ASTM D7152-23

Standard Practice for Calculating Viscosity of a Blend of Petroleum Products

SIGNIFICANCE AND USE
5.1 Predicting the viscosity of a blend of components is a common problem. Both the Wright Blending Method and the ASTM Blending Method, described in 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 given temperature may also be solved using either the Inverse Wright Blending Method or the Inverse ASTM Blending Method.  
5.3 The Wright Blending Methods are generally preferred since they have a firmer basis in theory, and are more accurate. The Wright Blending Methods require component viscosities to be known at two temperatures. The ASTM Blending Methods are mathematically simpler and may be used when viscosities are known at a single temperature.  
5.4 Although this practice was developed using kinematic viscosity and volume fraction of each component, the dynamic viscosity 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 found that viscosity blending using mass fractions gave more accurate results. For base stock blends, there was 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 an adjunct.3
SCOPE
1.1 This practice covers the procedures for calculating the estimated kinematic viscosity of a blend of two or more petroleum products, such as lubricating oil base stocks, fuel components, residual fuel oil with kerosene, crude oils, and related products, from their kinematic viscosities and blend fractions.  
1.2 This practice allows for the estimation of the fraction of each of two petroleum products needed to prepare a blend meeting a specific viscosity.  
1.3 This practice may not be applicable to other types of products, or to materials which exhibit strong non-Newtonian properties, such as viscosity index improvers, additive packages, and products containing particulates.  
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 practice uses common logarithms. If natural logarithms are used, the inverse function, exp(×), must be used in place of the base 10 exponential function, 10×, 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 responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and to determine the applicability of regulatory limitations prior to use.  
1.7 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

General Information

• Status: Published
• Publication Date: 30-Sep-2023
• ICS: 75.080 - Petroleum products in general
• Technical Committee: D02 - Petroleum Products, Liquid Fuels, and Lubricants
• Drafting Committee: D02.07 - Flow Properties

Relations

• Replaces: ASTM D7152-11(2016)e1 - Standard Practice for Calculating Viscosity of a Blend of Petroleum Products
• Effective Date: 01-Oct-2023
• Refers: ASTM D445-24 - Standard Test Method for Kinematic Viscosity of Transparent and Opaque Liquids (and Calculation of Dynamic Viscosity)
• Effective Date: 01-Apr-2024
• Refers: ASTM D4175-23a - Standard Terminology Relating to Petroleum Products, Liquid Fuels, and Lubricants
• Effective Date: 15-Dec-2023
• Refers: ASTM D445-23 - Standard Test Method for Kinematic Viscosity of Transparent and Opaque Liquids (and Calculation of Dynamic Viscosity)
• Effective Date: 01-Nov-2023
• Refers: ASTM D4175-23e1 - Standard Terminology Relating to Petroleum Products, Liquid Fuels, and Lubricants
• Effective Date: 01-Jul-2023
• Refers: ASTM D4175-23 - Standard Terminology Relating to Petroleum Products, Liquid Fuels, and Lubricants
• Effective Date: 01-Jul-2023
• Refers: ASTM D445-21e2 - Standard Test Method for Kinematic Viscosity of Transparent and Opaque Liquids (and Calculation of Dynamic Viscosity)
• Effective Date: 15-May-2021

Overview

ASTM D7152-23 is the globally recognized standard practice for calculating the viscosity of blends comprising two or more petroleum products. This standard, maintained by ASTM International, provides procedures to estimate the kinematic viscosity of blended petroleum products-such as lubricating oil base stocks, fuel components, residual fuel oil, kerosene, crude oils, and related substances-using the kinematic viscosities and blend fractions of individual components. Accurate prediction of blend viscosity is crucial in the petroleum industry for quality control, product formulation, and regulatory compliance.

Key Topics

Fundamental Methods:

• Wright Blending Method: Preferred for its theoretical basis and accuracy. Requires knowledge of component viscosities at two different temperatures.
• ASTM Blending Method: Simplifies calculations when component viscosities are only available at a single temperature.
• Modified Methods: Allow blending on a mass-percent or volume-percent basis, accommodating variations in component densities.

Inverse Problem-Solving:

• Both methods provide approaches to calculate either the resulting blend viscosity from known fractions or determine the necessary fractions to achieve a target viscosity.

Applicability and Limitations:

• Best suited for Newtonian fluids-common for petroleum products such as fuels and base stocks.
• Not designed for products with strong non-Newtonian properties, viscosity index improvers, additive packages, or blends containing particulates.

Calculation Aids:

• Practice includes transformations using the MacCoull-Walther-Wright function to linearize non-linear viscosity-temperature relationships, allowing reliable blend prediction.
• Electronic spreadsheets supporting these calculations are available as ASTM adjuncts.

