1. Introduction
Reverse osmosis (RO) technology is the most extensively used technology for the desalination of both seawater and brackish water [
1,
2]. Among the current desalination technologies used in full-scale plants, RO is the most energy-efficient one [
1]. Nonetheless, RO is an intensive energy consumption process [
3,
4]. One of the main challenges to improve RO efficiency is related to decreasing specific energy consumption (
) [
5,
6] and the fouling effects on spiral-wound membrane modules (SWMMs) of RO. In recent years, several studies have proposed alternatives to improve the efficiency of the process, such as using new membrane materials [
7,
8,
9] and optimizing the feed spacer geometry [
10,
11]. Generally, the studies related to new RO membrane materials have focused on improving certain membrane characteristics, namely their antifouling properties [
12,
13], the water permeability coefficient (
A), and the solute permeability coefficient (
B) [
14]. However, the feed spacers are an essential part of SWMMs and play an important role in the concentration polarization phenomena, the pressure drop along the membrane, and fouling [
10,
15,
16].
Research on feed spacer design has shown the impact of feed spacer geometry on feed channel hydrodynamics, which in turn affect other parameters. Many studies have been made on feed spacer geometry. In 1987, Schock and Miquel [
17] experimentally developed correlations for the friction factor (
) and Sherwood number (
) for SWMMs of RO membranes.
depends on the Reynolds number (
) and on two parameters, and
depends on
, the Schmidt number (
), and three parameters.
is related to the mass transfer coefficient (
k) and the polarization factor (
). V. Geraldes et al. [
18] modified the correlation of
by adding an additional factor (
) to take into consideration pressure losses in the feed of the pressure vessels (PVs) and SWMM fittings. In their work, these correlations were used to simulate and optimize medium-sized seawater reverse osmosis (SWRO) processes. Abbas [
19] used a different correlation for
obtained in a previous work [
20] for ultrafiltration (UF) membranes. This correlation depends on
and three parameters and was used to simulate an industrial water desalination plant. In 2004, Schwinge et al. [
21] used the correlation for UF membranes but removing one parameter. The fouling effect in SWMMs was studied using computational fluid dynamics (CFD) in the aforementioned work. These previous studies do not allow consideration to be given to different feed spacer geometries, which have different
and
. Koutsou et al. [
22] went a step further by proposing different correlations for the dimensionless pressure drop (proportional to the friction factor), taking into account the ratio of the distance between parallel filaments and the filament diameter (
), the angle between the crossing filaments (
), and the flow attack angle (
). In that work, a new equation to determine a dimensionless pressure drop was formulated. In a later study, Koutsou et al. [
23] used the same correlations of Schock and Miquel to estimate the
for different feed spacer geometries. These correlations are applicable to simulations of full-scale systems as long computation times are not required, as happens with the CFD. Guillen and Hoek [
24] considered the pressure drop, concentration polarization, and the shape of the filament in a performance study of the RO process. The study was carried out proposing a three parameters dependent correlation for
and the typical correlation for the
. Different geometries of the mesh were not considered in the study. Haidari et al. [
25] evaluated the performance of six commercial feed spacers in terms of pressure drop. The effect of the concentration polarization and membrane characteristics were not taken in account in that study.
A study of the different feed spacer geometries in a full-scale commercial RO SWMM required equations that can be applied without the computation requirements of CFD (Navier–Stokes equations). This is the reason simple correlations such as those proposed by Schock and Miquel [
17] or Koutsou et al. [
22,
23] are needed. Another important factor that needs to be taken into consideration concerns the permeability coefficients
A and
B of the membranes. Different values of these coefficients can play an important role in the optimization of feed spacer geometries. This paper provides simulations and a performance analysis for different permeability coefficients, feed spacer geometries for brackish water RO SWMMs, and feed concentrations (
).
2. Methodology
In this study, three RO SWMMs for BW were considered, FILMTEC
™ BW30-400, FILMTEC
™ ECO PRO-400, and FILMTEC
™ FORTLIFE
™ CR100 PRO-400 from Dow
® company (Midland, MI, USA). The Water Application Value Engine (WAVE) software from the same company was used to calculate the permeability coefficients
A and
B of the membranes.
Table 1 shows the calculated permeability coefficients.
In order to compare the three full scale BWRO membranes, the PVs of one element were simulated. A range between 1 and 15 g L
as
of NaCl was used with feed flow (
) and feed pressure (
) ranges from 3 to 17
and from 1 to 42 bar, respectively. The different feed spacer geometries studied by Koutsou et al. [
22] were considered. The performance of these three membranes wound with different feed spacer geometries was simulated. Solution–diffusion [
26,
27], which assumes that the membrane is nonporous (without imperfections), was the method of transport used. The theory is that transport through the membrane occurs as the molecule of interest dissolves in the membrane and then diffuses through the membrane. This holds true for both the solvent and solute in solution. In this model, the solvent and solute transport are independent of each other (Equations (
1) and (
2)). This is the most widely accepted model and provides results close to the real behavior of these systems. The transport equations use mean values of membrane elements, and pressure drop in the permeate as well as temperature changes along the RO system are disregarded.
