Chemistry. and Technology of Fuels and Oils. Vol. 33. No. 2, 1997

METHODS OF ANALYSIS

. , -~NALYSIS O F S C A L E S O F M E A S I o R 1 E M E N T E-N

Q U A L I F I C A T I O N T E S T E N G : M E T H O D S

V. G. Gorode t sk i i UDC 620.1.08:662.75

Chemmotology is among the scientific disciplines in which mathematical methods of investigation have not yet come

into general use. In particular, the introduction of such methods is being hindered by the inadequacy of the qualification test

methods used to evaluate the service properties of fuels and lubricants.

Abstract mathematical apparatus can be applied only under the condition that a particular empirical system is expressed

in numbers having a structure of ratios corresponding to the structure of this empirical system. If this condition is met, real

empirical systems can be studied by means of the corresponding numerical systems.

The conversion of empirical systems to numerical systems is accomplished by means of measurements. According to

the tenets of the formalized mathematical approach, measurement is defined as a procedure of assigning to an empirical element

a i of the set A (a i E A) a numerical element ni from the set N (n i E N). This procedure ensures that the relationship between

different numerical and empirical elements will be single-valued (isomorphous or homomorphous).

In order to perform a measurement, it is necessary to establish a system of relationships R, i.e., a set of rules, in

accordance with which the quantities to be measured are given numerical values [1]. The selected system of relationships R i

is true for the set of numbers obtained as a result of the measurements. Such systems of relationship are called scales of

m e a s u r e m e n t s .

Depending on the type of scale that is used, the numbers obtained as a result of a measurement may not have all the

properties of numbers, and hence it is not always permissible to perform all mathematical operations with these numbers. Scales

of four types are used for technical measurements. Each scale has its own structure of relationships among the numbers that

are determined on its basis [2].

The simplest is the scale of classification, or names, defined as one-to-one (injective) mapping of empirical (A; = )

and numerical (N; = ) systems. This scale reflects one-to-one correspondence between classes of empirical objects, identically

manifesting the property under consideration, and real numbers. The numbers furnished in correspondence to individual objects

permit only a determination of whether two objects are identical or not.

The procedure for measurement of an element a E A consists of comparing it with standard elements n E A. The

symbol standard is given to those elements that are equivalent to the standard.

For example, aviation kerosines are tested in accordance with a list of methods given in the technical standardization

documentation (TU, GOST, or set of qualification test methods). Those products that meet the requirements for a given grade

according to the standardized quality indexes are assigned the Code name for this grade: T-1. T-2, T-6, or T-8. The numbers.

which are used in marking the product, serve to distinguish one grade from another, and they do not have any informational

significance. These aviation kerosines do not differ from each other in any of their property indexes by a factor of 2, 6, or 8.

Any mathematical operation on these numbers will be completely meaningless.

With a better scale, objects can not only be distin~maished, but also ranked according to some indicator. Here we have

a scale of order , which provides a monotonically increasing, continuous mapping of an empirical system (A; = ; < ) by a

numerical system (N; = ; < ) . With such a scale, objects can be arranged in a series in increasing order of the index of the

measured property.

GNIIKh. Translated from Khimiya i Tekhnologiya Topliv i Masel, No. 2, pp. 41-42, March-April, 1997.

0009-3092/97/3202-0119518.00 �9 Plenum Publishing Corporation i19

The only characteristic feature of the numbers that are obtained is that they are ordered. Operations of addition,

subtraction, multiplication, and division cannot be performed on these numbers, hence it is impossible to estimate by how much

or by how many times one particular measured value is greater or less than another. A classic example of a scale of order is

the Mobs hardness scale for minerals.

In chemmotology, most of the methods for evaluating service properties provide for the determination of scales of

order. The simplest of these are realized in procedures for rating the results of stand or service tests on fuels and oils in gas

turbine engines. The rating is given by means of a comparison of the number and character of failures, and also the technical

conditions of the engines in testing or service on the test fuels and lubricants, in comparison with operation on standard

materials.

The finaI result of such tests does not have any numerical expression, but instead is represente'2 in the form of a

conclusion: The specific sample in the specific engine has "passed" or "failed" the test; it is either "worse" or "better" in its

service properties in comparison with a standard material, or it "does not differ" from the standard material. There is no

possibility of comparing results from tests on several samples with each other.

For piston engines, the results are rated in a "negative system of rating hard carbon and varnish deposits," the results

of which are expressed as arbitrary numerical ratings. There are five versions of such a procedure. The coefficients of rank

correlation between the results of tests using these methods may range from 0.1 to 0.9 [3]. In other words, depending on the

method used for evaluation, test oils may be rated at one level of properties or another.

The reason for these discrepancies is found in the arbitrary definition of relationships between the quantity of deposits,

the hardness of the deposits, and the numerical demerit rating. Such relationships differ from one method to another. Also,

a relationship selected for a particular method may vary over the different sections of the interval of measurements, owing to

specific features of visual evaluation. This is responsible for obtaining a scale of order and hence the ranking of any quantity

of test results, not only with test results on a standard sample, but also against each other.

