Accepted Manuscript
Dynamic simulation of the reverse osmosis process for seawater
using LabVIEW and an analysis of the process performance
Arun Joseph , Vasanthi Damodaran
PII:
DOI:
Reference:
S0098-1354(18)30738-5
https://doi.org/10.1016/j.compchemeng.2018.11.001
CACE 6268
To appear in:
Computers and Chemical Engineering
Received date:
Revised date:
Accepted date:
16 July 2018
17 October 2018
3 November 2018
Please cite this article as: Arun Joseph , Vasanthi Damodaran , Dynamic simulation of the reverse
osmosis process for seawater using LabVIEW and an analysis of the process performance, Computers
and Chemical Engineering (2018), doi: https://doi.org/10.1016/j.compchemeng.2018.11.001
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HIGHLIGHTS
 LabVIEW based Graphical User Interface to simulate the process behaviour.
 Simplified functional decomposition approach based dynamic modelling.
 Analysis of concentration polarization effect on process performance
 Reasonably high feed water temperature reduces specific energy consumption.
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Dynamic simulation of the reverse osmosis process for seawater using
LabVIEW and an analysis of the process performance
Arun Joseph*1, Vasanthi Damodaran2
CR
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Department of Instrumentation Engineering, Madras Institute of Technology, Anna University
Chromepet, Chennai, Tamil Nadu 600044, India
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Abstract. The reverse osmosis (RO) process has become one of the prominent membrane-based technologies for
water desalination to meet the demand for fresh water. This paper presents the results of simulations of the RO
desalination process based on simplified functional-decomposition approach-based modelling to understand the
process dynamics. The simulation model was validated by comparing the transient behaviour predicted by the
model with experimental data from an industrial seawater desalination process. The proposed work was carried
out using the Control Design and Simulation (CDSim) toolkit in the LabVIEW 2011 environment. The simulation
analysis showed that the specific energy consumption of the RO system could be reduced at different fractional
recovery rate by maintaining a reasonably high feed temperature.
Keywords: Reverse osmosis; Desalination; Dynamic simulation; Experimental validation
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1. Introduction
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The World Health Organization (WHO) statement in El-Dessouky and Ettouney (2002) stated that the rapid
depletion of freshwater resources was causing a clean drinking water shortage for about 1.1 billion people
across the world and was expected to affect 3 billion people by 2025. Seawater desalination is a potential
solution to meet the demands for drinking water around the globe due to the increasing and rapid exploitation
of freshwater resources. Seawater desalination is the process of removing or reducing the water salt content
to an acceptable limit. Today, the primary desalination processes used are the thermal such as multi-stage
flash desalination, multiple effect evaporation, and mechanical vapour compression and the reverse osmosis
(RO) processes. The RO process is more popular because it is less energy intensive than thermal processes.
The recent enhancements in the membrane’s performance has further increased the use of RO technology for
water desalination, and allowed the RO process to be used over wider ranges of pH, pressure and
temperature. The literature has reported different mechanisms and mathematical models that characterize the
separation performance in the RO process. Kim (2017) describes the mechanisms that explain the RO
transport phenomena as a sieving mechanism and a wetted-surface mechanism. Reid and Breton (1959)
explained the wetted-surface mechanism as a process in which water tries to adhere to the surface of the
membrane by treating the membrane as a wet material. According to a study by Sourirajan (1970), in the
sieving mechanism, the difference in sizes between the solvent and the solute molecules is responsible for
separation.
*Corresponding author
Email addresses: perhapsarun@gmail.com (Arun Joseph), vasanthi@annauniv.edu (Vasanthi Damodaran)
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J v  Lv (P   w ) ,
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The models for the RO process can be classified into three types, namely, the membrane transport model, the
lumped parameter model and the experimental model. The literature by Soltanieh and Gill (2007) shows that
the membrane transport model can be further subdivided into three: the non-porous model, the porous model,
and the irreversible thermodynamics model. Kedem and Katchalsky (1958) proposed the irreversible
thermodynamics model to represent the transport of non–electrolytes through a membrane by using Onsager
reciprocal relation. The non-porous model proposed by Lonsdale et al. (1965) assumes a homogeneous nonporous surface in which the solute and the solvent dissolve and then diffuse without much solute-solvent
interaction. This model is also known as the homogenous membrane model or the solution-diffusion model.
The literature by Sourirajan (1970) explains the porous transport model as a separation mechanism
characterized using pores on a membrane surface, where the pore size is twice the thickness of the water
layer on that surface. This model allows only solvent transport through the membrane and is also known as
the preferential sorption–capillary flow mechanism. The irreversible thermodynamic model presented in
Bitter (1991) can be described by the following equations:
J s  Cs,av (1   ) J v  Cs,av w .
(1)
(2)
Jv and Js represent the total volume flux and the molar solute flux, respectively. Lv is the filtration coefficient,
and σ is the Staverman coefficient, which is also known as the coupling coefficient. ∆P is the permeation
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pressure (net hydraulic pressure), ∆π is the net osmotic pressure, Cs,av is the logarithmic mean of the solute
concentration across the membrane and ω is the solute permeability. Spiegler and Kedem (1966) simplified
the complexity of this model due to the concentration dependences of the phenomenological coefficients by
proposing differential forms of Eqs. (1) and (2) with more constant phenomenological coefficients. The
limitations of these models are that they are black-box-type models in which the transport mechanisms are
not described in detail. The solution-diffusion model developed by Lonsdale et al. (1965) and presented in
Bitter (1991) can be described by the following equations:
J w  K w (P   w ) / l ,
(3)
J s  Ds ks (CR  CP ) / l .
(4)
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Jw and Js represent the solvent flux and the solute flux, respectively. Kw is the solvent permeability, l is the
membrane thickness, Ds is the solute diffusivity in the membrane and ks is the distribution coefficient of the
solute. CR and CP are the solute concentrations in both the retentate and the permeate, respectively. Among
