Saltwater Desalination in Reverse Osmosis Spiral Wound Membrane – From Experiments to 3D Model

Filtration with membranes is a widely used processing step with applications spanning from desalination of water, purification of chemicals and pharmaceuticals, energy conversion, and many more.

In this blog, we present a case study related to the desalination process of water via reverse osmosis in a commercial membrane. Experimental data from Technical University of Denmark, Department of Chemical and Biochemical Engineering, Pilot Plant, is used for parameter fitting and validation.

We illustrate our in-house developed homogenisation technique for membrane modelling in three dimensions, which is applicable to any membrane configuration (such as spiral wound or hollow fibre). This technique enables optimisation of membrane component geometry via insights into internal flow patterns and solute concentrations in both permeate and retentate sides.

Figure 1. Membrane Configurations. A: Hollow Fibre (HF) bundle. B: Spiral Wound (SW) bundle. Note that channel numbers, sizes, and curvatures are selected only for visualisation purposes. The red highlights indicate flow domains, which in A are geometrical cylinders (fibres) with direct flow out to the lumen and in B: spirally wounded membrane ensembles of stacked membrane sheets, permeate carrier (drain to centre tube), and feed spacer.

Introduction

Filtration processes are classified according to the filter membrane pore size. The following examples are ranked according to descending pore sizes: Microfiltration (MF), Ultrafiltration (UF), Nanofiltration (NF), Reverse Osmosis (RO). An MF use example could be to separate liquid from biomass and suspended matter of a fermentation broth. A typical use of RO is to remove ions (dissolved salt) from water to obtain low conductivity “RO Water”.

Filter modules typically consist of exchangeable filter membrane cartridges. The common membrane configurations are the following:

• Hollow Fibre (HF): See Figure 1 A. Numerous parallel hollow fibres are wound around the centre feed pipe.
• Spiral Wound (SW): See Figure 1 B. Membrane sheets are stacked in envelopes (membrane sheet, permeate carrier, membrane sheet, feed spacer) which are stacked and wound around a perforated centre pipe. The permeate carrier directs the permeate flow to the perforated centre pipe.

Figure 2 A and B illustrate simplified internal configurations of the HF and SW membranes, exemplified for the RO process. Note the difference between the two configurations on inlet/outlets of the permeate-side and retentate-sides and how the centre pipes are utilised for these.

Two solutions separated by a semi-permeable membrane possess an osmotic pressure difference depending on the solutes and their concentrations. The osmotic pressure difference reflects the preferred direction of solvent flow to reach an equilibrium. If the osmotic pressure difference is overcome by an external pressure, e.g., pure water can be obtained from saltwater corresponding to the RO process. Alternatively, a high osmotic pressure difference can be used to increase the volumetric flow rate in a high-pressure, concentrated solution to drive a turbine, thereby generating power. This concept is referred to pressure retarded osmosis (PRO) [1].

Figure 2. Example Flow Patterns for Common Membrane Configurations. A: Hollow Fibre Membrane. B: Spiral Wound Membrane.

Experiments

The pilot scale RO process is illustrated in Figure 3. It consists of a feed tank (1), high pressure pump (2), the feed line (3), the retentate line (4), the permeate line (5) the membrane module (6) that contains the membrane cartridge. Analog manometers at feed inlet and retentate outlet as well as flowmeters on retentate and permeate side are present. Note that only the permeate out from the centre pipe in the same side as the feed in tube of Figure 2 B is utilised in the setup.

The installed membrane cartridge is Aquaporin CLEAR Plus 4040 having a membrane area 7.9 m2.

The feed solution is demineralised water containing a variable concentration (0.75 to 10 g/L) of dissolved sodium hydrogen carbonate (NaHCO₃), mimicking water high salinity (e.g., saltwater).

Model Setup

The aim of the model is to capture the internal flow patterns and their impact on the membrane flux due to concentration gradients. Variations in concentrations imply significant changes to the attainable water flux due to changes in osmotic pressures, as described in the following subsection. The model is implemented in COMSOL Multiphysics.

The governing physics are summarised in Table 1.

Table 1. Governing Physics and Models.

Physics	Shell Side	Coupling	Lumen side
Momentum	Laminar Brinkmann equation for porous domain	Source term: Volumetric flux	Laminar Brinkmann equation for porous domain
Continuity	Solvent convection and flux Salt convection, diffusion, and flux	Source term: Species flux	Solvent convection and flux Salt convection, diffusion, and flux

The osmotic pressure is calculated using Van’t Hoff Equation (Equation 1) for dissociation of NaHCO₃ using i = 1.5, as bicarbonate HCO₃ is partly present as dissolved carbon dioxide.

