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Nascimento et al., 1:12http://dx.doi.org/10.4172/scientificreports.572

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Volume 1 • Issue 12 • 2012

Keywords: Hard and saline waters; Chemical mass balance model; Aqueous-solid phase interpretation

IntroductionChemical composition of natural waters (surface and subsurface

waters) is governed by the carbonate system given by H2CO3+CO2

(aq)+ H2O. The association of 3% of carbonic acid and 97% of carbon dioxide molecularly dissolved can be represented by H2CO3

* and, thus, the carbonate system is defined as H2CO3

*+H2O,when water has a very high saline concentration its carbonate system is defined by H2CO3

*+H2O+DS where DS represents dissolved salts [1].

The theory of the carbonate system was well defined by Loewenthal and Marais [2] in this system, the total species concentration, CT, is given by the sum of carbon dioxide, bicarbonate and carbonate species. Its definition requires the measurement of pH and of some parameter defined in terms of carbonic species. When CT is not known, it can be used Total Alkalinity or Alkalinity to define the other carbonic species (bicarbonate and carbonate, respectively). Thus, in practice, it is used pH and Alkalinity to define the aqueous phase in natural waters. The solid-aqueous phase requires the determination of calcium or total hardness which is represented by the sum of Carbonate Hardness, CH and Non Carbonate Hardness, NCH, respectively.

In high saline waters with total dissolved solids above 10000 mg/L, pH is influenced by the presence of the Residual Liquid Junction Potential, RLJP. In 1981, Cavalcanti [3] determined this influence and, thus, improved the modeling of the H2CO3

*+H2O carbonate system.

In high salinity and high ionic strength waters, it is observed the ion pairing formation; i.e., the complexation between ions of opposite charges in solution. This process affects ions activities in solution and also their concentrations modifying ionic strength and solubility products of saline waters.

In northeastern semi-arid region of Brazil, the great majority of surface waters show a high hardness and an excess of dissolved salts. These waters indicate the predominance of dolomite (association of calcium and magnesium sulphate and carbonate) and calcite (calcium carbonate) in the soil of Paraiba semi-arid region [4]. The non carbonate hardness is the chemical parameter prevailing in these waters and is given by the association of magnesium to chloride, sulphate, carbonate and bicarbonate salts. The resolution of equations involving

*Corresponding author: Nascimento L, Department-CED/UNIPÊ Civil Engineering, Campus UNIPÊ/BR-230-Km 22, Block-F, Cold Water, CEP: 58053-000, João Pessoa. E-mail: luciano.engenhariacivilunipe@gmail.com

Received September 29, 2012; Published December 14, 2012

Citation: Nascimento L, Agostinho LCL, Cavalcanti BF (2012) Study Chemical Mass Balance Model for Hard and Saline Waters. 1:572 doi:10.4172/scientificreports.572

Copyright: © 2012 Nascimento L, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

AbstractHard and saline waters with chlorine concentration above 1000 mg/L are easily found in the semi arid region

of Paraiba. The analysis of its chemical quality as routine is a very complex task because of various ion pairing substances formed due to the presence of several dissolved salts. A chemical mass balance model (CMB Model) was developed by applying the carbonated system chemistry associated to ion pairing formation in the aqueous solid phase. From experimental data of parameters pH, Alkalinity and hardness of an urban dam located in Campina Grande, PB, the model was validated by considering Total Hardness. It was evidentiated the predominance of non carbonate hardness represented by the magnesium sulphate which reduces significantly the calcium carbonate precipitation.

Study Chemical Mass Balance Model for Hard and Saline WatersNascimento L1*, Agostinho LCL2 and Cavalcanti BF3

1Civil Engineering, Department-CED/UNIPÊ, Campus UNIPÊ/BR, João Pessoa, Brazil2Chemistry Department-CD/CST-UEPB Street, Campina Grande-PB, Brazil3Civil Engineering, Academic Unity-CEAU/CTNR-UFCG Aprígio Veloso Avenue, Campina Grande-PB, Brazil

the substances originated from the ion pairing in these waters is a very hard and difficult task for a routine control [5].

This paper shows the development and application of a Chemical Mass Balance model, CMB model for hard and saline waters. The model allows, from the aqueous and solid aqueous phase equations, to analyze the interaction of the calcium magnesium carbonated species-pH system. CMB model utilizes CaCO3 scale, mg/L CaCO3) and considers unity activity; i.e., the activity coefficients of the species are always equals to unity. It were also applied some simplifications in the model such as, for instance, to consider the free species and associated species as total species.

