A Method for the Preparation of NIST Traceable

Fossil Fuel Standards with Concentrations

Intermediate to SRM Values

 W. Robert Kelly, Bruce S. MacDonald, and Stefan D. Leigh 1 2 3

Analytical Chemistry Division 1 

Chemical Science and Technology Laboratory

Measurement Services Division 2 

Technology Services

Statistical Engineering Division 3 

Information Technology Laboratory

National Institute of Standards and Technology

Gaithersburg, Maryland 20899

August 6, 2007

File: SRM-MIX19.wpd

NIST Special Publication 260-167

This publication is available free of charge from:

http://dx.doi.org/10.6028/NIST.SP.260-167
Page 2 of 29

A Method for the Preparation of NIST Traceable

Fossil Fuel Standards with Concentrations

Intermediate to SRM Values

W. Robert Kelly, Bruce S. MacDonald, and Stefan D. Leigh

Abstract: A procedure is presented whereby the fossil fuel community may design

and mix SRMs in different proportions and thereby produce in their laboratory standards

for sulfur in distillate fuel oil, residual fuel oil, and coal of almost any desired

concentration with uncertainties that are calculable and traceable to NIST SRM certified

values. The expanded uncertainty, U, of a binary blend is always less than the U of the

component with the largest U, and in some cases it is less than either of the SRM

components. Because the sulfur content of all fossil fuel SRMs was certified at NIST

with high accuracy and precision by isotope dilution thermal ionization mass

spectrometry, in almost all cases the total expanded uncertainties of the standards

produced from binary mixtures are an order of magnitude smaller than the

reproducibility of current methods used in commercial laboratories. The use of this

method gives the SRM user a continuum of concentrations available for calibrants and

quality control test samples. Unlike calibrants prepared from high purity components,

this method enables the SRM user to create a customized series of calibrants in the

fossil fuel matrix of interest. This should reduce or eliminate biases that result from

differences in matrix composition among standards and unknowns.
Page 3 of 29

List of Notations

Latin Symbols Greek Symbols

i

f mass fraction of component i :g microgram or 10 grams

-6

k coverage factor M partial derivative

M

Analyte concentration in a binary

mixture

Abbreviations

M bar Calculated concentration of mixture EDXRF Energy Dispersive X-Ray Fluorescence

n number of determinaitons EPA Environmental Protection Agency

s standard deviation CI Confidence Interval

t student’s t NIST National Institute of Standards and

Technology

U Expanded uncertainty RM Reference Material

ucstandard uncertainty SRM Standard Reference Material a NIST ®

certified reference material

Umix

Expanded uncertainty calculated for a

binary mixture

WDXRF W avelength Dispersive X-Ray

Fluorescence

Var(M) Variance in M

eff v

effective degrees of freedom

calculated from the WelchSatterthwaite equation

X Concentration in component x

Y Concentration in component y

X bar Mean concentration of X

Y bar Mean concentration of Y
Page 4 of 29

Introduction

Instrumental chemical determinations are commonly performed by measuring

the response of an unknown and comparing it to the response produced by a standard

of known concentration or to a response calibration curve constructed using several

standards that cover the concentration range of the unknowns. A polynomial function is

frequently used to interpolate between the predetermined calibration points. The

accuracy and precision of the results depend on the accuracy of the standards, the

precision of the method, and quantified systematic (Type B) uncertainties. One source

of systematic error results from difference in response of the analyte in the sample from

that in the standard. This can result from attenuation of the signal emitted or in the

case where there is a sample preparation step, the yields being different for sample and

standard. For example, in the determination of sulfur in liquid fossil fuels by x-ray

fluorescence (XRF) it is well established that the emission of K" line is dependent on

the C/H ratio in the sample. In the case of combustion techniques the analyte yields

may not be identical for different matrices because the conversion efficiency of various

2

forms of sulfur to SO may be different. Both of these systematic uncertainties, which

are difficult to quantify, can be greatly reduced or eliminated as the difference between

the matrix of the standard and sample approaches zero.

