Desalination 562 (2023) 116699
Contents lists available at ScienceDirect
Desalination
journal homepage: www.elsevier.com/locate/desal
Modeling and optimization of salt and boron removal in reverse
osmosis system
Ridha Ben Mansour
Interdisciplinary Research Center for Renewable Energy and Power Systems, Research Institute, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi
Arabia
H I G H L I G H T S
• Solution-diffusion and irreversible thermodynamic models for salt and boron transport model are presented.
• Salt and boron concentration polarization effect is considered.
• Variation of solution properties and transport mechanisms are considered.
• Solute rejection sensitivities to operating conditions of feed are discussed
• Design Optimization study for low energy consumption and high solute rejection is conducted.
A R T I C L E I N F O
A B S T R A C T
Keywords:
Desalination
Reverse osmosis
Boron
Rejection
Optimization
Energy consumption
Seawater reverse osmosis (SWRO) is a mature technology that has significantly evolved over the past few de­
cades. However, boron removal remains a serious challenge. A new RO transport model was developed by
combining the irreversible thermodynamic theory and solution-diffusion theory and considering the solute
concentration polarization phenomenon. The developed RO model supplemented by the use of variable solution
properties and transport parameters was validated with existing data and, it was then applied to identify the
main operation parameters and assess their effect on SWRO performance, with the aim of minimizing specific
energy consumption and satisfying water quality requirements. The results showed that the solution-diffusion
approach, cannot capture the interaction between transported boron and water species. For high pH, applied
feed pressure, and flow rate, the convective transport of boron through the seawater membrane is remarkable
and its contribution to the overall boron flux can reach over 20 %. The feed operating conditions have signifi­
cantly influenced the quality of the water production and the amount of energy used. The results showed that the
optimal SEC increased by approximately 40 %, and the recovery ratio decreased by 11.6 % as the feed flow rate
increased from 0.002 to 0.005 m3/s.
1. Introduction
The availability of portable water is one of the most severe chal­
lenges in many arid and semi-arid countries, such as those in the Gulf
region. The demand for freshwater is continually increasing because of
rapid population growth, prolonged droughts in many coastal areas, and
the limited availability of underground water. Therefore, seawater
desalination is important. Various thermal and membrane-based desa­
lination technologies have evolved to fulfill this growing demand.
Traditionally, thermal technologies such as multi-effect distillation
(MED) and multi-stage flash (MSF) have dominated the desalination
market in Gulf Arab countries. Thermal desalination technologies, on
the other hand, require too much energy because of the latent heat of
vaporization. Therefore, in the mid-90s, reverse osmosis (RO) began to
dominate thermal technologies as the primary desalination technology.
It is because of the low specific energy consumption and the major
breakthroughs in the operating efficiency of membrane-based systems
[1,2].
In desalination processes, RO encounters a variety of challenges;
however, fouling is the major problem when it comes to membrane
applications since it affects the produced water quality, capital, main­
tenance, and operation costs [3,4]. The capital cost is affected by fouling
due to the need for additional pre-treatment units, chemicals, energy,
and materials to overcome membrane fouling [5]. Boron removal is an
additional challenge for membranes in the reverse osmosis desalination
E-mail address: ridha.benmansour@kfupm.edu.sa.
https://doi.org/10.1016/j.desal.2023.116699
Received 4 January 2023; Received in revised form 24 April 2023; Accepted 13 May 2023
Available online 24 May 2023
0011-9164/© 2023 Elsevier B.V. All rights reserved.
R.B. Mansour
Desalination 562 (2023) 116699
Nomenclature
Symbols
A
BR
Cbb
Cbm
Cbp
Cbbo
Csb
Csm
Csp
Cspo
Db
DS
i
Jb
Js
Jv
ka1
kb
ks
l
Lb
Lso
Ls
Lvo
Lv
N
ΔPhyd
P
Q
RR
RO
S
SEC
SR
T
cross-sectional area, m2
boron rejection
bulk boron concentration, kg/m3
boron concentration at wall membrane, kg/m3
boron concentration in permeate, kg/m3
total boron concentration in permeate, kg/m3
bulk salt concentration, kg/m3
salt concentration at wall membrane, kg/m3
salt concentration in permeate, kg/m3
total salt concentration in permeate, kg/m3
solute diffusion coefficient of boron, m2/s
solute diffusion coefficient of NaCl, m2/s
section element
boron flux, kg/m2.s
salt flux, kg/m2.s
water flux, m3/s
apparent acid dissociation constant, mol/L
mass transfer coefficient of boron, m2/s
mass transfer coefficient of NaCl, m2/s
membrane length, m
boron permeability coefficient, m/s
intrinsic solute transport parameter, m/s
salt permeability coefficient, m/s
intrinsic solvent transport parameter, m/s.Pa
Greek symbols
γ0
fraction of boric acid
γ1
fraction of borate ions
εERD
energy recovery device efficiency
εp
pump efficiency
π
osmotic pressure, kPa
σb
boron reflection coefficient
Subscript
b
conv
diff
f
s
Year
MAC (mg/l)
2011
2001
2011
1998
2000
2004
1984
2001
2.4
1.5
4
1
1.4
<1.5
0.5
1
Advisory and targeted values
Ashkelon (Israel)
Canada
Dhekelia (Cyprus)
Perth (Australia)
State of Florida (USA)
State of Minnesota
State of New Hampshire (USA)
State of Wisconsin (USA)
Sydney (Australia)
<0.4
2.4
<1
<1
0.63
0.6
0.63
0.9
<1
a
boron
convective
diffusive
feed
salt
weight loss [7,10]. Several countries and international groups such as
the World Health Organization (WHO) and European Commission (EC)
have set new drinking water standards or advisory values for MAC in
drinking water and treated sewage [7,9,10]. Boron standards for
drinking water in several regions are listed in Table 1.
For agriculture, boron toxicity has shown a negative effect on plant
and crop growth when the amount is greater than the maximum
acceptable concentration (MAC) of boron. For instance, Eaton [15]
found that a boron concentration of 0.5 p.p.m. was optimal for the
growth of the sunflower but 1.0 p.p.m. proved definitely toxic. Nidal
et al. [16] reported in their comprehensive review paper on boron
removal that the maximum acceptable concentration (MAC) of boron in
soil water vary from 0.3 to 0.5 mg.L− 1 for extremely sensitive plants (e.
g., blackberry, lemon), 0.5 to 2 mg/l for sensitive plants (e.g., avocado,
grapefruit, orange, apricot, peach, Garlic, sweet potato, mung beam, red
paper) and 2–4 mg.L− 1 for tolerant plants (e.g., turnip, kentucky blue­
grass, tomato sorghum, cotton). The toxic effects of boron on plants have
been reviewed [16,17]. The morpho-anatomical, physiological and
biochemical effect of boron involves the impairment of root cell divi­
sion, retarded shoot and root growth, inhibition of photosynthesis,
decrease in leaf chlorophyll, reduction of the cytosolic pH, etc. [17]. The
MAC of boron concentration for irrigation applications recommended by
the World Health Organization (WHO) is <1 mg/l [11]. Furthermore, to
compensate for the deficiency of renewable water resources in many
world regions, such as the Middle East and North Africa (MENA),
seawater reverse osmosis is commonly used to provide clean water for
human and agricultural applications. A significant portion of desali­
nated water or treated water is contaminated with high levels of boron,
which can cause toxic effects on crop yield. Consequently, boron
removal from desalinated water is essential for producing portable and
irrigation water [8,12]. Having >90 % boron removal is often difficult
with a single-pass RO membrane [18]. The most significant methods for
managing boron concentration are multi-pass reverse osmosis with
membrane and pH adjustment, ion exchange methods using boronselective resins (BSRs), and hybrid processes based on adsorption
Table 1
Guidelines for MAC of boron in drinking water adapted from [11–14].
