ASTM D7152-05
(Practice)Standard Practice for Calculating Viscosity of a Blend of Petroleum Products
Standard Practice for Calculating Viscosity of a Blend of Petroleum Products
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, 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 stnadard. 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 and health practices and to determine the applicability of regulatory limitations prior to use.
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An American National Standard
Designation:D7152–05
Standard Practice for
Calculating Viscosity of a Blend of Petroleum Products
This standard is issued under the fixed designation D 7152; 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 (e) indicates an editorial change since the last revision or reapproval.
1. Scope D 445 Test Method for Kinematic Viscosity of Transparent
and Opaque Liquids (and the Calculation of Dynamic
1.1 This practice covers the procedures for calculating the
Viscosity)
estimated kinematic viscosity of a blend of two or more
D 7042 Test Method for Dynamic Viscosity and Density of
petroleum products, such as lubricating oil base stocks, fuel
Liquids by Stabinger Viscometer (and the Calculation of
components, residua with kerosine, crude oils, and related
Kinematic Viscosity)
products, from their kinematic viscosities and blend fractions.
1.2 This practice allows for the estimation of the fraction of
3. Terminology
each of two petroleum products needed to prepare a blend
3.1 Definitions of Terms Specific to This Standard:
meeting a specific viscosity.
3.1.1 ASTM Blending Method, n—a blending method at
1.3 This practice may not be applicable to other types of
constant temperature, using components in volume percent.
products, or to materials which exhibit strong non-Newtonian
3.1.2 blend fraction, n—the ratio of the amount of a
properties, such as viscosity index improvers, additive pack-
componenttothetotalamountoftheblend.Blendfractionmay
ages, and products containing particulates.
be expressed as mass percent or volume percent.
1.4 The values stated in SI units are to be regarded as
3.1.3 blending method, n—an equation for calculating the
standard. No other units of measurement are included in this
viscosity of a blend of components from the known viscosities
standard.
of the components.
1.5 Logarithmsmaybeeithercommonlogarithmsornatural
3.1.4 dumbbell blend, n—ablendmadefromcomponentsof
logarithms, as long as the same are used consistently. This
widely differing viscosity.
practice uses common logarithms. If natural logarithms are
3.1.4.1 Example—a blend of S100N and Bright Stock.
used,theinversefunction,exp(3),mustbeusedinplaceofthe
3.1.5 inverse blending method, n—an equation for calculat-
base 10 exponential function, 10 , used herein.
ing the predicted blending fractions of components to achieve
1.6 This standard does not purport to address all of the
a blend of given viscosity.
safety concerns, if any, associated with its use. It is the
3.1.6 mass blend fraction, n—The ratio of the mass of a
responsibility of the user of this standard to establish appro-
component to the total mass of the blend.
priate safety and health practices and to determine the
3.1.7 McCoull-Walther-Wright Function, n—a mathemati-
applicability of regulatory limitations prior to use.
caltransformationofviscosity,generallyequaltothelogarithm
2. Referenced Documents
of the logarithm of kinematic viscosity plus a constant,
log[log(v+0.7)]. For viscosities below 2 mm /s, additional
2.1 ASTM Standards:
terms are added to improve accuracy.
D 341 Viscosity-Temperature Charts for Liquid Petroleum
3.1.8 modified ASTM Blending Method, n—a blending
Products
method at constant temperature, using components in mass
percent.
3.1.9 modified Wright Blending Method, n—a blending
This practice is under the jurisdiction of ASTM Committee D02 on Petroleum
method at constant viscosity, using components in mass
Products and Lubricants and is the direct responsibility of Subcommittee D02.07 on
percent.
Flow Properties.
3.1.10 volume blend fraction, n—The ratio of the volume of
Current edition approved May 1, 2005. Published June 2005.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or a component to the total volume of the blend.
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
3.1.11 Wright Blending Method, n—a blending method at
Standards volume information, refer to the standard’s Document Summary page on
constant viscosity, using components in volume percent.
the ASTM website.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.
D7152–05
3.2 Symbols: 4.3 TheASTM Blending Method calculates the viscosity of
a blend of components at a given temperature from the known
viscositiesofthecomponentsatthesametemperatureandtheir
f = blending fraction of component i calculated at
ij
blending fractions. The viscosities of the components and the
temperature t. Blending fraction may be in mass
j
blend are mathematically transformed into MacCoull-Walther-
percent or volume percent.
