Prediction of Scale Formation in Calcium Carbonate ... - CAWQ

*Corresponding author; [email protected]

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Prediction of Scale Formation in Calcium Carbonate Aqueous Phase for Water Treatment and Distribution Systems

Alireza Bahadori

School of Chemical and Petroleum Engineering, Curtin UniversityGPO Box U1987, Perth, WA, Australia 6845

Accurate estimation of scale formation in distribution systems for drinking water and water treatment technologies is of utmost importance. A novel and simple method is presented here to predict the formation of calcium carbonate scaling as a function of pH, temperature, ionic strength of the solution, calcium cation, and bicarbonate anion concentrations, in order to evaluate the effect of solution conditions on precipitation tendency. The proposed simple method covers concentrations of calcium cations and bicarbonate anions up to 10,000 mg/L, temperatures up to 90°C, pressures up to 500 kPa, total ionic strength up to 3.6, and pH values ranging between 5.5 and 8. The predicted values are found to be in good agreement with the reported data with average absolute deviations being less than 2.6%. Predictive tool presented in the paper can be of immense practical value for engineers and researchers to have a quick check on the formation of calcium carbonate scaling at various conditions without opting for any experimental measurements. In particular, personnel dealing with water treatment and distribution systems would fi nd the proposed method to be user-friendly with transparent calculations involving no complex expressions.

Key words: calcium carbonate, scale, saturation index, ionic strength, water treatment

Introduction

Water quality is a major operational issue for drinking water and water treatment technologies. If the water is hard, scale control is required, and if it is soft, corrosion control becomes an issue (Bichai and Barbeau 2006). Internal corrosion in drinking water distribution systems of municipalities across the globe leads to investment of large amounts of funds in environmental technology, with the municipal sector controlling a considerable share of this sum (Sander et al. 1996). Distribution systems for drinking water and wastewater account for 80% of the investment in the municipal sector (Sander et al. 1996). Due to heating in most cases, the pH rise caused by the carbon dioxide loss involves c alcium carbonate precipitation, according to precipitation heterogeneous process involving a liquid and a solid phase. When the precipitate forms a deposit on the sides, in which case the term “scaling” is used (Gal et al. 2002). Water leaving the treatment plant should not be corrosive to pipes in the distribution system or in households, so as to protect pipes from corrosive agents in water namely, the pH (Ca2+) and alkalinity content of water, which are adjusted to calcium carbonate saturation equilibrium value at the temperature of water (Droste 1997). Normally, a slight tendency to precipitate calcium carbonate is maintained. This preserves a fi lm of calcium carbonate in distribution pipes and retards corrosion of pipes. This process is referred to as chemical stabilization of the water (Droste 1997). Water is considered to be stable when it is just

saturated with calcium carbonate (i.e. it will neither dissolve nor deposit calcium carbonate) (Droste 1997). Water that has a tendency to dissolve calcium carbonate is usually termed an aggressive water. An aggressive water is not necessarily innately water corrosive than a stable water. Owing to its ability to remove the protective CaCO3 barrier, aggressive water will indirectly enhance the corrosion of pipes (Droste 1997). The process of fouling in the water is very complicated (Chen et al. 2005) and it consists of four steps: (1) ions in water form salt molecules with low solubility; (2) molecules bond and arrange to form minicrystals and begin to granulate; (3) lot of crystals congregate, deposit, and cause fouling; (4) formation of various types of scale under different conditions (Xiaoyan et al. 2009). Due to the complexity of precipitation process, the saturation index (SI) is calculated to estimate calcium carbonate precipitation in the experiments. SI is generally used to describe the saturation state (from a thermodynamic point of view) of aqueous phase composition against different solids (Barat 2008). The SI parameter is widely used to estimate the potential for precipitation of different solids from an equilibrated aqueous phase speciation. When SI is equal to zero, the solution is considered to be in equilibrium; when SI is negative, the solution is considered to be undersaturated and no precipitation occurs; when SI is positive, the solution is considered to be supersaturated and precipitation could occur. Therefore, SI values can be used as a guide to evaluate the effect of the solution conditions on the tendency and extent of the precipitation (Barat 2008). Calcium carbonate dissolution is a chemical reaction limited process at room temperature, and therefore

Water Qual. Res. J. Can. 2010 · Volume 45, No. 3, 379–389Copyright © 2010, CAWQ

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c alcium carbonate dissolution occurs quickly relative to other processes operating in the system. In other words, the dissolution process is primarily controlled by the rate at which reactants/products are transported to/from the solid–liquid interface, so that increasing fl ow (transport) rates generally cause more rapid dissolution (Singurindy and Berkowitz 2005).