The transport equations used were the following:
where
is the permeate flow,
A is the membrane permeability coefficient,
is the net driven pressure (
), and
is the membrane area.
Solute transport equation:
where
is the solute flow through the membrane,
B is the solute permeability coefficient of the membrane, and
is the concentration gradient of solute on either side of the membrane.
Coefficient
A (Equation (
1)) usually depends on three variables: Average osmotic pressure on the membrane surface (
), temperature, and flow factor related to fouling and operating time (
) [
28].
is an important parameter below 1 that represents the decrease of the coefficient
A due to fouling [
29]. There are several methods that try to predict this parameter [
30]. As this work is about a comparison between different feed spacer geometries used in three different membranes based on simulations, it was considered that the fouling factor
was 1 (new membrane). Usually, the
decreases with the operating time as SWMMs get fouled [
29]. Feed temperature was considered 25 °C, so the temperature correction factor (
) is equal to 1 and the effect of osmotic pressure on
A was neglected.
where
is the initial water permeability coefficient. Next in the development of Equation (
1) is the expression of the
, which depends on
, pressure drop (
), permeate pressure (
),
, and average osmotic pressure of the permeate (
):
was calculated as follows [
31]:
where
L is the SWMM length (it was considered 1 m),
is the average feed-brine density (∼1000
for BW),
is the average feed-brine water velocity (
),
(
) is the hydraulic diameter of the feed channel,
is the porosity of the cross section area in the feed channel (0.89 [
17]), and
h is the height of the feed channel, which was considered 28 mili inches (
m) for the three membranes. In this study, the pressure losses in the permeate channel were not considered; a value of
psi (34,473.8 Pa) was used.
Figure 1 shows the different parameters of feed spacer geometries. The correlations used for
were proposed by Koutsou et al. [
22] (
Table 2).
was multiplied by the parameter
, which was introduced by Geraldes et al. [
18]. This factor takes into consideration additional pressure losses in the feed of the PVs and module fittings. Values between 1.9 and 2.9 were obtained in that study. A value of 2.5 was used in this paper.
As water flows across the membrane, the rejected solute can accumulate on the membrane surface where the solute concentration will increase. This concentration generates a diffusive flow back to the feed flow. Steady state conditions are established after a certain period of time in steady conditions.
provides the relationship between
and
. In order to calculate
, the average ionic permeability coefficient (
B) was used (Equation (
7)). This enables a calculation of the ion concentration of the permeate (
):
where
is the concentration factor,
is the osmotic pressure of feedwater, and
is the average feed-brine solute concentration.
where
m is the molal concentration of NaCl,
in the concentration of solute on the membrane surface,
J is the permeate flux per unit area, and
k is the mass transfer coefficient, which is given by
[
17]:
where
a,
b and
c are parameters,
is the Schmidt number,
(
) is the water density,
is the feed-brine velocity (
), and
(0.000891
for T = 25 °C) the dynamic viscosity. Koutsou et al. [
23] calculated correlations for the
for different feed spacer geometries (
Table 3). The solute diffusivity (
D (
)) was calculated as follows [
32]:
In order to calculate all the above variables, an algorithm already proposed by the authors was used [
33] and implemented in MATLAB
® (MathWorks, Natick, MA, USA). To calculate the
, a performance of 80% of the high pressure pump was assumed.
was determined with the feed pressure, feed flow, water density, and the abovementioned performance of the high pressure pump and dividing by permeate flow. The results that exceeded the operating limits established by the manufacturer were discarded (minimum concentrate flow of 3
, 19% as maximum element recovery, etc.).
3. Results and Discussion
Figure 2 shows the flux recovery (
R),
, and
of the FILMTEC
™ BW30-400 and FILMTEC
™ ECO PRO-400 membranes, with a a
= 5 g L
,
= 6 and
= 90° FILMTEC
™ ECO PRO-400 membrane has a higher
A than FILMTEC
™ BW30-400 (
Table 1). Consequently, high
R values are reached with lower
than with FILMTEC
™ BW30-400, but the operating range is wider for the BW30 than for the ECO PRO (
Figure 2a,b). The reason is that the ECO PRO membrane produces so much water that as the pressure rises, the concentrate flowrate decreases considerably, reaching the minimum established by the manufacturer with not very high pressures. This factor must be taken into account when this type of membrane is placed in series.
Figure 2c,d shows that low
were reached with
values ranging between 4 and 10
. This range varies if various SWMMs are arranged in series. The
decreased with increasing
and
due to
B being constant, and the higher the
, the lower the
and
. It should be noted that variations of
and/or of the permeability coefficients (due to fouling) could significantly change the values of the operating points.
