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' QC100 .U57 NO.590, 1980 C.1 NBS-PUB-C 19 NBS SPECIAL PUBLICATION 590

U.S. DEPARTMENT OF COMMERCE / National Bureau of Standards

"
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The Technological Importance of

Accurate Thermophysical Property Information

09 CTAKDAADB

UHUIt

OCT 1 0 1980

Hot <XLC-'di

Q-UDD

, US-7

Proceedings of a Session of the Winter Annual Meeting of

the American Society of Mechanical Engineers

Held in New York, NY, December 6, 1979

Editors:

Jan V. Sengers

Max Klein

Center for Thermodynamics and Molecular Science

National Measurement Laboratory

National Bureau of Standards

Washington, DC 20234

Sponsored by: The Committee on Thermophysical Properties of the Heat Transfer Division American Society of Mechanical Engineers 345 E. 47th St. New York, NY 10017

r/pec m.\ QiJih 1 1 etch

U.S. DEPARTMENT OF COMMERCE, Philip M. Klutznick, Secretary

Luther H. Hodges, Jr., Deputy Secretary

Jordan J. Baruch, Assistant Secretary for Productivity, Technology and Innovation

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

Issued October 1980
•

Library of Congress Catalog Card Number: 80-600108

National Bureau of Standards Special Publication 590

Nat. Bur. Stand. (U.S.), Spec. Publ. 590, 56 pages (Oct. 1980) CODEN: XNBSAV

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1980

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402

Price $3.75

(Add 25 percent for other than U.S. mailing)
FOREWORD

This publication contains a series of papers presented at a session of the Winter Annual Meeting of the American Society of

Mechanical Engineers held in New York, N.Y. , December 6, 1979. The

session was organized by the Committee on Thermophysical Properties (Committee K-7) of the Heat Transfer Division of the ASME.

The mandate of this committee is to encourage scientific research

in the field of thermophysical properties and to facilitate the

flow of information from science to engineering so as to provide

the engineering community with an adequate base for thermophysical

property information.

Of particular concern to the committee are the complications

that arise from lack of communication between the users and

generators of thermophysical property information. The user may

have access to a computer program yielding thermophysical property

values, but often does not know to what extent this information

is reliable. As a consequence the technological decisions may

unknowingly be affected by a lack of accuracy of the thermophysical

property information used in the analysis.

To call attention to these problems, the committee organized

a session devoted to a discussion of the importance of accurate

thermophysical property information for technology. The committee

is convinced that this issue deserves wider recognition in the

engineering community and expresses its appreciation to the

National Bureau of Standards for its willingness to publish the

proceedings of the meeting.

Jan V. Sengers, Chairman

Committee K-7

Heat Transfer Division, ASME

iii
ABSTRACT

These papers were presented at a meeting of the American Society

of Mechanical Engineers. The meeting session addressed the role of the

accuracy of thermophysical properties data in a number of applications

areas. The areas covered included aerospace sciences, where such data

have played a central role for a number of years; and geosciences, where

first steps are being taken toward using accuracy in describing

systems in terms of thermophysical properties. Also included were

a discussion of the economic value of accuracy in the chemical process

industry, a description of the role of data centers, and a description of

several high-»quallty data compilations. An example of a specific

problem in the design of a heat exchanger for geothermal applications

was also presented with the design uncertainties produced by data

in accuracies illustrated.

KEY WORDS

Aeroscience; data accuracy; design; geothermal; process; thermodynamics;

transport properties.

Disclaimer

Certain trade names and company products are identified in order

to adequately specify the experimental procedure. In no case does such

identification imply recommendation or endorsement by the National

Bureau of Standards, nor does it imply that the products are necessarily

the best available for the purpose. Views expressed by the various

authors are their own and do not necessarily represent those of the

National Bureau of Standards.

iv
CONTENTS

Foreword iii

Abstract iv

Table of Contents v

The Role of Data Accuracy in Application of Thermophysics : An

Introduction and Overview 1

M. Klein

Present and Future Sources of Fluid Property Data 11

N.A. Olien

The Influence of Thermophysical Properties on the Design and Sizing

of Geothermal Power Plant Components 18

H.E. Khalifa and J. Kestin

Thermophysical Properties of Rocks: A Perspective on Data Needs,

Sources, and Accuracy 27

H.P. Stephens and S. Sinnock

Thermophysical Property Data: Who Needs Them? 33

R.C. Hendricks

Problems and Procedures in Providing Values of Thermophysical

Properties of Fluids 43

P.E. Liley

v
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I

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I

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i

i

i

i
Max Klein

Thermophysics Division, Center for Thermodynamics

and Molecular Science,

National Bureau of Standards, Washington, D.C.

The Role of Data Accuracy in

Applications of Thermophysics:

An Introduction and Overview

The importance of thermophysical properties data to technology and to society is described. Arguments are presented for a rapidly growing importance for the role of the accuracy of such data. Specific examples are presented of instances where an economic value has been placed on typical uncertainties in such data.

INTRODUCTION

This session has as its essential purpose an examination of the need for accuracy in thermophysical

properties data. By the thermophysical properties

of a system, we mean those properties which measure

the response of the system to thermal and mechanical

stimuli. These include both the thermodynamic

properties (which describe the change of the system between initial and final equilibrium states) and

the transport properties (which describe the flow of heat or material resulting from a steady departure

from equilibrium). The speakers will describe the

role played by the accuracy of the thermophysical

properties data used in their research areas. This will be done by them both through historical examples

and through typical engineering calculations. The research areas associated with these papers include what can be called an area of mature users of accuracy

in thermodynamics (in the sense that their need for accuracy has been well established for a number of years). Our example of this is from aerospace

science. Included also is an instance of awakening

users of accuracy in thermodynamics (the chemical

process plant design users on whom pressure for accuracy is being applied due to rapid escalation in cost of energy and material) and an instance of new users of accuracy in thermodynamics (the geophysical

sciences, whose models and computational tools are only beginning to be able to use well-defined thermodynamic and transport property data of some reliability). In this introduction, we shall attempt to give

the flavor of the importance of thermodynamic data

to science and technology and shall indicate the growing role played by their accuracy. Our emphasis

will be on the role of fluid properties in process

plant design. Specific applications in several

*Numbers in parentheses in text in each paper refer to references at the end of that paper.

other broad areas and in greater detail will be presented by the individual session speakers who

will also discuss transport properties.

The science of thermodynamics deals with the flow of energy; it deals with relationships between

heat and work as forms of energy and especially

with the efficiency of the interconversion of various

forms of energy. This can be taken to mean that thermodynamics is that science which studies the effective conversion of energy into useful work and vice versa. The breadth of applicability of thermodynamics

is widely recognized. Its use in analysis and design

in the physical sciences and engineering is ancient

on the time scale of scientific advances. In recent

decades, there has been a rapid escalation in applications of thermodynamics stemming from the fact that

the flow of energy as heat and work has now become

necessary for the very existence of civilization and

of life itself. In our own society, the increase in the flow of energy in the last hundred years has been

directly responsible for a major increase in the productivities of labor and capital^ resulting thereby both in an effective and productive modern technology

and in a major increase in our standard of living.

Among the applications of thermodynamic data

are those which are direct and of obvious technological use. These applications occur in the design of chemical process plants, electric power generating

systems, natural gas processing plants, oil refineries, etc. There are, in addition to these purely

technological uses , applications which can be classified in a language appropriate to elucidate

social impact. A recent publication (l)* contains a list of social problems to whose solutions thermodynamics contributes. Although most of these are applications of technologies whose system designs are

in turn based on thermodynamic data (and are, so to speak, dependent on such data in second order), those data nevertheless play a central role in the design

of the means for solving the problems indicated. The social problems listed include the

1
"-Maintenance of the quality of the air we

breathe and the water we drink, and the integrity of

our natural resources of land and water; -Production, distribution, and consumption of

food and of energy; -Proper disposition, and recycling where

possible, of the waste produced by humans in the home,

in factories, on the farm, and in recreation;

-Proper disposition and use of the thermal

discharge from fossil fuel and nuclear power plants;

-Problems of transportation, local, national,

and international, by land, water, and air; -Problems of communication, local, national,

and international."

In addition, thermodynamics contributes to the design

and maintenance of health care facilities and even_

sometimes provides models for understanding biological systems (2)

.

Thermodynamics is not only necessary for solving the above problems , but is also needed for doing it efficiently, a concept becoming of primary

importance to our society. The escalating growth in dependence on energy and synthetic materials in the

last decades has caused almost all aspects of human

life to be dependent on systems designed with the use of thermodynamics (as the list above indicated) . As the demand for energy and synthetic materials

approaches the limit of availability of the raw

materials involved, our lives begin to depend on

small differences in the efficiencies of those

systems and hence on the accuracy of their designs.

As relates to energy, it has been suggested (3) that, in order to "stretch out our sources, o_f energy, and to make a given unit of energy do its maximum for use, we need to analyze every significant

process and reaction associated with human activity'

in the world and see that such activity is carried out under conditions that yield a maximum of

thermodynamic efficiency." The realization of this

has, in fact, even led to recent Congressional

legislation which directed certain Government

agencies to undertake a study of the methodology of thermodynamic efficiency calculations {h)

.

As relates to materials, it is clear that the direct effect of material shortages on the economy

can be devastating and that accurate thermodynamic data can play a large role in reducing such shortages. For example, a study made by the A.D. Little

Co. during the aftermath of the oil embargo projected

a loss of 1.6 million jobs across U.S. industry if feedstock supplies (mainly petrochemical) were

reduced by only 15%. (5). More efficient use of such feedstocks obviously, then, will have a direct

economic effect on the Nation. A specific example

of this and one in which the potential role of accurate data is apparent can be found in the feedstock situation for ethylene. A major part of the raw material supply for the petrochemical

industry consists of ethane, propane, and heavier raw

materials extracted in natural gas processing

plants. These materials account for three- fourths

of the ethylene produced in the U.S., almost half of which is derived from ethane. The production of these feedstocks is declining, however. Yet bigger

supplies are available as indicated by an industry

executive who stated that (6), "At present, about

85% of the ethane in domestic natural gas is not recovered and is burned as fuel. The recovered

portion could easily be raised from the existing 15% to somewhere between 50 and 10%. In the same way, the percentage of propane extracted from gas could be increased from the present 50% to between 75 and

90%." Increased efficiencies in natural gas processing can thus lead to material conservation and could play a major role in determining and lowering what could otherwise become an unbearably high price. Such increased separation efficiencies depend strongly

on the quality of the thermodynamic data used in process designs (7). Clearly, then, thermodynamics plays an all pervasive role in our society and the accuracy of thermodynamic data affects our daily lives through

its effect on the efficiency of energy and material

usage. Yet, despite this, support for research in thermodynamics has been noticeably drying up. Concern from within the field at the rapid reduction

in the number of research laboratories and in the number of graduate theses published has been vociferous (8). Yet this has not generated a shift in resources to reverse this trend. The reasons for such an apparent contradiction ( i . e , .between an obvious and growing strong national need for accurate thermodynamic data and a lack of resource support)

are not obvious. Among possible reasons are the following : Thermodynamics is based on two very general

laws which are totally independent of the properties

of any particular substance. This is at the same time the power of the discipline and a reason why its utility is often not understood well. Thermodynamics,

of itself, has nothing to say about particular sub- stances and is, in fact, nothing more than a "bare boned" computational framework until the properties

of particular substances are introduced. However,

it becomes an extremely powerful tool when good data

are availablfi^xadiicinRjan. efficiencv in the use. of property data which can be truly awesome (9). Surprisingly enough, the need for accurate data

is not always understood. That need is often clouded by the successes in the use of thermodynamics for those systems (often the ones' used in textbook

examples) for which accurate data do exist. Because

of the breadth of its applicability, success with

thermodynamics in one research area can lead to a feeling of guaranteed success in other similar

areas. This leads to a sense of false security

according to which it is assumed that success will be waiting when needed. This may in turn remove the pressure for program managers to support the taking

of such data, especially where the application lies in the future. Adequate support for thermodynamic data develop- ment might also be absent because of the structure of the measurement "system" for such data. By that system is meant the sum total of all measurements,

theories and correlations which produce tables or mathematical representations of thermodyanmic data. Measurements required for producing accurate thermodynamic property data are difficult and tend to use classical methods of measurement. Experiments require

extremely careful design and painstaking attention to

detail. The measurements are, furthermore, time

consuming. Such measurements are rarely in response

to an immediate technological need because the time needed is generally several times that available for the solution of a technological problem. As a result, such measurements are rarely carried out in industrial settings. Since the measurement methods

tend to be classical and the time scale long, it is also rare that such measurements can be made the basis for a graduate thesis. Even when they can be, the tendency must be for the measurements to be divided among several students in time sequence with

some loss of continuity. It is therefore only in the nonprofit and government laboratories that the

2
required measurement programs can possibly "be designed

properly and carried out. The advent of a strong

emphasis on short term relevance at those laboratories,

(perhaps in emulation of the industrial laboratory)

has made it difficult to support such programs even

there. Thus support for the accurate measurement of thermodynamic properties has tended to he left without

a natural sponsor. In fact, managers in the various

parts of the system tend to think the data they will

need are actually being compiled in another part of the system and are shocked when the data are not on the shelf when urgently needed. The lack of sufficient support for thermodynamic measurements has often led to a "band-aid" approach

to the production of thermodynamic data in which

measurements are made only as an immediate need for them is discovered. Because of the aforementioned

long time scale, however, only the very minimum

amount of data can generally be taken and most often

at relatively low accuracy. This has resulted in a literature replete with isolated data on various

substances and mainly with very poor accuracy. This

has, in the past, fortunately not resulted in a major industrial bottleneck since, until recently, the fuel and material required in technological and societal applications of thermodynamics have been

easily available as well as inexpensive. Hence

efficient use of energy and materials has often not been a major concern and the attainment of the

highest accuracy has rarely been a major driving

force in the designs of the system involved. In other words, the economic value placed on accurate

and consistent thermodynamic data for various

substances has not been sufficiently high to produce

a large industrial demand for data of such quality.

This situation is rapidly changing with demands now being voiced for designs based on thermodynamic data

of the highest accuracy. There are several reasons

for this change. Recent events have produced a dramatic awareness of impending shortages and of associated

increases in costs (both artifical and natural) in energy and materials supplies. Demands for accurate data are also accelerating because advancing

technology now produces individual plants of very

large capacity. This makes the economic payoff for better designs highly significant even in the design of a single plant. In the case of ethylene

producing plants, for example, there has been an eight fold increase in plant size for new plants in the last decade and a half (10). There has been a corresponding increase in capital cost for individ- ual plant construction. Overdesign has, therefore, become very costly in capital cost, in feedstock

cost and in energy cost. A more subtle additional reason for needing accurate data comes from the

strong legal requirements for minimizing the environmental impacts of technological processes, require- ments which include the need to file detailed

statements of expected environmental impact in advance of plant construction. This places strong demands on design predictability. It is obvious

that trace elements of toxic materials in the

output of a huge plant can produce large quantities

of environmentally unacceptable material even though such quantities are only a small (and even trivial) percentage of total material output. The demand for accurate data generated Vy the pressures of environmental considerations is often

for producing alternative designs, especially those

calling for tight control over waste energy and particular effluent materials . These call for very

accurate data. Waste energy and material come out of

large processes as small differences between large

numbers, i.e. the differences between the large amounts of energy and materials flowing in and the almost equally large amounts used up in the processes. For example, a particular plant which makes one million pounds per day of ethylene and a lesser

amount of propylene produces as waste having a potential detrimental environmental effect, TOO pounds per day of solid material (ll). Although

this is a very small difference between the almost two million pounds of input material and the almost

two million pounds of output material, {representing

only several parts in ten thousand of the material

flow) it is nevertheless enough to cause environmental

problems

.

I have tried, up to this point, to establish

the broad utility of thermodynamic data to technology

and to our daily lives. I have also attempted to indicate why, despite this, there has not been

pressure for producing the required large amounts of

such data. I have indicated why this is changing

and, in fact, why there is a growing need not only

for data but for accurate data. In what follows, I shall give a small number of specific examples in which the need for accurate thermodynamic data is clear. In some cases, the detrimental effects of the use of inaccurate data are presented.

THE ROLE OF ACCURACY

Accuracy plays an important and obvious role

in scientific applications of thermodynamic data. There, in each application, data inaccuracies place

a limit on the measurement accuracy obtainable. More important in the national scheme of things is the role of accuracy in technological applications.

We have already indicated that applications of thermodynamic data are all pervasive in our economy

and in our daily lives and that the importance of accuracy, though limited until recently, is rapidly

increasing.

In most technological applications to which we

shall refer, thermodynamic data are used in plant

and system design. In design, the data play an initial role in establishing the feasibility of a project. Once feasibility has been established, the data play a most important role in attaining adequate

process efficiency. The economic impact of accuracy

in the feasibility role can be quite large, the worst case being one where available (and inaccurate) data show a process to be feasible but where the inaccuracies are such that the completed plant

either does not work or turns out to be uneconomical

to operate. Written examples of this are hard to

find, for obvious reasons, but anecodotes do exist

outside the published literature. A more usual case

is one in which inaccuracies increase capital costs and/or reduce operating efficiencies unnecessarily.

The effect of data inaccuracies on systems operating

efficiency can be documented quite easily by using

computer models. Surprisingly enough, such calculations

have been rare. The fact that their number is growing, however, attests both to the increasing

importance of data inaccuracy considerations in design and to the ability of the designer to use

data of greater accuracy than is presently available

to him. Times have changed drastically in this

regard. Thus, in a book on design strategy (12) it

is pointed out that "in the past the accuracy of

data was on the same order as the accuracy of the methods of computation. Now the numerical accuracy

of the mathematics often far exceeds the accuracy of the basic data upon which the mathematical equations

3
are based." This says that the tools available to the engineer are now waiting for more accurate data. These tools are so good that , given a sufficient

data base to describe the behavior of the materials

used, the latest computer models for plant processes

can be used to design plants with fewer (and, in principle, even with no) pilot plant stages. One

can, in fact, use the combination of models and data

after a plant is operational to perform dynamic

optimizations of plant parameters (13). The hard- ware already exists (and development rapidly expanding) even for using microcomputers which are small enough for inclusion in run streams and which are yet powerful enough to solve quite complicated

mathematical models for process operations. An

example is the development of microprocessors for the control of automobile engines ilk) and those for control of industrial and consumer combustion

processes. The hardware and software technology for this is far ahead of the quality of the data

available. This is an instance where available

technology is far ahead of the kind of fundamental knowledge that it can already use. This situation

faults the technological community for lack of foresight and long range planning. We have indicated that thermodynamic data are important to science and technology and that their accuracy plays a rapidly expanding role in the national scheme of things. A prime example of what

can be done by industry with adequate data "on the

shelf" at the time of need is given by the petroleum

industry in the U.S.A. This industry became the beneficiary of much basic data on the thermodynamic,

thermochemical, physical, and spectroscopic properties

of hydrocarbons, beginning before World War II and continuing about 20 years. With these data, the petroleum industry was able to develop an almost magical power to determine the optimum conditions of temperature and pressure for carrying on its many

different refining operations involved in the production from petroleum of its numerous important

products for man.

THE SIZE OF THE DATA GATHERING PROBLEM

Now that we have examined the role in our society of thermodynamics and have indicated the need for accurate thermodynamic data, let us look at the size of thermodynamic data gathering problem. The number of material systems of potential technological interest is quite large as are the number of potentially useful properties of each such system. The total data set required is, in fact, staggering.

It has been suggested that for the design of energy plants alone, for each material system of interest , (15) "thermodynamic and related properties would

need to cover, as appropriate in specific cases, temperatures from 10 degrees absolute (10 K.) up to about 5000 degrees absolute (5000 K). Similarly,

for appropriate systems, measurements would need to cover pressures up to several hundred atmospheres."

This range of variables could not be spanned with

less than one or two thousand data points per

property per system of interest - too many points . to measure. Thus the data needs are large. These

needs are also, in a real sense, unpredictable.

Thus, with the exception of those very few substances whose utility is broad and long term, e.g. steam, the probability is quite small that a need will

exist at any given time for some particular subset

of thermodynamic properties for a particular sub- stance or mixture chosen at random. On the other

hand, at any particular time, the probability is

quite large that a need exists for thermodynamic

data of some kind for some substance and that this need was not previously predictable. Large unpre- dictable needs of this kind require the development

of an easily accessible data bank containing properties data for many substances.

It is hard to develop resources to take care of such large but unpredictable data needs . There

are those who would respond to such a task through measurement programs for producing data as needs

arise. Unfortunately, the time scale for producing

laboratory data is quite long, even where the needed measuring apparatus already exists. A "response by measurement" approach is therefore inadequate since

it would frequently produce data only after the need

for them had been satisfied in some less efficient

manner. The only sensible approach would involve a program for accumulating a bank of data in advance of need for all systems of possible interest. If a purely measurement approach is used for this, tech- nology predictions would need to be combined with

long range goals to anticipate needs far enough in the future to have data "on the shelf" when needed. Even where this can, in principle, be done there are problems because of the enormous amount of data which

could be of potential interest. The only realistic solution to this problem

requires the development of predictive models which

make use of a very small number of data points for each material system, these data being necessary to determine values for parameters contained in the

models. The use of models and intuition for estima- tion of data is a fairly advanced art in reaction

thermochemistry where the development of models is almost as old as modern chemistry itself. Thus it

is estimated (13) that a majority of the entries in the American Petroleum Institute Task kk publications

are estimates based on models. Model development for thermodynamic properties of non dilute phases has been slow and mostly empirical mainly because of the absence of adequate theories for the dense fluid and

for mixtures as well as the inadequacy of the accuracy

of much of the data base.

THE ECONOMIC BENEFITS OF MORE ACCURATE DATA

The potential economic leverage to be obtained

from resources applied toward achieving more efficient production of basic materials from petrochemical

processes can be gauged from the various uses to which a product is put. Take ethylene as an example. Table 1 contains a representative list of ethylene

uses generally not carried to final end product and

indicates the broad economic impact more efficient

designs of systems which use ethylene can have. It should be realized, of course, that the direct

dollar effects of improved ethylene data are quite

small as a percentage of the quantity of ethylene converted and therefore not a simple matter to document. Nevertheless, the breadth of the applications for ethylene multiplies this small effect by a huge number resulting in a very large total dollar

effect relative to the cost of any data gathering

program. This makes for considerable cost effectiveness leverage for any resourses expended in improving

such data. Economic payoff of accurate data can also be expected because of the extensive distribution of small energy conversion systems (with the automobile

and home heating units being prime examples). Thus, for example, a small increase in the energy conversion

efficiency of the automobile would have a very large

national effect on the use of energy and of petroleum
Table 1: Representative Uses for Ethylene

PRIMARY DERIVATIVECHEMICAL INTERMEDIATE AND END PRODUCTS

Di & Triethylene Glycol

ETHYLENE OXIDE

ETHYLENE

ETHYL. ALCOHOL

STYRENE MONOMER

Ethylene Glycol

Nonionic Surfactants Acrylonitrile

Ethanolamines

Glycol Ethers

Solvent Toiletries Acetaidehyde

Pharmaceuticals

SBR Rubber

Polystyrene Resins

Anesthetic ETHYLENE DIBROMIDE Refrigerant

Lead Scavenger(TEL)

Ethylene Diamine ETHYLENE DICHLORIDE

Vinyl Chloride Tetraethyl Lead ETHYL CHLORIDE

ETHYLENE-PROPYLENE

COPOLYMERS

Ethyl Cellulose

Rubber Specialties

Synthetic Rubber Plastics

Synthetic Fibers

Jet Fuel Additives Solvent

Chemical Intermediates

Tires Footwear Gaskets

Film

Foams Paneling

Wall Tile

Solvent Stabilizers Polyvinyl Chloride

Refrigerant

Gasoline Additive

Paper Coating

Lacquers Packaging

Urethane Foams Solvent Extraction

Polyester Resins

Antifreeze

Hydraulic Fluids Polyethylene Glycol

Plasticizers

Detergents

Cosmetics Textile Chemicals

Gas Scrubbing

Polyvinyl Derivatives

Acetylsalicyclic Acid

Chloroacetic Acid

Cellulose Acetate

Other Esters

Wire Insulation

Garden Hose Flooring & Sheets Rainwear Upholstery

Shower Curtains

Alkyd Coatings

Foams, Fibers & Film

Plasticizers

Lubricants Emulsifiers

Latex Paints Adhesives Textile Finishing

Coatings

Molding Compounds

Aspirin

2,lt-D & 2,1*,5-T Weed Killers

Rayon & Film

Lacquers Solvents Plasticizers

Jet Lubricants

products. It has been estimated (ih) that (as of the

end of 1974) "each one percent increase in auto

engine combustion efficiency saves about 1^.5 million

barrels of oil per year which saves this nation over

150 million [197*0 dollars per year in balance of

payments, [and] this example of payoff [is] conservative ... ." We have already pointed out that published

calculations of the effect of uncertainties in thermodynamic data on plant feasibility and operating efficiency have been few. It is only fair to point out that in many situations apparent economic

effects of data uncertainty are not simply related to plant operating economics. Uncertainties in the data

can be over-shadowed by large uncertainties in the design and operating characteristics of mechanical

components, in variations in feedstocks or in other variables not directed related to the original

design requirements. In such cases the "actual"

effect of data uncertainties can be negligible

(except insofar as a component of excessive size is used as a direct result of the data uncertainty) . In certain special cases, the effect of uncertainties

can be a strong function of an operating parameter

whose nominal value is either initially very hard to predict or is entirely dependent on the design of other components. Figure 1 taken from page 337 of reference (12) illustrates such a situation. When

the cooling water turns out to be needed at the temperature designated A, the effect of data un- certainty on the design is negligible. When temperaature B is needed, the effect of the same uncertainty

100

Cooling water temperature T Fig. 1. Propagation of uncertainty through a design.

5
in the data is large and is, in fact, an amplified

version of the original uncertainty.