TheoryIon pairing in aqueous solutions

Chemically, natural waters are considered as dilute solutions. The distribution of several soluble forms is described by equilibrium equations of mass parameters given by equilibrium constants.

In environmental solutions, metallic ions are always seeking a pair. When this environment is water, metallic cations are hydrated to form aqueous complexes [6]. The change reactions are denominated “coordination” and, in these reactions, water coordinated molecules are changed by some preferential ligand molecules.

Metal ions form ionic pairing with a number of organic and inorganic ions and, also, with molecules. The complexing number of a metal such as Me is defined as the number of “liaisons” formed of the metallic ion with atoms of ligand such as L, the following reaction shows this complexation [7]:

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Volume 1 • Issue 12 • 2012

( )x y

Me L Mel x y+ −+ → − (1)

( ).( )

( ( ))x y

Me Lke

MeL x y+ −

=−

(2)

where, ke is the stability constant by considering that the process is a complex formation; (Me) indicates activity concentration of, for instance, the metal ion Me.

For unity activity; i.e., for fMe , fL and fMeL (where “f ” refers to activity coefficient in molar scale, mol/L) equal to unity, equation (2) is rewritten as:

( ).( )

( ( ))x y

Me Lk e

MeL x y+ −

′ =−

(3)

In natural waters ions such as OH-, Cl-, SO42- and HCO3

- may form ion pairing. Hydroxyl ion, OH- is the strongest ligand. Calcium, Ca2+ may form a non stable complex with bicarbonate, HCO3

-. Similarly, the stability constants for others bicarbonates such as iron and manganese bicarbonate, respectively, are very small. The reason is that they are weak complexes and, thus, cannot affect the solubility relations of sodium carbonate [8].

Ion pairing in high salinity waters

In order to analyze the principal equations involving ionic pairs in high salinity waters, it was defined the ionic pairs formed by metallic species such as calcium and magnesium and the anionic species sulphate. These ion pairings represent a dynamic equilibrium and can be given by:

2 2 04 4Hc S HcO+ −+ → (4)

where, Hc refers to hardness cations which are or magnesium, Mg2+ or calcium, Ca2+, i.e., the main cations present in high ionic strength and high salinity waters.

Equilibrium constant for reaction given by equation (4) is:

04

2 24

4

( ).( )HcS

Hc SkHcS

+ −

=

(5)

where, kHcSO40= ion pair dissociation form for the equilibrium

constant.

Applying the definition of activity in molar scale (mol/L-1) into the above equation gives:

04

2 2 004 4

0 2 2 444

( ).( )HcS

Hc S kHcSk k HcSHcS fHc fS −

−

+ −

+ −′= = =

+ (6)

However, it can be defined the mean coefficient which is given by the product of the cation and anion coefficients as f± [9]. Thus:

( )1

2 2 224 4fH fSO fHcS

±+ − −+ = (7)

Substituting into equation (6):

44 2

4( )kHcSOk HcSOfHcSO±

′ =

(8)

where, fHcSO4± is the mean molar activity coefficient for HcSO4.

However, this coefficient cannot be obtained from table in literature because these tables do not distinguish between ion pairing and other effects. So, it is necessary to determine fHc2+ and fSO4

2-. In order to solve this problem, two solutions can be applied: (1) Ionic strength is obtained from each free species of the substance and (2) Activity coefficients of Hc and of SO4 are determined. To apply the second solution it is necessary to obtain data from tables for the hydration number, hand for parameters R and aº, respectively; i.e., for with these values one can apply, for instance, Glueckauf theory to obtain the mean

activity coefficient [10]. However, for some particular waters, it can be applied a more simplified procedure which is described as follows:

(1) Initially it is considered an analysis of the mass balance on the HcSO4 + H2O system by using molar concentration. The mass balance equations for the Hc and sulphate species are, respectively, given by:

2 2 04. .Hc t Hc f HcSO x+ + = + =

(9)

2 2 04 4 4. .SO t SO f HcSO x+ + = + =

(10)

In the above equations “t” refers to the sum of free species and ion pairs and “f ” to free species concentration.