Performance of operations of addition and subtraction on the results of measurements is provided by a scale of

intervals. Characteristic for this scale is the presence of relationships of order and equivalence not only between results of

measurement, but also between differences in pairs of numbers. In obtaining such a scale, a unit of measurement is necessary;

just what interval of the scale it may occupy is not important. The main concern is that the unit of measurement must remain

unchanged over the entire range of measurements. Numbers obtained on the scale of intervals have the properties of order and

additivity.

The most widely encountered scale of intervals is the scale of time measurement. An evaluation of the interval of time

between two events does not present any difficulty. However, in order to determine "by what factor is the time consumed

longer or shorter," a zero point must be indicated, i .e. , a point at which the timing is started.

If a natural zero exists on a scale of intervals (the absence of the measured property), this scale is converted to a scale

of rat ios . Thus, the temperature in degrees Celsius is measured on a scale of intervals, but the temperature in degrees Kelvin

is measured on a scale of ratios. The results of measurements obtained on a scale of ratios have all of the properties of

numbers.

Indirect evaluations of the properties of fuels and lubricants are used extensively in chemmotology. Here, properties

are expressed in terms of physical or chemical quantities that are measured on a scale of intervals or ratios. With such

measurements, it is necessary to take into account that scales of indirect indexes are valid for direct indexes if a linear

relationship exists between the direct and indirect indexes over the entire range of measurement.

If monotonic relationships exist, the scale of rat ios of direct indexes changes over to a scale of order of indirect

indexes. If the relationship between the indirect and direct indexes is extremal or if it has a point of discontinuity, the indirect

index can serve to rate the particular property only within that range of measurements in which the monotonic section of the

relationship between these indexes is maintained.

Thus, as an indirect rating index of the thermooxidative stability of aviation kerosines, measured by means of a TsITO-

M unit, we have the rate of decrease of the temperature t at the cooler outlet [4], and as a direct index the rate of increase of

the hydraulic resistance coefficient ~ of the fuel filter.

The relationship between direct and indirect rating indexes is described by the equation

! r d

= a t 2 + b t +'~c +

120

where a, b, c. d are constants that are determined by the construction of the unit, the test conditions, and the properties of the

aviation kerosines that are being tested.

Depending on the combination of constants, the function will assume one of six different forms. All of them have

maxima or minima, and four of them have one or two discontinuities. In this connection, the TsITO-M unit gives a scale of

order only within a very narrow range of variation of the indirect index.

If results are expressed in dimensionless units (ratings), the scales are transformed in accordance with the rules set forth

above. For exampIe, the tendency of aviation kerosines to form deposits on heated surfaces is rated visually in tests performed

in accordance with ASTM D I660 and GOST 17751, by comparing the darkest sections of the deposits on the rating tube of

the heater with a standard color scale with five or six ratings [5]. A direct rating index of this property is the mass or volume

of deposits. Owing to the physiological features of the eye, the relationship between direct and indirect rating indexes is

described by an indicator function.

The increase of deposit mass corresponding to an increase of the visual evaluation by one rating level in the interval

from 7 to 8 is ten times the increase of deposit mass in the interval from 1 to 2. However, this relationship would be preserved

only under the condition of maintenance of the law of variation of deposit thickness along the length of the rating tube for

different aviation kerosines. Since this condition is not met, there is no guarantee that a scale of order will be obtained.

These deficiencies were eliminated by the use of a deposit-measuring device consisting of a photoresistor having an

S-shaped characteristic with a wide linear section. The change of deposit thickness along the rating tube is taken into account

by means of an integral evaluation of the quantity of deposits on the entire surface. The test conditions for aviation kerosines

and diesel fuels have been selected so that the thickness of deposits for all samples will fall within the linear section of the

characteristic of the photoresistor [4]. As a result, a scale of ratios has been obtained successfully in this section.

Work is being conducted to develop methods for direct integral determination of deposit thickness on the rating tube,

which will make it possible to obtain a scale of ratios over the entire range of measurements [5].

In the development of qualification test methods, all of the attention is being given to obtaining the most highly

improved metrological characteristics. Questions of the scale of measurement have not even been raised, Therefore, the

overwhelming majority of qualification test methods provide for obtaining scales of order; and this is hindering the introduction

of mathematical methods of research into chemmotology and is retarding the growth of chemmotology as a scientific discipline.

R E F E R E N C E S

1.

9

3.

4.

5.

L. Finkelstein, IMECO Acta., I1, 11-27 (1973).

J. Pfanzagl, Theory of Measurement, Halsted Press, New York (1968).

V. M. Korobkov and D. M. Aronov, in: Service-Technical Properties and Application of Automotive Fuels, Lubricants, and Special-Purpose Fluids [in Russian], Transport, Moscow (1970), No. 6, pp. 127-189.

A. A. Gureev, E. P, Seregin, and V. S. Azev, Qualification Methods for Testing Petroleum Fuels [in Russian],

Khimiya, Moscow (1984).

R. E. Morris and R. N. Hazlett, Energ. Fuel, 3, No. 2, 18 (1989).

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