Like other national metrology laboratories, NIST frequently receives requests for

additional standards at concentrations specific to the needs of the user. To augment

the existing suite of Standard Reference Materials (SRMs) for fossil fuels which

currently include coals, cokes, crude oils, residual fuel oils, middle distillates, and

gasolines, with additional standards at sulfur concentrations that might be needed by

the user community would require a major effort. The approach (nicknamed the

Designer Method) presented in this paper is intended to solve this problem. It will

permit the user to design and prepare standards at any concentration desired and with

uncertainties that can be calculated and traced to NIST SRM certified values. This is

an excellent example of transfer of the high accuracy capability of isotope dilution

thermal ionization mass spectrometry (IDTIMS), a method which requires expensive

instrumentation and is labor intensive, to the user community via SRMs which permits

finite resources to be leveraged to meet a broad continuum of need. This approach

could be implemented immediately with existing SRM stocks, and be maintained in the

future with fewer SRMs and a much smaller expenditure of resources. Standards at the

level of accuracy obtained by IDTIMS are necessary for this method to be useful. The

well established technique of IDTIMS determination of sulfur will be able to meet the

accuracy requirements both now and into the foreseeable future. The method 1-3

proposed here will permit exact matrix matching of sample and standard at almost any

concentration desired. This capability will permit the analyst to reduce the numeric

interpolation to zero with a concomitant reduction in uncertainty. Although we focus

exclusively on sulfur in fossil fuels, the method is also being developed for other

analytes in fossil fuels such as mercury.
Page 5 of 29

Reduction of the sulfur content in diesel and gasoline motor fuels is the single

most important factor in efforts to reduce primary and secondary air pollution from

existing and future diesel and gasoline engines. The International Council on Clean

Transportation (ICCT) states the following: 4

Worldwide, many jurisdictions have recognized the public health and

environmental costs of allowing motor vehicle fuels to contain high levels

of sulfur. The European Union, United States, and Japan have led the

way in sulfur reduction, and will reach near-zero sulfur levels later in this

decade.

In addition to the ICCT, statements similar to the above have been made by the EPA

and the World Wide Fuel Charter and numerous trade organizations including the 5

Alliance of Automobile Manufacturers and the Engine Manufacturing Association. The

regulated upper sulfur limit in US on-road diesel fuel was dropped to 500 :g/g in 1993,

and in June 2006 it was reduced to 15 :g/g. A further reduction to near-zero (< 5 :g/g)

could be proposed before the end of this decade. Japan and Europe adopted a 50

:g/g limit in 2004 and 2005. Europe will phase in a 10 :g/g limit between 2005 and

2009 and Japan will adopt the same limit in year 2007. The incremental measurement

challenges increase non-linearly as sulfur concentrations decrease from 500 to near

zero levels. As the sulfur levels drop the demand for calibration standards will increase

both in number and absolute accuracy. Petroleum refineries will need to ensure they

are in compliance with regulations, but at the same time they will want to avoid reducing

the sulfur content more than required because of the high costs of desulfurization by

hydrogenation. The preparation of only three or four diesel fuel standards by NIST will

permit the user community to prepare gravimetrically for themselves a continuum of

concentrations between the end members which will meet all requirements that might

arise both now and in the future. In principle, the minimum number to cover an entire

range of need would be two SRMs for a given matrix - one on the low side and one on

the high side of the range needed.

Almost all the methods used for sulfur in fossil fuel must be externally calibrated,

and in many cases it is necessary to matrix match standards and unknowns to obtain

bias-free results. The EPA is moving towards a Performance Based Quality System

approach for the determination of sulfur in diesel fuel. This means that an analytical

laboratory need not use only an EPA method for compliance, but may employ other

methods demonstrated to yield accurate results. If these methods are sufficiently well

calibrated, then they are considered to demonstrate the requisite accuracy. Likewise

the sulfur content of coal and residual fuel oil must be determined accurately by both

buyer and seller to ensure compliance with EPA regulations for sulfur emissions and

contract specifications.
Page 6 of 29

The “Designer” Method

This Designer method for making standards at user defined concentration levels

is a simple, but effective, method of meeting calibration and quality control sample

needs. Take two miscible diesel or kerosine SRMs and mix them gravimetrically to

yield any target sulfur concentration between the two end member concentrations. This

permits essentially a continuum of concentrations to be prepared between the two end

member concentrations, and solves the long-standing problem of meeting and

satisfying the demand for diesel fuel standards of many different sulfur concentrations.

The actual preparation of the gravimetric mixes should be straightforward and their

accuracy can be checked. It requires only a four-place balance with an uncertainty of

less than 0.5 mg (see Appendix A). Ampoules could be poured directly into wide-mouth

bottles on a balance because it is not necessary to mix to a specified value, but rather

only necessary to be near a specified value and to know the mass of the mixing

proportions accurately. After additions to the bottle it should be closed and mixed

completely.