(2) The next step is to consider that the molar concentration of cation hardness is equal to the molar concentration of sulphate, however, different from X. The free species of this system are given by:

2 2 04. .Hc f Hc t HcSO+ + = − (11)

2 2 04 4 4. .SO f SO t HcSO− − = −

(12)

Applying equation (6) into equation (11) gives:

{ }2

2 2 24 42

4

.

1 . ..

Hc t

f Hc f SO SOHc f

k HcSO

+

+ − −

+

+ = ′

(13)

As to the value of free sulphate with influence of ionic strength, it is adjusted sequentially until the following equation:

{ }2 2 2 24 42

44

. . ..

SO f f Hc f SO HcSO t

k HcSO

− + − +

− + + = ′

(14)

Hence,

{ }24

2 2 242

44

.

1 . . ..

SO t

f Hc f SO HcSO f

k HcSO

−

+ − +

−

+ = ′

(15)

As it can be seen, it is necessary to determine the activity coefficients of the ion pairs by admitting that the free species concentrations are equal.

Values for k’ (ion pairs) are obtained from literature, activity coefficients can be calculated and are equals; i.e., can be determined as activity coefficients for monovalent and divalent ions for natural waters with low ionic strength (I< 0, 25) [11]. Also, the activity coefficient for ion paired species is equal to 1,0; i.e., f (ion pair)=1,0.

Now, considering the waters found in the semi – arid region of Brazil (Ceará, Paraiba and Pernambuco northeastern states), the cationic species that ion pair with sulphate are derived from alkaline earth chlorides as magnesium chloride, MgCl2 and, in a less scale, from the uni-univalent sodium chloride, NaCl. Thus, the system to be analyzed is defined as H2O+Cl-+Na++Hc2++SO4

2-. The main equations for the ionic pairs are as follows [12]:

( ) ( )( )

24 2

2 402 4

.Na SOk Na SO

Na SO

+ −

′= (16)

( ) ( )( )

2 24 0

404

.Hc SOk HcSO

HcSO

+ −

′= (17)

In the above equations “o” refers to neutral species of ion pair. Mass balance equations are given by:

02 4. .Na t Na f Na SO+ + = +

(18)

2 2 04. .Hc t Hc f HcSO+ + = +

(19)

Free species are defined as follows:

Citation: Nascimento L, Agostinho LCL, Cavalcanti BF (2012) Study Chemical Mass Balance Model for Hard and Saline Waters. 1:572 doi:10.4172/scientificreports.572

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Volume 1 • Issue 12 • 2012

{ }2 24 4

4 2 4

.

1 . . . ..

. . .

Na t

f Na f SO SONa f

f NaSO k Na SO

+

+ − −

+

+ = ′

(20)

{ }2

2 2 24 42

4 4

.

1 . . . ..

. . .

Hc t

f Hc f SO SOHc f

f HcSO k HcSO

+

+ − −

+

+ = ′

(21)

In order to solve this system which has four unknowns some assumptions are made as follows:

(a) Activity coefficient for neutral species is unity;

(b) All activity coefficients of the species of this system are equal; i.e., fHcSO4º = fNa2SO4º.

The term free sulphate is obtained from the following equation:

{ }{ }

24

242

4 2 2 22 4 4

4

.

1 . ..

1 . .

.

SO t

f Na SO NaSO f

k Na SO f Hc f SO Hc

k HcSO

−

+ − +

−

+ − +

+ = ′ + +

′

(22)

From the three main equations given by equations (20), (21) and (22) the procedure to define the system is given by:

(1) It is assumed an initial value for sulphate ion.

(2) The activity coefficients values for each ionic species are determined as if no ion pairing occurs.

(3) For metallic ions, concentrations are determined according to their particular system definition

(4) Sulphate value is given by the free sulphate equation by applying the free metal ions values previously obtained.

(5) If the sulphate concentration is greater than the initial value of sulphate or sulphate measured, it is necessary to reduce its concentration and the procedure is repeated with new value for activity coefficients and for the sulphate concentration adopted.

This same calculation is applied to other substances formed; i.e., to other dissolved salts such as chloride, bicarbonate and carbonate salts. Same procedure is applied to sodium dissolved salts.

Simplified mass balance model

In high salinity waters, ion pairing formation between cationic species such as sodium, magnesium, calcium and weak acid species of the carbonated system are observed. Generally, the concentrations of the weak acid species are lesser than those of the cations. Hence, the ion pair formed has little effect in the cationic species concentrations. However, a deep effect in the weak acid concentration is observed.