EXAMPLES OF THE EFFECT OF DATA UNCERTAINTIES ON PLANT

COSTS

Perhaps the first detailed estimate of the

economic effect of data uncertainty was published by

Baker (l6) almost two decades ago. This carefully reasoned paper had very little effect on research

support. There are those who take this to reflect

faults in our engineering educational system and find

it to be symptomatic of an uneasiness which most operating engineers feel with thermodynamics. More

likely, however, this reflects the historical low

cost of energy and raw materials. In either case the study by Baker had very little apparent impact. More

recently there have been some attempts at documenting more extensively (if with less detailed use of economics) the cost of data uncertainties. We have collected a small number of illustrations of such calculations. The examples we have collected are mainly (but not all) hypothetical and/or anonymous. They are, however, based on solid engineering procedures and hence are representative of actual situations. The

specific examples used by us should not be taken as being the most typical or as even being illustrative

of the most important situations. Our choice has depended on the availability of these examples and on the fact that they do illustrate problems which

engineers frequently meet. The examples are used to illustrate the economic value of uncertainties in the data where such a value is easily calculated. These

are not examples of underdesigns which would lead to plant failure or to drastic retrofit. Such extreme

examples are generally unavailable in the literature

for obvious reasons. Situations have also not been

included in which the "safest" design (generally also the most expensive) does not work, nor have we included estimates of the cost of reduced reliability

resulting from component overloads which result from corrections for low yields. In the following we have separated our examples into property and utility

categories. In most instances we simply indicate the conclusions of the author and leave it up to the

reader to go to the original paper for details

.

1. Retrofitting -

A paper by Squires and Orchard (17) illus- trates the problems met in "retrofitting" gas processing plants to correct for missing a plant

design point as a result of data uncertainties. In their first example, use of inaccurate K values for methane resulted in reduced propane recovery from the

stream. The method used to correct this led to- higher power consumption and extra cooling tower duty

cycle. A second necessary correction resulted in a reduction in the rate of removal of ethane in the

early stages of the stream. Thus lower efficiency of plant operations at a higher operating cost had to be

accepted in the retrofit.

2. Critical parameters -

Critical parameters are most widely used in corresponding states representations of P,V,T surfaces

(18). Such representations are among the best computational tools available to engineers especially

for predicting data for substances on which experimental measurements have not been made. Corresponding

states correlations, however, are only approximately based on fundamental notions. Since the basic researcher has not yet been able to produce an alternative of reasonable accuracy and ease of use, corresponding states methods will continue to be used

by engineers for some time . Perhaps the most widely

used corresponding states representation is one in which the critical parameters are used as reducing

variables. Generalized charts of such reduced

representations have been available for some time

(19). The need for good critical parameter data for using these representations can be gaged from the

effect of uncertainties in engineering methods used

to estimate the parameters (20). It has been estimated

(21) that at the limits of accuracy for such predictions, specific heats are obtained from the generalized

representations which can be in error by 25?. Such

errors in specific heats can result in a construction

cost difference of $600,000 (i960 dollars and plant

size) in the design of a gasoline plant and in an increased cost for the gasoline produced.

3. Vapor pressure -

Vapor pressures are among the most useful

of thermodynamic data. Obvious examples of their

utility are in safety calculations and in predictions

of relative volatility which, in turn, are needed in the design of fractionators . Zudkevitch (22) includes an interesting study of the effect of vapor pressure errors, at the state of the art of engineering correlations, on the cost and operating characteristics of a process designed to remove 91% of the isopentane from a naptha stream. (isopentane has been used to increase the octane rating of gasoline

thereby reducing the amount of lead additive required)

.

He found a spread in capital investment of $65,000

(1968 dollars) in a nominal cost of $550,000 for major equipment, a difference of approximately $100,000

(1968 dollars) in a nominal $1+00,000 investment in energy generating equipment and a difference of $100,000 per year (1968 dollars) in a design value of $U50,000 in operating expenses. In addition, he estimates that the design which uses published data

at one extreme of their range of uncertainty would

probably not work well enough to be satisfactory and

so would require expensive plant modification after a period of unsatisfactory process yield.

h. Volumetric properties -

Volumetric properties have many scientific

and technological applications especially in those thermodynamic calculations which require the equation

of state. However, our examples are drawn mainly from applications in the sale of large quantities of fluids (i.e. custody transfer). Uncertainties here produce an uncertain market and can destroy equity between buyer and seller in the market place. When

the market occurs at a national boundary, such uncertainties can contribute to uncertainty in the value of currency transfer between nations.

a. Custody transfer contracts for natural gas are based on heating value (in BTU) . Actual transfer

is based on composition and quantity of material. The latter is measured by a flowmeter which measures

pressure, temperature and flow rate. These are converted to quantity of material through the use of

an equation of state. Based on estimates of the

6
state of the art and on an arbitrary choice for the

cost of natural gas , Zudkevitch estimates that uncertainties in LNG density at the time of his publication would result in an uncertainty of $15,000.

in the transfer of the custody of the contents of a typical LNG ship. If the U.S. eventually imports LNG

from 500 such ships annually, the annual uncertainty

begins to approach $8,000,000. (Actually more at 1979

gas prices )

.

b. The critical point of ethylene is approximately 9-5°C. This is close to winter ambient

conditions in the Houston area where most custody

transfers of ethylene take place. Temperatures near critical are therefore sometimes "natural" ones for the custody transfer of ethylene. Properties of ethylene have been very poorly known (23) even several degrees above the critical temperature

making custody transfer at such temperatures very

uncertain. For this reason, many custody transfer

contracts call for the fabrication of a steam plant

at the metering station, for the sole purpose of heating the ethylene to a temperature where (generally

arbitrary) agreement can be reached between buyer and seller for its properties. Such a steam plant costs approximately $30,000 (1970 dollars) to build and

requires continuous energy generation. After the ethylene has passed through the flowmeter and custody transfer has been effected, its temperature is returned to its original value. On several occasions,

as a result of steam plant failure, because of the particular adiabatic path dictated by the steam plant

design, the ethylene temperature and pressure settled

into a state very close to critical. Because of very

large uncertainties in data correlations near the

critical point, the resulting error estimate for the metering process as to quantity transferred approached

total uncertainty (2*0.

c. To take care of supply and demand fluctuations, ethylene is often delivered to temporary

salt dome storage through a custody transfer arrangement. As a test on the accuracy of the custody transfer process, one such salt dome was completely

evacuated by its owners and the. amount of ethylene removed measured. Comparison with company records indicated that the metering process showed much more

ethylene had been removed .than had been stored, a clear indication of the inadequacy of the process used for conversion of flow parameters to quantity of material (25)! Since the equation of state plays a key role in that process, this is a clear indication

of the inadequacy of the basic thermodynamic data for ethylene.

d. A knowledge of volumetric properties is also required in the design of compressors. Zudkevitch illustrates the effect of data uncertainty

on the design of the ethylene compression stage in a hypothetical polyethylene plant. Compressor design

uncertainty in that case could lead to a 10% cost uncertainty resulting from overdesign of a compressor

(an uncertainty of roughly $100,000 1971

* dollars). When the error leads to an underdesign, potential

serious operating problems involving equipment overloads could result. Since such plants are designed

for continuous service with large continuous input of feed stock, shutdowns are very serious and costly.

Zudkevitch also points out that ethylene is a fortunate example because he considered its properties

to have been among the best known! The larger

uncertainties for other substances and especially for

their mixtures could lead to very costly errors

indeed.

5. K values -

Except under unusual circumstances, a liquid mixture in equilibrium with its vapor has a different composition than its vapor. The ratio of the concentration of a particular component in the vapor phase to that of the same component in the liquid phase is defined as the K value of that substance in the particular mixture at the temperature

and pressure of interest. Knowledge of the K values

of the constituents of a particular mixture are obviously important in the design of plants in which

certain species are to be removed from that mixture

.

In fact , the ratio of the K values for two constituents

in a mixture is a good measure of the ease with which

these two are separated and hence of the economics of the separation process. Albright (25) has examined

the implications of uncertainties in K value data on

the separation of ethane from methane, a process which is important to the natural gas industry (see

introduction). In addition to pointing out the dangers

inherent to the extrapolation of such data, Albright

presents several specific examples. Using two popular

correlations for K values , he obtained an uncertainty

of kl°F in the calculated bubble point . A large

difference in refrigeration cost between the two

extreme designs resulted. An indication of the cost

of this uncertanity can be seen in another example

given by him in which there was an uncertainty of

some 3°F in the predicted bubble point. In the latter case, an additional 12,000 horsepower of compression (and possibly an additional stage of refrigeration) was required with a difference of $1,000,000 in the cost of capital equipment! In yet

another illustration described by Albright, involving

the recovery of propane from natural gas , there was

an uncertainty of $200,000 in refrigeration equipment.

The paper by Squires and Orchard (17) already

mentioned above as containing examples of the cost of retrofitting contains two examples of the effect of K-value inaccuracies on the operation of actual gas processing plants. In one plant, the use of inaccurate methane K-values resulted in corrections which caused there to be higher fuel gas consumption (17%), higher

steam consumption {29%), higher cooling tower duty

cycle (30%) and higher electrical power useage (17%). In addition, ethane recovery was reduced. In a second plant cited in the paper, the use of inaccurate K-values was shown to be the cause of considerably

reduced propane recovery.

6. Enthalpies -

In I960, Ovid Baker of the Socony Mobil Company

published a very careful economic analysis of the effect of uncertainties in thermodynamic data on the

cost of capital equipment and on operating costs in petroleum refineries (l6). Restricting himself to effetts on the cost of heat exchangers in refinery

and natural gas plants, he found that uncertainties

in enthalpy correlations resulted (in terms of i960

economics) in an annual cost of $2,300,000 provided

one restricted the error in sign so as always to produce overdesigns. Obviously, errors which produce

inadequate designs would be more costly in terms of reduced yield (per dollar of total investment) and in terms of the high cost of design modification for retrofitting completed plants in order to make them

7
work better or at all. Baker also considered the

cost per barrel of output of overdesign in refineries

and obtained an estimate of roughly $1+ (in i960 dollars and at i960 oil prices) per barrel of new

capacity!

7. Liquified natural gas -

Problems in operating a natural gas liquifier arising from inadequate data were discussed

in a paper which appeared in 1973 (26). .We present

a number of direct quotes from that article. The

need for easily useable and accurate correlations is clearly stated. Italics are used by us for emphasis.

"...the lack of sufficient thermodynamic data

and the absence of computer programs forced the designer to choose the most conservative solution. Although a high operating pressure was desirable, it was limited to 39-5 atm in order to more

closely design the distillation columns removing the

C_ and heavier hydrocarbons, particularly the

aromatic components which tend to freeze up at these

temperatures. Data were not available during the design stages to safely consider operation above 1*0 atm. Actual performance of the distillation column

at a pressure of 1*3 atm proved that calculation

procedures were not only conservative but that separation at higher pressures was highly feasible. This higher operating pressure was necessary to correct a vapor-liquid equilibrium error which was discovered at the end of the natural gas condensation

curve for conditions of about 1. 5 atm at constant

temperature. This error was due to a lack of information concerning the exact behavior of helium (0.2%

mol) in a hydrocarbon mixture which also contains 6 mol% nitrogen. At the original design pressure, natural gas condensation was not completed in the ethylene cycle and was therefore carried through to

the first step of the methane cycle, resulting in a cycling steam flow rate for the turbocompressors

with a corresponding instability of the complex

steam cascade. The solution to the problem was found simultaneously but independently by the plant

operator and the process designer who had tested, by

then, the actual behavior of helium. The appropriate

increase in pressure determined by both was found to be equal. In order to minimize internal plant gas consumption, maximize LNG production, and provide

for a five-year payout on marginal investments , a minimum-power-consuming plant was required. The choice of cold suction compressors, which appeared

to meet these conditions, was the result of hasty

decisions primarily because of the slowness of hand

calculations. Actually, atmospheric temperature

suction compressors would have resulted in a lower overall power consumption but would have required a greater heat transfer area for the heat exchangers

.

The power distribution between the compressors for this case would have been better balanced and

startup procedures would have been greatly simplified.

Furthermore, connecting and interconnecting piping

could have been uninsulated carbon steel. The choice of the cold suction compressors was greatly

responsbile for the very high piping and insulation

costs, which reached 50% of the investment in the liquifaction units area. The lesson learned from this design and the resulting operational experience was that a major

effort in fundamental research was required in the area of hydrocarbon thermodynamics covering a temperature range from ambient down to -265°F for

pressures from atmospheric up to 100 atm, with

particular emphasis on the liquid-vapor equilibrium

of complex mixtures.

THE SESSION PAPERS

We now turn to the contributed papers. This session includes papers ranging from a research area

in which the need for accurate thermodynamic data was well established years ago to one in which the concept of a need for accurate data is only just

beginning to be felt and with other areas between. The subject areas selected could only be representative due to time constraints. An exhaustive examination of areas in which accuracy in thermophysical

properties plays an important role would have required

several days filled with papers. Running through

all the papers is a message that a need for more

accuracy already exists and that this is rapidly

becoming urgent.

It is interesting to note among the various papers the interplay between the ability to use more

accuracy and the drive for such accuracy. Thus in the 1950 's the appearance of much improved molecular

correlations for certain fluid properties so satisfied

the needs of the times that pressure for improvement abated (27). The time has again arrived where the ability to use accurate data has been developed far beyond the accuracy of the available data. Because

of a strong pressure for energy and materials

conservation and for the maintainance of environmental

integrity, there is a strong need for committing

national resources toward remedying this inconsistency.

This session's papers present strong arguments for

this. Also running through the session is an indication

of a strong need for close coupling between the producer of accurate data and the user of such data. This would ensure the use of the best data by user

and would enable the user to have some understanding

of limitations and uncertainties in the data.

REFERENCES

1 Rossini, F.D., "Conference on Thermodynamics

and National Energy Problems," June 10-12, 1971*, National Academy of Sciences, Washington D.C., p. 5. 2 Professor Schmidt-Nielsen, Duke University,

private communication referring to the use of the Stirling cycle for describing the metabolic cycle

of a particular desert mammal.

3 see reference 1.

1* Public Law 95-619, National Energy Policy

Act, Title VI part 5, section 683, (1979).

5 Quoted in Bissinger, F.L. , "Changing feedstocks - chemicals or calories," Chem. Eng.

Prog. 71, p. 30-33 (May 1975).

6 Bissinger, F.L. - see reference 5.

7 Private communications from several process design engineers on the staffs of large natural gas producer companies

.

8 Holley, C.E., Jr., Vanderzee, Cecil and

Westrum, E.F., Jr., Bull. Chem. Therm. 21, p 1*76-

1*79, 1978.

9 For example, the use of the two laws of thermodynamics leads to the Clapeyron equation which

relates the volume change in a phase change and the

slope of the phase boundary in a P-T plot (both, in essence, mechanical properties) to the heat involved

in the phase transition (a thermal quantity). Thus only two of these kinds of data are needed. With

the advent of a molecular theory of thermodynamics

the relationship between heat and mechanical energy

8
could "be "understood" but such a molecular theory

was not necessary for the development of the Clapeyron

relationship.

10 Reynolds, W.W. , Chem. Eng. Prog. 68_, p. 29-

35, September 1972, esp. Figure 5- 11 Private communication, plant manager of an ethylene plant.

12 Rudd, D.F. and Watson, C.C., "Strategy of Process Engineering", John Wiley and Sons, Inc., New

York, N.Y. , 1968, p. 349. 13 ibid, p. 455 where eleven process simulation languages are listed. That list is not exhaustive, however.

14. Hartley, D.L., "Technical Aspects of Efficient Energy Utilization," Summer Study 1974,

American Physical Society, New York, N.Y. , p. 23. See also Physics Today, Aug. 1975, p- 23-33 and references herein.

15 See reference 1. , Introduction p. vii.

16 Baker, 0., Proc. 39th Annual Convention Natural Gas Processors Association (i960).

17 Squires, E.W. and Orchard, J.C., Proc. 47th Annual Convention Natural Gas Processors

Assoc. p. 8O-85, March 19, 1968.

18 Leland, T.W. , Chappelear, P.S. and Gamson,

B.W. , AIChE J. 8_, p. 1+82 (1962).

19 Othmer, D.F., Ind. Eng. Chem., 3_4 p. 1072

and p. 1504 (1942).

20 Reid, R.C., Prausnitz, J.M. and Sherwood,

T.K. , "The Properties of Gases and Liquids, "McGrawHill, New York, N.Y., 1977.

21 Zudkevitch, D. , Hydrocarbon Processing,

March, 1975, p. 97-103.

22 ibid

23 This is in the process of being rectified

through a project supported by a combination of the

U*S. Government and an industrial consortium. For information, contact Dr. Howard White, Office of Standard Reference Data, National Bureau of Standards, Washington, DC 20234.

24 Private communication.

25 Albright, M.A. , Proc. 49th Annual Conven- Natural Gas Processors Assoc. p. 14-20, March 17,

1970. 26 Cryogenics and Industrial Gases, p. 9-13,

Sept/Oct. 1973.

27 See, for example, Hirshfelder, J.O.,

Curtiss, C.F. , and Bird, R.B. , "Molecular Theory of Gases and Liquids," John Wiley and Sons, New York

N.Y. , 1954.

9

N.A. Olien

Thermophysical Properties Division, National Engineering Laboratory,

National Bureau of Standards,

Boulder, Colo.

Present and Future Sources of

Fluid Property Data

Fluid Property calculations for the design and operation of large process systems

require that the data used by the engineer be in a computer compatible form. This,

in turn, places complex demands on those of us in the data generation and

correlation field. The responsibility of the producers of data, i.e., experimentalists,

theorists or correlators, to the ultimate users of the data such as design engineers is discussed, because the efficient transfer of data from the originator to the ultimate

user is absolutely essential. The specific requirements for data in the future will be

for 'black box' type computer-compatible routines to calculate broad ranges of

thermophysical properties for pure fluids and mixtures. Although calculational packages are very useful tools, reliance on them by the uninformed can lead to costly design errors and there is some evidence that the existence of the packages

may tend to reduce future research in fluid properties. Generic solutions to the future data requirements of the chemical process and energy industries will place

heavy reliance on theoretical approaches. Illustrations of the future data requirements ofspecific industries are given as examples.

ABSTRACT

Fluid Property calculations for the design and operation of large process systems require that the data used by the engineer be in a computer compatible

form. This in turn places complex demands on those

of us in the data generation and correlation field. The responsibility of the producers of data, i.e.,

experimentalists, theorists or correlators, to the ultimate users of the data such as design engineers

is discussed, because the efficient transfer of data from the originator to the ultimate user is absolutely essential.

The specific requirements for data in the future will be for 'black box' type computer-compatible

routines to calculate broad ranges of thermophysical

properties for pure fluids and mixtures. Although

calculational packages are very useful tools , reliance on them by the uninformed can lead to costly

design errors and there is some evidence that the existence of the packages may tend to reduce future research in fluid properties. Generic solutions to

the future data requirements of the chemical process

and energy industries will place heavy reliance on theoretical approaches. Illustrations of the future data requirements of specific industries are given as examples

.

INTRODUCTION

We have witnessed an increasing emphasis on more sophisticated forms of fluid property data over the past several decades. One large factor in this emphasis was the emergence of the aerospace industry

and the many requirements imposed by NASA, some of which were described in the previous paper (l). The

modern computer, of course, was another major factor, but NASA and its stringent demands for very high

accuracy and reliability truly set us on a path from looking up discrete values in handbooks to representing a continuum of properties with computer

programs. One of the pioneering efforts in this was

the refinement of the Benedict-Webb-Rubin equation of state by Strobridge (2) , an effort which was only

possible because of the modern digital computer.

Calculations, as such, however, are not new. James

Conant , the former president of Harvard tells a story, perhaps apocryphal, that took place during

World War I (3). When President Wilson appointed a board, with Thomas Edison as chairman, to give

scientific advice to the Navy during the course of

the war, one of the members chosen by Edison was a physicist from the National Bureau of Standards. Edison told the President that the reason for the presence of the physicist was, "we might have one mathematical fellow in case we have to calculate something out." I am not sure whether the story is appropriate or not in this centenary of Edison's

greatest invention [h) . Some things have changed

since 1918. The direction we are taking in mathematical modeling and the concurrent rapid

increase in speed and storage capacity of computers

means that the changes will come at an even faster

rate. The advent of the microprocessor and other offspring of large scale integration serve to magnify

this trend. Those of us producing data must be prepared to be active participants in the introduction of our data and the form of our data

into industrial automation. We must work with

current and emerging industries to see that they have

the best data and formulations available for their

use. It is not enough to make excellent measurements, develop magnificent equations of state and the like. I can say from experience that the

11
probability of use of data, models, etc. in industry

approaches zero as the estoric nature of the data and models increases. To put it bluntly, if data are difficult to find or hard to use they just will not

be utilized. The automation trend mentioned

previously serves only to strengthen this tendency.

I say this despite the large economic incentives of using more accurate data.

ECONOMIC IMPACT AND LEVERAGE

There have been several studies and estimates made of the economic impact on selected industries of inaccuracies in fluid property data (5,6,7,8,9). One such study is included in this meeting of the ASME. (10). David Zudketvitch has done a great deal

in this field and has recently shown (11) that the capital and operating costs of several types of plants can be significantly reduced as a result of increased accuracy (reliability and reduced error

bands) of thermophysical property data. Table 1 shows the relative importance of several kinds of data on the design of various parts of process

plants. The information in this table is taken from

the pioneering work of Zudkevitch (12). It is readily apparent that phase equilibria data are the most vital. This is because the equipment (heat

exchangers, distillation columns, compressors, etc.)

associated with fluid separation processes is the most capital and energy intensive part of process

plants. The large number of liquid-vapor equilibrium correlation techniques gives further credence to the industrial importance of this class of thermodynamic

properties. It is reasonably well established, then, that the accuracy of the thermophysical property data

of fluids can have a significant economic impact on the industries in which these fluids are used. Let u now look at the magnitude of this potential economic

impact.

The chemical process and fuels industries have current annual capital requirements in excess of $50

billion, with the bulk of this in conventional

processes and feedstocks. The period 1979-2000

however is a period of transition for these industries with a change to unconventional base feedstocks (principally coal). As an example the American Gas Association has estimated the capital

requirements for coal gasification/ synthetic gas

(SNG) for the period 1978-2000 to be $62.9 billion

(see table 2). Liquefied natural gas (LNG)

requirements will also be substantial with $7.9

billion for import terminal construction alone in the period 1978-1990. If we add to this the capital

requirements for associated distribution and storage

systems and dedicated auxiliary plants (e.g., air separation plants for coal gasification and LNG peak

shaving facilities) we have projected total requirements in the period 1978-1990 of $83.6 billion and in the period 1991-2000 of $91.5 billion. This $175.1

billion in capital investment will be for process

plants and associated equipment involving fluid mixtures ranging from six to eight component LNG to 20 plus component mixtures in coal gas plants. If we

remember that this is for supplemental gas for the gaseous fuel industry we can get some idea of the magnitude of the projected capital costs for the total of industries involving mixtures. The potential savings in new plant construction and modification of existing plant as a result of the availability of more accurate data and models is of Table 1.

RELATIVE IMPORTANCE OF SOME THERMODYN

ON DESIGN AND PERFORMANCE - EVALUAT

PETRICHEMICAL PRICESS EQUIP

AM

ION

ME*

C VARIABLES

OF BASIC

T VAPIR PRESSURE ANI: AHhi

C

p

AS

RATE DATA

DENSITY P-V-TCRITICALS PIASE

DISTRIBUTION ELECTROLYTEIONIZATION TRANSPORT REACTION

REACTORS C D B s B B B A FRACTIONATES B 6 A A B D B S EXTRACTORS 1 D A D or S C D B S

NEAT EXCHANGERS C B A s A C B S COMPRESSORS

& EXPANDERS A A A A B D S METERING

(AND SALES] A B s

MATERIALS OF CONSTRUCTION B B A S

POLLUTION ABATEMENT A A C A A

KEY: A - Mist important D - Considered only in preliminary

B - Very important selection

C - Influences calculations, N - Not applicable

but accuracy not critical S - Important in specific cases

12
Table 2. Capital Requirements - Supplemental Gas for U.S. (Billions of 1977 Dollars)

1978-1990 1991-2000 Total

Coal Gasification/ SNG 20.4 42.5 62.9 LNG Importation 7.9 2.0 9.9 Transmission, etc. 55.3 47 .0 102.3 Total 83.6 91.5 175.1

Source: Anderson, R. , AGA Monthly 60, 30-3 (Apr 1978).

the order of tens of millions of dollars per year. The studies mentioned above also tell us that the savings in operating costs over the life of the plant can be even greater than the savings in capital

costs

.

EXISTING TABLES OF FLUID PROPERTY DATA

Although there is a strong trend today toward

the use of computerized models for calculating fluid property data, tables of property data are still

widely used. Table 3 lists some of the more useful

of the existing collections which include data on many fluids. You will note that there is a lack of uniformity in the sources of these publications.

Table 3. Collections of Fluid Property Data

LNG "MATERIALS AND FLUIDS - A USER'S MANUAL OF PROPERTY DATA IN GRAPHIC FORMAT, D. B. Mann, Editor, National Bureau of Standards,

Thermophysical Properties Division, Boulder, CO 80303 (1977) (Supplement 1 - 1978; Supplement

2 - 1979)

THERMOPHYSICAL PROPERTIES OF MATTER/THE TPRC DATA SERIES, Y. S. Touloukian and C. Y. Ho, Editors, Plenum Press, N.Y.

