PEER-REVIEWED SCALE

Mineral Scale Management Part II. Fundamental Chemistry

ALAN W. RUDIE AND PETER W. HART

ABSTRACT: The mineral scale that deposits in digesters and bleach plants is formed by a chemical precipitation process.As such, it is accurately modeled using the solubility product equilibrium constant. Although solubility product identifies the primary conditions that must be met for a scale problem to exist, the acid-base equilibria of the scaling anions often control where in the process scale will occur. These equilibria are the primary control method to minimize or pre­ vent scale in a bleach plant. Both the acid-base equilibria and solubility product equilibria are influenced by temper­ ature and ionic strength. This paper reviews the chemistry of precipitation and acid-base equilibria. The Gibbs free energy expression is presented as a method to estimate equilibrium constants at temperatures in the bleach plant.The effect of ionic strength on ion activity and its influence on these processes are also discussed. Application: Preventing scale problems requires an understanding of the solubility product equilibrium, the acid-base equilibrium of the scaling anion, and the effects of temperature and ion activity on these equilibria.

ome pulp mills have always experi­ trations in the wood supply. Those conditions that barely exceed the Senced mineral scale buildup, but cases required more detailed equilibri­ saturation concentrations, it can this problem has increased with um modeling and will be handled in take hours or longer for an obvi­ efforts to comply with environmental the third paper of the series on non- ous precipitate to form. requirements.The recycling of washer process elements in the paper industry. filtrates to reduce effluent volume has • Some salts can exceed the solubil­ increased the concentrations of both OVERVIEW OF CHEMICAL cations and anions and with it the ity by an order of magnitude or PRECIPITATION more without precipitating [4]. potential for mineral scale deposits. Mineral scale formation is a chemical The switch from chlorine-initiated precipitation process. Although the This supersaturation condition bleach sequences to the use of chlo­ chemical phenomenon of precipita­ can be manipulated. One method rine dioxide in the first stage has tion can identify where and when of suppressing scale is to add decreased the ability of the bleach scale deposition is possible, it cannot chemicals that interfere with crys­ plant to remove calcium and barium determine that scale will definitely tal growth or interfere with crys­ in the first stage.The result has been a occur.The reasons are many; a few are listed here: tal nucleation [5,6]. Organic frag­ significant increase in the frequency ments may occur in bleach plant of calcium oxalate and barium sulfate filtrates that behave in these ways scale deposits in the first bleach stage • In locations where precipitation to suppress precipitation. and an increase in calcium carbonate is general and not directed deposits in the first extraction stage. toward a specific surface, fiber In particularly severe cases, the forma­ represents the largest surface • Numerous organic fragments can tion of calcium oxalate has also area in the process. Precipitates form complexes with trace met- occurred in later bleach stages [1,2]. that deposit on fiber are general- als.These complexes are in equi­ This paper is the second in a series ly-and at least temporarily-harm- librium with the free-solvated on mineral scale management.A collec­ less.These precipitates tend to trace metal and the organic frag- tion of case studies was presented in stay with the fiber and carry ment.The net effect of these the first paper [3]. Most of these scale trace elements further into the equilibrium processes is to problems were resolved using the fun­ bleaching process, where they reduce the concentration of free damental chemistry principles to be often cause problems. cations. For example, nearly all presented here. Several cases were carboxylic acids have a weak more difficult, usually because of • Precipitation is time and concen­ attraction for calcium and bari­ exceptionally high trace metal concen­ tration dependent [4]. Under um. Fragments with two acid VOL. 5: NO. 7 TAPPI JOURNAL 17 SCALE