Applications

Practical Uses in Industry:

• Lubricant Formulation: Helps refine and optimize base oil blends to meet viscosity specifications.
• Fuel Blending: Enables precise adjustment of fractions in diesel, gasoline, or residual oil blending to achieve desired flow characteristics.
• Quality Control: Supports manufacturers and refiners in meeting product consistency and regulatory viscosity requirements.
• Operational Optimization: Assists engineers and technicians in blending various stocks efficiently, saving resources and reducing off-spec material.
• Supply Chain Integration: Facilitates blending at various stages in the distribution pipeline, from refinery to end-use.

Blending Strategies:

• Use of both volume and mass fractions to accommodate density differences in components; for fuels, mass fraction blending is often more accurate.
• Tailors procedures for routine blending as well as custom batches or special product grades.

Related Standards

• ASTM D341 – Practice for Viscosity-Temperature Equations and Charts for Liquid Petroleum or Hydrocarbon Products.
• ASTM D445 – Test Method for Kinematic Viscosity of Transparent and Opaque Liquids (and Calculation of Dynamic Viscosity).
• ASTM D7042 – Test Method for Dynamic Viscosity and Density of Liquids by Stabinger Viscometer.
• ASTM D4175 – Terminology Relating to Petroleum Products, Liquid Fuels, and Lubricants.

Conclusion

Applying ASTM D7152-23 brings consistency, accuracy, and efficiency to the process of predicting or targeting blend viscosity of petroleum products. Whether for lubricant manufacturers, refineries, or fuel blenders, adopting this standard ensures adherence to best practices and streamlines decision-making across product development and supply chains. For improved blending outcomes, compliance with ASTM D7152-23, alongside its related standards, is considered essential in modern petroleum and fuels industries.

Keywords: viscosity blending, petroleum blends, kinematic viscosity, Wright Blending Method, ASTM viscosity calculation, fuel blending, lubricants, quality control

Standards Content (Sample)

