1、Designation: D4328 08 (Reapproved 2013)Standard Practice forCalculation of Supersaturation of Barium Sulfate, StrontiumSulfate, and Calcium Sulfate Dihydrate (Gypsum) inBrackish Water, Seawater, and Brines1This standard is issued under the fixed designation D4328; the number immediately following th
2、e designation indicates the year oforiginal adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon () indicates an editorial change since the last revision or reapproval.1. Scope1.1 This practice covers the
3、 calculation of supersaturation ofbarium sulfate, strontium sulfate, and calcium sulfate dihydrate(gypsum) in brackish water, seawater, and brines in whichbarium, strontium, and calcium ions either coexist or existindividually in solution in the presence of sulfate ions.1.2 This practice is not appl
4、icable for calculating calciumsulfate dihydrate supersaturation if the temperatures of salinewaters under investigation exceed 95C.At temperatures above95C, hemianhydrate and anhydrite would be major insolubleforms.1.3 The values stated in SI units are to be regarded asstandard. No other units of me
5、asurement are included in thisstandard.1.4 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory l
6、imitations prior to use.2. Referenced Documents2.1 ASTM Standards:2D511 Test Methods for Calcium and Magnesium In WaterD512 Test Methods for Chloride Ion In WaterD513 Test Methods for Total and Dissolved Carbon Dioxidein WaterD516 Test Method for Sulfate Ion in WaterD1129 Terminology Relating to Wat
7、erD3352 Test Method for Strontium Ion in Brackish Water,Seawater, and BrinesD3370 Practices for Sampling Water from Closed ConduitsD3561 Test Method for Lithium, Potassium, and SodiumIons in Brackish Water, Seawater, and Brines by AtomicAbsorption SpectrophotometryD3651 Test Method for Barium in Bra
8、ckish Water, Seawater,and BrinesD3986 Test Method for Barium in Brines, Seawater, andBrackish Water by Direct-Current Argon Plasma AtomicEmission Spectroscopy3. Terminology3.1 DefinitionsFor definitions of terms used in thispractice, refer to Terminology D1129.4. Significance and Use4.1 This practic
9、e covers the mathematical calculation of thesupersaturation of three principal sulfate scaling compoundsfound in industrial operations. Application of this standardpractice to the prediction of scale formation in a given system,however, requires experience. The calculations tell the user ifa water,
10、or mixture of waters, is in a scaling mode. Whether ornot scale will in fact form, how quickly it will form, where itwill form, in what quantities, and what composition are subjectto factors beyond the scope of this practice. However, based onhow supersaturated a given water or mixture of waters is,
11、 anobjective evaluation of the relative likelihood of scale forma-tion can be made.NOTE 1There are several personal computer (PC) type programs thatare both available commercially and publicly that will perform thesecalculations.5. Procedure5.1 Collect water samples for compositional analysis inacco
12、rdance with Practices D3370.5.2 Determine the calcium and magnesium concentrationsin accordance with Test Methods D511.5.3 Determine the barium concentration in accordance withTest Methods D3651 or D3986.5.4 Determine the strontium concentration in accordancewith Test Method D3352.1This practice is
13、under the jurisdiction of ASTM Committee D19 on Water andis the direct responsibility of Subcommittee D19.05 on Inorganic Constituents inWater.Current edition approved June 1, 2013. Published July 2013. Originally approvedin 1984. Last previous edition approved in 2008 as D4328 08. DOI: 10.1520/D432
