1、Designation: D 4328 03Standard 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 D 4328; the number immediately following the designation in
2、dicates 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 (e) indicates an editorial change since the last revision or reapproval.1. Scope1.1 This practice covers the calculation of
3、 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 applicable for calc
4、ulating calciumsulfate dihydrate supersaturation if the temperatures of salinewaters under investigation exceed 95C.At temperatures above95C, hemianhydrate and anhydrite would be major insolubleforms.1.3 This standard does not purport to address all of thesafety concerns, if any, associated with its
5、 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 limitations prior to use.2. Referenced Documents2.1 ASTM Standards:D511 Test Methods for Calcium and Magnesium in Water2D 512 Test Methods f
6、or Chloride Ion in WaterD 513 Test Methods for Total and Dissolved Carbon Diox-ide in Water2D 516 Test Method for Sulfate Ion in Water2D 1129 Terminology Relating to Water2D 1192 Specification for Equipment for Sampling Waterand Steam in Closed Conduits2D 3352 Test Method for Strontium Ion in Bracki
7、sh Water,Seawater, and Brines3D 3370 Practices for Sampling Water from Closed Con-duits2D 3561 Test Method for Lithium, Potassium, and SodiumIons in Brackish Water, Seawater, and Brines by AtomicAbsorption Spectrophotometry3D 3651 Test Method for Barium in Brackish Water, Seawa-ter, and Brines3D 398
8、6 Test Method for Barium in Brines, Seawater, andBrackish Water by Direct-Current Argon Plasma AtomicEmission Spectroscopy33. Terminology3.1 Definitions: For definitions of terms used in this prac-tice, refer to Terminology D 1129.4. Significance and Use4.1 This practice covers the mathematical calc
9、ulation 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, or mixture of waters, is in a
10、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, anobjective evaluation of the
11、 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 inaccordance with Practices D 3370 a
12、nd Specification D 1192.5.2 Determine the calcium and magnesium concentrationsin accordance with Test Methods D511.5.3 Determine the barium concentration in accordance withTest Methods D 3651 or D 3986.5.4 Determine the strontium concentration in accordancewith Test Method D 3352.1This practice is u
13、nder the jurisdiction of ASTM Committee D19 on Water andis the direct responsibility of Subcommittee D19.05 on Inorganic Constituents inWater.Current edition approved Jan. 10, 2003. Published January 2003. Originallyapproved in 1984. Last previous edition approved in 1997 as D 432897.2Annual Book of
14、 ASTM Standards, Vol 11.01.3Annual Book of ASTM Standards, Vol 11.02.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.5.5 Determine sodium and potassium concentrations inaccordance with Test Method D 3561.5.6 Determine sulfate ion con
15、centration in accordance withTest Method D 516.5.7 Determine chloride ion concentration in accordancewith Test Methods D 512.5.8 Determine carbonate and bicarbonate ion concentrationsin accordance with Test Methods D 513.5.9 Determine the concentrations of all other major inor-ganic constituents tha
16、t may be present in the water underinvestigation in accordance with appropriate test methods inAnnual Book of ASTM Standards, Vols 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 wa
17、ter under investi-gation as follows: 512(CiZi2(1)where: = ionic strength,Ci= molal concentration of each ion in solution, andZi= charge number of ion, i.7. Calculation of Barium Sulfate Supersaturation (Referto Appendix X1)7.1 Calculate barium sulfate solubility in the water underinvestigation, usin
18、g the equation as follows:S 5 =X21 4K 2 X!/2 (2)where:S = solubility, moles of solute per kilogram of watercorrected for the common ion effect,K = solubility product constant (molal) at the ionicstrength, temperature and pressure of the water underinvestigation. For BaSO4refer to Appendix X2, andX =
