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Estimation of the maximum conversion level in reverseosmosis brackish water desalination plantsEnrique Ruiz Saavedra a , Antonio Gómez Gotor b , Sebastián O. Pérez Báez b & AlejandroRamos Martín ba Departamento de Cartografía y Expresión Gráfica en la Ingeniería , Escuela de IngenieríasIndustriales y Civiles, University of Las Palmas de Gran Canaria. Edificio de Ingenierías,Campus Universitario de Tafira , 35017 , Las Palmas de Gran Canaria , Spain Phone: Tel. +34928 451851 Fax: Tel. +34 928 451851b Departamento de Ingeniería de Procesos , Escuela de Ingenierías Industriales y Civiles,University of Las Palmas de Gran Canaria. Edificio de Ingenierías, Campus Universitario deTafira , 35017 , Las Palmas de Gran Canaria , SpainPublished online: 10 Jul 2012.

To cite this article: Enrique Ruiz Saavedra , Antonio Gómez Gotor , Sebastián O. Pérez Báez & Alejandro Ramos Martín (2013)Estimation of the maximum conversion level in reverse osmosis brackish water desalination plants, Desalination and WaterTreatment, 51:4-6, 1143-1150, DOI: 10.1080/19443994.2012.704732

To link to this article: http://dx.doi.org/10.1080/19443994.2012.704732

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Estimation of the maximum conversion level in reverse osmosisbrackish water desalination plants

Enrique Ruiz Saavedraa,*, Antonio Gomez Gotorb, Sebastian O. Perez Baezb,Alejandro Ramos Martınb

aDepartamento de Cartografıa y Expresion Grafica en la Ingenierıa, Escuela de Ingenierıas Industriales y Civiles,University of Las Palmas de Gran Canaria. Edificio de Ingenierıas, Campus Universitario de Tafira, 35017 LasPalmas de Gran Canaria, SpainTel. +34 928 451851; Fax: +34 928 451999; email: eruiz@dcegi.ulpgc.esbDepartamento de Ingenierıa de Procesos, Escuela de Ingenierıas Industriales y Civiles, University of Las Palmas deGran Canaria. Edificio de Ingenierıas, Campus Universitario de Tafira, 35017 Las Palmas de Gran Canaria, Spain

Received 29 February 2012; Accepted 15 June 2012

ABSTRACT

This paper proposes a simple calculation method to estimate the maximum conversion levelin reverse osmosis (RO) brackish water desalination plants. The method is based on the scal-ing potential of different compounds found in the water to be treated. These compoundsinclude silica, calcium carbonate, calcium sulphate, barium sulphate, strontium sulphate andcalcium fluoride. Although the method was originally conceived for application to subterra-nean brackish waters in the Canary Islands, Spain (principally Gran Canaria, Fuerteventuraand Tenerife), it can be extrapolated to other types of region and water treatable with RO sys-tems. The required input data are the chemical composition of the feed water and its pH andtemperature. The programmed method then determines the maximum conversion level of theRO system without the risk of scaling of any of the solutes present in the water. The methodcan be used as an aid in design optimization of RO brackish water desalination plants withacid-free pre-treatment processes and only the use of scale inhibitors.

Keywords: Brackish water; Reverse osmosis; Desalination plants; Recovery; Conversion level

1. Introduction

The main salts that can be most expected to pre-cipitate in reverse osmosis (RO) systems [1–3] are sil-ica (SiO2), calcium carbonate (CaCO3), calciumsulphate (CaSO4), barium sulphate (BaSO4), strontiumsulphate (SrSO4) and calcium fluoride (CaF2). The firstthree of these, namely silica, calcium carbonate and

calcium sulphate, are the most commonly found saltsin the subterranean brackish waters of the CanaryIsland region. Of these three, silica has the highesteffect on conversion limits, followed by calcium car-bonate and finally calcium sulphate.

The scaling potential of these salts will depend ontheir concentration in the feed water (chemical analy-sis), on the pH value, the temperature, the RO sys-tem’s conversion level and on the solubility limits ofthe respective salts.

*Corresponding author.

Presented at the International Conference on Desalination for the Environment, Clean Water and Energy, European DesalinationSociety, 23–26 April 2012, Barcelona, Spain

Desalination and Water Treatmentwww.deswater.com

1944-3994/1944-3986 � 2013 Desalination Publications. All rights reserveddoi: 10.1080/19443994.2012.704732

51 (2013) 1143–1150

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2. Initial considerations

The following considerations were made in thepreparation of this paper:

(1) Use of specific scale inhibitors for CaCO3, CaSO4,BaSO4, SrSO4 and CaF2.