groups form much more stable • Cation—A molecule containing PRECIPITATION complexes, but complexes with a positive charge.The trace More detailed explanations of precipi­ one or two appropriately placed metal nonprocess elements are tation and acid base equilibria can be found in any good analytical chem­ alcohol groups can also form all cations.The common cations istry textbook[4].The scale that forms stronger complexes. At present, in bleach plant scales are calci­ in digesters and bleach plants is basi­ we can not catalog all the possi­ um (Ca2+) and barium (Ba2+). cally a localized chemical precipita­ ble complexes and determine • Monovalent and divalent—Terms tion process. As such, it is usually their formation constants. described using the solubility product that refer to the charge of an convention. For the generalized chem­ Fortunately, in the bleach plant, ion. Monovalent anions and ical reaction, organic fragments that can form cations contain a single negative strong complexes are usually at or positive charge; divalent mA + nB pC + qD low concentrations, and frag­ anions and cations contain two ments that are common tend to The chemical equilibrium is usually negative or two positive charges. written as form weak complexes. It Typically, salts of monovalent appears that both can largely be (1) ignored in bleach plant environ­ anions and cations are quite sol­ ments. Precipitation models that uble. Salts containing a divalent ignore these effects, however, anion or cation, and two mono­ For solubility product, there is typical­ ly just one product. Following the represent a worst case analysis. valent ions of the opposite charge, are also typically very equilibrium expression convention, the numerator is the concentration of • Chemistry is often defined under soluble. But salts where both the the product. But, what is the concen­ unrealistic conditions. For exam­ anion and cation are divalent are tration of a precipitate? By convention, ple, what does “infinitely dilute” typically sparingly soluble or the concentration or, rather, activity of insoluble.This trend cannot be the precipitate is defined as 1.0 and mean, and where can this condi­ the equilibrium expression is inverted: tion be found in a pulp mill? The extended to trivalent ions (ions obvious answer is that whatever containing three charges). mA + nC AmCn infinitely dilute means, it does Because the charge density of not apply anywhere in a pulp trivalent ions is so high, they The solubility product expression is mill or bleach plant.We need to rarely exist in the 3+ or 3- state in (2) understand that the approxima­ solution and often form charged tions that allow us to extend molecules that are soluble. For the common precipitates encoun­ chemical principles to the condi­ • Molarity (M) and molality (m)— tered in a bleach plant, the chemical tions in a mill are just approxi­ equation and corresponding equilibri­ Molarity (M) is the molar concen­ um equations are as follows: mations. Because of this, results tration of a dissolved substance are not absolutes and are subject relative to a volume of 1 L. For calcium carbonate (lime, calcite or to some interpretation. Molality (m) is the molar concen­ aragonite), Ca2+ + CO 2- CaCO tration relative to 1 kg of total 3 3 TERMS AND GENERAL mass. Activity (a) is ion mobility (3) PRINCIPLES and is related to both the concen­ Some common terms in aqueous inor­ tration of the substance and the ganic chemistry are essential for For calcium oxalate, concentration of other dissolved Ca2+ + C O 2- CaC O understanding the chemical process­ 2 4 2 4 es involved in scale formation: ions. Ion activity is usually consid­ (4) ered to be the product of con­ centration (either molarity or • Anion—A molecule containing a and for barium sulfate (barite), negative charge.The typical molality) and the appropriate ion 2+ 2- Ba + SO4 BaSO4 scale-forming anions in the activity coefficient (f). At “infi­ bleach plant are carbonate nite” dilution and 25°C, molarity, (5) (CO 2- ), oxalate (C O 2-), and sul­ molality, and activity of a sub­ 3 2 4 Assuming equal molar concentrations 2- stance are all the same. fate (SO4 ). of anion and cation, all three precipi­

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tate at about a 10-4 molar concentration or about 4 or 5 parts per million.The typical pulp mill bleach plant receives over a ton of calcium a day in the unbleached pulp, and all of this must be removed to avoid scale problems.

