1、Designation: D 7152 05e1An American National StandardStandard Practice forCalculating Viscosity of a Blend of Petroleum Products1This standard is issued under the fixed designation D 7152; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revi
2、sion, 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.e1NOTEAdjunct reference was added editorially in October 2007.1. Scope1.1 This practice covers the procedures f
3、or calculating theestimated kinematic viscosity of a blend of two or morepetroleum products, such as lubricating oil base stocks, fuelcomponents, residua with kerosine, crude oils, and relatedproducts, from their kinematic viscosities and blend fractions.1.2 This practice allows for the estimation o
4、f the fraction ofeach of two petroleum products needed to prepare a blendmeeting a specific viscosity.1.3 This practice may not be applicable to other types ofproducts, or to materials which exhibit strong non-Newtonianproperties, such as viscosity index improvers, additive pack-ages, and products c
5、ontaining particulates.1.4 The values stated in SI units are to be regarded asstandard. No other units of measurement are included in thisstandard.1.5 Logarithms may be either common logarithms or naturallogarithms, as long as the same are used consistently. Thispractice uses common logarithms. If n
6、atural logarithms areused, the inverse function, exp(3), must be used in place of thebase 10 exponential function, 103, used herein.1.6 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 establ
7、ish appro-priate safety and health practices and to determine theapplicability of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:2D 341 Viscosity-Temperature Charts for Liquid PetroleumProductsD 445 Test Method for Kinematic Viscosity of Transparentand Opaque Liquids (
8、and the Calculation of DynamicViscosity)D 7042 Test Method for Dynamic Viscosity and Density ofLiquids by Stabinger Viscometer (and the Calculation ofKinematic Viscosity)2.2 ASTM Adjuncts:Calculating the Viscosity of a Blend of Petroleum ProductsExcel Worksheet33. Terminology3.1 Definitions of Terms
9、 Specific to This Standard:3.1.1 ASTM Blending Method, na blending method atconstant temperature, using components in volume percent.3.1.2 blend fraction, nthe ratio of the amount of acomponent to the total amount of the blend. Blend fraction maybe expressed as mass percent or volume percent.3.1.3 b
10、lending method, nan equation for calculating theviscosity of a blend of components from the known viscositiesof the components.3.1.4 dumbbell blend, na blend made from components ofwidely differing viscosity.3.1.4.1 Examplea blend of S100N and Bright Stock.3.1.5 inverse blending method, nan equation
11、 for calculat-ing the predicted blending fractions of components to achievea blend of given viscosity.3.1.6 mass blend fraction, nThe ratio of the mass of acomponent to the total mass of the blend.3.1.7 McCoull-Walther-Wright Function, na mathemati-cal transformation of viscosity, generally equal to
12、 the logarithmof the logarithm of kinematic viscosity plus a constant,loglog(v+0.7). For viscosities below 2 mm2/s, additionalterms are added to improve accuracy.3.1.8 modified ASTM Blending Method, na blendingmethod at constant temperature, using components in masspercent.3.1.9 modified Wright Blen
13、ding Method, na blendingmethod at constant viscosity, using components in masspercent.3.1.10 volume blend fraction, nThe ratio of the volume ofa component to the total volume of the blend.3.1.11 Wright Blending Method, na blending method atconstant viscosity, using components in volume percent.1This
14、 practice is under the jurisdiction of ASTM Committee D02 on PetroleumProducts and Lubricants and is the direct responsibility of Subcommittee D02.07 onFlow Properties.Current edition approved May 1, 2005. Published June 2005.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orco
15、ntact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.3Available from ASTM International Headquarters. Order Adjunct No.ADJD7152. Original adjunct produced in 2006.1Copyright ASTM Internati
16、onal, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.3.2 Symbols:fij= blending fraction of component i calculated attemperature tj. Blending fraction may be in masspercent or volume percent.mi=slope of the viscosity-temperature line,Wi12 Wi0!Ti12 Ti0!mi-1= recipr
17、ocal of the viscosity-temperature slope, mitB= temperature, in Celsius, at which the blend hasviscosity vBtij= temperature, in Celsius, at which component i hasviscosity vijTij= transformed temperatureTij5 log273.151tij! (1)vB= predicted kinematic viscosity of the blend, inmm2/s, at temperature tBif
18、 component blend frac-tions are known, or desired viscosity of the blend ifcomponent blend fractions are being calculatedvij= viscosity of component i at temperature tjWij= MacCoull-Walther-Wright function, a transforma-tion of viscosity:Wij5 loglog vij1 0.7 1 exp21.47 2 1.84vij2 0.51vij2!# (2)where