SELECTED VALUES OF PROPERTIES OF HYDROCARBONS

AND RELATED COMPOUNDS, Thermodynamics Research

Center, Texas A&M Univ., College Station, TX 77843 (also a companion volume on other chemical

compounds)

GAS ENCYCLOPAEDIA, L'Air Liquide, Division

Scientif ique , Elsevier/NorthHolland, Inc. (1976)

ENGINEERING DATA BOOK, Gas Processors Assn., Tulsa, OK (1972)

ASHRAE THERMODYNAMIC PROPERTIES OF REFRIGERANTS,

Amer. Soc. of Heating, Refrigerating and Air Conditioning Engrs., 345 East 47th St.,' N.Y. 10017 (1969)

THERMODYNAMIC PROPERTIES AND REDUCED

CORRELATIONS FOR GASES, L. N. Canjar and F. S. Manning, Gulf Publishing Co. (1967)

PHYSICAL PROPERTIES - A GUIDE TO THE PHYSICAL, THERMODYNAMIC AND TRANSPORT PROPERTIES OF INDUSTRIALLY IMPORTANT CHEMICAL COMPOUNDS, C. L. Yaws, McGraw-Hill (1977)

MATHESON GAS DATA BOOK, W. Braker and A. L. Mossman, Matheson Gas Products, East Ratherford,

N.J. (1971)

They have been prepared by societies, government

agencies, private firms and universities. There are

also a number of sets of standard reference data or

at least quasi-standard data for equilibrium

properties for individual fluids (see table 4). You

will notice that some of these are in the process of being revised or at least new versions are definitely

planned. The argon and carbon monoxide publications

are in great need of revision, but to my knowledge,

no definite correlations or critical evaluations are underway. In the case of argon, we have a fluid of relatively small industrial importance, but argon is used so much as a standard for predictions as well as for testing new apparatus that its importance cannot

be overemphasized. The state-of-the-art in equations

of state has increased significantly since the publication of the Argon Standard Reference Data (13)

by the NBS-Office of Standard Reference Data. In addition, a large number of new measurements have

been made. The other fluid needing a new correlation

is carbon monoxide. I recently completed an informal

survey on CO and found to my surprise, that the best wide range tables (14,15) are nearly a quarter of a century old. Another set of tables (16), of slightly

newer vintage, does exist, but is limited to the temperature region below 300 K.

METHODS OF CALCULATING FLUID PROPERTY DATA

Many of the references given in table 4 include calculational methods (equations of state). Table 5 lists some calculational methods, the broadest of which is the lecently revised Reid, Prausnitz and Sherwood (17). A number of computer calculation

packages are available on time-sharing networks for a user fee or for outright purchase. There is even a computer package available in the Soviet Union called AVESTA as illustrated in figure 1. AVESTA stands for Automatic Variable Engineering System of Thermophysical Advance. There are dangers in using

computerized calculation packages, since the user can derive a false sense of security about the accuracy

of the data returned. The danger is amplified when

the data are used directly in computer calculations

for plant design and operation. In the latter case

the engineer never sees the data and he or she does

not have a chance to apply good engineering judgement

to the fluid property data. Often higher level managers in technical firms develop a feeling that

the calculation packages provide data which have very

small or non-existent error bars. This is both disquieting and dangerous. I have heard of a vice-president in the LNG industry who stated that they did not need any more work on LNG phase

equilibria, because his company subscribed to a computer package which provided all of that. To illustrate the folly of such a pronouncement, let us examine figure 2. Elliott, et al. (18) made a comparison of K-value calculations from ten different

13
Table 4. Standard Data for Individual Fluids Table 5. Calculation and Estimation Techniques

Fluid Source

H2 McCarty, R. D. , NASA SP-3089

(1975)

He McCarty, R. D. , J. Phys. Chem. Ref . Data 2, 923 (1973) and Angus, S., et al., Intern. Thermodynamic Tables of the Fluid

State - 4, Butterworths (1977)

N2 * Jacobsen, R. T. and Stewart,

R. B., J. Phys. Chem. Ref. Data

2, 757 (1973)

02 Roder, H. M. and Weber, L. A., NASA SP-3071 (1972)

F2 Prydz, R. and Straty, G. C.

,

NBS Tech. Note 392 Rev. (1973)

Ar Gosman, A. L., McCarty, R. D.,

et al., NSRDS-NBS 27 (1969) and Angus, S., et al., Intern. Thermodynamic Tables of the Fluid

State - 1, Pergamon (1971)

CO Din, F., Thermodynamic Functions

of Gases, Vol. I, Butterworths

(1956)

CO2 Angus, S., et al., Intern. Thermodynamic Tables of the Fluid

State - 3, Pergamon (1976)

NH3 Haar, L. and Gallagher, J. S.,

J. Phys. Chem. Ref. Data 7_, 635

(1978)

CH4 Goodwin, R. D. , NBS Tech. Note

653 (1974) and Angus, S. , et al., Intern. Thermodynamic Tables of the Fluid

State - 5, Pergamon (1978)

C2H6 Goodwin, R. D. , et al., NBS

Tech. Note 684 (1976)

C3H8 * Goodwin, R. D. , NBSIR 77-860

(1977)

n-c4H10 Goodwin, R. D. , NBSIR 79-

(1979)

i_c4H10 Goodwin, R. D. , NBSIR 79-

(1979)

C2H4 * Angus, S., et al., Intern. Thermodynamic Tables of the fluid State - 2, Butterworths (1974)

C3Hg * Juza, J., et al., Acta Tech.

(Prague) 23, 425 (1978)

THE PROPERTIES OF GASES AND LIQUIDS, Third

Edition, Reid, R. C, Prausnitz, J. M. and Sherwood, T. K. , McGraw-Hill (1977)

PHYSICAL PROPERTIES - A GUIDE TO THE PHYSICAL, THERMODYNAMIC AND TRANSPORT PROPERTIES OF INDUSTRIALLY IMPORTANT CHEMICAL COMPOUNDS, C. L. Yaws, McGraw-Hill (1977)

A NEW TWO-CONSTANT EQUATION OF STATE, D. Y. Peng and D. B. Robinson, Ind. Eng. Chem. Fundam. 15 , 59 (1976)(For a review of this and other phase

equilibria models, see Renon, H., Fluid Phase Equilibria 2, 101 (1978)

CUBIC EQUATIONS OF STATE - WHICH? , J. J. Martin,

Ind. Eng. Chem. Fundam, 18, 81 (1979)

A COMPARISON OF MATHEMATICAL MODELS FOR THE PREDICTION OF LNG DENSITIES, R. D. McCarty, Nat.

Bur. Stand. Interagency Report, NBSIR 77-867

(1977)

COMPUTER CALCULATION SYSTEMS, some examples are: CHEMTRAN/CHEMSHARE, CHESS, GPA CONV, SSI, FLOWTRAN, PDA, PPDS, TAP, etc.

TF..lEnP£CCP£K.1A.MA

TEl EI'RCSSRCKLAMA

Figure 1. AVESTA-Automated Property Calculation

Package from the USSR.

*Newer versions underway or planned.

11*
Figure 2. Comparison of K-Value Calculation Methods for Natural Gas.

computer packages. K-values are very useful in designing separation plants and are defined as K = y^x ± where: = molar concentration of

the i'*

1 component in the vapor phase and x^ = molar

concentration of the i'

component in the liquid

phase.

In figure 2 I have shown the deviation of five of these methods from a sixth, arbitrarily chosen. The horizontal axis gives the molecular species

(Ci=methane, C2=ethane, etc.), and the last item

is the total volume of all liquids condensed. I think it would be very difficult to maintain that any

of those methods represents scientific truth. In fact, the methods examined by Elliott and presented

here represent three different approaches to K-value

predicting - i.e., conformal solution theory, van der Waals' techniques and empirical methods. One further disadvantage of the widespread availability of these packages was hinted at above. In a conversation with Professor Kobayashi of Rice University a few months

ago, he and I agreed that the computer packages tend

to stifle research. The attitude expressed by the vice-president mentioned above certainly does not encourage grants and contracts for needed research

work. If it sounds as if I am advocating the

elimination of calculation techniques, especially

computerized methods, let me assure you that this is not the case

.

DISSEMINATION OF FLUID PROPERTY DATA IN THE FUTURE

I firmly believe that computerized calculation

methods for fluid properties, especially mixture

properties, will become commonplace in the future.

First, automation in design requires automation in

data; second, data needs are so great as to demand

the use of semi-automated calculations; and third, in

the case of mixtures, tables are just not practical.

How can we do this and still avoid the disadvantages

described above? It Is essential that calculational

packages be accompanied by well documented and justified confidence limits, the existence and use of which is clearly understood by the users of the packages. In addition, the package should contain

provisions for notifying the user when calculations

are requested which are outside the range of the particular method used. What is needed is a 'truth

in packaging' requirement for calculational tech- niques. A little earlier, I said that producers of data (experimenters, theorists or correlators) must

be prepared to participate in the introduction of their data and models into industry. They must also

do their part to prevent their data from being

misused, i.e., unwarranted extrapolations. The objective should be wide-range and accurate models,

which can be easily used and which, if they do not prevent improper use, at least clearly provide

warnings of perils ahead. One of the blessings of

15
the modern computer is the ease with which we can provide for warnings of this sort. Often the engineer is either faced with a need

for professional advice about calculational methods

and data or is at a loss as to where to turn. In these cases, it is important to make a personal contact with knowledgable experts in fluid properties. Table 6 lists several 'Data' or 'Information Analysis Centers' which can be of great

assistance to the engineer.

Table 6. Fluid Property Data Centers

Chemical Kinetics Information Center

NBS - Robert F. Hampson, (301) 921-1000,

extension 2565

Chemical Propulsion Information Agency Johns Hopkins, (301) 953-7100

Chemical Thermodynamics Data Center

NBS - Donald D. Wayman, (301) 921-1000,

extension 2773

Cryogenic Data Center

NBS - Neil A. Olien, (303) 499-1000, extension

3257

Electrolyte Data Center

NBS - Bert R. Staples, (301) 921-1000, extension

3632

Thermodynamics Research Center Texas A&M - R. C. Wilhoit, (713) 846-8765

Thermophysical Properties Research Center Purdue - W. H. Shafer, (800) 428-7675

EXPANDED NBS PROGRAM IN FLUID PROPERTY RESEARCH

The Thermophysical Properties Division at NBS-Boulder has embarked on a long range effort to develop generic techniques for predicting the thermo- physical properties of a broad range of industrial

fluids. We are building on the experience we have gained through our participation in programs in liquefied natural gas (LNG) (primarily funded by the American Gas Association and the Gas Research

Institute) and ethylene properties (a joint

government- industry program, managed by the NBS- Office of Standard Reference Data). Our work has established a rational approach to the development of accurate and useful mathematical models. This

approach involves the judicious marriage of experimental measurements, theoretical studies,

mathematical modeling and a continuing interaction

with current and future users of the models and data. The measurement aspect of this integrated program will occupy a substantial fraction of the available

resources, but even at that we realize that the plan will be measurement limited. The measurements will

be primarily on pure components and binary systems,

with a strong need for very careful choice in fluids

and measurement ranges. In addition the measurements

must be of high quality, as the literature is replete

with examples of measurements of little or no use because of the high uncertainty of the results. A

purely experimental approach to mixtures properties

rapidly leads to an infinite data requirement;

therefore, theoretically based models must play a

large role in the entire project. It is difficult to separate the theoretical efforts from the mathematical modeling work. We are conducting and have plans

to accelerate our experiments wherein fluids are modeled in a computer by the techniques of molecular dynamics (19). These methods have the potential of becoming very powerful tools In the quest for a basic understanding of fluid behavior and the development

of soundly based methods of predicting the properties

of complex fluid mixtures. One area which requires a large amount of attention Is the need for quantitative understanding of the interactions between unlike molecules. Included in this are molecules of disparate sizes (e.g., molecular mass ratios of 25 or greater) and even more complex Interactions (e.g.,

polar-nonpolar interactions.)

All of this cannot be accomplished by one group

In Boulder and we thus plan to continue a large number of very productive technical collaborations.

Two of these are with the Thermophysics Division and

the Office of Standard Reference Data, both located

in the National Measurement Laboratory of NBS-Gai ther sburg

.

CONCLUSION

Even the person on the street Is aware of the pervasiveness of the computer in all aspects of modern life, industrial and otherwise. This trend, will continue and people producing fluid property

data and models must consider this trend in consideration of the future. These computerized

mathematical models must be developed with a combination of intelligence and pragmatism. We must

have a clear picture of our engineering customers and their requirements. They In turn must understand

what they are getting from us and how best to use the tools we provide.

REFERENCES

1 Hendricks, R. C, "Thermophysical Property

Data - Who Needs Them," Amer. Soc. Mech. Eng.,

Winter Annual Meeting, Dec. 2-7, 1979, Paper WA-HT-.

2 Strobridge, T. R., "The Thermodynamic

Properties of Nitrogen from 64 to 300 K Between 0.1 and 200 Atmospheres," Nat. Bur. Stand. (U.S.), Tech. Note 129, 85 pp (1962).

3 Conant, J. B., "Modern Science and Modern

Man," Columbia Univ. Press (1952).

4 EPRI Journal, Vol 4, No. 2 (Mar 1979). A

Special Issue Commemorating the 100 tn Anniversary

of Edison's Invention of a Practical Electric

Lighting System.

5 Medina, A. G., McDermott, C. and Ashton, N.

,

"On the Effect of Experimental Error on the Calculation of the Number of Stages for a Given

Distillation Separation," Chem. Eng. Sci. Z^_, 2279

(1974).

6 Zudkevitch, D. , "Imprecise Data Impacts Plant Design and Operation," Hydrocarbon Proc. _54^ 97 (Mar 1975).

7 Williams, C. C. and Albright, M. A., "Better Data Saves Energy," Hydrocarbon Proc. 55 , 115 (May

1976).

8 Mah, R. S. H., "Effects of Thermophysical

Property Estimation on Process Design," Chem. Eng.

Comput. I, 183 (1977).

16
9 Yen, L.C. , Frith, J.F.S., Chao, K.C. and Lin,

H.M. , "Data Deficiency Hampers Coal Gasification Plant

Design, "Chem. Eng. _8Jj_, 127 (May 9, 1977).

10 Khalifa, H.E. and Kestin, J., "The Influence of Thermophysical Properties on the Design

and Sizing of Geothermal Power Plant Components,"

Amer. Soc. Mech. Eng., Winter Annual Meeting,

Dec. 2-7, 1979, Paper WA-HT-.

11 Zudkevitch, D. , "Impact of Thermodynamic and Fluid Properties Data Uncertainties on Design and Economics of Separation Operations," The Encyclopedia

of Chemical Processing and Design (to he published).

12 Zudkevitch, D. and Gray, R.D. , Jr., "Impact

of Fluid Properties on the Design of Equipment for Handling LNG," Adv. Cryogenic Eng. Vol 20, 103

(1975).13 Gosman, A.L. , McCarty, R.D. and Hust , J.

G. , "Thermodynamic Properties of Argon from the

Triple Point to 300 K at Pressures to 1000 Atmospheres," Nat. Stand. Ref. Data Ser. , Nat. Bur. Stand. No. 27, 152 pp (1969).

lit Hilsenrath, J., Beckett, C.W. , et al. , "Tables of Thermal Properties of Gases," Nat. Bur.

Stand. Circ. No. 564 (1955).

15 Din, F. , Editor, "Thermodynamic Functions of Gases, Vol. I, Ammonia, Carbon Dioxide and Carbon Monoxide," Butterworths Scientific Publications

(1956).

16 Hust, J.G. and Stewart, R.B. , "Thermodynamic Property Values for Gaseous and Liquid Carbon Monoxide from 70 to 300 K with Pressures to 300 Atmospheres," Nat. Bur. Stand. (U.S.), Tech. Note 202

(1963).

17 Reid, R.C., Prausnitz, J.M. and Sherwood,

T.K., "The Properties of Gases and Liquids," Third

Edition, McGraw-Hill (1977).

18 Elliot, D.G. , Chappelear, P.S., et al.

,

"Thermophysical Properties: Their Effects on Cryogenic Gas Processing," Phase Equilibria and Fluid

Properties in the Chemical Industry, ACS Symposium

Series, 60 , p. 289-315, T.S. Storvick and S.I. Sandler, Editors, American Chemical Soc. (1977).

19 Hanley, H.J.M. and Watts, R.O.

,

"Molecular Dynamics Calculation of the Thermodynamic

Properties of Methane," Aust. J. Phys. 28_, 315 (1975).

17

H. E. Khalifa

United Technologies Research Center,

East Hartford, Conn.

J. Kestin

Brown University, Providence, R.I.

The Influence of Thermophysical

Properties on the Design and

Sizing of Geothermal Power Plant

Components

The paper presents a study of the influence of uncertainties in the thermophysical

properties of the working fluids on the preliminary design and sizing of the major

components of a power plant. The effect of these uncertainties is discussed first qualitatively to characterize the nature of the problems resulting from them, then

quantitatively to determine the relative magnitude of the differences in component

design and size that would result if a power plant is designed on the basis of dif- ferent sets of working fluid properties. Special emphasis is placed on isobutane

which appears to be attractivefor geothermal energy extraction.

ABSTRACT

The paper presents a study of the influence of uncertainties in the thermophysical properties of the working fluids on the preliminary design and sizing

of the major components of a power plant. The effect

of these uncertainties is discussed first qualitatively to characterize the nature of the problems resulting

from them, then quantitatively to determine the relative magnitude of the differences in component design

and size that would result if a power plant is designed

on the basis of different sets of working fluid properties. Special emphasis is placed on isobutane

which appears to be attractive for geothermal energy

extraction. A preliminary evaluation of four equations

of state for isobutane was conducted to determine the important sizing parameters of the primary heat ex- changer and the working fluid turbine for a super- critical Rankine cycle. It is shown that the presence

of a pinch point in the heat exchanger plays a major

role in magnifying the effect of the differences be- tween the equations. These differences appear to be significant enough to alter the conclusions of optimization studies of geothermal power plants of the binary- fluid type.

INTRODUCTION

In low temperature power cycles , such as those employed in geothermal power generation and waste

energy recovery systems, large quantities of heat must

be transferred first from the primary source of energy

to the working fluid, then from the working fluid to the cooling medium after the work-producing process. Energy conversion systems operating at low heat addition temperatures are, therefore, burdened by a large

capital investment associated with large, expensive

heat exchangers. The economic optimization of the design of these systems requires a careful balance between the thermodynamic advantage of minimizing the entropy production in the system and the initial cost saving resulting from a cheaper, less efficient system.

In order properly to address the question of sys- tem optimization, the designer must have access to re- liable sources of the thermophysical properties of the working fluids. These properties affect the design

on two levels. On the first level, the equilibrium

properties of the working fluids are needed to define

the initial and final conditions for the processes con- stituting the thermodynamic cycle. On the second level, both the equilibrium and transport properties are needed

for the detailed design of the system components, in- cluding fluid flow mechanics and heat and mass transfer.

In this paper we evaluate the effect of the working

fluids on the design of geothermal power plant main

components - the heat exchangers and the turbines. A

qualitative assessment of the potential effect of these uncertainties is given at first. An evaluation of the uncertainties in the prediction of the thermodynamic

properties of isobutane is used subsequently to exem- plify the magnitude of the resulting effects on the surface area of the primary heat exchanger and the characteristic dimensions of the turbine in a binaryfluid geothermal power plant.

Nature of the Problem

The production of work from low-temperature energy

sources poses difficulties that are not normally en- countered with high-temperature sources. The main

difficulty resides in our inability economically to manufacture efficient expanders that would utilize a

19
low-grade thermal energy source directly. Thus, practical energy conversion systems for low-grade energy

sources must comprise a process through which a vapor

working fluid is generated, then subsequently expanded

in a conventional turbine to produce useful work. Among the most attractive of these practical systems

is the so-called binary-fluid system shown schemati- cally in Fig. 1-A. The binary-fluid system is based

on the simple Rankine cycle whose temperature- enthalpy

representation is shown in Fig. 1-B. Systems of this kind have been proposed and/ or built for the utilization of geothermal energy, solar energy, waste energy, ocean thermal energy, etc., with a wide selection of

working fluids for each case.

FEEDPUMP

IN OUT

PRIMARY FLUID

Figure 1-A. A flow diagram of a binary-fluid power

p 1 ant

.

ENTHALPY

Figure 1-B. A temperature-enthalpy representation of

a supercritical binary- fluid cycle.

The selection of the optimum working fluid for

any given application is a fundamental task in the design of binary- fluid energy conversion systems. Of

the large number of candidate working fluids for a given application, many can be excluded on the basis of such factors as chemical stability in the desired temperature range, toxicity, explosiveness , etc. The remaining ones must be screened according both to thermodynamic and to economic considerations. For

each fluid, preliminary performance and design data

must be obtained over a range of cycle parameters to determine the optimum conditions. Considering the necessity of repeated access to the thermophysical

properties of the working fluids over the whole domain

of operating conditions, and the sheer magnitude of

the effort involved, the use of a computer becomes

indispensible. Even so, it is often the case that the developers of computer optimization codes would opt for inaccurate, but simple, representations of the thermophysical properties of the working fluids for

the sake of reducing the computation time. Such a compromise would be acceptable if the results of the optimization studies are quoted with their associated

uncertainty or if the optimum is insensitive to the errors introduced by the inaccurate representation of

the properties. Unfortunately, this is not always the

case.

In the primary heat exchanger of a binary system, for example, the temperature profile exhibits a pro- nounced pinch as illustrated in Fig. 2. Also depicted

in Fig. 2 are the temperature profiles as would be obtained from alternative representations of the ther- modynamic properties of the working fluid. It is not uncommon to design these heat exchangers with a pinch

point temperature difference of 5°C, particularly in

low temperature energy conversion systems where the available temperature difference between the source

and the sink is low. The impact of temperature dif- ferences of the type shown in Fig. 2 on the surface area requirements in the primary heat exchanger can be substantial as will be shown later. — ALTERNATIVE REPRESENTATIONS OF THE PROPERTIES OF THE SECONDARY FLUID

AMOUNT OF HEAT TRANSFERRED

Figure 2. Temperature distribution in the primary

heat exchanger.

The problems resulting from the uncertainties in the properties of the working fluids are further com- pounded by the fact that low- temperature power cycles often operate in, or close to the critical region.

Additional uncertainties are, therefore, introduced

because the simple correlations used for optimization

studies are invariably analytic in the critical region and thus fail fundamentally to describe the anomalous

critical behavior. The effect of this uncertainty may

20
be reduced somewhat if refined analytic equations,

such as that of Keenan, Keyes et al. for steam, are developed for the large number of the organic working

fluids advocated for low temperature power cycles

.

Thermophysical Properties for Design

The most common representation of the equilibrium

thermodynamic properties of a working fluid is a combi- nation of a PVT equation and the ideal-gas properties

of the fluid which, together, formulate the fundamental equation for the fluid. Among the most widely used

PVT equations are the Benedict-Webb-Rubin (BWR) equa- tion for hydrocarbons (1,2_,3) and the Martin-Hou (MH) equation for fluorocarbons (2>4_,5) , or variations on

these. Starling has correlated the properties of a large number of light petroleum fluids and a number of

fluorocarbons by means of a modified Benedict-WebbRubin equation (MBWR) (3,6) . Optimum parameters for

the Martin-Hou equation as applied to a number of geo- thermal binary cycle working fluids can be found in

Ref. (7) . Both equations, augmented by an appropriate

expression for the specific heat in the ideal-gas

limit, have been extensively used for geothermal

binary cycle optimization. It should be mentioned,

however, that in most cases, the equation parameters

were derived from a limited set of experimental data, the accuracy of many of which was not reliably esta- blished. Reliable data on the transport properties of many

of the working fluids are noticeably lacking. This situation is partially mitigated by the fact that transport properties affect the design indirectly

through averaged parameters such as the friction factor, the overall heat transfer coefficient, the drag

coefficient, etc. These parameters tend to depend only

weakly on the transport properties of the working fluid

in many practical situations. It has been argued,

therefore, that transport properties need not be known

to the same degree of accuracy as equilibrium properties for preliminary screening and design optimization

studies. Nonetheless, reliable data would be needed

for the final design of critical components.

Equilibrium Properties of Isobutane Isobutane has been identified as one of the pri- mary candidates to be used as the working fluid in geothermal binary power plants (.7,8,9) . In fact,

geothermal pilot and demonstration plants, using iso- butane as a working fluid, have been either designed

or built both in this country and abroad (10)

.

An extensive survey and compilation of the equilibrium and transport properties of isobutane was con- ducted by Kestin, et al ( 11) . Several formulations of

the PVT properties of isobutane were identified,

notably:

[1] A modified Benedict -Webb- Rub in (MBWR-1) equa- tion developed by Starling (3)

.

[2] A refinement of the above equation (MBWR-2)

developed later by Starling et al . (6J

.

[3] A differential-regional BWR equation (DRBWR)

developed by Eubank et al . (12)

.

[4] A revised Martin-Hou equation (RMH) developed

by Milora et al . (5). In each case, the PVT equation was supplemented by an expression for the ideal gas enthalpy or isobaric spe- cific heat to complete the fundamental formulation of

the equilibrium properties.

The four equations were subjected to a critical

intercomparison as well as to comparison with raw ex- perimental results to characterize the nature of the differences among the four equations and between each equation and the experimental data ( 13) .

The four equations provide smooth representations

of the properties over a wide range of conditions ex- tending from the ideal gas limit to several times the critical density. Equation [4], however, results in intersecting isotherms in the high density region at supercritical pressures. The use of equation [4] without modifications in this region is, therefore, not

recommended. Starling's two equations [1] and [2] represent thermodynamically consistent formulations of

the equilibrium properties of isobutane. Aside from the ideal gas properties, which were taken from API project 44 (14) , equations [1] and [2] do not require

any supplementary correlations. The vapor pressure is obtained by equating the fugacity of the vapor and

liquid phases and the latent heats are guaranteed to satisfy the Clausius-Clapeyron equation. In contrast,

formulations [3] and [4] are supplemented by correlations for the vapor-pressure and for the saturated

liquid density. Consequently, thermodynamic consistency is not built in these formulations. Reference (L3) contains an extensive comparison between each of the four formulations and raw experi- mental data. The results are summarized in Tables 1-4 for the following sets of experimental PVT data:

(i) Data of Sage and Lacey ( 15 ) in the temperature

range 21-121°C in both the vapor and liquid

regions

.

(ii) Data of Beattie et al . ( 16) for the supercritical temperature range 150-300°C.

(iii) Data of Beattie et al. (1J7) in the critical

region.