(2) For economic reasons, namely their high cost, theauthors did not consider the use of specific silicascale inhibitors.

(3) The temperature of the reject water is the same asthat of the feed water, namely between 10 and30 ˚C (natural brackish water temperature rangein the Canary Islands region).

(4) The reject water pH value is lower than 8.3. Onthe one hand, this is equivalent to consideringthe feed water pH to be lower than 8, and on theother to considering total alkalinity ([HCO�

2 ] + 2

[CO2�3 ] + [OH�]) to be practically all due to

bicarbonate ions [4].(5) Ideal membrane performance––in terms of salt

rejection. This is equivalent to considering aCO2 rejection rate of 0%, and for the rest of thecompounds in the feed water a rejection rate of100%.

This fifth consideration assumes a theoretical mem-brane performance which might appear unreal in itsconservatism but which, in practice and from the per-spective of the analysis of possible scaling, is not so farfrom reality if it is taken into consideration that, as aresult of the effect of polarization of the concentrationon the membrane surface of the module operating inthe worst conditions, there is a higher concentration ofsalts than for the reject flow.

3. Procedure

The following sequential order was observed:

(1) Input data.Comprising the chemical analysis of the water to

be treated, as well as its temperature and pH.

(2) Calculation methodology.(2.1) Calculation of the maximum RO system recov-

ery level for there to be no silica scaling (R1 ¼ Rmax-SiO2 ).(2.2) Calculation of the maximum RO system

recovery level to be adopted (Rmax-adopt).(2.2.1) Calculation of the maximum RO system

recovery level for there to be, along with no silicascaling, no calcium carbonate scaling(R2 ¼ Rmax-SiO2-CaCO3

).(2.2.2) Calculation of the maximum RO system

recovery level for there to be, along with no silicascaling and no calcium carbonate scaling, no calciumsulphate scaling (R3 ¼ Rmax-SiO2-CaCO3-CaSO4

).(2.2.3) Calculation of the maximum RO system

recovery level for there to be, along with no silica orcalcium carbonate or calcium sulphate scaling, no bar-ium sulphate scaling (R4 ¼ Rmax-SiO2-CaCO3-CaSO4-BaSO4

).(2.2.4) Calculation of the maximum RO system

recovery level for there to be, along with no silica orcalcium carbonate or calcium sulphate or bariumsulphate scaling, no strontium sulphate scaling(R5 ¼ Rmax-SiO2-CaCO3-CaSO4-BaSO4-SrSO4

).(2.2.5) Calculation of the maximum RO system

recovery level for there to be, along with no silica orcalcium carbonate or calcium sulphate or bariumsulphate or strontium sulphate scaling, no calciumfluoride scaling (Rmax-adopt ¼ R6 ¼ Rmax-SiO2-CaCO3-

CaSO4-BaSO4-SrSO4-CaF2 ).(3) Practical application.(3.1) Input data.(3.2) Results.(4) Conclusions.

(1) Input data.Before proceeding with the actual calculations, the

concentrations in the feed water must be known ofthe following:

• Cations in mg/l: calcium (Ca)f, magnesium (Mg)f,sodium (Na)f, potassium (K)f, barium (Ba)f, stron-tium (Sr)f.

• Anions in mg/l: carbonates (0mg/l), bicarbonates(HCO3)f, sulphates (SO4)f, nitrates (NO3)f, chlorides(Cl)f, fluorides (F)f.

Table 1Feed water chemical analysis

Sample Ca2+ Mg2+ Na+ K+ HCO�3 SO2�

4NO�

3 Cl� SiO2 Fe TDS pH Tmin Tmax

1 96.10 139.70 958.27 32.30 668.70 695.20 382.50 963.00 35.00 0.10 3,970.77 7.80 22.0 22.0

2 282.00 275.90 682.80 18.00 248.90 482.20 12.00 1,864.69 48.00 0.00 3,914.49 7.10 23.0 24.0

3 681.50 489.10 413.34 26.30 74.30 573.50 115.10 2,760.50 22.50 0.10 5,156.14 6.90 22.0 24.0

4 58.60 89.10 2,920.43 45.20 475.30 1,063.40 21.50 3,832.20 22.20 0.10 8,530.93 7.70 24.0 26.0

5 163.70 220.70 1,066.76 31.20 998.10 1,159.00 51.20 1,140.5 27.80 0.00 4,858.96 7.78 23.0 24.0

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• Others: silica (SiO2)f (mg/l), pHf.• Temperatures in ˚C: minimum (Tmin), mean (Tmed)

and maximum (Tmax).