As it was shown, it is a very complicated and hard task to determine all the ion pairs formed between anionic species such as chloride, sulphate, bicarbonate and carbonate and cationic species of hard and saline waters by utilizing the theory previously discussed.

From observations that high salinity waters of the semi – arid region of Paraiba are generally very hard and corrosive, some simplifications were made on the mass balance equations previously defined. These assumptions are as follows:

1. Unity activity is adopted for al ionic species in solution

2. Definition of all parameters of aqueous – solid phase is made by using CaCO3 scale as mg/L CaCO3.

3. Mass balance is applied in parameters of aqueous phase and aqueous-solid phase.

In aqueous phase it is considered the interrelationship between Alkalinity, Acidity and pH. In high salinity waters, bicarbonate and carbonate species are total species as well as the hydroxyl ion of the water system. Hence, these species are defined as total species, (DS) t where DS refers to dissolved salts and “t” to free and ion pair species. In calcium carbonate scale, Alkalinity and Acidity are defined as follows [13]:

23 3Alk H HCO CO OH+ − − −= − + + + (23)

*3 2 3Ac H HCO H CO OH+ − −= + + − (24)

However, for high salinity waters the simplification in Alkalinity definition is given by:

23 3 3 3 3 3Alk AlkHCO HCO CO MgCO CaCO HcCO− − −= = + ≅ + = (25)

In other words, in high salinity waters Alkalinity is given mainly by the hardness cations carbonate.

Solid – aqueous phase is chemically characterized from the definition of the following parameters: pH, Alkalinity, Calcium, Total Hardness and Magnesium.

Total Hardness, TH is given by the sum of Carbonate Hardness, CH and Non Carbonate Hardness, NCH (also termed permanent hardness). According to KEMP [14] when Alkalinity is less than the Total Hardness, than it is equals to Carbonate Hardness. For pH values in the range 8, 0 to 9, 5, the following simplification can be made:

2 2 23 3 3 3 3CH AlkHCO AlkCO HCO HCO CO− − − − −= + = = + (26)

Permanent hardness in water is due to the presence of calcium and magnesium sulphate and chloride salts and, in less scale, by calcium carbonate partially soluble in water. Total Hardness, TH in high salinity waters was defined as follows [15]:

4 2 3TH NCH CH MgSO MgCl HCO Alk−= + = + + (27)

where, all parameters have been defined previously.

Saline waters have alkaline characteristics (pH >> 8, 5) and, thus, a simplification on the Total Carbonic species concentration can be done as follows:

23 3 3 3CTsw CO MgCO CaCO CO −≅ ≅ + + (28)

Simplified mass balance equations were then applied to principal cationic species of saline waters as follows:

1. Free and ion pairing calcium and magnesium species are defined as follows:

23.Ca t CaCO+ = (29)

23 2 4.Mg t MgCO MgCl MgSO+ = + + (30)

2. Free and ion pairing sodium species are given by:

.Na t NaCl= (31)

3. For the anionic species, the simplification was applied in chloride and sulphate species as follows, respectively:

2.Cl t NaCl MgCl− = + (32)24 4.SO t MgSO− = (33)

In CMB Model all calcium species are present as calcite or calcium

Citation: Nascimento L, Agostinho LCL, Cavalcanti BF (2012) Study Chemical Mass Balance Model for Hard and Saline Waters. 1:572 doi:10.4172/scientificreports.572

Page 4 of 5

Volume 1 • Issue 12 • 2012

carbonate, all sodium as sodium chloride and all sulphate as magnesium sulphate at high pH values. The presence in excess of magnesium in this type of water produces an association of this cationic species with carbonate and, thus, reduces considerably the mass of calcium carbonate precipitation.

For ionic strength calculations the definition for high salinity waters with predominance of alkaline earth chlorides and magnesium chloride was applied. Hence:

( )5 2 53. .10 . 2. . .10Isw sc c Mg c Cl− + − −= = + (34)

where, Isw is the ionic strength for saline waters, “sc” refers to saline concentration and “c” to concentration, respectively.

Validation of the Model and ResultsCMB Model was applied in an urban lake classified as a β–

mesosaprobic lake and known as “Açude Bodocongó”, located in Campina Grande, PB. This small dam was built in the confluence of Bodocongó river and Caracois river in order to increase the water offer in Campina Grande in the early decade of the last century.