In this proposed method the two SRMs are of a same matrix; therefore, there is

no change in the resulting matrix of the mixture, no matter the relative proportions. This

is extremely important in matrix dependent methods, like XRF, a common and widely

used technique. For example, XRF is subject to bias if there are differences in the C/H

ratio between standards and unknowns. This method of making calibrants avoids this 6

problem. The accuracy of the blends would need to be checked by measuring the

blends and comparing the interval between the measured values of the successive

blends to the interval between their corresponding gravimetric value (NIST traceable). 

If the difference between intervals is less than the repeatability of the method, then the

blends are considered successful.

In this paper examples of mixing ratios have been limited to 4 to 1, although

more extreme mixing ratios are possible. For example, if only three SRMs were

certified with sulfur concentrations of 10, 100, and 1000 :g/g, then this would permit the

preparation of samples with sulfur concentrations of 10, 28 - 82, 100, 280 - 820, and

1000 :g/g sulfur. The high accuracy of the IDTIMS technique permits the certification

of the end members to accuracies of approximately ± 1 to ± 5 :g/g or better over the

concentration range of 10 to 1000 :g/g. This translates to expanded uncertainties of

the mixtures that would be very small relative to the requirements of the petroleum

community. In some cases, over a limited concentration range the absolute uncertainty

of the blends can actually be smaller than that of either end member SRM as discussed

in the next section.

The approach presented in this paper will permit users to design and mix

standards at desired concentrations from binary mixtures of NIST SRMs, and to

calculate the concentration and uncertainty in the resulting mixture which are then

directly traceable to NIST values.
Page 7 of 29

(1)

(2)

Mixing and Statistical Considerations

There are several conditions that must be met: 1) the blends must be

homogeneous, 2) there can be no sample loss during blending, 3) the resulting mixture

must be of sufficient volume for the instrument being used, and 4) the mass of the two

end members should be of sufficient size to make the weighing uncertainty negligible. 

In the case of XRF, a commonly used technique, the sample size needed is commonly

about 5 mL, or about 4 grams. Condition #4 will be met if the sample mass of each end

member is > 0.2500 ± 0.0005 gram (see Appendix A).

For the technique to be useful, in addition to the obvious need to know the

concentration of the mixture, one must also be able to characterize credibly the

uncertainty of the mixture. The concentration of a mixture, M, composed of two SRM

end members, X and Y, is given by the following mass balance relation:

where f1 2 and f are the mass fractions of the respective end members subject to the

condition that their sum equals unity. The concentrations, X and Y, are themselves

determined 1 j 1 k from experimentally measured quantities (x ...x and y ...y ), calculated

using 1 2 functions F and F for NIST SRMs. The functions are essentially identical

because the experimental technique is the same for all determinations, but there are

differences in the way the input data are used in some cases. For example, regression

by least squares is used for low level determinations such as SRM 2723a. In general, 7

deviations in M resulting from deviations in the input variables of X and Y can be

approximated by the Taylor series expansion in the vicinity of the means :

8,9

where the overstrike designates means of the represented random variables. Equation

(2) involves only two variables, but it should be noted that it may be necessary to

consider all the variables in equation (1). For the sake of brevity the treatment is

presented for two variables only. Squaring, denominating by n (sample size), and

taking the Expectation yields the relationship:
Page 8 of 29

(3)

(4)

(5)

The third term is a covariance term which is negligible if X and Y are independent or

uncorrelated. If they are not independent, then it may be necessary to try to

approximate it. In equation (3) both Type A and Type B uncertainties will appear and

some cross products will be non-zero such as some uncertainties which correlate like

those of the IDTIMS spike calibration. This has been evaluated by Monte Carlo

simulation and found to be negligible.

Neglecting the covariance and higher order terms, a total expanded

uncertainty , U, can be expressed as the following: 10

The first term is the appropriate Student’s t factor for the effective degrees of freedom,

eff t(< ), which can be calculated from the Welch-Satterthwaite relationship, equation (5)

below. 

The Welch-Satterthwaite relation reduces the uncertainty propagation by a small
Page 9 of 29

(6)

amount in most eff cases; it is reduced near the middle of the range where < approaches

x y (df + df - 2) if the degrees of freedom and the variances are approximately equal. The

minimum in <eff becomes more asymmetric as the variances become unequal.