(iv) Data of Morris, Sage and Lacey ( 18) in the temperature range 38-238°C for pressures up

to 35 MPa in both the vapor and liquid regions. The deviations in the liquid region are large as a consequence of the steepness of the P-V isotherms in this region and do not necessarily indicate failure of

the equations in this region.

Table 1 Sage and Lacey Data ( 15)

[(P , -P )/P ] x 100% calc ex ex J Temp Subcritical

(°C) Eqn

.

Density

Supercritical

Density

21.11 [1] -0.,19% to +0.28% +4.5% max

[2] -0. 1% to +4.7% too large

[3] -1.,01% max too large

[4] -0., 4% max too large

71.11 [1] +2., 1% max -13% to +6%

[2] +2., 5% max +9% max

[3] +0. 25% max +36% to +6%

[4] + 1,. 3% max too large

121. 11 [1] +2,,4% max -13% to +29%

[2] +2..6% max -10% to +3%

[3] + 1., 3% max -2% to +3.5%

[4] + 1.,7% max -12.5% to 14%

21
Temp

(°C) 150

200

250

Table 2 Sage and Lacey Data ( 16)

[< P calcPex) /Pexl

X 100%

_ Subcritical

4 ' Density

[1] -0.14% to +0.24%

[2] -0.52% to +0.25%

[3] -0.56% to +0.02%

[4] -0.24% to +0.26%

[1] -0.1% to +2%

[2] -0.5% to +0.3%

[3] +0.25% max

[4] +1 . 3% max

[1] -0.3% to +2.4%

[2] -0.7% to +0.2%

[3] +0.3% max

[4] +1.8% max

Table 4 Morris, Sage and Lacey Data (18)

Supercritical

Density

-8.3% to +12.8%

-9.4% to +1.4%

+0.9% max

-1.8% to +2.5%

i

-0.3% to +6.9%

-5.7% to +1.6%

+1% max

-0.6% to +2.7%

+5.5% max

-2.2% to +0.8%

-0.3% to +1% +2.6% max

Temp

C°c)

37.8

71.1

104.4

Eqn.

[1]

[2]

[3]

[4]

[1]

[2]

[3]

[4]

[1]

[2]

[3]

[4]

£ (PcalcP ex) /PexJ * 100%

Subcritical

Density

(p < 220 kg/m3)

Supercritical

Density

(p > 220 kg/m3

) < 5% -20% (or more) -20% (or more)

excessive

M0-20%

5% max

+40% to -10% excessive

+25% to -15%

+5% to +10%

-10% to +4% excessive

137.8

Temp(K)

407.75

408.13

408.15

408.30

Table 3 Selected Data of Beattie et al. (around critical temp) ( 17) [(P , -P )/P ] LV x 100% calc ex' exJ

Eqn.

[1]

[2]

[3]

[4]

[1]

[2]

[3]

[4]

[1]

[2]

[3]

[4]

[1]

[2]

[3]

[4]

Subcritical

Density

-0.3% to -1% -1.5% to +0.2% +0.1% max

+0.1% max

-0.7% to -1% -0.5% to +1.7% +0.05% max

<0.05%

-1% max

-0.2% to +1.6%

+0.05% max

<0.05%

-0.4% to -0.95%

-1.6% max

-0.5% max

<0.05%

Supercritical

Density

-1% to +0.6%

-1.8% to -2.8%

-1% max

-0.1% to +0.1%

-0.3% to -1% -1.7% to -2.4% -0.45% max

<0.05%

-1% to +0.75%

-1.6% to -2.6%

-1% max

+0.15% max

-0.9% to +0.8%

-1.6% to -2.6%

-1% max

+0.15% max

171.1

204.4

237.8

[1]

[2]

[3]

[4]

[1]

[2]

[3]

[4]

[1]

[2]

[3]

[4]

[1]

[2]

[3]

[4]

+0.5% max

+0.7% max

-0.7% max

+0,4% max

-0.2% to +0.7%

-0.25% max

-0.4% to +0.1%

-0.1% to +0.5%

+0.5% max

-0.7% max

+0.4% max

+0.5% max

-0.5% to +1%

-1% max

-0.2% max

+1% max

+23% to -13%

+7% to -12% +5% max

+19% max

+10% to -11% +2% to -11%

+2% max

+3% max

+6% to -10% +0.7% to -13%

-4% max

+ 3% max

+5% to -5% +0.5% to -9% -0.7% max

+0.8 to -1.8%

A detailed analysis of the deviations and their

distribution ( 13) indicates that none of the four equations is decidedly superior to the others. One equation may be a better representation of the experi- mental data in one region but may be poorer than the other equations in other regions. The distributional

disparity of the deviations among the four equations

can produce significant differences when these equa- tions are used independently to design a given power

plant component or to optimize the design of a whole

system.

22
Effect on System Components

In order to demonstrate the practical importance

of the differences that exist among the four correlations, each correlation was used in a number of typical design calculations associated with a Rankine

cycle geothermal power plant.

Cycle efficiency . The four correlations were used to calculate the conditions at the four key

points in a supercritical Rankine cycle characterized

as follows:

• Turbine inlet temperature,

T

• Turbine inlet pressure,

• Condenser pressure, (T

2

)

175°C

7.5 MP a 0.5 MPa (38°C) The cycle thermodynamic efficiency was calculated

and is listed together with the other properties in Table 5. It can be seen that the cycle efficiency

computed from the four correlations are nearly the

same and that the differences in the boiler heat input

and in the turbine work output are small (about 2 percent). In other words, the differences among the four correlations do not manifest themselves as dif- ferences in the cycle efficiency.

Table 5 Comparison of Cycle Parameters

= 175 °C, P

1 = 7.5 MPa, P

2 = 0.5 MPa, (T2 ~38°C)

Eqn. J2 (°C) "1 (kJ/kg)

h 2 (kJ/kg)(hrh2 ) (kJ/kg)

[1] 49.8 428.5 335.9 92.6

[2] 48.6 425.8 334. 3 91.5

[3] 47.5 416.6 327.1 89.5

[4] 47.5 420.2 329.8 90.4

Eqn. (kJ/kg) h

4, (kJ/kg)

(h 1 -h4) (1^ (kJ/kg)-h

2 )/(h,-h4

) (%)

[1] 313.5 -3.9 432 21.4%

[2] 314.3 -1.8 428 21.4%

[3] 308.2 -5.4 422 21.2%

[4] 311.5 -1.8 422 21.4%

Primary heat exchanger . The four equations were used to determine the surface area of a counterflow primary heat exchanger (see Figs. 1, 2), subject to the following conditions:

• The hot fluid (geothermal water) is an imcom- pressible fluid with a constant specific heat

• No pressure loss in the heat exchanger passages.

• Constant local heat transfer coefficient.

The last assumption is a major simplification

since the local heat transfer coefficient in an actual

heat exchanger will tend to vary appreciably along the heat exchange surface due to changes in the local fluid

properties and due to the variation in the local foul- ing resistance. The heat exchanger was divided into one hundred

small sections and the surface area was determined by

a combination of numerical and graphical techniques

for the following specified conditions:

• Water inlet temperature, Twi 200°C

• Isobutane inlet temperature, Tj 35°C

• Water outlet temperature, Tw0 50°C

• Pinch temperature difference, AT 5 5 10°C

The results of these calculations are summarized

in Table 6. The last column of this table shows that for the same water mass flow, the four equations yield

heat exchanger areas that differ by as much as 10 percent for a specified pinch temperature difference of

10°C, and by as much as 18 percent for a pinch temperature difference of 5°C. Even for two equations as close as equations [1] and [2], the surface area differs by a significant 8 percent at the lower pinch

temperature difference. Typical temperature profiles

are shown graphically in Fig. 3 for equations [1], [3] and [4].

Table 6 Results of Calculations for a Water- Isobutane Counterflow Heat Exchanger

Ti = 35°C, TWQ = 50°C, Twi = 200°C

(a) Pinch-point temperature difference = 10°C

Equation

[1]

[2]

[3]

[4]

T0

(°C) 143

143

153 138

m/n^

1.43 1.43

1.22 1.72

m

2 /(kg/s)

331 339

351 318

(b) Pinch-point temperature difference = 5°C

Equation

[1]

[2]

[3]

[4]

To

(°C) 154 154

162 140

m/m

w

1.3

1.3 1.14 1.56

A/ m

2 /(kg/s)

500

539

540 458

Turbine . The specific available work (exergy)

at the turbine inlet (emerging from primary heat ex- changer) is given by

o , T (s -s ) r

v o t' (1)

in which h and s refer to the specific enthalpy and

entropy, respectively. The subscript r designates a reference dead state taken here as saturated liquid at 25°C. For a specified power output, W, the required

mass flow is given by

m = W/w° (2) The characteristic velocity in the turbine is proportional to the square root of w°, i.e.,

V*ct(w°) 1/2

(3)

while the characteristic turbine flow area is given by

A*am/p*V*. (4)

in which p* is a characteristic density taken here as the density at the turbine inlet. ^ The turbine

lit is more common to choose the turbine exit density

for this purpose.

23
characteristic dimension can thus be defined

A = (p*r

1/2 (wV 3/4

(5)

1.0 0.75 *0.50 0.25 0 FRACTION OF HEAT TRANSFERRED

Figure 3. Characteristics of primary heat exchanger.

Table 7 contains a comparison of the turbine characteristic dimension for the four correlations

when the specified pinch point temperature difference

is 10°C. It can be seen that the turbine characteristic dimension obtained on the basis of different equa- tions varies by as much as 10 percent. This is a direct consequence of the differences in the heat exchanger exit conditions (turbine inlet conditions) .

Table 7 Turbine Characteristic Dimension

Equation

[1]

[2]

[3]

[4]

Exergy at Turbine Inlet

(kj/kg)

9596

105

86

Ax 10'

2.90 2.89 2.98

2.70

Concluding remarks

It has been shown that alternative formulations of the equilibrium properties of a working fluid

may yield significantly different values of the key

design and sizing parameters for the major components

of a geothermal binary-fluid power plant. The origin of these differences resides in the sensitivity of

the size of the primary heat exchanger in these plants to the location of the pinch point and to the temperature differences in the vicinity of this

point. These effects are more pronounced for lower specified pinch temperature differences. It is thus conceivable that systems optimized on the basis of

one formulation could lead to optimum design and sizing parameters that differ from those obtained on

the basis of another formulation. It is emphasized

that these uncertainties strongly depend on the degree of success of the various correlations in representing experimental data and in incorporating the essential physical features of the fluid behavior over the domain of interest. An accurate representation in the critical domain, for instance, must account for

the singular nature of the critical point and for the anomalous behavior of the fluid there ( 19) . Users of computer design and optimization programs, therefore, must keep in mind that, with the limited accuracy of the experimental data for many of

the organic working fluids suggested for binary fluid

cycles, it would be unjustified to attach practical

significance to differences in cost of the order of

5 or 10 percent, unless, of course, it can be shown

that the design is relatively insensitive to the un- certainties in the thermophysical properties. Once a particular fluid has been identified as the most attractive working fluid for a given application, its properties must be accurately measured,

then carefully correlated to provide a standard for- mulation for subsequent detailed design and perfor- mance verification.

Acknowl edgments

The work described herein was carried out under

D0E/DGE Grant EY-76-S-02-4051 . A002 awarded to Brown University. Mr. B. Kumar performed most of the computations.

REFERENCES

1 Benedict, M. , Webb., G. B. and Rubin, L. C,

J. Chem. Phys. 8, 334 (1940).

2 Reid, R. C. , Prausnitz, J. M. and Sherwood,

T. K., "The Properties of Gases and Liquids" , 3rd Ed., McGraw Hill, New York (1977).

3 Starling, K. E., " Fluid Thermodynamic Properties of Light Petroleum Systems" , Gulf Pub. Co., Houston (1973) . 4 Martin, J. J., Ind. Eng. Chem. 59, 34 (1967).

5 Milora, S. L. and Combs, S. K. , "Thermodynamic

Representation of Ammonia and Isobutane" , Oak Ridge

National Laboratory Report 0RNL/TM-5847 (1977).

6 Kumar, K. H. , Gain, K. M. , Starling, K. E., Sliepcevitch, C. M. , Fish, L. W. , Aboul-Foutoh, K. H.

,

Lee, T. J., Milani, J. S. and Zemp, K. L. , " Development of Working Fluid Thermodynamic Properties for University of Oklahoma

Geothermal

Geothermal Cycles - Phase I Report ORO-5249-2 (1978).

7 Milora, S. L. and Tester, J. W Energy as a Source of Electric Power" , MIT Press, Cambridge, Massachusetts (1976)

.

8 Eskesen, J. H. , " Study of Practical Cycles for Geothermal Power Plants" , GE Report C00-2619-1, UC-66

(1976) . 9 Anderson, J. H., " The Vapor-Turbine Cycle for Geothermal Power Generation" , Article in Geothermal

Energy", P. Kruger and C. Otte, eds., Stanford Univer- sity Press (1973) .

2k
10 DiPippo, R. , " Geothermal Power Plants Around

the World" , Brown University Report COO-4051-42,

CATMEC/30 (1979).

11 Kestin, J., Khalifa, H. E. and Kumar, B.,

" Equilibrium and Transport Properties of Isobutane : A Survey of Available Data" , Brown University Report

COO-4051-35, CATMEC/27 (1978).

12 Das, T. R., Reed, C. 0. and Enbank, P. T.

,

J. Chem. Eng. Data 1_8, 253 (1973).

13 Kumar, B., " Critical Review of the Thermodynamic Properties of Isobutane" , Sc. M. Thesis,

Brown University (1979).

14 API Research Project No. 44, " Selected Values of Physical and Thermodynamic Properties of Hydro - carbons and Related Compounds" , Carnegie Press, Pittsburgh, Pennsylvania (1953)

.

15 Sage, B. H. and Lacey, W. N. , Ind. Eng. Chem.

30, 673 (1938) . 16 Beattie, J. A., Marple, S. J. and Edwards,

D. G. , J. Chem. Phys . 18_, 127 (1950).

17 Beattie, J. A., Edwards, D. G. and Marple,

S. J., J. Chem. Phys. 17, 576 (1949).

18 Morris, W. M. , Sage, B. H. and Lacey, W. N.

,

Amer. Inst. Mining Met. Eng. Tech. Publication No. 1128, 158 (1939).

19 Sengers, J. V. and Levelt Sengers, J. M. H.,

Ch. 4 in "Progress in Liquid Physics", C. A. Croxton,

ed., Wiley, New York (1978).

25

H.P. Stephens

S. Sinnock

Sandia Laboratories, Albuquerque, N.M.

Thermophysical Properties of

Rocks: A Perspective on Data

Needs, Sources and Accuracy

Recent emphasis on research in geologic isolation of nuclear wastes and geoenergy

resource development has created a renewed demandfor enginering thermophysical

property data of rocks and other geologic materials at elevated pressures and

temperatures. In contrast to fabricated engineering materials with specified

properties, rocks used in engineering design are complex, naturally occuring

materials having properties which must be characterized, rather than specified, for

engineering studies. Many difficulties in measuring, reporting, and using ther- mophysicalproperties ofrocks resultfrom: (a) rock inhomogeneity and anisotropy on both microscopic and macroscopic scales, (b) inclusion of pore fluids such as

water, and (c) measurement of laboratory properties under conditions quite dif- ferent from those of material in situ. Because measurements on in situ materials are

scarce, many analyses depend on extrapolated values of uncertain accuracy.

ABSTRACT

Recent emphasis on research in geologic isolation of nuclear wastes and geoenergy resource development has created a renewed demand for engineering

thermophysical property data of rocks and other geologic materials at elevated pressures and temperatures.

In contrast to fabricated engineering materials with

specified properties, rocks used in engineering de- sign are complex, naturally occurring materials having properties which must be characterized, rather

than specified, for engineering studies. Many difficulties in measuring, reporting, and using thermo- physical properties of rocks result from (a) rock in- homogeneity and anisotropy on both microscopic and macroscopic scales; (b) inclusion of pore fluids such

as water; and (c) measurement of laboratory properties

under conditions quite different from those of material

in situ. Because measurements on in situ materials

are scarce, many analyses depend on extrapolated

values of uncertain accuracy. A survey of thermophysical property data available for geologic thermal

transport studies indicates that caution must be taken

to effectively match data abstracted from the literature with project objectives.

INTRODUCTION

Recent emphasis on energy resource development

and understanding natural terrestrial thermal processes has stimulated a renewed demand for accurate thermophysical property data of rocks and other geo- logic materials at elevated temperatures and pressures. The purpose of this paper is to provide a current perspective on data needs , sources , and applications of several thermophysical properties of rocks which are

needed for engineering design. This perspective will

serve to stimulate discussion related to the theme of this session: "Thermophysical Property Information: What Difference Does it Make?" Both engineering and scientific endeavors have recently accelerated demand for thermophysical property

information. For example, systematic study of terrestrial heat flow began about 15 years ago, despite the historical occurrence of dramatic thermal events such

as colcanism. Serious analysis of the response of in situ geologic materials to man-induced thermal fields began even more recently. From an engineering standpoint, a knowledge of thermophysical properties of

rocks is necessary to design subsurface structures which will withstand the thermal environments to which

they will be subjected.

Deep mines have encountered high geothermal tem- peratures throughout history. However, improved mining

techniques have allowed ever deeper penetrations into the earth's interior with a concommitant increase in demand for thermophysical understanding. More recently, research towards developing energy sources other than

fossil fuel has created a need for engineering knowledge of thermophysical data for rocks at significantly

elevated temperatures and pressures as well as for heated rock systems subjected to non-steady state ther- mal flux. Although the experience of the authors is primarily related to those rock properties required for design of an effective heat-dissipating mined repository for heat-producing radioactive wastes, it should

be noted that other research activities , such as geo- thermal reservoir engineering for electrical generation

and thermal energy storage, require similar geothermal

understanding and contribute to the accelerating de- mand for lithologic thermophysical data. Any engineering design program consists of two

27
basic stages: first, defining the environment of the structure and second, determining the response of the materials to the environment. With respect to designs

which utilize thermal analysis, a knowledge of thermo- physical properties is needed for both stages. The exactness of the design and soundness of the resulting structure are related to data accuracy and the vali- dity of design assumptions. Although adequate data

are available for most manufactured structural mate-: rials, a general lack of thermophysical property in- formation for geologic engineering purposes can some- times hinder correct design practice. This lack of information is due to several factors, including tra- ditional reliance on simplicity of design and accep- tance of relatively high failure risks. However, in- creasingly complex design, dramatically rising con- struction costs, and social and economic demand for very low failure risks with respect to performance

and safety have placed added emphasis on the need for

accurate thermophysical property data of geologic

materials.

In the following sections of this paper, we will discuss the data sources for thermophysical

properties of rocks; the characteristics of rocks which affect the determination, accuracy, and reporting of property information; and the status and accuracy of specific thermophysical properties.

DATA SOURCES

The thermophysical properties chosen for dis- cussion in this paper are those that significantly

affect conductive heat transfer within the earth's

crust: thermal conductivity, thermal diffusivity,

specific heat and thermal expansion. Although a significant number of references on thermal radiative

properties exist, nearly all radiative properties

literature to date is associated with emissivity and reflectance of terrestrial surfaces for remote sensing

studies at ambient temperatures and is not considered

germane to the topic of this paper.

Two sources of published thermophysical property

data are available, namely, individual research papers

and data compilations. Because of the great amount of

time and effort required to find specific properties

of interest if they are scattered throughout a diffuse

literature, data compilations are a preferred source. However, there are currently no comprehensive, up-todate compilations of thermophysical property data

available for geologic materials. The last published

compilation devoted solely to properties of rocks (1) is now over 13 years old and by today's accelerated

demand is woefully out of date. A more recent monograph on geothermics (2) contains several tables of

thermophysical properties for rocks, but excludes thermal expansion. The most comprehensive and up-to-date

compilation of thermophysical property data for materials, the TPRC series (3), has few entries for rocks, and most of these are conductivity data reported be- fore 1963. Figure 1 shows a rapid increase in thermophysical property information after 1960, with over half

of the total references published between 1965 and

19 75. This growth curve emphasizes the need for a current compilation that incorporates post-1965 data. Hence, the geothermal engineer must currently rely on individually published papers as his primary source of

up-to-date information. Though the arduous task of searching for data is facilitated by a number of com- puterized bibliographic search and abstract services,

there, nonetheless, remains an urgent need for readily

available, up-to-date compilations.

°= 200

1920 1930 1910 1950

DATE REPORTED

I960 1970 1980

Figure 1. Time-growth curve for thermophysical pro- perty data. (Data from a computerized bibliographical

search by the Center for Information and Numerical

Data Analysis and Synthesis (CINDAS) , Purdue Industrial Research Park, Lafayette, Indiana)

.

In order to illustrate a cursory perspective of

the status of thermophysical property information for

rocks, properties reported in the references used to construct Figure 1 were grouped in Figure 2 according

to properties referenced, major rock category for which

the properties were determined, and possible technological category of usage for the data. Several gen- eral sets of observations emerge from these histograms.

First, thermal conductivity and diffusivity

data comprise half of all thermophysical property in- formation available, while little information (13% of

the total) is available for thermal expansion. About one-quarter of the references concern radiative mea- surements, which are of limited use for thermal analyses of subsurface conditions at elevated temperatures. These radiative properties, as noted above, are primarily associated with remote sensing applications.

The small percentage of data on the specific heat of

rocks reflects a dependence on calculations from data

on individual minerals, rather than laboratory measurements on the mineralogical assemblages of real rocks. Second, more thermophysical property studies

have been made on igneous and sedimentary rocks, in- cluding coal, than on metamorphic. It is difficult to speculate about the reasons for this sampling distribution, except to note that metamorphic rocks account

100-

60-g" t- 3" S

THERMOPHYSICAL

PROPERTY

ROCK CATEGORY

USAGE

Figure 2. Histograms of thermophysical property data.

28
for only about 5% of the continental surface areas, whereas sedimentary rocks account for about 75%, and igneous rocks about 20%. Third, it appears that there are more property determinations on rock types for structural use

than those for energy and nuclear waste management

use. However, the need for thermophysical property

data for energy and nuclear waste technology is growing, and proportionally more data associated with

these fields are expected to become available in the

future

.

PHYSICAL CHARACTERISTICS OF ROCKS

In contrast to manufactured engineering materials with properties which can be specified, rocks

are complex, naturally occurring materials having

properties which must be characterized, rather than

specified. A problem of utilizing published thermo- physical property data of rocks in engineering design

arises from the classification and characterization

of rocks for which the properties are reported. From

an engineer's perspective, a rock type is a set of lithospheric materials that behave similarly when

subjected to the same or similar environments. However, a geologist considers a rock type to be a visu- ally recognizable and classifiable set of lithospheric

materials which may have widely differing material

properties. The two objectives for classification

do not necessarily coincide. The geologist has cre- ated classes of rocks (igneous, sedimentary and meta- morphic) based on what he can infer or observe, such

as origin and texture, and the class names have been accepted throughout the technical community as a communication tool. Because thermophysical properties

depend on physical characteristics which usually can- not be quantified by visual inspection in the field or by microscopic observation, the geologic classifi- cation is of limited use for defining thermophysical

properties. The fact that rocks are complex materials

makes the complete characterization of their physical

state difficult, time consuming, and expensive. This

has led many investigators to rely only on the simpler method of describing the materials on which thermo- physical property measurements were made; that is, the geologic formation name and the location from which the rock was taken. Thus, tabulations of ther- mophysical property data are commonly grouped by geologic rock classification which results in wide ranges of properties for each rock type. What is needed are tabulations with respect to physical characteristics

of the rocks which affect thermophysical properties.

The physical factors which affect the thermo- physical properties of rocks can be broadly grouped

into two categories: composition and structure. Because rocks are complex aggregates of minerals and other substances, composition and structure mast be considered in terms of heterogeneity, fluid inclusions, voids and environmental conditions such as temperature and pressure. Additionally, because

engineering analyses may be applied on scales ranging

from millimeters to kilometers, all compositional and

structural effects must be considered in terms of the scale of interest. If the units are very small (mil- limeters to centimeters) variation among the mineralogical constituents of a rock are the element of heterogeneity of concern. At successively larger

scales, bedding, foliation, microfractures, porosity,

vugs, joints, compositional and textural gradients,

and finally structural discontinuities dominate the heterogeneity of rock bodies (Figure 3)

.

Figure 3. An illustration of the effect of scale on various chemical and physical characteristics of rocks. Lower left : Mineral lattice anisotropy. Upper left : Microsection - mineral phases, cleavage, microfractures,

and fluid inclusions. Lower right : Hand specimen - bedding, foliation, porosity, voids, vugs and joints.

Upper right : Block diagram - facies changes, veins,

fractures, faults, folds, caverns, and watertable.

For many users the assignment of discrete thermo- physical properties to geometrically discrete units of

rock is required. Scale must again be considered be- cause anisotropy as well as heterogeneity of thermo- physical properties is associated with the structure

and composition of rock bodies (Figure 3) . On the microscopic scale, anisotropy may be due to differences

in orientation of mineral lattice, while on macroscopic

scales compositional variations due to bedding and foliation planes may reasonably be expected to impart

a degree of anisotropy to the properties. Structurally, fracture planes may concentrate along certain directions lending a structural element to anisotropy.

Other significant factors which affect rock pro- perties are fluid content and environmental conditions,

i.e., pressure and temperature. The total fluid content, whether hydrocarbon or water, is a function of

porosity and may affect thermophysical properties to

a degree which can be dominant. The dependence of in situ thermophysical properties upon both temperature

and pressure may also be an important consideration

since both increase with depth in the earth's crust.

THERMOPHYSICAL PROPERTIES OF ROCKS: STATUS AND ACCURACY

Before presenting a brief discussion of the sta- tus and accuracy of specific heat, thermal conductivity

and expansion data for rocks, additional caution con- cerning the use of published data for modeling thermal processes in actual lithologic units is needed. Since

in situ field measurements are expensive and difficult,

most thermophysical properties of rocks are determined

by laboratory measurements. The condition of labora- tory samples and the environment under which the mea- surements are made may vary considerably from the in situ rock body from which the sample was taken. Additionally, laboratory determinations are subject to sampling errors because of the heterogeneity of rock bodies and the size constraints placed on the specimen.