Prediction of Carbonate Scaling Tendency

Langelier (1936) proposed the SI concept initially, followed by Ryznar with the concept of stability index (Patton 1986). Hard water usually refers that water containing a high content of metallic ions, mainly calcium (Ca), magnesium (Mg), and iron (Fe) (Chilingar et al. 2008). The total hardness of water (in terms of mg/L of CaCO3), is determined from a water analysis by converting the mg/L of Ca++, Mg++, and Fe++’ to CaCO3, equivalent in mg/L. The total alkalinity is determined by converting mg/L of HCO3—, CO3—, and OH— to mg/L of CaCO3 (Chilingar et al. 2008). The term ‘scale’ refers to any hard deposit on the surface of equipment in the presence of water. Carbonate, hydroxide, oxide, and sulfi de scales may be removed by acidifi cation, whereas sulfate, phosphate, and ferricyanide scales are not soluble in acid. The latter are very diffi cult, if not impossible to remove by means other than mechanical. Calcium carbonate scaling is a function of pH, temperature (T), ionic strength of the solution (I), calcium cation, and bicarbonate anion concentrations (Chilingar et al. 2008). Table 1 presents factors for conversion of ion concentration (mg/L or meq/L) to I (Chilingar et al. 2008).

The chemistry of calcium carbonate deposition can be understood by examining the following formulae:

(1)

(2)

So overall reaction will be:

(3)

(4)

As pressure decreases during production, CO2 is released and CaCO3 precipitates:

Deposition of calcium carbonate will occur if reactions 3 and 4 are shifted to the right. The following changes to several parameters may cause the equilibria to shift to the right (Chilingar et al. 2008):

1. An increase in temperature2. Decrease in pressure3. A loss of dissolved carbon dioxide4. An increase in pH

Langelier (1936) was the fi rst scientist to develop the scale prediction formula:

(5)

(6)

Stiff and Davis (1952) have simplifi ed the work of Langelier (1936) on scaling index of oilfi eld waters (i.e. their tendency to deposit calcium carbonate scale). They defi ned the stability index (SI) as follows:

(7)

(8)

It is a c ommon practice to adjust waters to SI value of 0.2 by addition of the appropriate alkalinity or acidity agent (Droste 1997). Lime changes both calcium and alkanity concentrations. Other agents that can be used to adjust the water to the desired conditions include Na2C03, CO2, and strong acids or bases such as HCl and NaOH (Droste 1997).The SI is widely used as a qualitative indication of the amount of potential CaCO3 deposition.

In light of the above mentioned status and issues faced by the water treatment industry, there is a current and essential need for the development of a practical, reliable, and easy-to-use predictive tool for practice engineers and researchers for accurate determination of pH required for the precipitation of CaCO3. The present study discusses the formulation of such a simple predictive tool which can be of signifi cant importance to water practitioners.

Prediction of Calcium Carbonate Scale Formation

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Methodology for the Development of a Novel Predictive Tool

The required data to develop the tool includes reported data (Stiff and Davis 1952; Chilingar et al. 2008) for correction factor (K) as a function of T and I. The following methodology has been applied to develop the tool.

Firstly, K is correlated as a function of I for different T values. Secondly, the calculated coeffi cients for these equations are correlated as a function of T. The derived polynomials are then applied to calculate new coeffi cients for equation 9 to predict K. Table 2 shows the tuned coeffi cients for equations 10 to 13. In brief, the following steps are repeated to tune the correlation’s coeffi cients.

1. Correlate K as a function of I for a given T in K.2. Repeat Step 1 for other total T values.3. Correlate corresponding polynomial coeffi cients, which were obtained for different I versus T in K are,

a = f (T), b = f(T), c = f(T), d = f(T) (see equations 15-18).

Equation 14 represents the proposed governing equation in which four coeffi cients are used to correlate K as a function of T and I, where the relevant coeffi cients have been reported in Table 2.

(9)

Where:

(10)

(11)

(12)

(13)

These optimum tuned coeffi cients help to predict K as a function of I for T up to 90°C, as well as I up to 3.6. The optimum tuned coeffi cients given in Table 2 can be retuned quickly according to proposed approach if more data are available in future. The above mentioned methodology is applied to correlate the solubility factor (Sf) as a function of T and P and the equations 14-18 are the results of these formulations.

(14)

Where:

(15)

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(16)

(17)

(18)

Then R’ factor is calculated to take into account of the Sf, CO2 mole fraction.