Figure 1a shows the difference between using the Welch-Satterthwaite relation

versus using the simpler multiplier of 2 which is favored by some laboratories. The drop

lines in the figure illustrate the difference in magnitude of the two approaches. The

Welch-Satterthwaite is a more conservative approach typically yielding a bigger

coverage factor leading to a larger expanded uncertainty. The figure illustrates that the

difference between the two approaches differs little for 50-50 mixtures and that the

curves approach each other as n increases.

However, as will be seen in subsequent examples, from a practical point of view

either approach is acceptable relative to the magnitude of the reproducibility of ASTM

methods at this time. Figure 1b is a hypothetical example of the uncertainty

propagation derived using the Welch- Satterthwaite relation to calculate a 95 %

confidence interval for a mixture composed of 10 and 100 :g/g end members both

having the same absolute uncertainty of 1 :g/g (lines a, b, and c). Note that the

minimum in the absolute uncertainty occurs at the equal mass mixture which occurs at

55 :g/g. If the uncertainties in the end members are equal, then the minimum in the

absolute uncertainty always occurs at the 50-50 mixture (see Appendix B) and is equal

to the common end member uncertainty divided by the square root of 2 times the

student’’s t factor for the effective degrees of freedom which approaches the sum of the

end member degrees of freedom. Line c shows the effect of two different degrees of

freedom of the end members. Line d shows the effect of a difference in the

uncertainties of the end members on the uncertainty curve for n=12. This large value

for n was used only to achieve visual separation of the curve from the other curves. As

the difference between the uncertainties of the end members becomes larger the

resulting propagated uncertainty becomes linear with concentration because the

standard 1 1 2 2 deviation approaches either f s or f s depending on which dominates.

In this paper a third approach will be used which is simple, easy, conservative,

and closely approximates the output from the more complicated Welch-Satterthwaite

approach discussed above. This approach uses data directly from the SRM

certif cicates. The SRM certificates report the total expanded uncertainty, U, where u is

the combined standard uncertainty and k is the coverage factor as shown in equation

(6).9

The first quantity is rigorously defined, but there is some latitude in choosing the value

for k. On all sulfur in fossil fuel certificates published since 1994 at NIST the value for k

was determined using Welch-Satterthwaite and is typically about 2.3 although it may
Page 10 of 29

(7)

(8)

approach 4.3 for very low (< 10 :g/g) concentrations. In this paper the total expanded

uncertainties for the mixes are calculated as:

Therefore, if one uses the uncertainty directly from the SRM certificates, then equation

(7) can be recast into equation (8) below in which one takes the expanded uncertainty

i

(U) directly from the appropriate certificates.

Figure 2 shows the difference among the different approaches for the case of

mixing two NIST crude oil SRMs that were recently certified. The dark red line is a plot

of equation (8) for the mixing of the two crude oil SRMs. It is clear that in this case

equation (8) is an excellent approximation to the more complicated calculation involving

equation (5). In this paper, equation (8) will be used to determine the total expanded

uncertainty for sulfur in the fossil fuel mixtures.

Sulfur in Diesel and Kerosine

NIST currently has six different diesel fuel SRMs and one kerosine SRM certified

for sulfur concentration. The certified values and uncertainties are listed in Table 1. 

There are 21 possible binary end member combinations and these are listed in Table 2. 

The uncertainties are small enough to permit mixes below 50 :g/g with expanded

uncer 1 2 tainties below 1 :g/g. Varying the mixing fractions f and f of the two components

chosen for each combination yields of course an infinite number of mixtures

intermediate between each choice of end points. Figure 3a is a log-log plot of the

uncertainty versus the mixture concentration for ten mixes. It demonstrates that there is

essentially complete and continuous coverage between 2 :g/g and 3900 :g/g with the

existing SRMs in Table 1 using limiting mixing ratios of 4 to 1 and 1 to 4. With the

existing SRMs there is considerable overlap; for example, compare mixes 3 and 13, 1

and 18, 2 and 10, and 4 and 8.

