Membrane Water Treatment, Vol. 5, No.

3 (2014) 000-000
DOI: http://dx.doi.org/10.12989/mwt.2014.5.3.000 000

 
Scaling predictions in seawater reverse osmosis desalination
Houda Hchaichi 1a, Saanoun Siwar 1b, Hamza Elfil 2c and Ahmed Hannachi 1
1
Laboratory of Process Engineering and Industrial Systems, National Engineering School of Gabes,
University of Gabes, Ibnel khattab Street, 6029, Zrig Gabès, Tunisia
2
LabTEN-Water Research and Technologies Center, Soliman, Tunisia

(Received May 22, 2014, Revised July 19, 2014, Accepted July 21, 2014)

Abstract. Simulations were conducted to predict supersaturation along Reverse Osmosis (RO) modules
for seawater desalination. The modeling approach is based on the use of conservation principles and
chemical equilibria equations along RO modules. Full Pitzer ion interactive forces model for concentrated
solutions was implement to calculate activity coefficients. An average rejection rate for all ionic species was
considered. Supersaturation has been used to assess scaling. Supersaturations with respect to all calcium
carbonate forms and calcium sulfate were calculated up to 50% recovery rate in seawater RO desalination.
The results for four different seawater qualities are shown. The predictions were in a good agreement with
the experimental results.

Keywords:   seawater; desalination; reverse osmosis modules; supersaturation; scaling assessment

1. Introduction 

Natural fresh water sources can no longer meet the ever increasing water demand from our
rising population. Distillation has been traditionally used to get pure water from saline or brackish
water sources. Other processes such as ion exchange and electrodialysis have been employed for
water purification as well. Lately, Reverse Osmosis (RO) has been established to be the most
economical technology for the desalination of brackish and sea waters. RO membranes are capable
of rejecting most ions and even monovalent ions such as Na+ and Cl- present in seawater with 99%
rejection rate. In Seawater Reverse Osmosis (SWRO), it is compulsory to pretreat feed water to
limit fouling and avoid scaling. The nature of fouling is strongly dependent on feed water source.
Seawater is characterized by high total dissolved solids (TDS), typically ranging from 18 to 45 g/L,
as well as particulate and colloidal matter. Fouling and scaling can lead to significant reduction in
membrane performance. Poor feed water quality leads to short RO membrane lifetime, short
operation period, and high maintenance cost. Consequently, a main factor for successful SWRO
operation is maintaining a stable high feed water quality (Valavala et al. 2011, Lau et al. 2014).
Inorganic fouling or scaling is the formation of hard mineral deposits on the membrane surface as

Corresponding author, Ph.D., E-mail: ahmed.hannachi@enig.rnu.tn

a
Ph.D. Student, E-mail: hchaichihouda@yahoo.fr
b
Ph.D. Student, E-mail: siwar_saanoun@hotmail.fr
c
Ph.D., E-mail: h_elfil@yahoo.com

Copyright © 2014 Techno-Press, Ltd.

http://www.techno-press.org/?journal=mwt&subpage=7 ISSN: 2005-8624 (Print), 2092-7037 (Online)
 Houda Hchaichi, Saanoun Siwar, Hamza Elfil and Ahmed Hannachi

the feed water salt contents increase along RO modules. The term scale refers to adherent
inorganic deposits due to supersaturation. Depending on the operating recovery and rejection
efficiencies, RO reject flux has typically salt contents 2 to 3 times higher than feed water.
Scaling remains a major impediment to successful implementation of high recovery water
desalination. In RO scale deposition cannot be tolerated because of its highly destructive effects on
production capacity and specific energy consumption. As permeate recovery is increased, retentate
stream is concentrated, particularly near and at the membrane surface. In desalination calcium
carbonate and calcium sulfate dihydrate are the main salts involved in scaling (Hannachi et al.
2009). These mineral salts may crystallize in the bulk and onto the membrane surface, leading to
mineral scale formation and thus permeate flux decline, and eventually the shortening of
membrane life (Rahardianto et al. 2006).
The principal factor determining the intensity of scaling is supersaturation level of
deposit-forming species. Supersaturations are achieved when a solution is concentrated beyond the
solubility limits of one or more of its constituents by separation of pure water as for RO. In scaling
due to calcium carbonate, scale formation depends primarily on the level of calcium hardness and
bicarbonate alkalinity of the feed water (Antony et al. 2011). Although calcium carbonate is
reported to exist in six different forms, in SWRO and because of the operating conditions, the most
likely form that can cause scaling is calcite (Elfil and Roques 2006). The reaction involved is

