Handbook of Corrosion Engineering Episode 1 Part 5 potx

Brucite saturation levels were includedbecause of the potential for magnesium silicate formation as a resultcalcu-of the adsorption calcu-of silica upon precipitating magnesium hydroxide

The PSI is calculated in a manner similar to the Ryznar stabilityindex Puckorius uses an equilibrium pH rather than the actual system

pH to account for the buffering effects:

PSI 2 (pHeq)  pHs

where pHeq 1.465 log10[Alkalinity]  4.54

[Alkalinity] [HCO3 ]  2[CO3 ]  [OH]

Larson-Skold index. The Larson-Skold index describes the corrosivity

of water toward mild steel The index is based upon evaluation of insitu corrosion of mild steel lines transporting Great Lakes waters Theindex is the ratio of equivalents per million (epm) of sulfate (SO4 )and chloride (Cl) to the epm of alkalinity in the form bicarbonate pluscarbonate (HCO3  CO3 )

Larson-Skold index

As outlined in the original paper, the Larson-Skold index correlatedclosely to observed corrosion rates and to the type of attack in theGreat Lakes water study It should be noted that the waters studied inthe development of the relationship were not deficient in alkalinity orbuffering capacity and were capable of forming an inhibitory calciumcarbonate film, if no interference was present Extrapolation to otherwaters, such as those of low alkalinity or extreme alkalinity, goesbeyond the range of the original data

The index has proved to be a useful tool in predicting the siveness of once-through cooling waters It is particularly interestingbecause of the preponderance of waters with a composition similar tothat of the Great Lakes waters and because of its usefulness as anindicator of aggressiveness in reviewing the applicability of corrosioninhibition treatment programs that rely on the natural alkalinityand film-forming capabilities of a cooling water The Larson-Skoldindex might be interpreted by the following guidelines:

aggres-Index  0.8 Chlorides and sulfate probably will not

inter-fere with natural film formation

0.8  index  1.2 Chlorides and sulfates may interfere with

nat-ural film formation Higher than desired sion rates might be anticipated

corro-Index  1.2 The tendency toward high corrosion rates of a

local type should be expected as the indexincreases

Stiff-Davis index. The Stiff-Davis index attempts to overcome theshortcomings of the Langelier index with respect to waters with hightotal dissolved solids and the impact of “common ion” effects on thedriving force for scale formation Like the LSI, the Stiff-Davis indexhas its basis in the concept of saturation level The solubility productused to predict the pH at saturation (pHs) for a water is empiricallymodified in the Stiff-Davis index The Stiff-Davis index will predictthat a water is less scale forming than the LSI calculated for the samewater chemistry and conditions The deviation between the indicesincreases with ionic strength Interpretation of the index is by thesame scale as for the Langelier saturation index.

Oddo-Tomson index. The Oddo-Tomson index accounts for the impact ofpressure and partial pressure of CO2on the pH of water and on the sol-ubility of calcium carbonate This empirical model also incorporates cor-rections for the presence of two or three phases (water, gas, and oil).Interpretation of the index is by the same scale as for the LSI and Stiff-Davis indices

Momentary excess (precipitation to equilibrium). The momentary excessindex describes the quantity of scalant that would have to precipitateinstantaneously to bring water to equilibrium In the case of calciumcarbonate,

Kspc [Ca2 ] [CO32 ]

If water is supersaturated, then

[Ca2 ] [CO32 ] spcPrecipitation to equilibrium assumes that one mole of calcium ionswill precipitate for every mole of carbonate ions that precipitates Onthis basis, the quantity of precipitate required to restore water to equi-librium can be estimated with the following equation:

[Ca2  X] [CO3

2  X] Kspc

where X is the quantity of precipitate required to reach equilibrium.

X will be a small value when either calcium is high and carbonate low,

or carbonate is high and calcium low It will increase to a maximumwhen equal parts of calcium and carbonate are present As a result,these calculations will provide vastly different values for waters withthe same saturation level Although the original momentary excessindex was applied only to calcium carbonate scale, the index can beextended to other scale-forming species In the case of sulfate, momen-

tary excess is calculated by solving for X in the relationship

110 Chapter Two

ty of a water.