ACID-BASE EQUILIBRIA A key issue in precipitation is that the anions that partici pate in the precipitation process are the divalent anions, - - - not HCO3,HC2O 4 , or HSO4 . This means that the conditions for scale formation are strongly influenced by the process pH. The general chemical equation for an acid equilibrium is written as HA ➝H+ + A-. The resulting equilibrium expression is shown in Eq. 6:

(6) Figure 1. The pH dependence of carbonic acid, bicar + + bonate, and carbonate. It is common to express H as H3O , recognizing that the proton is heavily solvated and does not exist independent of the surrounding water. This convention has not been adopted here for simplicity.The choice as to how to repre sent this cation does not affect the equilibria or calculation to be discussed in this paper. For all three cases contributing to scale, there are two acid dissociations to consider, but only the second of the two is important to the precipitation process. For carbon ic acid,

➝+ - H2CO 3 H + HCO3 - ➝+ 2 HCO3 H + CO3 The corresponding equilibrium equations are presented in Eq. 7; Fig. 1 shows the pH dependence of the carbonates.

Figure 2. The pH dependence of oxalic acid. (7a,b)

The carbonate ion dominates at pH above 10, but it is still measurable at pH levels down to 7. Bicarbonate dominates between pH 6 and 10, and carbonic acid dominates at pH below 6. Since many paper machines operate with calcium carbonate filler at neutral pH, we know that lime scale is somewhat stable down to a pH of 7. The chemical equations for oxalic acid are

➝+ - H2CO 2 4 H + HC2O 4 - ➝+ 2 HC2O 4 H + C2O 4

Figure 3. Speciation of sulfate and bisulfate relative (8a,b) to pH.

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The oxalate ion exists at any pH above approximately 2. It is the dominant form of oxalate at pH above 4. Figure 2 shows the acid-base speciation of oxalic acid. Sulfuric acid is a strong acid. For practical purposes, when sulfuric acid is diluted with water, the first proton is always dissociated.Thus, only the second acid dissociation constant usually needs to be considered:

-➝+ 2 HSO4 H + SO4 .

(9)

Figure 3 shows the pH dependence of sulfuric acid and the sulfates. The sulfate ion dominates at any pH above 2 and Figure 4. Effect of pH on precipitation of calcium car still exists at pH near 0. bonate. Carbonates at 1 M, Calcium at 0.01 mM. When evaluating the likelihood of precipitation, both the acid-base behavior of the anion and the solubility prod uct need to be considered. Precipitation is likely only when the basic form, the divalent anion, and the cation com bined exceed the solubility product. Figure 4 shows a cal culation for precipitation of calcium carbonate. Precipitation starts at a pH of 8, about the same pH where the graph shows a measurable amount of carbonate. For this graph, carbonate was at 1 M and calcium at 0.01 mM. Calcium carbonate precipitation was determined using ESP equilibrium software from OLI Systems, Inc. (Morris Plains, New Jersey), and the scale for the precipitate was adjusted to make it fit on the graph. A similar graph of calcium oxalate precipitation is pro vided in Fig. 5, in which the oxalate pH data are the same as those in Fig. 2, at a 1 M concentration. Calcium oxalate precipitation was calculated for a solution with a 1mM Figure 5. Calcium oxalate precipitation relative to pH. starting concentration of both calcium and oxalate. Calcium oxalate precipitation curve calculated for cal These two graphs demonstrate the same point: precip cium and oxalate at 1 mM starting concentration. itation does not usually occur at pH conditions where the divalent ion is at low concentration. For calcium carbon ate, this pH is 7-8, and for calcium oxalate it is about 2.5. For sulfate, this would be a pH around 0.5. This feature makes pH control the most powerful tool for eliminating calcium scales in bleach plants. Although solubility product and the acid-base chemistry of the precipitating anions have the biggest influence on when and where a process will develop mineral scale, other process variables also influence scaling. Temperature is probably the next in significance. Most salts become more soluble as the temperature increases, and this is true for bar ium sulfate and calcium oxalate. However, the solubility of calcium carbonate decreases with temperature (Fig. 6).The temperature sensitivity of this equilibrium is the reason that calcium carbonate scale is common in digester heaters and other process heat exchangers.The temperature effect may Figure 6. Change in solubility product with tempera ture. K for barium sulfate has been multiplied by also contribute to calcium oxalate and barium sulfate scale sp on washer wires. As the filtrate penetrates the mat and 1010 and calcium carbonate by 109 to fit both curves enters the drop leg, it cools a few degrees. on the same graph. Notice that Ksp increases with temperature for barium sulfate, but decreases with temperature for calcium carbonate. 20 TAPPI JOURNAL JULY 2006 SCALE

Figure 7. Measured activity coefficient for NaCl, CaCl2, Figure 8. Concentration of sulfate produced when

Na2CO3, and CdSO4. using sulfuric acid or sodium sesquisulfate for pH adjustment of water.