Regulatory values
WHO
Abu Dhabi
Australia
European Commission
New Zealand
Israel
Saudi Arabia (SASO)a
Singapore
water permeability coefficient, m/s.Pa
number of modules
hydraulic pressure drop along a spiral wound element, Pa
pressure, Pa
volumetric flow rate, m3/s
recovery ratio, %
reverse osmosis
salinity, ppm
specific energy consumption, kWh/m3
salt rejection, %
temperature, K
Saudi Arabian Standards Organization
process in order to achieve freshwater quality requirements [6]. Existing
commercial RO desalination membranes have been shown to success­
fully reject most dissolved ions (>99 %). However, the surface chemistry
of polyamide membranes is not effective at separating nonpolar and
small-sized molecules, such as boric acid (B(OH)3 ), the primary form of
boron in aquatic environments (seawater) at low pH. Boron is present in
water at a relatively low concentration, typically varying between 4 and
6 mg/l [7] and reaches up to 7 mg/l in the Gulf countries [8]. Exces­
sively high boron levels are disastrous for humans, animals, and the
environment [9]. Boron poisoning in humans can cause, for example,
nausea, vomiting, diarrhea, dermatitis, lethargy, loss of appetite, and
2
R.B. Mansour
Desalination 562 (2023) 116699
High Pressure
Pump (HPP)
RO module stack
Product water
Qp,Csp,Cbp, Tf
Feed Solution
Qf,Csf,Cbf, Tf
Booster
pump
Brine discharge
Qb,Csb,Cbb, Tf
Energy Recovery
Devise (ERD)
Fig. 1. Illustration of the RO desalination system.
Fig. 2. Schematic of the ith element of the RO membrane.
membrane filtration [6,16,19,20]. Integrating these alternatives into
many real reverse osmosis pilot plants has reduced boron content to an
acceptable value. However, this integration can cause additional oper­
ational issues that may lead to an increase in product water costs [20]. It
is believed that improving RO operation will be possible by using boron
and fouling mitigation measures that contribute to boosting RO opera­
tion without compromising product quality, or energy consumption.
The performance of RO plants is sensitive to the quality of feed
water, operating conditions (i.e., permeate recovery, flux, feed tem­
perature, solute concentration polarization, and fouling), and the
configuration of the RO membrane [21–24]. Various mechanisms and
thermodynamic models of membrane transports and chemical equilib­
rium have been proposed to predict the RO performance and the quality
of the produced water [25–28]. RO thermodynamic transport models
are classified into three categories according to membrane surface
structures: diffusion-based, pore-based, and irreversible thermodynamic
models [18,29–31]. Among these models, the solution-diffusion model
for salt transport through RO membranes is the most widely accepted for
explaining and predicting the performance of RO systems [18]. In this
case, the solute (salt) reflection coefficient (σs) is close to unity. Thus,
the convective effect on salt is neglected and, thus the solute and solvent
species diffuse independently across the membrane. Nevertheless, the
convective transport of boron through the seawater membrane is
remarkable, and the coupling of the mass transport of boron and water
in RO process modeling should be considered; the boron reflection co­
efficient (σB) is usually lower than unity. The thermodynamic solution-
diffusion model, commonly used to describe salt and boron transport,
cannot accurately predict boron distribution through RO membranes
[7,28].
Thus, the irreversible thermodynamic model, which considers both
diffusion and convection for mass transport, can successfully simulate
boron rejection under different operating conditions [28,32,33]. How­
ever, several studies have made simplified approximations of the irre­
versible thermodynamic model (i.e., a single-species approach, constant
properties and transport parameters of seawater, and no concentration
polarization effect) [28,32]. Using a single-species approach, the effect
of pH on boron rejection was ignored. However, boron management
strongly depends on pH, as reported in many experimental works
[8,34,35]. Furthermore, at least two major ionic species of boron are
present in seawater: boric acid and borate. Their evaluation and distri­
bution are critical for studying the kinetics of the boric acid-borate
equilibrium and the borate‑carbonate system [31,36,37]. Dissolved
boron can also affect the alkalinity balance, buffering, and physical
properties of seawater [16].
Given that the majority of published research articles have focused
on the solution-diffusion approach that assumes the solute and solvent
species diffuse independently across the membrane and neglect the
possible interaction between transported water, salt and boron, and the
membranes [38]. However, this study aimed to develop a new RO
transport model by combining the irreversible thermodynamic theory
and solution-diffusion theory and taking into account the solute con­
centration polarization phenomenon. The developed RO model
3
R.B. Mansour
Desalination 562 (2023) 116699
supplemented by the use of variable solution properties and transport
parameters will be utilized to optimize RO process performance under a
wide range of operating conditions (feed flow rate, applied pressure,
temperature, pH, and seawater salinity) and configurations (different
numbers of membrane elements). The validated model was then applied
to identify and investigate the operation window for different con­
straints on the specific energy consumption and water product quality.
Js (i) =
(
)
Qs (i)
= Ls Csm (i) − Csp (i)
A(i)
(2)
where Jv (i) and Js (i) are the average permeate and salt fluxes, respec­
tively, in the ith element section. Qp(i) and Qs(i) are the volumetric flow
rates of water and salt, respectively. The driving pressure (Δpm (i)–
Δπm (i) ) in Eq. (1) represents the difference between the net hydraulic
and osmotic pressures along the ith element of the RO membrane.
2. Mathematical modeling of RO
ΔPd (i)
2
(3)
2.1. System description
Δpm(i) = Pf (i) − Pp(i) −
A schematic of a typical RO desalination system is shown in Fig. 1.