This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the
Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
Designation: D7152 − 23
Standard Practice for
Calculating Viscosity of a Blend of Petroleum Products
This standard is issued under the fixed designation D7152; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope* 2. Referenced Documents
2.1 ASTM Standards:
1.1 This practice covers the procedures for calculating the
D341 Practice for Viscosity-Temperature Equations and
estimated kinematic viscosity of a blend of two or more
Charts for Liquid Petroleum or Hydrocarbon Products
petroleum products, such as lubricating oil base stocks, fuel
D445 Test Method for Kinematic Viscosity of Transparent
components, residual fuel oil with kerosene, crude oils, and
and Opaque Liquids (and Calculation of Dynamic Viscos-
related products, from their kinematic viscosities and blend
ity)
fractions.
D4175 Terminology Relating to Petroleum Products, Liquid
1.2 This practice allows for the estimation of the fraction of
Fuels, and Lubricants
each of two petroleum products needed to prepare a blend
D7042 Test Method for Dynamic Viscosity and Density of
meeting a specific viscosity.
Liquids by Stabinger Viscometer (and the Calculation of
Kinematic Viscosity)
1.3 This practice may not be applicable to other types of
products, or to materials which exhibit strong non-Newtonian
2.2 ASTM Adjuncts:
properties, such as viscosity index improvers, additive
Calculating the Viscosity of a Blend of Petroleum Products
packages, and products containing particulates.
Excel Worksheet
1.4 The values stated in SI units are to be regarded as
3. Terminology
standard. No other units of measurement are included in this
standard. 3.1 Definitions:
3.1.1 For definitions of terms used in this practice, refer to
1.5 Logarithms may be either common logarithms or natural
Terminology D4175.
logarithms, as long as the same are used consistently. This
3.2 Definitions of Terms Specific to This Standard:
practice uses common logarithms. If natural logarithms are
3.2.1 ASTM Blending Method, n—a blending method at
used, the inverse function, exp(×), must be used in place of the
constant temperature, using components in volume percent.
×
base 10 exponential function, 10 , used herein.
3.2.2 blend fraction, n—the ratio of the amount of a com-
1.6 This standard does not purport to address all of the
ponent to the total amount of the blend. Blend fraction may be
safety concerns, if any, associated with its use. It is the
expressed as mass percent or volume percent.
responsibility of the user of this standard to establish appro-
3.2.3 blending method, n—an equation for calculating the
priate safety, health, and environmental practices and to
viscosity of a blend of components from the known viscosities
determine the applicability of regulatory limitations prior to
of the components.
use.
3.2.4 dumbbell blend, n—a blend made from components of
1.7 This international standard was developed in accor-
widely differing viscosity.
dance with internationally recognized principles on standard-
3.2.4.1 Example—a blend of S100N and Bright Stock.
ization established in the Decision on Principles for the
Development of International Standards, Guides and Recom-
3.2.5 inverse blending method, n—an equation for calculat-
mendations issued by the World Trade Organization Technical
ing the predicted blending fractions of components to achieve
Barriers to Trade (TBT) Committee.
a blend of given viscosity.
1 2
This practice is under the jurisdiction of ASTM Committee D02 on Petroleum For referenced ASTM standards, visit the ASTM website, www.astm.org, or
Products, Liquid Fuels, and Lubricants and is the direct responsibility of Subcom- contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM
mittee D02.07 on Flow Properties. Standards volume information, refer to the standard’s Document Summary page on
Current edition approved Oct. 1, 2023. Published October 2023. Originally the ASTM website.
ɛ1 3
approved in 2005. Last previous edition approved in 2016 as D7152 – 11 (2016) . Available from ASTM International Headquarters. Order Adjunct No.
DOI: 10.1520/D7152-23. ADJD7152-EA. Original adjunct produced in 2006.
*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
D7152 − 23
3.2.6 mass blend fraction, n—The ratio of the mass of a and the blend are mathematically transformed into MacCoull-
component to the total mass of the blend. Walther-Wright functions. The temperatures at which each
component has two reference viscosities are calculated. The
3.2.7 McCoull-Walther-Wright Function, n—a mathematical
transformed reference temperatures are summed over all com-
transformation of viscosity, generally equal to the logarithm of
ponents as a weighted average, with the blend fractions as the
the logarithm of kinematic viscosity plus a constant, lo-
weighting factors. The two temperatures at which the blend has
g[log(v+0.7)]. For viscosities below 2 mm /s, additional terms
the reference viscosities are used to calculate the blend
are added to improve accuracy.
viscosity at any other temperature.
3.2.8 modified ASTM Blending Method, n—a blending
4.2 The Inverse Wright Blending Method calculates the
method at constant temperature, using components in mass
blend fractions of components required to meet a target blend
percent.
viscosity from the known viscosities and temperatures of the
3.2.9 modified Wright Blending Method, n—a blending
components. The viscosities and temperatures of the compo-
method at constant viscosity, using components in mass
nents and the blend are mathematically transformed into
percent.
MacCoull-Walther-Wright functions. The temperatures at
3.2.10 volume blend fraction, n—The ratio of the volume of