(19)

Equation 20 is used to calculate the pH of solution.

(20)

Equations 21 and 22 relate pCa and pAlk parameters as functions of calcium cation and (HCO3– and CO3–) con-centrations.

(21)

(22)

Step-by-Step Proposed Method for Prediction of CaCO3 Scaling

The following steps are followed in case of CaCO3:

1. Determine I using Table 1.2. Determine K from equations 9-13 and Table 2:

3. Determine pCa from equation 21:

4. Determine pAlk from equation 22:

Calculate pHs from equation 6:

5. Calculate Sf from equations 14-18 and Table 3:

6. Calculate R’ ratio from equation 19:

7. Determine pH from equation 20:

8. Calculate SI from equation 8:

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Our efforts have been directed at formulating simple-to-use predictive tool that can help engineers to evaluate the effect of the solution conditions, on both the tendency and extent of the precipitation as a function of pH, temperature, ionic strength of the solution, calcium cation, and bicarbonate anion concentrations. The correlation proposed in the present work is simple and unique expression which is non-existent in the literature. We have additionally selected exponential functions to develop the correlation, because these functions are smooth and well-behaved (i.e. smooth and non-oscillatory) equations which will enable more accurate predictions (Bahadori et al. 2008; Bahadori and Vuthaluru 2009; Bahadori et al. 2009).

Results and Discussion

Figures 1 and 2 show the results of the proposed method for predicting the correction factor as a function of temperature and ionic strength, in comparison with literature reported data (Stiff and Davis 1952; Chilingar et al. 2008). It is evident from Figs. 1 and 2 that there is a good agreement between predicted values (for wide range of temperatures and total dissolved solid) and the reported data in literature (Stiff and Davis 1952; Chilingar et al. 2008). Table 4 shows the accuracy of proposed method in terms of average absolute deviation percent with some typical reported data. It shows the proposed correlation has an average absolute deviation

Fig.1. Comparison of K against literature reported data for various ionic strengths (Stiff and Davis 1952; Chilingar et al. 2008).

Fig. 2. Comparison of predicted K against literature reported data for various ionic strengths for T more than 50°C (Stiff and Davis 1952; Chilingar et al. 2008).

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percent less than 2.6, which is very small deviation from the reported data. Figure 3 illustrates the performance of proposed correlation to predict K for various ionic strengths. This graph shows smooth performance of the proposed method. Figure 4 shows prediction of Sf against literature reported data wherein good agreement

between predicted values and reported data is evident. Figure 5 shows the performance of proposed method to predict the relationship between pH and R’ value. Figures 6 and 7 illustrate the variation of pCa and pAlk from concentrations of Ca2+ and (HCO3

-) and (CO32-) against

literature reported data.

Fig. 3. Performance of proposed correction for K for various I.

Fig. 4. Prediction of solubility factor against literature reported data, (Variation of Sf with temperature and pressure) (Jones 1988; Chilingar et al 2008).

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Fig. 5. Relationship between pH and R’ value (Jones 1988, Chilingar et al. 2008).

Fig. 6. Determination of pCa from concentrations of Ca2+ against literature reported data (Langelier 1936; Chilingar et al. 2008).

The proposed simple method covers the concentration of calcium cations and bicarbonate anions up to 10,000 mg/L, temperatures up to 90°C, P up to 500 kPa, I up to 3.6, and pH between 5.5 and 8. Figure 8 shows Parity chart to illustrate the accuracy of the proposed tool to predict K. Sample calculations shown below clearly demonstrate the simplicity of the proposed method, and the benefi ts associated with such estimations. The present approach is of practical signifi cance for water treatment industries in terms of assessing operational issues. In particular, the proposed correlation gives an advance

indication of key parameters which could potentially enable practice engineers to take appropriate remedial measures to control the quality of water to avoid scale formation in water distribution systems.

Sample calculation for the practice engineers

Given below are classic examples showing how the information evolving out of this proposed predictive tool can be used to understand and estimate the SI issues which could potentially infl uence the quality of water.

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Fig. 7. Determination of pAlk from concentrations of [HC03-+CO32-] against literature reported data (Langelier 1936; Chilingar et al. 2008).

Example 1. Determine the SI CaCO3 according to the data in Table 5, assuming water is saturated with a gas containing 5 mol % CO2 at 1 bar total P for 30°C. Table 5 shows water analysis for these example calculations. The following steps are followed in the case of CaCO3:

1. Determine I using Table 1:

Fig. 8. Parity chart to show accuracy of proposed tool to predict K.