(2) Calculation methodology.(2.1) Calculation of the maximum RO system

recovery level for there to be no silica scaling(R1 ¼ Rmax-SiO2 ).

Estimate carbon dioxide (CO2) content:

ðCO2Þf ¼ ½HCO�3 �f=10ðpHf�6;3Þ ð1Þ

Calculate the maximum soluble silica concentra-tion level for the minimum temperature (SiO2)Tmin

and pH ranging between 7 and 7.8 [1,5,6]:

ðSiO2ÞTmin ¼ 4Tmin ð2Þ

Calculate the concentration factor required for sil-ica concentration in the reject water to be (SiO2)Tmin:

CFmin-SiO2¼ ð4TminÞ=ðSiO2Þf ð3Þ

Calculate in mg/l as CaCO3 the expected concen-tration of bicarbonates in the reject water, for theabove concentration factor:

½HCO�3 �r-max-SiO2

¼ ½HCO�3 �f�CFmin-SiO2

ð4Þ

Calculate the expected pH value in the reject waterfor the above concentration factor:

pHr-max-SiO2¼ 6:3þ logðð½HCO�

3 �r-max-SiO2Þ=ðCO2ÞfÞ ð5Þ

Calculate the pH coefficient for estimation ofthe maximum silica concentration level in the rejectwater:

If 7 � pHr-max-SiO2� 7:8 :CpH ¼ 1 ð6Þ

If pHr-max-SiO2\7 :CpH ¼ 1:819� ð0:117�pHr-max-SiO2

Þð7Þ

If pHrmin[7:8 :CpH ¼ 0:47þ 0:0006�ðeÞ0:87pHr-max-SiO2

ð8Þ

Calculate the concentration factor required toobtain the maximum silica concentration level in thereject water:

CFmax-SiO2¼ ð4TminÞ�CpH=ðSiO2Þf ð9Þ

Calculate the required conversion in % to obtainthe above concentration factor:

R1 ¼ Rmax-SiO2¼ 100�ðCFmax-SiO2

� 1Þ=CFmax-SiO2ð10Þ

(2.2) Calculation of the maximum RO systemrecovery level to be adopted (Rmax{\hyphen}adopt).

(2.2.1) Calculation of the maximum RO systemrecovery level for there to be, along with no silicascaling, no calcium carbonate scaling (R2 ¼Rmax-SiO2-CaCO3).

The calcium carbonate scaling trend level was veri-fied for the conversion R1 ¼ Rmax-SiO2

[7,8]:

Calculate ½Ca2þ�r-max-SiO2¼ ½Ca2þ�F�CFmax-SiO2

ð11Þ

Calculate ½HCO�3 �r-max-SiO2

¼ ½HCO�3 �f�CFmax-SiO2

ð12ÞCalculate pHr-max-SiO2

¼ 6:3

þ logðð½HCO�3 �r-max-SiO2

Þ=ðCO2ÞfÞð13Þ

Calculate p-½Ca2þ�r-max-SiO2¼ logð105=½Ca2þ�r-max-SiO2

Þð14Þ

Calculate p-½HCO�3 �r-max-SiO2

¼ logð5�104=ð½HCO�3 �r-max-SiO2

ÞÞ ð15Þ

Calculate ðTDSÞr-max-SiO2¼ ðTDSÞf�CFmax-SiO2

ð16Þ

⁄If ðTDSÞr-max-SiO2� 10; 000. Calculate the Langelier

Saturation Index (LSI) [9]:

If ðTDSÞr-max-SiO2� 6; 000:

Calculate Cr-max-SiO2¼ ðð½logðTDSÞr-max-SiO2

� � 1Þ=10Þ� ð13:12� log½Tmax þ 273:15�Þ þ 34:46 ð17Þ

If 6,000 < (TDS)r� 10.000:

Calculate Cr-max-SiO2¼ 0:2778� ð13:12� log½Tmax þ 273:15�Þ þ 34:46 ð18Þ

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Calculate pHsr-max-SiO2¼ p-½Ca2þ�r-max-SiO2

þ p-½HCO�3 �r-max-SiO2

þ Cr-max-SiO2ð19Þ

Calculate LSIr-max-SiO2¼ pHr-max-SiO2

� pHsr-max-SiO2ð20Þ

From the value obtained in (20), the following con-siderations were made:

If LSIr-max-SiO2\0. The addition of scaling inhibitoris not necessary. R2(Rmax-SiO2-CaCO3) =R1(Rmax-SiO2 ) isadopted and the calcium sulphate scaling trend levelis verified for this conversion.