Figure 3 illustrated the relationship between salt concentration and osmotic pressure. The osmotic pressure has a significant effect on the pressure required for producing RO Water, since this must be overcome by the feed pump pressure.

External concentration polarisation occurs near the membrane wall due to the presence of a stagnant liquid layer. This effect is more pronounced for laminar flow regime. In this layer, the concentration driving force may differ from the driving force based on the bulk concentrations according to Equation 2.

Equation 2

J_v is volumetric flux,  k_salt is mass transfer coefficient, c_p is the permeate bulk concentration, c_r is the retentate bulk concentration, and c_rm is the retentate polarisation concentration.

For laminar flow between parallel sheets, a dependency of Reynold’s number to the power of 0.33 on the mass transfer coefficient can be found. Hence, Equation 3 was adopted with k_salt,ref treated as an adjustable parameter.

Equation 3

The volumetric flux J_v and salt specie flux  J_salt   are given by Equation 4 and Equation 5, respectively.

Equation 4

Equation 5

A_w and B_salt are parameters, ∏ is the osmotic pressure, and p is the hydraulic pressure. The subscripts r and p refers to retentate-side and permeate-side, respectively. Fluxes from retentate-side to permeate-side is defined as the negative direction.

Numerical Example: Reverse Osmosis (RO):

For RO operation, hydraulic pressure drives the water flux through the membrane.

With hydraulic pressure from pumping of 15[bar]:

flow from feed/retentate side to permeate side

Without hydraulic pressure (if pumping stops):

flow from permeate side to shell side (side references are based on intended functionalities)

Building a 3D Model from Experimental Data

The experimental raw data consists of the following measurements reported at steady state at varying conditions (feed pressure and feed concentration):

• Temperature
• Feed
  • Pressure
  • Flow rate
  • Concentration (converted from conductivity)
• Retentate pressure
  • Pressure
  • Flow rate
  • Concentration (converted from conductivity)
• Permeate pressure
  • Pressure
  • Flow rate
  • Concentration (converted from conductivity)

A total of five data sets were provided based on five different experimental runs. Relationships between conductivity and concentration were established for the individual experimental runs executed by engineering students during practical courses (Technical University of Denmark, see Acknowledgement).

Illustrative physical and dimensional parameters are summarised in Table 2 and Table 3. The membrane area specified by the vendor was used to calculate specific membrane area used in model calculations. An internal geometry-based estimation of the membrane area agrees well with the reported membrane area.

Table 2. Assumed Physical Parameters.

Parameter	Description	Unit	Value
Dsalt	Diffusion coefficient NaHCO3	m2s-1	1.26e-9
Pp	Density retentate side	kg m-3	1000
μr	Viscosity retentate side	Pa s	1e-3
Pp	Density permeate side	kg m-3	1000
μp	Viscosity permeate side	Pa s	1e-3
MWsalt	Molecular mass NaHCO3	g mol -1	84

Table 3. Assumed Dimensional Parameters.

Parameter	Description	Unit	Value
Lbundle	Length of fibre bundle	mm	892
dmodule,inner	Diameter fibre bundle inner	mm	19
dmodule,outer	Diameter fibre bundle outer	mm	100
dfiber,inner	Lumen inner channels thickness	µm	500
dfibre,outer	Lumen fibre thickness	µm	600
dfeed	Feed spacer thickness	µm	500
Amembrane	Membrane area	m2	7.9
εmembrane	Packing density	m3 m-3	0.6

The pressure drops on both retentate and permeate sides were found to be less than the experimental reading of the analogue pressure indicators (±0.5 bar). Hence, these were assumed to be negligible compared to the trans-membrane pressure (p_s – p_l) when determining the water flux parameter A_w according to Equation 6. Experimental data together with the obtained linear correlation obtained from Equation 6 are illustrated in Figure 3A. Thus A_w = 1.5 . 10^-11[ m s^-1 Pa^-1]

Figure 5. Summary of Experimental Runs (ID1, ID2, ID3, ID4, and ID5). A: Relationship between Trans-Membrane Pressure and Area Specific Flux in accordance with Equation 4 with Demineralised Water as feed. B: Relationship between Average Concentration Driving Force and Area Specific Salt Flux in Accordance with Equation 7.

Permeability coefficients for the Brinkmann equations that accounts for momentum loss of the bulk fluid in the membrane are fitted to yield an approximate pressure drop of both retentate side and permeate side of ∆p = 0.2 [bar ] at inlet flow rate Q_in = 2400 [ L h^-1].

Due to the relative small change in concentration in the permeate-side within the membrane module, a reasonable linear relationship of salt flux and average concentration driving force for Equation 5 is achieved as illustrated in Figure 5B. The retentate-side external polarisation is accounted for as the volume flux is measured in Equation 4.