The interest at the low sulfur end has increased greatly with the implementation

of the ultra low sulfur diesel regulations in June 2006. Figure 3b is an expanded scale

verison of Figure 3a that shows the possible coverage below 50 :g/g sulfur. At the

present time complete coverage is possible between 2 an 40 :g/g sulfur with

uncertainties of less than 1 :g/g using mixtures of just three standards - RM 8771, SRM

1616b and SRM 2770.
Page 11 of 29

Table 1. Diesel and Kerosine SRMs

SRM

Mean Sulfur

Concentration

in :g/g

Absolute

Uncertainty

95 % CI (U)

% Relative

Uncertainty

95 % CI (U)

RM 8771 0.071 0.014 20

2723a 11.0 1.1 10

1616b 8.41 0.12 1.4

2770 41.57 0.39 0.94

2724b 426.5 5.7 1.3

1617a 1730.7 3.4 0.20

1624d 3882 20 0.52

Figure 3a and 3b serve to indicate that it may be possible in the future to meet

the entire ensemble of needs of the industry with only three or four SRMs of judiciously

chosen sulfur concentration. The total expanded uncertainty in all the distillate fuel oil

mixes is an order of magnitude smaller than the reproducibility of the current ASTM

methods mix . The U is always lower than the U of either end member and in some cases

lower than the U of both end members. Mixes 12 and 19 in Table 2 are unique

because the uncertainty of these mixes decreases with increasing sulfur content.

As will be seen in Figure 3a, the current relatively large uncertainty of 5.7 :g/g

for SRM 2724b dominates the uncertainty budget of any mixture in which it is included,

but mixtures using the 8771-1671a pair give the same coverage. The same also

applies to SRM 2723a (see FIG. 3b). But with even the relatively large uncertainty for

SRM 2723a note from Table 2 that mixture #4 gives coverage between 2 to 9 :g/g with

an expanded uncertainty of less than 1 :g/g. Both of these SRMs may be re-certified in

the near future using our improved analytical capabilities which may reduce the

uncertainty by a factor of two or more.

Sulfur in Residual Fuel Oil

Residual fuel oil is a heavy oil of relatively high caloric content left over from the

refining of crude oil. It is used to fire boilers in electric generating plants, particularly in

the northeastern US. The sulfur emissions from these plants are regulated by the EPA
Page 12 of 29

Table 2. Possible Ranges in Mixtures and Uncertainties

with Existing Diesel Fuel and Kerosine SRMs

Mixture

#

SRM

End Members

S Concentration of 

End Members

:g/g

Range in

Mixture

:g/g

Range in a

Uncertainty

:g/g

1 8771/1624d 0.071 - 3882 776 - 3106 4 - 16

2 8771/1617a 0.071 - 1730.7 346 - 1385 0.7 - 3

3 8771/2724b 0.071 - 426.5 85 - 341 1 - 5

4 8771/2770 0.071 - 41.57 8.4 - 33 0.08 - 0.3

5 8771/2723a 0.071 - 11 2.3 - 8.8 0.2 - 0.9

6 8771/1616b 0.071 - 8.41 1.7 - 6.7 0.03 - 0.1

7 1616b/2723a 8.41 - 11 8.9 - 10.5 0.2 - 0.9

8 1616b/2770 8.41 - 41.57 15 - 35 0.1 - 0.3

9 1616b/2724b 8.41 - 426.5 92 - 343 1 - 5

10 1616b/1617a 8.41 - 1730.7 353 - 1386 0.7 - 3

11 1616b/1624d 8.41 - 3882 783 - 3107 4 - 16

12 2723a/2770 11 - 41.57 17 - 35 0.9 - 0.4

13 2723a/2724b 11 - 426.5 94 - 343 1 - 5

14 2723a/1617a 11 - 1730.7 355 - 1387 1 - 3

15 2723a/1624d 11 - 3882 785 - 3108 4 - 16

16 2770/2724b 41.57 - 426.5 119 - 350 1 - 5

17 2770/1617a 41.57 - 1730.7 379 - 1393 0.8 - 3

18 2770/1624d 41.57 - 3882 810 - 3114 4 - 16

19 2724b/1617a 426.5 - 1730.7 687 - 1470 5 - 3

20 2724b/1624d 426.5 - 3882 810 - 3114 6 - 16

21 1617a/1624d 1730.7 - 3882 2161 - 3452 5 - 16

 Uncertainties apply to values in previous column and are total expanded uncertainties a

derived by application of equation (8) to end member certified uncertainties.
Page 13 of 29

and a typical compliance fuel has a sulfur content of approximately 1%. It is quite

common for a seller to blend two or more different fuel oils to a target sulfur value

specified by the buyer. Therefore, it is absolutely essential to determine accurately the

sulfur content of the resulting mixture to ensure that the target value for the

consignment blend will be met. Since the first residual fuel oil standards were certified