which each component has the target blend viscosity are
a component to the total volume of the blend.
calculated. The component transformed temperatures are
summed over all components, as a weighted average, to meet
3.2.11 Wright Blending Method, n—a blending method at
the target blend transformed temperature. The weighting fac-
constant viscosity, using components in volume percent.
tors are the desired blend fractions, which are obtained by
3.3 Symbols:
inverting the weighted summation equation.
f = blending fraction of component i calculated at tem-
ij 4.3 The ASTM Blending Method calculates the viscosity of
perature t . Blending fraction may be in mass percent
j
a blend of components at a given temperature from the known
or volume percent.
viscosities of the components at the same temperature and their
m = slope of the viscosity-temperature line,
i
blending fractions. The viscosities of the components and the
W 2 W blend are mathematically transformed into MacCoull-Walther-
~ !
i1 i0
T 2 T Wright functions. The transformed viscosities are summed
~ !
i1 i0
over all components as a weighted average, with the blend
-1
m = reciprocal of the viscosity-temperature slope, m
i i fractions as the weighting factors. The transformed viscosity is
t = temperature, in Celsius, at which the blend has
B untransformed into viscosity units.
viscosity v
B
4.4 The Inverse ASTM Blending Method calculates the
t = temperature, in Celsius, at which component i has
ij
blend fractions of components required to meet a target blend
viscosity v
ij
viscosity at a given temperature from the known viscosities of
T = transformed temperature
ij
the components at the same temperature. The viscosities of the
T 5 log 273.151t (1)
~ !
ij ij
components and the blend are mathematically transformed into
MacCoull-Walther-Wright functions. The component trans-
formed viscosities are summed over all components, as a
v = predicted kinematic viscosity of the blend, in mm /s,
B
weighted average, to equal the target blend transformed vis-
at temperature t if component blend fractions are
B
cosity. The weighting factors are the desired blend fractions,
known, or desired viscosity of the blend if component
which are obtained by inverting the weighted summation
blend fractions are being calculated
equation.
v = viscosity of component i at temperature t
ij j
W = MacCoull-Walther-Wright function, a transformation
ij
of viscosity: 5. Significance and Use
W 5 log log v 10.71exp 21.47 2 1.84v 2 0.51v
@ ~ ~ !!#
5.1 Predicting the viscosity of a blend of components is a
ij ij ij ij
(2)
common problem. Both the Wright Blending Method and the
where log is the common logarithm (base 10) and
ASTM Blending Method, described in this practice, may be
exp(x) is e (2.716.) raised to the power x.
used to solve this problem.
5.2 The inverse problem, predicating the required blend
W = arbitrary high reference viscosity, transformed using
H
Eq 2 fractions of components to meet a specified viscosity at a given
W = arbitrary low reference viscosity, transformed using temperature may also be solved using either the Inverse Wright
L
Eq 2 Blending Method or the Inverse ASTM Blending Method.
5.3 The Wright Blending Methods are generally preferred
4. Summary of Practice
since they have a firmer basis in theory, and are more accurate.
4.1 The Wright Blending Method calculates the viscosity of The Wright Blending Methods require component viscosities
a blend of components at a given temperature from the known to be known at two temperatures. The ASTM Blending
viscosities, temperatures, and blending fractions of the com- Methods are mathematically simpler and may be used when
ponents. The viscosities and temperatures of the components viscosities are known at a single temperature.
D7152 − 23
5.4 Although this practice was developed using kinematic 6.1.6 Calculate the untransformed viscosity of the blend, ν ,
B
viscosity and volume fraction of each component, the dynamic at the given temperature:
viscosity or mass fraction, or both, may be used instead with
W
B
Z' 5 10 (8)
B
minimal error if the densities of the components do not differ
Z'
B
Z 5 10 2 0.7 (9)
B
greatly. For fuel blends, it was found that viscosity blending
2 3
v 5 Z 2 exp@20.7487 2 3.295Z 10.6119Z 2 0.3193Z # (10)
using mass fractions gave more accurate results. For base stock
B B B B B
blends, there was no significant difference between mass
where Z' and Z are the results of intermediate calculation
B B
fraction and volume fraction calculations.
steps with no physical meaning.
5.5 The calculations described in this practice have been
NOTE 2—For viscosities between 0.12 and 1000 mm /s, the transform-
computerized as a spreadsheet and are available as an adjunct.
ing Eq 3 and Eq 4 and the untransforming equations Eq 9 and Eq 10 have
a discrepancy less than 0.0004 mm /s.
NOTE 3—See the worked example in Appendix X3.
6. Procedure
Procedure B
Procedure A
6.2 Calculating the Blend Fractions of Components to Give
6.1 Calculating the Viscosity of a Blend of Components With
a Target Viscosity Using the Inverse Wright Blending Method:
Known Blending Fractions by the Wright Blending Method:
6.2.1 This section describes the general procedure to predict
6.1.1 This section describes the general procedure to predict
the required blending fractions of two components to meet a
the viscosity of a blend, given the viscosity-temperature
target blend viscosity at a given temperature, given the
properties of the components and their blend fractions. Any
viscosity-temperature properties of the components. This is
number of components may be included. If the blend fractions
known as the Inverse Wright Blending Method.
are in volume percent, this is known as the Wright Blending