Interpreting the indices. Most of the indices discussed previouslydescribe the tendency of a water to form or dissolve a particular scale.These indices are derived from the concept of saturation For example,saturation level for any of the scalants discussed is described as theratio of a compound’s observed ion-activity product to the ion-activity

product expected if the water were at equilibrium Ksp The followinggeneral guidelines can be applied to interpreting the degree of super-saturation:

1 If the saturation level is less than 1.0, a water is undersaturatedwith respect to the scalant under study The water will tend to dis-solve, rather than form, scale of the type for which the index wascalculated As the saturation level decreases and approaches 0.0,the probability of forming this scale in a finite period of time alsoapproaches 0

2 A water in contact with a solid form of the scale will tend to dissolve

or precipitate the compound until an IAP/Ksp ratio of 1.0 isachieved This will occur if the water is left undisturbed for an infi-nite period of time under the same conditions A water with a satu-ration level of 1.0 is at equilibrium with the solid phase It will nottend to dissolve or precipitate the scale

3 As the saturation level (IAP/Ksp) increases above 1.0, the

tenden-cy to precipitate the compound increases Most waters can carry

a moderate level of supersaturation before precipitation occurs,and most cooling systems can carry a small degree of supersatu-ration The degree of supersaturation acceptable for a systemvaries with parameters such as residence time, the order of thescale reaction, and the amount of solid phase (scale) present inthe system

Environments 111

2.2.4 Ion association model

The saturation indices discussed previously can be calculated basedupon total analytical values for all possible reactants Ions in water,however, do not tend to exist totally as free ions.24Calcium, for example,may be paired with sulfate, bicarbonate, carbonate, phosphate, and oth-

er species Bound ions are not readily available for scale formation Thisbinding, or reduced availability of the reactants, decreases the effectiveion-activity product for a saturation-level calculation Early indices such

as the LSI are based upon total analytical values rather than freespecies primarily because of the intense calculation requirements fordetermining the distribution of species in a water Speciation of a waterrequires numerous computer iterations for the following:25

■ The verification of electroneutrality via a cation-anion balance, andbalancing with an appropriate ion (e.g., sodium or potassium forcation-deficient waters; sulfate, chloride, or nitrate for anion-defi-cient waters)

■ Estimating ionic strength; calculating and correcting activity ficients and dissociation constants for temperature; correctingalkalinity for noncarbonate alkalinity

coef-■ Iteratively calculating the distribution of species in the water fromdissociation constants A partial listing of these ion pairs is given inTable 2.13

■ Verification of mass balance and adjustment of ion concentrations toagree with analytical values

■ Repeating the process until corrections are insignificant

■ Calculating saturation levels based upon the free concentrations ofions estimated using the ion association model (ion pairing)

The ion association model has been used by major water treatmentcompanies since the early 1970s The use of ion pairing to estimate theconcentrations of free species overcomes several of the major shortcom-ings of traditional indices While indices such as the LSI can correctactivity coefficients for ionic strength based upon the total dissolvedsolids, they typically do not account for common ion effects Commonion effects increase the apparent solubility of a compound by reducingthe concentration of available reactants A common example is sulfatereducing the available calcium in a water and increasing the apparentsolubility of calcium carbonate The use of indices which do not accountfor ion pairing can be misleading when comparing waters in which theTDS is composed of ions which pair with the reactants and of ionswhich have less interaction with them

112 Chapter Two

The ion association model provides a rigorous calculation of the freeion concentrations based upon the solution of the simultaneous non-linear equations generated by the relevant equilibria.26 A simplifiedmethod for estimating the effect of ion interaction and ion pairing issometimes used instead of the more rigorous and direct solution of theequilibria.27 Pitzer coefficients estimate the impact of ion associationupon free ion concentrations using an empirical force fit of laboratorydata.28This method has the advantage of providing a much less calcu-lation-intensive direct solution It has the disadvantages of beingbased upon typical water compositions and ion ratios, and of unpre-dictability when extrapolated beyond the range of the original data.The use of Pitzer coefficients is not recommended when a full ion asso-ciation model is available.