The flux proportionality constant, B_salt (Equation 5), and the mass transfer coefficient,  k_salt (Equation 2), are fitted in the COMSOL Multiphysics model to experimental data set. Figure 6 depicts both simulation and experimental data used to fit B_salt and  k_salt . A reasonable fit is achieved. The experimental conditions can be seen in the figure caption. The feed flow rate at feed pressure 20[barg] was limited to 1500 [ L h^-1] rather than 2400 [ L h^-1] as the rest of the data, due to limitations in feed pump capacity.

Figure 6. Simulation versus Experimental Results for Feed Pressure P_in.s = (10, 13, 16, 20) [barg], Inlet Concentration C_in = (10,10,10,10) [g L^-1] , and Feed Flow rate Q_in.s = (2400, 2400, 2400, 1500) [ L h^-1]. The Permeate Concentration in subfigure C is not visible as it is measured as a factor of 10 larger than the remaining datasets.

Model Fidelity Versus Objectives

Based on the determined main membrane properties and identified operational parameters different approaches can be followed to have a closer look into flow properties within the membrane to enhance understanding and identify bottle necks in configuration and operation.

A 0D approach may be sufficient when describing the average behaviour. A 1D approach may allow the description of how the flux changes along the membrane to account for its impact on polarisation. This may be relevant for investigating long membrane modules. Additionally, a 2D model can describe the concentration profiles in both lumen-side and salt-side in parallel sheets reflected by the repeated layers of unwounded spirals. A 3D approach allows for investigating uneven inlet flow distribution and/or decline in membrane performance due to fouling or precipitation. Furthermore, the 3D approach serves as a strong tool for visualisation to facilitate learning for non-technical stakeholders or engineering students.

We adopted 3D modelling approach in this study, to get highest model resolution and potential insights. Figure 7 reveals the detailed insights that the present 3D model allows, as the left-hand side column provides visualisation of a simple uniform feed concentration field versus a non-uniform feed concentration field in the right-hand side column. The average feed concentrations in both examples are the same (uniform 10 [g L^-1]  versus non-uniform 10 [g L^-1] . z/d _{moudule.outer}). Interestingly, the total flux was estimated as 0.2% higher for the non-uniform case (447 L/h) versus the uniform case (446 L/h). Note however that this remains a theoretical comparison to illustrate the impact on the 3D domains.

Figure 7. Simulation of a uniform feed concentration field versus a non-uniform concentration feed field. P_in.s = 16 [barg], Inlet Concentration   C_in._avg = 10 [g L^-1] , and Feed Flow rate Q_in.s =2400 [ L h^-1].  A and B: Concentration field in plane perpendicular to the inlet flow direction. C and D: Unwound envelope volumetric flux. The horizontal axis is feed flow direction (from left to right) and the vertical axis is the arclength of the spiral. The permeate flow goes downwards towards the centre pipe. E and F: Wound envelope volumetric flux.

Conclusions

With this blog post, we can extract the following conclusions:

• System understanding should be established sequentially starting from the simplest system. This approach is adopted by initially studying the impact of osmotic pressure (literature data), followed by establishing the water flux/pressure relation without salt being present, before studying the final system.
• Use experimental data to verify the model and /or use model to verify experimental data.
• We established a 3D model suitable for simulating membrane filtrations, which accounts for multiple curved domains (e.g., spiral wound and hollow fibre membranes), osmotic pressure, and external membrane polarisation.
• Simulation, using the developed model, is a powerful tool to optimise membrane design, e.g. to gain insights of the impact flow or concentration gradients on performance (baffle design, local fouling, distributers).

COMSOL Multiphysics enabled this work.

Acknowledgement

The experiments were conducted and kindly provided by the Department of Chemical and Biochemical Engineering, Technical University of Denmark, Pilot Plant.

Literature

[1] Achilli, Andrea, and Amy E. Childress. “Pressure Retarded Osmosis: From the Vision of Sidney Loeb to the First Prototype Installation — Review.” Desalination 261(3) (2010): 205–11. https://doi.org/10.1016/j.desal.2010.06.017.

[2] J.C. Peiper, KS Pitzer. “Thermodynamics of aqueous carbonate solutions including mixtures of sodium carbonate, bicarbonate, and chloride”. The Journal of Chemical Thermodynamics (14)(7) 1982: 613-638. https://doi.org/10.1016/0021-9614(82)90078-7

[3] A. Achilli, T.Y. Cath, A.E. Childress. “Selection of inorganic-based draw solutions for forward osmosis applications.” J. Membr. Sci. 364 (2010): 233–241. https://doi.org/10.1016/j.memsci.2010.08.010.