Raw water, with a feed concentration of TDS and a feed flow rate, is
pretreated by a filtration process (dual-media filter, ultrafiltration, or
microfiltration) to provide suitable RO feed water quality. After pretreatment, the feed water is pressurized by a high-pressure pump to
the PF and enters a reverse osmosis membrane, where over 99 % of the
dissolved ions (e.g., salt, sodium, and calcium) from the raw water are
rejected. Consequently, the feed water is split into two streams: one with
a low solute (permeate stream) and the other with a high solute
(concentrate stream). In improving the efficiency of the entire RO sys­
tem, the mechanical energy of the concentrate stream at high pressure is
transferred to the feed flow through an energy recovery device (ERD).
where Pf(i) and Pp (i) are the feed and permeate hydraulic pressures in
the ith element section, respectively. Shock and Miquel [37] developed
the following equations to calculate the pressure loss (ΔPd (i)) in a spiral
wound element:
( 2)
λρν
ΔPd =
(4)
2d
λ = 6.23Re−
Re =
This section presents a mathematical model of the RO process based
on a thermodynamic transport model for water, salt, and boron solu­
tions. This model considers the concentration polarization effects of
both the salts and boron. Subsequently, the governing system of equa­
tions, composed of the mass transfer, pressure drop, and concentration
polarization equations, was solved using the finite difference approach.
This approach, based on the discretization of the RO membrane stack
into a series of elements (i.e., modules), is used to estimate the profiles of
both the state and process variables for each element (Fig. 2). Thus, the
main overall performance parameters of the RO system (i.e., recovery,
salt and boron removal, and energy consumption) can be adequately
deduced.
The developed process model for RO was formulated through the
adaptation of the following assumptions:
(6)
Ls(i) = Lsoexp
[(
)]
β1 (Tb (i) − 293 )
293
(8)
The salt concentration on the permeate side (Csp ) of the ith element
membrane is calculated as follows:
Csp(i) =
- The transport parameters for dissolved components in seawater are
the same as those for salt (NaCl), except for boron. The dissolved
boric and borate components were considered in this study.
- The solution-diffusion model applies to the transport of water and
salt through a membrane.
- The irreversible model is valid for boron transport, and the driving
forces are pressure and concentration gradients.
- The diffusion coefficient is independent of solute concentration.
- The electrostatic interactions between the solute and the membrane
are not considered.
- The brine concentration varies linearly along the RO element.
- The pressure drop on the permeate side is neglected.
- The concentration polarization effect for the salt and boron systems
is adequately estimated using thin film theory.
Qs (i) Js (i)
=
Qp (i) Jp (i)
(9)
Based on thin film theory [41], the salt concentration at the mem­
brane wall (Csm ) is related to the bulk salt concentration (Csb ) by the
following equation:
(
)
Jp (i)
Csm(i) = Csp(i) + (Csb(i) − Csp(i) )exp
(10)
ks
where ks is the salt mass transfer coefficient related to the Sherwood and
Schmidt numbers (Sh, Sc) by [37]:
Sh =
ks Ds
= 0.065 Re0.875 Sc0.25
dh
(11)
Sc =
μ
ρDs
(12)
where dh is the hydraulic diameter of the spacer-filled flow channel for
spiral wound modules as estimated using Shock and Miguel’s correlation
[28].
2.3. Water and salt transport model
According to the diffusion model, the following relations define the
fluxes of water and salt passage through the ith element section along
the feed flow direction:
Qp (i)
= Lv (i)(Δpm(i)–Δπm(i) )
A(i)
ρνd
μ
where λ and Re are the friction factor and Reynolds number, respec­
tively, calculated based on bulk seawater properties.
(
)
In Eq. (2), the term Csm (i)–Csp (i) represents the difference in
average salt concentrations at the ith membrane wall and permeate
compartment.
Lv and Ls are the water and salt permeability constants, respectively,
and are calculated using Eqs. (7) and (8) [39,40].
[(
](
)
)
α1 (Tb (i) − 293 )
As
Lv (i) = Lvoexp
− α2 Pf (i) 1 −
(7)
293
Am
2.2. Model development
Jv (i) =
(5)
0.3
2.4. Boron transport model
(1)
Based on the irreversible thermodynamic model introduced by
Spiegler and Kedem [42], the boron flux is the sum of the diffusive and
convective fluxes through the ith element section, which can be
4
R.B. Mansour
Desalination 562 (2023) 116699
expressed as follows:
Jb (i) = Lb (Cbm(i)–Cbp(i) ) + (1 − σb )Cb Jv (i)
Cboric and Cborate are the concentrations of borate acid (B(OH3 )) and
borate ions (B(OH)− 4 ), respectively, which can be estimated for a given
pH and apparent first acid dissociation constant for boric acid (Ka1 )
which can be derived from the dissociation reaction of boron species in
seawater, as defined by Eq. (22). Notably, Ka1 was assumed to be tem­
perature- and salinity-dependent and was calculated from Eq. (24) using
the salt concentration at the membrane wall (Csm) [46].
(13)
where Lb isthe overall boron permeability constant; σb is the overall
boron reflection coefficient, which represents the boron water coupling
phenomenon; and Cb is the average boron concentration of feed at the
permeate side.
In order to investigate the relative importance of the contribution of
the mechanisms to the overall boron transfer, two flux terms, boron
diffusive flux (Jb,diff ) and boron convective flux (Jb,conv ), were defined.
They represent the contributions of diffuse and convective transport,
respectively, in the passage of boron through the ith element section.
Jb (i) = Jb,diff (i) + Jb,conv (i)
Rb,diff (i) =
Jb,diff
Jb,diff (i)
(i) + Jb,conv (i)
B(OH)3 + H2 O ⇔ B(OH)− 4 + H +
ka1 (i) =
(14)
− logK a1 (i) =
BRt (i) =
(19)
Qf (i + 1) = Qf (i) − Qp (i)
γ1 =
Ka1
Cborate
=
+ Ka1 Cboric+borate
[H + ]
(26)
(27)
Csf (i + 1) =
Qf (i)Csf (i) − Qp (i)Csp (i)
Qf (i + 1)
(28)
Cbf (i + 1) =
Qf (i)Cbf (i) − Qp (i)Cbp (i)
Qf (i + 1)
(29)
2.5. Performance parameters for RO system
Salt and boron rejection (SR and BR), water recovery ratio (Rec), and
specific energy consumption (SEC) are the most important parameters
characterizing the performance of an overall RO system. They are
defined as follows:
SR = 1 −
Cspo =
Cspo
Csf 0
∑n
∑n
Cspi ΔQpi
i=1 Cspi ΔQpi
∑n
= i=1
Qpo
i=1 Qpi
BR = 1 −
where Lboric,0 and Lborate,0 are the permeability constants of boric acid
(B(OH3 )) and borate ions (B(OH)− 4 ) estimated at T0 = 298 k. a and b
are experimentally estimated constants. γ0 and γ1 are the fractions of
boric acid and borate ions, respectively, and calculated using the
following equations [46]:
Cboric
[H + ]
γ0 = +
=
[H ] + Ka1 Cboric+borate
(25)
Furthermore, the permeate mass balance and total solute (salt and
boron) balance relationship were also used to calculate the permeate
flow rate and salt and boron concentrations for the subsequent element
(i + 1):
whereas ω and φ are constants experimentally estimated [36].
