ASTM D7152-11(2016)

NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.
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Designation: D7152 − 11 (Reapproved 2016)
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.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope and Opaque Liquids (and Calculation of DynamicViscos-
ity)
1.1 This practice covers the procedures for calculating the
D7042Test Method for Dynamic Viscosity and Density of
estimated kinematic viscosity of a blend of two or more
Liquids by Stabinger Viscometer (and the Calculation of
petroleum products, such as lubricating oil base stocks, fuel
Kinematic Viscosity)
components, residua with kerosine, crude oils, and related
2.2 ASTM Adjuncts:
products, from their kinematic viscosities and blend fractions.
Calculating the Viscosity of a Blend of Petroleum Products
1.2 This practice allows for the estimation of the fraction of
Excel Worksheet
each of two petroleum products needed to prepare a blend
meeting a specific viscosity.
3. Terminology
1.3 This practice may not be applicable to other types of
3.1 Definitions of Terms Specific to This Standard:
products, or to materials which exhibit strong non-Newtonian
3.1.1 ASTM Blending Method, n—a blending method at
properties, such as viscosity index improvers, additive
constant temperature, using components in volume percent.
packages, and products containing particulates.
3.1.2 blend fraction, n—the ratio of the amount of a com-
1.4 The values stated in SI units are to be regarded as
ponent to the total amount of the blend. Blend fraction may be
standard. No other units of measurement are included in this
expressed as mass percent or volume percent.
standard.
3.1.3 blending method, n—an equation for calculating the
1.5 Logarithmsmaybeeithercommonlogarithmsornatural
viscosity of a blend of components from the known viscosities
logarithms, as long as the same are used consistently. This
of the components.
practice uses common logarithms. If natural logarithms are
3.1.4 dumbbell blend, n—ablendmadefromcomponentsof
used, the inverse function, exp(×), must be used in place of the
widely differing viscosity.
×
, used herein.
base 10 exponential function, 10
3.1.4.1 Example—a blend of S100N and Bright Stock.
1.6 This standard does not purport to address all of the
3.1.5 inverse blending method, n—an equation for calculat-
safety concerns, if any, associated with its use. It is the
ing the predicted blending fractions of components to achieve
responsibility of the user of this standard to establish appro-
a blend of given viscosity.
priate safety and health practices and to determine the
3.1.6 mass blend fraction, n—The ratio of the mass of a
applicability of regulatory limitations prior to use.
component to the total mass of the blend.
2. Referenced Documents
3.1.7 McCoull-Walther-WrightFunction,n—amathematical
transformation of viscosity, generally equal to the logarithm of
2.1 ASTM Standards:
the logarithm of kinematic viscosity plus a constant, lo-
D341Practice for Viscosity-Temperature Charts for Liquid
g[log(v+0.7)]. For viscosities below 2mm /s, additional terms
Petroleum Products
are added to improve accuracy.
D445Test Method for Kinematic Viscosity of Transparent
3.1.8 modified ASTM Blending Method, n—a blending
method at constant temperature, using components in mass
This practice is under the jurisdiction ofASTM Committee D02 on Petroleum
percent.
Products, Liquid Fuels, and Lubricants and is the direct responsibility of Subcom-
3.1.9 modified Wright Blending Method, n—a blending
mittee D02.07 on Flow Properties.
Current edition approved Jan. 1, 2016. Published February 2016. Originally
method at constant viscosity, using components in mass
approved in 2005. Last previous edition approved in 2011 as D7152–11. DOI:
percent.
10.1520/D7152-11R16.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
Standards volume information, refer to the standard’s Document Summary page on Available from ASTM International Headquarters. Order Adjunct No.
the ASTM website. ADJD7152. Original adjunct produced in 2006.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
D7152 − 11 (2016)
3.1.10 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
3.1.11 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
3.2 Symbols:
inverting the weighted summation equation.
4.3 TheASTM Blending Method calculates the viscosity of
f = blending fraction of component i calculated at tem-
ij
perature t. Blending fraction may be in mass percent a blend of components at a given temperature from the known
j
viscositiesofthecomponentsatthesametemperatureandtheir
or volume percent.
m = slope of the viscosity-temperature line, blending fractions. The viscosities of the components and the
i
blend are mathematically transformed into MacCoull-Walther-
~W 2 W !
i1 i0
Wright functions. The transformed viscosities are summed
T 2 T
~ !
i1 i0
over all components as a weighted average, with the blend
-1
fractions as the weighting factors.The transformed viscosity is
m = reciprocal of the viscosity-temperature slope, m
i i
untransformed into viscosity units.
t = temperature, in Celsius, at which the blend has
B
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) componentsandtheblendaremathematicallytransformedinto
ij ij
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,ordesiredviscosityoftheblendifcomponent
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 5. Significance and Use
ij
of viscosity:
5.1 Predicting the viscosity of a blend of components is a
common problem. Both the Wright Blending Method and the
W 5 log@log~v 10.71exp~21.47 2 1.84v 2 0.51v !!#
ij ij ij ij
ASTM Blending Method, described in this practice, may be
(2)
used to solve this problem.
where log is the common logarithm (base 10) and
exp(x) is e (2.716.) raised to the power x.
5.2 The inverse problem, predicating the required blend
fractionsofcomponentstomeetaspecifiedviscosityatagiven
W = arbitrary high reference viscosity, transformed using
H
temperaturemayalsobesolvedusingeithertheInverseWright
Eq 2
Blending Method or the Inverse ASTM Blending Method.