19、 log is the common logarithm (base 10) andexp(x) is e (2.716.) raised to the power x.WH= arbitrary high reference viscosity, transformed usingEq 2WL= arbitrary low reference viscosity, transformed usingEq 24. Summary of Practice4.1 The Wright Blending Method calculates the viscosity ofa blend of com
20、ponents at a given temperature from the knownviscosities, temperatures, and blending fractions of the com-ponents. The viscosities and temperatures of the componentsand the blend are mathematically transformed into MacCoull-Walther-Wright functions. The temperatures at which eachcomponent has two re
21、ference viscosities are calculated. Thetransformed reference temperatures are summed over all com-ponents as a weighted average, with the blend fractions as theweighting factors. The two temperatures at which the blend hasthe reference viscosities are used to calculate the blendviscosity at any othe
22、r temperature.4.2 The Inverse Wright Blending Method calculates theblend fractions of components required to meet a target blendviscosity from the known viscosities and temperatures of thecomponents. The viscosities and temperatures of the compo-nents and the blend are mathematically transformed int
23、oMacCoull-Walther-Wright functions. The temperatures atwhich each component has the target blend viscosity arecalculated. The component transformed temperatures aresummed over all components, as a weighted average, to meetthe target blend transformed temperature. The weighting fac-tors are the desir
24、ed blend fractions, which are obtained byinverting the weighted summation equation.4.3 The ASTM Blending Method calculates the viscosity ofa blend of components at a given temperature from the knownviscosities of the components at the same temperature and theirblending fractions. The viscosities of
25、the components and theblend are mathematically transformed into MacCoull-Walther-Wright functions. The transformed viscosities are summedover all components as a weighted average, with the blendfractions as the weighting factors. The transformed viscosity isuntranformed into viscosity units.4.4 The
26、Inverse ASTM Blending Method calculates theblend fractions of components required to meet a target blendviscosity at a given temperature from the known viscosities ofthe components at the same temperature. The viscosities of thecomponents and the blend are mathematically transformed intoMacCoull-Wal
27、ther-Wright functions. The component trans-formed viscosities are summed over all components, as aweighted average, to equal the target blend transformed vis-cosity. The weighting factors are the desired blend fractions,which are obtained by inverting the weighted summationequation.5. Significance a
28、nd Use5.1 Predicting the viscosity of a blend of components is acommon problem. Both the Wright Blending Method and theASTM Blending Method, described in this practice, may beused to solve this problem.5.2 The inverse problem, predicating the required blendfractions of components to meet a specified
29、 viscosity at a giventemperature may also be solved using either the Inverse WrightBlending Method or the Inverse ASTM Blending Method.5.3 The Wright Blending Methods are generally preferredsince they have a firmer basis in theory, and are more accurate.The Wright Blending Methods require component
30、viscositiesto be known at two temperatures. The ASTM BlendingMethods are mathematically simpler and may be used whenviscosities are known at a single temperature.5.4 Although this practice was developed using kinematicviscosity and volume fraction of each component, the dynamicviscosity or mass frac
31、tion, or both, may be used instead withminimal error if the densities of the components do not differgreatly. For fuel blends, it was found that viscosity blendingusing mass fractions gave more accurate results. For base stockblends, there was no significant difference between massfraction and volum
32、e fraction calculations.5.5 The calculations described in this practice have beencomputerized as a spreadsheet and are available as an adjunct.36. ProcedureProcedure A6.1 Calculating the Viscosity of a Blend of Components WithKnown Blending Fractions by the Wright Blending Method:6.1.1 This section
33、describes the general procedure to predictthe viscosity of a blend, given the viscosity-temperatureproperties of the components and their blend fractions. Anynumber of components may be included. If the blend fractionsare in volume percent, this is known as the Wright BlendingMethod. If the blend fr
34、actions are in mass percent, this isknown as the Modified Wright Blending Method.D715205e126.1.2 Compile, for each component, its blend fraction, andviscosities at two temperatures. The viscosity of component i attemperature tijis designated vij, and its blend fraction is fi.Iftheviscosities are not