19、 molal excess of soluble common ion.7.2 Calculate the amount of barium sulfate, moles perkilogram of water, in the sample based 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
20、under-saturated with respect to BaSO4. If the amount of BaSO4present is greater than its solubility, the water is supersaturatedwith respect to BaSO4. Calculate the amount of supersaturationas the difference between the two values:supersaturation 5 concentration 2 solubility (3)NOTE 2Supersaturation
21、 may also be calculated directly from theequation (1)4Ba11# 2 y!SO45# 2 y! 5 K (4)where:Ba2+= concentration of barium, molal,SO42= = concentration of sulfate, molal,y = excess (supersaturation) of BaSO4, molal, andK = solubility product constant (molal) of BaSO4attest conditions.The value X may then
22、 be determined from the quadraticequation (see Appendix X1):X 52B 6 =B22 4 AC2AReport BaSO4supersaturation in molal terms of the weightof BaSO4per volume of water, mg/L.BaSO4supersaturation, mg/L5 BaSO4, molal2! 3 1033 233 3S1000 3 DTDS10001 1000Dwhere D = sample density.8. Calculation of Strontium
23、Sulfate Supersaturation(Refer to Appendix X1)8.1 Calculate strontium sulfate solubility using the samesteps described for BaSO4(Section 7), but substituting theappropriate values for SrSO4in Eq 2 (Refer toAppendix X3 orAppendix X4).NOTE 3If barium sulfate supersaturation exists, the amount of sulfat
24、eavailable for strontium sulfate will be less by the amount of sulfateequivalent to the calculated BaSO4supersaturation.NOTE 4If carbonate ions are present, strontium carbonate mayprecipitate. The amount of strontium may then be corrected by thatrequired for strontium carbonate precipitation prior t
25、o the calculation ofSrSO4solubility. (6) Practically speaking, however, due to the extremelylow solubility of SrCO3, this correction 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
26、 concentration.8.3 If the amount of SrSO4in the sample (8.2) is less thanits calculated solubility (8.1), the water in question is under-saturated with respect to SrSO4. If the amount of SrSO4presentis greater than its solubility, the water is supersaturated withrespect to SrSO4. Calculate the amoun
27、t of supersaturation,moles per kilogram water by difference (Eq 3), or by substi-tuting appropriate data in Eq 4 (Note 2).8.3.1 Report SrSO4supersaturation in terms of the weight ofSrSO4per volume of water as follows:SrSO4supersaturation mg/L5 SrSO4, molal! 3 1033 184 3S1000 3 DTDS10001 1000D9. Calc
28、ulation of Calcium Sulfate Supersaturation (Referto Appendix X1)9.1 Calculate calcium sulfate solubility using the same stepsdescribed for BaSO4(Section 7), but substituting the appropri-ate values for CaSO4in Eq 2 (Refer to Appendix X5).9.2 Calculate the amount of calcium sulfate moles perkilogram
29、in the sample based on the lesser of the calcium orremaining sulfate ion.4The boldfaced numbers in parentheses refer to a list of references at the end ofthis standard.D 4328 0329.3 If the amount of CaSO4in the sample (9.2) is less thanits calculated solubility (9.1), the water in question is under-
30、saturated with respect to CaSO4. If the amount of CaSO4present is greater than its solubility, the water is supersaturatedwith respect 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 CaSO4supers
31、aturation in terms of the weightof CaSO42H2O (gypsum) per volume of water after convertingmoles per data obtained above to mg/L as follows:CaSO2H2O supersaturation, mg/L5 CaSO42H2O2, moles/kg 3 172.17 3 1033 D10. Keywords10.1 barium sulfate; brines; calcium sulfate dihydrate;strontium sulfateAPPENDI
32、XES(Nonmandatory Information)X1. SAMPLE CALCULATION OF BaSO4 SUPERSATURATION AT 95CAnalysis of Water Ionic StrengthComponent Ions mg/L 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 3