6.2.1.1 In principle, the blend fractions may be calculated
Method. If the blend fractions are in mass percent, this is
for more than two blending components, if additional con-
known as the Modified Wright Blending Method.
straints are specified for the final blend. Such calculations are
6.1.2 Compile, for each component, its blend fraction, and
beyond the scope of this practice.
viscosities at two temperatures. The viscosity of component i at
6.2.2 Compile the viscosities of the components at two
temperature t is designated v , and its blend fraction is f . If the
ij ij i
temperatures each. The viscosity of component i at temperature
viscosities are not known, measure them using a suitable test
t is designated v . If the viscosities are not known, measure
ij ij
method. The two temperatures may be the same or different for
them using a suitable test method. The two temperatures do not
each component.
have to be the same for both components, nor do they have to
NOTE 1—Test Methods D445 and D7042 have been found suitable for
be the same as the temperature at which the target viscosity is
this purpose.
specified.
6.1.3 Transform the viscosities and temperatures of the
NOTE 4—Test Methods D445 and D7042 have been found suitable for
components as follows:
this purpose.
Z 5 v 10.71exp~21.47 2 1.84v 2 0.51v ! (3)
ij ij ij ij 6.2.3 Transform the viscosities and temperatures of the
components using Eq 3, Eq 4, and Eq 5.
W 5 log@log~Z !# (4)
ij ij
6.2.4 Use the target blend viscosity, v , as a reference
B
T 5 log t 1273.15 (5)
@ #
ij ij
viscosity. Transform v to W using equations Eq 3 and Eq 4.
B B
where v is the kinematic viscosity, in mm /s, of component
6.2.5 Calculate the transformed temperatures at which each
ij
i at temperature t in degrees Celsius, exp() is e (2.716) raised
component has that viscosity:
ij
to the power x, and log is the common logarithm (base 10).
T 2 T
~ !
i1 i0
6.1.3.1 If the kinematic viscosity is greater than 2 mm /s, T 5 ~W 2 W !1T (11)
iL L i0 i0
~W 2 W !
i1 i0
the exponential term in Eq 3 is insignificant and may be
6.2.6 Calculate the predicted blend fraction of the first
omitted.
component:
6.1.3.2 Transform the temperature at which the blend vis-
cosity is desired using Eq 5. This transformed temperature is
T 2 T
~ !
B 0L
f 5 (12)
designated T .
B T 2 T
~ !
1A 0L
6.1.4 Calculate the inverse slope for each component, as
and the fraction of the second component is f = (1 – f )
2 1
follows:
because the total of the two components is 100 %.
~T 2 T !
i1 i0
m 5 (6)
NOTE 5—See the worked example in Appendix X4.
i
W 2 W
~ !
i1 i0
Procedure C
6.1.5 Calculate the predicted transformed viscosity, W , of
B
the blend at temperature T , as follows:
6.3 Calculating the Viscosity of a Blend of Components With
B
21 Known Blending Fractions Using the ASTM Blending Method:
T 1 f m W 2 T
~ !
B i i i0 i0
(
W 5 (7)
6.3.1 This section describes the general procedure to predict
B
f m
~ !
( i i
the viscosity of a blend at a given temperature, given the
where the sum is over all components. viscosities of the components at the same temperature and their
D7152 − 23
blend fractions. Any number of components may be included. test method. If the viscosity of a component is not known at the
If the blend fractions are in volume percent, this is known as reference temperature, but is known at two other temperatures,
the ASTM Blending Method. If the blend fractions are in mass calculate the viscosity at the reference temperature using
percent, this is known as the Modified ASTM Blending Viscosity-Temperature Charts D341 or Eq 10.
Method.
NOTE 8—Test Methods D445 and D7042 have been found suitable for
6.3.2 Compile the viscosities of the components at a single
this purpose.
temperature (the reference temperature). The viscosity of
6.4.3 Transform the viscosities of the components and the
component i at that temperature is designated v . If the
i
target blend using Eq 4.
viscosities are not known, measure them using a suitable test
6.4.4 Calculate the blend fraction of the first component:
method.
W 2 W
~ !
B 2
f 5 (16)
NOTE 6—Test Methods D445 and D7042 have been found suitable for
~W 2 W !
1 2
this purpose.
where W is the transformed viscosity of component i at the
i
6.3.2.1 If the viscosity of a component is not known at the
given temperature and f is the blending fraction of component
reference temperature, but is known at two other temperatures,
1. The blending fraction of the second component is f = (1 –
use Viscosity-Temperature Charts D341 or Eq 10 to calculate
f ) because the total of the two components is 100 %.
its viscosity at the reference temperature.
6.3.3 Transform the viscosities of the components using Eq NOTE 9—See the worked example in Appendix X6.
2.
7. Report
6.3.4 Calculate the transformed viscosity of the blend as a
weighted average of the component transformed viscosities, 7.1 Report the predicted viscosity of the blend at the given
using the blend fractions as the weighting factors:
temperature, if known blending fractions were given.
7.2 Report the calculated blending fractions, if a target
f W
@ #
i i
(
W 5 (13)
B
blend viscosity was given.
f
@ #
( i
7.3 Report which procedure was used for the calculation.
where W is the transformed viscosity of the blend, f is the
B i
blend fraction of component i, and W is the transformed
i
8. Measurement Uncertainty
viscosity of component .
i
8.1 The calculations in this practice are exact, given the
6.3.4.1 Normally, the sum of blend fractions is 100 %:
input data.
f 5 1 (14)
~ !
i
(
8.2 Measuring or compiling the input data can introduce
and the denominator in Eq 12 may be omitted. However, the sources of variation. For example, the measured viscosities of
more
...