When indices are used to establish operating limits such as mum concentration ratio or maximum pH, the differences betweenindices calculated using ion pairing can have some serious economicsignificance For example, experience on a system with high-TDS watermay be translated to a system operating with a lower-TDS water Thehigh indices that were found acceptable in the high-TDS water may be

maxi-Environments 113

TABLE 2.13 Examples of Ion Pairs Used to Estimate Free Ion Concentrations

Aluminum

[Aluminum] [Al 3 ]  [Al(OH) 2 ]  [Al(OH) 2 ]  [Al(OH) 4 ]  [AlF 2 ]  [AlF 2 ] 

[AlF 3 ]  [AlF 4 ]  [AlSO 4 ]  [Al(SO 4 ) 2 ]

unrealistic when translated to a water where ion pairing is less icant in reducing the apparent driving force for scale formation Table2.14 summarizes the impact of TDS upon LSI when it is calculatedusing total analytical values for calcium and alkalinity, and when it iscalculated using the free calcium and carbonate concentrations deter-mined with an ion association model.

signif-Indices based upon ion association models provide a common inator for comparing results between systems For example, calcitesaturation level calculated using free calcium and carbonate concen-trations has been used successfully as the basis for developing modelswhich describe the minimum effective scale inhibitor dosage that willmaintain clean heat-transfer surfaces.29The following cases illustratesome practical usage of the ion association model

denom-Optimizing storage conditions for low-level nuclear waste. Storage costsfor low-level nuclear wastes are based upon volume Storage is thereforemost cost-effective when the aqueous-based wastes are concentrated tooccupy the minimum volume Precipitation is not desirable because itcan turn a low-level waste into a high-level waste, which is much morecostly to store Precipitation can also foul heat-transfer equipment used

in the concentration process The ion association model approach hasbeen used at the Oak Ridge National Laboratory to predict the optimumconditions for long-term storage.30 Optimum conditions involve theparameters of maximum concentration, pH, and temperature Figures2.17 and 2.18, respectively, depict a profile of the degree of supersatura-tion for silica and for magnesium hydroxide as a function of pH and tem-perature It can be seen that amorphous silica deposition may present aproblem when the pH falls below approximately 10, and that magne-sium hydroxide or brucite deposition is predicted when the pH risesabove approximately 11 Based upon this preliminary run, a pH range

of 10 to 11 was recommended for storage and concentration Otherpotential precipitants can be screened using the ion association model toprovide an overall evaluation of a wastewater prior to concentration

114 Chapter Two

TABLE 2.14 Impact of Ion Pairing on the Langelier Scaling Index (LSI)

LSI Water Low TDS High TDS TDS impact on LSI

Limiting halite deposition in a wet high-temperature gas well. There areseveral fields in the Netherlands that produce hydrocarbon gas asso-ciated with very high TDS connate waters Classical oilfield scaleproblems (e.g., calcium carbonate, barium sulfate, and calcium sul-fate) are minimal in these fields Halite (NaCl), however, can be pre-cipitated to such an extent that production is lost in hours As aresult, a bottom-hole fluid sample is retrieved from all new wells.Unstable components are “fixed” immediately after sampling, and pH

is determined under pressure A full ionic and physical analysis is alsocarried out in the laboratory

The analyses were run through an ion association model computerprogram to determine the susceptibility of the brine to halite (and otherscale) precipitation If a halite precipitation problem was predicted, theion association model was run in a “mixing” mode to determine if mixingthe connate water with boiler feedwater would prevent the problem This

0 2 4 6 8 10 12 14

16

Temperature

pH

Figure 2.17 Amorphous silica saturation in low-level nuclear wastewater as a function

of pH and temperature (WaterCycle).

approach has been used successfully to control salt deposition in the wellwith the composition outlined in Table 2.15 The ion association modelevaluation of the bottom-hole chemistry indicated that the water wasslightly supersaturated with sodium chloride under the bottom-hole con-ditions of pressure and temperature As the fluids cooled in the well bore,the production of copious amounts of halite was predicted.

