NAT'L INST. OF STAND & TECH REFERENCE

A 11 ID 5 T7M131

MIST

PUBLICATIONS

o

\

Q

\

\

F

NBS TECHNICAL NOTE 1165

^•fAU o< *

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

A Thermodynamic

Surface for the

Critical Region

of Ethylene

100

NO. Il(,5
NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards' was established by an act of Congress on March 3, 1901. The Bureau's overall goal is to strengthen and advance the Nation's science and technology

and facilitate their effective application for public benefit. To this end, the Bureau conducts

research and provides: (1) a basis for the Nation's physical measurement system, (2) scientific and technological services for industry and government, (3) a technical basis for equity in trade, and (4) technical services to promote public safety. The Bureau's technical work is per- formed by the National Measurement Laboratory, the National Engineering Laboratory, and

the Institute for Computer Sciences and Technology.

THE NATIONAL MEASUREMENT LABORATORY provides the national system of

physical and chemical and materials measurement; coordinates the system with measurement

systems of other nations and furnishes essential services leading to accurate and uniform

physical and chemical measurement throughout the Nation's scientific community, industry,

and commerce; conducts materials research leading to improved methods of measurement,

standards, and data on the properties of materials needed by industry, commerce, educational

institutions, and Government; provides advisory and research services to other Government

agencies; develops, produces, and distributes Standard Reference Materials; and provides

calibration services. The Laboratory consists of the following centers:

Absolute Physical Quantities2 — Radiation Research — Chemical Physics —

Analytical Chemistry — Materials Science

THE NATIONAL ENGINEERING LABORATORY provides technology and technical ser- vices to the public and private sectors to address national needs and to solve national problems; conducts research in engineering and applied science in support of these efforts; builds and maintains competence in the necessary disciplines required to carry out this research and technical service; develops engineering data and measurement capabilities;

provides engineering measurement traceability services; develops test methods and proposes

engineering standards and code changes; develops and proposes new engineering practices;

and develops and improves mechanisms to transfer results of its research to the ultimate user. The Laboratory consists of the following centers:

Applied Mathematics — Electronics and Electrical Engineering2 — Manufacturing

Engineering — Building Technology — Fire Research — Chemical Engineering2

THE INSTITUTE FOR COMPUTER SCIENCES AND TECHNOLOGY conducts

research and provides scientific and technical services to aid Federal agencies in the selection, acquisition, application, and use of computer technology to improve effectiveness and

economy in Government operations in accordance with Public Law 89-306 (40 U.S.C. 759), relevant Executive Orders, and other directives; carries out this mission by managing the Federal Information Processing Standards Program, developing Federal ADP standards

guidelines, and managing Federal participation in ADP voluntary standardization activities; provides scientific and technological advisory services and assistance to Federal agencies; and

provides the technical foundation for computer-related policies of the Federal Government.

The Institute consists of the following centers:

Programming Science and Technology — Computer Systems Engineering.

'Headquarters and Laboratories at Gaithersburg, MD, unless otherwise noted; mailing address Washington, DC 20234. 'Some divisions within the center are located at Boulder, CO 80303.
A Thermodynamic Surface for the

Critical Region of Ethylene

J.M.H. Levelt Sengers, J.W. Gallagher,

F.W. Balfour, and J.V. Sengers

Thermophysics Division

Center for Chemical Engineering

National Engineering Laboratory

National Bureau of Standards

Washington, DC 20234

t*T OF

*^fAU 0*

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

Issued October 1982
National Bureau of Standards Technical Note 1165

Natl. Bur. Stand. (U.S.), Tech. Note 1165, 85 pages (Oct. 1982)

CODEN: NBTNAE

U.S. GOVERNMENT PRINTING OFFICE WASHINGTON: 1982

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

Price $5.00

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

1. INTRODUCTION

2. FUNDAMENTAL EQUATION

3. THE EQUATION OF STATE

4. COEXISTENCE PROPERTIES

5. SPEED OF SOUND

6. OTHER FORMULATIONS

7 . THE EFFECT OF PRESSURE AND TEMPERATURE ERRORS ON DENSITY

3. THE EFFECT OF IMPURITY ON DENSITY

9. REFERENCES

TABLE I PARAMETERS IN THE THERMODYNAMIC POTENTIAL FOR ETHYLENE ....

APPENDIX A. REVISED AND EXTENDED SCALING EOUATIONS FOR THE THERMODYNAMIC

PROPERTIES OF FLUIDS

APPENDIX B. COMPARISON WITH EXPERIMENT

APPENDIX C. TABLES OF THERMODYNAMIC PROPERTIES

APPENDIX D. LISTING OF COMPUTER PROGRAMS

APPENDIX E. UNITS AND CONVERSION FACTORS

FIGURES

Page

2

3

5

6

6

7

8

8

10

12

13

19

31

57

67

68

m

A Thermodynamic Surface for the Critical Region of Ethylene

by

J. M. H. Levelt Sengers, J. S. Gallagher,

F. W. Balfour, and J. V. Sengers

Thermophysics Division

Center for Chemical Engineering

National Engineering Laboratory

National Bureau of Standards

Washington, DC 20234

F. W. Balfour's present address is Ingalls Shipbuilding, Pascagoula, MS 39567. In the work

reported on here she served as a Graduate student

under J. V. Sengers whose principal association is

with the Institute for Physical Sciences and Technology, University of Maryland, College Park, MD 20742.

Tables are presented of thermodynamic properties of ethylene in the range 279-300 K in

temperature, 5.75 - 10.5 mol/dm 3 in density, which range includes the critical point. The

tables presented here are based on the critical-point scaling laws and incorporate the

critical anomalies in a proper fashion. The tables thus complement the formulation of the

equation of state of fluid ethylene by McCarty and Jacobsen (NBS Tech. Note 1045, 1981)

which does not claim accuracy near the critical point. The predictions of the present

formulation are compared with four sets of recent PVT data, and with speed-of-sound data.

Tables are presented of pressure, energy, enthalpy, entropy, specific heats and speed of

sound as function of temperature along finely-spaced isochores. The computer program

required for table generation is included. Even if the surface were perfect, the reliability of densities calculated at experimental pressures and temperatures of limited accuracy

declines rapidly as the critical point is approached. Contour plots in P-T space are presented of regions to be avoided in custody transfer for given uncertainties in pressure,

temperature and sample composition.

Key words: critical region; custody transfer; density; enthalpy; ethylene;

equation of state; impurity; scaling laws; specific heat;

speed of sound; tabular values; thermodynamic properties.

This work was part of a Joint Industry - Government project under the sponsorship of

Celanese Chemical Company, Cities Service Company, Continental Oil Company, Gulf Research

and Development, Mobil Chemical Company, Monsanto Polymers and Petrochemicals Company,

Phillips Chemical Company, Union Carbide Corp. and the National Bureau of Standards.
1. Introduction

A formulation is presented of the thermodynamic behavior of ethylene in a region around

the critical point extending from 5.75 to 10.5 mol/dm 3 in density and from 279 to 300 K in

temperature. A correct formulation of this near-critical region is more urgent for ethylene

than for most other fluids, because in the climatic conditions of the United States the

fluid transported in pipes can assume states located in this region. It is well recognized

that most engineering equations of state are deficient in representing near-critical states

[1,2]. Our formulation of the thermodynamic behavior of ethylene derives from a thermodynamic potential which obeys the critical-point scaling laws; it contains a first correction to

scaling and also a revision to scaling designed to accommodate the lack of symmetry of the

gas-liquid phase transition. The adjustable parameters in the potential were obtained by a fit to the PVT data of Hastings et al . [3] and to the speed-of-sound data of Gammon [4].

The advantage of our formulation is that the critical anomalies that are common to all

fluids are properly incorporated. For instance, the flatness of the critical isotherm,

which is hard to describe by analytic equations of state, is built into our potential. Its strength is particularly striking when it comes to representing the specific heat at con- stant volume, C , and the speed of sound, C . The weak divergence of C cannot be described

by analytic free energy surfaces. This divergence, however, causes the speed of sound to

approach the value zero at the critical point, a feature properly incorporated in our potential. The excellent speed-of-sound data of Gammon therefore form a crucial test for the

adequacy of our thermodynamic surface. We stress that, by the use of so-called parametric

variables, we have closed-form expressions for all thermodynamic properties.

We will describe how our potential is constructed, and proceed to compare it with

recent experimental PVT data from three sources and with vapor pressures and coexisting

densities from two sources. Comparisons are also made with the predictions of the global

equation of state of ethylene recently published by McCarty and Jacobsen [5], From these

comparisons it will be evident that our potential will serve as a useful and necessary

supplement in a region where the global equation is essentially deficient. In appendices, we present the equations defining our potential and a comparison of all data points me tioned above with the predictions of our surface. A table of the thermodynamic properties

pressure, energy, entropy, enthalpy, specific heats C

p and C and speed of sound C , is

presented along finely-spaced isochores with temperature as an entry. A table of saturation

properties is included. The computer programs for generation of these tables are included.

They contain an inversion routine which permits transformation from pressure to density as an independent variable.

For the convenience of the user concerned with custody transfer, we conclude the main

body of the paper with a discussion of the uncertainties introduced in the density calculated from our surface due to limited precision in the measurement of pressure and temperature, and due to the presence of impurity. Contour plots in P-T space indicating regions in

PT space to be avoided if a certain precision in density is desired, are included in this

paper. Our work has been part of a joint industry-U.S. Government project to determine. the

thermodynamic properties of ethylene.
2. Fundamental Equation

At a critical point, thermodynamic behavior is anomalous. The critical point is characterized by the facts that the compressibility KT

= - (I/V)(aV/3P) T and the specific heat

C diverge and the coexisting densities Pj>p

v becomes equal. We write, asymptotically near

the critical point

K* = r|AT*|" Y

,

Ap* = B|aT*| B. (1)

Here asterisks denote reduced properties, while AT* = (T-T )/T and Ap* = (pj~p v )/2p

c

- The

critical exponent y equals 1, 3 equals 1/2 for classical equations of state of the type of

Van der Waals* equation. In real fluids, y equals about 1.24 and 6 is of the order 1/3.

The critical-point scaling laws are constructed so that they yield the correct critical

exponents; although one can define as many critical exponents as one sees fit, only two of

them are independent. Their values are given by theory and they are the same for all fluids.