This document is 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. Because
it may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current version
of the standard as published by ASTM is to be considered the official document.
´1
Designation: D7152 − 11 (Reapproved 2016) D7152 − 23
Standard Practice for
Calculating Viscosity of a Blend of Petroleum Products
This standard is issued under the fixed designation D7152; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
ε NOTE—Editorially updated Footnote 3 in February 2020.
1. Scope Scope*
1.1 This practice covers the procedures for calculating the estimated kinematic viscosity of a blend of two or more petroleum
products, such as lubricating oil base stocks, fuel components, residua with kerosine,residual fuel oil with kerosene, crude oils, and
related products, from their kinematic viscosities and blend fractions.
1.2 This practice allows for the estimation of the fraction of each of two petroleum products needed to prepare a blend meeting
a specific viscosity.
1.3 This practice may not be applicable to other types of products, or to materials which exhibit strong non-Newtonian properties,
such as viscosity index improvers, additive packages, and products containing particulates.
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 practice
uses common logarithms. If natural logarithms are used, the inverse function, exp(×), must be used in place of the base 10
×
exponential function, 10 , 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 responsibility
of the user of this standard to establish appropriate safety, health, and environmental practices and to determine the applicability
of regulatory limitations prior to use.
1.7 This international standard was developed in accordance with internationally recognized principles on standardization
established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued
by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
2. Referenced Documents
2.1 ASTM Standards:
D341 Practice for Viscosity-Temperature Equations and Charts for Liquid Petroleum or Hydrocarbon Products
D445 Test Method for Kinematic Viscosity of Transparent and Opaque Liquids (and Calculation of Dynamic Viscosity)
D4175 Terminology Relating to Petroleum Products, Liquid Fuels, and Lubricants
This practice is under the jurisdiction of ASTM Committee D02 on Petroleum Products, Liquid Fuels, and Lubricants and is the direct responsibility of Subcommittee
D02.07 on Flow Properties.
Current edition approved Jan. 1, 2016Oct. 1, 2023. Published February 2016October 2023. Originally approved in 2005. Last previous edition approved in 20112016 as
ɛ1
D7152 – 11.D7152 – 11 (2016) . DOI: 10.1520/D7152-11R16E01.10.1520/D7152-23.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM Standards
volume information, refer to the standard’s Document Summary page on the ASTM website.
*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
D7152 − 23
D7042 Test Method for Dynamic Viscosity and Density of Liquids by Stabinger Viscometer (and the Calculation of Kinematic
Viscosity)
2.2 ASTM Adjuncts:
Calculating the Viscosity of a Blend of Petroleum Products Excel Worksheet
3. Terminology
3.1 Definitions:
3.1.1 For definitions of terms used in this practice, refer to Terminology D4175.
3.2 Definitions of Terms Specific to This Standard:
3.2.1 ASTM Blending Method, n—a blending method at constant temperature, using components in volume percent.
3.2.2 blend fraction, n—the ratio of the amount of a component to the total amount of the blend. Blend fraction may be expressed
as mass percent or volume percent.
3.2.3 blending method, n—an equation for calculating the viscosity of a blend of components from the known viscosities of the
components.
3.2.4 dumbbell blend, n—a blend made from components of widely differing viscosity.
3.2.4.1 Example—a blend of S100N and Bright Stock.
3.2.5 inverse blending method, n—an equation for calculating the predicted blending fractions of components to achieve a blend
of given viscosity.
3.2.6 mass blend fraction, n—The ratio of the mass of a component to the total mass of the blend.
3.2.7 McCoull-Walther-Wright Function, n—a mathematical transformation of viscosity, generally equal to the logarithm of the
logarithm of kinematic viscosity plus a constant, log[log(v+0.7)]. For viscosities below 2 mm /s, additional terms are added to
improve accuracy.
3.2.8 modified ASTM Blending Method, n—a blending method at constant temperature, using components in mass percent.
3.2.9 modified Wright Blending Method, n—a blending method at constant viscosity, using components in mass percent.
3.2.10 volume blend fraction, n—The ratio of the volume of a component to the total volume of the blend.
3.2.11 Wright Blending Method, n—a blending method at constant viscosity, using components in volume percent.
3.3 Symbols:
f = blending fraction of component i calculated at temperature t . Blending fraction may be in mass percent or volume
ij j
percent.
m = slope of the viscosity-temperature line,
i
~W 2 W !
i1 i0
T 2 T
~ !
i1 i0
-1
m = reciprocal of the viscosity-temperature slope, m
i i
t = temperature, in Celsius, at which the blend has viscosity v
B B
t = temperature, in Celsius, at which component i has viscosity v
ij ij
Available from ASTM International Headquarters. Order Adjunct No. ADJD7152-EA. Original adjunct produced in 2006.
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T = transformed temperature