If 0 � LSIr-max-SiO2� 2:5. The addition of scaling

inhibitor is necessary. R2(Rmax-SiO2-CaCO3) =R1(Rmax-SiO2

)is adopted and the calcium sulphate scaling trendlevel is verified for this conversion.

If LSIr-max-SiO2[2:5. The conversion levelR2(Rmax-SiO2-CaCO3

) <R1(Rmax-SiO2) is reduced until the

new LSIr-max-SiO2-CaCO3 � 2:5.⁄If ðSTDÞr-max-SiO2

[10; 000. Calculate the Stiff &Davis Stability or Saturation Index (S&DSI) [10]:

Calculate the ionic strength of the feed waterfrom the molal concentrations of all the ions presentin it:

ISf ¼ 0; 5�½4ðmCaÞf þ 4ðmMgÞf þ ðmNaÞf þ ðmKÞfþ 4ðmBaÞf þ 4ðmSrÞf þ ðmHCO3

Þf þ 4ðmSO4Þf

þ ðmNO3Þf þ ðmClÞf þ ðmFÞf� ð21Þ

Calculate the ionic strength of the reject water:

ISr-max-SiO2¼ ISf�CFmax-SiO2

¼ A ð22Þ

Calculate the coefficient KTmaxðAÞ from:

K10� ðAÞ ¼ 1:3944ðAÞ3 � 4:8733ðAÞ2 þ 4:8189ðAÞ þ 2:28

ð23Þ

K20� ðAÞ ¼ 1:4389ðAÞ3 � 5:0767ðAÞ2 þ 5:0578ðAÞ þ 2:06

ð24Þ

K25� ðAÞ ¼ 1:5861ðAÞ3 � 5:4283ðAÞ2 þ 5:2222ðAÞ þ 1:96

ð25Þ

K30� ðAÞ ¼ 1:3417ðAÞ3 � 4:7350ðAÞ2 þ 4:7933ðAÞ þ 1:87

ð26Þ

If the value of Tmax is different from the previousvalues (10˚, 20˚, 25˚ and 30˚C), KTmax (A) is obtained byinterpolating between the values immediately aboveand below.

Calculate pHsr-max-SiO2¼ p-½Ca2þ�r-max-SiO2

þ p-½HCO�3 �r-max-SiO2

þ KTmaxðAÞ ð27Þ

Calculate S&DSIr-max-SiO2¼ pHr-max-SiO2

� pHsr-max-SiO2

ð28Þ

The following considerations are made based onthe value obtained in (28):

If S&DSIr-max-SiO2\0. The addition of scaling inhibi-

tor is not necessary. R2(Rmax-SiO2-CaCO3) =R1(Rmax-SiO2

) isadopted and the calcium sulphate scaling trend levelis verified for this conversion.

If 0 � S&DSIr-max-SiO2 � 2. The addition of scalinginhibitor is necessary. R2(Rmax-SiO2-CaCO3

) =R1(Rmax-SiO2)

is adopted and the calcium sulphate scaling trendlevel is verified for this conversion.

If S&DSIr-max-SiO2[2. The conversion levelR2(Rmax-SiO2-CaCO3) <R1(Rmax-SiO2 ) is reduced until thenew S&DSIr-max-SiO2-CaCO3

� 2.

(2.2.2) Calculation of the maximum RO systemrecovery level for there to be, along with no silicascaling and no calcium carbonate scaling, no calciumsulphate scaling (R3 ¼ Rmax-SiO2-CaCO3-CaSO4

).

The calcium sulphate scaling tendency level isverified for the conversion R2 ¼ Rmax-SiO2-CaCO3

[11]:

Calculate CFmax-SiO2-CaCO3¼ 100=ð100

� Rmax-SiO2-CaCO3Þ ð29Þ

Calculate the ionic product of the calcium sulphatein the reject water:

IPCaSO4r-max-SiO2-CaCO3¼ ½ðSO4Þf�CFmax-SiO2-CaCO3

=96; 000��½ðCaÞf�CFmax-SiO2-CaCO3

=40; 080�ð30Þ

Calculate the ionic strength of the reject water:

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ISr-max-SiO2-CaCO3¼ ISf�CFmax-SiO2-CaCO3

ð31Þ

Calculate the solubility product of the calciumsulphate in the reject water [12]:

KCaSO4r-max-SiO2-CaCO3¼ 0:0016ðISr-max-SiO2-CaCO3

Þð0:6742Þ ð32Þ

The following considerations are made based onthe values obtained in (30) and (32):

If IPCaSO4r-max-SiO2-CaCO3 � 0:8 KCaSO4r-max-SiO2-CaCO3 .The addition of scaling inhibitor is not necessary.R3ðRmax-SiO2-CaCO3-CaSO4Þ ¼ R2ðRmax-SiO2-CaCO3Þ is adoptedand the barium sulphate scaling trend level is verifiedfor this conversion.

