1、Designation:D7152051Designation: D7152 11Standard Practice forCalculating Viscosity of a Blend of Petroleum Products1This standard is issued under the fixed designation D7152; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the yea
2、r 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.1NOTEAdjunct reference was added editorially in October 2007.1. Scope*1.1 This practice covers the procedures for calculating
3、 the estimated kinematic viscosity of a blend of two or more petroleumproducts, such as lubricating oil base stocks, fuel components, residua with kerosine, crude oils, and related products, from theirkinematic viscosities and blend fractions.1.2 This practice allows for the estimation of the fracti
4、on of each of two petroleum products needed to prepare a blend meetinga specific viscosity.1.3 This practice may not be applicable to other types of products, or to materials which exhibit strong non-Newtonianproperties, such as viscosity index improvers, additive packages, and products containing p
5、articulates.1.4 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard.1.5 Logarithms may be either common logarithms or natural logarithms, as long as the same are used consistently. This practiceuses common logarithms. If natural l
6、ogarithms are used, the inverse function, exp(3), must be used in place of the base 10exponential function, 103, used herein.1.6 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibilityof the user of this standard to establish ap
7、propriate safety and health practices and to determine the applicability of regulatorylimitations prior to use.2. Referenced Documents2.1 ASTM Standards:2D341 Practice for Viscosity-Temperature Charts for Liquid Petroleum ProductsD445 Test Method for Kinematic Viscosity of Transparent and Opaque Liq
8、uids (and Calculation of Dynamic Viscosity)D7042 Test Method for Dynamic Viscosity and Density of Liquids by Stabinger Viscometer (and the Calculation of KinematicViscosity)2.2 ASTM Adjuncts:Calculating the Viscosity of a Blend of Petroleum Products Excel Worksheet33. Terminology3.1 Definitions of T
9、erms Specific to This Standard:3.1.1 ASTM Blending Method, na blending method at constant temperature, using components in volume percent.3.1.2 blend fraction, nthe ratio of the amount of a component to the total amount of the blend. Blend fraction may beexpressed as mass percent or volume percent.3
10、.1.3 blending method, nan equation for calculating the viscosity of a blend of components from the known viscosities of thecomponents.3.1.4 dumbbell blend, na blend made from components of widely differing viscosity.3.1.4.1 Examplea blend of S100N and Bright Stock.3.1.5 inverse blending method, nan
11、equation for calculating the predicted blending fractions of components to achieve a blendof given viscosity.1This practice is under the jurisdiction of ASTM Committee D02 on Petroleum Products and Lubricants and is the direct responsibility of Subcommittee D02.07 on FlowProperties.Current edition a
12、pproved May 1, 2005. Published June 2005. DOI: 10.1520/D7152-05E01.Current edition approved Jan. 1, 2011. Published March 2011. Originally approved in 2005. Last previous edition approved in 2005 as D7152051. DOI:10.1520/D7152-11.2For referenced ASTM standards, visit the ASTM website, www.astm.org,
13、or contact ASTM Customer Service at serviceastm.org. For Annual Book of ASTM Standardsvolume information, refer to the standards Document Summary page on the ASTM website.3Available from ASTM International Headquarters. Order Adjunct No. ADJD7152. Original adjunct produced in 2006.1This document is
14、not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Becauseit may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropri
15、ate. In all cases only the current versionof the standard as published by ASTM is to be considered the official document.*A Summary of Changes section appears at the end of this standard.Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States
16、.3.1.6 mass blend fraction, nThe ratio of the mass of a component to the total mass of the blend.3.1.7 McCoull-Walther-Wright Function, na mathematical transformation of viscosity, generally equal to the logarithm of thelogarithm of kinematic viscosity plus a constant, loglog(v+0.7). For viscosities
17、 below 2 mm2/s, additional terms are added toimprove accuracy.3.1.8 modified ASTM Blending Method, na blending method at constant temperature, using components in mass percent.3.1.9 modified Wright Blending Method, na blending method at constant viscosity, using components in mass percent.3.1.10 vol
18、ume blend fraction, nThe ratio of the volume of a component to the total volume of the blend.3.1.11 Wright Blending Method, na blending method at constant viscosity, using components in volume percent.3.2 Symbols:fij= blending fraction of component i calculated at temperature tj. Blending fraction m