14、8-08R13.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.Copyright ASTM International, 100 Barr Harbor Drive,
15、PO Box C700, West Conshohocken, PA 19428-2959. United States15.5 Determine sodium and potassium concentrations inaccordance with Test Method D3561.5.6 Determine sulfate ion concentration in accordance withTest Method D516.5.7 Determine chloride ion concentration in accordancewith Test Methods D512.5
16、.8 Determine carbonate and bicarbonate ion concentrationsin accordance with Test Methods D513.5.9 Determine the concentrations of all other major inor-ganic constituents that may be present in the water underinvestigation in accordance with appropriate test methods inAnnual Book of ASTM Standards, V
17、ols 11.01 and 11.02.5.10 Determine temperature and pressure of the watersystem under investigation.6. Calculation of Ionic Strength6.1 Calculate the ionic strength of the water under investi-gation as follows: 512(CiZi2(1)where: = ionic strength,Ci= molal concentration of each ion in solution, andZi
18、= charge number of ion, i.7. Calculation of Barium Sulfate Supersaturation (Referto Appendix X1)7.1 Calculate barium sulfate solubility in the water underinvestigation, using the equation as follows:S 5 =X214K 2 X!/2 (2)where:S = solubility, moles of solute per kilogram of watercorrected for the com
19、mon ion effect,K = solubility product constant (molal) at the ionic strength,temperature and pressure of the water under investiga-tion. For BaSO4refer to Appendix X2, andX = molal excess of soluble common ion.7.2 Calculate the amount of barium sulfate, moles perkilogram of water, in the sample base
20、d on the lesser of thebarium or sulfate ion concentration.7.3 If the amount of BaSO4in the sample (7.2) is less thanits calculated solubility (7.1), the water in question is under-saturated with respect to BaSO4. If the amount of BaSO4present is greater than its solubility, the water is supersaturat
21、edwith respect to BaSO4. Calculate the amount of supersaturationas the difference between the two values:supersaturation 5 concentration 2 solubility (3)NOTE 2Supersaturation may also be calculated directly from theequation (1).3Ba11# 2 y!SO45# 2 y! 5 K (4)where:Ba2+= concentration of barium, molal,
22、SO42= = concentration of sulfate, molal,y = excess (supersaturation) of BaSO4, molal, andK = solubility product constant (molal) of BaSO4attest conditions.The value X may then be determined from the quadraticequation (see Appendix X1):X 52B6=B22 4 AC2AReport BaSO4supersaturation in molal terms of th
23、e weightof BaSO4per volume of water, mg/L.BaSO4supersaturation, mg/L5BaSO4, molal2! 31033233 3S1000 3DTDS100011000Dwhere:D = sample density.8. Calculation of Strontium Sulfate Supersaturation(Refer to Appendix X1)8.1 Calculate strontium sulfate solubility using the samesteps described for BaSO4(Sect
24、ion 7), but substituting theappropriate values for SrSO4in Eq 2 (refer to Appendix X3 orAppendix X4).NOTE 3If barium sulfate supersaturation exists, the amount of sulfateavailable for strontium sulfate will be less by the amount of sulfateequivalent to the calculated BaSO4supersaturation.NOTE 4If ca
25、rbonate ions are present, strontium carbonate mayprecipitate. The amount of strontium may then be corrected by thatrequired for strontium carbonate precipitation prior to the calculation ofSrSO4solubility (6). Practically speaking, however, due to the extremelylow solubility of SrCO3, this correctio
26、n may usually be omitted.8.2 Calculate the amount of strontium sulfate moles perkilogram water in the sample based on the lesser of thestrontium or remaining sulfate ion concentration.8.3 If the amount of SrSO4in the sample (8.2) is less thanits calculated solubility (8.1), the water in question is