If 0:8KCaSO4r-max-SiO2-CaCO3\IPCaSO4r-max-SiO2-

CaCO3�2:5KCaSO4r-max-SiO2 -CaCO3. The addition of scaling inhibi-

tor is necessary. R3ðRmax-SiO2-CaCO3-CaSO4Þ ¼R2ðRmax-SiO2-CaCO3Þ is adopted and the barium sulphatescaling trend level is verified for this conversion.

If 2:5KCaSO4r-max-SiO2-CaCO3\IPCaSO4r-max-SiO2-CaCO3

. Theconversion level R3ðRmax-SiO2-CaCO3-CaSO4

Þ\R2ðRmax-SiO2-CaCO3Þ is reduced until for thenew conversion IPCaSO4r-max-SiO2-CaCO3-CaSO4

� 2:5KCaSO4r-max-SiO2-CaCO3-CaSO4 .

(2.2.3) Calculation of the maximum RO systemrecovery level for there to be, along with no silica orcalcium carbonate or calcium sulphate scaling, no bar-ium sulphate scaling (R4 ¼ Rmax-SiO2-CaCO3-CaSO4-BaSO4

).The barium sulphate scaling tendency level is

verified for the conversion R3 ¼ Rmax-SiO2-CaCO3-CaSO4

[11]:

Calculate CFmax-SiO2-CaCO3-CaSO4

¼ 100=ð100� Rmax-SiO2-CaCO3-CaSO4Þ ð33Þ

Calculate the ionic product of the barium sulphatein the reject water:

IPBaSO4r-max-SiO2-CaCO3-CaSO4¼ ½ðSO4Þf

�CFmax-SiO2-CaCO3-CaSO4=96; 000�

�½ðBaÞf�CFmax-SiO2-CaCO3-CaSO4=137; 340� ð34Þ

Calculate the ionic strength of the reject water:

ISr-max-SiO2-CaCO3-CaSO4¼ ISf�CFmax-SiO2-CaCO3-CaSO4

ð35Þ

Calculate the solubility product of the barium sul-phate in the reject water [12]:

KBaSO4r-max-SiO2-CaCO3-CaSO4¼ 0:000000007

� ðISr-max-SiO2-CaCO3-CaSO4Þ0:835

ð36Þ

The following considerations are made based onthe values obtained in Eqs. (34) and (36):

If IPBaSO4r-max-SiO2-CaCO3-CaSO4� 0:8KBaSO4r-max-SiO2-

CaCO3-CaSO4.

The addition of scaling inhibitor is not necessary.R4ðRmax-SiO2-CaCO3-CaSO4-BaSO4

Þ ¼ R3ðRmax-SiO2-CaCO3-CaSO4Þ

is adopted and the strontium sulphate scaling trendlevel is verified for this conversion.

If 0:8KBaSO4r-max-SiO2-CaCO3\IPBaSO4r-max-SiO2-CaCO3-CaSO4�40KBaSO4r-max-SiO2-CaCO3-CaSO4 :

The addition of scaling inhibitor is necessary.R4ðRmax-SiO2-CaCO3-CaSO4-BaSO4

Þ ¼ R3ðRmax-SiO2-CaCO3-CaSO4Þ

is adopted and the strontium sulphate scaling trendlevel is verified for this conversion.

If 40KBaSO4r-max-SiO2-CaCO3-CaSO4 \IPBaSO4r-max-SiO2-

CaCO3-CaSO4.

The conversion level R4ðRmax-SiO2-CaCO3-

CaSO4-BaSO4Þ\R3ðRmax-SiO2 -CaCO3 -CaSO4Þ is reduced until for

the new conversion IPBaSO4r-max-SiO2-CaCO3-CaSO4-BaSO4�40KBaSO4r-max-SiO2-CaCO3-CaSO4-BaSO4

.