33、1054 0.001Sr 444 0.00506 521.42 3 1054 0.021Cl 64 870 1.830 1.883 1 1.883SO41210 0.012596 1296.14 3 1054 0.052HCO3317 0.005 0.005 1 0.005TDS = 106 536 Total ionic strength = 2.29Density = 1.078 g/ml KBaSOrat 95 (Appendix X1) = 83.22 3 109AConvert moles/L to molal 5 moles/L 31000Sp gr 3 1000! 2TDS100
34、05 moles/L 310001078 2 106.55 moles/L 3 1.029X1.1 BaSO4solubility (refer to 7.1)S 5 =X21 4K 2 X!/2where:X = molal excess of common ion (in this case SO4),X = (1296.14 3 105) (4.52 3 105)= 1291.62 3 1054K = 4(83.22 3 109) = 332.88 3 109, or 3328.8 3 1010S =1291.62 3 1025!21 3328.8 3 10210! (1291.62 3
35、 105)/2Solubility S = 0.644 3 105molalX1.2 BaSO4present (refer to 7.2):X1.2.1 Ba present = 4.52 3 105molalX1.2.2 SO4present = 1296.14 3 105molalX1.2.3 Based on lower value (Ba), BaSO4present = 4.52 3 105molalX1.3 Amount of BaSO4supersaturation (refer to 7.3)X1.3.1 BaSO4present based on Ba2+= 4.52 3
36、105molalX1.3.2 Calculated BaSO4solubility, S = 0.64 3 105molalX1.3.3 BaSO4excess; i.e. supersaturation = 3.88 3 105molal; or 8.8 mg/L of sampleX1.4 Useful Information:Mol WeightEquivalentWeightGravimetric ConversionFactorsBa 137.33 68.66 Ba 3 1.6995 = BaSO4Ca 40.08 20.04 Ca 3 3.3967 = CaSO4Sr 87.62
37、43.81 Sr 3 2.0963 = SrSO4SO496.06 48.03BaSO4233.39 116.70 SO43 2.4296 = BaSO4CaSO4136.14 68.07 SO43 1.4172 = CaSO4D 4328 033Mol WeightEquivalentWeightGravimetric ConversionFactorsCaSO42H2O 172.14 86.07 SO43 1.9121 = SrSO4SrSO4183.68 91.84X1.5 The amount of supersaturation (excess BaSO4) mayalso be c
38、alculated 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:4.52 3 1025# 2 X! 1296.14 3 1025# 2 X! 5 832.2 3 10210Multiplying: 5858.55 3 10210!21300.66 3 1025!X 1 X25 832.2 3 10210Combining: X22 1300.66 3 1025! X
39、1 5026.35 3 102105 0X1.5.2 Substituting the above coefficients of X in thequadratic equation:X 52 b 6 = b22 4 ac2aand solving, X = 3.88 3 105molal; or 8.8 mg/Lof sample.X2. SOLUBILITY DATA FOR BaSO4NaClH2O SYSTEMS (2)SolutionIonic Strength,Solubility Product Constant, K (Molal)25C 35C 50C 65C 80C 95
40、C0.1 1.54 3 1092.00 3 1092.70 3 1093.34 3 1093.76 3 10 3.97 3 1090.2 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 44.94 62.002.0 15.63 19.04
41、 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 SYSTEMS (3)Solution IonicASolub
42、ility Product Constant, K (Molal)Strength, 40C (104F) 71C (160F)0.1 0.250 3 1050.160 3 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 2.17 1.863.25 2.19 1.87
43、3.50 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 6)forestimating the solubility (S)ofSrSO4. For more precise K values at temperatures up to 300F (149C) and pressures up to 30
44、00 psig add SI unit, refer to Appendix X4.D 4328 034X4. Equation for Calculating SrSO4 Solubility (4)X4.1 Experimental SrSO4solubility data have been re-duced to the following regression equation for calculating thesolubility product constant ( K) at various solution ionicstrengths over a temperatur
45、e range of 100 to 300F (38 to149C) and pressures up to 3000 psig. The equation isadaptable to computer calculation which can then substitute thevalue for K in Eq 2 (Section 6) for computing the solubility ofSrSO4at desired conditions.Log KSrSO4= X/Rwhere:X =1/T,R = A+BX+C1/2+D+EZ2+FXZ+G1/2Z,Z = pres
46、sure (psig), = solution ionic strength,T = temperature, K.X4.1.1 Coefficients of the above equation for R are asfollows:A = 0.266948 3 103B = 244.828 3 103C = 0.191065 3 103D = 53.543 3 106E = 1.383 3 1012F = 1.103323 3 106G = 0.509 3 109X5. SOLUBILITY PRODUCT DATA FOR CaSO42NaClH2O SYSTEMS (5)Solut
47、ion IonicStrength, Solubility Product Constant, K (Molal)10C 35C 50C 80C0 1.02 3 1041.27 3 1041.25 3 1040.89 3 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 15.3
48、9 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 30
49、.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 24.83D 4328 035REFERENCES(1) Ostroff, A. G., “Introduction To Oilfield Water Technology,” a NACEpublication, second edition, 1979.(2) Templeton, C. C., “Solubility of Barium Sulfate In Sodium ChlorideSolution From 25C to 95C,” J. Chem. and Engineering Data, 5 No