19、ay be in mass percent or volumepercent.mi=slope of the viscosity-temperature line,Wi12 Wi0!Ti12 Ti0!mi-1= reciprocal of the viscosity-temperature slope, mitB= temperature, in Celsius, at which the blend has viscosity vBtij= temperature, in Celsius, at which component i has viscosity vijTij= transfor
20、med temperatureTij5 log273.151tij! (1)D7152-11_2vB= predicted kinematic viscosity of the blend, in mm2/s, at temperature tBif component blend fractions are known, ordesired viscosity of the blend if component blend fractions are being calculatedvij= viscosity of component i at temperature tjWij= Mac
21、Coull-Walther-Wright function, a transformation of viscosity:Wij5 loglog vij1 0.7 1 exp21.47 2 1.84vij2 0.51vij2!# (2)D7152-11_3 where log is the common logarithm (base 10) and exp(x) is e (2.716.) raised to the power x.WH= arbitrary high reference viscosity, transformed using Eq 2WL= arbitrary low
22、reference viscosity, transformed using Eq 24. Summary of Practice4.1 The Wright Blending Method calculates the viscosity of a blend of components at a given temperature from the knownviscosities, temperatures, and blending fractions of the components. The viscosities and temperatures of the componen
23、ts and theblend are mathematically transformed into MacCoull-Walther-Wright functions. The temperatures at which each component hastwo reference viscosities are calculated. The transformed reference temperatures are summed over all components as a weightedaverage, with the blend fractions as the wei
24、ghting factors. The two temperatures at which the blend has the reference viscositiesare used to calculate the blend viscosity at any other temperature.4.2 The Inverse Wright Blending Method calculates the blend fractions of components required to meet a target blend viscosityfrom the known viscosit
25、ies and temperatures of the components. The viscosities and temperatures of the components and the blendare mathematically transformed into MacCoull-Walther-Wright functions. The temperatures at which each component has thetarget blend viscosity are calculated. The component transformed temperatures
26、 are summed over all components, as a weightedaverage, to meet the target blend transformed temperature. The weighting factors are the desired blend fractions, which areobtained by inverting the weighted summation equation.4.3 The ASTM Blending Method calculates the viscosity of a blend of component
27、s at a given temperature from the knownviscosities of the components at the same temperature and their blending fractions. The viscosities of the components and the blendare mathematically transformed into MacCoull-Walther-Wright functions. The transformed viscosities are summed over allcomponents a
28、s a weighted average, with the blend fractions as the weighting factors. The transformed viscosity is untransformedinto viscosity units.4.4 The Inverse ASTM Blending Method calculates the blend fractions of components required to meet a target blend viscosityat a given temperature from the known vis
29、cosities of the components at the same temperature. The viscosities of the componentsand the blend are mathematically transformed into MacCoull-Walther-Wright functions. The component transformed viscositiesare summed over all components, as a weighted average, to equal the target blend transformed
30、viscosity. The weighting factorsare the desired blend fractions, which are obtained by inverting the weighted summation equation.5. Significance and Use5.1 Predicting the viscosity of a blend of components is a common problem. Both the Wright Blending Method and the ASTMBlending Method, described in
31、 this practice, may be used to solve this problem.5.2 The inverse problem, predicating the required blend fractions of components to meet a specified viscosity at a giventemperature may also be solved using either the Inverse Wright Blending Method or the Inverse ASTM Blending Method.D7152 1125.3 Th
32、e Wright Blending Methods are generally preferred since they have a firmer basis in theory, and are more accurate. TheWright Blending Methods require component viscosities to be known at two temperatures. The ASTM Blending Methods aremathematically simpler and may be used when viscosities are known
33、at a single temperature.5.4 Although this practice was developed using kinematic viscosity and volume fraction of each component, the dynamicviscosity or mass fraction, or both, may be used instead with minimal error if the densities of the components do not differ greatly.For fuel blends, it was fo