(2.2.4) Calculation of the maximum RO systemrecovery level for there to be, along with no silica orcalcium carbonate or calcium sulphate or barium sul-phate scaling, no strontium sulphate scaling ðR5 ¼Rmax-SiO2-CaCO3-CaSO4-BaSO4-SrSO4

Þ.The strontium sulphate scaling tendency level

is verified for the conversion R4 ¼Rmax-SiO2-CaCO3-CaSO4-BaSO4

[11]:

Calculate CFmax-SiO2-CaCO3-CaSO4-BaSO4

¼ 100=ð100� Rmax-SiO2-CaCO3-CaSO4-BaSO4Þ ð37Þ

Calculate the ionic product of the strontium sul-phate in the reject water:

IPSrSO4r-max-SiO2-CaCO3-CaSO4-BaSO4

¼ ½ðSO4Þf�CFmax-SiO2-CaCO3-CaSO4BaSO4=96; 000�

�½ðSrÞf�CFmax-SiO2-CaCO3-CaSO4-BaSO4=87; 620� ð38Þ

Calculate the ionic strength of the reject water:

ISr-max-SiO2-CaCO3-CaSO4-BaSO4¼ ISf�CFmax-SiO2-CaCO3-CaSO4-BaSO4

ð39Þ

Calculate the solubility product of the strontiumsulphate in the reject water [12]:

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KSrSO4r-max-SiO2-CaCO3-CaSO4-BaSO4

¼ 0:00001ðISr-max-SiO2-CaCO3-CaSO4-BaSO4Þð0:6916Þ ð40Þ

The following considerations are made based onthe values obtained in (38) and (40):

If IPSrSO4r-max-SiO2-CaCO3-CaSO4-BaSO4� 0:8KSrSO4

r-max-SiO2-CaCO3-CaSO4-BaSO4. The additionof scaling inhibitor is not necessary.R5ðRmax-SiO2-CaCO3-CaSO4-BaSO4-SrSO4

Þ ¼ R4ðRmax-SiO2-CaCO3-

CaSO4-BaSO4Þ is adopted and the calcium fluoride scaling

trend level is verified for this conversion.If 0:8KSrSO4r-max-SiO2-CaCO3-BaSO4\IPSrSO4r-max-SiO2-

CaCO3-CaSO4-BaSO4 � 40KSrSO4r-max-SiO2-CaCO3-CaSO4-BaSO4 . Theaddition of scaling inhibitor is necessary.R5ðRmax-SiO2-CaCO3-CaSO4-BaSO4-SrSO4

Þ ¼ R4ðRmax-SiO2-CaCO3-

CaSO4-BaSO4Þ is adopted and the calcium fluoride scalingtrend level is verified for this conversion.

If 40KSrSO4r-max-SiO2-CaCO3-CaSO4-BaSO4\IPSrSO4r-max-

SiO2-CaCO3-CaSO4-BaSO4. The conversion level

R5ðRmax-SiO2-CaCO3-CaSO4-BaSO4-SrSO4Þ\R4ðRmax-SiO2-CaCO3-

CaSO4-BaSO4Þ is reduced until for the

new conversion IPSrSO4r-max-SiO2-CaCO3-CaSO4-BaSO4-SrSO4�

40KBSrSO4r-max-SiO2-CaCO3-CaSO4-BaSO4-SrSO4 .

(2.2.5) Calculation of the maximum RO systemrecovery level for there to be, along with no silica orcalcium carbonate or calcium sulphate or bariumsulphate or strontium sulphate scaling, nocalcium fluoride scaling ðRmax-adopt ¼ R6 ¼Rmax-SiO2-CaCO3-CaSO4-BaSO4-SrSO4-CaF2Þ.

The calcium fluoride scaling tendency level is veri-fied for the conversion R5 ¼ Rmax-SiO2-CaCO3-CaSO4-

BaSO4-SrSO4[1,2,12]:

Calculate CFmax-SiO2-CaCO3-CaSO4-BaSO4-SrSO4

¼ 100=ð100� Rmax-SiO2-CaCO3-CaSO4-BaSO4-SrSO4Þ ð41Þ

Calculate the ionic product of the calcium fluoridein the reject water:

IPCaF2r-max-SiO2-CaCO3-CaSO4-BaSO4-SrSO4

¼ ½ðFÞf�CFmax-SiO2-CaCO3-CaSO4-BaSO4-SrSO4=19; 000�

�½ðCaÞf�CFmax-SiO2-CaCO3-CaSO4-BaSO4-SrSO4=40; 080�

ð42Þ

The following considerations are made based onthe value obtained in (42):

If IPCaF2r-max-SiO2-CaCO3-CaSO4-BaSO4-SrSO4� 4�10ð�11Þ.