Eq. (13) implies that boron flux through the ith element section may
result from the concentration and pressure gradients defined by water
flux (Eq. (1)). In contrast with the irreversible thermodynamic model,
the diffusion model does not consider the convective effect on solute
transport; salt flux is directly proportional to the concentration gradient
(Eq. (2)). Therefore, only two transport parameters (salt permeability
and mass transfer coefficients) should be experimentally estimated to
predict the performance of the membrane [33,43–45] However, in an
irreversible thermodynamic model, three transport parameters, namely,
boron permeability (Lb), mass transfer (kb), and reflection coefficients
(σb) should be simultaneously evaluated by experimental studies com­
bined with a non-linear optimization method [31,46,47].
Based on the experimental work of Hung and Kim [46], the overall
permeability and reflection coefficients (Lb , σ b ) can be expressed as
functions of the permeability and reflection parameters of borate ions
and boric acid and temperature:
σ b = γ0 .σboric,0 + γ1 .σ borate,0
Cbm (i) − Cbp (i) σb .[1 − exp( − Jv (i)(1 − σ b )/Lb ) ]
=
Cbm (i)
[1 − σ b .exp( − Jv (i)(1 − σ b )/Lb ) ]
BR(i)
Cbb (i) − Cbp (i) σ b .[1 − exp( − Jv (i)(1 − σ b )/Lb ) ]
( )
=
=
1 − BR(i)
Cbb (i)
(1 − σb ) exp Jvk(i)
b
(17)
(18)
(24)
By combining Eqs. (13), (16), and (25), the observed rejection BR of
the boron through the ith element section can be calculated as follows
[31,42]:
whereas kb is the boron mass transfer coefficient that can be expressed as
follows:
Lb = γ0 .Lboric,0 exp[(a(Tb − T0 ) ] + γ0 .Lborate,0 exp[(b(Tb − T0 ) ]
2291.9
+ 0.01756 Tb (i) − 3.385 − 3.904 Csm 1/3
Tb
(23)
To solve the problem of boron transport coupled with concentration
polarization in reverse osmosis membranes, Spiegler and Kedem [42]
substituted the average concentration (Cb ) in Eq. (13) to obtain the
following equation for true boron rejection (BRt ):
(15)
The fraction of diffusion flux, expressed by Eq. (15), is close to unity,
and the mass transport of boron and water may be decoupled. Conse­
quently, the irreversible thermodynamic model can be simplified to a
solution-diffusion model to study and simulate both salt and boron
removal during the reverse osmosis desalination process.
Similar to the concentration polarization of salt, Eq. (10), the con­
centration of boron at the membrane wall (Cbm ) is higher than that in the
bulk solution (Cbp ) and can be derived from film theory as follows:
(
)
Jp (i)
Cbm(i) = Cbp(i) + (Cbb(i) − Cbp(i) )exp
(16)
kb
kb = ω.exp[(φ(Tb − T0 ) ]
[Cborate ][H + ]
[Cboric ]
(22)
Cbpo
Cbf 0
∑n
i=1 Cbpi ΔQpi
Cbpo =
RR =
(20)
Qpo
Qf 0
SEC =
(21)
5
Qpo
( )− 1
Pf Qf εp
− Pb Qb εERD
Qpo
(30)
(31)
(32)
(33)
(34)
(35)
R.B. Mansour
Desalination 562 (2023) 116699
Fig. 3. Estimation of model parameters for the following operating conditions: Tf = 15–35 ◦ C, Pf = 4000–8000 kPa, pH = 6–9,Qf = 5.4–12.6 m3/h and Csf =
35,000 ppm.
Table 2
Comparison of model predictions with experimental data for a typical RO plant (Tf = 19◦ C, Csf = 42,000 ppm) [49].
Pf (kPa)
6300
6100
5800
5700
5200
Qf (m3/h)
43.5
40.7
33.8
39.5
35.9
Qp (m3/h)
Permeate TDS (ppm)
Experimental [49]
Model
Error (%)
Experimental [49]
Model
Error (%)
12.5
11.7
9.8
10.0
7.9
13.2
12.1
10.1
10.4
8.0
5.6
3.4
3.1
4
1.3
191
210
250
215
270
208
219
258
234
289
4.1
1.9
2.4
8.8
7.1
comprises the following steps:
- The input data include the feed conditions, feed channel character­
istics, and the number of elements in the RO module integrated into
the model.
- For each element, the membrane-specific model parameters of water,
salt, and boron transport, namely, the mass transfer coefficients and
permeability constants, are calculated using Eqs. (7), (8), (9), (17),
and (18).
- For each element, the water and salt transport and concentration
polarization equations (Eqs. (1), (2), and (10)) are solved simulta­
neously to obtain the water and salt fluxes (Jv and Js), which are
considered inputs for the boron transport simulation program. Sub­
sequently, Jb,diff and Jb,conv through each elemental section can be
estimated (Eqs. (13)–(16)).
- The key RO performance parameters for all RO membranes (e.g.,
water recovery, boron and salt rejection, and specific energy) are
estimated from Eqs. (30)–(35).
Fig. 4. Boron rejection at different pH levels, based on model predictions and
experimental data [46].
3. Model calibration and validation
The model parameters, including the solvent and solute mass transfer
coefficients, permeability constants, and boron reflection coefficient,
were estimated experimentally [36,46] or determined using the design
software FilmTec Reverse Osmosis System Analysis (ROSA 6) [48]. For
large variations in operating conditions, the system equations were
solved using a non-linear regression method to determine the water and
salt transport parameters of the SW30HR380 wound spiral membrane
[48]. As shown in Fig. 3, the predictions of the present model agree well
with the ROSA design software data.
Additional verification was performed using the experimental results
from a typical RO plant that used the same modules. Table 2 presented
the experimental data [49] and the predicted data at 19 ◦ C for the
where Qpo is the total permeate volumetric flow rate. Parameters
εp and εERD are the pump and ERD efficiencies, respectively.
2.6. Numerical procedure
In this section, we explain how to determine the profiles of RO
process variables for any seawater composition, membrane, or feed
conditions. The governing Eqs. (1)–(26) are improved using the updated
seawater thermophysical properties library, which comprises the effects
of salinity, temperature, and pressure on the correlations of the prop­
erties [36]. These equations are non-linear, implicit, and should be
solved using iterative methods. The proposed simulation procedure
6
R.B. Mansour
Desalination 562 (2023) 116699
spiral wound membrane modules (FilmTec SW30HR-380) and produces
~600 m3/day of fresh water. All membrane module characteristics used
in this comparison were presented in Table 5. Table 6 presented the
experimental data [50] and the predicted data for the outlet pressure,
permeate flow and salt concentration at two values of feed pressure and
temperatures. The predictions of our model showed a good agreement
with field data reported by Geraldes et al. [50]. The relative errors were
found to be 3.18 %–9.81 % and 2.18 %–7.58 %, in terms of permeate
water and salt concentration, respectively. Based on these calculations,
the membrane parameters of SW30HR-380, Lvo and Ls0 were estimated
to be 8.05 10− 12 and 12.33 10− 9 and these values with the membrane
module characteristics were used in the subsequent simulation.
Table 3
Membrane module characteristics and performance parameters used in actual
simulation and experimental work [28].