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Thus, I (sum of the above) is equal to 1.653.

a = 2.078 (from equation 10)b = 2.199 (from equation 11)c = -1.087 (from equation 12)d = -1.087 (from equation 13)K = 3.410 (from equation 9)(Ca2+) = 164 mg/L (from table 5)(HCO3

–) = 55 mg/L (from table 5)Determine pCa = 2.2422 (from equation 21)

Determine pAlk = 2.0887 (from equation 22)

2. Thus,

pHs = K + pCa + pAlk = 7.7411 (from equation 6)

Determine ratio R’ (assuming that the gas in contact with water contains 5 mol % CO2 at total P of 1 bar):

(from equation 19)

,where mole fraction of CO2 is determined from gas analysis and Sf is determined from equation 14 at a temperature of 60°C (333.15 K) and P of 100 kPa,

a = -1.225 x 102 (from equation 15)b = 1.298 (from equation 16)c = -4.160 x10-3 (from equation 17)d = 4.208 x 10-6 (from equation 18)Sf = 34.363 (from equation 14)

Determine pH from equation 20 (pH versus R’):

pH = 5.716 (from equation 20)pH decreases with increasing concentration of CO2 in water.

Determine the SI:

SI = pH(actual) –pHS (from equation 8)SI = 5.716 - 7.7411 = -2.025

If the SI is negative, CaCO3 scale formation likely does not occur in water distribution systems.

Example 2: Given below is another classic example (Chilingar et al. 2008) showing how the information evolving out of the proposed predictive tool can be used to understand and estimate the SI issues which could potentially infl uence the quality of water. On assuming a mixture of 50% volume seawater and 50% volume produced concentrate water from membrane treatment of sea water (see Table 6), determine the SI CaCO3. Assume that the water mixture is saturated with a gas containing 5 mol % CO2 at 1 bar total P for 30°C and

60°C. Table 6 shows water analysis for these example calculations. The following steps are followed in the case of CaCO3:

3. Determine I using Table 1:

Thus, I (sum of the above) is equal to 1.653.

a = 2.078 (from equation 10)b = 2.199 (from equation 11)c = -1.087 (from equation 12)d = -1.087 (from equation 13)K = 3.410 (from equation 9)(Ca2+) = 7237 mg/L (from table 6)(HCO3

) = 325.5 mg/L (from table 6)Determine pCa = 0.804 (from equation 21)Determine pAlk = 2.088 (from equation 22)

4. Thus,

pHs = K + pCa + pAlk = 6.303 (from equation 6)

Determine ratio R’ (assuming that the gas in contact with water contains 5 mol% CO2 at total P of 1 bar):

(from equation 19)

,where mole fraction of CO2 is determined from gas analysis and Sf is determined from equation 14 at a temperature of 60°C (333.15 K) and a P of 100 kPa,

(from equation 15) (from equation 16) (from equation 17) (from equation 18) (from equation 14)

Determine pH from equation 20 (pH versus R’):

pH = 8.4206 (from equation 20)pH decreases with increasing concentration of CO2 in water.

Determine the SI:

SI = pH(actual) - pHS (from equation 8)SI = 8.4206-5.487 = 2.933

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As the SI is positive, once again CaCO3 scale formation is likely to occur in water distribution systems.

The results are compared with the Rothberg Tamburini & Winsor Model (AWWA 1996), and data reported in the literature (Chilingar et al. 2008) show SI of around 5.37. The other reported SI value by Chilingar et al. (2008) is 3.5, suggesting that the proposed predictive tool can provide accurate results. This is due to calculating SI via ionic strength, which as proposed here, is a more accurate determination of SI. In addition, the proposed predictive tool employs basic algebra equations so it can be quickly and easily solved by spreadsheet. The proposed tool is easy to use which employs simple algebraic equations and can be solved by a simple calculator quickly by any water practitioner.

Conclusions

Water leaving the treatment plant should not be corrosive to the pipes in the distribution system or in households to prevent pipes from corrosive agents in the water such as pH, Ca2+, and alkalinity content of water, which are adjusted to the calcium carbonate saturation equilibrium value at the temperature of water. In this work, an attempt has been made to predict the formation of calcium carbonate scaling as a function of pH, temperature, ionic strength of the solution, calcium cation, and bicarbonate anion concentrations, to study the effect of solution conditions on the tendency and extent of the precipitation. Results from the proposed method have been compared with reported data and found good agreement with average absolute deviation being around 2.6%. The proposed tool appears to be superior owing to its accuracy and simple background, wherein the relevant coeffi cients can be retuned quickly if new and more accurate data are available in the future. Examples shown for the benefi t of water practitioners clearly demonstrate the usefulness of the proposed tool for practice engineers.