Thus, laboratory measurements may not accurately re- present properties of rocks in situ.

29
The most significant advance in thermophysical

property measurement techniques over the past several decades has been in measurement speed, not accuracy.

The time required for laboratory measurement of many properties has been reduced from hours to minutes as

a result of advances in instrumentation and highspeed data acquisition techniques. However, the accuracy of current measurement capabilities has re- mained about the same. This is undoubtedly due to the fact that the range in reported values for a single rock is dominated more by sample- to-sample

variation than instrument error. Another factor

which may contribute to experimental inaccuracies is a lack of appropriate standard reference materials

for instrumental calibration. Many calibration measurements rely on well-characterized materials

such as alumina and quartz which have properties

that only approximate those of the rocks to be measured. Because of the variability of even "homogeneous", intact rocks, the development of an accepted

"rock" standard material is not likely.

Specific Heat Even though there are relatively few data on the specific heat of rocks, reasonably accurate values may be obtained from data published for minerals for

several reasons. First, there is little variation

in the specific heat for different rock types at con- stant temperature. At room temperature, for example,

the specific heat of almost all types of dry rock is 0.20 ±0.03 cal/g K.l Second, the variation with tem- perature of the specific heat of minerals is well characterized, and the variation with respect to li- thospheric pressures of engineering concern is insig- nificant. Third, the specific heat of rock at fixed

temperatures depends only on composition. Because

there are tabulations (3-2.) °f tne specific heat of

most minerals and oxides as a function of temperature,

the specific heat of rocks may be calculated, if the composition is known, by summing the contribution of

each constituent phase at the desired temperature:

I x.C.

i Pi (1)

where x^ = the weight fraction and Cp. = the specific

heat of the i tn constituent. 1 Specific heat measurements on rock samples may

be made by drop calorimetry, adiabatic calorimetry,

and several dynamic comparative techniques such as differential scanning calorimetry. Depending on the type of apparatus and temperature range, the instru- mental accuracy of these techniques ranges from a fraction of a percent to several percent. Most

routine determinations for rocks have an accuracy of

2 to 10 percent. Because the specific heat of most rock-forming minerals is known to comparable or better accuracy (4) , the heat capacities of rocks

can be calculated, according to equation (1) to an accuracy of better than 10%. Table 1 illustrates

the above points by comparing experimental values

(8,9) for the specific heat of four rocks with the values calculated by equation (1) . The calculated

values are close to or within the range of the re- ported (8_,9) experimental values.

In the use of mineralogical data for calculating the specific heat of rocks, several other factors

such as water content, phase changes and chemical decomposition reactions must be considered. Water

can contribute significantly to the specific heat of

rock, and its heat of vaporization can give rise to a large thermal effect. Temperature related phase

changes are common for many minerals and care must

be taken to use the appropriate specific heat. One

must also be careful not to extrapolate specific heat equations for minerals beyond the temperature of

chemical decomposition.

Thermal Conductivity and Diffusivity

Unlike specific heat which depends only on com- position, thermal conductivity and its related quantity, thermal diffusivity, depend on both the compo- sition and structural condition of the rock. The thermal conductivity k is derived from the equation

for the heat flux q* which for the one-dimensional case

is given by dT

dx (2) where dT/dx is the temperature gradient. The thermal diffusivity a, which determines the rate of heat pro- pagation in transient thermal processes, is defined

in terms of the conductivity, specific heat C and density p: p

pCT (3)

Both k and a can be determined experimentally.

As pointed out above, about half the literature

on thermophysical properties for rocks concerns ther- mal conductivity and diffusivity. It is beyond the scope of this paper to review the extent of this literature in detail. However, it is worthwhile to note that recent investigations are devoted to un- raveling the complexities of the effects of rock com- position and structural condition upon thermal con- ductivity. Among the characteristics and parameters

studied are cracks and porosity (10- 14) , chemical and mineral composition (15-17) , moisture and fluid con- tent (18-20) , anisotropy (21-22) , and temperature and pressure (9,23-27) . Until this decade, most conductivity data were reported by rock type. This led to wide ranges in values for each category reported (Figure 4) . Only

recently have investigators started correlating physical and chemical characteristics of rocks with con- ductivity (17,28,29).

THERMAL CONDUCTIVITY

1 1.0 cal/g K= 4.184 kj/kg K in SI units. Figure 4. The range in thermal conductivity date re- ported for various rock types

.

30
TABLE 1

Comparison of Experimental and Calculated

Specific Heat for Several Rocks

Rock Type Source

1 C L 1 I j H 1 L Mi nPT3 1

An a 1 vq i <^ Vol . % Temp (K) Specific Heat

Exp (Ref 8) (cal Exp

g K ) (Ref 9) Cal c

Sioux Quartzite Jasper, MN Quartz 99+ 300 *r o 1 74 0.178

a 380 0.. 219 0,, 201 0.209

500 o 2 31 0. 237

800 0 303 ±

T 0 . 267

nui b luii I'ldX u i

c

M1U AV J. lie, 99 300 t 0 ,198 0. 197^ TN lvltlJ£ll.C l. J. LC 380 r\u

.

u

.

, Z £. U 0. 227

S purite

< 1 500 n

U , 246 0.251

800 u 292 T 0.282

D/-> Va r -i 1 1 o HiiotI- KUtM/lllC l^Udl 7 L. L 1\U LK V111C, MlrllLiULlliltr 1 -1 T"l d 34 373 0..222 f 0. 210 C

\Sc\r\ 7 C\T\ n + O MN 29 800 0..278 t 0 .271 Quart z Biotite 6 Hornblend < 1 S apatite

Dresser Basalt Dresser, Plagioclase 50 300 t 0..186 0. 176

d WI Pyroxene 45 380 0.,231 0 ,209 0.205 Magnetite 5 500 0.,246 0,.234 0.230

800 0 ,283 t 0.261

f

- beyond experimental range or not reported, a - calculation based on quartz, b - calculation based on

calcite. c - calculation based on maximum microcline, albite, quartz, and phlogopite. d - calculation based

on anorthite, diopside, and magnetite. Data for calculations from reference 4.

Brief descriptions of current laboratory tech- niques for thermal conductivity and diffusivity

measurements are found in several recent publications

(2_,2£, 30) . Although the inaccuracy of most instru- ments is within several percent, un characterized sam- ple conditions may cause measurement imprecisions of

10 to 20% in experiments which are otherwise care- fully controlled. Under some circumstances the ex- perimental error may be much greater. For example,

it has recently been reported (20, 31) that errors up

to 100% may result when the conductivity of porous

rocks saturated with low conductivity fluids is measured. Metamorphic rocks have been found to exhibit

conductivity anisotropics of 20 to 50% ( 22) . Additionally, the conductivity of low porosity, dry rock measured in the laboratory can be a factor of two

( 18) lower than the conductivity in situ, where the

rock may be saturated with water and lithostatic pressure can close cracks. Thus, before thermal con- ductivity data are used, their source must be care- fully evaluated to ensure that the accuracy matches

the required need.

Thermal Expansion

The thermal expansion of rocks, like thermal conductivity, depends on both rock composition and structural condition. The term "thermal expansion"

may refer to either the coefficient of linear expansion or volumetric expansion. The coefficient of

linear expansion e represents the change in length AL of a unit length L resulting from a temperature

change AT of one degree:

given by

= 3e (5)

L AT

(4)

For materials which have isotropic expansion charac- teristics, the volumetric expansion coefficient 3 is

However, most rocks expand anisotropically and therefore 3 must be derived from their volumetric dilation

or from measurement of e in several directions.

As shown in Figure 2, data for thermal expansion of rocks are sparse, and only within the last several years have studies been initiated to deter- mine the influence of the composition and structural condition on expansion. Several investigations have

shown that thermal expansion of rock at ambient pressure depends on the constituent minerals (32) , poro- sity ( 33) , the presence and development of micro- cracks within the rock (33-35) , and dehydration of

glasses and minerals (33). For an unconfined sample, the presence of microcracks leads to a smaller value of the thermal expansion coefficient than that pre- dicted from the constituent minerals. However, de- velopment of microcracks in a sample during measurement significantly increases the expansion coefficient. Dehydration can be responsible for a net con- traction at temperatures where the dehydration occurs. Because extent of cracking and dehydration depends on heating rate, laboratory determinations of thermal expansion at different heating rates may show wide

variations for the same rock sample. Hysteresis may

also be evident when multiple measurements are made during heating and cooling cycles. As an example of errors which may be encountered, one investigator

( 33) reports 10-15% variations for laboratory expan- sion measurements on different samples of the same rock specimen. The effect of lithostatic pressure on the thermal expansion of rocks is largely unevaluated. It has been calculated from compressibility data that a lithostatic load of 100 MPa reduces the thermal

31
expansion coefficient of porous rocks as much as 25%

(26) . Determinations (36) at pressures up to 400 MPa

indicate that above a rock dependent critical pressure

between 50 and 200 MPa, thermal expansion approaches

the value calculated for the mineral aggragates. Be- cause the lower range of these critical pressures is close to those encountered in environments for deep

geologic isolation of nuclear waste, it is important

to quantify this effect.

ACKNOWLEDGMENT

Sandia Laboratories is a U. S. Department of

Energy facility. This work was supported by the Department of Energy under contract DE-AC04-76DP00789.

REFERENCES

1 S. P. Clark, Jr. , ed, , Handbook of Geophysical

Constants, Memoir 97, Geological Society of America,

Inc. (1966).

2 0. Kappelmeyer and R. Haenel, Geothermics

with Special Reference to Application, Geopublication

Associates, Geoexploration Monographs, Gebruden Borntraeger, Berlin (1974).

3 Thermophysical Properties of Matter, the

TPRC Series. Y. S. Touloukian, Series Ed., C. Y. Ho

Series Technical Editor. Volume 2, Thermal ConductivityNonmetallic Solids (1971); Volume 5, Specific Heat- Nonmetallic Solids (1970); Volume 8, Thermal Radiative

Properties-Nonmetallic Solids (1972); Volume 10, Thermal Diffusivity (1973); Volume 13, Thermal Expansion

(1977).

4 H. C. Helgeson, J. M. Delany, H. W. Nesbitt

and D. K. Bird, "Summary and Critique of the Thermo- dynamic Properties of Rock-Forming Minerals", Amer.

J. Sci. 278-A (1978) . 5 R. A. Robie, B. S. Hemingway and J. R. Fisher,

"Thermodynamic Properties of Minerals and Related

Substances at 298.15 K and 1 Bar (10 5 Pascals) Pressure and at Higher Temperatures", Geol. Surv. Bull. 1452 (1978).

6 D. R. Stall and H. Prophet, "JANAF Thermochemical Tables", NSRDS-NBS 37 (June 1971).

7 K. K. Kelley, "Contributions to the Data on Theoretical Metallurgy XII, High-Temperature Heat

Content, Heat Capacity, and Entropy Data for the Ele- ments and Inorganic Compounds", Bureau of Mines

Bulletin 584 (1960)

.

8 D. R. Lindroth and W. E. Krawza, "Heat Content and Specific Heat of Six Rock Types at Temperatures to 1,000°C", Bureau of Mines BMRI 7503 (1971).

9 E. J. Hanley, D. P. Dewitt and R. E. Taylor,

"The Thermal Transport Properties at Normal and Ele- vated Temperature of Eight Representative Rocks",

Proc. 7th Symp. on Thermophysical Properties, May

10-12, 1977, Gaithersburg, MD.

10 W. Woodside and J. H. Messmer, "Thermal Conductivity of Porous Media", 2, Consolidated Rocks,

J. Appl. Phys. 32, 1699 (1961).

11 J. H. Sass, R. J. Munroe and A. H. Lachenbruch, "Measurements of Geothermal Flux through Poorly

Consolidated Sediments", Earth and Plan. Sci. Letters

4, 293 (1968) . 12 W. H. Sommerton, "Some Thermal Characteristics of Porous Rocks at Elevated Temperatures", Soc

.

of Pet. Engrs. (May 1960).

13 A. Sugawara and Y. Yoshizawa, "An Investigation on the Thermal Conductivity of Porous Materials

and Its Application to Porous Rock", Austral. J. Phys.

14, 469 (1960)

.

14 W. H. Somerton and G. D. Boozer, "Thermal Characteristics of Porous Rocks at Elevated Temperatures", J. Petrol. Tech. 1_2, 77 (1960).

15 J. H. Sass, "Thermal Conductivity of Fifteen Feldspar Specimens", J. Geophys. Res. 70, 4064 (1965).

16 K. Horai, "Thermal Conductivity of Rock- Forming Minerals", J. Geophys. Res. 76_, 1278 (1971).

17 K. Horai and S. Baldridge, "Thermal Conduc- tivity of Nineteen Igneous Rocks, II. Estimation of

the Thermal Conductivity of Rock from the Mineral and Chemical Compositions", Phys. Earth Planet. Interiors

5, 157 (1972).

18 J. B. Walsh and E. R. Decker, "Effect of

Pressure and Saturating Fluid on the Thermal Con- ductivity of Rock", J. Geophys. Res. 2i» 3053 (1966).

19 M. Prats and S. M. O'Brien, "The Thermal Conductivity and Diffusivity of Green River Oil Shales", J. Petrol. Tech. 27, 97 (1975).

20 A. E. Beck, " A Potential Systematic Error

When Measuring the Thermal Conductivity of Porous

Rocks Saturated with a Low-Conductivity Fluid",

Tectonophysics 41_, 9 (1977)

.

21 P. Majal and I. Fatt, "Thermal Anisotropy

in Rocks", Nature 212 , 1418 (1966).

22 M. Chessman, G. Simmons and. W. H. Diment,

"Anisotropy of Thermal Conductivity in Metamorphic

Rocks", (abstr.), EOS (Amer. Geophys. Union Trans.)

55_, 422 (1974) . 23 J. Kanomori, N. Fuji and H. Mizatami, "Thermal Diffusivity of Rock-Forming Minerals from 300 to 1100 K", J. Geophys. Res. 73, 595 (1968).

24 V. I. Moiseenko, "Thermal Conductivity of

Rocks at High Temperatures", Friebert. Forschungsh.

238C , 89 (1968) . 25 G. I. Petrunin, R. P. Yurchak and G. F. Thach, "Thermal Conductivity of Basalts at 300-1200 K", Bull. Acad. Sci. .USSR, Earth Phys. 2, 126 (1971) Engl. Trans.

26 J. N. Sweet, "Pressure Effects on Thermal Conductivity and Expansion of Geologic Materials",

Sandia Laboratories Report, SAND 78-1991 (1979).

27 E. J. Hanley, D. P. Dewitt and R. F. Roy, "The Thermal Diffusivity of Eight Well-Characterized

Rocks for the Temperature Range 300-1000 K", Engr.

Geol. 2i, 31 (1978).

28 P. B. Corson, "Correlation Functions for Predicting Properties of Heteroheneous Materials. IV. Effective Thermal Conductivity of Two-Phase Solids",

J. Appl. Phys. 45, 3180 (1974).

29 M. S. Reddy, "Estimating the Thermal Conduc- tivity of Rocks -- An Analytic Approach", Proceedings

of the 7th Symposium on Thermophysical Properties,

May 10-12, 1977, Gaithersburg, MD. 30 A. P. Dmitriyev, L. S. Kuzyayev, Yu. I. Protasov and V. S. Yanshchikov" , NASA Translation, NASA TTF-684 (1969)

.

31 A. E. Beck, "An Improved Method of Computing

the Thermal Conductivity of Fluid-Filled Sedimentary

Rocks", Geophys. 41_, 133 (1976).

32 J. B. Walsh, "Theoretical Bounds for Thermal Expansion, Specific Heat, and Strain Due to Internal Stress", J. Geophys. Res. 78 7637 (1973).

33 A. R. Lappin, "Preliminary Thermal Expansion Screening Data for Tuffs", Sandia Laboratories

Report SAND 78-1147, Albuquerque, NM (1979).

34 D. Richter and G. Simmons, "Thermal Expansion Behavior of Igneous Rocks", Int. J. Rock Mech.

Min. Sci. Geomech. Abstr. 21, 403 (1974).

35 H. W. Cooper and G. Simmons, "The Effect of

Cracks on the Thermal Expansion of Rocks", Earth and

Planet. Sci. Lett. 36 404 (1977).

36 T. F. Wong and W. F. Brace, "Measurement of

Thermal Expansion of Rocks at High Pressure", Abstr.,

EOS (Am. Geophys. Union Trans.) 58, 1236 (1977).

32
R. C. Hendricks

NASA Lewis Research Center, Cleveland, Ohio

Thermophysical Property Data:

Who Needs Them?

Specific examples are cited herein to illustrate the universal needs and demands for

thermophysical property data. Applications of the principle of similarity in fluid

mechanics and heat transfer and extensions of the principle to fluid mixtures are

discussed. It becomes quite clear that no matter how eloquent theories or ex- periments in fluid mechanics or heat transfer are, the results of their application can

be no more accurate than the thermophysical properties required to transform these

theories into practice, or in the case of an experiment, to reduce the data. Present- day projects take place on such a scale that the needfor international standards and

mutual cooperation is evident.

ABSTRACT

Specific examples are cited herein to illustrate

the universal needs and demands for thermophysical

property data. Applications of the principle of

similarity in fluid mechanics and heat transfer and extensions of the principle to fluid mixtures are discussed. It becomes quite clear that no matter

how eloquent theories or experiments in fluid mechanics or heat transfer are, the results of their application can be no more accurate than the thermophysical

properties required to transform these theories into practice, or in the case of an experiment, to reduce

the data. Present day projects take place on such a scale that the need for international standards and

mutual cooperation is evident.

NOMENCLATURE

Roman

D diffusion coefficient

FA scale function for thermal conductivity

?

scale function for viscosity

scale function of fluid a relative a reference fluid

G Gibbs free energy

GR reduced mass flow rate, Gr=pu/G*

G* mass flow normalizing parameter,

G* = /P

CP C/Z

C h scale function of fluid a relative a reference fluid

m molecular weight

P pressure

PR= P/P

C reduced pressure

R gas constant

T temperature

Tr=T/Tc

= reduced temperature

u = velocity

v = specific volume

x = mole fraction

Z = PV/RT = compressibility factor

Greek

n = viscosity

6 = shape factor

A = thermal conductivity

u = symmetric function

v = asymmetric function

Sag = binary interaction parameter

p = density

(f> = elementary asymmetric function

$ = shape factor

't'ag = binary interaction parameter

Subscripts

c = critical

m = mixture

o' = reference fluid

C* = computed fluid

a,g = binary interaction aa.gg = pure component interaction

INTRODUCTION

Who needs thermophysical property data? Ask any company manager with a deadline to meet and no way to proceed until thermophysical properties data become

available. When this happens, management will permit

its engineers to go to extremes to acquire the needed

information quickly. The number of times this occurs makes it clear that data, or methods for their prediction, are needed on the shelf in anticipation of need.

33
Furthermore, present day applications take place on such a scale with materials and energy so costly that

it is no longer acceptable to simply use "just any old properties" to describe a fluid, but rather more

faithful reproduction of the fluid properties at the desired conditions is now required. The need for accurate, consistent, universally

acceptable thermophysical property data and representative computer programs are requirements of industry,

government and universities alike throughout the world

in advance of specific applications.

In a treatise on thermodynamics, Zeleznik (1) wrote that thermodynamics perhaps more than any other

physical theory pervades the fabric of physical science; as a corollary, I would suggest that thermo- physical properties which heuristically relate the physical nature of matter, pervade our daily lives. Applied and basic disciplines alike in such areas as engineering, medicine, physics, chemistry, biology,

to cite only a few, rely heavily on adequate thermo- physical property bases. Yet thermophysical property

data usually arouse little interest or concern on the part of the engineers and management until such in- formation is needed and found to be unavailable; an even more detrimental situation arises when manage- ment thinks that the data are available, but the information - which has not been critically evaluated

is wrong. Somehow it is always assumed that such properties either will be available or predictable

when needed. Due to this prevailing philosophy many of the advances in thermophysical property measurements, techniques of representation and computer

programs for rapid production of this information

are developed in response to an urgent request. The aerospace industry found a need for new property data

sets with nearly every major project and more recently

a similar need has arisen in the natural gas industry.

On some rare occasions, and through the diligent

efforts of a very few, new property sets have been

available when required. Organizations as NBS, CODATA, NASA, IUPAC at Imperial College, TPRC at Purdue, AGA in conjunction with the AIChE, the ASME

and the Electric Power Utility Industry have sponsored

such programs

.

How can engineers and scientists benefit from systematic studies of accurate thermophysical pro- perty information? Subsequent sections will discuss

some project needs related to the development of data

bases using para- hydrogen as an example of a well defined program and data set, and RP1 (JP etc.) as examples of sets where more efforts are required.

Furthermore, we shall cite a few property related

projects in the area of fluid mechanics using pro- perty similarity principles and in the area of metallic, ceramic and plastic materials. Finally, we shall look into the Van der Waals' one- fluid model

to relate thermodynamic and transport properties of

some one-component and multi component fluids and indicate directions toward generalization of the application of corresponding states.

SOME DEVELOPMENTS IN THERMOPHYSICAL PROPERTIES INSTI- GATED BY THE AEROSPACE INDUSTRY

The following section will illustrate some projects and related development of one of the world's

finest data bases using para-hydrogen as a specific

example, and indicate some current activities in- cluding multicomponent mixtures and RP (kerosene) .

Some Developments Related to Para-Hydrogen

Even before this country had a space program, mission analysis codes clearly demonstrated the

advantages of propellants with high specific impulse. From the combustion analysis program of Huff, Gordon

and Morrell (2) H2 -02 and H2 -F 2 were identified as two of the most promising propel lant combinations. Early

literature Searches for properties of H 2 (3) , 02 (4) and F 2 (5) revealed a dearth of information and the" need for thermophysical property data for these fluids became urgent.

With hydrogen designated as the engine coolant

and NACA transformed into NASA, a substantial effort

was launched in collaboration with the National Bureau of Standards at Boulder to determine the properties of

hydrogen, oxygen and fluorine. We will look specifically at the development of the hydrogen data base where the classic work of Woolley, Scott and Brick- wedde (6) was our initial guide but whose limitations

had become transparent.

One of the early problems we faced was the long term storage of liquified hydrogen. Over 75% of

the liquified hydrogen just vanished after a few days,

clearly an intolerable situation for any space mission. While the tank insulations were poor, they were not

that poor. We discovered that at ambient temperatures

hydrogen wasn't really hydrogen at all, but a mixture of 75% ortho and 25% para hydrogen. Further, the equilibrium composition varied with temperature, with

substantial property changes, notably in enthalpy,

specific heat and thermal conductivity; it turned out that at 20K hydrogen consists of 99% parahydrogen as illustrated in fig. 1 and 2. Thus the ortho-hydrogen would simply boil off leaving the smaller quantity of

para- hydrogen . Ortho-para conversion units were re- searched and installed (7) and long term storage of

hydrogen became a reality, but only after the addi- tional development over a period of years of the thermophysical properties of insulations and super- insulations (see fig. 3)

.

100 200 300K Temperature K

Figure I. - Composition dependence of hydrogen

Concurrent with the thermophysical properties

work at NBS-Boulder, heat transfer and fluid dynamics

studies were undertaken, with results that appeared

completely contradictory to known theories and exper- mental results. For example, in fully developed tur- bulent flows, the wall temperature increases in a monotone manner over the length of the heated tube. However, with hydrogen, the profile increased to a maximum followed by a monotone rise. (9_, 1_0, 11) (see

fig. 4) . As a consequence, the need for thermophysical property data of para-hydrogen and for understanding catalytic conversion became even more acute.

3h
10 20 40 60 100 200 300K

Temperature, K

Figure 2a. - Enthalpy of normal and para hyrogen atone atmosphere.

2.0

1.8

1.6

1.4

1.2

1.0

0.8

0.6

0.4

0.2

normal

100 200 Temperature K

300K

Figure 2b. - Thermal Conductivity of Gaseous Hydrogen

at One Atmosphere.

Goodwin's data compilation ( 12) and Goodwin's simplified equation of state ( 13) along with a computer pro- gram developed by Harry ( 14) and generalized property

charts of Thodos et al . (15,16) proved adequate to resolve a few of the early heat transfer and fluid

dynamics problems. But, as in any field where accurate, consistent property data are lacking, we found different researchers, manufacturers and people from the nuclear industry in disagreement as to which computer

codes and properties to use. On many occasions we would sit around a table, peek at our computer output

and ask, "What number did you get?" as if there ex- isted some magical set of proprietary properties to explain the differences in the calculated results for

that particular application. Recognizing this problem, NASA launched an early effort toward unification. For example, early computer codes by Roder (1_7) and Farmer

( 18) though fast, lacked uniformity, and suffered from

the lack of adequate quantitative data.

rate, input, P, perature,

w Q, psia T

irv Btu/sec °R — — Supercritical 706 0.166 3316 720 48.2 —

Subcritical 542 .155 22.7 80 40.8 — Supercritical 700 .168 35.1 280 46.7 —

Subcritical 539 .112 13.6 140 41.5 — Gas 315 .029 13.8 206 115 —

Gas 1059 .03 13.7 620 525

Fluid state Run Mass (low Heat Pressure, Inlet ternFigure 3. High efficiency insulation (MLI),

12 16 Length, in.

Figure 4. - Surface temperature distribution with axial position for nearcritical and gaseous hydrogen. Tube inside diameter, 0. 335 inch.