Table 3. Residual Fuel Oil and Crude Oil SRMs

SRM Mean Sulfur

%

Absolute

Uncertainty

95 % CI (U)

% Relative

Uncertainty

95 % CI (U)

Residual Fuel Oil

1623c 0.3806 ± 0.0024 0.63

1619b 0.6960 ± 0.0077 1.1

1621e 0.9480 ± 0.0057 0.60

1622e 2.1468 ± 0.0041 0.19

2717a 2.9957 ± 0.0032 0.11

1620c 4.561 ± 0.0015 0.33

Crude Oil

2722 0.21037 ± 0.0084 0.40

2721 1.5832 ± 0.0044 0.28

for sulfur by NIST in the early 1960s, their number has increased to six which now

covers the entire sulfur range of interest from 0.4 to 4.5 % sulfur. The complete list of

currently available standards is given in Table 3. At the bottom of Table 3 are the first

crude oil samples to be certified by NIST for sulfur. There are 15 possible binary

combinations using the six residual fuel oil SRMs. This large number makes the

optimal choice of end members somewhat difficult, but the graphical display of the

solution presented in Figure 4 is straightforward. The solution requires three criteria to

be met simultaneously: 1) complete coverage over the entire concentration range

represented by the standards, 2) the uncertainties of the mixes must be as small as

possible, and 3) the composite range be determined with the fewest number of SRMs.
Page 14 of 29

Table 4. Recommended Binary Blends and Uncertainties

from Residual Fuel Oil SRMs

Mixture

#

SRM

End Members

End Members

%

Range

% S

Absolute

Uncertainty

95 % CI (U)

:g/g

Residual Fuel Oil

2 1623c/1621e 0.3806/0.9480 0.49 - 0.84 23 - 43

3 1623c/1622e 0.3806/2.1468 0.73 - 1.79 22 - 32

4 1623c/2717a 0.3806/2.9957 0.90 - 2.47 21 - 26

13 1622e/2717a 2.1468/2.9957 2.32 - 2.83 33 - 28

14 1622e/1620c 2.1468/4.5610 2.63 - 4.08 46 - 109

15 2717a/1620c 2.9957/4.5610 3.31 - 4.25 41 - 110

Crude Oil

2722/2721 0.21037/1.5832 0.48 - 1.31 12 - 32

The red lines in Figure 4 show the 5 end member mixes that cover the entire range. 

The solid circles are the end members. Note that the distances between the end of the

red lines and the SRM compositions (red circles) increase as the values of the end

members increase. This figure also makes it easy to see which three end members

could be used to make identical concentration mixes with identical uncertainties. This

condition occurs at the intersection of lines. For example, line 4 intersects both lines 3

and 13. There is much redundancy for mixes in the 1.3 to 2 % concentration range. 

Table 4 lists the 6 best binary end member choices based on the graphical solution

presented in Figure 4. Table 4 lists the ranges in both the concentrations and the

computed uncertainties of the resulting mixes. The last entry in Table 4 gives results

for the mixing of the two crude oil SRMs, originally presented earlier in Figure 2. Table

5 gives the ranges and uncertainties for remainder of the mixes.
Page 15 of 29

Table 5. Remainder of Residual Fuel Oil Mixtures

(Use Precluded by Graphical Analysis in Figure 3)

Mixture

#

SRM

End Members

End Members

 % S

Range

% S

Absolute

Uncertainty

95 % CI (U)

:g/g

Residual Fuel Oil

1 1623c/1619b 0.3806/0.6960 0.44 - 0.63 26 - 57

5 1623c/1620c 0.3806/4.561 1.22 - 3.73 37 - 112

6 1619b/1621e 0.6960/0.9480 0.75 - 0.90 63 - 50

7 1619b/1622e 0.6960/2.1468 0.99 - 1.86 60 - 38

8 1619b/2717a 0.6960/2.9957 1.16 - 2.54 58 - 31

9 1619b/1620c 0.6960/4.561 1.47 - 3.79 71 - 117

10 1621e/1622e 0.9480/2.1468 1.19 - 1.91 46 - 36

11 1621e/2717a 0.9480/2.9957 1.36 - 2.59 45 - 29

12 1621e/1620c 0.9480/4.561 1.67 - 3.84 57 - 112

Sulfur in Coal

The determination of sulfur in coal is another case where the methods used in

industry require external calibration. Commonly, the coal mining industry is interested

in sulfur determinations in coal within a very narrow range of sulfur content which

frequently falls between two standards requiring interpolation of varying degrees. An

actual recent example of this is shown in the upper right corner of FIG. 5. A coal

company produces coal of 4.2 % sulfur (unwashed) and after washing has a sulfur

content of 3.5 %. Both of these values are between SRMs 2684b (3.076 % S) and

2685b (4.73 % S). The method described here may allow calibration mixes at or very

near the concentrations of interest.