The addition of scaling inhibitor is notnecessary. R6ðRmax-SiO2-CaCO3-CaSO4-BaSO4-SrSO4-CaF2Þ ¼R5ðRmax-SiO2-CaCO3-CaSO4-BaSO4-SrSO4Þ is adopted.

If 4�10ð�11Þ\IPCaF2r-max-SiO2-CaCO3-CaSO4-BaSO4-SrSO4 �4�10ð�9Þ. The addition of scaling inhibitor isnecessary. R6ðRmax-SiO2-CaCO3- CaSO4-BaSO4-SrSO4-CaF2Þ ¼ R5

ðRmax-SiO2-CaCO3-CaSO4-BaSO4- SrSO4Þ is adopted.

If 4�10ð�9Þ\IPCaF2r-max-SiO2-CaCO3-CaSO4-BaSO4-SrSO4. The

conversion level R6ðRmax-SiO2-CaCO3-CaSO4-

BaSO4-SrSO4-CaF2Þ\R5ðRmax-SiO2-CaCO3-CaSO4-BaSO4-SrSO4Þ is

reduced until for the new conversion

IPCaF2r-max-SiO2-CaCO3-CaSO4-BaSO4-SrSO4-CaF2 � 4�10ð�9Þ.

The maximum RO system recovery level to beadopted will be:

Rmax-adopt ¼ R6 ¼ Rmax-SiO2-CaCO3-CaSO4-BaSO4-SrSO4-CaF2

Other types of scaling, as might occur if the pres-ence of trace metals, metal oxides or metal hydroxidesis detected in the feed water, were not considered.

(3) Practical application.(3.1) Input data.Five samples of brackish water from wells in the

Canary Island region were used for this study. Thechemical analysis of the samples, used as feed waterfor RO desalination plants, was as follows (concentra-tions in mg/l as ion, temperatures in ˚C) (Table 1).

(3.2) Results.

The results of the calculations as described abovewere shown in Table 2:

4. Conclusions

It is deduced from the results obtained (Table 2)that the limiting compound of the maximum conver-sion level for the first four samples is silica(Rmax-adopt ¼ Rmax-SiO2Þ, with the limitation for the fifthsample being imposed by calcium carbonateðRmax-adopt ¼ Rmax-SiO2-CaCO3

Þ.Since, for the third sample, 0:8KCaSO4r\

IPCaSO4r � 2:5KCaSO4r, the addition of a specific scalinginhibitor to the feed water is required to avoid thistype of scaling.

In all the samples, the S&DSIr or, failing that, theLSIr (sample 2), is positive. Therefore, the addition tothe feed water in all cases of specific scaling inhibitoris required to avoid calcium carbonate scaling.

The RO system design of a brackish water desali-nation plant employing this system, will need to con-sider, in addition to the maximum conversion asdetermined by the calculations previously described,

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other limiting factors including the plant production,the feed water SDI value, the type of RO element tobe employed, the desired water quality, the maximumoperating pressure, etc.

The proposed Eqs. (1)–(42) enable the use of a sim-ple calculation software programme which can beintegrated into the definitive calculation programmeused for the RO system design. In this way, latersimulations can be easily applied with a high degreeof confidence.

List of symbols

Cjf –– concentration of the j ion/componentin the feed water

(Cj)f –– idem (expressed in mg/l)

[Cj]f –– idem (expressed in ppm as CaCO3)

Cjr –– concentration of the j ion/componentin the reject water

(Cj)r –– idem (expressed in mg/l)

[Cj]r –– idem (expressed in ppm as CaCO3)

CpH –– SiO2 saturation pH coefficient

CF –– concentration factor

CFmax –– maximum concentration factor

CFmin –– minimum concentration factor

IP –– ionic product

IPBaSO4r –– ionic product of the barium sulphate ofthe reject water

IPCaF2r –– ionic product of the calcium fluoride ofthe reject water

IPCaSO4r –– ionic product of the calcium sulphateof the reject water

IPSrSO4r –– ionic product of the strontium sulphateof the reject water

IS –– ionic strength

ISf –– ionic strength of the feed water

ISr –– ionic strength of the reject water

KBaSO4r –– reject water barium sulphate solubilityproduct

KCaSO4r –– reject water calcium sulphate solubilityproduct

KSrSO4r –– reject water strontium sulphatesolubility product

KT –– temperature and ionic strengthparameter of the S&DSI

LSI –– Langelier saturation index.