Parameter
RE4040-SR
Length of the membrane, (m)
Width of the membrane, (m)
Feed channel height, (m)
Permeate channel height, (m)
Number of membrane leaves
Membrane area, (m2)
Salt transport parameter, (Ls)25 ◦ C, m/s,
Water transport parameter, (Lv)25◦ C,800psi, m/s-Pa
Reflection coefficient for H3BO3, σboric,0
Reflection coefficient for (B(OH)−4 ), σborate,0
Permeability constant for (H3BO3)25◦ C, Lboric,0 , (m/day)
Permeability constant for (B(OH)−4 ) 25◦ C, Lborate,0 , (m/day)
0.88
0.8
8.10− 4
5.10− 4
5
3.52
1.58310−
5.29810−
0.975
0.998
0.0473
0.0076
8
12
4. Results and discussion
4.1. Factors involving in boron rejection
permeate flow and concentration at various feed flow rates and feed
pressure. An excellent agreement was observed between the model
predictions and the experimental data as the maximum variations in
permeate flow rate and permeate concentration were <5.6 % and 8.8 %,
respectively.
For boron rejection, the permeability constants and the reflection
coefficients were initially predicted based on Hyung and Kim’s experi­
mental work [46] and used to validate the proposed boron model. The
permeability constants at 25◦ C were Lboric,0 =0.0473 m/day and
Lborate,0 =0.0076 m/day for boric acid and borate ions, respectively.
Fig. 4 presents a comparison between the simulation and experimental
results of the boron rejection values against the water flux values for two
pH values: 6.2 and 9.5. Other operating conditions were kept constant:
Tf = 25 ◦ C; feed salt concentration; Csf = 32,000 ppm; and overall re­
covery ratio, RR = 8 %. An excellent agreement was found between the
model prediction and the experimental data for boron rejection because
the maximum deviation was <2 %.
Additionally, the performance of the presented model has been
compared against experimental data reported by Mane et al. [28] for the
permeate flow, salt concentration and boron rejection in a multicom­
ponent mixture at various feed flow, feed pressure and pH values and
using RE40440-SR spiral wound membrane type. The operating condi­
tions were maintained constant: Tf = 25◦ C; Csf = 32,000 ppm; RR = 8 %.
Other parameters related to the characteristics and performance of the
RE40440-SR membrane element used in the simulation are provided in
Table 3. Table 4 presented the experimental data [28] and the predicted
data for the permeate flow and salt rejection. An excellent agreement
was observed between the model predictions and the experimental data
as the maximum errors in permeate flow rate and salt rejection were
<5.4 % and 0.20 %, respectively. Furthermore, Fig. 5 showed the
variation of boron rejection with applied pressure (600–800 psi) for
different pH values based on model predictions and experimental data
[28]. An excellent agreement was observed between the results obtained
from the model predictions and the experimental data as the relative
error was lower than 2.5 % for all the ranges of pHs and pressures
considered.
Finally, the model performance has been compared against the field
data of a full-scale SWRO train of the desalination plant of Porto Santo
Island (Portugal) [50]. This train comprises 12 pressure vessels with 4
Some significant results related to the boron mechanisms obtained
by the application of thermodynamic approaches for salt, boron, and
water transport coupled with concentration polarization are presented
and discussed in this section, with an emphasis on the effects of the main
variables (e.g., pH, temperature, salinity pressure, and feed flow rate) on
the presence and rejection of boron by the RO membrane. The RO
Fig. 5. Boron rejection at various applied pressures and pHs, based on model
predictions and experimental data [28] (Tf = 25 ◦ C, Csf = 32,000 ppm, RR =
8 %).
Table 5
Main parameters for SW30HR-380 membrane [22,48–50].
Membrane specific parameters
Value
Cross section area of RO element, A, (m)
Hydraulic diameter, (m)
Brine channel height of RO element, (m)
Spacer thickness, (m)
The brine channel length of RO element, lbr, (m)
The brine channel width of RO element, wbr, (m)
The overall void fraction of the brine channel
The specific surface area of the spacer, α, (m− 1)
constant for solvent transport, α1
constant for solvent transport, α2, (bar− 1)
constant for solute transport, β1
35.3
9.35 10−
0.84 10−
7.11 10−
0.8665
1.34
0.9
11,249
8.6464
0.0149
14.648
4
3
4
Table 4
Comparison of model predictions with experimental data for RE40440-SR membrane element (Tf = 25 ◦ C, Csf = 32,000 ppm) [28].
Pf (psi)
800
750
700
650
600
Qf (m3/day)
50
44.625
41
33.75
28.25
Qp (m3/day)
Salt removal (BR)
Experimental [28]
Model
Error (%)
Experimental [28]
Model
Error (%)
4.00
3.57
3.28
2.70
2.26
4.04
3.61
3.15
2.64
2.14
1.0 %
1.1 %
4.1 %
2.2 %
5.4 %
0.997
0.997
0.997
0.996
0.996
0.999
0.998
0.998
0.998
0.997
0.20
0.13
0.10
0.20
0.15
7
%
%
%
%
%
R.B. Mansour
Desalination 562 (2023) 116699
Table 6
Comparison of model predictions with experimental data for SW30HR-380 membrane (Csf = 38,000 ppm) [28].
Tf (◦ C)
19
19
19
18
Pf (Mpa)
Qf (L/s)
5.90
5.90
5.90
5.71
22.5
22.9
20.2
19.5
Outlet pressure (Mpa)
Qp (L/s)
Permeate TDS (ppm)
Experimental [50]
Model
Experimental [50]
Model
Experimental [50]
Model
5.80
5.80
5.80
5.65
5.83
5.83
5.84
5.66
6.96
7.36
6.60
6.01
6.52
6.64
6.39
5.78
287
275
264
278
271
269
284
297
Fig. 6. Distribution of boric acid and borate ions in seawater by the change in
pH for N = 6, Pf = 6000 kPa, Qf = 0.0025 m3/s, Csf = 35,000 ppm, Cbf = 5 ppm,
and Tf = 25◦ C.
Fig. 8. Variation in boron flux by the change in pH for N = 6, Pf = 6000 kPa,
Qf = 0.0025 m3/s, Csf = 35,000 ppm, Cbf = 5 ppm, and Tf = 25◦ C.
Fig. 9. Variation in boron concentration by the change in pH for N = 6, Pf =
6000 kPa, Qf = 0.0025 m3/s, Csf = 35,000 ppm, Cbf = 5 ppm, and Tf = 25◦ C.
Fig. 7. Variation in boron permeability and reflection coefficient by the change
in pH N = 6, Pf = 6000 kPa, Qf = 0.0025 m3/s, Csf = 35,000 ppm, Cbf = 5 ppm,
and Tf = 25◦ C.
pH, and reached a value close to unity at pH > 10 (Fig. 6). This behavior
can be explained by the small size of boric acid and negatively charged
borate ions, (B(OH)− 4 ). According to the reaction shown in Eq. (22),
increasing the applied pH (e.g. decreasing the [H+] in the solution) leads
to an enhancement of the dissociation of (B(OH)3 ), which increases the
concentration of B(OH)− 4 . The electrostatic repulsive forces that are
generated between the negatively charged borate ions and the nega­
tively charged membrane surface can effectively improve boron
removal.