Our fundamental equation incorporates the scaling laws. The thermodynamic potential

used in our work is that introduced by Ley-Koo and Green [6]. It is the dependent variable

p = p*/y* as a function of y = y*/T* and T = -1/T*. Here P is the pressure, y is the chemical potential and T the absolute temperature. Asterisks denote reduced properties: P* = P/P_»

T* = T/T and y* = yp /P , where P is the critical pressure, T the critical temperature

and p the critical density. In terms of this potential, we have

(3P/3T) ~ = U ,

(8P/3y)~ = p , (2)

where U is the reduced energy density U = U*/V* and p the reduced mass density, while the

other thermodynamic functions: Helmholtz energy density A = A*/V*, enthalpy density

H = H*/V* and entropy density S = S*/V* follow from

(3)

Since all variables are intensive, the coexistent phases collapse onto a curve, which, in

the y, T plane, can be parametrized by the analytic relation

y (T) = y

c + z y\j ATJ',

where AT = (T-T )/T. In scaling, the physical variables y, T are transformed to a new coordinate system, one axis of which is the curve y (T), while the other intersects the

first at the critical point. The two scaling variables are linear combinations of v-\i a and

AT:

A

=

P y

- P »

H = P

- U f 5

S

= H

-

P y ,
u^ = jj(T) - yQ

(T) = Ay/a ,

U t

= AT + C Ay , (4)

where a is a constant related to the scale of y. The term cAy breaks the liquid-vapor

symmetry.

The potential P is decomposed into two parts, one part, P , that is regular in the

scaling variables and one, AP, that contains the critical anomalies with correct power-law

dependence. We have assumed for P„,„ : r reg

^reg

= K^ + A

^ + Pn A

^ A^ '

-

i (5)

P n (T) = 1 + E P. (AT) J

. ° j=l J

AP, in scaled form, is given by

*>- akci u

ti 2"° 4vJi+ ak ^ti

2"°+ii

»i(£v) (6)

\l u

t

l / \l u tl /

The first term represents asymptotic scaling, the second a correction to scaling. The

critical exponents a, 3, 6 are those characterizing the divergence of the specific heat at constant volume C , the shape of the coexistence curve, and the shape of the critical isotherm,

respectively. The leading term contains one more adjustable constant k , while the function

g is universal, i.e., the same for all fluids. The correction term contains a new independent critical exponent A-,, also given by theory, and a new free constant k

1

. The

function g 2 is the same for all fluids.

All thermodynamic functions can be given in algebraically closed form by the device of

transformation to parametric variables [7]

Ay = au = r 36

a e (1-e 2

) ,

ut

= r (l-b 2

e 2

) (7)

The variable r measures "distance from the critical point", while e is measured along a contour of constant r. e reaches the values +1 on the phase boundary; b

2 is a constant

predicted to be universal. The critical anomalies are all imbedded in the r-dependence

while the dependence of the thermodynamic functions on e is always in the form of simple

polynomials or their ratios. All relevant equations are given in Appendix A. Note that the

functions are listed separately for the one- and two-phase regions.

The constants defining our potential were obtained as follows. The critical exponent

values a,B,y,6,A 1 are those predicted by theory [8]. The critical parameters, the five

parameters in the scaling function: a, k , k l5 c, b

2 and the four "background" parameters
P ls P 2 , P3 and P u were determined by a fit to the PVT data of Hastings et al . [3], while we imposed the condition that the slope of the vapor pressure curve at the critical point be

that of the vapor pressure data of Levelt Sengers and Hastings [9], that the critical point

lie on the vapor pressure curve and that the diameter of the coexistence curve be that

measured by Douslin and Harrison [10]. This implies that the values of T and P are con- strained to be on the vapor pressure curve and cannot be fitted independently. Two background parameters vi>V3 were determined by a fit to the speed-of-sound data of Gammon [4].

The other two, y and yls are related to the zeros for energy, entropy and enthalpy, and were fixed by tying the surface to that of McCarty and Jacobsen [5] at one point, 298.15 K and 6 mol/dm 3

. The parameters characterizing our potential are listed in Table I. The

range of validity of the potential is indicated in Fig. 1.

3. The Equation of State

We compare the predictions of our potential for the equation of state of ethylene with

experiment. The experimental data are those of Hastings et al . [3] for a 99.993% pure

sample, to which the potential was fitted, those of Douslin and Harrison [10], Trappeniers

et al. [11] and Thomas and Zander [12,13]. Older data have been adequately reviewed in the

IUPAC formulation of Angus et al . [14], and in the reviews of Date [15] and Vashchenko [16].

The potential represents the data of Hastings et al. with a reduced chi-square of 1.3

if the uncertainties are estimated as 5 x 10" 5 MPa in pressure, 3 x 10~ 3 mol/dm 3 in density

and 5 x 10

-t+ K in temperature. It is to be kept in mind that our data were fitted to these

close tolerances even though the deviation plots of Figs. 2-13 show occasionally large

density deviations. The percentage differences in density between the data and our surface,

assuming the pressures to be the same, and, alternatively, the percentage differences in

pressure, assuming the densities to be the same, are shown for the various isotherms in

Figs. 2-13. At 298. 15K (Fig. 2) the surface represents our own data to well within 0.1% in

density. The agreement between the data sets of [3], [10] and [11] is almost within the

0.1% tolerance originally set as a goal for the U.S. Government - Industry joint project on properties of ethylene. The data set of Thomas and Zander [12,13] shows considerably more scatter than the other three sets, without, however, showing systematic departures from our formulation. The pressure deviations are similarly small at this temperature, with a tendency to grow in the highly compressed fluid, as is to be anticipated [Fig. 3]. When the

critical point is approached, the density departures between the data sets, and their

departures from the surface, increase dramatically, while the pressure deviations remain more or less the same (Figs. 4-10). At the temperatures from 0.7-3.7 K above the critical

temperature, the density departures reach values larger than 0.5% and on isotherms spanning

the critical the largest departure is 15%. The pressure deviations, however, remain as well-behaved as at 298. 15K if not better, the departures being of the order of 0.02% in the

range around critical (Figs. 11-13). This is a good illustration of the difference between

"density" and "field" variables in the vicinity of a critical point. ("Density" variables

are those that are different in coexisting phases while "field" variables are the same.)

Due to the strong divergences of the compressibility and expansion coefficients, small
systematic differences in temperature and pressure scales between the various laboratories

are amplified when the densities are compared. Furthermore, the effect of impurity is

largest at the critical point, and small differences in sample composition can lead to large variations in density.

A study of the plots Figs. 2-13 will convince the reader that most of the region

covered in this report should be avoided if an accuracy of 0.1% in density is desired in

custody transfer. Even if our surface were perfect, the finite precision of industrial

pressure- and temperature measurement will result in large errors if the density is calculated from the equation of state.

Appendix B, Table II, contains the deviations of the PVT data sets [3], [10], [11],

[12], [13] and [14] from the present formulation.

4. Coexistence Properties

Vapor pressures from 279.15 K to the critical temperature are compared in Fig. 14.

Data sources are those of Levelt Sengers and Hastings [9] and those of Douslin and Harrison

[10]. These two data sets were shown to agree within combined error of 10" 4 MPa at temperatures below 240 K [9]; the departures are systematic at higher temperatures, and reach a maximum of 7 x 10_l+ MPa at the critical point. A satisfactory explanation for the differ- ence has not been given. It is larger than expected on the basis of the agreement of pres- sure scales (1 in 20,000) and temperature scales (1 mK) and not quite of the form expected

for a difference in purity [7]. Nevertheless, the agreement between the data sets [9] and

[10], better than 2 parts in 104

, is an order better than that between these sets and the

older data (cf. [10], p. 311). Table III in Appendix B contains the deviations of the vapor

pressures data sets [9] and [10] from our formulation.

Coexisting densities of Refs. [3] and [10] are compared with our formulation in

Fig. 15. The agreement between the two data sets and the formulation, to +0.02 mol/dm3

, is

satisfactory in this region close to the top of the coexistence dome.

5. Speed of Sound

As we mentioned before, we determined the parameters m

2

, jL in our potential from a fit

to Gammon's speed-of-sound data [4], accepting his density and temperature values as independent variables. It should be stressed that the anomalous contribution to the speed of

sound that drives speed of sound to zero at the critical point has. been completely predicted

from the part of the potential that was determined by the PVT data alone. A substantial loss

of accuracy is to be expected when second derivatives are calculated from the potential. We

therefore consider the result of our procedure, a prediction of the speed of sound that is

generally well within 1% from experiment, as very satisfactory. A global view of the speed

of sound within the range of our correlation is shown in Fig. 16. Fig. 17 shows the departures of the speed of sound from our surface. It should be mentioned that we had to omit a few of Gammon's data points because our surface predicted them to be inside the two-phase

region. Also, we omitted the data points on the critical isotherm within + 10% from the
critical density, these points being heavily affected by dispersion.

Fig. 16 and 17 reveal one defect of our model: on subcritical isotherms, the speed of

sound, instead of continuing to fall as the phase boundary is approached, passes through a minimum and then experiences a minute increase in the last percent of density from coexistence. We believe this behavior to be unphysical. It was not present when we fitted our potential to the experimental data for steam. We have, however, not been able to eliminate

this artifact by the device of clamping more tightly on the PVT data near the phase boundary, nor by reducing the range of the fit. It is likely that speed-of-sound data of the quality

of [4] may contain more information than even high-quality PVT data; it would be interesting

to use the sound data to determine some of the parameters in the scaled part of the potential.

Table IV in Appendix B contains a listing of the departures of the experimental data

from the present formulation.

6. Other Formulations

A recent comprehensive correlation of the properties of ethylene, in the form of an equation of state based on the same data sets considered in this paper, is that of McCarty

and Jacobsen [5]. It was preceded by several other correlations, two of which we will

consider here: the IUPAC formulation by Angus et al . [14], which formulation is based on a part-graphical, part-analytic representation of the PVT properties of ethylene obtained

prior to 1972; and the correlation obtained by graphical means by Harrison and Douslin [7]

of their own data. The solid curves in Figs. 2-13 indicate the departures of the McCarty - Jacobsen formulation from our own. Since the Helmholtz function of McCarty and Jacobsen is

analytic, it has difficulty representing the flatness of near-critical isotherms, as was recognized by the authors. At 298.15 K the departures, though systematic, are limited to a maximum of 0.3% in density, but as the temperature approaches the critical the departures

become more severe. At temperatures within 1 K from critical where our formulation agrees

with all data to well within 0.1% in pressure, the McCarty-Jacobsen formulation departs by

several tenths of a percent in pressure in a systematic fashion. These differences are magnified when derived properties are considered. An example is shown in Fig. 17 for the

enthalpy of ethylene, where enthalpies according to three formulations are compared along

the 283.15 K, 288.15 K, and 298.15 K isotherms. The graphical method of Harrison and

Douslin, if applied with care to excellent data, should be expected to give better results

than can be obtained with a fit to an empirical thermodynamic surface that is seldom quite

true to the data. A possible exception is the near-critical regime: The anomalous curva- ture of isochores may be missed by graphical techniques and by analytic surface alike, but

is correctly incorporated in our potential. The intercomparison in Fig. 18 shows that

the Harrison and Douslin enthalpies show no density-dependent departures from our surface

and have, therefore, been yery carefully evaluated. At 298.15 K the offset is about 8 J/mol

and could have been eliminated had we tied our enthalpy at 298.15 K, 6 mol/dm 3 to that of

Harrison and Douslin, rather than to that of McCarty and Jacobsen. At the other two temperatures a systematic offset of 20 J/mol is observed. We do not know why a 12 J/mol

enthalpy difference is picked up between 298.15 and 288.15 K.