The ion association model predicted that the connate water wouldrequire a minimum dilution with boiler feedwater of 15 percent to pre-vent halite precipitation (Fig 2.19) The model also predicted that over-injection of dilution water would promote barite (barium sulfate)formation (Fig 2.20) Although the well produced H2S at a concentra-tion of 50 mg/L, the program did not predict the formation of iron sul-fide because of the combination of low pH and high temperature Boilerfeedwater was injected into the bottom of the well using the downhole

0 5000 10000 15000 20000 25000 30000

injection valve normally used for corrosion inhibitor injection Injection

of dilution water at a rate of 25 to 30 percent has allowed the well toproduce successfully since start-up Barite and iron sulfide precipita-tion have not been observed, and plugging with salt has not occurred

Identifying acceptable operating range for ozonated cooling systems. Ithas been well established that ozone is an efficient microbiological con-trol agent in open recirculating cooling-water systems (cooling towers)

It has also been reported that commonly encountered scales have notbeen observed in ozonated cooling systems under conditions wherescale would otherwise be expected The water chemistry of 13 ozonat-

ed cooling systems was evaluated using an ion association model Eachsystem was treated solely with ozone on a continuous basis at the rate

of 0.05 to 0.2 mg/L based upon recirculating water flow rates.31

0 0.5 1 1.5

2 2.5

Figure 2.19 Degree of saturation of halite in a hot gas well as a function of temperature and reinjected boiler water (DownHole SAT).

The saturation levels for common cooling-water scales were lated, including calcium carbonate, calcium sulfate, amorphous silica,and magnesium hydroxide Brucite saturation levels were includedbecause of the potential for magnesium silicate formation as a result

calcu-of the adsorption calcu-of silica upon precipitating magnesium hydroxide.Each system was evaluated by31

■ Estimating the concentration ratio of the systems by comparingrecirculating water chemistry to makeup water chemistry

■ Calculating the theoretical concentration of recirculating waterchemistry based upon makeup water analysis and the apparent, cal-culated concentration ratio from step 1

■ Comparing the theoretical and observed ion concentrations to mine precipitation of major species

deter-■ Calculating the saturation level for major species based upon boththe theoretical and the observed recirculating water chemistry

■ Comparing differences between the theoretical and actual istry to the observed cleanliness of the cooling systems and heatexchangers with respect to heat transfer surface scale buildup,scale formation in valves and on non–heat-transfer surfaces, andprecipitate buildup in the tower fill and basin

chem-118 Chapter Two

TABLE 2.15 Hot Gas Well Water Analysis

Bottom hole connate Boiler feedwater

Three categories of systems were encountered:31

■ Category 1. The theoretical chemistry of the concentrated waterwas not scale-forming (i.e., undersaturated)

■ Category 2. The concentrated recirculating water would have amoderate to high calcium carbonate scale–forming tendency Waterchemistry observed in these systems is similar to that in systems runsuccessfully using traditional scale inhibitors such as phosphonates

■ Category 3. These systems demonstrated an extraordinarily highscale potential for at least calcium carbonate and brucite These sys-tems operated with a recirculating water chemistry similar to that

of a softener rather than of a cooling system The Category 3 waterchemistry was above the maximum saturation level for calcium car-bonate where traditional inhibitors such as phosphonates are able toinhibit scale formation

0 0.5 1 1.5

2 2.5

3 3.5

Figure 2.20 Degree of saturation of barite in a hot gas well as a function of temperature and reinjected boiler water.

TABLE 2.16 Theoretical vs Actual Recirculating Water Chemistry

TABLE 2.17 Theoretical vs Actual Recirculating Water Saturation Level

Table 2.16 outlines the theoretical versus actual water chemistry forthe 13 systems evaluated Saturation levels for the theoretical andactual recirculating water chemistries are presented in Table 2.17 Acomparison of the predicted chemistries to observed system cleanli-ness revealed the following:31

■ Category 1 (recirculating water chemistry undersaturated) The

sys-tems did not show any scale formation

■ Category 2 (conventional alkaline cooling system control range).