27、under-saturated with respect to SrSO4. If the amount of SrSO4presentis greater than its solubility, the water is supersaturated withrespect to SrSO4. Calculate the amount of supersaturation,moles per kilogram water by difference (Eq 3), or by substi-tuting appropriate data in Eq 4 (Note 2).8.3.1 Rep
28、ort SrSO4supersaturation in terms of the weight ofSrSO4per volume of water as follows:SrSO4supersaturation mg/L5SrSO4, molal! 31033184 3S1000 3DTDS100011000D9. Calculation of Calcium Sulfate Supersaturation (Referto Appendix X1)9.1 Calculate calcium sulfate solubility using the same stepsdescribed f
29、or BaSO4(Section 7), but substituting the appropri-ate values for CaSO4in Eq 2 (refer to Appendix X5).3The boldfaced numbers in parentheses refer to a list of references at the end ofthis standard.D4328 08 (2013)29.2 Calculate the amount of calcium sulfate moles perkilogram in the sample based on th
30、e lesser of the calcium orremaining sulfate ion.9.3 If the amount of CaSO4in the sample (9.2) is less thanits calculated solubility (9.1), the water in question is under-saturated with respect to CaSO4. If the amount of CaSO4present is greater than its solubility, the water is supersaturatedwith res
31、pect to CaSO4. Calculate the amount of supersaturationmoles per kilogram by difference (Eq 3) or by substitutingappropriate data in Eq 4 (Note 2).9.3.1 Report CaSO4supersaturation in terms of the weightof CaSO42H2O (gypsum) per volume of water after convertingmoles per data obtained above to mg/L as
32、 follows:CaSO2H2O supersaturation, mg/L5 CaSO42H2O2, moles/kg 3172.17 31033D10. Keywords10.1 barium sulfate; brines; calcium sulfate dihydrate;strontium sulfateAPPENDIXES(Nonmandatory Information)X1. SAMPLE CALCULATION OF BaSO4SUPERSATURATION AT 95CAnalysis of Water Ionic StrengthComponent Ions mg/L
33、 moles per litreAmolalAConcentration Z2=12 ,Z,2(Section 6)Na 27 120 1.180 1.214 1 1.214Ca 10 890 0.272 0.280 4 1.120Mg 1679 0.69 0.071 4 0.284Ba 6.4 0.000044 4.52 1054 0.001Sr 444 0.00506 521.42 1054 0.021Cl 64 870 1.830 1.883 1 1.883SO41210 0.012596 1296.14 1054 0.052HCO3317 0.005 0.005 1 0.005TDS
34、= 106 536 Total ionic strength = 2.29Density = 1.078 g/ml KBaSO4at 95 (Appendix X1) = 83.22 109AConvert moles/L to molal5 moles/L 31000sSp gr31000d 2TDS10005moles/L 3100010782 106.55moles/L 31.029X1.1 BaSO4Solubility (Refer to 7.1):S 5 =X214K 2 X!/2where:X = molal excess of common ion (in this case
35、SO4),X = (1296.14 105) (4.52 105)= 1291.62 1054K = 4(83.22 109) = 332.88 109, or 3328.8 1010S =1291.6231025!213328.8310210! (1291.62 105)/2Solubility S = 0.644 105molalX1.2 BaSO4Present (Refer to 7.2):X1.2.1 Ba present = 4.52 105molalX1.2.2 SO4present = 1296.14 105molalX1.2.3 Based on lower value (B
36、a), BaSO4pres-ent = 4.52 105molalX1.3 Amount of BaSO4Supersaturation (Refer to 7.3):X1.3.1 BaSO4present based on Ba2+=4.52105molalX1.3.2 Calculated BaSO4solubility, S =0.64105molalX1.3.3 BaSO4excess; that is, supersaturation = 3.88 105molal; or 8.8 mg/L of sampleX1.4 Useful Information:Mol WeightEqu
37、ivalentWeightGravimetric ConversionFactorsBa 137.33 68.66 Ba 1.6995 = BaSO4Ca 40.08 20.04 Ca 3.3967 = CaSO4Sr 87.62 43.81 Sr 2.0963 = SrSO4SO496.06 48.03BaSO4233.39 116.70 SO4 2.4296 = BaSO4CaSO4136.14 68.07 SO4 1.4172 = CaSO4CaSO42H2O 172.14 86.07 SO41.9121=SrSO4SrSO4183.68 91.84X1.5 The amount of
38、supersaturation (excess BaSO4) mayalso be calculated directly using the expression (Eq 4):Ba11# 2 X!SO45# 2 X! 5 KBaSO4X1.5.1 Using the molal values from the water analyis abovethis becomes:D4328 08 (2013)34.52 31025# 2 X!1296.14 31025# 2 X! 5 832.2 310210Multiplying:5858.55 310210! 2 1300.66 31025!