ij
T 5 log~273.151t ! (1)
ij ij
v = predicted kinematic viscosity of the blend, in mm /s, at temperature t if component blend fractions are known, or desired
B B
viscosity of the blend if component blend fractions are being calculated
v = viscosity of component i at temperature t
ij j
W = MacCoull-Walther-Wright function, a transformation of viscosity:
ij
W 5 log@log~v 10.71exp~21.47 2 1.84v 2 0.51v !!# (2)
ij ij ij ij
where log is the common logarithm (base 10) and exp(x) is e (2.716.) raised to the power x.
W = arbitrary high reference viscosity, transformed using Eq 2
H
W = arbitrary low reference viscosity, transformed using Eq 2
L
4. Summary of Practice
4.1 The Wright Blending Method calculates the viscosity of a blend of components at a given temperature from the known
viscosities, temperatures, and blending fractions of the components. The viscosities and temperatures of the components and the
blend are mathematically transformed into MacCoull-Walther-Wright functions. The temperatures at which each component has
two reference viscosities are calculated. The transformed reference temperatures are summed over all components as a weighted
average, with the blend fractions as the weighting factors. The two temperatures at which the blend has the reference viscosities
are 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 viscosity
from the known viscosities and temperatures of the components. The viscosities and temperatures of the components and the blend
are mathematically transformed into MacCoull-Walther-Wright functions. The temperatures at which each component has the
target blend viscosity are calculated. The component transformed temperatures are summed over all components, as a weighted
average, to meet the target blend transformed temperature. The weighting factors are the desired blend fractions, which are
obtained by inverting the weighted summation equation.
4.3 The ASTM Blending Method calculates the viscosity of a blend of components at a given temperature from the known
viscosities of the components at the same temperature and their blending fractions. The viscosities of the components and the blend
are mathematically transformed into MacCoull-Walther-Wright functions. The transformed viscosities are summed over all
components as a weighted average, with the blend fractions as the weighting factors. The transformed viscosity is untransformed
into viscosity units.
4.4 The Inverse ASTM Blending Method calculates the blend fractions of components required to meet a target blend viscosity
at a given temperature from the known viscosities of the components at the same temperature. The viscosities of the components
and the blend are mathematically transformed into MacCoull-Walther-Wright functions. The component transformed viscosities
are summed over all components, as a weighted average, to equal the target blend transformed viscosity. The weighting factors
are the desired blend fractions, which are obtained by inverting the weighted summation equation.
5. Significance and Use
5.1 Predicting the viscosity of a blend of components is a common problem. Both the Wright Blending Method and the ASTM
Blending Method, described in 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 given
temperature may also be solved using either the Inverse Wright Blending Method or the Inverse ASTM Blending Method.
5.3 The Wright Blending Methods are generally preferred since they have a firmer basis in theory, and are more accurate. The
Wright Blending Methods require component viscosities to be known at two temperatures. The ASTM Blending Methods are
mathematically simpler and may be used when viscosities are known at a single temperature.
5.4 Although this practice was developed using kinematic viscosity and volume fraction of each component, the dynamic viscosity
or mass fraction, or both, may be used instead with minimal error if the densities of the components do not differ greatly. For fuel
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blends, it was found that viscosity blending using mass fractions gave more accurate results. For base stock blends, there was 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 an adjunct.
6. Procedure
Procedure A
6.1 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 properties
of the components and their blend fractions. Any number of components may be included. If the blend fractions are in volume
percent, this is known as the Wright Blending Method. If the blend fractions are in mass percent, this is known as the Modified
Wright Blending Method.
6.1.2 Compile, for each component, its blend fraction, and viscosities at two temperatures. The viscosity of component i at
temperature t is designated v , and its blend fraction is f . If the viscosities are not known, measure them using a suitable test
ij ij i
method. The two temperatures may be the same or different for each component.
NOTE 1—Test Methods D445 and D7042 have been found suitable for this purpose.
6.1.3 Transform the viscosities and temperatures of the components as follows:
Z 5 v 10.71exp~21.47 2 1.84v 2 0.51v ! (3)
ij ij ij ij
W 5 log log Z (4)
@ ~ !#
ij ij
T 5 log t 1273.15 (5)
@ #
ij ij
where v is the kinematic viscosity, in mm /s, of component i at temperature t in degrees Celsius, exp() is e (2.716) raised to
ij ij
the power x, and log is the common logarithm (base 10).