W = arbitrary low reference viscosity, transformed using
L
5.3 The Wright Blending Methods are generally preferred
Eq 2
since they have a firmer basis in theory, and are more accurate.
The Wright Blending Methods require component viscosities
4. Summary of Practice
to be known at two temperatures. The ASTM Blending
4.1 TheWright 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.
computerizedasaspreadsheetandareavailableasanadjunct.
4.2 The Inverse Wright Blending Method calculates the
blend fractions of components required to meet a target blend
6. Procedure
viscosity from the known viscosities and temperatures of the
Procedure A
components. The viscosities and temperatures of the compo-
nents and the blend are mathematically transformed into 6.1 CalculatingtheViscosityofaBlendofComponentsWith
MacCoull-Walther-Wright functions. The temperatures at Known Blending Fractions by the Wright Blending Method:
D7152 − 11 (2016)
6.1.1 Thissectiondescribesthegeneralproceduretopredict 6.2.1 Thissectiondescribesthegeneralproceduretopredict
the viscosity of a blend, given the viscosity-temperature the required blending fractions of two components to meet a
properties of the components and their blend fractions. Any target blend viscosity at a given temperature, given the
number of components may be included. If the blend fractions viscosity-temperature properties of the components. This is
are in volume percent, this is known as the Wright Blending known as the Inverse Wright Blending Method.
Method. If the blend fractions are in mass percent, this is
6.2.1.1 In principle, the blend fractions may be calculated
known as the Modified Wright Blending Method.
for more than two blending components, if additional con-
6.1.2 Compile, for each component, its blend fraction, and
straints are specified for the final blend. Such calculations are
viscositiesattwotemperatures.Theviscosityofcomponentiat
beyond the scope of this practice.
temperaturet isdesignatedv ,anditsblendfractionisf.Ifthe
ij ij i 6.2.2 Compile the viscosities of the components at two
viscosities are not known, measure them using a suitable test
temperatureseach.Theviscosityofcomponentiattemperature
method.Thetwotemperaturesmaybethesameordifferentfor
t is designated v . If the viscosities are not known, measure
ij ij
each component.
themusingasuitabletestmethod.Thetwotemperaturesdonot
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
components as follows:
NOTE 4—Test Methods D445 and D7042 have been found suitable for
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
W 5 log@log~Z !# (4)
ij ij
components using Eq 3, Eq 4, and Eq 5.
T 5 log t 1273.15 (5)
@ #
ij ij
6.2.4 Use the target blend viscosity, v , as a reference
B
where v is the kinematic viscosity, in mm /s, of component viscosity. Transform v to W using equations Eq 3 and Eq 4.
ij B B
i at temperature t in degrees Celsius, exp() is e (2.716) raised
6.2.5 Calculate the transformed temperatures at which each
ij
to the power x, and log is the common logarithm (base 10).
component has that viscosity:
6.1.3.1 If the kinematic viscosity is greater than 2 mm /s,
~T 2 T !
i1 i0
the exponential term in Eq 3 is insignificant and may be T 5 ~W 2 W !1T (11)
iL L i0 i0
W 2 W
~ !
i1 i0
omitted.
6.1.3.2 Transform the temperature at which the blend vis- 6.2.6 Calculate the predicted blend fraction of the first
component:
cosity is desired using Eq 5. This transformed temperature is
designated T .
B
~T 2 T !
B 0L
f 5 (12)
6.1.4 Calculate the inverse slope for each component, as 1
T 2 T
~ !
1A 0L
follows:
and the fraction of the second component is f =(1– f )
2 1
~T 2 T !
i1 i0
m 5 (6) because the total of the two components is 100%.
i
W 2 W
~ !
i1 i0
NOTE 5—See the worked example in Appendix X4.
6.1.5 Calculate the predicted transformed viscosity, W ,of
B
the blend at temperature T , as follows:
B Procedure C
T 1 f m W 2 T
~ !
B i i i0 i0
( 6.3 CalculatingtheViscosityofaBlendofComponentsWith
W 5 (7)
B
f m
~ ! Known Blending Fractions Using the ASTM Blending Method:
( i i
6.3.1 Thissectiondescribesthegeneralproceduretopredict
where the sum is over all components.
the viscosity of a blend at a given temperature, given the
6.1.6 Calculatetheuntransformedviscosityoftheblend, ν ,
B
viscositiesofthecomponentsatthesametemperatureandtheir
at the given temperature:
blend fractions. Any number of components may be included.
W
B
Z' 5 10 (8)
B
If the blend fractions are in volume percent, this is known as
Z'
B
theASTM Blending Method. If the blend fractions are in mass
Z 5 10 2 0.7 (9)
B
2 3 percent, this is known as the Modified ASTM Blending
v 5 Z 2 exp@20.7487 2 3.295Z 10.6119Z 2 0.3193Z # (10)
B B B B B
Method.
where Z' and Z are the results of intermediate calculation
B B 6.3.2 Compile the viscosities of the components at a single
steps with no physical meaning.
temperature (the reference temperature). The viscosity of
component i at that temperature is designated v.Ifthe
i
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 viscosities are not known, measure them using a suitable test
a discrepancy less than 0.0004 mm /s.
method.
NOTE 3—See the worked example in Appendix X3.
NOTE 6—Test Methods D445 and D7042 have been found suitable for
Procedure B
this purpose.
6.2 Calculating the Blend Fractions of Components to Give 6.3.2.1 If the viscosity of a component is not known at the
a Target Viscosity Using the Inverse Wright Blending Meth
...