(mi)f –– molal concentration of the i ion in thefeed water

(mi)r –– molal concentration of the i ion in thereject water

p-[Ca2+] –– parameter of the LSI

p-[Ca2+]r –– parameter of the LSI of the reject water

pHf –– feed water pH value

pHr –– reject water pH value

pHrmax –– reject water maximum pH value

pHrmin –– reject water minimum pH value

pHs –– saturation pH value

pHsr –– reject water saturation pH value

p-[HCO�3 ] –– parameter of the LSI

p-[HCO�3 ]r –– parameter of the LSI of the reject water

Rmax-adopt –– maximum recovery adopted

Rmax-BaSO4 –– maximum recovery for bariumsulphate

Rmax-CaCO3 –– maximum recovery for calciumcarbonate

Rmax-CaF2 –– maximum recovery for calciumfluoride

Rmax-CaSO4 –– maximum recovery for calciumsulphate

Rmax-SiO2 –– maximum recovery for silica

Rmax-SrSO4 –– maximum recovery for strontiumsulphate

RO –– reverse osmosis

SDI –– silt density index

S&DSI –– Stiff and Davis saturation or stabilityindex

TDS –– total dissolved salts

T –– feed water temperature (˚C)

Tmax –– maximum feed water temperature (˚C)

Tmin –– minimum feed water temperature (˚C)

Subscripts

f –– feed

r –– reject

i,j –– ion/component

Table 2Results of the calculations

Sample Rmax-SiO2Rmax-adopt ISf ISr (TDS)r LSIr S&DSIf IPCaSO4

KCaSO4r

1 67.47 67.47 0.0745 0.2289 12,206.00 – 1.75 0.000164 0.000592

2 47.83 47.83 0.0907 0.1738 7,502.80 1.11 – 0.000130 0.000492

3 74.43 74.43 0.1367 0.5346 20,166.00 – 0.53 0.001600 0.001000

4 79.45 79.45 0.1559 0.7586 41,506.00 – 1.35 0.000383 0.001300

5 76.56 69.59 0.0992 0.3262 15,976.00 – 2.00 0.000533 0.000752

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References

[1] E. Du Pont de Nemours & Co, Permasep Engineering Man-ual, Bulletin 502: Pretreatment for Membrane Scaling, 1982.

[2] Dow Chemical Co. Filmtec Co, Filmtec Membranes Techni-cal Manual, Section 3: Water Chemistry and Pretreatment,1995.

[3] American Society for Testing and Materials (ASTM), StandardTest Method, Annual Book, Designation: D 4189-82, 1982.

[4] Instituto Geologico y Minero de Espana (IGME), IsotoposAmbientales en el Ciclo Hidrologico. Principios y Aplicac-iones, Capıtulo 9: Quımica del Acido Carbonico del Agua,Programa Hidrologico Internacional, Unesco (2001) 101–107.

[5] G.B. Alexander, W.M. Hester, R.K. ller, The solubility ofamorphous silica in water, J. Phys. Chem. 58 (1954) 453–455.

[6] American Society for Testing and Materials (ASTM), StandardPractice for Calculation and Adjustment of Silica (SiO2) Scal-ing for Reverse Osmosis, Annual Book, Designation: D 4993-89, 1989.

[7] Water Quality and Treatment, 4th ed., Prepared by the Amer-ican Water Works Association, McGraw-Hill, New York, NY,1990.

[8] Water Treatment Handbook, 6th ed., Degremont Company,vol. 1, 1991 (Chapter 3), pp. 13.

[9] American Society for Testing and Materials (ASTM), StandardPractice for Calculation and Adjustment of the Langelier Sat-uration Index for Reverse Osmosis, Annual Book, Designa-tion: D 3739-88, 1988.

[10] American Society for Testing and Materials (ASTM), StandardPractice for Calculation and Adjustment of the Stiff and DavisStability Index for Reverse Osmosis, Annual Book, Designa-tion: D 4582-86, 1986.

[11] American Society for Testing and Materials (ASTM), StandardPractice for Calculation and Adjustment of Sulphate ScalingSalts (CaSO4, SrSO4, and BaSO4) for Reverse Osmosis, AnnualBook, Designation: D 4692-87, 1987.

[12] M. Al-Shammiri, A. Salman, S. Al-Shammari, M. Ahmad,Simple program for the estimation of scaling potential in ROsystems, Desalination 184 (2005) 139–147.

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