Ca 2   CO32   CaCO3 (1)

Thermodynamically, scaling occurs when the water is supersaturated with respect to CaCO3.
Supersaturation is defined by the ratio of Ion Activity Product (IAP) and the equilibrium constant

IAP
 (2)
Ksp

Where, Ksp is the ion activity product at equilibrium. Accordingly, Ω higher than one implies a
supersaturated solution where scaling can occur, whereas Ω lower than one involves an under
saturated solution. Because of the chemistry of the calcocarbonic system several equilibrium
equations have to be considered. These are related to speciation of carbonate forms depending on
the solution pH level. That is why supersaturation can be expressed as a difference between
solution pH and a pH of an equivalent saturated solution. Several saturation indexes, in terms of
pH difference, were put forward to assess scaling likelihood. Langelier Saturation Index (LSI) and
Monohydrated Langelier Index (MLSI) are used for brackish waters and the Stiff & Davis
Saturation Index (S&DSI) for sea waters. A positive S&DSI and LSI indicate the tendency to form
calcium carbonate scale, while a negative value indicates no tendency for scale formation
(Hannachi et al. 2007).
Very few experimental investigations to study scaling likelihood within RO modules were
reported (Brusilovsky et al. 1992, Hasson et al. 1998, Drak et al. 2000, Pahiadaki et al. 2005). The
aim of these studies was mostly focusing on determining antiscalant dosage to prevent scaling.
Perhaps the most ambitious work that aimed to determine the recovery rate for which scaling
could be observed through membrane permeability decline was that of Drak et al. (2000).
However because of the complexity of the phenomena involved in scaling and the inherent
experimental limitations, the reported predictions can only relate to a probable scaling recovery
rate interval. That is why simulation is the only technique that could predict for which exact
 Scaling predictions in seawater reverse osmosis desalination

recovery rate supersaturation within RO modules occurs, i.e., a net positive driving force for
scaling.
For a better scaling assessment it is very important to have accurate estimates of pH, ionic
species’ concentrations and activity coefficients at any stage of the RO operation for all water
fluxes. This can be obtained by deriving mass conservation equations while considering chemical
equilibriums and charge conservation equations along RO modules. Rejection of CO2 through the
membrane, affect the equilibrium of carbonate ions and change the pH in concentrate and
permeate. The best estimates of the activity coefficients can be derived from Pitzer model as the
former takes into account the ionic specific interaction (Krumgalz 2001). Indeed, for seawater
Pitzer model predicts activity coefficients more accurately than Davis or extended Debye Huckel
models.
This approach has been successfully applied to conduct scaling assessment with respect to
calcium carbonate and calcium sulfate in brackish water (Hchaichi et al. 2012). The aim of this
study is to extend this approach for seawater where the composition and carbonated species’
interactions with RO membrane are much different. Particularly adequate CO2 rejection rate
should be applied. The case of four different seawaters will be considered.

2. Model development

For scaling assessment along RO modules there is a need to describe the change of scaling and
non-scaling ions concentration along the RO modules. Concentrations of carbonate species in
water are related to dissolved CO2 concentration. Permeability of the membrane to gases
particularly to CO2 plays a significant role in scaling and the prediction of scale formation. A
model has been developed to calculate concentrations of different carbonate species along RO
modules for different recovery rates. For CaCO3 scale it is important to track, along RO modules,
- 2- -
the concentration of the following species: H2CO3, HCO3, CO3 , H3O+, OH and Ca2+ ions. All
chemical reactions involving these species have to be considered. These are given in Fig. 1.
Concentration of carbonate species along RO modules are related by chemical equilibrium
equations given by
[H 3O  ] H 3O  [ HCO3 ] HCO 
K1  3
(3)
[H 2CO3 ] H 2 CO 3

[H 3O  ] H 3O  [CO32  ] CO 2
K2  3
(4)
[HCO3- ] HCO -
3

CO 2(g)  3H 2O  H 2CO3  2H 2O  HCO 3  H 3O   H 2O  CO32   2H 3O 

Increasing pH

Fig. 1
 Houda Hchaichi, Saanoun Siwar, Hamza Elfil and Ahmed Hannachi

This is also true for water dissociation which yields

K w  [ H 3O  ] H 3O  [OH  ] OH  (5)