Scale formation was observed in eight of the nine Category 2 tems evaluated

sys-■ Category 3 (cooling tower as a softener) Deposit formation on

heat-transfer surfaces was not observed in most of these systems.The study revealed that calcium carbonate (calcite) scale formedmost readily on heat-transfer surfaces in systems operating in a cal-cite saturation level range of 20 to 150, the typical range for chemical-

ly treated cooling water At much higher saturation levels, in excess of

1000, calcite precipitated in the bulk water Because of the whelming high surface area of the precipitating crystals relative to themetal surface in the system, continuing precipitation leads to growth

over-on crystals in the bulk water rather than over-on heat-transfer surfaces.The presence of ozone in cooling systems does not appear to influencecalcite precipitation and/or scale formation.31

Optimizing calcium phosphate scale inhibitor dosage in a high-TDS cooling system. A major manufacturer of polymers for calcium phosphatescale control in cooling systems has developed laboratory data on theminimum effective scale inhibitor (copolymer) dosage required to pre-vent calcium phosphate deposition over a broad range of calcium andphosphate concentrations, and a range of pH and temperatures Thedata were developed using static tests, but have been observed to cor-relate well with the dosage requirements for the copolymer in operat-ing cooling systems The data were developed using test waters withrelatively low levels of dissolved solids Recommendations from thedata were typically made as a function of calcium concentration, phos-phate concentration, and pH This database was used to project thetreatment requirements for a utility cooling system that used geother-mal brine for makeup water An extremely high dosage (30 to 35 mg/L)was recommended based upon the laboratory data.25

It was believed that much lower dosages would be required in theactual cooling system because of the reduced availability of calciumanticipated in the high-TDS recirculating water As a result, it wasbelieved that a model based upon dosage as a function of the ion asso-ciation model saturation level for tricalcium phosphate would be more

122 Chapter Two

appropriate, and accurate, than a simple lookup table of dosage sus pH and analytical values for calcium and phosphate Tricalciumphosphate saturation levels were calculated for each of the laborato-

ver-ry data points Regression analysis was used to develop a model fordosage as a function of saturation level and temperature

The model was used to predict the minimum effective dosage for thesystem with the makeup and recirculating water chemistry found inTable 2.18 A dosage in the range of 10 to 11 mg/L was predicted, ratherthan the 30 ppm derived from the lookup tables A dosage minimizationstudy was conducted to determine the minimum effective dosage Thesystem was initially treated with the copolymer at a dosage of 30 mg/L

in the recirculating water The dosage was decreased until depositionwas observed Failure was noted when the recirculating water concen-tration dropped below 10 mg/L, validating the ion association–baseddosage model

2.2.5 Software Systems

Some software systems are available for water treatment personnel.The products combine the calculation sophistication of university-based mainframe programs with a practical, commonsense engineer-ing approach to evaluating and solving water treatment problems.Color-coded graphics in combination with 3-D representation can bequite useful in visualizing water treatment problems over a user-defined probable dynamic operating range Graphics reduce advancedphysical chemistry concepts and profiles to a level where even laypeo-ple can understand the impact of changing parameters such as pH,

Environments 123

TABLE 2.18 Calcium Phosphate Inhibitor Dosage Optimization Example

Water analysis at 6.2 cycles Deposition potential indicators

Magnesium (as CaCO3) 496 Aragonite 32.9

Bicarbonate (as HCO3) 294 Fluorite 0.0

Silica (as SiO 2 ) 62 Simple indices

temperature, or concentration These products serve niche watertreatment markets, including the cooling-water and oilfield markets.

An ion association model engine forms the basis for the sophisticatedpredictions of scale, corrosion, and inhibitor optimization provided bythese software systems

Scaling of cooling water. Watercycle is a computer-based system thatallows a water treatment chemist to evaluate the scale potential forcommon scalants over the range of water chemistry, temperature, and

pH anticipated in an operational cooling system.32 This computer tem, which was developed to allow water treaters to readily evaluate thescale potential for common scalants over the broadest of operatingranges without the necessity for tedious manual calculations, has beenused to generate the analyses presented in this section

sys-Even when scaling indices can be calculated, they often offer flicting results that can easily cloud the interpretation of what theyare foretelling The program can be applied to long- as well as short-residence-time systems The computer system uses the mean saltactivities for estimating ion-activity coefficients based upon tempera-ture and ionic strength.24The use of ion pairing expands the useful-ness of calculated saturation levels The system can assist the coolingtower operator or water treaters in establishing control limits based onconcentration ratio (cycles of concentration), pH, and temperatureprofiles The program can be used to

con-■ Develop an overall profile of scale potential for common system scalants over the entire range of critical operating parame-ters anticipated

cooling-■ Evaluate the scale potential of an open recirculating cooling systemversus concentration ratio as an aid in establishing control limits