7
At 298.15 K our enthalpies agree closely with those of McCarty and Jacobsen, but the

density dependence of the two formulations is different. Increasing departures build up as the critical point is approached.

The departures of the IUPAC formulations show strong systematic trends. This formulation

was based on older data and was never claimed to possess high quality in the critical region.

First and second derivatives according to the McCarty - Jacobsen formulation are com- pared with our own in Figs. 19, 20. The first derivatives U, H and S have somewhat different density dependence in the two formulations. Moreover, appreciable departures build up

around the critical density and near the critical temperature. The departures of C , C and the speed of sound are substantial. They are about 1% at 298.15 K, 5 - 10%, at 288.15 K and 20 - 40% at 283.15 K (0.8 K above critical). An analytic representation cannot describe

the divergence of C and the accompanying decline to zero of the (thermodynamic) speed of

sound while the divergence of C is not strong enough; so these large departures are not

surprising. The authors themselves did not claim accuracy in the critical region. Since we

have represented the speed-of-sound data to about 1% in accuracy, we are confident that our

model represents thermodynamic behavior, such as a weakly diverging C , accurately.

7. The Effect of Pressure and Temperature Errors on Density

In custody transfer, the density of ethylene will be calulated from its measured pres- sure and temperature. Since these quantities are measured with limited accuracy, an error

in density will result that is given by

3p _ iov \ if

or ^ - (PK

T

) f , (8)

& . .„ 6T . -K

T (f) «T . (9)

K V

In view of the strong divergence of the compressibility KT and the expansion coefficient a , the density error resulting from inaccuracy in the measurement of P or T is a maximum at the

critical point. We show the region in P-T space that should be avoided if an accuracy of

0.1% in density is desired and the pressure is measured with an accuracy of 0.1, 0.05 and

0.02%, respectively, (Fig. 21); or the temperature is measured to 0.02, 0.01 or 0.005 K,

respectively, (Fig. 22).

8. The Effect of Impurity on Density

The present formulation of the equation of state of ethylene is based on the PVT data

obtained for 99.993% pure ethylene, with ethane as the prime impurity. The formulation

permits the calculation of the density of an ethylene sample from its pressure and temperature. If impurities are present in the sample of interest, the predicted density will

differ from the actual one. It is of interest to know what effect a known impurity has on density, and how the effect varies with the temperature and pressure.

Under simplifying assumptions, this question can be answered. We will assume that the

impure fluid is in corresponding states with the pure host, and that the impure system

8
displays pseudo-critical constants that are shifted from those of the pure host by amounts

linear in concentration:

Txc

= T

c

(1 + ax) ,

Pxc

- P

c

(1 + bx) .

Vxc

= V

c

(1 + (a-b)x) . (10)

Both assumptions are reasonable and readily justifiable in dilute mixtures; the only difficulty with the model is the actual assignment of the values of a and b, parameters characteristic of the host-impurity interaction. They can be determined from the critical parameters of the pure components in the case that the critical points are connected by a continuous critical line. For the sake of developing our estimate of the density error introduced by impurity, we will consider these parameters a,b as known.

An equation for the impurity-induced density error was derived by us [3]. It was obtained by applying the law of corresponding states to the pure host and the dilute mixture

at the same pressure and temperature. The following result was obtained for the change in

density:

SJL = - X [(a-b) + b PK

T

- aTa

p

]

= -x[(a-b) + bPK

T

- a(PK

T

) (I |£)] , (11)

where KT

is the compressibility, a the expansion coefficient of the pure host at T, P. It

is clear that Eq. (11) permits calculation of the impurity-induced error in density at any

point in P-T space once the constants a, b are known. The relation (11) should not be applied

too close to the critical point since the coefficient of the term in x diverges. More

seriously, an expansion in x has as little justification as one in p, which is known to be

invalid at the critical point.

A scrutiny of Eq. (11) immediately reveals that impurity-induced density errors will be

largest near the critical point. This is a consequence of the fact that both KT and a diverge strongly at this point. The precise nature of this density error will, of course,

depend on the values of a and b. Since these values form the most controversial part of our

model, we will consider only a few extreme cases.

(1) a = -.5, b = 0: a highly volatile impurity that depresses the critical temperature of the mixture strongly without affecting the critical pressure.

(2) a = .5, b = 0: a highly nonvolatile impurity that increases the critical temperature of the mixture strongly without affecting the critical pressure.

The cases (1) and (2) have opposite effects on the density. The impurity-induced density

error is given by

^=±0.5 x II - (P KT

) (£!£)] (5)

9
where the + sign refers to case 1, the - sign to case 2. In Fig. 23, we show the region in P-T space

that should be avoided in custody transfer if an accuracy in density of 0.1% is desired and if various amounts of an impurity very different in volatility from ethylene are present.

9. Tables of Thermodynamic Properties

In Appendix C we present the thermodynamic properties of ethylene in the critical region. It was not possible to organize this table along isobars, as in [5]. The extremely rapid variation of the

"density"-like properties p, U, H, S with P and T would preclude interpolation in such a table. We have therefore tabulated the properties along isochores, or at constant density, using temperature as the second entry (Table V). In addition, we present tables of saturation properties first with temperature, then with pressure as an entry (Table VI, VII).

The computer program required for the generation of thermodynamic properties of ethylene is listed

in Appendix D. Appendix E contains units and conversion factors.

Acknowledgements

R.D. McCarty and B.E. Gammon provided us with results of their work prior to publication.

9. References

[I] Sengers, J.V. and Levelt Sengers, J.M.H., The critical region, Chem. and Eng. News 46, 104, 1968.

[2] Levelt Sengers, J.M.H., Scaling predictions for thermodynamic anomalies near the gas-liquid critical

point, Ind. Eng. Fund. Si, 470, 1970.

[3] Hastings, J.R. , Levelt Sengers, J.M.H. and Balfour, F.W., The critical-region equation of state of

ethylene and the effect of small impurities, J. Chem. Thermodynamics J_2, 1009, 1980.

£4] Gammon, B.E., Velocity of sound in ethylene, presented at the Advisory Committee Meeting of the

Joint Industry-Government Ethylene Project, Boulder, Colorado (Dec. 6, 1978).

[5] McCarty, R.D. and Jacobsen, R.T., An equation of state for fluid ethylene, N.B.S. Tech. Note 1045,

1981.

[6] Ley-Koo, M. and Green, M.S., Consequences of the renormalization group for the thermodynamics of

fluids near the critical point, Phys. Rev. A 23, 2650, 1981.

[7] Schofield, P., Parametric representation of the equation of state near a critical point, Phys.

Rev. Letters 22, 606, 1969.

[8] Le Guillou, J.C. and Zinn-Justin, J., Critical exponents from field theory, Phys. Rev. B 21_, 3976, 1980.

[9] Hastings, J.R. , and Levelt Sengers, J.M.H. , Vapor pressure, critical pressure, and critical isochore

of ethylene, in Proceedings 7th Symposium on Thermophysical Properties, Cezairliyan, A., editor,

ASME, New York, 794 (1977).

[10] Douslin, D.R. , and Harrison, R.H., Pressure, volume, temperature relations of ethylene, J. Chem. Thermodynamics 8, 301 (1976).

[II] Trappeniers, N.J. Wassenaar, J., and Wolkers, G.J., Isotherms and thermodynamic properties of

ethylene at temperatures between and 150 C and at densities up to 500 amagat, Physica 82A , 305

(1976).

[12] Thomas, W. , Zander, M. , Quietzsch, G. , and Hartmann, H., Dichte des Aethylens fuer Temperaturen

von -30 C bis 80 C bei Drucken bis zu 100 bar, Herausgeber Hoechst AG, Frankfurt/M-Hoechst (1976).

[13] Thomas, W. , and Zander, M. , Pressure-density-temperature measurements of ethylene, Int. J. Thermophysics J_, 383 (1980).

10
[14] Angus, S. , Armstrong, B. , de Reuck, K.M. , Featherstone, W. , and Gibson, M.R. , International

Thermodynamic Tables of the Fluid State , Ethylene , 1972 , International Union of Pure and Applied

Chemistry, Division of Physical Chemistry, Commission on Thermodynamic and Thermochemistry,

Thermodynamic Tables Project, Butterworths, London (1974).

[15] Date, K. , Watanabe, J., and Uematsu, U. , Evaluation of P-V-T properties data, the most probable

values of the compressibility factor of gaseous ethane and ethene, Review of Phys. Chem. Japan 4_3, 92 (1973).

[16] Vashchenko, D.M. , Voinov Yu, F. , Voityuk, B.V., Dregulyas, E.K., Kolomiets Ya. , A., Labinov,

S.D. , Morozov, A. A., Neduzhii, I. A., (Principal Author), Provotar, V.P., A. Yu. Soldatenko,

Storozhenko, E.I., and Khmara, Yu. I., Thermodynamic and transport properties of ethylene and

propylene, (translated from the Russian as published by the State Committee of Standards of the

Soviet Ministry, U.S.S.R. , State Office of Standards and Reference Data, Series: Monograph No. 8,

1971), Office of Standard Reference Data, National Bureau of Standards, U.S. Department of Commerce,

Washington, D.C. (June 1972).

[17] Harrison, R.H. and Douslin, D.R., Derived thermodynamic properties of ethylene, J. Chem. Eng. Data

22, 24 1977.

[18] Waxman, M. and Davis, H.A., Equations of State in Engineering and Research, Adv. in Chem. Series

182, Chao, K.C., Robinson, R.L., Jr., editors. ACS, Washington, p. 285, 1979.

11
Table I. Parameters in the Thermodynamic

Potential for Ethylene

Critical Exponents

(fixed) B = 0.325

6 = 4.82

A = 0.50

Critical Parameters T

c

= 282.3452

p = 7.634 mol/dm 3 c

Parameters in

P c

= 5.0403 MPa (derived)

Scaling Function a = 23.9809

k

o = 1.37617

k

l = 0.7662

c

= -0.007833

b

2 = 1.67472

Pressure background

parameters Pi = 5.3439

h = -16.9686

hi = -0.181762 (derived)

Caloric background

parameters ^0

= -36.4812

h

= -27.35945

y 2 = -12.5003

^3

= -10.5742

12
APPENDIX A: Revised and Extended Scaling Equations for the Thermodynamic

Properties of Fluids.