the different transport models, the most popular model is the solution-diffusion model because the transmembrane chemical potential mostly emphasizes the transport of the solvent and the solute.
Gambier et al. (2007) developed a MATLAB-Simulink-based block-set implementation to represent the
dynamic model for a single-stage RO process by using physical laws. In this dynamic model, the two streams,
namely, the permeate stream and the brine stream, are mathematically symbolized using four differential
equations representing the balances of mass, concentration, pressure, and temperature, respectively. The
membrane transport model uses Poisuelle’s flow-equation-based mathematical expression. The variations in
the permeate flow rate and concentration for different brine valve openings and feed temperatures were
analysed using that model. Oh et al. (2009) proposed a simplified simulation model for analyzing the
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performance of an RO system. Lee et al. (2010) proposed an Aspen Custom Modeler Platform-based
dynamic simulation model of an industrial desalination plant. The equations and the parameters for the
simulation model proposed by Lee et al. (2010) were taken from the literature by Senthilmurugan et al.
(2005). The effects of the feed concentration and pressure on the permeate flow rate were analysed using the
developed model. The model was based on solution-diffusion theory and multiple fouling mechanisms.
Sobana and Panda (2013) developed a transient model of the seawater/brackish desalination process
comprising an equalization tank, a brine tank and a permeate tank. The validation of the developed model
was performed using the experimental data collected from a seawater-based desalination process with a
capacity of 3.8 million litres per day (MLD) of drinking water located in Narippaiyur village of the
Ramanathapuram district, Tamil Nadu, India. A multi-input multi-output RO process model was developed
using transient model data with pump pressure and recycle ratio as inputs and the permeate flow,
concentration and pH as outputs. The membrane transport model uses partial differential equation solutions
based on the Crank–Nicholson method to represent the axial and the radial flows along the centres of the
membrane tubes. Sobana and Panda (2014) proposed centralized and decentralized techniques for the control
of the RO process by using the developed multi-input multi-output RO process model. Barello et al. (2015)
assessed the performance in terms of permeate quality and salinity as a function of feed pressure and feed
salinity of a batch reverse osmosis desalination process by using laboratory experiments and process
modeling. The work investigated the dependence of water and salt permeability constant on feed salinity in a
batch reverse osmosis process. Al-Obaidi et al. (2016) developed steady-state and dynamic models of reverse
osmosis process for wastewater treatment plant. The solution-diffusion model coupled with the concentration
polarization mechanism has been used to develop the dynamic model. The developed model was validated
against experimental data for wastewater treatment to study the impact of operating parameters such as feed
flow rate, pressure, temperature and concentration of pollutant on salt rejection, recovery ratio and permeate
flux.
The proposed work attempts to present a dynamic simulation model based on a simplified functional
decomposition approach. The simplified functional decomposition approach minimizes the complexity of the
modelling in three ways. Firstly, the permeate and the brine sub-entities are mathematically characterized
using two differential equation, one representing the material mass and the other the concentration balance.
Secondly, the membrane transport model is mathematically described using the active membrane area.
Thirdly, the brine stream flow is mathematically formulated as flow through an equal percentage valve to
understand the process dynamics for different product requirements. In the proposed work, the membrane
transport model characterizing the passage of water and salt is modified to represent the temperature
dependences of the permeate flow rate and concentration by using the Arrhenius equation. The proposed
dynamic simulation model is validated using the experimental data for the seawater-based desalination
process described in Sobana and Panda (2013). Finally, a Graphical User Interface (GUI) based on the
widely used dataflow programming environment in LabVIEW is developed for simulating the process
behaviour under the influences of various performance-affecting factors, such as the feed pressure,
temperature, and concentration, and the recovery rate.
2. Simulation model
The RO process simulation model is developed in the LabVIEW environment by using a simplified
functional-decomposition modelling approach. The simplified functional-decomposition approach-based
representation of the RO process is shown in Fig. 1. The RO process is decomposed into three parts: namely,
the brine sub-entity, the RO membrane unit, and the permeate sub-entity. The brine sub-entity is
characterized by three variables: namely, the brine flow rate (Fb), concentration (Cb) and pressure (Pb).
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Similarly, the permeate sub-entity is characterized by three variables: namely, the permeate flow rate (Fp),
concentration (Cp) and pressure (Pp). Finally, the RO membrane is characterized by three variables: namely,
the water passage (Fm), the membrane surface concentration (Cm) and the salt passage (Fs). The known
process variables for the dynamic simulation model are the feed flow rate (Ff), concentration (Cf) and
pressure (Pf). The dynamic simulation model helps in analyzing the dynamic behaviour of the process under
the influences of various performance-affecting factors. The transient responses of permeate flow, salt flow,
brine flow, permeate concentration and brine concentration can be analysed using the simulation model. The
dynamic simulation model developed in the LabVIEW 2011 environment is as shown in Fig. 2. The model
equations cited in this paper and used for developing the RO process simulation are summarized in Table 1.
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Fig. 1. Functional decomposition representation.
Fig. 2. Developed RO process simulation in the LabVIEW environment.
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The paper proposes a way to formulate the maximum (Fbmax) and the minimum (Fbmin) values of the brine
flow rate by using the permeate mass balance as shown in Eq. (1). The mathematical definition of the
permeate recovery rate shown in the literature by El-Dessouky and Ettouney (2002) is considered for the
formulation of the maximum and the minimum permeate flow rates as shown in Eq. (2) and (3). The
maximum and the minimum values of the permeate recovery rate correspond to the minimum (Hmin) and the
maximum (Hmax) percentage openings of the reject valve, respectively. Now, the brine flow rate (Fb) for any