ION ACTIVITY The solubility product and acid-base equilibria presented 6 Å, and for barium and carbonate, 5 Å. Because of the log thus far are accurate only for very dilute conditions. To scale, the exact values do not have a large effect on f, and move from the laboratory to conditions in the bleach it is common to use 0.5 for A and either 1.0 or 1.5 for ba. plant, we must understand how other dissolved ions affect I is ionic strength, defined as the equilibrium. As salts build up in solution, the anions and cations begin to organize to reduce repulsion of like I = (C z 2 + A z 2)/2 (11) charges.With increasing ionic strength, the weak organiza­ i i i i tion of solution charges begins to strengthen and impede ion mobility. For a calcium cation to come into contact where Ci represents the cations in solution, Ai the anions, with a carbonate anion, it may need to “escape” a weakly and z their respective charges.The sums are over-all anions attractive cage of chloride and hydroxide anions and the and cations in solution. surrounding weakly repulsive cage of sodium, potassium, The extended Debye-Hückel equation is considered and magnesium cations.The influence of ionic strength is accurate to 0.05 molar ionic strength and provides sufficient known as ion activity. Figure 7 shows activity coefficients accuracy for use in bleach plant equilibrium modeling. It is for sodium chloride (NaCl), calcium chloride (CaCl ), sodi­ 2 not accurate at the high ionic strengths found in the pulp um carbonate (Na CO ), and cadmium sulfate (CdSO ).The 2 3 4 mill and recovery. The Pitzer equations provide better esti­ ionic strength in the bleach plant is around 0.05 M in the first two stages and drops to about 0.02 M in the later mates at high ionic strength and are more suitable for equi­ stages.The activity of the monovalent ions ranges from 0.8 librium modeling of these areas of the mill [7,8]. to 0.9 and that of the divalent ions from about 0.45 to 0.6. In practical terms, the real solubility of calcium carbonate, EFFECT OF TEMPERATURE calcium oxalate, or barium sulfate is about five times the As shown in Fig. 6, solution equilibria are often influenced solubility as determined by the solubility product, without by temperature. Chemical equilibria are related to Gibbs considering ion activity. energy by the expression Most standard chemical references provide tables of activity coefficients suitable for evaluating the solubility G = -RT ln(K) = H— T S (12) limit for scale formation. For modeling purposes, it is use­ ful to estimate the activity coefficient using the extended where G, H, and S are the Gibbs energy of reaction, enthalpy Debye-Hückel equation: of reaction, and entropy of reaction, respectively, R is the gas constant, and T is temperature in K. Graphing ln(K) vs 1/T provides a straight-line relationship where the intercept (10) is S/R and slope is H/R.This provides a mechanism to esti­ mate acid dissociation constants and solubility products for temperatures that have not been directly measured or are slightly beyond the range of convenient laboratory experi­ The values A and b vary slightly with temperature, but are ments. As with activity coefficients, the free energy rela­ around 0.5115 and 0.3291, respectively. The value of a is tionship is not always accurate, but the deviation from lin­ anion- and cation-specific. For calcium and manganese, a is earity is usually over extended temperature ranges or out-

