and solute flux no longer changed were obtained after simulation corresponding to a few minutes of realtime flow had been performed. It was confirmed that the simulations obeyed overall mass balance, and that the flux balance equation, Equation (6), was satisfied on both sides of the membrane.
In order to simulate an FO system, the present model requires information about the three membrane parameters
The solute resistivity to diffusion within the porous layer,
Membrane water fluxes at different crossflow conditions. Measurements were performed experimentally using chamber A (see
The obtained membrane parameters are summarized in
Experimentally determined membrane parameters.
Parameter  Value  Unit 



A  0.44 ± 0.05  L (m^{2 }h bar)^{−}^{1}  5  3 
B  0.087 ± 0.018  L (m^{2 }h)^{−}^{1}  5  2 
K  0.72 ± 0.23  s

5  5 
The major obstacle in simulating threedimensional flows is the amount of computer time required. It is therefore common to simplify problems to twodimensional cases, which in most instances can provide valuable and accurate insights into many aspects of a given problem at a fraction of the computational cost [
It is essential that the computational grids used in threedimensional CFD analyses are capable of resolving all significant flow features. It is equally important not to use too fine a grid because that will dramatically increase computation time. In effect, a compromise has to be made between accuracy and computation time. To decide on this compromise, in this work we require GCI_{coarse} for coarse computational grids to be less than 1% when comparing them to finer grids with approximately three times the number of cells (see
One of the major advantages of threedimensional CFD models over analytical models is the ability to optimize a given design without needing to first construct and test a wide range of expensive physical prototypes first. For such an approach to be meaningful, it is required that the CFD model accurately depicts any given problem and the model should therefore be validated against experimental data. With this goal in mind, we chose to investigate experimental and numerical results for water and solute fluxes for two significantly different geometries. It is noted that CFD models face computational limitations for very complex and large systems.
Comparative experimental and numerical experiments were performed with 1 M draw solutions, pure water feed solutions and using constant crossflows of 50 mL min^{−}^{1 }. According to
Experimental and simulated water and solute fluxes in chambers A and B. Experiments as well as simulations were carried out using a 1 M draw solution, a pure water feed solution, and a crossflow of 50 mL min^{−}^{1}. The units of
Simulated  Experimental  

Chamber  
A  5.46  1.35  5.64 ± 0.52  1.44 ± 0.28 
B  5.54  1.37  5.72 ± 0.40  1.60 ± 0.39 
Experimental and numerical results for water fluxes in chamber A at different crossflow velocities. In all experiments a 1 M draw solution and a pure water feed solution was used.
Approximating chamber A as a simple box with a steady crossflow velocity, the mass transfer coefficient
Comparison of kd values in chamber A obtained with an analytical model and with the present CFD model at different crossflow velocities. Calculations were made with 1 M draw solutions and pure water feed solutions.
Simulating membrane separation processes using a CFD approach is not limited to the testing of various chamber geometries for optimized water and solute flux; it also allows visualization of the flow fields within the chambers, which may reveal information relevant for masstransfer optimization. To demonstrate this, we compare ECP on the draw solution side of the membranes in chambers A and B by visualizing spatial ECP maps as shown in
In both the chambers, inlets are pointing towards the membrane, causing concentrated incoming draw solution to promote areas on the membrane with decreased ECP. This is similar to the way spacers are used in membrane chambers to promote eddymotions in the flow, which cause the bulk solution to “wash away” ECP on the surface. The opposite effect is observed at the outlet of chamber A and the sideregion of chamber B, where lower convection presumably increases ECP. It is noted that the ECP profile of chamber A changes notably from inlet to outlet, whereas in chamber B the ECP distribution between inlet and outlet is more uniform and the distribution changes significantly along the width of the chamber. The reason that chambers A and B reach similar total water and solute fluxes (see
The ECP maps in
ECP maps on the draw solution side of the membrane for chambers A and B. The membrane concentrations are scaled relative to the bulk draw solution concentration,
Since the only quantity in Equation (14) that is not directly simulated is
Knowledge of the concentrations at the membrane surfaces and at the composite membrane interfaces provides separate information on the significance of ICP and ECP. These polarization effects influence the effective osmotic driving pressure across the membrane, and hence the water flux. In
ICP maps showing the concentration at the interface between the porous support and the active separation layer of the composite membrane relative to the bulk concentration of solute in the draw. The inlets of both chambers are at the top of the figure, and correspondingly the outlets are at the bottom. Both simulations were performed with 1 M draw solutions, pure water feed solutions and a 50 mL min^{−}^{1 }crossflow. Contour lines are shown for arbitrary scalars to guide the eye.
Spatial distribution of membrane water flux in the two chambers A and B. Inlets are at the top of the figure, and outlets are at the bottom. Both simulations were performed with 1 M draw solutions, pure water feed solutions and a crossflow of 50 mL min^{−}^{1 }. Contour lines are drawn for arbitrary scalars to guide the eye.
To further investigate the two flow chambers, the velocity flow fields in the draw solution compartments are illustrated using streamlines traced from the inlets of both chambers in
Velocity streamlines traced from the inlets of draw solution compartments in chambers A and B. The velocity streamlines are colored according to the magnitude of the velocity field (scale on right), and the membrane plane is colored according to the effective osmotic driving pressure across the membrane (bottom scale).
In this work, we experimentally validate a computational fluid dynamics (CFD) model, which was developed specifically for simulating forward osmosis (FO) membrane systems with composite membranes. For the model to be able to simulate a given FO problem, three membrane parameters are required, namely the pure water permeability coefficient, the solute permeability coefficient and the solute diffusion resistivity coefficient for the porous layer. These three membrane parameters can be readily determined experimentally, which was done here for a number of similar samples. Significant variability for the three parameters was observed between different membrane samples, which can likely be attributed to slight differences in the experimental setups, as well as actual sample differences.
The CFD model was validated against experiments performed with two significantly different complex membrane chambers under flow conditions where external concentration polarization (ECP) cannot be ignored. Both chambers were meshed with computational domains consisting of approximately 500,000 cells, which were found to be sufficient for achieving grid independence of simulated water and solute fluxes. By looking at the average fluxes through the membranes, it was found that the numerical results were in excellent agreement with experimental results. The obtained numerical results were compared with results from commonly used analytical approximations for ECP, and it was observed that compared with the CFD approach, the analytical approach severely underestimates ECP.
Very similar experimental results were found for fluxes over the membrane in the two different chambers, which may initially be thought to indicate that membrane characteristics dominate over chamber geometry in determining the fluxes. Inspection of simulated results, however, indicate that flux distributions in the two chambers is markedly different for cases in which ECP cannot be ignored, meaning that chamber geometry optimization may be possible. The chambers investigated here are designed for testing membrane performance, and do therefore not represent final commercial modules in any way. In realistic FO applications, and especially large scale commercial applications, it is essential that the flow chambers and conditions are fully optimized. It is therefore expected that in a final application, eddypromoting spacers will be used to enhance mass transfer by reducing ECP effects. CFD models such as the one presented here provides valuable tools for such optimization through parametric studies, as they allow for easy testing of the effects of chamber modifications, as well as inclusion of different spacer geometries.
This work was supported by the Environment & Water Industry Programme Office of Singapore (EWI) through a collaboration project #MEWR 651/06/169 and by the Danish Agency of Science of Technology and Innovation through the grant “Natural ingredients and Green Energy”.