Table 6 lists the 8 coal SRMs that are currently available. The coal SRMs have

larger uncertainties than do residual fuel oils of comparable sulfur content because of

their intrinsic heterogeneity resulting from variable mineral and moisture content. 

Because of this intrinsic heterogeneity, the best way to use this technique for coal

standards would be to add the two components directly to the combustion crucible and

combust the total sample. The moisture content would be determined on separate
Page 16 of 29

samples. The effect of moisture content on the sample mass determination has been

studied in detail, and it was demonstrated that coals may exhibit “anomalous” drying

profiles. Only coals of the similar rank should be blended to make calibration 11

standards. The mixing of SRMs of different matrices can not be assumed to yield

blends that will yield the expected derived value when analyzed by a given method and,

although sometimes possible, it is not recommended. This is clearly a problem when

the instrument-response characteristics of the selected SRM end members are

different. For example, coal and coke SRMs are not recommended for blending for

subsequent analysis by methods that use high temperature combustion techniques

because of their different burn profiles. But if the unknown sample were a mixture of

coal and coke, then a calibration curve should be constructed from similar blends.

Table 6. Coal SRMs

SRM Sulfur Mean

%

Absolute

Uncertainty

95 % CI (U)

% Relative

Uncertainty

95 % CI (U)

Sub-Bituminous Coal

1635 0.3616 ± 0.0017 0.47

2682b 0.4917 ± 0.0079 1.6

Bituminous Coal

2693 0.4571 0.0067 1.5 a

2692b 1.170 ± 0.020 1.7 a

1632c 1.462 ± 0.051 3.5 a

2683b 1.955 ± 0.041 2.1 a

2684b 3.076 ± 0.031 1.0

2685b 4.73 ± 0.068 1.4

a

 The uncertainties for these three SRMs were calculated as 95 %

prediction intervals.

Figure 5 shows the coverage that is possible with the existing standards. The

mean concentrations of the existing seven SRMs have been projected onto the

abscissa to show the gaps in concentration that exist. The solid green circles on the

mixing lines denote 50-50, 60-40, and 40-60 mixtures. Drop lines and the connecting
Page 17 of 29

horizontal lines indicate the coverage that is possible. One might wish to restrict mixing

of coals to much smaller ranges because of weighing considerations. Nevertheless, it

should be both possible and practicable to cover almost the entire range of sulfur

concentrations with the SRMs now available.

Conclusions

The Designer method makes possible the construction of multipoint calibration

curves at or near the concentration of interest. This method should be ideal for

analytical techniques that require multi-point calibration curves such as XRF and

combustion techniques or where the analyst wishes to bracket an unknown

concentration with several calibrants. This last feature means that non-linear response

of instruments can be easily overcome. The ability to design and prepare in one’s own

laboratory diesel fuel calibrants with a specific sulfur concentration and uncertainties

that are calculable and traceable to NIST values gives the analyst the ability to bracket

very closely any unknown diesel fuel which should translate to an unprecedented

flexibility and accuracy capability in the petroleum sector laboratories. 

In addition, just as NIST certified values are currently used to verify analytical

methods, the designer blends can be used to create NIST traceable test samples and 12

Quality Control (QC) Test-Standards. These mixtures can be used to verify calibrations

and the accuracy of subsequent results of unknowns derived from the calibration. 

Quality Control (QC) Test-Standards must be different from the blends used for the

calibration curve, though they may be composed of the same parent SRMs.

Although the method described here is ideally suited for miscible liquids, it can

be used for complete combustion methods for sulfur in coals and other solids. In the

case of coal, one would weigh the two different coals directly into the combustion

crucible. This technique is being investigated for use with other analytes such as

mercury in coal and trace elements in fuels.