percentage opening of the reject valve (H) can be represented using the proposed generalized expression as
shown in Eq. (4). A reject valve is a flow regulating valve that controls the percentage of the feed that is
flowing as the permeate and the concentrate. In the dynamic simulation, the feed that is flowing as the
permeate can be controlled by using the percentage opening of the reject valve, and the permeate flow rates
as functions of time for various percentage openings of the reject valve are shown in Fig. 3.
Fig. 3. Permeate flow rates for different opening percentages of the reject valve. Simulation condition are Ff = 50
kg/s; Pf = 4870.833 kPa; Cf = 41350 ppm; Tf = 30 oC.
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The percentage opening of the reject valve manipulates the brine pressure (Pb), thereby changing the
trans-membrane pressure of the system. The mathematical definition of the trans-membrane pressure (∆P) is
given by Lee (1975) [Eq. (5)]. As the percentage opening of the reject valve decreases, the trans-membrane
pressure increases due to an increase in the brine pressure (Pb). Hence, the assumed maximum and minimum
recovery rates are achieved when the valve’s opening percentages are 10% and 100%, respectively. The
variation in the trans-membrane pressure in the simulation model for the RO system with the percentage
opening of the reject valve is shown in Fig. 4.
Fig. 4. Variation in the trans-membrane pressure with the opening percentage of the reject valve. Simulation
conditions are Ff = 50 kg/s; Pf = 4870.833 kPa; Cf = 41350 ppm; Tf = 30 oC.
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The manipulation of the reject valve opening varies the differential pressure (Pb - Pbo) across the valve.
Eckman (1958) recommends equal percentage valves when the pressure drop across the valve varies. Hence,
in this study, the reject valve is modelled as an equal percentage valve. The brine flow rate can be
mathematically represented in terms of the differential pressure by using the inherent characteristic of an
equal percentage valve, which is shown in Eq. (6). The mathematical modelling of the reject valve using the
inherent characteristic of an equal percentage valve was developed in the LabVIEW environment and is
shown in Fig. 5. The brine pressure (Pb) is computed using Eq. (7), which is formulated by rearranging Eq.
(6).
Fig. 5. Equal percentage control valve model in the LabVIEW environment.
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The solution-diffusion model was applied to predict the membrane water transport and salt transport in
the RO system. The solution-diffusion model was modified using analytical film theory and the Arrhenius
equation to describe the effects of concentration polarization and feed temperature, respectively, on the water
passage [Eq. (8)] and the salt passage [Eq. (9)]. The solution-diffusion model assumes that both the solvent
and the solute dissolve in the membrane surface layer, which is homogenous and non-porous, and then
diffuse across the membrane surface. The diffusions of the solute and the solvent across the membrane are
uncoupled due to the chemical potential gradient across the membrane. The chemical potential gradient due
to the differences in pressure and concentration across the membrane results in water passage and salt
passage, respectively. The effective membrane area (Aem) for computing water passage and salt passage is
formulated using the membrane area (Am), the number of pressure vessels (nv) and the number of elements in
a pressure vessel (ne), which is shown in Eq. (10). The temperature dependence of water passage and salt
passage is defined using Arrhenius equation, which is shown in Eq. (11) and (12). The net osmotic pressure
[Eq. (13)] for the formulation of water passage is represented using the feed osmotic pressure [Eq. (14)], the
brine osmotic pressure [Eq. (15)] and the permeate osmotic pressure [Eq. (16)]. The net concentration for the
formulation of salt passage is represented using the feed flow rate (Ff), the brine flow rate (Fb), the feed
concentration (Cf) and the brine concentration (Cb), which is shown in Eq. (17). In the simulation model, the
solution-diffusion model is coupled with the concentration polarization factor for analyzing the concentration
polarization effect on process performance. The concentration polarization factor [Eq. (28)] is
mathematically characterized using the membrane surface concentration (Cm), the permeate concentration
(Cp), the permeate flux (J), the bulk concentration (CB) and the mass transfer coefficient (k). The intrinsic
membrane resistance (Rm) and the cake-layer resistance (Rc) were considered for modelling the permeate flux
[Eq. (20)]. The cake-layer resistance [Eq. (21)] represents the impact of membrane fouling due to the
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Table 1. Equations for the simulation model
Name
Representation
M
Fb max  F f  Fp min
R
F p max  r max F f
100
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Maximum
permeate flow
rate
Minimum
permeate flow
rate
F p min 
Rr min
100
Ff
CE
Trans-membrane
pressure
PT
F
F
 Fb min 
 Fb min 
 H max   b max
 H
Fb  Fb max   b max
 H max  H min 
 H max  H min 
Brine
flow rate
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Inherent
reject valve
characteristics
Brine pressure
Water passage
Eq. No.
Fb min  F f  Fp max
Minimum and
maximum brine
flow rates
Salt passage
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accumulation of suspended particles on the surface of the membrane. The intrinsic membrane resistance, also
the clean membrane resistance, for the RO was taken from Mulder (2003). The transient behaviour of the
brine flow rate is mathematically characterized using the brine mass balance differential equation [Eq. (34)].
The transient behaviour of the brine concentration is mathematically characterized using the brine
concentration balance differential equation [Eq. (35)]. The transient behaviour of the permeate flow rate is
mathematically characterized using the permeate mass balance differential equation [Eq. (36)]. The transient
behaviour of the permeate concentration is mathematically characterized using the permeate concentration
balance differential equation [Eq. (37)]. The parameters used for the RO process simulation are shown in
Table 2. The effects of the feed pressure and concentration, the recovery ratio, the feed temperature, and the
concentration polarization on the water passage and the salt passage were investigated over a wide range of
operating conditions. The LabVIEW-based RO process simulation was performed using nominal operating
conditions for the seawater desalination process described in the literature by Sobana and Panda (2013) to
determine the percentage deviation between the steady-state outputs of the real-time process and those from
the simulation model. Finally the dynamic characteristics of the brine and the permeate sub-entities from the
RO process simulation were compared with the experimental data collected from the brine and the permeate
streams in an actual seawater desalination process.
P 
P f  Pb
2
 Pp
 H  
 100  1
  P P
Fb  R 
b
bo
  H 
21 