Nowadays, this dam receives polluted discharges from two districts nearby (Vila dos Teimosos and Bodocongó districts). Small industry complex utilizes its water and also part of the Campus of the State University of Campina Grande.

Sampling periods applied were dry and raining seasons. In the dam, eight sampling points were chosen as illustrated in figure 1. Two of these points are sewage discharge points and one of them is the discharge of the dam. Figure 2 shows the dam in dry season. It is convenient to remind that in semi – arid regions there are only two seasons: dry period (from August to March) and raining season (from April to July).

All solid-aqueous phase parameters were determined according to Agostinho et al. [16]. Alkalinity was determined by titration using a modified Gran titration with experimental methodology according to Cavalcanti [17]. The following parameters were determined: Total Dissolved Solids, TDS (mg/L), pH, Alkalinity (mg/L CaCO3), Total Hardness, TH (mg/L CaCO3), Calcium, Ca2+ (mg/LCaCO3), chloride, Cl- mg/L) and sulphate, SO4

2- (mg/L). Ionic strength for this water was determined by using equation (34). Hardness classification was performed by utilizing KǗNIN scale given by [18]: TH < 60X indicates soft water (X is equal to mg/L CaCO3); for 61X < TH < 120X water is slightly hard; for 120X < TH < 180X water is hard and for TH > 180X water is very hard.

In table 1 are listed the results of the eight selected sampling points of the urban dam in dry and rain season, respectively. Table 2 shows the results of the dissolved salts and were obtained by applying the mass balance equations of the CMB model. It was also determined Non Carbonate Hardness and Total Alkalinity. Validation of the CMB model was performed by comparison of field data values of Total Hardness to those determined by using this model.

ConclusionsThe results of the mass balance Model here developed, CMB Model,

applied to the waters of the Bodocongó urban dam in Campina Grande allow the following conclusions:

(1) The chemical quality analysis of the water evidentiated the presence of medium salinity, but these waters are very hard and corrosive. There is predominance of Non Carbonate Hardness or permanent hardness which is represented by the presence of the cationic species magnesium in the sulphate and carbonate ion pairs.

(2) The analysis of the cationic and anionic species of these waters allows t their classification as calcium – magnesium – sulphated waters.

(3) In dry season (results are expressed as “d” in tables 1 and 2, respectively) it can be observed a greater magnesium carbonate formation. Consequently, the calcium carbonate precipitation in these waters is reduced.

Figure 1: Location of the sampling points in the Bodocongó açude area, an urban dam located in Campina Grande, PB.

Figure 2: An aerial view of the Bodocongó urban dam in Campina Grande, PB.

Samplingpoints

TDS(*)(mg/L) pH Alk

(mg/LCaCO3)TH(**)

(mg/LCaCO3)Ca2+

(mg/LCaCO3)Cl-1

(mg/L)SO4

2-

(mg/L)

Bd1(dp)(rp)

1380 8,3 516 703 202 610 3,071544 8,3 309 745 291 331 7,00

Bd2(dp)(rp)

1437 8,3 488 792 232 598 1,001697 8,2 303 703 281 385 74,7

Bd3(dp)(rp)

1405 8,4 479 711 191 680 3,101918 8,3 319 663 281 374 4,0

Bd6(dp)(rp)

12228 8,3 465 686 192 579 3,611817 8,1 310 702 260 365 6,5

Bd7(dp)(rp)

1428 8,4 513 720 220 613 2,781499 8,3 325 727 277 397 1,1

Bd8(dp)(rp)

1642 8,4 489 679 167 620 5,471639 8,3 286 721 266 376 6,4

Bd9(dp)(rp)

1510 8,4 478 627 276 576 3,51522 8,2 306 685 264 378 8,6

Bd10(dp)(rp)

2043 8,4 480 707 196 609 5,231531 8,3 313 752 281 349 5,40

(*) TDS = Total Dissolved Solids; (**) TH = Total HardnessTable 1: Experimental results at 25ºC of chemical parameters in dry period (dp) and rain period (rp), respectively.