Figure 3 and
Figure 4 show the exponential growth of
with the increase of
. As
increases. there is a slight increase in the separation of the exponential curves of each feed spacer geometry. This reveals that the effect of the feed spacer geometry on
in seawater desalination is more pronounced than in brackish water. The
was lower for the membrane with the higher coefficient
A, but the separation between curves was higher for the ECO PRO membrane than for the BW30-400. This shows that the impact of the feed spacer geometry with the
was higher for the FILMTEC
™ ECO PRO-400 membrane.
As happened with
,
also showed an exponential growth with the increase of
for both membranes (
Figure 5 and
Figure 6). Again, bigger differences between curves were reached at higher
values and were even more pronounced for the membrane with the highest coefficient
A. The membrane with the lowest coefficient
B has the lowest
as was expected.
The studied was carried out considering four different feedwater conditions, where the average
R were, for the cases 1 and 2, 8.63, 13.59, and 9.41% for the membranes FILMTEC
™ BW30-400, FILMTEC
™ ECO PRO-400, and FILMTEC
™ FORTLIFE
™ CR100 PRO-400, respectively. For the cases 3 and 4, in the same order of membranes, the average
R were 9.11, 13.74, and 9.86%.
Table 4 shows the
results for the three different membrane studied, considering different feed spacer geometries. In case 1, the
variations were 1.23, 3.17, and 1.55%. The membrane with the highest
A was more influenced by the feed spacer geometry in terms of
. The second case is similar to the first one, but
was reduced from 12 to 8
. In this case,
Table 4 only shows results for the FILMTEC
™ BW30-400 and FILMTEC
™ FORTLIFE
™ CR100 PRO-400 membranes, as the results obtained for the FILMTEC
™ ECO PRO-400 were outside the recommended range of the manufacturer. The variations were higher than in the previous case, namely 2.42 and 2.74%, respectively. The
values were lower in the second case, as pressure losses decreased as a consequence of the reduction of the velocity in the feed channel. For the next cases (3 and 4),
increased from 5 to 10 g L
and
from 13 to 18 bar. The results of case 3 showed higher
values and variations of 3.7, 6.83, and 4.19%. The higher the
, the more pronounced the
variations, because the highe the
was, the higher the concentration polarization effect was on membrane performance and the role played by spacer geometries was more pronounced in terms of membrane production. These phenomena can be appreciated in
Figure 3 and
Figure 4: The higher the
, the more separated the curves are. The decrease of
to 8
had a pronounced impact on the
variation. The variations in the third case were 4.95 and 5.46% for the FILMTEC
™ BW30-400 and FILMTEC
™ FORTLIFE
™ CR100 PRO-400 membranes, respectively. Variation of the FILMTEC
™ ECO PRO-400 membrane was 2.95%, but the results for two feed spacer geometries were not considered, as they were outside the recommended range. The
was affected by feed spacer geometry because it also affected the pressure drop along the membrane and the
. The higher the pressure losses are, the lower the permeate production is, and the higher the concentration polarization (polarization factor) is, the higher the osmotic pressure on the membrane surface and the lower the permeate production. The lowest
for each membrane corresponded with the same feed spacer geometry (
and
= 120°). The membranes reached the highest
with
and
= 90°, except the FILMTEC
™ BW30-400 and FILMTEC
™ FORTLIFE
™ CR100 PRO-400 membranes in case 1, where the highest
was reached with
and
= 90°.
Table 5 shows the results obtained for
in the same four cases. In general, the impacts of the feed spacer geometries were higher for
than for
. In the first case, the
had variations of 6.18, 10.42, and 6.86%, respectively. The FILMTEC
™ ECO PRO-400 membrane had higher variations than the other membranes due to the coefficient
A, so the velocity in the feed channel also had higher variations for the FILMTEC
™ ECO PRO-400 membrane than others, which makes the impact of feed spacer geometries more pronounced for the mentioned membrane. In the salt rejection, the coefficient
B plays an important role, but so too does coefficient
A. The coefficients
B of the FILMTEC
™ ECO PRO-400 and FILMTEC
™ FORTLIFE
™ CR100 PRO-400 membranes are very similar, though slightly higher for the FILMTEC
™ ECO PRO-400 membrane. However, the values of
were higher for the FILMTEC
™ FORTLIFE
™ CR100 PRO-400 membrane due to
R. The FILMTEC
™ ECO PRO-400 membrane showed a 4% higher recovery than the other two, which resulted in a decrease of
despite the increase of
. The lowest values of
were reached with
and
= 120° for the three membranes. The highest values corresponded to
,
, and
= 90°, depending on the case.
It should be noted that the simulations were carried out considering only one SWMM in the PV. These small variations in terms of and could be increased by studying more SWMMs in a series. Full-scale BWRO desalination plants usually have two stages with 5 or more SWMMs in a series per stage and even variations in the .