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side the range of interest in the bleach proton (cation) and f2 is the activity and plant. 2- + coefficient for the divalent sulfate. SO4 = Se + H (22) Writing the equation this way recog­ EXAMPLE OF PH CONTROL nizes that the activity coefficients for and substituting into Eq. 17 gives As an example of the use of these the monovalent proton and bisulfate equilibrium concepts, consider the anion are nearly the same, and, for use of sulfuric acid and sodium practical purposes, equal within the sesquisulfate for adjusting pH. Sodium accuracy of the formulas for estimat­ sesquisulfate (Na HS O ) is a bisalt of ing activity coefficients.They cancel. Again, reorganizing this into a quad­ 3 2 8 2- sodium bisulfate and sodium sulfate Substituting Eq. 16 for [SO4 ] and ratic equation: - that can be obtained as the spent acid Eq. 15 for [HSO4 ], Eq. 17 becomes from some chlorine dioxide genera­ tors. The acid equilibrium was pre­ sented earlier as Eq. 9. Sulfuric acid is a strong acid, and the first of the two protons is always dissociated under Reorganizing into a quadratic and (23) normal laboratory conditions.The sec­ reinserting the square brackets gives ond dissociation is still a strong acid, the following: Figure 8 shows the results, where but it has been estimated with a pKa process pH is plotted against sulfate around 2.The reaction is ion concentration when using sulfuric acid and sodium sesquisulfate for pH control. At pH above 4, sodium H SO ➝H+ + HSO -➝2H+ + SO 2- 2 4 4 4 sesquisulfate results in four times the sulfate ion concentration of pH con­ Determining the amount of acid trol with sulfuric acid. At pH 2.5, the needed to reach a target pH using sesquisulfate forms a buffer. The sulfuric acid requires the following (18) amount of sesquisulfate required mass balance equations: increases the sulfate concentration to This is solved using the quadratic for­ more than six times the sulfate con­ + + 2- mula, providing the value of [H ] for centration when using sulfuric acid. H = 2(SO4 ) + HSO4 (13) S = SO 2-- + HSO (14) any given total charge of sulfuric acid. The two key issues raised by Fig. 8 are T 4 4 Equations 15 and 16 can then be used as follows: 1.Use of sodium sesquisulfate to where ST is the total amount of sulfu­ to determine the solution concentra- tions of HSO- and SO 2­. control the pH substantially increases ric acid added. Note that for simplici­ 4 4 the concentration of sulfate in the ty, the square brackets indicating bleach plant and with it the potential Similarly, for sodium sesquisulfate, the molar concentration have been for encountering barium sulfate scale. dropped. chemical reaction is 2.It is not possible to decrease the These two equations are solved to sulfate ion concentration and the + 2- - 2- - give SO and HSO in terms of hydro­ Na3 HS 2O 8 3Na + SO4 + HSO4 potential for barium sulfate scale 4 4 + 2- + - gen and S : 3Na + (1+x)SO4 + xH + (1-x)HSO using sulfuric acid. The sulfate ion T concentration continues to rise, even HSO - = 2S — H+ (15) This leads to the mass balance at very low pH. 4 T equations CONCLUDING REMARKS SO 2- = H+ — S (16) 4 T H+ = Se — HSO - (19) The chemical process that forms min­ 4 eral scale in pulp mills and bleach Rewriting Eq. 9 with the ion activity plants is precipitation.The conditions 2Se = SO 2- + HSO - (20) coefficients added to the equation 4 4 that lead to scale formation are readi­ gives ly understood in terms of the solubili­ where Se is used to indicate total ty product for the precipitate and the sesquisulfate. acid-base behavior of the scaling anion. An evaluation of these equilib­ 2- - ria demonstrates that calcium oxalate (17) Solving for SO4 and HSO4 as before gives scale is unlikely to form at a pH of 2.5 and below, and calcium carbonate where f is the activity coefficient for 1 HSO - = Se — H+ (21) scale is unlikely to form at a pH below the monovalent bisulfate anions and 4 8. A simplified solubility product cal­