Citation: Nascimento L, Agostinho LCL, Cavalcanti BF (2012) Study Chemical Mass Balance Model for Hard and Saline Waters. 1:572 doi:10.4172/scientificreports.572

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Volume 1 • Issue 12 • 2012

Samplingpoints

Ionic Strength

NCH(X)

Alk(X)

NaCl(X)

MgCl2(X)

MgSO4(X)

MgCO3-

(X)CaCO3

(X)

Bd1(dp)(rp)

0,035 516 186 676,6 183,0 3,2 314,0 202,00,039 309 436 438,0 428,7 7,3 180,0 271,0

Bd2(dp)(rp)

0,036 488 304 544,6 298,8 5,2 256,0 232,00,042 303 400 148,0 395,0 5,0 22,0 281,0

Bd3(dp)(rp)

0,035 479 232 631,9 228,8 3,5 288,0 191,00,048 319 344 232,8 339,7 4,3 38,0 281,0

Bd6(dp)(ds)

0,031 465 221 599,4 217,2 3,8 273,0 192,00,045 310 392 129,6 385,2 6,8 50,0 260,0

Bd7(dp)(ds)

0,036 513 207 660,4 204,2 2,9 293,0 220,00,038 325 402 163,7 396,3 5,7 48,0 277,0

Bd8(dp)(ds)

0,041 489 190 697,4 187,2 2,9 322,0 167,00,041 286 435 102,0 428,3 6,7 20,0 266,0

Bd9(dp)(ds)

0,035 478 145 729,1 145,4 3,6 202,0 276,00,038 306 379 163,2 370,0 9,0 42,0 264,0

Bd10(dp)(ds)

0,051 480 277 634,7 224,2 2,7 284,0 196,00,039 518 434 492,2 428,4 5,6 137,0 281,0

NCH = Non Carbonate Hardness; (X) = mg/LCaCO3.Table 2: Results from the application of CMB model in the Bodocongó urban dam.

(4) Validation of CMB Model (as illustrated in figure 3) shows that the sampling point 10 that represents sewage discharge (in dry and rain seasons) does not reflect the hardness variation due to the domestic wastewater and saline water mixture of the urban dam.

(5) This model, after calibration, can be used for predicting the Total Hardness and Non Carbonate Hardness of high salinity and high ionic strength waters.

Acknowledgements

The National Council for Scientific and Technological Development-CNPq for the financial support of this research.

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9. Cavalcanti BF, Urtiga EF (1992) Analysis of a Treatment System Low Cost pair Removal of Iron and Manganese in Groundwater. In: 7th Brazilian Congress on Groundwater, MG. Brazilian Groundwater Association.

10. Nascimento L, Agostinho LCL, Cavalcanti BF (2009) Modeling Thermodynamics of Gaseous Chlorine Disinfection. Techno-logic 13: 86-92.

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12. Cavalcanti BF (1981) Residual Liquid Junction Potential in Binary Chloride Systems. M.Sc. Thesis, University of Cape Town, South Africa.

13. Cavalcanti BF (1994) Standard QUALI for Interpretation of Water Quality to Use Natural Municipal and Irrigation. Magazine Writing. State University of Paraiba, Campina Grande, PB 48-61.

14. Kemp R (1972) Water Softening by ion exchange. In: Proceedings of 14th Water Quality Conference. University of Illinois, EUA.

15. American Public Health Association (2000) Standard Methods for the Examination of Water and Wastewater. (19th edn), Washington D.C, USA.

16. Agostinho LCL, Cavalcanti BF, Nascimento L (2010) Treatment of eutrophic waters Using Electrolytic Process, Environmental Engineering, Espírito Santo do Pinhal 7: 73-86.

17. Cavalcanti BF (1993) Feman Proposed Method for the Removal of Iron and Manganese in Natural Waters Surface. In: 17th Brazilian Congress on Sanitary and Environmental Engineering. Annals of ABES 2: 298-314.

18. Kǘnin R (1972) Water Softening by Ion Exchange. Proc. 14th Water Quality Conf, Univ. of Illinois, USA.

0

100

200

300

400

500

600

700

800

900

1000

mg/

L Ca

CO3

scal

e

Sampling points in dry (d) and rain (r) seasons.

Non Carbonate Hardness, NCH (mg/LCaCO3)Alk = AlkHCO3-(mg/LCaCO3)CMB Model Total Hardness, THCMBModel (mg/LCaCO3) Total Hardness, TH (mg/LCaCO3)

Figure 3: Results obtained from the application of the CMB Model for calculating Total Hardness in the Bodocongó urban dam in both dry and rain seasons.

Citation: Nascimento L, Agostinho LCL, Cavalcanti BF (2012) Study Chemical Mass Balance Model for Hard and Saline Waters. 1:572 doi:10.4172/scientificreports.572