100  2
Pb  R  
Fb  Pbo
Fm  K w P   Aem Tm


Fs  K s  C  C p Aem Ts
(1)
Ref.
El-Dessouky
and Ettouney
(2002)
(2)
El-Dessouky
and Ettouney
(2002)
(3)
El-Dessouky
and Ettouney
(2002)
(4)
-
(5)
Lee (1975)
(6)
Brian Nesbitt
(2011)
(7)
-
(8)
(9)
El-Dessouky
and Ettouney
(2002)
El-Dessouky
and Ettouney
(2002)
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Table 1 (Cont’d)
Name
Tm
 T f  Tref 

aT 


Tf

e 
 T f  Tref 

bT 


Tf

Ts  e 
 f  b
 
 p
2
Net osmotic
pressure
Eq. No.
Ref.
(10)
-
(11)
Oh et al.
(2009)
CR
IP
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Representation
Aem  nv ne Am
Effective
membrane area
Arrhenius
equations
(12)
(13)
Oh et al.
(2009)
El-Dessouky
and Ettouney
(2002)
El-Dessouky
and Ettouney
(2002)
El-Dessouky
and Ettouney
(2002)
El-Dessouky
and Ettouney
(2002)
 f  75.84 10 3 C f
Brine osmotic
pressure
b  75.84 103Cb
(15)
Permeate osmotic
pressure
 p  75.84 10 3 C p
(16)
F f C f  Fb Cb
(17)
El-Dessouky
and Ettouney
(2002)
(18)
Kim and
Hoek (2005)
(19)
Sobana and
Panda (2013)
 R m  R c 
(20)
Mulder
(2003)
Rc  M d
(21)
Park et al.
2008
0.17  C  0.77 
D 


 B 


  
 dm 
(22)
Avlonitis et
al. (2007)
Fm
Ac
(23)
Koo et al.
(2014)
Net concentration
M
C
Cross-flow
velocity
ED
J
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PT
CB 
AC
Mass transfer
coefficient
F f  Fb
J
 exp 
CB  C p
k
Bulk
concentration
Permeate flux
(14)
Cm  C p
Concentration
polarization
Cake-layer
resistance
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Feed osmotic
pressure
 ud 
k  0.5510 m 
  
C f  Cb
2
P  
0.4

 
D
u
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Table 1 (Cont’d)
Name
Representation
Solute
diffusion
coefficient
Ac 
d m 2

D  6.725 10 6 exp 0.154 10  3 C fd 


Seawater
kinematic
viscosity

Intrinsic salt
rejection
Seawater
dynamic
viscosity

Cp
Cm
exp J k 
SRi  1  SRi  exp J k 
   w r 10 3


Sassi and
Mujtaba
(2012)
(26)
-
(27)
Mallevialle
et al. (1996)
(28)
Mallevialle
et al. (1996)

M
 w  exp  3.79418  604.129 139.18  T f
 r  1  As  Bs 2
(29)
El-Dessouky
and
Ettouney
(2002)
ED
A  1.474  10 3  1.5  10 5 T f  3.927  10 8 T 2
f

5

8

10
2
B  1.0734 10  8.5 10 T f  2.23 10
T
f
  10 3  a1 f1  a 2 f 2  a3 f 3  a 4 f 4 
Seawater
density
PT
a1  4.032219 g1  0.115313g 2  3.26 10 4 g 3
a 2  0.108199 g1  1.57 10 3 g 2  4.23 10 4 g 3
a3  0.012247 g1  1.74 10 3 g 2  9 10 6 g 3
a 4  6.92 10 4 g1  8.7 10 3 g 2  5.3 10 5 g 3
g1  0.5 ; g 2  b ; g 3  2b 2  1 ; b  2C f 1000  150 150
CE
AC
Observed salt
rejection
-
(25)


AN
US

T

T f  ref T f
2513

D
T f Tref
273.15  T f 


SRi  1 
Concentration
polarization
factor
(24)
4
Ref.
CR
IP
T
Membrane
cross-sectional
area
Eq.
No.


f1  0.5 ; f 2  a ; f 3  2a 2  1 ; f 4  4a 3  3a
a  2T f  200 160
Cp
SRo  1 
CB

(30)
El-Dessouky
and
Ettouney
(2002)
(31)
Mallevialle


et al. (1996)
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Table 1 (Cont’d)
Name
Recovery rate
Rr 
Brine mass
balance equation
Fp
Ff
100
dmb
 F f  Fb  Fm
dt
dCb
dt

F f C f  Cb  Fm Cm  Cb 
1
mb
dm p
 Fm  F p  0
dt
Permeate
concentration
balance equation
dC p
1
mp
FmCm  F p C p 
M
dt