Figs. 7 and 8 show that when the pH changed, the overall flux of
boron (Jb ) and the permeability coefficient (Lb ) followed the same
pattern. For pH ranges of 7 and 10, both parameters (Jb and Lb ) signif­
icantly decreased. For instance, Jb decreased from 3.98 × 10− 6 to 0.76 ×
10− 6 kg/m2.s as pH increased from 7 to 10. On the other hand, the pH
had no effect on Jb and Lb at low pH (below 7) and high pH (>10).
Regarding the boron transport mechanism across the RO membrane,
process model and commercial membrane specifications were estimated
from [19,45–47], as listed in Table 5.
4.1.1. Effect of pH feed solution
To investigate the effect of pH variation on boron removal and to
assess the relative importance of the contributing mechanisms, the
profiles of boron transport parameters and boron diffusive and
convective fluxes are presented in Figs. 6–9. The curves are plotted at
various values of pH for N = 6, Pf = 6000 kPa, Qf = 0.0025 m3/s, Csf =
35,000 ppm, Cbf = 5 ppm, and Tf = 25 ◦ C. An example of the variation in
the distribution of boron species with changes in the solution feed pH is
shown in Fig. 6. At low pH values, the fraction of boric acid (γ0) is high,
which indicates that the dominant species in the boron system is boric
acid (B(OH)3 ). At high pH, borate ions (B(OH)− 4 ) prevail. Overall boron
reflection constant (σb ) ranged from 0.982 and 0.998, increased with
8
R.B. Mansour
Desalination 562 (2023) 116699
Fig. 10. Distribution of boric acid in seawater against the feed temperature for
N = 6, Pf = 6000 kPa, Qf = 0.0025 m3/s, ppm, Cbf = 5 ppm, Tf = 25 ◦ C and pH
= 8.
Fig. 12. Variation in boron flux against the feed temperature for N = 6, Pf =
6000 kPa, Qf = 0.0025 m3/s, ppm, Cbf = 5 ppm, Tf = 25 ◦ C and pH = 8.
Fig. 11. Variation in boron transport parameters against feed temperature for
N = 6, Pf = 6000 kPa, Qf = 0.0025 m3/s, ppm, Cbf = 5 ppm, Tf = 25 ◦ C and pH
= 8.
Fig. 13. Variation in boron concentration and boron rejection against feed
temperature for N = 6, Pf = 6000 kPa, Qf = 0.0025 m3/s, ppm, Cbf = 5 ppm, Tf
= 25 ◦ C and pH = 8.
Fig. 8 shows that the values of diffusion flux (Jb,dif f ) are usually more
important than those of convective flux (Jb,conv ), particularly for high pH
values. Thus, the fraction of diffusive flux (Rb,diff ) represents >90 % of
total boron flux for pH beyond 8.2. This trend results from the fact that
boric acid dissociates readily at high pH levels (Fig. 6), which causes an
increase in the reflection coefficient (σb), reducing then the convective
contribution (Jb,conv ) in boron transport. This suggested that the coupling
of water and boron transport might be ignored, and a diffusion-based
approach could estimate the boron transport through the membrane
with acceptable accuracy.
Decreasing the permeability values (Lb ) with increasing pH reduces
the boron flux, which involves a reduction in boron concentration on the
permeate side (Fig. 9). Consequently, the boron rejection rates
(BR and BRt ), estimated using Eqs. (25), (32), were improved at high pH
values, confirming the strong correlation between boron rejection and
the pH of the feed solution. Experimental data has consistently shown a
correlation between pH and boron rejection for different reverse osmosis
membranes [46,51–53]. For instance, under natural pH conditions, the
BRt is 85.5 %, and it approaches unity at high values of pH beyond 10.
An enhancement of boron removal from seawater can be achieved by
adjusting feed solution pH. Based on boron concentration polarization
(Eq. (16)), the boron permeate flux influences the boron wall concen­
tration (Cbm) and boron rejections (BR and BRt ). The maximum con­
centration polarization level occurs at low pH values, corresponding to a
high permeate flux, as shown in Figs. 8 and 9. For seawater conditions
and the single-stage SWRO considered in this study, the feed solution pH
suggested should be higher than 8.3 to ensure the performance guideline
of concentration of boron for irrigation and drinking water purpose (0.5
mg/l boron in permeate).
4.1.2. Effects of feed temperature and salinity
In illustrating the effect of feed temperature and salinity on boron
transport, the distribution of boric acid (B(OH)− 4 ), borate ions
(B(OH)− 4 ), and boron transport parameters (Kb and Lb) have been
considered for several cases with a temperature range from 10 to 50◦ C
and three feed salinity values (Csf = 25,000 ppm, 35,000 ppm, and
45,000 ppm). Based on the correlation of the apparent acid dissociation
constant (Ka1 ), (see Eq. (24)), an increase in feed temperature or salinity
results in a decrease Ka1 , which directly enhances (B(OH)− 4 ) content in
seawater. As illustrated in Fig. 10, the borate acid fraction (γ0) decreases
9
R.B. Mansour
Desalination 562 (2023) 116699
by approximately 17 % as the feed temperature increases from 10 to 50
◦
C. Theoretically, this behavior may lead to an increase in boron
rejection with increasing temperature if we neglect the strong effects of
other boron transport parameters (Kb and Lb ).
Furthermore, there is a strong correlation between the solution
temperature and boron transport parameters, according to Eqs. (17) and
(18), respectively. As shown in Fig. 11, an increase in temperature leads
to an exponential growth of Kb and Lb. Thus, the coefficients (Lb and kb)
are respectively augmented by 13 times and five times as the tempera­
ture is increased from 10 to 50 ◦ C. The effect of boron concentration
polarization is reduced as the mass transfer coefficient (kb) increases,
resulting in a theoretically high boron rejection by the SWRO mem­
brane. The boron permeability coefficient increased with temperature
and had a positive effect on boron transport through the RO membrane,
resulting in low boron rejection. As shown in Figs. 12 and 13, the boron
flux and boron concentration in the permeate significantly increase as
the temperature increases, indicating that the effect of temperature on
boron permeability is much stronger than the corresponding decrease in
the pKa1 of boric acid and the boron concentration polarization caused
by the increase in Kb. These predictions are consistent with those of
experimental and analytical studies [28,46,52,53].
Regarding the effect of feed salinity on boron transport mechanisms,
the variation in the inlet feed salinity slightly affects the distribution of
B(OH)− 4 , B(OH)− 4 , parameters Kb and Lb, as shown in Figs. 10 and 11.