A.l Reduced thermodynamic quantities

T P T T

T = - -£ S - H . S-± p = Z . _c

1 T * T P

c

' TPc

R - p fi - U X c _ S

T

c p " p- ' u -v*p- • s -v*p- ' c c c (A.l)

T

A = A . Is. h = JL.Ic ^ = [ l£

VT P

c

' VT P

c

' XT Uy

C T C T

c = JL _£ £--£•-£-

v V P P V P c c

(T is temperature, y is chemical potential, P is pressure, p is density,

U is energy, S is entropy, A is helmholtz free energy, H is enthalpy,

V is volume, CL. is heat capacity at constant V, C is heat capacity at

constant P).

A. 2 Thermodynamic relations

dP = Udf + pdy

dA = -UdT + ydp

(A. 2)

dH = -fdU + pdy

dS = -TdD - ydp

13
A = py - P

H = P - TU CA.3)

S=H-py=-TU-A

A. 3 Fundamental equations

AT = T + 1 (A.4a)

Ay = y - y

Q

(T) (A. 4b)

P = PQ

(T) + Ay + P

12 AyAT + AP (A. 5)

with

3

y (f) = y

c + Z y-CAT) 3 CA.6a)

j=l

~ ~ 3 ..... . Po

(T) = 1 + I P. (AT) 3 (A. 6b)

j=l

A. 4 Derived thermodynamic quantities

p. .at + l-^-l

\SAy/

AT

U = —=- - p—^- + P., Ay + tt^- (A. 8)

8 2AP

14
2~ 2~

C d P <Ty P. .2 v o ~

Ko 11

T dTZ dr XT

+

*• 2

1 1' - HS)J Cp = C

y

+ ^ |

> - T(-^r) (A.12)

A. 5 Critical exponents

a

Q

= a , a

x = a - Ax

3

Q

= B , 8

X = 8 + Ax (A. 13)

Yo

= Y • Yl = Y " A

]

with

2 - a = 8(6+1) , y = 8(6-1) (A. 14)

A. 6 Parametric equations for singular terms

Ay = r

B6a6(l-e

2

) (A. 15)

AT = r(l-b

2

6

2

) - cAy (A. 16)

15
* 2-ct

AP = .E r l ak.p.(6) (A. 17) 1=0 x x

(tf)Af " Jo [

r$ik

i e + "^-iH (A ' 18)

8AT J

i=0

/ 9AP

\8AT

E r ^ak.s.(6) (A. 19)

Ay

("~l)

= Jo [r

"YiT u

i<e) +2crBi- 1

k

ivi

(e) +c

2r-a

iak.w

i (e)] (A.:

> - i r i

"AP ft- 1 r»- ^ = ,?n r^-'k v (6) + cr'^ak w (6) (A.21)

3

2.,

3AuAT

2 ~\ 1

9 ^| - .Z r"a

iak.w.(6) (A. 22)

A. 7 Auxiliary functions

Pi

CG) = Poi

+ ?2i e2 + P4i

04 (A * 23)

S

i

(6) = S oi

+ S 2i

02

» S

i (6) = 2s2i

9 (A * 24)

q(0) = 1 + {b

2 (2B6-l)-3}62

- b

2

(2B6-3)6

4

(A. 25)

^(8) = [1 - b

2

(l-2B

i )6

2

]/q(e) (A.26)

v.O) = [3

i Cl-36

2

)6 - B6(l-e

2

)e]/q(6) (A.27)

16
w^S) = [(l-ai)(l-36

2

)s

i

(e) - 36(l-e

2

)es!(6)]/q(e) (A.28)

with

36-3Si

-b

2

a

iYi

^oi 4

2b (2-a.)(l-a.)a.

xy 06-36. -b

2

a. (266-1)

P2i

2b

2

(l-a.)a

i

P4i y 266-3

2a.

l

s . 01

= (2-a.)p .

36-36.

2b

2a.

i

S 2i

A. 8 Two-phase properties

Variables :

e = ±1

Ay =

AT = r(l - b

2

)

(A. 29)

(A. 30)

(A. 31)

Vapor pressure:

1 P = P (T) + Z r i ak.p. (1) (A. 32) vap o

v J i=o ii

17
coexisting densities:

PL+Pv - - 1-cw

p. -p. 2 i=0 i (A. 33)

helmholtz free energy:

A = p y

o

(T) - P

Q

(T) I r

" i'ak.p.(l)

i=0 ii (A. 34)

energy:

dP dy (T) 1 5 = -^ ~ P—

+ —4 Z (2-<*.) r * ak p (1)

dT dT l-t> i-0 x x (A.35)

entropy:

S = -P P (T) + P (T) - T

rdP dy

o

Ho

L dT dT -

1 ~ i + .1 r

2 ' ai ak.p.(l) - -^2 E (2-a.)r1_Cti ak.p.(l) (A. 36)

i=o i -1 i_t/ i=o

specific r heat C : v

C d

2 P d

2y / \2 1 -a. ^ = -zf-P-^ + -S-) - E (2-a.)(l-a)r X ak p (1) (A.37)

T

2 dT 2 dT

2 Vl-b2 / 1=0 X X X X

18
Appendix B. Comparison with Experiment

In Table II, the experimental PVT data are compared with the formulation (a) as pressure differences

under the assumption that the densities are exact and (b) as density differences under the assumption

that the pressures are exact. In Table III, saturation pressures and densities from two sources are compared with the formulation. In Table IV, the speed-of-sound data [4] are compared with the

theoretical prediction. The density (DENS) is in mol/dm3 and the speed of sound w in m/s. The legend