39、X1X25 832.2 310210Combining:X22 1300.66 31025! X15026.35 3102105 0X1.5.2 Substituting the above coefficients of X in thequadratic equation:X 52b6= b22 4 ac2aand solving, X =3.88105molal; or 8.8 mg/L of sample.X2. SOLUBILITY DATA FOR BaSO4NaClH2O SYSTEMS (2)SolutionIonic Strength,Solubility Product C
40、onstant, K (Molal)25C 35C 50C 65C 80C 95C0.1 1.541092.00 1092.70 1093.34 1093.7610 3.971090.2 2.70 3.36 4.76 5.93 7.06 7.740.4 4.49 5.63 7.92 10.61 13.69 16.130.6 6.08 7.74 11.03 15.38 20.45 24.970.8 7.74 9.60 13.69 20.16 26.57 33.491.0 9.22 11.24 16.38 24.02 32.76 42.021.5 12.54 15.38 22.20 32.40 4
41、4.94 62.002.0 15.63 19.04 27.23 39.60 56.17 78.962.5 18.23 21.90 31.33 44.94 63.50 93.643.0 20.74 24.65 34.97 49.73 70.23 107.573.5 23.41 27.56 38.81 53.82 76.73 120.414.0 25.92 30.63 42.44 58.08 82.94 132.504.5 28.56 34.23 45.80 63.00 89.40 144.40X3. SOLUBILITY PRODUCT DATA FOR SrSO42NaClH2O SYSTEM
42、S (3)Solution IonicASolubility Product Constant, K (Molal)Strength, 40C (104F) 71C (160F)0.1 0.250 1050.160 1050.2 0.390 0.2500.3 0.505 0.3450.4 0.617 0.4400.5 0.723 0.5180.75 1.02 0.7851.0 1.26 1.041.25 1.48 1.251.5 1.68 1.411.75 1.86 1.572.0 2.00 1.682.25 2.09 1.762.5 2.14 1.812.75 2.16 1.843.0 2.
43、17 1.863.25 2.19 1.873.50 2.20 1.88AThe above table may be used to interpolate the solubility product (K) for SrSO4in brines at 0 psig. The interpolated values can be substituted in Eq 2 (Section 7)forestimating the solubility (S)ofSrSO4. For more precise K values at temperatures up to 300F (149C) a
44、nd pressures up to 3000 psig add SI unit, refer to Appendix X4.D4328 08 (2013)4X4. EQUATION FOR CALCULATING SrSO4SOLUBILITY (4)X4.1 Experimental SrSO4solubility data have been reducedto the following regression equation for calculating the solu-bility product constant (K) at various solution ionic s
45、trengthsover a temperature range of 100 to 300F (38 to 149C) andpressures up to 3000 psig. The equation is adaptable tocomputer calculation which can then substitute the value for Kin Eq 2 (Section 7) for computing the solubility of SrSO4atdesired conditions.Log KSrSO4= X/Rwhere:X =1/T,R = A+BX+C1/2
46、+D+EZ2+FXZ+G1/2Z,Z = pressure (psig), = solution ionic strength,T = temperature, K.X4.1.1 Coefficients of the above equation for R are asfollows:A = 0.266948 103B = 244.828 103C = 0.191065 103D = 53.543 106E = 1.383 1012F = 1.103323 109G = 0.509 109X5. SOLUBILITY PRODUCT DATA FOR CaSO42NaClH2O SYSTE
47、MS (5)Solution IonicStrength, Solubility Product Constant, K (Molal)10C 35C 50C 80C0 1.021041.27 1041.25 1040.89 1040.1 3.04 3.29 3.31 2.820.2 4.99 5.23 5.28 4.670.3 6.87 7.11 7.17 6.440.4 8.68 8.91 8.96 8.130.5 10.41 10.64 10.68 9.750.6 12.07 12.30 12.30 11.300.7 13.65 13.88 13.85 12.780.8 15.16 15
48、.39 15.32 14.180.9 16.60 16.83 16.71 15.521.0 17.96 18.20 18.02 16.791.25 21.05 21.29 20.96 19.701.5 23.69 23.93 23.46 22.221.75 25.90 26.12 25.52 24.392.0 26.67 27.88 27.18 26.222.25 29.03 29.22 28.47 27.732.5 30.00 30.15 29.40 28.922.75 30.60 30.71 30.01 29.813.0 30.84 30.90 30.32 30.423.25 30.77
49、30.77 30.36 30.733.5 30.39 30.34 30.15 30.763.75 29.76 29.66 29.73 30.514.0 28.90 28.75 29.13 29.974.25 27.85 27.66 28.37 29.144.5 26.65 26.43 27.49 28.024.75 25.34 25.13 26.52 26.585.0 23.98 23.80 25.48 24.83REFERENCES(1) Ostroff, A. G., “Introduction To Oilfield Water Technology,” a NACEpublication, second edition, 1979.(2) Templeton, C. C., “Solubility of Barium Sulfate In Sodium C