Fig. 12 shows a slightly reduced boron flux as the feed salinity increases
from 25,000 to 45,000 ppm. These findings can be attributed to the
pressure driving force that decreased with the increased feed salinity,
resulting in a decrease in water and boron fluxes and, consequently, an
increase in boron concentration on the permeate side. This suggested
that high boron rejection was obtained at low seawater salinity. For
instance, at high seawater temperatures (50◦ C), BR decreased from 69 %
to 65 % as Csf increased from 25,000 to 45,000 ppm. As shown in Fig. 13,
high values of boron rejection can be achieved in the seawater reverse
osmosis process at low salinity and temperatures. These findings are
consistent with those of Farhat et al. [15], who observed an increase in
boron rejection at low temperatures and salinity for various SWRO
membranes.
Regarding the boron transport contribution, Fig. 13 shows that
increasing the feed temperature had a positive effect on the boron
diffusive flux. For instance, the fraction of diffusive flux increases from
74 % to 97 % in the case of low salinity feed (i.e., Csf = 25,000 ppm) as
temperature increases from 10 to 50◦ C. Hence, under high feed tem­
perature conditions, the thermodynamic solution-diffusion model can
accurately predict boron removal through RO membranes. Nonetheless,
in low temperature and low salinity cases, convective boron transport
cannot be neglected because its contribution to overall boron flux is
relatively high and can be >20 %.
For a typical single-pass, reverse osmosis seawater desalination
plant, the feed temperature should be <17.5 ◦ C, and the same operating
conditions should be used to remove boron up to the target value, which
is suitable for irrigation and drinking purposes. However, most of the
countries that are at risk of running out of water and rely heavily on
seawater desalination technologies are in dry, hot places where the
average seawater temperature can be above 20 ◦ C.
Fig. 14. Variation in boron flux against the feed pressure for N = 6, Csf =
35,000 ppm, Cbf = 5 ppm, Tf = 25 ◦ C, and pH = 8.
Fig. 15. Variation in boron concentration and boron rejection against feed
pressure for N = 6, Csf = 35,000 ppm, Cbf = 5 ppm, Tf = 25 ◦ C, and pH = 8.
4.1.3. Effects of feed pressure and flow rate
In investigating the effect of applied pressure and flow rate on the
boron transport process, the distribution of boric acid and borate ions,
boron transport parameters and boron flux have been considered for a
range of applied pressure from 4000 to 10,000 kPa and two feed flow
rates (Qf = 0.002 m3/s and 0.005 m3/s). Figs. 14 and 15 depict that the
feed pressure and flow rate affect boron transport. For the same flow
feed rate, increasing the applied feed pressure results in an increased
pressure driving force, which causes an increase in the water and boron
fluxes. Similarly, increasing the feed flow rate led to an increase in the
boron flux. The simulation results also showed that at high flow rates,
Fig. 16. Variation in boron concentration and boron rejection for different
membrane modules for Pf = 8000 kPa, Qf = 0.0025 m3/s, Csf = 35,000 ppm,
Cbf = 5 ppm, Tf = 25 ◦ C, and pH = 8.
10
R.B. Mansour
Desalination 562 (2023) 116699
Fig. 17. Variation in main performance parameters for different applied feed pressure and flow rate. Simulation conditions: Csf = 35,000 ppm, Cbf = 5 ppm, Tf = 25
◦
C, and pH = 8: a) Recovery ratio, b) Salt rejection, c) Boron rejection d) Energy consumption.
11
R.B. Mansour
Desalination 562 (2023) 116699
pressures (>8000 kPa), the convective boron transport cannot be
neglected because the fraction of diffusive flux is lower than 80 %. This
behavior is also shown in Fig. 15, in which the boron concentration on
the permeate side and boron rejection are plotted for various applied
pressures and feed flow rates. In the lower-pressure region, boron
rejection increased mainly because of the increase in the pressure
driving force. At high pressures, the boron concentration polarization
layer played a vital role in reducing the boron concentration increment
on the permeate side. Based on the results of these simulations, a high
boron removal rate was obtained at a high feed flow rate and applied
pressure.
Table 7
Optimization results for imposed feed flow rate.
Applied
feed flow
rate (m3.
s− 1)
0.0020
0.0025
0.0030
0.0035
0.0040
0.0045
0.0050
Optimal
feed
pressure
(kPa)
RR
(%)
Average
flux (L.
m− 2 h− 1)
SEC
(kWh/
m3)
SR
(%)
BR
(%)
4600
4800
4950
5150
5300
5500
5650
35.91
35.82
34.99
34.61
33.67
33.14
32.17
12.21
15.22
17.84
20.59
22.89
25.34
27.34
2.52
2.65
2.80
2.96
3.13
3.32
3.52
99.34
99.47
99.56
99.62
99.66
99.70
99.72
84.60
86.65
87.98
89.00
89.70
90.29
90.70
4.1.4. Effect of the number of modules
The effect of the number of RO modules on boron concentration and
rejection is displayed in Fig. 16 for the following operating conditions:
N = 8, Pf = 8000 kPa, Qf = 0.0025 m3/s, Csf = 35,000 ppm, Cbf = 5 ppm,
and Tf = 25 ◦ C. Boron concentration on the permeate side increases
substantially along the vessel from the first to the last module. This
variation is due to the decrease in the net pressure force along the
membrane, leading to an increase in the feed boron concentration and a
decrease in the permeate flux, which reduces the boron rejection factors,
as presented in Fig. 6. A reduction BRt from 95.57 % at the vessel inlet to
92.89 % at the outlet of the vessel is observed. The last module had the
highest permeate boron concentration and lowest boron rejection factor.
Despite the increase in the overall permeate flow and recovery ratio,
vessels with a high number of elements (i.e., high membrane area)
produced higher salt and boron rejection.
4.2. Performance analysis of the RO system
The main process variables reflecting the water quality and energy
consumption of the SWRO system were the total water recovery rate,
specific energy consumption, and rejection ratios. Therefore, studying
the influence of the operating conditions (e.g., feed flow rate, feed
pressure, seawater temperature, and seawater salinity) on SWRO per­
formance to minimize the specific energy consumption and satisfy water
quality standards in terms of the MAC of boron and salt for portable and
irrigation water is important.
Figs. 17 (a–d) depict the main performance variables for a singlestage SWRO using six membrane modules in series, operating with
feed TDS of 35,000 ppm and seawater temperature Tf = 25 ◦ C, as a
function of applied pressure and feed flow rate. These results indicate
that the recovery rate increased as the applied pressure increased. For a
feed flow rate of 0.002 m3/s, for example, the recovery ratio increased
from 32 % at low pressure (40 bar) to 69 % at high pressure (100 bar).
This increase is explained by the increase in the pressure driving force (i.
e., increased applied pressure), which has a strong effect on salt and
boron rejection, particularly in the lower-pressure region (Pfeed < 5000
kPa). The effect of solute concentration polarization in the feed brine
solution was more pronounced at higher applied pressures, attenuating
the effect of the pressure gradient on solute removal. Figs. 17 (b and c)
showed nearly constant rejection ratios for applied pressures >6000
kPa. As shown in Figs. 17 (a and c), increasing the feed flow rate results
in a low recovery ratio (RR) and increased salt and boron rejection (SR
and BR) at the same applied pressure.