AN
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Brine
concentration
balance equation
Permeate mass
balance equation
Eq. No.
Ref.
(32)
El-Dessouky
and Ettouney
(2002)
CR
IP
T
Representation
Cp
SR  1 
Cf
Theoretical salt
rejection
(33)
El-Dessouky
and Ettouney
(2002)
(34)
Gambier et
al. (2007)
(35)
Gambier et
al. (2007)
(36)
Gambier et
al. (2007)
(37)
Gambier et
al. (2007)
Table 2. Parameters for the RO process simulation [Oh et al. (2008) 1, El-Dessouky et al. (2002) 2]
Parameter
Value
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Number of RO stages
Membrane area per one RO element – FilmTec SW30HR-380, Am [m2] 1
Number of elements in a pressure vessel, ne
Number of pressure vessels, nv
Minimum recovery rate, Rrmin [%]
Maximum recovery rate, Rrmax [%]
Salt rejection, SR [%]
Water permeability coefficient of membrane, Kw [m3/m2s kPa] 2
Salt permeability coefficient of membrane, Ks [m3/m2s] 2
Membrane water passage temperature constant, aT
Membrane salt passage temperature constant, bT
Reference temperature, Tref [K]
Feed pressure, Pf [kPa]
Feed flow, Ff [kg/s]
Feed concentration, Cf [ppm]
Feed temperature, Tf [oC]
Permeate pressure, Pp [kPa]
Brine down stream pressure, Pbo [kPa]
Reject valve rangeability, R
1
35.3
6
56
10
35
97.5
2.05x10-6
2.03x10-5
9.0
8.08
30
4870.833
50
41350
30
101
101
50
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3. Model Validation
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A schematic of the simplified process flow for the seawater desalination process considered for data
collection is shown in Fig. 6. The developed dynamic model was validated using experimental data obtained
from the literature by Sobana and Panda (2013). The experimental facility chosen for model validation
consist of a pre-filtering stage, feed tank, high pressure (HP) pump, RO unit, brine tank and permeate tank.
The pre-filtering stage includes dual media filter, disc filter and cartridge filter. The high pressure pump
boosts the feed water pressure from 1078.731 kPa to 5883.990 kPa. The RO unit consist of two RO beds.
The number of RO vessels in one RO bed is 28. Single RO vessel consists of six RO modules (FilmTEC
SW30HR-380). The salt rejection and the recovery rate of the experimental facility is found to be 97.94%
and 44.44% respectively. Experimental data represent three stages of measurements. The first-stage
measurements consist of the dynamic characteristics of the feed flow rate, concentration, and pH in the
mixing tank. The second-stage measurements consist of the dynamic characteristics of the brine flow rate,
concentration, and pH in the brine tank. The third-stage measurements consist of the dynamic characteristics
of the permeate flow rate, concentration, and pH in the permeate tank. Data were obtained during the first 20
minutes after starting the process. The proposed dynamic model was tested under nominal operating
conditions with the model input parameters shown in Table 3.
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Fig. 6. Simplified process flow for nominal operating conditions in (kg/s, kPa, ppm).
Table 3. Simulation model input parameters for testing nominal operation of the RO process.
Variable
Value
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Feed flow, Ff [kg/s]
Feed pressure, Pf [kPa]
Feed concentration, Cf [ppm]
Feed temperature, Tf [oK]
Salt rejection, SR [%]
Recovery rate, Rr [%]
Minimum recovery rate, Rrmin [%]
Maximum recovery rate, Rrmax [%]
Reject valve percentage opening, H [%]
50
5883.99
41350
301.65
97.94
44.44
10
50
47.6507
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The transient behaviours of the brine stream and the permeate stream in the simulation model for the nominal
operating condition of the RO process are shown in Figs. 7 and 9, respectively. Table 4 presents the results
of a comparison between the final steady-state values of the proposed model and of the process under
nominal operating conditions. The validations of dynamic behaviours of the brine stream and the permeate
stream in the proposed simulation model by using the experimental data for a seawater desalination process
are shown in Figs. 8 and 10, respectively. The transient behaviours of the output streams in the proposed
simulation model are in good agreement with the real-time process responses.
(b)
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Fig. 7. Transient responses of the (a) brine flow and the (b) brine concentration.
(a)
Fig. 8. Validations of the (a) brine flow and the (b) brine concentration.
(b)
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25
60000
22.22
850
26.578
62505.9
21.1661
851.99
6.312
4.1765
4.743
0.234
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Fb (kg/s)
Cb (ppm)
Fp (kg/s)
Cp (ppm)
% error
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Table 4. Steady-state error analysis
Variable
Process data
Model data
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(b)
Fig. 9. Transient responses of the (a) permeate flow and the (b) permeate concentration.
(a)
Fig. 10. Validations of the (a) permeate flow and the (b) permeate concentration.
(b)
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Finally, an R2 analysis was performed to determine how well the output data of the proposed model
explain the process variations with respect to time. In Fig. 10(b), the process data representing the permeate
concentration show a large variation due to the variation in the demand for potable water. The results of the
R2 analysis for the proposed simulation model are shown in Table 5. The R2 values for the transient model
developed by Sobana and Panda (2013) were found to be 0.9293, 0.9962 and 0.9795 for the permeate flow,
the brine flow, and the permeate concentration, respectively. A number of variables, such as the feed flow,
pressure, temperature, and concentration, that can be manipulated, are taken into consideration in the
LabVIEW-based simulation model. The model proposed by Sobana and Panda (2013) considered two
variables, namely, the feed pressure and the ratio of the feed’s flow to the brine flow, that could be
manipulated.
Table 5. Results of R2 analyses of the simulation model’s output data
R2 value
R2 value
R2 value
R2 value
permeate flow
brine flow
permeate concentration
brine concentration
0.8396
0.88974
0.80314
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0.92683
4. Steady state simulation: Process performance analysis
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The permeate flow rate and the salt rejection are key performance parameters representing the
effectiveness of the RO filtration process. The developed LabVIEW-based simulation model was used in this
research for the performance analysis of the process steady state under the influence of variable parameters,
include the feed concentration and pressure, the recovery rate and the feed temperature. The effects of the