The method described here should significantly improve calibration while

reducing the number of certified standards that must be maintained by national

metrology laboratories.
Page 18 of 29

References:

1. Paulsen, P. J. and Kelly, W. R., Anal. Chem. 1984, 56, 708-713.

2. Kelly, W. R., Vocke, Jr., R. D., Sieber, J. R., and Gills, T. E. 1993, FUEL, 72,

1567-1569.

3. Kelly, W. R., Paulsen, P. J., Murphy, K. E., Vocke, Jr., R. D., and Chen, L.-T.

Anal. Chem. 1994, 66, 2505-2513.

4. International Council on Clean Transportation, see documents on low

sulfur gasoline and diesel fuel (www.cleantransportcouncil.org)

 5. World Fuel Charter, December 2002, 51 pp. 1 - 51 (www.autoalliance.org

or www.enginemanufacturers.org)

6. ASTM D 2622-03 Standard Test Method for Sulfur in Petroleum Products

by Wavelength Dispersive X-ray Fluorescence Spectrometry, 2003, 1-6,

American Society of Testing and Materials, West Conshohocken, PA

7. Kelly, W. R., Vocke, R. D., Mann, J. L., and Guthrie, W. F., in preparation

8. Bevington, P. R. and Robinson, D. K. Data Reduction and Error Analysis

for the Physical Sciences, 2nd Edition, McGraw-Hill, Boston, 1992.

9. Ku, H. H. J. Res. NBS, 1966, 70C, 263-273.

10. Taylor, B. N. and Kuyatt, C. E. NIST Technical Note 1297, 1994.

11. Mann, J. L., Kelly, W. R., and MacDonald, B. S. Anal. Chem. 2002, 74,

3585-3591.

12. Taylor, J. K. Standard Reference Materials: Handbook for SRM Users.

National Bureau of Standards Special Publication No. 260-100, U.S.

Department of Commerce, Washington, DC, 1985.
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Page 26 of 29

(A-1)

(A-2)

(A-3)

(A-4)

Appendix A

The Effect of Weighing Accuracy on the Uncertainty

To approximate the affect of weighing uncertainty on the uncertainty of the resulting

mixture, the mass fractions of equation (1) are written in terms of the measured

quanti 1 2 ties, the masses m and m :

If one assumes that X and Y are constants, then M = f(m1, m2). Taking the total

differential or 1 2 increment of M with respect to the masses, m and m , as shown in A-2:

and then dividing by M and squaring gives the relative variance in M which can be

written in terms of the relative standard deviation as in A-3:

where i 1t is assumed that one uses the same balance to determine the masses, m and

m2 permitting the following approximation in equation (A-3):

where Fb is the standard deviation for the uncertainty of the balance which for a four

place balance is assumed to be 0.0005 g. Equation (A-3) is plotted in FIG. A-1 for the

hypothetical end members of concentration 10 and 100 :g/g. It is obvious that if one

weighs as least 1 gram of each end member then the uncertainty expressed as a

standard deviation from this source is less than 0.05 % which is negligible for most

applications.
Page 27 of 29

The accuracy of equation (A-3) was checked by Monte Carlo simulation using equation

(A-1). Random numbers were generated assuming a normal distribution with a

standard dev 1 2 iation of 0.0005 g for different values of m and m . The results from the

Monte Carlo simulation were in excellent agreement with those calculated by equation

(A-3). Equation (A-3) was also checked assuming a uniform distribution with standard

deviation equal to 0.0005//3 and this showed good agreement also.
Page 28 of 29

[B-1]

[B-2]

[B-3]

[B-4]

[B-5]

Appendix B

Calculation of the Minima in the Uncertainty for a Binary System

We wish to calculate the minimum in the uncertainty for a given binary mixture. The

variance is given by equation (B-1):

Us 1 2 ing the constraint that the sum of f and f must equal unity, the above can be written

in the following form:

Taking 1 the derivative of the variance with respect to f and setting equal to zero gives

1

the value of f that minimizes the variance:

2 1 f can be calculated from the difference in f from unity to give the following relations:

It is obvious from these equations that if the uncertainties are equal then the minimum

1 2 in the uncertainty is located at f = f = 0.5. The location of the minimum is highly

sens 1 2 itive to the differences in s and s because they are squared quantities. This can

best 1 be seen by rewriting the expression for f in the following manner:

where the first expression is for the absolute uncertainty and the second expression is

the for the relative uncertainty. As the second expression shows, the minimum occurs

at f1 = 0.5 if the relative uncertainties are equal.
Page 29 of 29