Fig. 17 (d) shows how the specific energy consumption changes with
the applied pressure under typical operating conditions aforementioned.
The specific energy consumption behavior is affected by both applied
pressure and feed flow rate. Increasing the applied pressure increased
the pumping energy and the amount of water produced. Consequently,
the specific energy consumption (SEC), corresponding to the total en­
ergy consumption per unit of water production, has an optimum value.
Under the previous operating conditions, the optimum value for specific
energy was 2.52 kWh/m3 at a recovery ratio of 35.9 % and a feed flow
rate of 0.002 m3/s. Optimum SEC varies with the main operating vari­
ables, as shown in Fig. 17 (a) and Table 7. Table 7 presents also the
Fig. 18. Variation in main performance parameters for different applied feed
temperatures and salt concentration. Simulation conditions: Qf = 0.0025 m3/s,
Cbf = 5 ppm, Tf = 25 ◦ C, and pH = 8: a) Recovery ratio and b) Energy
consumption.
the proportion of diffusive flux decreased as the feed pressure increased.
As shown in Fig. 14, for a high feed flow rate (Qf = 0.005 m3/s), the
fraction of diffusive flux decreases linearly in the lower-pressure region
(Pf < 7000 kPa) owing to an increase in the pressure driving force. At
high pressures, the decrease in the diffusive flux across the membrane
was low. This trend is because of the possible accumulation of boron on
the membrane, which results in an increased concentration of driving
force. As the operating pressure increased, the concentration polariza­
tion layers of salt and boron gradually built up on the membrane surface,
lowering the permeate water, salt, and boron fluxes. Thus, for high
12
R.B. Mansour
Desalination 562 (2023) 116699
Fig. 19. Contours of specific energy and salt and boron concentration for imposed feed flow rate and pressure. Simulation conditions: Cbf = 5 ppm, Tf = 25 ◦ C, and
pH = 8. a) Csf = 35,000 ppm, b) Csf = 25,000 ppm.
optimal energy consumption and other important operating variables as
a function of the applied feed flow rate with an interval of 0.005 m3.s− 1.
The results show that optimum SEC and corresponding applied pressure
increases as the feed flow rate increases. Moreover, because the recovery
ratio is inversely proportional to the applied flow rate, it decreased. As
the feed flow rate increased from 0.002 to 0.005 m3/s, the optimal SEC
increased by approximately 39.6 %, and the recovery ratio decreased by
11.6 %. In addition, the optimum permeate water flux increased linearly
with increased feed flow rate, improving from 12.21 to 27.34 L.m− 2 h− 1
for the same increment of the feed flow rate. According to Eqs. (9) and
(13), the permeate salt and boron concentrations decreased as the
permeate water flux increased. The increased flow rates caused the salt
and boron rejections (SR and BR) to increase from 99.34 % to 99.72 %
and 84.60 % to 90.70 %, respectively. These results findings confirm the
relationship between salt and boron permeabilities. The boron and salt
fluxes increase (mainly due to the increased salt and boron permeabil­
ities) with the recovery decreases. These findings are consistent with
those of Taniguichi et al. [33], who determined a correlation between
salt and boron permeabilities. As discussed in Section 4.1, high salt and
boron rejection rates were achieved at low recovery ratios and high
applied feed flow rates.
Figs. 18 (a) and (b) show the effect of seawater temperature on the
RO system recovery ratio and energy consumption for various feed salts.
The mass transfer equations for salt and boron are strongly correlated
with salinity and temperature, as described in the previous section. As
the temperature increased, the salt and boron flow rates across the
membrane increased, reducing solute rejection and negatively affecting
the product water quality. For instance, at high seawater temperatures,
high levels of salt and boron concentrations on the permeate side can be
reached and can harm human health. On the other hand, a high seawater
salinity reduces the solute rejection and recovery ratios and increases
energy consumption, as shown in Fig. 18. Therefore, RO plants require a
lot of energy to operate in seawater with high salinity, such as that near
the Gulf countries.
Figs. 19 (a) and (b), which show the contours of the specific energy
consumption, salt, and boron concentrations for a given feed flow rate
and pressure, can be used to determine the operating window for
different constraints and optimize the RO process in terms of energy use
and water quality. The simulation conditions are: Cbf = 5 ppm, Tf =
25 ◦ C, and pH = 8; a) Csf = 35,000 ppm and b) Csf = 25,000 ppm. Ac­
cording to the following performance guidelines; the specific energy and
permeate boron and salinity concentrations must be <3 kWh/m3, 0.5
13
R.B. Mansour
Desalination 562 (2023) 116699
mg/l, and 500 ppm, respectively, and the corresponding contour curves
must be overlaid to determine the operation window satisfying the
guidelines. The colored areas in Figs. 19 (a) and (b) represent the ranges
of the operational conditions. For the selected combination of flow rate
and pressure, the salinity concentrations were always lower than the
target permeate salinity concentration at different feed salinity values.
However, the high osmotic pressure caused by an increase in feed
salinity had a significant impact on the boron rejection and specific
energy. For instance, to satisfy the performance guidelines at Csf =
35,000 ppm, the feed flow rate and applied pressure should be lower
than 0.0036 m3/s and 7470 kPa, respectively. Fig. 19 (b) shows a wide
range of operating conditions for the same performance guidelines at Csf
= 25,000 ppm.
Acknowledgments
The authors acknowledge the resources provided by the Interdisci­
plinary Research Center for Renewable Energy and Power Systems at the
King Fahd University of Petroleum and Minerals through the IRC-REPS
project (No. INRE2223).
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5. Conclusion
A mathematical model of the RO system was developed based on two
thermodynamic approaches for salt and boron transport coupled with
membrane concentration polarization. The validated model was used to
investigate and optimize RO process performance under a wide range of
operating conditions. The main conclusions are summarized as follows:
• Boron rejection is primarily controlled by diffusion transfer, and a
thermodynamic diffusion-based model can be considered for large
simulation conditions. Convective boron transport, however, cannot
be ignored in some cases (i.e., high pH, applied feed pressure, and
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Increasing the feed salinity and flow rate significantly reduced the
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• Boron and salt rejection increased when the applied feed pressure
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• Increasing the applied feed pressure increased the amount of
pumping energy and water produced. Consequently, SEC has an
optimum value that varies according to the main operating condi­
tions. This optimum value is 2.52 kWh/m3 at a recovery ratio of
35.9 % and feed flow rate of 0.002 m3/s. The optimization results
showed that the optimum SEC and corresponding applied pressure
increased and the recovery decreased as the feed flow rate increased.
The optimal SEC increased by approximately 39.6 %, and the re­
covery ratio decreased by 11.6 % as the feed flow rate increased from
0.002 to 0.005 m3/s.
CRediT authorship contribution statement
Ridha Ben Mansour: Conceptualization, Methodology, Software,
Visualization, Investigation, Writing – review & editing.
Declaration of competing interest
The authors declare that they have no known competing financial
interests or personal relationships that could have appeared to influence
the work reported in this paper.
Data availability
No data was used for the research described in the article.
14
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