feed concentration on the performance parameters are shown in Fig. 11. The variation in the permeate flow
for feed concentrations varying from 41350 to 49150 ppm are shown in Fig. 11(a), where the permeate flow
rate decreases with increasing feed concentration due to a decrease in the differential pressure across the
membrane [see Eq. (8)]. The decrease in the differential pressure is due to an increase in the net osmotic
pressure. The net osmotic pressure increases as the feed concentration increases [see Eq. (13)]. Figure 11(b)
shows the variations in the salt passage and the salt rejection for feed concentrations varying from 41350 to
49150 ppm. The salt passage (Fs) is seen to increase with increasing feed concentration [see Eq. (9)]. The
increase in the salt passage increases the permeate concentration, thereby decreasing salt rejection [see Eq.
(32)]. However, Fig. 11 (b) shows that increasing feed concentration within the selected range has
inconsiderable impact on solute rejection where it decreases from 97.39 to 97.37%
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(a)
(b)
Fig. 11. Dependences of (a) permeate flow (■) and net osmotic pressure (▲) and of (b) salt passage (■) and salt
rejection (▲) on feed concentration. Simulation condition are Ff = 50 kg/s; Pf = 4870.883 kPa; Tf = 30 oC.
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The effects of the feed pressure on the performance parameters are shown in Fig. 12. The variations in the
permeate flow and the trans-membrane pressure for feed pressures varying from 4870.883 to 5670.883 kPa
are shown in Fig. 12(a). The permeate flow rate can be seen to increase with increasing feed pressure due to
an increase in the differential pressure (∆P - ∆Π) across the membrane [see Eq. (8)]. The trans-membrane
pressure can be seen to increase as the feed pressure increases [see Eq. (5)], leading to a higher differential
pressure across the membrane. Figure 12(b) shows the variations of the salt passage and the salt rejection
with the feed pressure.
(a)
(b)
Fig. 12. Dependences of the (a) permeate flow (■) and trans-membrane pressure (▲) and of the (b) salt passage (■)
and salt rejection (▲) on the feed pressure. Simulation conditions are Ff = 50 kg/s; Cf = 41350 ppm; Tf = 30 oC.
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The salt passage can be seen to increase with increasing feed pressure due to concentration polarization [see
Eq. (9)]. Concentration polarization refers to an increase in the salt concentration in the boundary layer near
the membrane surface to a level larger than the salt concentration in the bulk solution. The boundary layer is
formed due to water passage through the membrane and salt rejected by the membrane. In the dynamic
simulation model, the concentration polarization is described using the analytical film theory (FT) model
proposed by Michaels (1968) [see Eq. (18)].
El-Dessouky and Ettouney (2002) states that the actual permeate flow rate and salt passage differ from
theoretical estimates due to the concentration polarization effect. Mallevialle et al. (1996) quantifies the
effect of concentration polarization on the water passage and the salt passage by using a factor called beta
[see Eq. (28)], also known as the concentration polarization factor (CPF). In an RO process, the value of beta
is always greater than 1.0. The deviations between actual and theoretical estimates of the water passage and
the salt rejection due to the concentration polarization effect are shown in Figs. 13 and 14, respectively. Beta
is assumed to be 1.0 for computing the theoretical estimates of the water passage and the salt passage. Figure
13 shows the variations in both the permeate flow and the beta for valve percentage openings varying from
10% to 100%. As the permeate flow rate increases with decreasing percentage opening of the reject valve,
the concentration at the membrane surface increases [see Eq. (18)]. As the membrane surface concentration
increases, the net osmotic pressure increases with increasing beta [see Eq. (8)]. As a result, the effect of
concentration polarization reduces the actual permeate flow rate compared to the theoretical estimate. The
deviation between the theoretical and the actual estimates of the permeate flow becomes significant for beta
greater than 1.09943.
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Fig. 13. Concentration polarization effect on the permeate flow, theoretical estimate (■) and actual estimate (▲).
Simulation conditions are Ff = 50 kg/s; Pf = 4870.833 kPa; Cf = 41350 ppm; Tf = 30 oC. In the figure, the effect on
beta is shown by the symbol (•).
Figure 14 shows the variations in the salt rejection and the beta for valve percentage openings varying
from 10% to 100%. The theoretical estimate of salt rejection appears to be insignificantly increasing because
the salt passage is unaffected by the increase in the trans-membrane pressure due to the decrease in the
percentage opening of the reject valve. As a result, the permeate concentration decreases as more water flows
across the membrane, thereby increasing the salt rejection [see Eq. (32)].The actual estimate of the salt
rejection decreases insignificantly with decreasing reject valve opening due to the increase in the membrane
surface concentration. As the membrane surface concentration increases, the permeate concentration also
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increases for a given intrinsic salt rejection [see Eq. (27)]. The increase in the permeate concentration
decreases the observed salt rejection [see Eq. (31)]. Hence, the effect of the concentration polarization
reduces the actual salt rejection rate compared to the theoretical estimate.
Fig. 14. Concentration polarization effect on the salt rejection, theoretical estimate (■) and actual estimate (▲).
Simulation conditions are Ff = 50 kg/s; Cf = 41350 ppm; Pf = 4870.833 kPa; Tf = 30oC. In the figure, the effect on
beta is shown by the symbol (•).
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The effects of the recovery rate on the performance parameters are shown in Fig. 15. Figure 15(a) shows
the variations in the permeate flow and the net osmotic pressure for feed flows varying from 157.7147 to
12.32525 kg/s. The permeate flow rate can be seen to decrease with increasing recovery rate [see Eq. (33)].
As the feed flow decreases, the net osmotic pressure (∆Π) across the membrane increases. The increase in
the net osmotic pressure reduces the pressure driving force for water passage through the membrane. Figure
15(b) shows the variations in the salt passage and the salt rejection for feed flows varying from 157.7147 to
12.32525 kg/s. The decrease in the pressure driving force results in less water passage relative to salt passage