35、 known, measure them using a suitable testmethod. The two temperatures may be the same or different foreach component.NOTE 1Test Methods D 445 and D 7042 have been found suitable forthis purpose.6.1.3 Transform the viscosities and temperatures of thecomponents as follows:Zij5 vij1 0.7 1 exp2 1.47 2
36、1.84vij2 0.51vij2! (3)Wij5 loglog Zij!# (4)Tij5 logtij1 273.15 (5)where vijis the kinematic viscosity, in mm2/s, of componenti at temperature tijin degrees Celsius, exp() is e (2.716) raisedto the power x, and log is the common logarithm (base 10).6.1.3.1 If the kinematic viscosity is greater than 2
37、 mm2/s,the exponential term in Eq 3 is insignificant and may beomitted.6.1.3.2 Transform the temperature at which the blend vis-cosity is desired using Eq 5. This transformed temperature isdesignated TB.6.1.4 Calculate the inverse slope for each component, asfollows:mi2 15Ti12 Ti0!Wi12 Wi0!(6)6.1.5
38、Calculate the predicted transformed viscosity, WB,ofthe blend at temperature TB, as follows:WB5TB1 ( fimi21Wi02 Ti0!( fimi2 1!(7)where the sum is over all components.6.1.6 Calculate the untransformed viscosity of the blend, nB,at the given temperature:Z8B5 10WB(8)ZB5 10Z8B2 0.7 (9)vB5 ZB2 exp20.7487
39、 2 3.295ZB1 0.6119ZB22 0.3193ZB3#(10)where Z8Band ZBare the results of intermediate calculationsteps with no physical meaning.NOTE 2For viscosities between 0.12 and 1000 mm2/s, the transform-ing Eq 3 and Eq 4 and the untransforming equations Eq 9 and Eq 10 havea discrepancy less than 0.0004 mm2/s.NO
40、TE 3See the worked example in Appendix X3.Procedure B6.2 Calculating the Blend Fractions of Components to Givea Target Viscosity Using the Inverse Wright Blending Method:6.2.1 This section describes the general procedure to predictthe required blending fractions of two components to meet atarget ble
41、nd viscosity at a given temperature, given theviscosity-temperature properties of the components. This isknown as the Inverse Wright Blending Method.6.2.1.1 In principle, the blend fractions may be calculatedfor more than two blending components, if additional con-straints are specified for the fina
42、l blend. Such calculations arebeyond the scope of this practice.6.2.2 Compile the viscosities of the components at twotemperatures each. The viscosity of component i at temperaturetijis designated vij. If the viscosities are not known, measurethem using a suitable test method. The two temperatures d
43、o nothave to be the same for both components, nor do they have tobe the same as the temperature at which the target viscosity isspecified.NOTE 4Test Methods D 445 and D 7042 have been found suitable forthis purpose.6.2.3 Transform the viscosities and temperatures of thecomponents using Eq 3, Eq 4, a
44、nd Eq 5.6.2.4 Use the target blend viscosity, vB, as a referenceviscosity. Transform vBto WBusing equations Eq 3 and Eq 4.6.2.5 Calculate the transformed temperatures at which eachcomponent has that viscosity:TiL5Ti12 Ti0!Wi12 Wi0!WL2 Wi0! 1 Ti0(11)6.2.6 Calculate the predicted blend fraction of the
45、 firstcomponent:f15TB2 T0L!T1A2 T0L!(12)and the fraction of the second component is f2=(1f1)because the total of the two components is 100 %.NOTE 5See the worked example in Appendix X4.Procedure C6.3 Calculating the Viscosity of a Blend of Components WithKnown Blending Fractions Using the ASTM Blend
46、ing Method:6.3.1 This section describes the general procedure to predictthe viscosity of a blend at a given temperature, given theviscosities of the components at the same temperature and theirblend fractions. Any number of components may be included.If the blend fractions are in volume percent, thi
47、s is known asthe ASTM Blending Method. If the blend fractions are in masspercent, this is known as the Modified ASTM BlendingMethod.6.3.2 Compile the viscosities of the components at a singletemperature (the reference temperature). The viscosity ofcomponent i at that temperature is designated vi.Ift
48、heviscosities are not known, measure them using a suitable testmethod.NOTE 6Test Methods D 445 and D 7042 have been found suitable forthis purpose.6.3.2.1 If the viscosity of a component is not known at thereference temperature, but is known at two other temperatures,use Viscosity-Temperature Charts
49、 D 341 or Eq 10 to calculateits viscosity at the reference temperature.6.3.3 Transform the viscosities of the components using Eq2.D715205e136.3.4 Calculate the transformed viscosity of the blend as aweighted average of the component transformed viscosities,using the blend fractions as the weighting factors:WB5(fiWi#(fi#(13)where WBis the transformed viscosity of the blend, fiis theblend fraction of component i, and Wiis the transformedviscosity of componenti.6.3.4.1 Normally, the sum of blend fractions is 100 %:(fi! 5 1 (14)and the denomi
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