6.1.3.1 If the kinematic viscosity is greater than 2 mm /s, the exponential term in Eq 3 is insignificant and may be omitted.
6.1.3.2 Transform the temperature at which the blend viscosity is desired using Eq 5. This transformed temperature is designated
T .
B
6.1.4 Calculate the inverse slope for each component, as follows:
~T 2 T !
i1 i0
m 5 (6)
i
W 2 W
~ !
i1 i0
6.1.5 Calculate the predicted transformed viscosity, W , of the blend at temperature T , as follows:
B B
T 1 f ~m W 2 T !
B ( i i i0 i0
W 5 (7)
B
f m
~ !
i i
(
where the sum is over all components.
6.1.6 Calculate the untransformed viscosity of the blend, ν , at the given temperature:
B
W
B
Z' 5 10 (8)
B
Z'
B
Z 5 10 2 0.7 (9)
B
2 3
v 5 Z 2 exp 20.7487 2 3.295Z 10.6119Z 2 0.3193Z (10)
@ #
B B B B B
where Z' and Z are the results of intermediate calculation steps with no physical meaning.
B B
NOTE 2—For viscosities between 0.12 and 1000 mm /s, the transforming Eq 3 and Eq 4 and the untransforming equations Eq 9 and Eq 10 have a
discrepancy less than 0.0004 mm /s.
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NOTE 3—See the worked example in Appendix X3.
Procedure B
6.2 Calculating the Blend Fractions of Components to Give a Target Viscosity 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 target
blend viscosity at a given temperature, given the viscosity-temperature properties of the components. This is known as the Inverse
Wright Blending Method.
6.2.1.1 In principle, the blend fractions may be calculated for more than two blending components, if additional constraints are
specified for the final blend. Such calculations are beyond the scope of this practice.
6.2.2 Compile the viscosities of the components at two temperatures each. The viscosity of component i at temperature t is
ij
designated v . If the viscosities are not known, measure them using a suitable test method. The two temperatures do not have to
ij
be the same for both components, nor do they have to be the same as the temperature at which the target viscosity is specified.
NOTE 4—Test 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, v , as a reference viscosity. Transform v to W using equations Eq 3 and Eq 4.
B B B
6.2.5 Calculate the transformed temperatures at which each component has that viscosity:
T 2 T
~ !
i1 i0
T 5 W 2 W 1T (11)
~ !
iL L i0 i0
W 2 W
~ !
i1 i0
6.2.6 Calculate the predicted blend fraction of the first component:
~T 2 T !
B 0L
f 5 (12)
~T 2 T !
1A 0L
and the fraction of the second component is f = (1 – f ) because the total of the two components is 100 %.
2 1
NOTE 5—See the worked example in Appendix X4.
Procedure C
6.3 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 blend at a given temperature, given the viscosities
of the components at the same temperature and their blend fractions. Any number of components may be included. If the blend
fractions are in volume percent, this is known as the ASTM Blending Method. If the blend fractions are in mass percent, this is
known 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 component
i at that temperature is designated v . If the viscosities are not known, measure them using a suitable test method.
i
NOTE 6—Test Methods D445 and D7042 have been found suitable for this purpose.
6.3.2.1 If the viscosity of a component is not known at the reference temperature, but is known at two other temperatures, use
Viscosity-Temperature Charts D341 or Eq 10 to calculate its viscosity at the reference temperature.
6.3.3 Transform the viscosities of the components using Eq 2.
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6.3.4 Calculate the transformed viscosity of the blend as a weighted average of the component transformed viscosities, using the
blend fractions as the weighting factors:
f W
@ #
i i
(
W 5 (13)
B
f
@ #
( i
where W is the transformed viscosity of the blend, f is the blend fraction of component i, and W is the transformed viscosity
B i i
of component .
i
6.3.4.1 Normally, the sum of blend fractions is 100 %:
~f ! 5 1 (14)
( i
and the denominator in Eq 12 may be omitted. However, the more general formula may be used when more convenient, for
example to save re-normalizing the base stock fractions in an oil containing other components (for example, additives).
6.3.5 Calculate the predicted (untransformed) viscosity of the blend at the reference temperature:
2 3
v 5 Z 2 0.7 2 exp 20.7487 2 3.295 Z 2 0.7 10.6119 Z 2 0.7 2 0.3193 Z 2 0.7 (15)
~ ! @ ~ ! ~ ! ~ ! #
B B B B B
NOTE 7—See the worked example in Appendix X5.
Procedure D
6.4 —Calculating the Blend Fractions of Components to Give a Target Viscosity using the Inverse ASTM Blending Method
6.4.1 This section describes the general procedure to predict the required blending fractions of two components to meet a target
blend viscosity at a given temperature, given the viscosity of the components at the same temperature. This is known as the Inverse
ASTM Blending Method.
6.4.1.1 In principle, the blend fractions may be calculated for more than two blending components, if additional constraints are
specified for the final blend. Such calculations are beyond the scope of this practice.
6.4.2 Compile the viscosities of the components at the temperature at which the target blend viscosity is specified. The viscosity
of component i at this temperature is designated v . If the viscosities are not known, measure them using a suitable test method.
i
If the viscosity of a component is not known at the reference temperature
...