for the various data sources is as follows

1 DH [10]

2A HLSB [3], 99.993% sample

2B HLSB [3], 99.999% sample

3 TWW [11],

4 TZ [13]

19
Table II. Comparison of the experimental PVT data

from four sources with the formulation

EXPT TEMPERATURE PRESSURE (MPA) % DENSITY (M0L/DM3) % ID K EXP CALC DIFF EXP CALC DIFF

2A 298. 1500 8.32377 8.31908 .056 10.542100 10.547447 - .051

2A 293. 1500 7.33162 7.32880 .039 10.544500 10.548586 - .038

2A 289. 1500 6.54857 6.54693 .025 10.546700 10.549579 - .027

2A 283.6500 5.49438 5.49414 .004 10 .5^9500 10.550146 - .006

2A 282.3440 5.24955 5.24D57 - .000 10.550200 10.550143 .001

2A 281 .1393 5.02650 5.02643 .001 10.550*00 10. 551053 - .002

2A 280.6394 4.93481 4.93461 .004 10. 551000 10.551327 - .009

2A 280.3394 4.88010 4.87976 .007 10. 551200 10.552670 - .014

2A 280.0394 4.82552 4.82505 .012 10.551300 10.553901 - .025

2A 279.7394 4.77146 4. 77051 .020 10.551500 10.556070 - .043

2A 298. 1500 7.89748 7.89935 - .024 10.023900 10.021 107 .028

2A 285.6500 5.68640 5.68744 - .018 10.029900 10.026154 .037

2A 233.6500 5.34587 5.34697 - .020 10.030:»00 10.025659 .052

2A 282.3440 5. 12725 5. 12824 - .019 10.031500 10.025416 .061

2A 281 . 1393 4.92924 4.92977 - .01 1 10.0C2!00 10.027673 .044

2A 280.8393 4.88062 4.88086 - .005 10.032200 10.029998 .022

2A 280.7393 4.85455 4.86459 - .001 10.032300 10.0319C0 .004

2A 293. 1500 7.46225 7.46412 - .025 9.285400 9.281 344 .044

2A 293. 1500 6.68170 6.68233 - .009 9.287&00 9.285594 .021

2A 239. 1500 6.06666 6.06664 .000 9.289400 9.209482 - .001

2A 285.6500 5.53899 5.538 79 .004 9.290900 9.2923e4 - .016

2A 283.6500 5.24431 5.24431 - .000 9.291800 9.291 775 .000

2A 282.3440 5.05644 5.05660 - .003 9.292400 9.283973 .037

2A 281 .8393 4.98547 4.98552 - .001 9.292000 9.290874 .019

2A 281 .7693 4.97849 4.97853 - . 00 1 9.292600 9.291361 .013

2 A 298. 1500 7.29472 7. 29582 - .015 8.910500 8.907691 .032

2A 293. 1500 6.56545 6.56539 .001 8.912600 8.912e40 - .003

2a 289. 1500 5.99031 5.93965 .01 1 8.914300 ^8.918022 - .042

2A 285.6500 5.49642 5.49573 .013 8.915800 8.923034 - .082

2A 233.6500 5.22054 5.22022 .006 8.916700 8.923166 - .073

2A 282.3440 5.04511 5.04512 - .000 8.917200 8.916409 .009

2A 282. 1893 5.02483 5.02482 .000 8.917300 8.917943 - .007

2A 282.0993 5.01308 5.01306 .000 8.917300 8.918628 - .015

2 A 282.0949 5.01251 5.01249 .000 8.917300 8.918978 - .019

2A 282.0943 5.01246 5.01241 .001 8.917300 8.921296 - .045

2A 282.0936 5.01233 5.01232 .000 8.917300 8.918123 - .009

2A 282.0893 5.01 181 5.01 176 .001 8.917300 8.921527 - .047

2A 282.0891 5.01 176 5.01 173 .001 8.917300 8.919558 -.025

2A 282.0877 5.01 156 5.01 155 .000 8.917300 8.9181 14 - .009

2A 298.1500 7.23391 7.23474 • .01 1 8. 757700 8.755431 .026

2A 283.6500 5.21388 5.21 352 .007 8.763800 8.772971 - .105

2A 282.3440 5.04288 5.04269 - .000 8.764300 8.763615 .008

2A 282.2193 5.02695 5.02697 - .000 B. 76^300 8.762402 .022

2A 282. 1916 5.02346 5.C2345 .000 8 . 764400 8.766152 - .020

2A 282 . 1911 5.02344 5 02338 .001 8 764400 8.771465 - .081

2A 232 . 1 909 5.02335 5.02326 - .000 8. 764409 8.763 508 .010

2A 282. 1893 5.02316 5.023)5 .000 8. 76440? 8.765213 - .009

2A 282.1708 5.C2097 5.02080 .003 8 . 764400 8.784795 - .233

20
Table II. (Continued)

EXPV TEMPERATURE PRESSURE (MPA) % DENSITY (M0L/DM3) %

ID K EXP CALC DIFF EXP CALC DIFF

2A 303.1500 7.47231 7.47347 -.009 7.672200 7.670365 .024

2A 298.1500 6.88257 6.e8269 - .002 7.674000 7.67356C .006

2A 293.1500 6.29461 6.29437 .004 7.675800 7.677184 - .018

2A 289. 1500 5.82681 5.82639 .007 7.677200 7.681 333 - .054

2A 285.6500 5.42007 5.41985 .004 7.678500 7.683527 * .065

2A 284.6500 5.30464 5.30441 .004 7.678900 7.687088 .107

2A 283.6500 5.18952 5. 18940 .002 7 .679200 7.687745 -.111

2A 283.1500 5.13214 5. 13210 .001 7.679400 7.684553 - .067

2A 282.6500 5.07498 5.07498 - .000 7.679600 7.678838 .OtO

2A 282.5000 5.05789 5.05789 - .000 7.679600 7.675203 .057

2A 282.3440 5.04020 5.04016 .001 7.679700 7. 762056 -1 .072

2A 303. 1500 7.45336 7.45393 - .008 7.621 770 7.620178 .021

2A 298.1500 6.86844 6.86851 - .001 7.623570 7.623313 .003

2A 293. 1500 6.28553 6.28531 .003 7.625370 7.626623 - . 0^6

2A 269.1500 5.82149 5.821 17 .006 7.626300 7.629959 - .041

2A 285.6500 5.41783 5.41766 .003 7.628050 7.631947 - .051

2A 284.6500 5.30310 5.30300 .002 7.628420 7.632191 - .049

2A 283.6500 5. 18875 5. 18869 .001 7.628780 7.632357 - .053

2A 283. 1500 5.13169 5. 13171 - .000 7.628950 7.626546 .032

2A 282.6500 5.07481 5.07486 - .001 7.629130 7.606356 .299

2A 282.3440 5.04007 5.04016 - .002 7.629240 7.492949 1 .786

2A 303.1500 7.43832 7.43893 - .008 7.582800 7.581088 .023

2A 298.1500 6.85752 6.85760 - .001 7.584500 7.584204 .004

2A 293.1500 6.27857 6. 27834 .004 7.586300 7.587617 - .017

2A 289. 1500 5.81749 5.81716 .006 7.587800 7.591089 - .043

2A 285.6500 5.41617 5.41598 .004 7.589000 7.593476 - .059

2A 284.6500 5.30198 5.30191 .001 7. 589400 7.591987 - .034

2A 283.6500 5.18817 5. 18815 .000 7.589700 7.591210 - .020

2A 283. 1500 5. 13139 5. 13141 - .000 7.539900 7.587625 .030

2A 282.6500 5.07473 5.07477 - .001 7.590100 7.572202 .236

2A 282.3440 5.04016 5.04016 - .000 7.590200 7.534342 .729

2A 303.1500 7.40673 7.40710 - .005 7.499400 7.498349 .014

2A 298. 1500 6.83445 6.83453 - .001 7.501200 7.500903 .004

2A 293. 1500 6.26383 6.26359 .004 7.502900 7.504331 - .019

2A 289. 1500 5.80890 5.80863 .005 7.504300 7.505977 - .036

2A 285.6500 5.41252 5.41240 .002 7.505600 7.508351 - .037

2A 284.6500 5.29966 5.29959 .001 7.505900 7.508313 - .032

2A 283.6500 5. 18698 5. 18699 - .000 7.506300 7.505527 .010

2A 283.1500 5. 13070 5. 13076 - .001 7.506500 7.498144 .111

2A 282.6500 5.07449 5.07457 - .002 7.506600 7.471538 .467

2A 282.3440 5.0401

1

5.04016 - .001 7.506700 7.392577 1 .520

2A 298. 1500 6.58548 6.58491 .009 6.579700 6.581888 - .033

2A 293. 1500 6. 10120 6. 10096 .004 6.531300 6.582547 - .020

2 A 239. 1500 5.71 173 5. 71 176 - .001 5.582500 6.582234 .004

2A 285.6500 5.36833 5 36860 - .005 6. 583600 6.578960 .070

2A 233.6500 5.16997 5. 17027 - .006 6.534200 6.573036 . 170

2A 298.1500 6.38762 6.33666 .015 5.899000 5.902252 - .055

2A 262.3440 5.02541 5.02552 - .002 5.903300 5.900 275 .051

2A 232.0393 4.99780 4 . 99739 • .004 5.503400 5.097413 .101

21
Table II. (Continued)

EXPT TEMPERATURE PRESSURE (MPA) % DENSITY (M0L/DWI3) %

ID K EXP CALC DIFF EXP CALC DIFF

2E 298.1500 6.39638 8.38978 .079 10.617200 10.624430 -.068

2B 280.0394 4.84374 4.84231 .029 10.626500 10.632286 - .054

2B 279.5394 4.75176 4.74989 .039 10.626800 10.635088 -.078

2B 279.3625 4.71942 4.71724 .046 10.626800 10.636740 - .094

2B 298.1500 7.23094 7.23176 - .011 8.750000 8.747744 .026

2B 282.3700 5.04648 5.04613 .007 8.756600 8.784006 - .313

2B 282.3440 5.04315 5.04280 .007 8.756600 8.784956 -.324

2B 282.2143 5.02663 5.02627 .007 8.756600 8.794163 -.429

2B 282. 1893 5.02347 5.02309 .007 8.756700 8. 797239 -.463

2B 303. 1500 7.44551 7.44643 - .012 7.602300 7.599740 .034

2B 298. 1500 6.86296 6.86306 - .002 7.604100 7.603709 .005

2B 293. 1500 6.28229 6.28184 .007 7.605900 7.608538 - .035

2B 289. 1500 5.81975 5.81916 .010 7.607300 7.613134 - .077

2B 2e5.6500 5.41734 5.41682 .010 7.608500 7.620681 - .160

2B 284.6500 5.30307 5.30245 .012 7.608900 7.631 131 - .292

2B 283.6500 5.18886 5. 18842 .008 7.609300 7.640665 - .412

2B 283. 1500 5.13189 5. 13156 .006 7.609400 7.652152 - .562

2B 282.6500 5.07514 5.07482 .006 7.609600 7.739052 -1 .701

2B 282.5500 5.06378 5.06349 .006 7.609600 7.787493 -2.338

2B 282.4500 5.05243 5.05216 .005 7.609700 7.848875 -3.143

2B 282.3440 5.04045 5.04016 .006 7.609 700 7. 732198 -1 .610

2B 298. 1500 6.56656 6.56593 .010 6.51 1200 6.513592 -.037

28 293. 1500 6.08870 6.08818 .009 6.51280C 6.515674 - .044

2B 289. 1500 5.70401 5.70374 .005 6.51400C 6.51631

1

- .035

2B 285.6500 5.36469 5.36453 .003 6.515000 6.517597 - .040

2B 2e3.6500 5. 16848 5. 16836 .002 6.515600 «. 519783 - .064

2B 282.3440 5.03822 5.03807 .003 6.516000 6.534596 - .285

2B 298. 15C0 5.38612 6.38517 .015 5.894200 5.897429 - .055

2B 293. 1500 5.96311 5.96213 .016 5.895500 5.900023 - .077

2B 289.1500 5.62133 5.62040 .017 5.896600 5.902760 -.104

2B 285.6500 5.31829 5.31759 .013 5.897600 5.905107 - . 127

2B 283.6500 5.14244 5. 14189 .011 5. 898 I 00 5.907296 - .156

2B 282.3440 5.02570 5.02534 .007 5.898500 5.908266 - .166

2B 282.2393 5.01624 5.01591 .007 5.898500 5.90ei49 - .164

23 282. 1393 5.00720 5.00688 .006 5.898600 5.908367 - .166

2B 281 .9393 4.98901 4.98878 .005 5.898600 5.906675 - .137

2B 281 .8393 4.97992 4.97970 .004 5.898600 5*906706 -.137

26 281 .7393 4.97071 4.97062 .002 5.898700 5,902345 - .062

282.3500 5.04197 5.04084 .022 7.635000 7.797934 -2.134

282.3600 5.04288 5.04198 .018 7.635000 7.800451 -2.167

282.3700 5.04403 5.04311 .016 7.635000 7.809395 -2.284

282.3800 5.0451E 5.04424 .019 7.635000 7.818024 -2.397

282^3900 5.04626 5.04538 .018 7.635000 7.827379 -2.520

282.4000 5.04744 5.04651 .018 7.635000 7.836230 -2.636

282.4100 5.04858 5.04764 .019 7.635000 7.845222 -2.753

282.4200 5.04978 5.04878 .020 7.635000 7.854504 -2.875

282,. 4300 5.05083 5.04991 .018 7.635000 7.862487 -2.980

282 '.4500 5.05324 5.05218 .021 7.635000 7.878148 -3. 185

282.5500 5.06452 5.06352 .020 7.635001' 7.930706 -3.873

22
Table II. (Continued)

EXPT TEMPERATURE PRCSSURE (MPA)