Wright functions. The transformed viscosities are summed
~W 2 W !
m =
i1 i0
i
over all components as a weighted average, with the blend
slope of the viscosity-temperature line,
~T 2 T !
i1 i0
fractions as the weighting factors. The transformed viscosity is
-1 untranformed into viscosity units.
m = reciprocal of the viscosity-temperature slope, m
i i
4.4 The Inverse ASTM Blending Method calculates the
t = temperature, in Celsius, at which the blend has
B
blend fractions of components required to meet a target blend
viscosity v
B
viscosity at a given temperature from the known viscosities of
t = temperature, in Celsius, at which component i has
ij
the components at the same temperature. The viscosities of the
viscosity v
ij
components and the blend are mathematically transformed into
T = transformed temperature
ij
MacCoull-Walther-Wright functions. The component trans-
T 5 log~273.151t ! (1)
ij ij
formed viscosities are summed over all components, as a
weighted average, to equal the target blend transformed vis-
v = predicted kinematic viscosity of the blend, in
B
cosity. The weighting factors are the desired blend fractions,
mm /s, at temperature t if component blend frac-
B
which are obtained by inverting the weighted summation
tions are known, or desired viscosity of the blend if
equation.
component blend fractions are being calculated
v = viscosity of component i at temperature t
ij j
W = MacCoull-Walther-Wright function, a transforma- 5. Significance and Use
ij
tion of viscosity:
5.1 Predicting the viscosity of a blend of components is a
W 5 log[log ~v 1 0.7 1 exp~21.47 2 1.84v
ij ij ij
common problem. Both the Wright Blending Method and the
2 0.51v !!# (2)
ASTM Blending Method, described in this practice, may be
ij
where log is the common logarithm (base 10) and
used to solve this problem.
exp(x) is e (2.716.) raised to the power x.
5.2 The inverse problem, predicating the required blend
W = arbitraryhighreferenceviscosity,transformedusing
fractions of components to meet a specified viscosity at a given
H
Eq 2
temperature may also be solved using either the InverseWright
W = arbitrary low reference viscosity, transformed using
L Blending Method or the Inverse ASTM Blending Method.
Eq 2
5.3 The Wright Blending Methods are generally preferred
since they have a firmer basis in theory, and are more accurate.
4. Summary of Practice
The Wright Blending Methods require component viscosities
to be known at two temperatures. The ASTM Blending
4.1 The Wright Blending Method calculates the viscosity of
Methods are mathematically simpler and may be used when
a blend of components at a given temperature from the known
viscosities are known at a single temperature.
viscosities, temperatures, and blending fractions of the com-
5.4 Although this practice was developed using kinematic
ponents. The viscosities and temperatures of the components
viscosity and volume fraction of each component, the dynamic
and the blend are mathematically transformed into MacCoull-
viscosity or mass fraction, or both, may be used instead with
Walther-Wright functions. The temperatures at which each
minimal error if the densities of the components do not differ
component has two reference viscosities are calculated. The
greatly. For fuel blends, it was found that viscosity blending
transformed reference temperatures are summed over all com-
usingmassfractionsgavemoreaccurateresults.Forbasestock
ponents as a weighted average, with the blend fractions as the
blends, there was no significant difference between mass
weightingfactors.Thetwotemperaturesatwhichtheblendhas
fraction and volume fraction calculations.
the reference viscosities are used to calculate the blend
5.5 The calculations described in this practice have been
viscosity at any other temperature.
computerized as a spreadsheet and will soon be available as an
4.2 The Inverse Wright Blending Method calculates the adjunct.
blend fractions of components required to meet a target blend
viscosity from the known viscosities and temperatures of the 6. Procedure
components. The viscosities and temperatures of the compo-
Procedure A
nents and the blend are mathematically transformed into
MacCoull-Walther-Wright functions. The temperatures at
6.1 Calculating the Viscosity of a Blend of Components With
which each component has the target blend viscosity are
Known Blending Fractions by the Wright Blending Method:
calculated. The component transformed temperatures are
6.1.1 This section describes the general procedure to predict
summed over all components, as a weighted average, to meet
the viscosity of a blend, given the viscosity-temperature
the target blend transformed temperature. The weighting fac-
properties of the components and their blend fractions. Any
tors are the desired blend fractions, which are obtained by
number of components may be included. If the blend fractions
inverting the weighted summation equation. are in volume percent, this is known as the Wright Blending
D7152–05
Method. If the blend fractions are in mass percent, this is target blend viscosity at a given temperature, given the
known as the Modified Wright Blending Method. viscosity-temperature properties of the components. This is
6.1.2 Compile, for each component, its blend fraction, and known as the Inverse Wright Blending Method.
viscositiesattwotemperatures.Theviscosityofcomponent iat 6.2.1.1 In principle, the blend fractions may be calculated
temperaturet isdesignatedv ,anditsblendfractionisf.Ifthe for more than two blending components, if additional con-
ij ij i
viscosities are not known, measure them using a suitable test straints are specified for the final blend. Such calculations are
method.The two temperatures may be the same or different for beyond the scope of this practice.