With the classical data of Goodwin (1_9) and the extension of the BWR (Benedict-Webb-Rubin) equation of state proposed by Strobridge and Stewart (20)

,

Roder and Goodwin ( 21 ) produced the first accurate representation of the PVT surface for para-hydrogen

at temperatures up to 300K. With this equation of

state, based on accurate, consistent and extensive

data and the measurement of transport properties by

Diller and Roder, the entire industry began to settle

down. Experimental heat transfer and fluid dynamics

results could now be placed in proper perspective

even though many could not yet be correlated and experimentalists and engineers stopped trying to assess the impact of differences between poor properties and the fact that our understanding of the dy- namics of the application was totally inadequate (2_4) . The loss of many man-years of effort, duplication

and unnecessary proof of concept projects could per- haps have been avoided if adequate thermophysical

property information had been available when needed. Since that time, the Lewis Research Center of NASA

has supported an ongoing effort at NBS and an effort

at the University of Maryland to minimize the recur- rance of such events; to date we have been moderately

3':

.
successful in assessing the state of the art in the

areas of high pressures, fluid mixtures, transport

properties and thermophysical properties in the cri- tical region of fluids. We have not yet been successful in the attempt at unification, but it is an area which must be confronted and overcome both on a local and international scale. I might add that the hydrogen and oxygen data bases represent the most extensive, accurate and consistent sets in existence. Current efforts are toward exploring a) the thermophysical properties of hydrogen and oxygen to

100 MPa (^15000 psia) for future mission applications,

and b) the basic concepts needed for predicting the thermophysical properties of fluid mixtures, and c) the nature of thermal conductivity and viscosity in- cluding their anomalous behavior near the critical

point.

Why are we still interested in property data?

It is obvious that high pressure applications will increase payload and decrease the costs while the spinoffs to landbased power systems appear substantial in terms of increased efficiency. As for mixtures, if we could determine how to predict the PVTx

properties of a simple mixture of an organic- inorganic

fluid, with substantially different critical points

and vapor pressure curves, from the extensive yet smaller data sets associated with the pure components, we could project a generalized method for predicting

the PVTx surface of any simple mixture. The near

critical region provides a key to understanding ther- mophysical property surfaces, and while thermodynamics

of the critical region have received much attention,

the transport properties have not. Sengers et al. ( 25 ) have been able to assess the anomalous thermal con- ductivity in the critical region for a number of

fluids. The anomalous thermal conductivity is strong

and can be related to the divergence of compressibility. Recently Basu and Sengers have also proposed an equation to account for a very weak anomaly in the viscosity of fluids near the critical point (2^6)

.

Efforts in these areas are making remarkable advances.

Some developments related to RP1 Concurrent with the effort to develop high per- formance propellants, a large effort was launched

to improve the propellant kerosene or RP1 as it was

designated. In this case, a sound systematic pro- gram as completed for hydrogen, was not undertaken

and unfortunately I must report that thus far little

has been added to our fundamental understanding.

Neither a uniform PVT computer code or data base for

these fluids is available covering high pressures

and the transport properties are of questionable

value. The effort could benefit from a mixtures program and pure component hydrocarbon data bases. Even though the data base is of questionable value, we are currently seeking to understand the effects of coking both in the fluid and combustion gas states. Theoretically, early RP rocket engines were not cooled adequately to prevent burnout of the coolant

passages. A careful inspection revealed that a thin

layer of coke formed on the thruster side of the coolant passage which protected it against the ex- treme temperatures and thermal fluxes. Coking has been studied by petrol producers, (27,28,29) and was found to be quite sensitive to oxygen and sulfur

compounds in the fuel. These compounds also markedly

changed the reported heated tube data ( 30) where

coking was found. No systematic effort has been undertaken to determine the nature or limitations of coking in coolant passages (thermostability) even though hydrocarbons are the mainstay of our trans- portation industry in the form of fuels and

lubricants. The problem is compounded when shale derived fuels are considered.

We should assess the availability of data for RP, incorporating results of the mixtures and pure com- ponent data base programs, and provide the industry

with a representation of the PVT and transport pro- perties data to 100 MPa (~15000 psia) . We should then investigate the limits of heat transfer to 80MW/m2 (~50Btu/in^sec) with wall temperatures to perhaps as high as 2000K. While these examples serve to illustrate the de- velopments related to aerospace, the results have been extensively used by industry in general. Data bases for oxygen (31) , fluorine (32) , FLOX (33) , nitrogen

(34) , helium ( 35 ) and selected hydrocarbons (36, 37, 38) have been established for NASA by NBS-Boulder.

Some Other Property Bases and Related Applications

In this section, we cite some other data bases of interest to NASA and industry. Some organizations where such data can be found are covered in the papers of Olien and Liley presented at this meeting. NASA has had projects concerned with the thermo- physical properties of systems other than fluids with

the purpose of establishing data bases for superconductors, slushes and gels, combustion, and such materials as metals, refractories and plastics. We will only briefly mention some of these.

In the area of superconducting magnet technology

and low temperature physics NASA has produced several magnets, developments in magnet wire and coatings such

as formvar. Currently there is some interest in MHD. In the area of ultra high pressures and transition points, the potential of an ambient temperature

superconductor initiated a study on the possibility

of compressing hydrogen to the metallic state which may require a pressure of 4 Mbars . Many semiconductor

to metal transitions have also been studied (39,40) . More recently the production of metallic neon has been achieved (41) . A spinoff of this work is the gadolinium heat pump which has the potential of achieving near Carnot efficiency (4_2_,4_3,44) . Free radical fuels offer very high impulse potentials and have stimulated work in producing atomic hydrogen propellant; however, free radicals are difficult to stabilize and produce and little effort is currently given to it. Slush propellants have increased bulk densities,

increased coolant capacity and reduced boiloff losses. A slush is readily produced in small quantities

through evacuation of the container, but NBS produced

P-H2 slush using a novel refrigeration scheme ( 45) . NBS has also determined the properties of some slushes. Gels have been considered for thermal stability of fuels and fire inhibitors, and in some cases for providing increased performance ( 46 ) . The problems

with gels and slushes is in transfering them: they tend to clog up pumps and adhere to the containers

and for RP mixtures the tendency is toward formation

of waxes

.

In the area of plastics, the need for high tem- perature (to 600°F) polymer matrix composites led Serafini (47,48) to develop PMR (in situ polymerization of monomer reactants) polyimides. In the PMR

approach, the reinforcing fibers are impregnated with

a solution containing a mixture of monomers dissolved

in a low boiling point alkyl alcohol solvent. The monomers are essentially unreactive at room temperature, but react in situ at elevated temperatures to form a thermo-oxidatively stable polyimide matrix. These highly processable addition-type polyimides can be processed by either compression or autoclave molding techniques. PMR offers superior processing

36
versatility, high temperature properties and finds application in advanced engine and airframe concepts.

Refractories are used in many engine components

where complexity precludes adequate cooling for con- ventional materials (49). For example, a two-layer

system with a bond coating of nickel-chromium-aluminumyttrium (Ni-16Cr-6Al- .6Y) and a ceramic coating of yttria-stabilized zirconia (Zr02-12Y203) has been

tested in several applications. Similar refractory

coatings are being applied to turbine blades and rub- bing surfaces (50,51,52) to reduce gas path sealing

losses and increase engine efficiency ( 53) .

Directions toward better property representation

In this section we shall a) discuss the application of the principle of similarity to thermophysical properties and fluid mechanics (i.e., a move to- ward generalized transforms) and b) suggest a merger

of the extended corresponding states concepts with

the thermophysical properties function of Zeleznik

( 54) i.e., a move toward generalized thermophysical

property representations.

Toward a Generalized Transform

The strongest impetus toward generalization is the insight gained by comparing experimental results

for fluids a and B; the implication that experimental

data taken with a cryogen are applicable to, say

water, and vice versa, is of significant value. Based on the engineering needs for properties

in heat transfer and fluid flow computations we advo- cated earlier that simple fluids could be represented

accurately, consistently and extensively by a form

similar equation, but with different coefficients. Based on Bender's equation for five fluids, (55) , we were able to produce a uniform properties computer

code GASP for eight fluids (currently twelve) and subsequently the code WASP for water. Armed with

these codes and the principle of similarity we began

to explore the utility of this approach. It was

found that we could

i) extend fluid ranges in PVT and determine the character of the surface derivatives,

ii) produce reduced Joule-Thomson coefficients and

the reduced Joule-Thomson locus for many fluids,

iii) produce representations for the anomalous be- havior of the thermal conductivity in the critical region for most of these fluids,

iv) correlate two-phase choked flow data and predict

these results analytically,

v) group experimental heat transfer results over a relatively wide range of fluid conditions, and

vi) produce a wide variety of normalized property

parameters for several fluids which could then

be represented in reduced form on a single

chart

.

Currently order for many of these fluid property

related projects and concepts can be found using the work of NBS and Mollerup (57-59) , where the properties

of two pure substances can be related by the

equations-'-

Zm^.T.x] ZQ [v/h,T/f]

qjv.T.x] = fG

0 [v/h,T/f] + RT(Exalnx

a

- lnh)

where o denotes the reference fluid and the properties are termed configurational , because they have similar molecular potentials, i.e. both are adequately described by two-parameter potentials. For x= 1,

the equations relate the properties of two pure com- ponents while for x/ 1 the relation expresses the pro- perties of a multi component mixture. The functions f

and h are dependent on the ratio of the critical tem- perature and volume, and for pure components,

- T

c > f =1 —ie !,

the parameters 6 and $ being weakly dependent functions

of temperature and volume (60,61)

.

For mixtures, we need to account for the energy of mixing, introduce some "mixing rules", and redefine

f and h as h=Z£xx0 h 0 a g a B ag

fh = ZExx„f n h„

a 3 a 3 aB aB where

aB

SB 1 aa BB

l-This is the so-called van der Waals or one- fluid

model

.

and where E, a$ and <$> aQ are the binary interaction

parameters

.

Hanley et al . (62 ,63) applied these configuration

functions and proposed that thermal conductivity and viscosity of mixtures could be related in a similar

manner. For pure components

*[P,T] = Ao [ph,T/F]F

A

,

n[p,Tj = n0 [ph,T/f]Fn ,

For mixtures, the functions f and h are as de- fined previously and F^, F^ are redefined using the Enskog theory for the transport properties.

The use of configurational functions f and h, along with an accurate reference equation of state, greatly enhances the users capability to accurately

relate thermophysical properties. Its greatest utility comes when a dearth of information exists for pure component a, or a multicomponent mixture, and in gaining mechanistic insights when analyzing the data from transport processes with different fluids or

mixtures. However, it does have the disadvantage of being more complex. It requires a very accurate pure component representation; the molecular potentials

must be similar and one needs to determine the configuration factors and, for the case of mixtures, the in- teraction parameters. While fluid mixtures represent

a very difficult problem, some progress is being made. Mollerup has determined some interaction parameters of

interest for LNG and has written a computer program

to predict properties of a few simple fluid mixtures

whose configurational properties are closely associated with methane (the major constituent of LNG). We have pointed out in a separate paper ( 56 ) that the conservation equations can be made coordinate AND

fluid invariant, noting that the conservation equa- tions and the transport relations for heat, momentun

and diffusion are tensors, and the coefficients of

proportionality (X,n,D) can be transformed nearly in- dependently of the fluid. In support of such a proposal,

37
several examples of applications were cited, where the data sets for different geometries and fluids could

be related through the use of similarity, including

(56) : 1. Two phase choked flows could be grouped for

several geometries and multiple fluids (64-66) , free

jet flows through tubes with Borda and sharp edge in- lets (67_,68) , circular, square, rectangular and tri- angular inlet geometries ( 69) , and for choked flows of gases a general relation was developed for tubes, annular and tapered convergent annular flows ( 70) . 2. Heat transfer data for developed turbulent

flows through tubes, from several investigators,

could be grouped for multiple gases, liquids and near

critical fluids using volumetric expansion parameters

and a density fluctuations model (71)

.

3. Application of the generalized transformation

to calculating two-phase-choked flows, using the various reference fluids, methane, nitrogen and oxygen, and compared to the experimental data ( 66 ) as illustrated in figs. 5 and 6. The theoretical cal- culations are for the most part in good agreement in- dependent of the working fluid and the reference

fluid used to calculate the results.

The point here is that many insights have been

gained through analysis of the properties and appli- cation of the similarity principle. Even more in- sights could be gained if a uniform method of repre- senting properties were available.

Fluid Reduced

temperature

Figure 5. Choked flow rate for reduced temperature of ^1.025.

Fluid Reduced

temperature

O (ED 0 "tf IS o Oxygen l.026±0.00l

Nitrogen 1.025*0.001

0 °- 4 18 1.2 1.6 2.0 2.4 2.8 Reduced pressure, Pp

Figure 6. Pressure ratio for reduced temperature

of M.025.

Other Thermodynamic Properties Representations

Zeleznik has proposed an elegant linearized rela- tion to represent thermodynamic data which conforms to

all the principles of thermodynamics Q,5_4 ,72) . The relation isN

X c Jl=l

N N

1 j=l

(y. . + v In x.)x. x.

where G is the thermodynamic chemical potential, x^ are the mole fractions, o)^ are the elementary symme- tric functions, Ujj the symmetric contributions to G, while Vjj In Xj introduces asymmetry.

In the space considered by Zeleznik, points re- present the pure components, edges the binary inter- actions, and so on to higher order spaces. The theory

is quite complex, requiring very large accurate data

sets and accurate numerical representation procedures, but the range and potential of this formulation are well documented ( 72) using data for mixtures as etha- nol and n-heptane and ionic solutions such as NaCl + H 20. As a logical next step in this approach, it would

appear that one should, a) combine the work of Zeleznik,

Mollerup and NBS, b) attempt to integrate the principles of fluid similarity, and c) return to mixtures of

simple fluids.

In the very restricted framework of fluids whose properties are configurational with methane, we can:

1. usually predict pure component properties

which represent end points in Zeleznik 's space whether

or not such properties in fact exist.

2. often predict properties for binary mixtures

which represent the edges or lines joining the points

in Zeleznik 's space, again whether or not in fact such properties exist. Once the points and edges of such a space are generated (requiring a lot of computation) , one can then use Zeleznik 's representation to give properties

on and within the surface. Applying these concepts, the work of Zeleznik

(54,72) can probably be extended from a method of re- presenting thermodynamic data to a technique for PRE- DICTING thermophysical properties. But such a tech- nique would not be as accurate as a formal represen- tation of an extensive data set, is very computational

time intensive, and one would probably seek a more simplistic resolution of the problem.

SUMMARY

In summary, we have looked at some problems and development of fluid data bases along with other data bases and some related applications, discussed mecha- nistic (flow modeling) insights gained from application of the principle of similarity to the conserva- tion and thermophysical property equations; discussed

moves toward generalization of thermophysical property

representations, and suggested a technique to extend mixture methods.

We have also cited the need for a continuous

effort to produce accurate, consistent, extensive thermophysical property data bases which are placed

in a form readily accessible to the user and acceptable at the international level.

It should follow that maintainance of an ongoing program in thermophysical properties and international

standardization are vital not only to our aerospace

and related industrial growth, but our scientific

growth as well

.

It would seem that too often we operate on the principle that the squeaky wheel gets the grease, but

38
I think that a well lubricated, properly maintained

machine is the most efficient in terms of cost, maintainance, down time, longevity and conservation of

basic resources. So who needs properties? - we all do ! - and we must continue to support the accurate

consistent determination of thermophysical properties.

REFERENCES

1 Zeleznik, F. J., "Thermodynamics", Journal of

Mathematical Physics , Vol. 17, No. 8, Aug. 1976,

pp. 1579-1610.

2 Huff, N., Gordon, S. and Worrell, V. E .

,

"General Method and Thermodynamic Tables for Computation of Equilibrium Composition Temperatures of

Chemical Reactions", NASA TR 1037 , National Aeronautics and Space Administration, 1951.

3 Love, W. K. , Private Communication.

4 Ellers, R. C, Private Communication.

5 Schmidt, H. W. and Ellers, R. C, Private

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6 Woolley, H. W. , Scott, R. B. and Brickwedde,

F. J., "Compilation of Thermal Properties of Hydrogen

in its Various Isotopic and Ortho-Para Modifications", Journal of Research of the National Bureau of Standards , Vol. 41, Nov. 1948, pp. 379-475. See also: Johnson, V. J., "A Compendium of the Properties of

Materials at Low Temperature (Phase I). Part I. Properties of Fluids", WADD Technical Report 60-56 , Wright Air Development Division, 1960.

7 "Ortho-Para Conversion", Subject Index, Ad- vances in Cryogenic Engineering , Vol. 20, Plenum

Press, New York, 1975, p. 491.

8 "Superinsulation", Subject Index, Advances

in Cryogenic Engineering , Vol. 20, Plenum Press, New York, 1975, pp. 475-477, 509-510.

9 Hendricks, R. C, Graham, R. W., Hsu, Y. Y. and Friedman, R., "Experimental Heat Transfer and Pressure Drop of Liquid Hydrogen Flowing Through a Heated Tube", NASA TN D-765 , National Aeronautics

and Space Administration, 1961.

10 Hendricks, R. C, Graham, R. W., Hsu, Y. Y. and Medeiros, A. A., "Correlation of Hydrogen Heat Transfer in Boiling and Supercritical Pressure States", ARS Journal , Vol. 32, No. 2, Feb. 1962, pp. 244-252.

11 Hendricks, R. C, Graham, R. W. , Hsu, Y. Y. and Friedman, R. , "Experimental Heat Transfer Results

for Cryogenic Hydrogen Flowing in Tubes at Subcritical Pressures to 800 pounds per square inch "absolute", NASA TN D-3095 , National Aeronautics and Space Ad- ministration, 1966.

12 Goodwin, R. D. , "Apparatus for Determination

of Pressure- Density-Temperature Relations and Specific Heats of Hydrogen to 350 Atmospheres at Temperatures above 14 K", Journal of Research of the National Bureau of Standards , Vol. 65C, No. 4, Oct. -Dec. 1961,

pp. 231-243.

13 Goodwin, R. D. , "Approximate Wide-Range

Equation of State for Hydrogen", Advances in Cryo - genic Engineering , VoT. 6, Plenum Press, New York,

1961, pp. 450-456.

14 Harry, D. P., "Formulation and Digital

Coding of Approximate Hydrogen Properties for Application to Heat Transfer and Fluid Flow Computations", NASA TN D-1664 , National Aeronautics and Space

Administration, 1963.

15 Stiel, L. I. and Thodos, G. , "The Viscosity

of Polar Gases at Normal Pressures", AIChE Journal , Vol. 8, No. 2, May 1962, pp. 229-232.

16 Schaefer, C. A. and Thodos, G., "Thermal Conductivity of Diatomic Gases: Liquid and Gaseous

States", AIChE Journal , Vol. 5, No. 3, Sept. 1959,

pp. 367-372. See also: Stiel, L. I. and Thodos, G., "The Prediction of the Transport Properties of Pure

Gaseous and Liquid Substances", Proceedings 2nd Sym- posium on Thermophysical Properties , American Society

of Mechanical Engineers, 1962, pp. 352-365.

17 Hall, W. J., McCarthy, R. D. and Roder, H. M., "Computer Program for Thermodynamic and Transport Pro- perties of Hydrogen", NBS Report 9288 , National Bureau of Standsrds, 1967 and NBS Report 625 , National Bureau of Standards, 1972.

18 Farmer, 0. A., Springer, T. E. and Fisher,

B. B., "Fortran IV Hydrogen Tabular Codes", Report LA

3381 , Los Alamos Scientific Laboratory, 1965.

19 Goodwin, R. D. , Diller, D. E., Roder, H. M. and Weber, L. A., "Pressure Density-Temperature Rela- tions of Fluid Parahydrogen from 15 to 100 K at Pressures up to 350 Atmospheres", Journal of Research of

the National Bureau of Standards , Vol. 67A, No. 2, March-April, 1963, pp. 173-192.

20 Strohridge, T. R. , "The Thermodynamic Properties of Nitrogen from 64 to 300 K between 0.1 and 200 Atmospheres", NBS Technical Note 129 , National Bureau

of Standards, 1962.

21 Roder, H. M. and Goodwin, R. D., "Provisional

Thermodynamic Functions for Para-Hydrogen", NBS Technical Note 130 , National Bureau of Standards, 1961

.

22 Diller, D. E., "Measurements of the Viscosity

of Parahydrogen", Journal of Chemical Physics , Vol. 42 No. 6, March 15, 1965, pp. 2089-2100.

23 Diller, D. E. and Roder, H. M. "Thermal Con- ductivity Measurements on Fluid Hydrogen at 17 to 200 K and Pressures to 10 MN/m2 ", Advances in Cryogenic

Engineering , Vol. 15, Plenum Press, New York, 1970,

pp. 58-64.

24 Hendricks, R. C, Simoneau, R. J. and Smith,

R. V. "Survey of Heat Transfer to Near Critical Fluids", NASA TN D-5886 , National Aeronautics and Space Administration, 1970.

25 Hanley, H. J. M. , Sengers, J. V. and Ely,

J. F., "On Estimating Thermal Conductivity Coefficients

in the Critical Region", Thermal Conductivity 14 , Plenum Press, 1976, pp. 383-408.

26 Basu, R. S. and -Sengers, J. V., "Viscosity of Nitrogen near the Critical Point", Journal of Heat Transfer, Vol. 101, No. 1, Feb. 1979, pp. 3-8.

27 Taylor, W. F., "Deposit Formation from Deoxygenated Hydrocarbons. I. General Features", I and EC Product, Research and Development , Vol. 13, 1974

,

pp. 133-138.

28 Taylor, W. F., "Deposit Formation from Deoxygenated Hydrocarbons. II. Effects of Trace Sulfur

Components", I and EC Product, Research and Develop - ment , Vol. IS, No. 1, 1976, pp. 64-68.

29 Taylor, W. F. and Frankentel, J. W., "Deve- lopment of High Stability Fuel", Final Report Contract N00140-74-C-0618 , Exxon Research Corporation, 1975.

30 Anonymous, "Investigation of Cooling Problems

at High Chamber Pressures", Final Report Contract NAS8 - 20225 , Rocketdyne R6529, NASA Marshall Space Flight

Center, 1966.

31 Weber, L. A., "Thermodynamic and Related Properties of Oxygen from the Triple Point to 300 K at Pressures to 1000 Bar", NASA RP I011/NBS Internal Report 77-805 , National Bureau of Standards, 1977.

32 Schmidt, H. W., "Fluorine and Fluorine-Oxygen

Mixtures in Rocket Systems", NASA SP 3037 , National

Aeronautics and Space Administration, 1967.

33 Prydz, R. and Straty, G. C. , "The Thermodynamic Properties of Compressed Gaseous and Liquid

Fluorine", NBS Technical Note 392 , National Bureau

of Standards, 1973.

39
34 Jacobsen, R. T. , Steward, R. B. , McCarty,

R. D. and Hanley, H. J. M. , "Thermophysical Properties of Nitrogen from the Fusion Line to 3500 R for Pressures to 150,000 psia", NBS Technical Note 648 , National Bureau of Standards, 1973.

35 McCarty, R. D., "Thermodynamic Properties of

Helium 4 from 2 to 1500 K at Pressures to 10 8 Pa", Journal of Physical and Chemical Reference Data , Vol

.

2, No. 4, 1973, pp. 923-1042.

36 Goodwin, R. D. , "Thermophysical Properties

of Methane from 90 to 500 K at Pressures to 700 bar", NBS Technical Note 653 , National Bureau of Standards,

1974. 37 Goodwin, R. D., Roder, H. M. and Straty,

G. C, "Thermophysical Properties of Ethane from 90 to 600 K at Pressures to 700 Bar", NBS Technical

Note 684 , National Bureau of Standards, 1976.

38 Goodwin, R. D. , "Provisional Thermodynamic

Functions of Propane from 85 to 700 K at Pressures

to 700 Bar", NBS Internal Report 77-860 , National Bureau of Standards, 1977.

39 Spain, I. L., NASA Grant NGR 21-002-400,

University of Maryland, College Park, MD, 1979. 40 Etters, R. E., NASA Grant NGR 06-002-159, Colorado State University, Ft. Collins, CO, 1979.

41 "Squeezing Xenon to a Metal, Sulfur to a Superconductor", Physics Today , Vol. 32, No. 4, April 1979, pp. 17-18.

42 Brown, G. V., "Magnetic Heat Pumping near

Room Temperature", Journal of Applied Physics , Vol.

47, No. 8, Aug. 1976, pp. 3673-3680.

43 Brown, G. V., "Magnetic Stirling Cycles: A New Application for Magnetic Materials", IEEE Tran- sactions on Magnetics , Vol. Mag- 13, No. 5, Sept. 1977, pp. 1146-1148.

44 Brown, G. V. and Papell, S. S., "Regeneration Tests of a Room Temperature Magnetic Refrigeration Heat Pump", to be published.

45 Voth, R. 0., "Producing Liquid-Solid Mix- tures of H2 using an Auger", NBS Internal Report

78-875 , National Bureau of Standards, 1978.

46 "NASA Conference for Gas Industry Gels", NASA SP 5013, National Aeronautics and Space Administration, 1975. 47 Serafini, T. T. , "Recent Developments in PMR Polyimides at NASA Lewis Research Center", NASA Con- ference Publication 2079 , National Aeronautics and Space Administration, 1979. 48 Serafini, T. T., "Status Review of PMR Polyimides", NASA TM 79039 , National Aeronautics and

Space Administration, 1979. 49 Liebert, C. H. and Stepke, F. S. , "Industry

Tests of NASA Ceramic Thermal Barrier Coating", NASA

SP 1425 , National Aeronautics and Space Administration, 1979. 50 Bill, R. C, Shiembob, L. T. and Stewart,

0. L., "Development of Sprayed Ceramic Seal System

for Turbine Gas Path Sealing", NASA TM 79022 , National Aeronautics and Space Administration, 1978.

51 Bill, R. C. and Wisander, D. W., "Prelimi- nary Study of Cyclic Thermal Shock Resistance of

Plasma- Sprayed Zirconium Oxide Turbine Outer Air

Seal Shrouds", NASA TM 73852 , National Aeronautics

and Space Administration, 1978.

52 Taylor, C. M. and Bill, R. C. , "Thermal

Stresses in a Plasma-Sprayed Ceramic Gas Path Seal", Journal of Aircraft, Vol. 16, No. 4, April 1979,

pp. 239-246.