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culation is a good starting point for article was written and prepared by Winston, Inc., New York, 1969, pp. understanding scale problems in a U.S. Government employees on 164-173. bleach plant, but both the solubility official time, and it is therefore in 5.Guo, J. and Severtson, S.J., TAPPI J., product and acid equilibrium con the public domain and not subject 1(8): 21(2002). stants are temperature dependent. In to copyright. The use of trade or addition, the high dissolved ion con 6.Guo, J. and Severtson, S.J., Ind. firm names in this publication is centration that exists in pulp mill Eng. Chem. Res., 42(14): bleach plants reduces ion activity.The for reader information and does 3480(2003). effect of temperature and ion activity not imply endorsement by the U.S. 7.Pitzer, K.S., J. Phys. Chem., 77(2): is to increase the solubility of calcium Department of Agriculture of any 268(1973). oxalate and barium sulfate by about product or service. 8.Pitzer, K.S. and Kim, J.J., J. Am. one order of magnitude.These effects Chem. Soc., 96(18): 5701(1974). need to be included when performing LITERATURE CITED 9.Rudie, A.W. and Hart, P.W., accepted a rigorous analysis of scale formation for publication TAPPI J. in a bleach plant. 1.Dexter, R.J. and Wang, X.H., TAPPI In the third paper of this series[9], 1998 Pulping Conference other factors that influence the solu Proceedings, TAPPI PRESS, Atlanta, This paper is also published on bility of trace cations in bleach plants Georgia, USA, p. 1341. www.tappi.org will be discussed and a detailed equi 2.Anker, L.S., Zidovec, D.F., and Korol, and summarized in the June, 2006 librium analysis performed for one of R.T., TAPPI 2001 Pulping Conference the mill case studies presented in part Solutions! for People, Processes Proceedings, TAPPI, Atlanta (CD and Paper magazine (Vol. 89 No. 6). I of this series[3].TJ only). 3.Hart, P.W. and Rudie, A.W., TAPPI J., Received: June 29, 2005 5(6): 22(2006). Note: The Forest Products Laboratory Revised: April 11, 2006 is maintained in cooperation with 4.Skoog, D.A. and West, D.M., Accepted: April 19, 2006 the University of Wisconsin. This Fundamentals of Analytical Chemistry, Holt, Rinehart, and

INSIGHTS FROM THE AUTHORS uses the ion exchange, acid equilibrium for oxalate An unanticipated outcome of the switch from chlo­ and solubility product for calcium oxalate to deter­ rine initiated bleaching sequences to chlorine diox­ mine the likelihood of mineral scale problems for a ide as the first stage bleaching agent was a consid­ specific set of conditions and a process change. erable increase in the number of mills experienc­ Most calcium oxalate scale problems can be ing mineral scale deposits. After five years of effort resolved by adjusting the first chlorine dioxide eliminating scale deposit problems, it had become stage terminal pH to 2.5. Many barium sulfate scale

clear that there was not a general understanding of problems can be resolved by replacing ClOx gener­ the basic chemistry controlling scale deposits in ator spent acid with commercial sulfuric acid. pulp mills and bleach plants. This series of papers will help mill operators and This is a three-part series addressing mineral scale process engineers to understand why these problems. changes work and how to evaluate alternative • The first paper related a series of case studies when these simple solutions fail. where scale has been eliminated. The process Rudie is with the U. S. Department of Agriculture Forest adjustment that succeeded in eliminating the scale Service, Forest Products Laboratory, Madison, Wisconsin, problem is presented and the relevant chemistry USA; Hart is with MeadWestvaco Corporation, Chillicothe, discussed. Ohio, USA; email Rudie at [email protected]. • The second paper in the series presented the sol­ ubility product equilibria for calcium carbonate, calcium oxalate and barium sulfate, and the acid equilibria for the precipitating anions. It uses the acid equilibrium for sulfuric acid to demonstrate the impact of using sodium sesquisulfate for pH control in a bleach plant. • The third paper provides a detailed analysis of one case study showing how pH adjustment can eliminate calcium oxalate scale in a mill. This paper Rudie Hart VOL. 5: NO. 7 TAPPI JOURNAL 23