34、und that viscosity blending using mass fractions gave more accurate results. For base stock blends, therewas no significant difference between mass fraction and volume fraction calculations.5.5 The calculations described in this practice have been computerized as a spreadsheet and are available as a
35、n adjunct.36. ProcedureProcedure A6.1 Calculating the Viscosity of a Blend of Components With Known Blending Fractions by the Wright Blending Method:6.1.1 This section describes the general procedure to predict the viscosity of a blend, given the viscosity-temperature propertiesof the components and
36、 their blend fractions. Any number of components may be included. If the blend fractions are in volumepercent, this is known as the Wright Blending Method. If the blend fractions are in mass percent, this is known as the ModifiedWright Blending Method.6.1.2 Compile, for each component, its blend fra
37、ction, and viscosities at two temperatures. The viscosity of component i attemperature tijis designated vij, and its blend fraction is fi. If the viscosities are not known, measure them using a suitable testmethod. The two temperatures may be the same or different for each component.NOTE 1Test Metho
38、ds D445 and D7042 have been found suitable for this purpose.6.1.3 Transform the viscosities and temperatures of the components as follows:Zij5 vij1 0.7 1 exp2 1.47 2 1.84vij2 0.51vij2! (3)Wij5 loglog Zij!# (4)Tij5 logtij1 273.15 (5)where vijis the kinematic viscosity, in mm2/s, of component i at tem
39、perature tijin degrees Celsius, exp() is e (2.716) raised tothe power x, and log is the common logarithm (base 10).6.1.3.1 If the kinematic viscosity is greater than 2 mm2/s, the exponential term in Eq 3 is insignificant and may be omitted.6.1.3.2 Transform the temperature at which the blend viscosi
40、ty is desired using Eq 5. This transformed temperature is designatedTB.6.1.4 Calculate the inverse slope for each component, as follows:mi2 15Ti12 Ti0!Wi12 Wi0!(6)6.1.5 Calculate the predicted transformed viscosity, WB, of the blend at temperature TB, as follows:WB5TB1 ( fimi21Wi02 Ti0!( fimi2 1!(7)
41、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 2 3.295ZB1 0.6119ZB22 0.3193ZB3# (10)where Z8Band ZBare the results of intermediate calculation steps with no physical meaning.
42、NOTE 2For viscosities between 0.12 and 1000 mm2/s, the transforming Eq 3 and Eq 4 and the untransforming equations Eq 9 and Eq 10 have adiscrepancy less than 0.0004 mm2/s.NOTE 3See the worked example in Appendix X3.Procedure B6.2 Calculating the Blend Fractions of Components to Give a Target Viscosi
43、ty Using the Inverse Wright Blending Method:6.2.1 This section describes the general procedure to predict the required blending fractions of two components to meet a targetblend viscosity at a given temperature, given the viscosity-temperature properties of the components. This is known as the Inver
44、seWright Blending Method.6.2.1.1 In principle, the blend fractions may be calculated for more than two blending components, if additional constraints arespecified for the final blend. Such calculations are beyond the scope of this practice.D7152 1136.2.2 Compile the viscosities of the components at
45、two temperatures each. The viscosity of component i at temperature tijisdesignated vij. If the viscosities are not known, measure them using a suitable test method. The two temperatures do not have tobe the same for both components, nor do they have to be the same as the temperature at which the tar
46、get viscosity is specified.NOTE 4Test Methods D445 and D7042 have been found suitable for this purpose.6.2.3 Transform the viscosities and temperatures of the components using Eq 3, Eq 4, and Eq 5.6.2.4 Use the target blend viscosity, vB, as a reference viscosity. Transform vBto WBusing equations Eq
47、 3 and Eq 4.6.2.5 Calculate the transformed temperatures at which each component has that viscosity:(11) TiL 5 Ti1 2 Ti0!Wi1 2 Wi0!WL 2 Wi0! 1 Ti06.2.6 Calculate the predicted blend fraction of the first component:(12) f1 5 TB 2 T0L!T1A 2 T0L!and the fraction of the second component is f2=(1f1) beca
48、use 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 With Known Blending Fractions Using the ASTM Blending Method:6.3.1 This section describes the general procedure to predict the viscosity of a ble
49、nd at a given temperature, given the viscositiesof the components at the same temperature and their blend fractions. Any number of components may be included. If the blendfractions are in volume percent, this is known as the ASTM Blending Method. If the blend fractions are in mass percent, this isknown as the Modified ASTM Blending Method.6.3.2 Compile the viscosities of the components at a single temperature (the reference temperature). The viscosity of componenti at that temperature is designated vi. If the viscosities are not known,
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