53 Kennedy, R. E. and Bill, R. C. , "Thermal

Stress Analysis of Ceramic Gas Path Seal Components

for Aircraft Turbines", NASA TP 1437 , National Aeronautics and Space Administration, 1979.

54 Zeleznik, F. J., "A Class of Nonideal Solutions. I. Definition and Properties", NASA TP, National Aeronautics and Space Administration, to be published.

55 Bender, E., "Equations of State Exactly Re- presenting the Phase Behavior of Pure Substances",

Proceedings 5th Symposium on Thermophysical Properties , American Society of Mechanical Engineers, 1970,

pp. 227-235.

56 Hendricks, R. C. and Sengers, J. V., "Application of the Principal of Similarity to Fluid Mechanics", Proceedings 9th Conference on the Properties

of Steam, Munich, Sept. 1979 , Pergamon Press, New York,

in press.

57 Mollerup, J., "Thermodynamic Properties of

Natural Gas", Petroleum Gas and Related Mixtures: Enthalpy Predictions", Advances in Cryogenic Engineering , Vol. 23, Plenum Press, New York, 1978,

pp. 550-560.

58 Mollerup, J., "Correlated and Predicted

Thermodynamic Properties of LNG and Related Mixtures

in the Normal and Critical Regions", Advances in Cryogenic Engineering , Vol. 20, Plenum Press, New

York, 1975, pp. 174-194.

59 Mollerup, J., "Thermodynamic Properties from Corresponding States Theory", Paper 459, 71st Annual Meeting of the AIChE , American Institute of Chemical Engineers, 1978. 60 Leach, J. W. , "Molecular Structure Correction

for Applying the Theory of Corresponding States to Nonspherical Pure Fluids and Mixtures", Ph.D. Thesis , Rice University, Houston, TX, 1967.

61 Leach, J. W. , Chappelear, P. S. and Leland,

T. W. , "Properties of Hydrocarbon and Quantum Gas Mixtures from the Corresponding States Principle",

Proceeding of the American Petroleum Institute , Vol.

46, 1966, pp. 223-234.

62 Rainwater, J. C. and Hanley, H. J. M. , "Pre- diction of the Transport Properties of Natural Gas and Similar Mixtures", Advances in Cryogenic Engineering , Vol. 23, Plenum Press, New York, 1978, pp. 561-565. 63 Hanley, H. J. M., "Prediction of the Thermal Conductivity of Mixtures", Proceedings 7th Symposium

on Thermophysical Properties , American Society of

Mechanical Engineers, 1977, pp. 668-673.

64 Simoneau, R. J. and Hendricks, R. C. "Two- Phase Choked Flow of Subcooled Cryogenics in Converging-Diverging Nozzles", NASA TP 1484 , National Aero- nautics and Space Administration, in press.

65 Simoneau, R. J. and Hendricks, R. C, "Gen- eralized Charts for Computation of Two-Phase Choked

Flow of Simple Cryogenic Liquids", Cryogenics , Vol. 17, No. 2, Feb. 1977, pp. 73-76.

""'

66 Hendricks, R. C. , Simoneau, R. J. and Barrows,

R. F., "Two-Phase Choked Flow of Subcooled Oxygen and Nitrogen", NASA TN 8169 , National Aeronautics and Space Administration, 1976. 67 Hendricks, R. C, "Some Aspects of a Free Jet Phenomena to 105 L/D in a Constant Area Duct", Paper Bl-78, XVth International Congress of Refrigeration, Venice, Sept. 1979, International Institute of

Refrigeration.

68 Hendricks, R. C, "Free Jet Phenomenon in a 90°-Sharp Edge Inlet Geometry", to be submitted to Advances in Cryogenic Engineering , Plenum Press, New York.

69 Hendricks, R. C. and Poolos, N. , "Critical

Mass Flux through Short Borda Type Inlets of Various

Cross Sections", Paper Bl-77, XVth International Con- gress of Refrigeration , Venice, Sept. 1979, International Institute of Refrigeration.

1*0
70 Hendricks, R. C, "Some Flow Characteristics

of Conventional Tapered High Pressure Drop Simulated

Seals", Proceedings ASLE/ASME Joint Lubrication

Conference, Dayton, OH, 1979 . 71 Hendricks, R. C, Yeroshenko, V. M. , Yaskin,

L. A. and Starostin, D. D., "Bulk Expansion Factors

and Density Fluctuations in Heat and Mass Transfer",

Paper B1-B19, XVth International Congress of Refrigeration, Venice, Sept. 1979 . 72 Zeleznik, F. J. and Donovan, L. F., "A Class of Nonideal Solutions. II. Application to Experimental Data", NASA TP , National Aeronautics and Space

Administration, to be published.

in

P.E. Liley

Senior Researcher, CINDAS,

Professor of Mechanical Engineering, Purdue University, West Lafayette, Ind.

Problems and Procedures in

Providing Values of

Thermophysical Properties of

Fluids

For many years, it has been evident that a better knowledge of the thermophysical,

i.e., thermodynamic and transport, properties of matter is needed for many

technological applications. The present paper gives a brief historical review ofsome

developments made to remedy this situation. This is followed by a survey of

correlating equations used for the specific heat at constant pressure, thermal

conductivity, viscosity, and Prandtl number of fluids. Finally, recommendations

forfuture work are listed.

ABSTRACT

For many years it has been evident that a "better knowledge of the thermophysical, i.e., thermodynamic

and transport, properties of matter is needed for many

technological applications. The present paper gives a brief historical review of some developments made to remedy this situation. This is followed by a survey

of correlating equations used for the specific heat at constant pressure, thermal conductivity, viscosity,

and Prandtl number of fluids. Finally, recommendations for future work are listed.

INTRODUCTION

In the middle 1950 's some definitive progress in the study of thermophysical properties occurred. This,

in part, was produced by war-time technological needs which, for security reasons, only saw a slow declassification and publication. In part, also, they re- flected the large expansion in research which occurred

then. One item was the publication (l) of "Tables

of Thermal Properties of Gases." Originally issued

in loose-leaf form ( 2_) , these tables represented a large effort and also were possibly the first extensive use of machine (i.e., "computer") generation of thermodynamic functions. At about the same time the "Tables of Thermodynamic Functions of Gases" started

to appear. Three volumes were issued ( 3-5 ) Each substance was allotted one chapter and different

authors were involved. It is unfortunate that consistency in the above of units and bases was not achieved.

In large measure, these publications rested on the labors of the late F. Din who made greater use of graphical and approximate methods. The U.K. publications ( 3-5 ) concentrated somewhat more on the liquidvapor boundary, while the U.S. works ( 1-2 ) were much

preferable at the higher temperatures.

The publications referred to above were followed

for several years by a somewhat surprising lack of further material. It is supposed that most persons

thought that they fulfilled all needs. But deficiencies became evident in addition to those mentioned

above. The study of steam was delegated to a specialist group (6_) . The almost complete lack of information on transport properties was noted and slowly

remedied by the organization of specialist conferences

(7.) and research programs and publications (8_) . More detailed studies of thermodynamic properties did result - in the 1960's - and were concentrated in a few centers, such as N.B.S. Boulder, Texas A & M University,

etc

.

Coupled with the above technological type developments, more scientific type activities appeared.

The monumental "Mathematical Theory of Non-Uniform

Gases" (9.), published in 1939 > concentrated on transport properties , and its appearance was soon over- shadowed by the World War. Its second edition, in 1952, almost paralleled the separate publication of

the "Molecular Theory of Gases and Liquids" in draft

( 10 ) and book (l_l) form. The latter publication also covered thermodynamic properties as" well as combustion

and quantum chemistry, and thus received wider attention. Its breater use of computer facilities exactly

parallels the difference between publications (l_) and

(3_) referred to earlier. The stimulus it gave for engineers to regard a hitherto abstract part of physical chemistry as being useful and usable, which may

be exemplified by their summary paper (l2_) , in the opinion of the author, is one of the landmarks of progress in the utilization of thermophysics in this century.

1*3
I

The above efforts must be regarded as being

coupled with some other long-term activities. One of these was the American Petroleum Institute Research

Project 44, now published with the former Manufacturing Chemists Association tables by the Thermodynamics Research Center (13) . In addition to the TRC publications on compounds, an International Data Series on Mixtures has been initiated, and data sheets are cur- rently being issued in two series. Series A covers mixtures of non-electrolytes other than water. Details can be obtained from TRC, College Station, Texas

77843. Series B covers mixtures of organic non-electrolytes in water. Details can be obtained from the Engineering Science Data Unit, 151 Regent Street, London. A further Series D, on metal alloys, is under consideration. Another was the Joint Army, Navy and Air Force JANAF thermochemical tables ( 14 ) . The cumu- lative effect of all these efforts was the realization

of the need for research centers where studies could

be systematically undertaken. These were enlarged

and/or established in the late 1950' s, as exemplified

by the author's own institution (15) , the Cryogenic Data Center of the National Bureau of Standards ( 16 )

,

the enlargement of the Mechanical Engineering Research Laboratory (17) , etc. The growing awareness of such needs by other countries has led to other institutes

being established and international planning and coop- eration (18) . The material so far presented has aimed

at acquainting the reader with a personal, general

perspective of historical developments. What follows

is a much more detailed account of ways in which four different thennophysical properties have been represented by correlating equations. The four properties were selected due to their importance to heat transfer

calculations. In addition, a real lack of knowledge

of the transport properties has long been evident in contrast somewhat to the better state of knowledge of the thermodynamic properties. The mission, in part,

at the author's center has been to provide values of such properties.

GENERAL APPROACH TO PROPERTY TABULATION

arbitrary selection must be made, an example based on the securing of agreement in values for chemically

similar families of substances. Whichever case occurs, the selected values are then often represented by a function which is a mathematically convenient, yet physically realistic, | representation of the variation of the property. Table 1 lists various representations of thermophysical properties which have been found to be useful where only a temperature dependence is involved. In cases where a simple mathematical function can represent values as well as can a more fundamental function, the simpler function is to be chosen from the viewpoint of user convenience. However, this pro- cedure is not to be adopted in cases where it is feared that the user might be tempted to use an ap- proximate form outside regions of its validity. In

a few cases a graphical representation may be necessary. This usually occurs close to transition points,

etc.

Table 1 Some Useful Representations for Thermophysical

Properties, P, as a Function of Absolute Temperature, T

Eq. No.

1 P A + BT

2 P A + BT + CT2

3 P A + BT + CT 2 + DT 3

4 In P A + B/T

5 Jin P A + B/T + C/T2

6 P /T/[A + B/T • exp(-C/'T)]

7 P /T/(A + B/T)

8 P /F/(A + B/T + C/T 2

) 9 P /l/(A + B/T + C/T 2 + D/T 3

) 10 in P A + B/T + CT 2 + DT 3 11 P /T/(A + BT + CT 2

) 12 P A + BT + CT 2 + DT 3 + ET"

13 In P A + B In T

14 P aTs

For a particular property and physical state, the literature has to be searched, values extracted, and

the entire assemblage of values converted to a given

system of units (now S.I.). The -property is then plotted as a function of temperature and/or as a func- tion of pressure to detect gross errors or inconsistencies. The selection of the most probable values as reliable input information depends upon several factors. If the values are experimental, the apparatus,

method, use, consideration of corrections, etc. are

all noted and a comparative ranking of the different

sets of data made. If the values are theoretical,

the method of calculation is noted, with consideration

of any variation in input material, consistency checks,

etc. The result of such analysis leads either to a

set of experimental data considered reliable, or a set

of theoretical values, or both, depending on the input information. In some cases, both sets can show satisfactory agreement with no preference given to either,

in which case the average can be taken as input. In other cases, significant differences exist which can

be explained and which lead to the selection of either experimental or theoretical values as the more probable

basis. In some cases, while significant difference

occur, the reasons cannot be explained and a more

'Care should be taken not to confuse the much more

recent ( 19 ) organization of an American "National

Engineering Laboratory" with the same-named British

one.

In addition to these semiempirical or empirical

representations, a more theoretical approach should

be taken whenever feasible. This has generally been restricted to the dilute gas phase. One convenient

region for applying theoretical models is that of the dilute gas at high temperature, where the graph on page 566 of ( 11 ) predicts a variation with the 2/3rds power of absolute temperature in viscosity and thermal conductivity for the Lennard-Jones 6-12 potential.

Since the publication of ( 11 ) , a considerable amount

of effort has gone into extending the 6-12 potential

into an m-6 and then m-6-8 model, where the m is a variable replacing the 12, the 8 being explained in

(20). Simple models, like P = aTs (Eq. 14), are very

useful, as referred to on pages 565 and 566 of (11)

.

Vargaftik ( 21 ) and others make frequent use of func- tional like eqs. (13) and (14) over large temperature

ranges with apparently good accuracy. The question of the possible relationship between "s" and the "m" of the potential is of some interest. This relates to the question of fitting the second-virial coefficient

data to, say, an m-6-8 model and using the parameters

to calculate transport properties. The fact that m

and s are related is demonstrated in Table 2. An ap- proximate graph for the collision integral fi 2 2 is shown in Figure 1, while Figures 2 and 3 plot values

of logi 0 a and n as functions of m. An example

hh
Table 2

Values of a, n in fi 22 = aT*nfor m-6 Potentials

m Log a -n Note m Log a -n Note

8 0.1087 0 211 b 16 0.0527 0 119 b

9 0.09648 0 1912 a 18 0.04601 0 1072 a 10 0.0863 0 175 b 20 0.0414 0 097 b 12 0.07183 0 1523 a 21 0.03944 0 0936 a 14 0.0609 0 134 b 24 0.03295 0 0823 a 15 0.05841 0 1270 a 30 0.02558 0 0668 a Notes :

a. Deduced from tabulation (67)

.

b. Approximate, from Figures 2 and 3.

20 30 4 0 60 60 IOO L0G,0 T»

Figure 1. Log 10 £2 22 versus log 10 T* for m-6 Potentials

Figure 2. Variation of log 10 a with m

Figure 3. Variation of n with m

of the use of this approach has been given by the author elsewhere (22) in the evaluation of the high

temperature thermal conductivity of krypton. This will be elaborated upon in the material on this property below.

THERMAL CONDUCTIVITY

Saturated Liquid

Figure 4 provides a schematic of the variation of thermal conductivity with temperature for a fluid. If one starts heating a liquid at the normal melting

point (T = Tm) , in general2 the thermal conductivity

decreases. Many correlations and analyses in the lit- erature have suggested that the decrease is linear

with increasing temperature so that one traces out the path ABC. The variation eventually becomes more rapid

according to the simple description and one follows

the curve CD to the critical point X. For the saturated vapor, far less information is available in the literature. Increasing temperature has been hypothesized to result in a curve from T = Tm along E to X, again according to the simple description.

The extensive Engineering Science Data Unit

correlation activity ( 23 ) originally used the simple

Riedel (24) equation

k

L

= A [1 + 20/3 (1-T

r

) 2/3

] (15)

to represent the variation of thermal conductivity of

a liquid, kj^, with reduced temperature, Tr

, where A is a numerical constant to allow for the choice of arbitrary units and Tr is the actual temperature, T, divided by the critical temperature, Tc , of the fluid.

At low temperatures, Tp«l, the variation predicted by

eq. (15) is almost indistinguishable from a linear variation. More recently, a correlation at the National

Engineering Laboratory (25) used a more complex

expression

k

L

= A [1 + B (1 -T

r

) 1/3 + C (l-T

r

) 2/3 + D (1-T

r

)] (16)

Missenard (26) and the author ( 27 ) found that the thermal conductivities for chemically similar sub- stances converged at one point, assuming a linear de- pendence on temperature. By careful analysis, values

could be estimated to a moderately good degree of precision using this technique. More detailed analyses

2 A few exceptions occur, the most prominent being

hydrogen and water.

1*5
(SOLID)

TEMPERATURE

where the thermal conductivity of the liquid, kL

, is related to parameters H and N dependent upon structure

and density; Hv], is the enthalpy of vaporization at the normal boiling point, Tb ; C

p and p are the specific heat and density of the liquid and Tr is the reduced temperature, T/Tc , where Tc is the critical

temperature. "Rarely did the errors exceed ten percent . . . but the testing was invariably carried out

for 0.5 < Tr< 0.7" (28) . The second, a combined Sato- Riedel et al. correlation, predicts (24,28)

3+20 (1 - T ) r 2/3

L

/M" 3 + 20 (1-T ) 2/3 (18)

where the "a" depends on the unit choice for kL, M is the molecular weight, and the Tr and Tr, are, respectively, T/Tc and Tb /Tc , where Tb

is the normal boiling

point temperature. For this choice, "the errors noted vary widely" (28). The third, based on Missenard (26)

,

predicts that

3 + 20 (1-T ) 2/3

r o 3 + 20 (1 - 273/T

c

)

' J (19)

The values predicted were generally too large. Reid

et al. then made recommendations as to which of these equations should be used, the choice depending on

temperature, substance, available data, etc. For re- duced temperatures above Tr

< 0.8, a generalized cor- relation for the gaseous state (see below) was suggested. A thorough comparison of the efficiency of 26 equations to represent values for 12 liquids has since appeared (30) . These authors recommend eq. (17) and also a further equation by Scheffy and Johnson (31).

- 0.00126 (T-T )

T 0-216 M

0.3 m

(20)

where Tm is the melting temperature, and a is a variable constant depending on unit choice. Some other equations were also recommended. All the above refers to the saturated liquid

state. The same Reid et al. source (3) compares two correlations of pressure, those of Lenoir (32) , which

basically graphically relate two values of conductivity

to two values of reduced temperature and pressure, and Missenard ( 26 ) , which relates the augmentation due to the pressure to the reduced pressure, and says that

the correlations are equivalent. This suggests that an analytic form such as

Figure 4. Schematic Thermal ConductivityTemperature Graph

of such substances have been made. As stated by Reid

et al. (28) , "there is no scarcity of estimation tech- niques to calculate the thermal conductivity of a pure

liquid. Almost all are empirical and, with only limited examination, some may appear more accurate

than they are." Three of what they consider to be the best are then reviewed. The first, that of Robbins

and Kingrea ( 29 ) , has been widely used and predicts

that

0.088 - 4.94 * 10 H \ H . /T, +R£n (273/T. ) vb b b

0.55

N V

4/3

(17)

k(P,T) = k(sat. T) [l + f(P ,T ) (21)

where the f represents a function which can be tabulated in terms of both variables and n is a constant

[suggested as 0.7 according to (26) ], could possibly

be used as a basis for a bivariate least mean squares

fit. Equations 15, 16, 18, 19, and 21 all imply that a functional relationship exists between k and Tr , with

certain varying parameters. A systematic evaluation

of these forms could be useful, although the- lack of high experimental precision for a sufficiently varied

collection of substances will probably result in un- certainty in the conclusions therefrom. More serious

is the complete lack of allowance in all the above for special effects, such as the following:

h6
Pre-Melting . The variation of thermal conductivity with temperature close to the melting point is suggested as becoming nonlinear ( 33 ) , the curve ap- pearing like MB. Physically, this is suggested as being due to the formation of cybotactic groups. However, a few substances appear to exhibit the op- posite effect, following a curve more like HBJ.

Critical Region . The thermal conductivity does not approach a value kc at T = Tc for the saturated

states but, instead, the liquid curve follows path L

and the vapor curve path V, both curves showing a tendency to approach a very high or infinite value

at or slightly above the critical temperature. In analysis of experimental data, one could suggest that extra care be taken with all data within ten percent

of the critical temperature for pressures from one half to twice critical, although the attainment of some theoretical predictions ( 34 ) may only be realized

in a very much more restricted region around the critical point. The formulation according to these pre- dictions results in an equation of the form

A(p,T) = A(0,T) + A. d (p,T) + kT^FO^-l, P r-1) (9P/3T)

p

2 /(6TTMC) (22)

3

where the value at density p and temperature T depends

on a background function (id) and on a critical excess function that depends on the compressibility Kj, the viscosity, p, as well as a friction factor %, and an empirical function F of reduced temperature and density. A detailed numerical formulation of thermal conductivity using a simplified version of eq. (22) is the calculation by Watson of the properties of Refrigerant 12 ( 35 ) . The values so obtained do show a systematic difference with experiment ( 36 )

.

Radiation . Completely neglected in all the above

discussions is the possibility of energy absorption

in the fluid, either preferential or total. This effect is a strongly varying function of the chemical

structure of the fluids, some fluids absorbing none

and some absorbing much of the energy. The effect is also a function of specimen thickness for any finite

thicknesses (37) . Hence, the implication is that the thermal conductivity definition should be written

Watts per meter squared (area of specimen) , per meter

(thickness), per degrees Kelvin, and not in the usual

form with specimen thickness also being cited.

Decomposition . While the normal elements and diatomic compounds are usually fairly stable, the higher molecular weight organic compounds are only

one of many classes of complex structured molecules

which decompose with increasing temperature. The usual experimental evidence for this is in an augmentation of the thermal conductivity, as the lighter

fragments can carry energy more rapidly. But theoretical estimates of such decomposition are scarce.

Saturated Vapor

Except for a few well-known fluids, values for the thermal conductivity of the saturated vapor phase are lacking in the literature. Two principal approaches

to their estimation were made. The first was to use

the generalized correlation method for diatomic fluids, even in cases where the molecular complexity was of

3 In eq. (22) only, the symbol A is used to denote

thermal conductivity to avoid confusion with the Boltzmann constant, k.

higher order and to adjust the curve to merge with the dilute gas values at the normal boiling point and/or

also with pseudo-critical values. The second was to use the Liley ( 38 ) correlation

Ak = k(Sat. Liq., T) - k(Sat. Vapor, T) = aL(T) (23)

which relates the thermal conductivities of the liquid

and vapor phases at a given temperature T to the en- thalpy of vaporization, or latent heat, L(T), of the fluid. As stated by Liley, this method cannot be ex- pected to extend over a large interval away from the critical point, so it was used to produce values near

the critical point and a smooth curve extrapolation

was then used to obtain values down to the normal boiling point value determined from the dilute gas values. Thus, a graph of Ak versus L should be linear near the origin, the origin, of course, being the critical point, where L = 0. Figures 5-7 (38) , and

8 ( 39 ) show that the linearity does apply near the origin, i.e., that eq. (23) is a valid representation. After these figures were prepared, superposition re- vealed almost exact coincidence for the oxygen and nitrogen graphs. The possibility of a corresponding

states correlation of k with L thus exists. Furthermore, the regular variation in the slopes of the Ak

versus L graphs for refrigerants of a common series is

Figure 5. Variation of Ak with L for Nitrogen

Figure 6. Variation of Ak with L for Oxygen

hi
Figure 7. Variation of Ak with L for Water

o R- II A R-12

R - 1

3

O R-14

o

o

O

D A O A

C°

> D A o A o

D A O A

°

0OA

O

J A O

O

O A

20 30 40 LATENT HEAT, cal. gen"

1

Figure 8. Variation of Ak with L for Rll, R12,

R13, and R14

a useful check of the inter-consistency of the various

thermal conductivity values presented in the respective tables. One or more polynomial fits were usually

able to represent the saturated vapor values. The uncertainty in such values is usually estimated at ten percent or less, a figure felt to be entirely

characteristic of the present-day uncertainty in most measurements and tabulations.

analysis is probably that of Mason and Monchick ( 40 ) for nonpolar polyatomic molecules . Involved in this formulation is the rotational collision number. Lack

of adequate knowledge of it has hampered the application of this theory. Probably the most detailed treat- ment is that of Brokaw (41) . A disturbing fact of an analysis of Barrales-Rienda ( 42 ) is that the trend of the experimental Eucken factor with temperature may be quite opposite to the theoretical results. While gen- eral reduced thermal conductivity versus reduced tem- perature correlations have been made for families of chemically similar substances by Thodos ( 43 ) and others, the more reliable approach would seem to be

that of the group contribution method ( 44 ) . But very

real difficulties still exist in the interpretation

of thermal conductivity of gases of even the simplest

structure. For example, Kestin ( 45 ) could only con- clude that thermal conductivity measurements of the monatomic gases were subject to "unknown systematic

error." Maczek and Highton ( 68 ) also state that "Approximations to rigorous kinetic theory which pro- vide reliable predictions for all the transport properties in monatomic gases and for viscosity and dif- fusion coefficients in polyatomic gases lose their usefulness when applied to heat transport in polyatomic gases . . . Formal theories of heat transport

in polyatomic gases exist . . . But since there is no reliable method by which the necessary relaxation

times can be measured, the accurate prediction . . . remains unachieved."

Analyses of thermal conductivity in other works

has varied from a systematic calculation of viscosity, thermal conductivity (and possibly other properties) based on molecular models for dilute ( 46 ) and com- pressed (47) fluids to a tabulation and error assessment of selected values ( 48 ) with no general attempt

at correlation. In general, the approximation

k - b /r a

2 nm

(24)

equivalent to treating the internal energy as a perturbation to the omega function has been used. The omega

functions were again approximated by a series of reciprocal temperatures , so that the above approximate form

was further modified to the relations in eqs. (6-9). In some cases it was found that the trend in the values calculated from rigorous theory or from more approximate forms such as the above did not differ significantly from a linear or quadratic relation (eqs. 1,2)

which were, therefore, used for simplicity "* . The average uncertainty produced, about five percent or less,

is felt to be entirely comparable to most experimental

data and theoretical calculations.

Our correlational efforts have, in part, been

based on the following expressions. (The ranges stated

are usually the case.)

1. For saturated liquids, T

r <0.9 T

c (22, 26-28 ,49) k

L

= a bT

2. For saturated liquids, T = 0.9 T ( 24 )

k = a T-T

(25)

(26)

Dilute Gas Phase . The thermal conductivity of a gas contains, in addition to the translational motion,

the effect of the internal degrees of freedom which

manifests itself in the Eucken correction. A detailed

calculation of thermal conductivity of a gas requires

calculation of viscosity, diffusion coefficient, in- ternal and translational specific heat at constant volume and of relaxation time. The most thorough

3. For saturated vapors, T<0.9 T

c

( 27 ) = a + bT + cT^ (27)

''No attempt was made to evaluate the effect of dissociation. While in many cases this is completely negligible up to 1000 K, instances do occur where the effect

does become pronounced at much lower temperatures

.
For saturated vapors, T =0.9 T

£

( 38 ) ah

fg (28)

where h. is the enthalpy of vaporization,

fg For dilute gas ( 27 ) k = /T/[A + B/T + C/T 2 + D/T 3

] (29) For dilute gas ( 22 ) k/k

Q = (T/T

o

>* (30)

where the zero state is usually 273.15 K. For the three regions saturated liquid, saturated vapor, and dilute gas (22,28,49 ,50) k = f(P ,T ) (31)

r r r where the f fefers to a generalized correlation.