through the membrane. Hence, the salt passage increases and the salt rejection decreases with increasing
recovery rate.
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(b)
(a)
Fig. 15. Dependences of the (a) permeate flow (■) and net osmotic pressure (▲) and of the (b) salt passage (■) and
salt rejection (▲) on the recovery rate assuming constant feed pressure. Simulation conditions are Pf = 4870.833
kPa; Cf = 41350 ppm; Tf = 30 oC.
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The effects of feed temperature on the performance parameters are shown in Fig. 16. Figure 16(a) shows
the variations in the permeate flow and the seawater’s dynamic viscosity for feed temperatures varying from
19 to 43oC in steps of 3oC. An increase in the feed temperature increases the permeate flow rate due to the
decrease in the dynamic viscosity of the seawater [see Eq. (29)]. The percentage change in the permeate flow
rate with feed-water temperature in the simulation model is 2.995%/oC. Figure 16(b) shows the variations in
the salt rejection and the salt diffusivity for feed temperatures varying from 19 to 43 oC in steps of 3oC. The
increase in the feed temperature decreases the salt rejection due to the increase in the salt passage. Salt
rejection decreases with increasing salt passage due to the increased salt diffusion at higher temperatures [see
Eq. (25)]. The percentage change of salt rejection with feed-water temperature in the simulation model is
0.00561%/oC. Hence, the proposed LabVIEW-based simulation model helps in understanding the variations
in the critical variables – permeate flow (product quantity) and salt rejection (product quality) – under the
influence of different factors affecting the process.
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(b)
(a)
Fig. 16. Dependences of the (a) permeate flow (■) and dynamic viscosity (▲) and of the (b) salt rejection (■) and salt
diffusivity (▲) on feed temperature. Simulation conditions are Pf = 4870.833 kPa; Cf = 41350 ppm; Ff = 50 kg/s.
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Goosen et al. (2002) investigated the improvement in the water recovery in the RO process by increasing
the feed water temperature. The investigation reported an increase of 60% in the permeate flux when the feed
temperature was increased from 20 to 40oC. The steady-state performance of a small-scale seawater
desalination unit was studied by Abbas (2006). The effects of temperature on the steady-state performance
were investigated by varying the temperature from 22 to 28oC. The permeate flux increased by 2.8%, and the
salt rejection decreased by 0.007% for every 1oC increase in the feed temperature.
The literature by Zhu et al. (2009) describes the energy consumption of a reverse osmosis desalination
system by using a metric called the specific energy consumption (SEC). The SEC is defined as the energy
consumption per volume of permeate produced. The mathematical definition of the SEC for a simplified RO
system [see Fig. 1] is given as
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P f  Po
.
Rr
The normalisation of the SEC with respect to the osmotic pressure of the feed stream is given by
SEC 
(42)
SEC
.
SECnorm 
f
(43)
Bartman et al. (2010) performed an experimental study on UCLA’s experimental RO membrane water
desalination system to analyse the variation in the specific energy consumption with respect to the fractional
water recovery. A similar analysis of specific energy consumption with respect to fractional water recovery
for different feed water temperatures was performed using the developed simulation model, and the results
are shown in Fig. 17. The normalised specific energy consumption of the RO system for a fixed permeate
flow can be decreased by increasing the feed temperature.
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Fig. 17. Specific energy consumption with respect to fractional water recovery for different temperature conditions.
Simulation conditions are Ff = 50 kg/s; Cf = 41350 ppm. Normalised SEC at Tf = 17 oC (•), normalised SEC at Tf =
30 oC (■), and normalised SEC at Tf = 43 oC (▲).
5. Conclusions
6. Symbols
aT
− Membrane water passage temperature constant
2
− Effective membrane area, m
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Aem
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A dynamic simulation model for the reverse osmosis process in seawater was developed. The process
GUI for dynamic analysis was created using the CDSim toolkit in LabVIEW. Detailed simulations using the
dynamic model were performed to understand the effects of feed concentration, pressure, temperature and
flow rate on the performance of the process measured in terms of the rates of permeation and salt rejection.
The effect of concentration polarization on process performance was analysed using the principle of mass
transfer. The results of the performance analysis indicated that the normalised SEC could be reduced by
minimizing the feed pressure at a reasonably high temperature. The R2 analysis showed that the simulated
results were in good agreement with the real process data. In future work, the dynamic simulation model
presented will be dedicated towards process monitoring and model-based control. The proposed dynamic
simulation model can also be used for further simulation to study the impact of feed temperature on energy
consumption of RO process during feed salinity fluctuation.
Ac
bT
CB
Cb
2
− Membrane cross-sectional area, m
− Membrane salt passage temperature constant
− Bulk concentration, ppm
− Brine concentration, ppm
Cfd
− Feed concentration, ppm
3
− Feed concentration, kg/m
Cm
− Membrane surface concentration, ppm
Cf
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Fs
Fbmax
Fbmin
Fpmax
Fpmin
Hmax
Hmin
H
J
k
Ks
Kw
mb
mb
ne
nv
Md
Pb
Pbo
Po
∆P
− Brine flow rate at maximum percentage opening of reject valve, kg/s
− Brine flow rate at minimum percentage opening of reject valve, kg/s
− Permeate flow rate at minimum percentage opening of reject valve, kg/s
− Permeate flow rate at maximum percentage opening of reject valve, kg/s
− Maximum percentage opening of reject valve, %
− Minimum percentage opening of reject valve, %
− Percentage opening of reject valve, %
− Permeate flux, m/s
− Mass transfer coefficient, m/s
3
2
− Salt permeability coefficient of membrane, m /m s
3
2
− Water permeability coefficient of membrane, m /m s kPa
− Brine material mass, kg/s
− Permeate material mass, kg/s
− Number of elements in a pressure vessel
− Number of pressure vessels
2
− Accumulate particle mass per unit area = 5.44 g/m
− Brine upstream pressure, kPa
− Brine downstream pressure, kPa
− Raw seawater pressure, kPa
− Trans-membrane pressure, kPa
-1
− Cake layer resistance, m
13
-1
− Intrinsic membrane resistance = 9 x 10 m
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Rc
− Permeate flow rate, kg/s
− Membrane solute flow rate, kg/s
Rm
Rr
Rrmax
Rrmin
s