Where: K1 and K2 are the first and the second carbonic acid dissociation constants; Kw is the
water dissociation constant; γi and [i] are activity coefficient and concentration of species i
respectively. In addition to these equations one has to consider transport equations for all species
as the recovery rate increases.
Fig. 2 gives the various water fluxes through finite volumes for both the retentate and the
permeate compartments for an elementary increase of the recovery rate (dτ). When a steady state
pseudo plug flow is assumed, the concentration of the ion i in the elementary permeate flux, within
a finite volume of an RO module yielding a recovery rate of dτ, is related to the bulk concentration
on the retentate side by the following equation

d Fc [i ]c 


d Fp [i ] p  (6)
d d
Where: F is the flow rate; the indices p and c are relative to permeate and concentrate
respectively. τ is the recovery rate.
The permeate concentration at any recovery rate can be derived from applying conservation
equation yielding
[i ] p  [i ] f (1  Ri ) (7)

Where: Ri is the rejection rate of the ionic species.

Integration of the transport equation, Eq. (6), between the feed and at given recovery rate τ
yields
[i ] f
[i ]c  1   (1  Ri )  (8)
1

Concentrations in retentate and permeate of species not involved in chemical reactions such as
(Ca2+, Mg2+, Na+, Cl-, SO42- ...) are determined by applying mass and charge conservation
equations with an average rejection rate for each ionic species. The retentate can be expressed in
terms of recovery rate, membrane retention and feed concentration.

Fc,τ Fc,τ + dτ retentate side

Membrane

Fp,τ + dτ permeate side

Fp,τ

Increasing τ

Fig. 2 Water fluxes through finite volume of an RO module

 Scaling predictions in seawater reverse osmosis desalination

2- - 2-
For the species involved in chemical equilibriums (H3O+, OH-, CO3 , HCO3 and CO3 ), retentate
and permeate concentrations for a given recovery rate are obtained by solving the set of Eqs.
(3)-(5) and (7) along with charge conservation equation given by

 m M    a A 
i i
mi 
i i
ai 
(9)

Where: Mi is a cation of a charge (+mi) and Ai is an anion of a charge (‒ai). Note that in this
approach, Eq. (7) is applied for total carbonated species, i.e., carbonates, bicarbonates and aqueous
CO2 are considered as single species. A set of non linear equation is obtained and need to be
solved by an adequate iterative procedure taking into consideration an average rejection rate for
total inorganic carbon. Since equilibrium equations involve activity coefficients at each recovery
rate step that must be evaluated, the Pitzer model, being able to adequately express the
thermodynamic properties of the concentrated solution over a wide range of concentrations and
temperatures (Krumgalz 2001), was used to calculate activity coefficients as a function of solution
ionic strength. In the Pitzer model, interactions of all ions present in the solution are accounted for
using concentration dependent interaction coefficients. Values of these interaction coefficients
have been determined for many ions and were tabulated in the literature over a large range of
temperatures (0-140°C). The database was founded on the original variable-temperature Pitzer
parameters supplemented by parameter data from several other sources (Maureen et al. 2005).
Feed water chemical analysis was corrected according the error intervals for each chemical
species concentration to account for charge neutrality. Concentration polarization is an inevitable
effect of the increased salt concentration in the boundary layer, close to the membrane surface.
Salt molecules are accumulated in the boundary layer, after being transported by the permeate
flow, which crosses the membrane. Most of these salts will be rejected by the membrane itself. For
this reason concentration polarization should be taken into account to get more precise scaling
potential. Polarization concentration depends on the bulk stream mixing intensity in RO elements
and varies from 1.13 to 1.2. Thus, salt concentration at membrane surface is 13-20% greater than
in the bulk stream (Hchaichi et al. 2012). For a selective membrane, the polarization factor (Pf) is
defined as the ratio of the limiting concentration of the aqueous solution in the polarization layer
and that of average bulk solution. The concentration at the surface membrane for the species i is
then given by the following equation
[i ]lim  Pf [i ]c (10)

After calculating the concentrations along the RO modules, supersaturation of the scaling salts
is checked by calculating the corresponding IAP and scaling indexes at a given recovery rate. The
computational strategy follows the algorithm given in Fig. 3.