VISCOSITY5

This is a transport property in which the internal degrees of freedom do not play a significant part. The procedures adopted parallel that for thermal con- ductivity so the following account can be made very

concise.

Liquids

The most common relationship for expressing the variation of liquid viscosity with temperature is the logarithmic equation (eq. 4 of Table 1). Equations given as eqs. (5) and (10) were also occasionally utilized in cases where eq. (4) did not yield

satisfactory agreement with the experimental data and/or did not extend over a sufficiently wide tem- perature range. Close to the critical temperature, the dependence of liquid viscosity with temperature has often been represented merely by a graph or by a generalized reduced correlation, again usually in graphical

form. References (27,28,50) may be found helpful as sources of additional information. We have found it convenient to represent values close to the critical

point by equations of simple polynomial type (eqs. 1-3 of Table 1) . An appreciable range of temperature

usually exists over which the polynomial fits merge

smoothly with the logarithmic. Uncertainties of five

to ten percent are quite common and are entirely

representative of the rather unsatisfactory state of the art for this property and phase.

Saturated Vapor

In some cases the viscosity of the saturated vapor was related to that of the dilute gas by a density function

P = P,., , + f (p) sat vap dilute gas

(32)

where the f(p) is a polynomial or a graphical representation. The particular representation most com- monly used was that of Jossi et al. (51) . Density

values were selected from sources considered most

reliable. Values for the viscosity of the saturated vapor so obtained could invariably be represented by

a polynomial (eqs. 2 or 3 of Table 1), and have an uncertainty of ten percent or thereabouts.

The remarks on viscosity which follow refer to work

sponsored at CINDAS. The reader may also be interested to note a separate, independent work (69)

.

GasesEquation (24) for thermal conductivity is an even more valid approximation for viscosity in the form

y

- (33) o

2 n(T)

Many empirical forms have been suggested to portray

the actual dependence of !2 on T. Over a sufficiently

limited temperature range, the omega function can often be represented as a polynomial in 1/T, so that

eqs. (7-9) result. Equations (6) and (11) represent

two other approximating functions. For a temperature

range of several hundred degrees, eq. (9) found to invariably be able to represent the input viscosity

values to within a few percent.

SPECIFIC HEAT AT CONSTANT PRESSURE

Specific heat is a thermodynamic, and not a transport, property and as such can, in principle,

be calculated from the partition function. This, in practice, requires a knowledge of the equation of state. Study of these is a considerable effort. The procedure adopted was merely to compare values calculated by different equations with experimental values,

and to attempt a rational analysis of the assembly so obtained

.

Liquids

Either a single cubic polynomial (fitted from

about the normal boiling point up to about 90% of the critical temperature) or two cubic polynomials (fitted

separately to about the lower two-thirds and the upper

one-third of this range) was able to represent to within several percent the specific heat of most substances

studied. The few exceptions include the immediate

vicinity of the critical temperature, for which graphical methods were used. Both for liquids and saturated

vapors the distinction between Cp and C sat , as ex- pressed by the equation

C . = T sat

'3P

' s ,dlj (34)

should be kept in mind.

Saturated Vapor

Our usual procedure has thus been to estimate

specific heat from the enthalpy temperature variation

along isobars , and then to extrapolate these values

to saturation conditions if the available tables did not provide saturation data. While the accuracy so obtained has usually been of the order of five percent,

two restrictions have been kept in mind. The first is that this accuracy is not secured close to the critical

temperature, at which the specific heat becomes infinite. Secondly, the estimates are predicated upon the accuracy of the enthalpy data. Since, usually, the latter are derived from equation of state data, our procedure is thus essentially that of deriving specific heats from an equation of state. The fact that specific heats are related to the pressure-volumetemperature data by a function containing the second derivative of volume implies that the uncertainty in

the specific heat will probably never be less than

one percent except in the few cases where the fluid

and the temperature range are technologically important and experimentally accessible for direct measurement .

h9
Dilute Gas State For zero pressure values, the results of statistical mechanical calculations within the last 20 years

or so usually prove to be reasonably self-consistent where more than one calculation is available and en- able a table of values to be prepared frequently to within a 1% uncertainty. The values can invariably

be represented over quite large temperature ranges

by cubic polynomials in temperature, i.e., eq. (3) of Table 1. A few exceptions have been found where the molecular structure is sufficiently complex that cor- rections for anharmonicity , etc., are significant.

The ultimate accuracy obtainable thus decreases

steadily with increasing complexity of the molecule.

The representation of specific heat values by a cubic polynomial is sufficiently well known that no examples

are felt to be necessary here.

Real Gas State For the real gas state (i.e., for values at atmospheric pressure), two approaches have been used.

By treating the available experimental and tabular information as a set, values of the specific heat were derived, again using a cubic polynomial as the interpolation device. In some cases, inconsistencies between the ideal and atmospheric pressure values were detected and have pointed up the need for further evaluation, almost invariably found to occur in the atmospheric pressure values.

PRANDTL NUMBER

The Prandtl number combines the three preceding

properties. It has, until recently, received only

scant analysis due largely to lack of information on

the thermal conductivity. One exception was the cor- relation of Codegone (52,53) some 25 years ago. With

the increasing need for and knowledge of thermophysical properties the situation has improved. The col- lection of all three constituent properties for 38 substances ( 27 ) enabled a more up-to-date evaluation

of the Prandtl number to be made ( 54 ) . Figure 9 is a simplified version of that appearing in the original publications ( 54 ) and shows the general way in which the Prandtl number is expected to vary with

reduced temperature, Tr = T/Tc

, for any liquid. As stated in the original publications, the preliminary

analysis there presented could be improved, particularly for the saturated vapor and dilute gas states.

OTHER PROPERTIES

Similar to the Prandtl number other properties

exist which are various functions of constituent

properties. Three of particular interest in heat transfer applications are the kinematic viscosity,

V = u/p (35) (where p is the density) thermal diffusivity, a = k/(p Cp

) (36)

and convective transfer

convective transfer = gB/v 2 (37)

where 8 = 1/v* (8v/3T)p. Another combination extensively reviewed by the author in an early work ( 55 ) is the Eucken factor,

f = k/(yC ) (38)

0.0 10 2.0 3.0 4(I-Tr

)

Figure 9 . Reduced Prandtl Number versus Reduced Temperature Graph for Liquids

While the ability of any given intermolecular

potential function to represent the thermophysical

properties of a substance is an open question - a subject that is mentioned in the recommendations for further work below - in many cases it is desirable to know the intermolecular potential parameters for a certain potential so that one can use that potential

to calculate the properties desired. While a few ex- tensive tables of inter-molecular potential parameters

are available ( 56 ) , the thought occurred that some relationships might exist between the parameters and

the position of a substance in a chemical series or group of series. This was made the subject of a thesis study ( 57 ) later published ( 58 ) where the con- clusion was reached that the parameters could indeed be related to the position of the substance in a chemical series.

RECOMMENDATIONS FOR FUTURE WORK

1. The recommendations of an ad-hoc group of specialists both for the compilation of critically

evaluated data and for the reporting of experimental

thermal conductivity measurements ( 59 ) seem to have

merit. Instances still occur in a disturbingly large number where such a consistent program is not followed. This work is again listed here in the hope that it will become more widely known and that it may be de- veloped for other properties.

2. The growth of data banks, data units, data

centers, etc. raises both hopes and fears. The hopes include that of making values of at least reasonable

accuracy available very rapidly to users needing such values for design, etc. The fears include those that entry to these facilities may become prohibitively

expensive for a thorough evaluation of different data

and that access may also become restricted to certain

groups only, denying their use to the scientific com- munity at large. An exact parallel seems to exist here with the problem of copyright and the printed

word. Study of those problems is recommended.
3. The very considerable amount of work required

( 60 ) in order to obtain a potential which exactly

represents the data for a dilute monatomic gas leads one to suspect that the labor may be prohibitive for

a real and complex gas and even more so for saturation states. The development of semiempirical func- tionals - maybe like our eqs. (1-14,24-31) - with

parameters that vary regularly with chemical series

and, if possible, groups of series should be of great

help to (a) persons who only require that the func- tional give values of reasonable accuracy, (b) persons who would use the parameters to estimate properties for so far untabulated substances, and (c) compilers of data banks

.

4. The work of Klein et al. (61) on the ability

of an intermolecular potential to represent pairs of properties has been followed by some studies (62) where more properties are included. It is suggested

here that some other properties such as the Prandtl

number and the Eucken factor could also be used and

the properties contained within these could also suggest further quantities to be considered.

5. Despite the widely accepted conclusion that

the principle of corresponding states fails to predict accurately enough the properties of any substance

it is felt that for the more complex substances, and more so for mixtures, the principle is still capable

of utilization, and it is suggested that study of such quantities as the acentric factor ( 63 ) be con- tinued so that predictions of reasonable accuracy

can be made.

6. A disturbingly unknown effect in moderately

dense gas to saturation conditions is the effect of association. Only for a few substances such as steam

does this seem to have received much attention.

7. Many instances ( 64 ) are available where a lack of sufficiently accurate knowledge of thermo- physical properties is pointed out. Here I would

just like to mention the surprising uncertainty in the thermal conductivity of air, in the dilute ( 65 ) and dissociated ( 66 ) gaseous state.

8. The establishment of a critically evaluated

data base of international recognition for the com- mon substances is recommended so that the analyses

suggested in some of the preceding items may be processed and not be vitiated by later discovery of an unsatisfactory base choice. '

ACKNOWLEDGMENT

Much of the above resulted from studies sponsored

by ASHRAE and the continuing support of the Office of Standard Reference Data, National Bureau of Standards,

with Dr. H. W. White as Program Monitor. These are gratefully acknowledged.

REFERENCES AND NOTES

1 Hilsenrath, J., Beckett, C.W., et al., "Tables

of Thermal Properties of Gases," NBS Circular 564,

1955, 488 pp.; republished with corrections as Tables

of Thermodynamic and Transport Properties , Pergamon

Press, 1960, 478 pp.

2 National Bureau of Standards - National Advisory Council on Aeronautics, "Tables of Thermal Properties of Gases," issued loose-leaf, 1948-1952.

3 Din, F. , ed., Thermodynamic Functions of Gases , Vol. 1, Butterworths , London, 1956, 175 pp.

4 Din, F., ed., Thermodynamic Functions of Gases , Vol. 2, Butterworths, London, 1956, 201 pp.

5 Din, F., ed., Thermodynamic Functions of Gases , Vol. 3, Butterworths, London, 1961, 218 pp.

6 For information on the International Association for the Properties of Steam, contact Dr. H. W. White, OSRD, National Bureau of Standards, Washington,

DC, 20234.

7 That for thermal conductivity may be exemplified by the volume, Thermal Conductivity 15 (V. V. Mirkovich, ed.), Plenum, New York, 1978, 493 pp. This volume also contains a list of earlier thermal conductivity conference publications.

8 Two detailed surveys of work on transport

properties by the author in Thermodynamic and Transport Properties of Gases, Liquids and Solids (Y. S. Touloukian, ed.), ASME, New York, 1959, pp. 40-69,

and in Progress in International Research on Thermodynamic and Transport Properties (E. F. Lype and J. Masi, eds.), ASME, New York, 1962, pp. 313-339, may

be cited as examples. The symposium volumes them- selves are further evidence.

9 Chapman, S. and Cowling, T.G., The Mathematical Theory of Non-uniform Gases , 1st ed., Cambridge

University Press, 1939. (The second edition, of 431

pages, appeared in 1952 and the third, with D. Burnett,

of 422 pages, appeared in 1970.)

10 For the material on reasonably dilute gases,

Bird, R.B. and Spotz, E.L., "The Virial Equation of State," CM 599, 1950, University of Wisconsin, 136 pp., may be cited as an example. Report CF 1504-A, 1952, 168 pp., served as an update. Similar revisions of other material occurred.

11 Hirschfelder , J.O., Curtiss, C.F., and Bird, R.B., Molecular Theory of Gases and Liquids , Wiley, New York, 1954, 1219 pp. (A revision, of 1249 pp., appeared in 1964.)

12 Bird, R.B., Hirschf elder , J.O., and Curtiss,

C.F., Transactions of the American Society of Mechanical Engineers , Vol. 76, 1954, pp. 1011-38.

13 Zwolinski, B., Wilhoit, R.C., and Reed, CO.

published a comprehensive index of 732 pages as TRC Publication 100, Texas A & M University, 1974.

14 Stull, D.R. and Prophet, H. , "JANAF Thermochemical Tables," 2nd ed., NSRDS-NBS 37, 1971, 1141

pp. Supplements are being published at irregular

intervals in the Journal of Physical and Chemical Reference Data.

15 Touloukian, Y.S., Transport Properties in Gases (A. B. Cambel and J. B. Fenn, eds.), Northwestern University Press, 1958, pp. 12-24. Information on later developments are contained in the Center's Annual Reports

.

16 Johnson, V.J. and Diller, D.E. gave, in a not generally available NBS Report 9782, 1970, 57 pp., an extensive account of their work and publications. A

greatly reduced description in 1976 was given by

Diller, D.E., Advances in Cryogenic Engineering , Vol.

21, pp. 522-31. Frizen, D.J. and Mendenhall, J.R., NBS TN 1005, 1978, 112 pp., list publications and services from 1953 to 1977.

17 Grunberg, L. , Achema Jahrbuch, 1971-3, pp. 634-8, reviewed the work of the NEL fluids group. NEL Publication Yl/203, 1979, 26 pp., is an index to all NEL publications on fluids from 1961 to 1978. Note that this index does not list earlier MERL publications . 18 Various issues of the CODATA Newsletter, 51 Blvd. de Montmorency, Paris, France may be consulted. Another source is Angus, S., PC/R30, 1975, IUPAC Thermodynamics Tables Center, Imperial College, London,

17 pp.

19 NBS Administrative Bulletin 78-21, May 18, 1978, 6 pp., lists managerial personnel for the new organizational structure.

20 See references 9, 11, 12, 28, 50, etc.

51
21 Possibly the most accessible source in English is the account on page 89 of the M.I.T. Press

1965 translation of Thermal Conductivity of Gases and Liquids , by N. V. Tsederberg.

22 Ho, C.Y., Powell, R.W., and Liley, P.E., "Thermal Conductivity of the Elements - A Comprehensive Review," Journal of Physical and Chemical Reference Data , Vol. 3, Suppl. 1, 1974, 796 pp.

23 Reynard, K.W. and Walton, J., "Thermal Con- ductivity of Liquid Aliphatic Hydrocarbons," Engineering Science Data Unit Item No. 67018, 1967, 14 pp.

24 Riedel, L., "New Measurements of Thermal

Conductivity of Organic Liquids," (in German), ChemieIngenieur-Technik , Vol. 23, No. 13, 1951, pp. 321-4.

25 Irving, J.B. and Jamieson, D.T., "Thermal Conductivity Measurement by an Improved 'Hot Wire' Method," NEL 609, 1976, National Engineering Laboratory, East Kilbride, Scotland, 46 pp. 26 Missenard, A., "Researches on the Conductivity of Liquids and of Organic Gases," (in French), Cahiers de la Thermique , No. 2, Paris, France, 1971,

146 pp.

27 Liley, P.E., Thermophysical Properties of Refrigerants , ASHRAE, New York, 1973, 237 pp; 2nd ed.,

1976.

28 Reid, R.C., Prausnitz, J.M., and Sherwood,

T.K. , The Properties of Gases and Liquids , 3rd ed.,

McGraw-Hill, New York, 1977, 669 pp.

29 Robbins, L.A. and Kingrea, C.L., "Estimation

of Thermal Conductivities of Organic Liquids Over Useful Temperature Ranges," Petroleum Refiner , Vol.

41, No. 5, 1962, pp. 133-41.

30 Latini, G. and Pacetti, M. , "Liquid Thermal

Conductivity, Correlations and Estimations," Bulletin

I.I.F./I.I.R. , Vol. 57, No. 6, 1977, pp. 1445-74. A

greatly condensed version appears in Thermal Conductivity 15 (V. V. Mirkovich, ed.), Plenum, New York,

1978, pp. 245-53.

31 Scheffy, W.J. and Johnson, E.F., "Thermal Conductivities of Liquids at High Temperatures,"

Journal of Chemical and Engineering Data , Vol. 6, 1961, pp. 245-9.

32 Lenoir, J.M., "Effect of Pressure on the Thermal Conductivity of Liquids," Petroleum Refiner , Vol. 36, No. 8, 1957, pp. 62-4.

33 Venart, J.E.S. and Mani, N. , "Thermal Con- ductivity, Anomaly in Temperature Dependence for Liquids," Canadian Journal of Chemistry , Vol. 49, 1971, pp. 2468-9; See also Mani, N. and Venart, J.E.S., "The Thermal Conductivity of Some Organic Fluids:

HB-40, Toluene and Dimethylphthalate," Proceedings

of the 6th Symposium on Thermophysical Properties

(P. E. Liley, ed.), ASME, New York, 1973.

34 Hanley, H.J.M., Sengers, J.V., and Ely, J.F., "On Estimating Thermal Conductivity Coefficients in the Critical Region of Gases," Thermal Conductivity 14 ((P.G. Klemens and T.K. Chu, eds.), Plenum Press, New

York, NY, 1976, pp. 383-408.

35 Watson, J.T.R. , "Thermophysical Properties

of Refrigerant 12," H.M.S.O., Edinburgh, Scotland,

1975, 183 pp.

36 Venart, J.E.S. and Mani, N., "The Thermal

Conductivity of Refrigerant 12," Transactions of the CSME , Vol. 3, 1975, pp. 1-9.

37 Schodel, G., Combined Heat Conduction and Heat Radiation in Convection Free Fluid Films , (in

German), Ph.D. Thesis, Technische Hochschule, Munich,

Germany, 1970, 133 pp.

38 Liley, P.E., "Correlations for Thermal Con- ductivity and Latent Heat of Saturated Fluids Near

the Critical Point," Proceedings of the 5th Symposium

on Thermophysical Properties (C. F. Bonilla, ed.), ASME, New York, 1970, pp. 197-199.

39 Chang, T.K., Correlations and Calculations

for the Enthalpy of Vaporization, Thermal Conductivity

and Viscosity of Refrigerants , M.S. Thesis, Purdue

University, 1972, 136 pp. 40 Mason, E.A. and Monchick, L. , "Heat Conductivity of Polyatomic and Polar Gases," Journal of Chemical Physics , Vol. 36, 1962, pp. 1622-39.

41 Brokaw, R.S., "Predicting Transport Properties of Dilute Gases," Industrial and Engineering

Chemistry Process Design and Development , Vol. 8, 1969, pp. 240-53.

42 Barrales-Rienda, J.M., Dependence of the Thermal Conductivity on Temperature for Polyatomic

Polar Gases , Ph.D. Thesis, Madrid University, Spain,

1963, 135 pp. 43 Stiel, L. and Thodos, G., "The Prediction of the Transport Properties of Pure Gaseous and Liquid

Substances," Progress in International Research on Thermodynamic and Transport Properties (E. F. Lype,

ed.), ASME, New York, 1962, pp. 352-65.

44 Roy, D. and Thodos, G., "Thermal Conductivity

of Gases: Hydrocarbons at Normal Pressures," Industrial and Engineering Chemistry, Fundamentals , Vol. 7, 1968, pp. 529-34; "Thermal Conductivity of Gases: Organic Compounds at Normal Pressure," Industrial and Engineering Chemistry, Fundamentals , Vol. 9, 1970,

pp. 71-9.

45 Kestin, J., Ro, S.T., and Wakeham, W.A. , "An Extended Law of Corresponding States for the Equilibrium and Transport Properties of the Noble Gases,"

Physica , Vol. 58, 1972, pp. 165-211.

46 See, e.g., Childs, G.E. and Hanley, H.J.M.,

"The Viscosity and Thermal Conductivity Coefficients

of Dilute Nitrogen and Oxygen," NBS Technical Note

350, 1966, 27 pp.

47 See, e.g., Angerhofer, P.E. and Hanley, H.J.M., "The Viscosity and Thermal Conductivity Coefficients

of Nine Fluids: Preliminary Values," NBS Report 10700,

1971, 43 pp. Except for hydrogen and helium the values have been updated and republished in Journal of Physical and Chemical Reference Data , Vol. 1, 1972,

p. 1101; Vol. 2, 1973, p. 619; Vol. 3, 1974, p. 979; Vol. 6, 1977, p. 597; Physica , Vol. 60, 1972, p. 322; and NASA SP 3071, 1972, 426 pp. 48 Jamieson, D.T. , Irving, J.B., and Tudhope,

J.S., "Liquid Thermal Conductivity - A Data Survey to

1972, " H.M.S.O., Edinburgh, Scotland, 1975, 221 pp.

49 Touloukian, Y.S., Liley, P.E., and Saxena,

S.C., Thermal Conductivity - Nonmetallic Liquids and Gases , IFI/Plenum, New York, 1970, 707 pp. 50 Bretsznajder , S., Prediction of Transport

and Other Physical Properties of Fluids , Pergamon

Press, Oxford, 1971, 408 pp. 51 Jossi, J. A., Stiel, L.I., and Thodos, G.

,

"The Viscosity of Pure Substances in the Dense Gaseous

and Liquid Phases," AIChE Journal , Vol. 8, 1962, pp. 59-63.

52 Codegone, C, "The Prandtl Number of Refrigerants," Inst. Int. Froid Bull., 1953, pp. 61-6.

53 Codegone, C. , "Corresponding States for Viscosity, Thermal Conductivity and Prandtl Number,"

Allgem. Warmetech ., Vol. 8, 1957, pp. 49-53.

54 Johnson, M.W. , Correlations and Calculations

of the Prandtl Number of Refrigerants , M.S. Thesis, Purdue University, 1976, 90 pp; Johnson, M.W. and

Liley, P.E., Proceedings of the 7th Symposium on Thermophysical Properties (A. Cezairliyan, ed.), ASME, New York, 1978, pp. 739-43.

55 See the first reference cited in item 8 above.

56 See, e.g., references 11, 28, 50.

57 Bishop, P.J., Correlations of Potential Parameters of the Lennard-Jones m-6 Potential for the Methane Derivative Refrigerant Gases , M.S. Thesis, Purdue University, 1972, 97 pp. 52
58 Bishop, P.J. and Liley, P.E., Proceedings of the 6th Symposium on Thermophysical Properties (P. E. Liley, ed.), ASME, New York, 1973, pp. 111-16.

59 Hanley, H., Klein, M. , et al., "Recommendations for Data Compiling and for the Reporting of Measurements of the Thermal Conductivity of Gases," Journal of Heat Transfer , 1971, pp. 479-80; NBS Technical News Bulletin , Vol. 56, 1972, pp. 65-66.

60 Of the very many papers, two can be selected

as being representative. Aziz, R.A. , Chemical Physics

Letters , Vol. 40, 1976, pp. 57-60, selected an m-6 potential for neon by considering the three dilute

gas properties of second virial, viscosity and self- diffusion while for inversion to obtain the potential

see the Maitland and Smith paper in Proceedings of the 7th Symposium on Thermophysical Properties (A. Cezairliyan, ed.), ASME, New York, 1978, pp. 412-20.

61 Hanley, H.J.M. and Klein, M. , "Selection of the Intermolecular Potential Function," I. NBS Tech- nical Note 360, 1967, 82 pp; II. Transactions of the Faraday Society , Vol. 64, 1968, pp. 2927-38; III. Journal of Chemical Physics , Vol. 50, 1969, pp. 4765-70.

62 See, e.g., the first reference cited in item

60. A fuller account appears in Journal of Chemical

Physics , Vol. 65, 1976, pp. 3242-9.

63 See the extensive tabulation in the appendix

to reference 28. 64 For the thermal conductivity of the elements

see Powell, R.W. and Touloukian, Y.S., Science , Vol.

181, 1973, pp. 999-1008. For selected fluids see references 22, 27, and 49.

65 Liley, P.E., Proceedings of the 4th Symposium

on Thermophysical Properties (J. R. Moszynski, ed.),

1968, pp. 323-49; Irving, J.B., Jamieson, D.T., and

Paget, D.S., Transactions of the Institute of Chemical

Engineers (U.K.) , Vol. 51, 1973, pp. 10-13.

66 Liley, P.E., Proceedings of the 6th Conference on Thermal Conductivity (M. L. Minges and G. L. Denman, eds.), AFML, Dayton, Ohio, 1966, pp. 3-14.

67 Klein, M. , Journal of Research of the National Bureau of Standards , Vol. 72A, 1968, pp. 359-

423; AEDC-TR-68-92, 1968, 70 pp.

68 Maczek, A.O.S. and Highton, P.J., "The Cal- culation of Thermal Conductivity in Dilute Gas Mixtures of Polyatomic Species," paper presented at "Transport Properties of Fluids and Fluid Mixtures:

Their Measurement, Estimation, Correlation and Use,"

NEL Symposium, 10-11 April 1979, East Kilbride, U.K.

69 Stephan, K. and Lucas, K. , Viscosity of Dense

Fluids , Hemisphere, New York, 1979, 268 pp.

53 6 U. S. GOVERNMENT PRINTING OFFICE : 1300 311-046/253
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4. TITLE AND SUBTITLE The Technological Importance of Accurate Thermophysical

Property Information

5. Publication Date October 1980

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7. AUTHOR(S)

Jan V. Sengers and Max Klein

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16. ABSTRACT (A 200-word or less factual summary of moat significant inlonnation. If document includes a significant bibliography or

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separated by semicolons) Aeroscience; data accuracy; design; geothermal; process; thermodynamics; transport

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