each component. 6.2.2 Compile the viscosities of the components at two
temperatureseach.Theviscosityofcomponent iattemperature
NOTE 1—Test Methods D 445 and D 7042 have been found suitable for
t is designated v . If the viscosities are not known, measure
ij ij
this purpose.
themusingasuitabletestmethod.Thetwotemperaturesdonot
6.1.3 Transform the viscosities and temperatures of the
have to be the same for both components, nor do they have to
components as follows:
be the same as the temperature at which the target viscosity is
Z 5 v 1 0.7 1 exp~2 1.47 2 1.84v 2 0.51v ! (3)
specified.
ij ij ij ij
NOTE 4—Test Methods D 445 and D 7042 have been found suitable for
W 5 log@log ~Z !# (4)
ij ij
this purpose.
6.2.3 Transform the viscosities and temperatures of the
T 5 log@t 1 273.15] (5)
ij ij
components using Eq 3, Eq 4, and Eq 5.
where v is the kinematic viscosity, in mm /s, of component
6.2.4 Use the target blend viscosity, v , as a reference
ij
B
i at temperature t in degrees Celsius, exp() is e (2.716) raised
viscosity. Transform v to W using equations Eq 3 and Eq 4.
ij
B B
to the power x, and log is the common logarithm (base 10).
6.2.5 Calculate the transformed temperatures at which each
6.1.3.1 If the kinematic viscosity is greater than 2 mm /s,
component has that viscosity:
the exponential term in Eq 3 is insignificant and may be
~T 2 T !
i1 i0
omitted. T 5 ~W 2 W ! 1 T (11)
iL L i0 i0
~W 2 W !
i1 i0
6.1.3.2 Transform the temperature at which the blend vis-
6.2.6 Calculate the predicted blend fraction of the first
cosity is desired using Eq 5. This transformed temperature is
component:
designated T .
B
6.1.4 Calculate the inverse slope for each component, as ~T 2 T !
B 0L
f 5 (12)
~T 2 T !
follows:
1A 0L
T 2 T and the fraction of the second component is f=(1– f )
~ !
i1 i0 2 1
2 1
m 5 (6)
i
~W 2 W ! because the total of the two components is 100 %.
i1 i0
6.1.5 Calculate the predicted transformed viscosity, W ,of
NOTE 5—See the worked example in Appendix X4.
B
the blend at temperature T , as follows:
B
Procedure C
T 1 ( f m W 2 T !
~
B i i i0 i0
W 5 (7)
6.3 Calculating the Viscosity of a Blend of Components With
B 2 1
( ~fm !
i i
Known Blending Fractions Using the ASTM Blending Method:
where the sum is over all components.
6.3.1 This section describes the general procedure to predict
6.1.6 Calculatetheuntransformedviscosityoftheblend, n ,
B
the viscosity of a blend at a given temperature, given the
at the given temperature:
viscositiesofthecomponentsatthesametemperatureandtheir
W
B blend fractions. Any number of components may be included.
Z8 5 10 (8)
B
If the blend fractions are in volume percent, this is known as
theASTM Blending Method. If the blend fractions are in mass
Z8
B
Z 5 10 2 0.7 (9)
B
percent, this is known as the Modified ASTM Blending
Method.
2 3
v 5 Z 2 exp@20.7487 2 3.295Z 1 0.6119Z 2 0.3193Z #
B B B B B
6.3.2 Compile the viscosities of the components at a single
(10)
temperature (the reference temperature). The viscosity of
where Z8 and Z are the results of intermediate calculation
B B component i at that temperature is designated v.Ifthe
i
steps with no physical meaning.
viscosities are not known, measure them using a suitable test
2 method.
NOTE 2—For viscosities between 0.12 and 1000 mm /s, the transform-
ing Eq 3 and Eq 4 and the untransforming equations Eq 9 and Eq 10 have
NOTE 6—Test Methods D 445 and D 7042 have been found suitable for
a discrepancy less than 0.0004 mm /s.
this purpose.
NOTE 3—See the worked example in Appendix X3.
6.3.2.1 If the viscosity of a component is not known at the
Procedure B
reference temperature, but is known at two other temperatures,
6.2 Calculating the Blend Fractions of Components to Give use Viscosity-Temperature Charts D 341 or Eq 10 to calculate
a Target Viscosity Using the Inverse Wright Blending Method: its viscosity at the reference temperature.
6.2.1 This section describes the general procedure to predict 6.3.3 Transform the viscosities of the components using Eq
the required blending fractions of two components to meet a 2.
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