3. Case studies

Scaling assessment in SWRO following the modeling approach detailed in section two will be
conducted for four different seawaters. Natural seawater contains over 70 elements. But, only six
of them represent over 99% by weight of all the dissolved solids in seawater. Table 1 gives typical
chemical contents of the considered seawaters. Salinity of feed water to RO process varies from
location to location and may vary with time at a given location as well. Inlet seawaters have a
Houda Hchaichi, Saanoun Siwar, Hamza Elfil and Ahmed Hannachi

Input inlet water minerals contents, T and pH

Calculate inlet water activity coefficients

Correct initial concentration

Predict inlet carbonated species concentrations

no
Check for charge balance
yes
Conversion rate incrementation

Calculate concentrate non carbonated species

Predict concentrate carbonated species

Calculate concentrate activity coefficients

Correct concentrate
carbonated species
no Check for
Concentrate charge balance

yes
Calculate permeate non carbonated species

Predict permeate carbonated species

Calculate permeate activity coefficients

Correct permeate carbonated

species concentrations
Check for charge
no balance in permeate

yes

Calculate Supersaturation, pH and scaling index

no Check if recovery
rate limit is obtained

yes
Out put results

Fig. 3 Computational algorithm

 Scaling predictions in seawater reverse osmosis desalination

Table 1 Inlet water chemical contents at 22°C

[Ca2+] [Mg2+] [Na+] [K+] [Cl -] [SO2-4 ] [HCO3- ] TDS
Seawaters pH
(mg/L) (mg/L) (mg/L) (mg/L) (mg/L) (mg/L) (mg/L) (mg/L)
Arabian Gulf * 500 1665 12500 300 23100 3100 155.3 7.8 41119
Gulf of Gabes 488 1373 13300 481 23567 3621 164.0 8.0 42994
Curacao * 466 1406 11741 460 20695 2952 115.6 8.2 37654
Pacific Ocean ** 395 1360 11175 398 18875 2533 114.0 8.1 34750
* (Suresh Patel 2009), ** (Anonymous 2005)

relatively small scaling tendency with respect to CaCO3. This is demonstrated with the relatively
low S&DSI ranging between -0.1 and 0.2.

4. Results and discussion

Simulations were conducted to assess the scaling potential for four different seawaters. The
carbon dioxide gas was supposed to freely pass through RO membranes. In this study, an average
rejection rate was assumed for all ionic species at all recovery rates. pH variations in the permeate
and concentrate compartments, as predicted by the calculation procedure, are presented in Figs. 4
and 5.

Fig. 4 Concentrate pH vs. recovery rate for different seawaters

 Houda Hchaichi, Saanoun Siwar, Hamza Elfil and Ahmed Hannachi

Fig. 5 Permeate pH vs. recovery rate for different seawaters

Table 2 Comparison of calculated pH with experimental pH for Pacific Ocean and Golf of Gabes (T = 22°C)
Pacific Ocean (at recovery rate 50%) Golf of Gabes (at recovery rate 38%)
Concentrate Permeate Concentrate Permeate
Experimental pH 7.90* 6.50* 7.90 5.40
Calculated pH 7.84 6.53 7.86 5.46
Relative difference -0.76% 0.46% -0.51% 1.11%
* Anonymous (2005)

The dissolved CO2 gas that passes through the membrane allows for an arrangement of
carbonate species which causes pH variation in both retentate and permeate compartments. Up to
around 45% recovery rate, a slight and steady decrease in the concentrate pH was predicted. The
observed retentate average pH decrease rate was 0.024 per unit of recovery rate percentage. This
trend can be related to the CO2 passage through the membrane in accordance with an increase in
the concentration of the various carbonate forms. Regardless of the seawater origin, the permeate
pH decrease is more important, ranging from 0.3 to 0.8. It is much sharper and occurs basically for
low recovery rates. For higher recovery rates, above 10% to 15% depending on the seawater
contents, the permeate acidity reaches a pseudo plateau with slight decrease with τ. Unlike the
concentrate, it seems that the permeate adjusts its pH value within the first 10% recovery rate.
Referring to Table 2, a comparison of calculated and real values for pH in concentrate and
permeate solutions was performed for the experimental results that were available. There is very
 Scaling predictions in seawater reverse osmosis desalination