SRi
SRo
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Fp
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Fm
− Brine flow rate, kg/s
− Membrane solvent flow rate, kg/s
M
Fb
2
− Diffusivity coefficient at feed temperature, m /s
− Feed flow rate, kg/s
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Ff
− Hydraulic diameter, m
2
− Diffusivity coefficient, m /s
PT
C
dm
D
DT
− Permeate concentration, ppm
− Net concentration, ppm
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Cp
− Recovery rate, %
− Maximum recovery rate, %
− Minimum recovery rate, %
− Feed concentration, gm/kg
− Intrinsic salt rejection
− Observed salt rejection
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Tm
Ts
Tf
Tref
u
− Theoretical salt rejection
− Arrhenius equation based water passage temperature dependence factor
− Arrhenius equation based salt passage temperature dependence factor
o
− Feed temperature, C
o
− Reference temperature, C
− Cross-flow velocity, m/s
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SR
Greek
Πf
Πb
Πp
− Net osmotic pressure, kPa
− Feed osmotic pressure, kPa
− Brine osmotic pressure, kPa
− Permeate osmotic pressure, kPa
3
− Seawater density, kg/m
− Concentration polarization factor
ρ
β
μ
ηr
ηw
η
ηTo
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∆Π
2
− Seawater kinematic viscosity, m / s
− Seawater dynamic viscosity concentration correlation
− Seawater dynamic viscosity temperature correlation
− Seawater dynamic viscosity, kg/m-s (Pa-s)
α
15
− Specific cake resistance = 4.15 x 10 m/kg
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η
− Seawater dynamic viscosity at reference temperature, kg/m-s (Pa-s)
− Seawater dynamic viscosity at feed temperature, kg/m-s
T
Acknowledgment
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References
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The author* would like to thank the Centre for Research of Anna University for providing financial
assistance through the Anna Centenary Research Fellowship program.
AC
Abbas, A. (2006), “Enhancement of productivity in reverse osmosis desalination processes”, Asian J. Water, Environ.
Pollut., 4(2), 23-29.
Al-Obaidi, M.A., Mujtaba, I.M. (2016), “Steady state and dynamic modeling of spiral wound wastewater reverse
osmosis process”, Comput. Chem. Eng., 90, 278-299.
Barello, M., Manca, D., Patel, R., Mujtaba, I.M. (2015), “Operation and Modeling of RO desalination process in batch
mode”, Comput. Chem. Eng., 83, 139-156.
Bartman, A. R., Zhu, A., Christofides, P.D. and Cohen, Y. (2010), “Minimizing energy consumption in reverse osmosis
membrane desalination using optimization-based control”, Proceedings of American Control Conference, New York
City, USA, July.
Avlonitis, S.A., Pappas M. And Moutesidis, A. (2007), “A unified model for the detailed investigation of membrane
modules and RO plant performance”, Desal., 203, 218-228.
Bitter, J.G.A. (1991), Transport Mechanism in Membrane Separation Process, Plenum Press, New York.
Brian, N. (2011), Handbook of Valves and Actuators: Valves Manual International, Elsevier, USA.
ACCEPTED MANUSCRIPT
AC
CE
PT
ED
M
AN
US
CR
IP
T
El-Dessouky, H.T. and Ettouney, H.M. (2002), Fundamentals of Sea Water Desalination, Elsevier Science B. V.,
Amsterdam, The Netherlands.
Eckman, D.P. (1958), Automatic Process Control, Wiley Eastern, New Delhi.
Gambier. A., Krasnik, A. and Badreddin, E. (2007), “Dynamic modeling of a simple reverse osmosis desalination plant
for advanced control purposes”, Proceedings of American Control Conference, New York City, USA, July.
Goosen, M.F.A., Sablani, S.S., Al-Maskari, S.S., Al-Belushi, S.S. and Wilf, M. (2002), “Effect of feed temperature on
permeate flux and mass transfer coefficient in spiral-wound reverse osmosis systems”, Desal., 144, 367-372.
Kim, S. and Hoek, E.M.V. (2005), “Modeling concentration polarization in reverse osmosis processes”, Desal. 186,
111-128.
Kim, A.S. (2017), “Review of basics reverse osmosis process modeling: A new combined fouling index propose”,
Membr. J., 27(4), 291-312.
Kedem, O. and Katchalsky (1958), “Thermodynamic analysis of the permeability of biological membranes to nonelectrolytes”, Biochim. Biophys. Acta, 27, 229-246.
Koo, C.H., Mohammad A.W., Suja F. (2014), “Effect of cross-flow velocity on membrane filtration performance in
relation pt membrane properties”, Desalin. Water Treat., 55(3), 1-15.
Lee, C.H. (1975), “Theory of reverse osmosis and some other membrane permeation operations”, J. Appl. Poly. Sci.,
19(1), 83-95.
Lee, C.J., Chen, Y.S. and Wang, G.B. (2010), “A dynamic simulation model of reverse osmosis”, Proceedings of Fifth
International Symposium on Design, Operation and Control of Chemical Process, PSE ASIA, Singapore, July.
Lonsdale, H.K., Merten, U. and Riley, R.L. (1965), “Transport properties of cellulose acetate osmotic membrane”, J.
Appl. Poly. Sci., 9(4), 1341-1362.
Mallevialle, J., Odendaal, P.E., Wiesner, M.R. (1996), Water Treatment Membrane Processes, McGraw-Hill, US.
Michaels, A.S. (1968), “New separation technique for the CPI”, Chem. Eng. Prog., 64, 31-43.
Mulder, M. (2003), Basic Principle of Membrane Technologies, Kluwer Academic Publisher, Dordrecht, The
Nehterlands.
Oh, H.J., Hwang, T.M., Lee, S. (2009), “A simplified simulation model of RO system for seawater desalination”, Desal.
238(3), 128-139.
Park, C., Lee, Y.H., Lee, S., Hong, S. (2008), “Effect of cake layer structure on colloidal fouling in reverse osmosis
membrane”, Chem. Eng. Trans., Desal., 220, 335-344.
Reid, C.E. and Breton, E.J. (1959), “Water and ion flow across cellulosic membranes”, J. Appl. Polymer Sci., 1(2), 133143.
Sassi, K.M. and Mujtaba, I.M. (2012), “Effective design of reverse osmosis based desalination process considering
wide range of salinity and seawater temperature”, Desal., 306, 8-16.
Senthilmurugan, S., Ahluwalia, A., Chatterjee, A. and Gupta S.K. (2005), “Modeling of a spiral-wound module and
estimation of model parameters using numerical techniques”, Desal. 173(3), 269-286.
Sobana, S. and Panda, R.C. (2013), “Development of a transient model for the desalination of sea/brackish water
through reverse osmosis”, Desalin. Water Treat., 51(13-15), 2755-2767.
Sobana, S. and Panda, R.C. (2014), “Modeling and control of reverse osmosis desalination using centralized and
decentralized techniques”, Desal., 344(7), 243-251.
Sourirajan, S. (1970), Reverse Osmosis, Academic Press, Los Angeles, CA.
Soltanieh, M. and Gill, W. N. (2007), “Review of reverse osmosis membranes and transport models”, Chem. Eng.
Commun., 12(4-6), 279-363.
Spiegler, K.S. and Kedem, O. (1966), “Thermodynamics of hyperfiltration (reverse osmosis): criteria for efficient
membranes”, Desal., 1(4), 311-326.
Zhu, A., Christofides, P.D. and Cohen, Y. (2009), “Effect of thermodynamic restriction on energy cost optimization of
RO membrane water desalination”, Ind. Eng. Chem. Res., 48, 6010-6021.