■ Evaluate the benefits of pH control with respect to scale potentialand to estimate acid requirements

■ Review these indicators as water quality changes or environmentalconstraints force operation with reduced water quality andincreased scale potential

■ Learn about the interaction of water chemistry and operating tions (pH, temperature) by using the program as a system simulator.Many cooling-water evaluations assume that the cooling system isstatic Indices for scale potential are calculated at the “harshest” con-ditions for the foulant under study What-if scenario modeling providesone of the greatest benefits from using Watercycle The “what-if scenario”modules allow one to

condi-124 Chapter Two

■ Visualize what will happen to the scale potential and corrosivity of acooling water as operating parameters and water chemistry change.

■ Evaluate the current cooling water over the entire range of ing parameters

operat-■ Predict water scaling behavior for use in evaluating new cooling tems, and as an aid in establishing control ranges and operatingparameters

sys-In the case of calcium carbonate scale, indices are typically

calculat-ed at the highest expectcalculat-ed temperature and highest expectcalculat-ed pH—theconditions under which calcium carbonate is least soluble In the case

of silica, the opposite conditions are used Amorphous silica has itslowest solubility at the lowest temperature and lowest pH encoun-tered Indices calculated under these conditions would be acceptable inmany cases Unfortunately, cooling systems are not static Thefoulants silica and tricalcium phosphate are used as examples todemonstrate the use of operating range profiles in developing an in-depth evaluation of scale potential and the impact of loss of control

Silica. Guidelines for the upper silica operating limits have been welldefined in water treatment practice, and have evolved with the treatmentprograms In the days of acid chromate cooling-system treatment, anupper limit of 150 ppm silica as SiO2was common The limit increased to

180 ppm with the advent of alkaline treatments and pH control limits up

to 9.0 Silica control levels approaching or exceeding 200 ppm as SiO2

have been reported for the current high-pH, high-alkalinity all-organictreatment programs where pH is allowed to equilibrate at 9.0 or higher.26

The evolution of silica control limits can be readily understood byreviewing the silica solubility profile As depicted in Fig 2.21, solubility

of amorphous silica increases with increasing pH Silica solubility alsoincreases with increasing temperature In the pH range of 6.0 to 8.0 andtemperature range of 20 to 30°C, cooling water will be saturated withamorphous silica when the concentration reaches 100 ppm (20°C) or 135ppm (30°C) as SiO2 These concentrations correspond to a saturationlevel of 1.0 The traditional silica limit for this pH range has been 150ppm as SiO2 As outlined in Table 2.19, a limit of 150 ppm would corre-spond roughly to a saturation level of 1.4 at 20°C and 1.1 at 30°C

At the upper end of the cooling-water pH range (9.0), silica

solubili-ty increases to 115 ppm (20°C) and 140 ppm (30°C) A control limit of

180 ppm would correspond to saturation levels of 1.5 and 1.3, tively In systems where concentration ratio is limited by silica solu-bility, it is recommended that the concentration ratio limit bereestablished seasonally based on amorphous silica saturation level orwhenever significant temperature changes occur.26

respec-Environments 125

Calcium phosphate. Neutral phosphate programs can benefit from ration-level profiles for tricalcium phosphate Treatment programsusing orthophosphate as a corrosion inhibitor must operate in a nar-row pH range in order to achieve satisfactory corrosion inhibitionwithout catastrophic calcium phosphate deposition occurring.Operating-range profiles for tricalcium phosphate can assist the watertreatment chemist in establishing limits for pH, concentration ratio,and orthophosphate in the recirculating water Such profiles are alsouseful in showing operators the impact of loss of pH control, chemicaloverfeed, or overconcentration.

satu-Scaling of deep well water. DownHole SAT is another specialized puter program that allows a water treatment specialist to evaluate the

com-126 Chapter Two

20 26

32 38 44 50 56

7 7.6 8.4 8.6 8.9 0

50 100 150

Figure 2.21 Solubility of amorphous silica as a function of temperature and pH.