ID K EXP CALC

1 282.6500 5.07586 5.07488

1 282.7500 5.08723 5.08624

1 282.8500 5.09858 5.09761

1 282.9500 5.10994 5. 10893

1 283.0500 5. 12136 5. 12037

1 283.1500 5.13277 5. 13176

1 283.3500 5.15567 5. 15455

1 284.1500 5.24722 5.24593

1 285.1500 5.36197 5.36053

1 286.1500 5.47701 5.47548

1 287.1500 5.59247 5.59074

1 288.1500 5.70808 5.70626

1 293.1500 6.28886 6.28704

1 298.1500 6.87365 6.87171

1 303.1500 7.46149 7.45904

1 283.1500 5. 10345 5. 10241

1 288.1500 5.54964 5.54816

1 293.1500 5.98672 5.98515

1 298.1500 6.42028 6.41773

1 303.1500 6.84890 6.84738

1 283.1500 5.11928 5. 1 1846

1 238.1500 5.60692 5.60572

1 293.1500 6.08774 6.08577

1 298.1500 6.56526 6.56281

1 303.1500 7.03963 7.03798

1 283.1500 5.12707 5. 12625

1 288.1500 5.65366 5.65253

1 293.1500 6. 17782 6. 17599

1 298.1500 6.70124 6.69893

1 303.1500 7.22319 7.22170

1 283.1500 5.13169 5. 13071

1 283.1500 5.69652 5.69483

1 293.1500 6.26526 6.26308

1 298.1500 6.83652 6.83420

1 303.1500 7.40872 7.40733

1 233.1500 5. 13594 5. 13481

1 283.1500 5.74088 5.73870

1 293.1500 6.35743 6.35480

1 298.1500 6.98029 6.97763

1 303.1500 7.60625 7.60492

1 283.1500 5.14271 5. 14141

1 288.1500 5.79342 5.79106

1 293.1500 6.46250 6.46020

1 298.1500 7.14174 7. 13977

1 303 . 1 500 7.82674 7.82622

1 283.1500 5. 15732 5. 15588

1 288.1500 5.86313 5.86107

1 293.1500 6.59227 6.59056

1 298.1500 7.33468 7.33347

1 303.1500 8.08490 8.08531

1 283.1500 5.18994 5. 18874

1 288.1500 5.96313 5.96149

1 293.1500 6.76196 6.76038

% I DENSITY (M0L/DM3) Yo DIFF :.XP CALC DIFF

.019 7. 635000 7.914154 -3 656

.019 7. 635000 7.873055 -3 .1 18

.019 7 635000 7.830066 -2 .555

.019 7 635000 7.795675 -2 . 104

.019 7 635000 7.776276 -1 .850

.020 7 635000 7.759454 -1 .630

.022 7 635000 7.741249 -1 .392

.025 7 635000 7.696503 - .806

.027 7 635000 7.675567 - .531

.028 7 635000 7.664 342 - .392

.031 7 635000 7.660746 - .337

.032 7 635000 7.656S58 - .284

.029 7 635000 7.645534 - .13,3

.028 7 635000 7.642283 - .095

.033 7 635000 7.641778 - .009

.020 6 000000 6.023921 - .399

.027 6 000000 6.01 1648 -

. 194

.026 6 000000 6.007560 -. 1?6

.040 6 000000 6.008853 -

. 148

.022 6 000000 6.004 152 - .069

.016 6 500000 6.539665 - .610

.021 6 500000 6.512006 - .185

.032 6 500000 6.510856 - .167

.037 6 500000 6.509280 -

. 143

.023 5 500000 6.504772 - .073

.016 7 000000 7.080309 - 1 .147

.020 7 000000 7.013259 -. 189

.030 7 000000 7.010358 - .155

.034 7 000000 7.009055 -. 129

.021 7 000000 7.C04380 - .063

.019 7 50CC00 7.624604 - 1 .£61

.030 7 500000 7.52041C - .272

.035 7 500000 7.512838 -

. 171 .034 7 500000 7.508308 - .119

.019 7 500000 7.503930 -• .052

.022 8 000000 8. 103823 -1 .296

.038 8 000000 8.0235C6 - .294

.041 8 000000 8.014007 - .175

.038 8 000000 8.009298 - .116

.017 6 ooocoo 8.003442 - .043

.025 8 500000 8.562742 - .738

.041 8 500000 8.519981 - .235

.036 8 500000 8.510251 - . 121 .028 8 .500000 0.505906 - .069

.007 8 500000 8.501 175 - .014

.028 9 .000000 9.031 780 - .353

.035 9 .000000 9.012601 - ,140

.026 9 .000000 9.006005 - .067

.017 9 .000000 9.002977 - .033

.005 9 .000000 8.999225 .009

.023 9 . 500000 9.512497 -. 132

.028 9 .500000 9.506879 - .072

.023 9 .500000 9.504175 - .044

23
Table II. (Continued)

EXPT TEMPERATURE PRESSURE (MPA) % DENS I TV (M0L/DM3) %

ID K EXP CALC DIFF EXP CALC DIFF

1 298 1500 7.57508 7 . 57459 .00 7 9 . 500000 9. 500 £59 - .010

1 303 1500 8.39804 8.39918 - .014 9.500000 9.498235 .019

1 283 1500 5.25792 5.25693 .019 10 .000000 10.005284 - .053

1 288 1500 6.11098 6. 10974 .020 10.000000 10.003532 - .035

1 293 1500 6.99048 6.98814 .033 10.000000 10.004588 - .046

1 298 1500 7.88201 7.88257 .003 1 . 000000 10.000366 - .004

1 303 1500 8.79026 8. 78816 .024 10.000000 10.002596 - .026

1 283 1500 5.38690 5.38340 .065 10.500000 10.510550 - . 1 00

1 288 1500 6.33296 6.32812 .076 10.500000 10.509354 • .009

1 293 1500 7.30284 7.29650 .087 10.500000 10.509159 - .037

1 298 1500 8.29048 8.28063 .119 10.500000 10.51 1444 - .109

1 303 1500 9.28873 9.27603 . 137 10.500000 10.51241

|

- .1 1C

1 280 1500 4.83757 4.83427 .063 10.500000 10.515588 - .148

1 280 1500 4.81814 4.81532 .059 10.100300 10.415616 - . 150

1 260 1500 4.81214 4.80947 .055 10.365500 10.381 149 - .151

1 280 1500 4.80596 4.80366 .048 10.329100 10.343470 - .139

1 260 1500 4.80263 4. 80031 .04 9 1 . 307000 10.322035 - .146

1 280 1500 4.79995 4. 79910 .018 9.900000 9.905268 - .053

1 280 1500 4.79989 4. 79910 .016 8.250000 6.253402 - .041

1 280 1500 4.79970 4. 79910 .013 6.800000 6.801 760 - .026

1 280 1500 4.79960 4. 79910 .010 5.8C0000 5.801068 - .016

1 281 1500 5.01853 5.01542 .062 10.500000 10.512315 - .1 17

1 231 1500 4.92924 4. 92778 .030 10.000000 10.012537 - .125

281 1500 4.91885 4.91745 .029 9.899000 9.913674 - .148

1 281 1 500 4.91325 4.91 176 .030 9.833000 9.850774 - .181

1 281 15C0 4.91 168 4.9I022 .030 9.813400 9. 83 i 534 - .185

1 281 1500 4.91022 4.90873 .030 9.793600 9.812843 - .196

1 281 1500 4.90938 4.90777 .033 9.780300 9.601638 - .218

1 281 1500 4.90885 4.90731 .031 9.773700 9.794532 - .213

1 281 1500 4.90837 4.90736 .02) 9.767300 9.781 1 15 - .141

1 281 1500 4.90826 4.90736 .018 9.300000 9.31 1 185 - . 120

1 281 1500 4.90822 4.90736 .018 8. 100000 8. 108141 - . 101

1 281 1500 4.90804 4.90736 .014 6.200000 6.203784 - .061

1 281 1500 4.90601 4.90524 ,016 5.500000 5.516828 - .306

1 281 6500 4.97260 4.97138 .025 9.592500 9.612074 - .204

1 281 6500 4.96918 4.96794 .025 9.530000 9.552898 - .240

1 281 6500 4.96762 4.96647 .023 9.500000 9.522903 - .241

1 281 6500 4.96606 4.96479 .026 9.462700 9.490067 - .289

1 281 6500 4.96472 4.96353 .024 9.432000 9.459807 -.295

1 281 6500 4.96393 4.96262 .026 9.408050 9.440300 .343

1 281 6500 4.96300 4.96253 .009 5.900000 5.904845 - .082

1 281 6500 4.96067 4.95983 .017 5.800000 5.829248 - .504

1 281 6500 4.95740 4.95639 .020 5.700000 5.727739 -.487

1 281 6500 4.94814 4.94693 .024 5.500000 5.521962 - .399

1 282 . 1500 5.20165 5. 19852 .060 10.500000 10.510703 - .102

1 282 . 1500 5.0921

5.09120 .018 10.000000 10.006037 - .060

1 282 . 1500 5.04078 5.03979 .020 9.500000 9.515163 - .160

1 282 . 1500 5.02594 5.02584 .022 9.200000 9.231517 - .343

1 262 . 1500 5.02425 5.02305 .024 9. 100000 9. 143214 - .475

1 282 . 1500 5.02198 5.02096 .020 9.000000 9.048220 - .536

1 282 . 1 500 5.02051 5.01945 .023 8 . 900000 8.968625 - .773

1 282 . 1500 5.01990 5.01884 .021 8.845200 8.918881 - .833

1 282 . 1500 5.01959 5.01845 .023 8.802400 8.888712 - .981

1 282 . 1500 5.01951 5.01843 .022 8.000C00 8.883761 - .952

24
Table II. (Continued)

EXPT TEMPERATURE PRESSURE (MPA)

ID K EXP CALC

1 282 1500 5 01843 5 01759

1 282 1500 5 01741 5 01656

1 282 1500 5 01606 5 01515

1 282 1500 5 01 181 5 01089

1 282 1500 5 00892 5 00790

1 282 1500 5 00530 5 00423

1 282 1500 4 98973 4 98840

1 282 2500 5 03540 5 03427

1 282 2500 5 03228 5 03123

1 232 2500 5 03142 5 03035

1 282 2500 5 03089 5 02978

1 282 2500 5 03035 5 02954

1 282 2500 5 02995 5 02904

1 282 2500 5 02939 5 02843

1 282 2500 5 02842 5 02755

1 282 2500 5 021 18 5 0201 1

1 282 2500 4 99803 4 99666

1 282 3500 5 23803 5 23536

1 282 3500 5 12506 5 12417

1 282 3500 5 07067 5 06935

1 282 3500 c 04902 5 04762

1 282 3500 5 04295 5 04166

1 282 3L>00 5 04200 5 04087

1 282 3500 5 04200 5 04085

1 282 3500 5 04194 5 04084

1 282 3500 5 04186 5 04082

1 282 3500 5 04178 5 04067

1 282 3500 5 03966 5 03853

1 252 3500 5 03051 5 02931

1 282 3500 5 00613 5 00491

1 282 ^000 5 04746 5 0465!