good matching between experimental and calculated data. The differences did not exceed 0.06 on
pH scale for both retentate and permeate regardless of the seawater origin.
S&DSI variation with recovery rate for the considered seawaters is shown in Fig. 6. The
scaling indices were calculated at membrane surface using an average polarization concentration
of 1.2 for all chemical species. Seawaters entering RO modules have a relatively small scaling
tendency as predicted by the low S&DSI, ranging from -0.1 to 0.2, at entrance. As the recovery
rate increases the scaling propensity for the considered seawaters increase with slightly different
trends because of their slightly different mineral compositions. The scaling index increase has two
trends. For recovery rates below around 30%, S&DSI increases steadily. When recovery rates are
higher, the scaling character of the retentate increases exponentially. Curacao seawater, which has
the highest S&DSI at entrance, will be as scaling as the Golf of Gabes for 45% recovery rate.
Scaling assessment could be based on supersaturation with respect to precipitating salts.
Supersaturation depends on mineral composition of water and its temperature. The solubility of
salts is not only the consequence of ions concentrations. It is also dependent on the presence of
other ions in solution. The adopted approach was able to account for the effects of concentration
level through a good estimate of the activity coefficient along RO membranes.
Supersaturation for calcium carbonate is given by

[Ca 2  ] Ca 2 [CO32  ] CO 2
CaCO 3  3
(11)
KspCaCO 3

Where, KspCaCO3 is the solubility product of the appropriate CaCO3 form at a given temperature.

Fig. 6 S&DSI vs. recovery rate for different seawaters

 Houda Hchaichi, Saanoun Siwar, Hamza Elfil and Ahmed Hannachi

Fig. 7 Retentate supersaturation with respect to Calcite vs. recovery rate for different seawaters

Fig. 8 Retentate supersaturation with respect to Aragonite and Vaterite vs. recovery rate
for different seawaters
 Scaling predictions in seawater reverse osmosis desalination

As for pH and S&DSI, calculations were limited to 50% recovery rates. Supersaturations relative
to all calcium carbonate forms were predicted for various recovery rates. Results for calcite which
is the most likely form to cause scaling are shown in Fig. 7. Similarly, as for S&DSI, the curves
suggest that the driving force for scaling is positive and increases with recovery rates. That is why
a thorough pretreatment and short residence time are needed to prevent scaling within RO
modules.
Supersaturations of the remaining calcium carbonate forms (aragonite and vaterite) which are
exceeding one are shown in Fig. 8. Curacao seawater has the highest supersaturation values with
respect to calcite, aragonite and vaterite. Supersaturations with respect to aragonite are above 1,
but lower than for calcite, for all recovery rates in all seawater cases. However for vaterite,
supersaturation exceeded one only for Curacao and Golf of Gabes seawaters after recovery rates of
5% and 30% respectively.
The degree of supersaturation with respect to gypsum was also predicted for the considered
seawaters. The corresponding supersaturation is defined by

[Ca 2  ] Ca 2 [ SO 24  ] SO 2 aH2 2 O
CaSO 4 , 2H 2 O  4
(12)
KspCaSO 4 , 2H 2 O

Where, KspCaCO3,2H3O is the equilibrium solubility product of gypsum and aH2O is the water
activity.

Fig. 9 Supersaturation of gypsum as function of recovery rate

 Houda Hchaichi, Saanoun Siwar, Hamza Elfil and Ahmed Hannachi

The results are presented in Fig. 9. For all cases supersaturation were below 1 meaning that
there is no risk of CaSO4 scaling. Unlike for CaCO3, Golf of Gabes seawater has the highest
supersaturation with respect to gypsum.

5. Conclusions

A theoretical approach for scaling assessment in reverse osmosis seawater desalination was
presented. The mathematical model is based on conservation principles and chemical equilibria
equations along RO modules. An average rejection rate for ionic species was considered. Pitzer’s
model was used for the activity coefficient calculations. The modeling approach can estimate the
supersaturation of different salts at different recovery levels for any type of RO desalination
modules. Scaling indexes were calculated for four different seawaters. Permeate and concentrate
pH were calculated along RO modules. Effects of pH and composition variations on scaling
propensity with respect to calcite and gypsum can be investigated and discussed for all seawaters.
Experimental results were in accordance with simulation results.

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