TABLE 2.19 Silica Limits for Three Treatment Schemes

Low pH (6.0) Moderate pH (7.6) High pH (8.9)

Silica level (ppm) 130 150 150 150 180 180 Saturation level limit 1.2 1.1 1.4 1.1 1.5 1.3

scale potential for common scalants over a broad range of water istry parameters, such as temperature, pressure, pH, and pCO2.33Aswith the previous computer system, “what-if scenario” modules pro-vide an easy way to visualize what could happen to the scale potentialand corrosivity of a water as environmental parameters and waterchemistry change The what-if scenarios also allow evaluating theimpact of bringing a water to the surface, or finding the safe ratios formixing waters under varying conditions The scenarios can provide apredictor for use in anticipating problems in new or proposed wells.The following indices and the scaling behavior of the solid speciesshown in Table 2.20 are all calculated by DownHole SAT.

pro-■ The common foulants group includes calcite, barite, witherite, andanhydrite saturation levels

■ The common indices group includes the Langelier, Stiff-Davis, Tomson, and Ryznar indices

Amorphous iron Fe(OH)3

Amorphous silica SiO2

Strengite FePO 4 2H 2 O

Tricalcium phosphate Ca3(PO4)2

Hydroxyapatite Ca5(PO4)3(OH)

Thenardite Na 2 SO 4

Iron sulfide FeS

■ The calcium carbonate group includes calcite saturation level, theLangelier saturation index, the Stiff-Davis index, and the Oddo-Tomson index.

Dosages for scale inhibitors should be applied as a function of a drivingforce for scale formation and growth (e.g., calcite saturation level), tem-perature as it affects reaction rates, pH as it affects the dissociationstate of the inhibitor, and time A version of the computer programallows the development of mathematical models for the minimum effec-tive scale inhibitor dosage as a function of these parameters: drivingforce, temperature, pH, and time

Mathematical models. Mathematical models for an inhibitor are oped by the program using multiple regression The goodness of fit forthe data can be presented in table and graphical format Models arediscussed by parameter The basic parameter to which scale inhibitordosages have been correlated historically is the driving force for crys-tal formation and crystal growth Early models attempted to developmodels based upon the Langelier saturation index or the Ryznar sta-bility index Most water treaters are in agreement that dosagerequirements increase with the driving force for scale formation.Calcite saturation level provides an excellent driving force for calciumcarbonate scale inhibitor models, gypsum saturation level for calciumsulfate in the cooling-water temperature range, and tricalcium phos-phate saturation level for calcium phosphate scale prevention Themomentary excess indices can also be used effectively to model dosagerequirements

A second critical factor in determining an effective dosage or oping a model for an inhibitor is time Time is the residence time ofscale-forming species in the system you wish to treat The time factorfor scale inhibition can be as short as 4 to 10 s in a utility condensersystem, or extend into days for cooling towers In high-saturation-levelsystems, the induction period can be very short In systems wherewater is barely supersaturated, the induction time can approach infin-ity Scale inhibitors have been observed to extend the induction timebefore scale formation or growth on existing scale substrate occurs.34

devel-Inhibitors extend the time before scale will form in a system byinterfering with the kinetics of crystal formation and growth Ratedecreases as inhibitor dosages increase Additional parameters includetemperature, as it affects the rate of crystal formation and/or growth.Dosage changes with temperature can be modeled with a simpleArrhenius relationship pH is an important parameter to include inthese models when an inhibitor can exist in two or more forms withinthe pH range of use, and one of the forms is much more active as a

128 Chapter Two

scale... of 1. 0 The traditional silica limit for this pH range has been 15 0ppm as SiO2 As outlined in Table 2 .19 , a limit of 15 0 ppm would corre-spond roughly to a saturation level of 1. 4... 20°C and 1. 1 at 30°C

At the upper end of the cooling-water pH range (9.0), silica

solubili-ty increases to 11 5 ppm (20°C) and 14 0 ppm (30°C) A control limit of

18 0 ppm would