1 232 4000 5 04741 5 04650

1 282 4.500 5 05343 5 05247

1 282 4500 5 05322 5 05225

1 282 4500 5 05309 5 05219

1 282 4500 5 05309 5 05216

1 232 4500 5 05303 5 05209

1 282 4500 5 05283 5 05183

1 282 4500 5 .05235 5 05146

1 282 5500 5 .06449 5 06354

1 282 5500 5 .06446 5 06347

1 282 6500 5 .08928 5 08795

1 282 6500 5 .07993 5 07874

1 282 6500 5 .07695 5 07585

1 282 6500 5 .07616 5 07515

1 282 6500 5 .07590 5 07491

1 282 .6500 5 .07575 5 07479

1 232 .65W7 5" .07556 5 07456

1 262 .6500 5 .07481 5 .07389

1 282 .6500 5 .07333 5 07294

1 282 .6500 5 .07221 5 07136

1 282 .6500 5 .06950 5 06867

% DENSITY (MO I. /DM3) a'n DIFF EXP CALC DIFF

017 6 400000 6 454023 . 844

017 6 300000 6 390674 -1 439

018 6 200000 6 265869 -1 062

018 6 000000 6 036959 - 616

020 5 900000 5 932741 - 555

021 5 800000 5 827858 - 480

027 5 500000 5 520626 - 375

022 9 000000 9 047636 - 529

021 8 800000 8 872435 - .823

021 8 700000 8 792945 -1 068

022 8 600000 8 716073 -1 350

016 6 750000 6 818349 -1 021

018 6 600000 6 701767 -1 542

019 6 500000 6 785221 -4 388

017 6 400000 6 515809 -1 81C

021 6 000000 6 040185 - 67C

027 5 500000 5 520597 - 374

051 10 500000 10 508902 - 085

017 10 000000 10 005617 - 056

026 9 500000 9 518329 - 193

028 9 000000 9 C52224 - 580

026 8 500000 8 635545 -1 595

022 8 000000 8 176168 -2 202

023 7 750000 7 916312 -2 172

022 7 500000 7 656720 -2 090

021 7 250000 7 397917 -2 040

022 7 000000 7 158214 -2 260

022 6 500000 6 704560 -3 147

024 6 000000 6 042159 - 703

024 5 500000 5 517730 - 322

019 7 650000 7 S51210 -2 630

018 7 600000 7 801216 -2 648

019 8 OCOOOO 8 202698 -2 534

019 7 750000 7 982894 -3 .005

018 7 650000 7 893216 -3 .179

018 7 600000 7 848177 -3 .265

019 7 500000 7 762555 -3 .502

019 7 250000 7 579103 -4 .539

018 7 000000 7 925805 13 .226

019 7 650000 7 .938433 -3 .770

019 7 6C0000 7 .906237 -4 .029

026 9 ooooco 9 039806 - .442

023 8 500000 8 593304 -1 .098

022 8 000000 8 191538 -2 .394

020 7 750000 7 997926 -3 . 199

019 7 650000 7 925024 -3 .595

019 7

7 600000

"500000

7 886625 73

-4

.771

02 0" 7 827609 .368

018 7 250000 7 625743 -5 . 183

018 7 000000 7 275154 -3 .931

017 6 750000 6 882392 -1 .961

016 6 500000 6 567970 -1 .046

25
Table II. (Continued)

EXPT TEMPERATURE PRESSURE (MPA) % DENSITY (M0L/DM3) %

ID K EXP CALC DIFF EXP CALC DIFF

282.6500 5.05791 5.05683 .021 6 . 000000 6.031517 - .525

282.8500 5. 10045 5.09937 .021 8.000000 8. 145839 -

.823

282.8500 5.09920 5.09812 .021 7.750000 7.941939 -2 .477

282.8500 5.09867 5.09767 .020 7.650000 7.846700 -2 .571

282.8500 5.09845 5.09746 .019 7.600000 7.803523 -2 .678

282.8500 5.09804 5.09702 .020 7.500000 7.720402 -2 .939

282.8500 5.09675' 5.09584 .018 7.250000 7.447809 -2 .728

202.8500 5.09507 5.09431 .015 7 . 000000 7. 122422 -1 .749

283. 1500 5. 13368 5. 13266 .020 7.750000 7.867914 -1 .521

233. 1500 5. 12950 5. 12868 .016 7.250000 7.348742 -1 .362

283. 1500 5. 12379 5. 12302 .015 6.750000 6.304352 - .805

283.3500 5. 18470 5. 18327 .028 9 . 000000 9.028782 - .320

283.3500 5.16320 5. 16669 .029 8.500000 8.561 573 - .724

283.3500 5. 15981 5. 15853 .025 8.000000 8.094200 -1 . 178

233.3500 5. 15692 5. 15573 .023 7.7 50000 7.856452 -1 .374

283.3500 5. 15419 5. 15318 .020 7.500000 7.598528 -1 .314

233.3500 5.15144 5. 15055 .017 7.2 50000 7.332635 m *

. 140

283.3500 5.14829 5. 14749 .016 7.000000 7.061960 - .885

283.3500 5. 14440 5. 14357 .016 6. 750000 6. 790297 - .716

283.3500 5.13908 5. 13827 .016 6.500000 6.533322 - .520

283.3500 5. 12159 5. 12056 .020 6.0150000 6.021887 - .365

283.3500 5.08842 5.08697 .028 5. 50(0000 5.516599 - .302

2S4. 1500 5.57352 5.56985 .066 10. 500000 10. 509930 - .095

284.1500 5.42568 5.42462 .020 10 . 000000 10.004796 - .048

284. 1500 5.34153 5.34013 .026 9.500000 9.51 1 175 - .118

284. 1500 5.29548 5.29375 .033 9.000000 9.025101 - .279

284. 1500 5.27042 5.26863 .033 8.500000 8.544784 - .527

284 . 1 500 5.25551 5.25395 .030 8.000000 8.062361 -

. 7eo

28 4. 1500 5.24954 5. 24834 .025 7. 750000 7.809672 - .770

284. 1500 5.24427 5.24314 .022 7 . 500000 7.554759 - .730

284. 1500 5.23885 5.23789 .018 7.250000 7.294869 - .619

284. 1500 5.23306 5.23214 .017 7.000000 7.038093 - .544

284. 1500 5.22627 5.22541 .017 6.750000 6.779889 - .443

234. 1500 5.21797 5.21709 .017 6.500000 6.524 163 - .372

234. 1500 5.19400 5. 19278 .023 6.000000 6.020025 - .334

284. 1500 5.15364 5. 15210 .030 5.500000 5.515228 - .277

28c !500 5.67503 5.67387 .020 7.250000 7.264C67 -

. 194

28C . 1 500 5.63106 5.63007 .018 6.750000 6. 760909 -

. 162

4 283. 1700 5.10770 5. 10684 .017 6.060000 6.001 330 - .352

4 287.3700 5.48740 5.43630 .020 6.06C0CC 6.069942 - .164

A 293.3400 6.01530 6.01471 .010 6.060000 6.062838 - .047

A 2Q8.1S00 6.43890 6.43815 .012 5.056000 6.058623 • .043

A 285.5400 5.42540 5.42420 .022 8.063000 8.037968 - .310

A 291 .9000 6.21 100 6.21070 .005 8.063000 8.064815 - .023

A 292.7500 6.31690 6.31702 - .002 8.063000 8.062361 .008

A 293.1500 7.20000 7.20188 - .026 10.362000 10.359027 .029

A 293.6900 7.30330 7.30472 - .019 10.362000 10.359812 .021

A 298. 1400 7.99060 8.C1997 - .358 10. 190000 10. 148722 .405

A 298.1400 6.99690 6.99828 - .020 8.072000 8.067244 .059

A 298.1400 6.69610 6.69977 -.055 7.007000 6.992544 .206

3 283.6500 5.14322 5. 14226 .019 5.904244 5.920517 - .276

3 285.6500 5.31888 5.31822 .012 5.90424 4 5.91 1351 - .120

3 289. 1500 5.62216 5.62158 .010 5.904244 5.908078 - .065

3 293. 1500 5.96416 5.96409 .001 5.9042 44 5.904564 - .005

3 298.1500 6.33314 6.38329 - .002 5. 9Q4244 5 903 725 .009

3 283.6500 5. 16045 5. 15947 .019 6.253953 6.279469 - .408

3 285.6500 5.34820 5.34 725 .018 6.25395 3 6.267369 - .215

3 289. 1500 5.67198 5.67135 .01 1 6.253953 6.25S864 - .079

26
Table II. (Continued)

EXPT TEMPERATURE PRESSURE (MPA) % DENSITY (M0L/DM3) % ID K EXP CALC DIFF EXP CALC DIFF

3 293. 1500 6.03833 6.03300 .005 6. 253953 6. 255661 - .027

3 298. 1500 6.49362 6.49302 .009 6. 253953 6.256160 - .035

3 2B3.6500 5. 16362 5. 16330 .006 6. 35694 7 6.366096 - . 144

3 285.6500 5.35447 5.35445 .000 6. 356917 6.357318 - .006

3 289. 1500 5.68487 5.63458 .005 6 . 356947 6.359283 - .037

3 293. 1500 6.05796 6.05836 - .007 6. 356947 6.354826 .033

3 298. 1500 6.52247 6.52256 - .001 5. 356947 6. 356629 .005

3 283.6500 5.17651 5. 17573 .015 6. 815134 6.853609 - .565

3 285.6500 5.381 11 5.381 14 - .001 6 . 815134 6.814490 .009

3 289.1500 5.73825 5.73773 .009 6. 815134 6.820042 - .072

3 293. 1500 6. 14315 6. 14339 -.004 6. 815134 6.813733 .021

3 298.1500 6.64913 6.64915 - .000 6. 815134 6.815047 .001

3 283.6500 5. 17738 5. 17672 .013 6 863326 6.897564 - .499

3 285.6500 5.38421 5.38356 .012 6 863326 6.876538 - .193

3 289. 1500 5.74278 5. 74291 - .002 6 86332b 6.862075 .018

3 293. 1500 6.15210 6. 15195 .002 6 863326 6.864198 - .013

3 298. 1500 6.66181 6.66217 - .005 6 863326 6.861933 .020

3 283.6500 5.18517 5. 18383 .026 7 283386 7.377382 -1 .284

3 285.6500 5.40368 5.40289 .015 7 283886 7.302369 - .254

3 289. 1500 5.78719 5. 78633 .015 7 283886 7.292606 - .120

3 293. 1500 6.22585 6.22534 .008 7 283886 7.286930 - .042

3 298. 1500 6.77549 6.77529 .003 7 283386 7.284672 - .01 1 3 283.6500 5. 18830 5. 18668 .031 7 484253 7.599153 -1 .535