It is expected that our efforts in this investigation will pave the way by arriving at an accurate measure of the effect of the solution conditions on the tendency and extent of the precipitation which can be used by the water treatment personnel for monitoring the operational parameters periodically. The simple correction factor proposed in the paper can be of immense practical value for engineers and researchers to have a quick check on quality of water at various conditions without employing any experimental measurements. In particular, personnel dealing with water treatment and distribution systems would fi nd the proposed method to be user-friendly involving no complex expressions with transparent calculations.

Acknowledgements

Useful comments from two anonymous reviewers and the editor are acknowledged and led to improvements in the original version of the paper.

List of symbols A: Tuned coeffi cientB: Tuned coeffi cientC: Tuned coeffi cientD: Tuned coeffi cientI: Total ionic strengthK: Correction factor for total ionic strength and temperaturepH: Actual pH value in the systempHs: pH value when the calcium carbonate achieves saturation in the systemSf: Solubility factorSI: The saturation indexT: Temperature, KP: Pressure, kPa

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References

AWWA (American Water Works Association). 1996. The Rothberg Tamburini & Winsor Model for Corrosion Control and Process Chemistry, Version 3.0, AWWA. Denver, Colorado.

Barat R, Montoya T, Borrás L, Ferrer J, Seco A. 2008. Interactions between calcium precipitation and the polyphosphate-accumulating bacteria metabolism. Water Res. 42:3415-3424.

Bahadori A, Vuthaluru HB. 2009. Prediction of Bulk modulus and Volumetric Expansion Coeffi cient of Water for Leak Tightness Test of Pipelines. Int. J. Pres. Ves. Pip. 86:550-554.

Bahadori A, Vuthaluru HB, Mokhatab S. 2009. Simple Correlation Accurately Predicts Aqueous Solubility of Light Alkanes. Energy Sources Part A. 31:761-766.

Bahadori A, Vuthaluru HB, Tade MO, Mokhatab S. 2008. Predicting Water-Hydrocarbon Systems Mutual Solubility. Chem. Eng. Technol. 31:1743-1747.

Bichai F, Barbeau B. 2006. Assessing the disinfecting power of chlorite in drinking water. Water Qual. Res. J. Can. 41:375-382.

Chen T, Neville A, Yuan MD. 2005. Calcium carbonate scale formation - assessing the initial stages of precipitation and deposition. J. Petrol Sci. Eng. 46:185-194.

Chilingar GV, Mourhatch R, Al-Qahtani GD. 2008. The Fundamentals of Corrosion and Scaling for Petroleum and Environmental Engineers. Gulf Publishing Company, Texas, United States.

Droste RL. 1997. Theory and Practice of Water and Wastewater Treatment. John Wiley & Sons, New York.

Gal JY, Fovet Y, Gache N. 2002. Mechanisms of scale formation and carbon dioxide partial pressure infl uence. Part II. Application in the study of mineral waters of reference. Water Res. 36:764-773.

Jones LW. 1988. Corrosion and Water Technology for Petroleum Producers. Oil and Gas Consultants Inc., Tulsa, Oklahoma.

Langelier WG. 1936. The analytical control of anti-corrosion water treatment. J. Am. Water Works Ass. 28:1500.

Patton CP. 1986. Applied Water Technology. Campbell Petroleum Series, Normanhurst, Oklahoma.

Sander A, Berghult B, Broo AE, Johansson EL, Hedberg T. 1996. Iron corrosion in drinking water distribution systems. The effect of pH, calcium and hydrogen carbonate. Corros. Sci. 38:443-455.

Singurindy O, Berk owitz B. 2005. The role of fractures on coupled dissolution and precipitation patterns in carbonate rocks. Adv. Water Resour. 28:507-521.

Stiff HA, Davis LE. 1952. A method for predicting the tendency of oilfi eld waters to deposit calcium carbonate. Pet. Trans. AIME 195:213.

Xiaoyan L, Jung ang L, Qianya Z, Jinlai F, Yingli L, Jingxin S. 2009. The analysis and prediction of scale accumulation for water-injection pipelines in the Daqing Oilfi eld. J.Petrol.Sci. Eng. 66:161-164.

Received: 1 October 2009; accepted: 2 April 2010.

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Prediction of Scale Formation in Calcium Carbonate ... - CAWQ