3 285.6500 5.41282 5. 41 149 .025 7 484253 7.515553 - .418

3 289. 1500 5.80755 5.80660 .016 7 484253 7.493849 - . 128

3 293. 1500 6.261 15 6.26031 .013 7 484253 7.489230 - .067

3 298.1500 6.82979 6.82986 - .001 7 484;'53 7.483969 .004

3 283.6500 5. 19154 5. 18995 .031 7 718022 7.824272 -1 .377

3 285.6500 5.42238 5.42158 .015 7 718022 7.736250 - .236

3 289. 1500 5.83135 5.83065 .012 7 718022 7.724856 - .089

3 293. 1500 6.30224 6. 30201 .004 7 718022 7.719340 - .017

3 298. 1500 6.89369 6. 89516 - .02 1 7 718022 7.712568 .371

3 283.6500 5.19785 5. 19597 .036 8 101763 8. 19567C - 1 .171

3 285.6500 5.44163 5.43957 .038 8 101763 8. 141620 - .492

3 289. 1500 5.87440 5.87290 .026 8 101753 8. 1 14814 - .161

3 293. 1500 6.37711 6.37482 .036 8 101763 8. 1 13628 - . 146

3 298.1500 7.00764 7.00873 - .016 8 101763 8.098042 .046

3 283.6500 5.21258 5.21 157 .019 8 712710 8.739165 - .304

3 285.6500 5.47945 5.47805 .025 8 712710 8. 730205 - .201

3 289. 1500 5.95566 5.95555 .002 8 .712710 8. 713427 - .008

3 293. 1500 6.51 140 6.51 185 - .007 8 .712710 8. 710873 .021

3 298.1500 7.21383 7.21747 - .051 6 .712710 8. 702549 .117

3 283.6500 5.21 950 5.21694 .049 8 .845913 8.899487 - .606

3 285.6500 5.49165 5.46927 .043 8 .845913 8.872083 - .296

3 289. 1500 5.97733 5.97759 - .004 8 .845913 3.844349 .018

3 293.1500 6.54496 6.54693 - .030 8 .845313 B. 838375 .085

3 298. 1500 7.26451 7.26953 - .069 8 .845913 8.837640 .150

3 233.6500 5.24750 5.24722 .005 9 .326219 9. 329455 - .035

3 285.650C 5.54389 5.54371 .003 9 .326219.327456 • .013

3 289.1500 6.07423 6.07534 - .018 9 . 326219 9.321444 .051

3 293. 1500 6.69265 6.69582 - .047 9 .326219 9.316844 . 101

3 298.1500 7.47712 7.46426 - .096 9 .326219 9.310961 . 164

3 283.6500 5.28952 5.29032 - .015 9 .7031 19. 702464 .058

3 285.6500 5.61008 5.60953 .010 9 . 7C81 17 9. 71081

- .028

3 289. 1500 6. 17898 6. 18074 - .028 9 . 708 I 1

9. 702399 .059

3 293. 1500 6.84089 6.84694 - .088 9 . 7081 1

9.693777 . 148

3 298. 1500 7.68440 7.69341 -.117 9 . 708 1 19.692157 . 164

3 283.6500 5.50719 5.50804 - .015 10 . 586729 10. 584434 .021

3 285.6500 5.89065 5.89055 .002 10 . 566729 10.586956 - .002

3 289.1500 6.56807 6.57052 - .037 10 . 586729 10.582517 .040

3 293.1500 7.35645 7.36010 - .050 10 .586729 10.581675 .048

3 298. 1500 8.35838 S. 36077 - .029 10 .586729 10.584057 .025

27
u- ;* in<TCNintDCOajCD<£> —

ao- coaocNt~-ror*cx — n(N^ooop('->-o

lfl(N<rO<DOOOT Lococoomor^cn — O O — <N — O O CO —

•—5 r~coaif-car^ina>io<T>

u)Q -miON'T'roiD'-ai z \ ao cm to co — siioao i_i -I — C\OCOO — — CO QO oocooooooo

CDCN<TCOCDCj — Orft^- incoiNr-cocDtocoio

oo •-;atNO ooooooooo

c

o

•r—

+-> (0 ^—3

c: F

o s-

•r— o +J hfO

S- cu

13 _c

4J +J

03

00 .c

+-> i— •^

CO 3 -(-> c 00

ai a> E •i—

•r- +-> S- •i— aj CO Q_ c

X O)

0) a

m- -a o c

ra

c:o 00

to 0)

•1— SS- ^

fO oo Q_ 00 E ai o s-

<_) Q.

CD -O

Q <

co a. z x

u- a*

lice

oo <

CO O. ai £

cra.

< -i

a. <

2 u

UJ

<r

130000

UJ

a. a.

a. x

coco — t-uDf^uoaiioc) TC0C0r^*TTt7>t0— CO 0<J>ta<j><rr~<T>oa>ao r-cDocNLOi--coT^rtTomointDLnococo

oooooooooo COOOOOOOOOO *r<r — oot^ — r~oo

or-r^cn<TcD — acoco f-ioocNinc-cncOTc-

^omomoimaiom

cacNCMTincaLOCMCD MnOOIOlfiO'-T

mcococnmoo cdcncd mocNaor-coc^^rco

oocococDOcocncn

ooooooooo OOr-»co<q-oc^inr~

cNCNCNt-»^rr>-cDcoa) mcoc)- cooiinocn inonoiMD^oico

ocoicoooooinin

cntT>rococotor^of»r»coa>a> oo— ---------

ooooooooooooo

CNCNC!cof-f-inir>r--t^ooico

TTcotr!r--r-cDCD3aDc;o)r! ooooooooooooo ooooooooooooo ooooooooooooo

ininoocoioioiocoa} — «rcn CMCN — — COCO^T«TO*CN<7>in —

cocoCTcnt^r-iNCNacococim

CnCDCOCJlOOlOlO — — CNCNfO lDlDr^t~CT)010>0)00000

r»r-oocjcoro- — inm — <oc*

to COP>> •- —COCO — — COT -

cococncDaocarococncn'TOio oicnoioiooioio-'- cncoco cocor»iNo>cno)cnooooo

^rTTTV'j <r t to m m in m

CNO — COtOiniOintO OOOOOOOOO OOOOOOOOO

OOCNTT — inOtOCN COO — CO cn to CM CO OOOOOOOOO

OOOOOOOOO

<rf»cD<Nr~<NC^(Nf~ «3Mocociaj(Do(cn

CO — COlOCNCOOTOTOO (Nin<f<TMflOOO

.^ajeoffloioiooo

it wriminin

CJtDOlOajt^t^QOCjl r^f-VCDlOOOI'TCI

co — to in o( mji en r> CMinTTOCOOOO r-oococooaiooo

i wrt t in in m

ui

cr»-<

a: ac Uia

OOOOOOOOOOOOOOOOOOOOOOTTTTOOnrorOO ooooooooooooocor^ — "jinMnoooiaioiToioinoxD

inminininininmininoinonaicocoiO'- iocoiooococD(DcocDr»<o«T — — — — — — 0309 — — c*<Ncoinmr-o — ro — (OiOTiommMOOOO

WOOO — — — — CN«NCNCNtN0)O — CNCNCnCN — — CD O O O — — CN Ol CN

f*« c^cOCOQOCDCOOOCDCDCOQOCOf^COOOCOCOr^OOODCTr^CDCDCOQDGOCDOOCO

«c*oio«o<oioicio«cno»wcno»oic>io«c><c>ic^oio(oic>ic>ic>ic>io«mc«oi

4<<<<coaj<im<<<<<<«(<<

CMC<0«OI040IC(0«CMC(OIOIOICMC<C(CICI

?8
CD inififTTT«onin'j-NOM^ini-noidainnoro(NCNio<ro(PiocMnmT OOOOOOOOOOOOO/OOOOOOOOOOOOOOOOOOOOOO ooooooooooooooooooooooooooooooooooo

o

u

UJ

a.

1/5 UJ

cc

Q.

iOLOiricT)'-ocNOr^o«-0'^ir)Lr!t~-rJLr:c2t,,!r:(-:'^)C)-\'-cocO'=-rjcNiT-^-(r)o w rj t->,i- wi-o»-NNi-on^w<-'-c?, *»-'-<-T-rTC«r-r-T-oi->-*n OOOOOOOOOOOOt-OOCCCOOOOOOOCOCOOOOOOO ooooooooooooooooooooooooooooooooooo ooooooooooooooooooooooooooooooooooo

CD .a — o

< -I

Q. <

r-oioinr)noiioa)--N-iv»(D^-o !rnin(NOinn(,)t--OTroncD«-'-'-

C5ijDc^.'oot^cr)rooa)UD'-cri'-co^rrjt^'-Lr)(j)CDC^r)Or^ojt^'-inr'jiDai<TicD »-^ot^Toair-io<T)OLnoiir)CNO(j)--'-ocN'-oc^^TOCN — r- omowcoo ooocDaiaJcocicnaiocacicoc^r^iooooooocDaiCTioooooiooiaio)

UJcr

COto CNCooLOiii(jDc^OLOu3a5r^o<N05CT)tDroc\cDt^'-'-cNtor~cNOir)coCT)roocoa5 u o^CNt^in^cN<^inc7)Ot^aDnroooo(LncT>c\tD'TCNr^<a->T<3-tT)r)r~-rocr)coc^<J)

a: a ot^r^rioc^nc^a5CDU3^r^^ro^cNC^T-a3cricDr--roor~-cNto»-LOCNtocjicDLO

a. x cjr-ot^-'g-ocTit^LurooLonLOCNOCTi'-'-ooj'-or^'TOCN'-'^-or^cocoooo

uj oooc^aicn^cnaiciaiajcTicDt^c^tDoooooocnoitTioooocncncnoicT)

Z3 nooooooonnpufn^iTfnnnoooooonnnnnpinnn najoooooocnoKJioioioiciioimaioicnoooooooioioioiaimoicncn (oni/itnininiriinajnnnnnnmnnconiiimini/iiflinajniBroroconnd

(NOIOl-i-T-Ol-T-^^O'-OOlOlOlNCMOKNtMM'-'-'-CMOJOICMT-'-T-^^

coa}COcoooa}c^cocococscoa}a^c^r^r«coc3c>coa3a)cocx)coaoa3aDcocoa}a}aoco C^CNC^C^C^CNtNCNCNCNCNCNCNCNCNC^CNCNCNCNtNCNCSCNC^CNC-JCgOJCNO^CNnCNOf

<<<<<<<<<<<<<<<mmmcoo3mLrimmmajmmmmmma3CQLa

CNC^CNMCJOJWO(CNWCJCJO(CNeN<NCNCNCNC>iCN<NCNOJCNOJCNCNCNCJOJC><CJC4C>J

29
Table LV. Comparison of the experimental speed

of sound with- the formulation.

DENS T,K W.EXP W.CAL DELTA VJ % DIFF

5.50000

5.54900

5.58000

5.60300

5.61300

5.61600

6.00000

6.05700

6.09900

6. 12500

6. 13600

6.50000

6.57000

6.61900

6.64800

6.660C0

7.00000

7.08200

13900

171C0

.50000

,59400

.65900

.69500

8.00000

6. 10400

8. 17900

8.21900

8.23300

8.50000

8.61100

8.69800

8.74200

.75700

,00000

1 1100

,21400

,26300

.28100

. 50000

.60300

,72500

,78300

.80200

.80900

.81400

10.00000

10.08800

10.22700

10.29800

10.32100

10.32800

10.33400

10.34400

298.

293.

288.

284.

282.

281 . 298.

293.

288.

284.

282.

298.

293.

288.

284.

282.

298.

293.

288.

284.

298.

293.

288.

284.

298.

293.

288.

284.

282.

298.

293.

288.

284.

282.

298.

293.

288.

284.

282.

298.

293.

288.

284.

282.

281 . 281 . 298.

293.

288.

284.

282.

281 . 281.

280

150

150

150

150

350

650

150

150

150

150

350

150

150

150

150

350

150

150

150

150

150

150

150

150

150

150

150

150

350

150

150

150

150

350

150

. 150

. 150

.150

.350

. 150

. 150

. 150

. 150

.350

.650

. 150

. 150

. 150

. 150

. 150

.350

.650

.150

.150

241 . 232.

222.

212.

205.

201 . 241 . 231 . 219.

205.

194.

242.

231 . 217.

200.

174.

245.

233.

217.

196.

250.

238.

220.

196.

258.

245.

226.

200.

172.

269.

255.

236.

21 1 . 185.

282.

269.

251 . 228.

210.

300.

287.

271

251

238

231

224

322

309

296

279

269

264

261

252

91000

93200

62800

16600

51200

86200

57300

57400

51300

84400

09100

77200

74000

77400

18300

9C900

75100

76300

89400

29800

88600

05900

.57500

.03000

.50200

. 18700

.69700

.89600

.35400

.04300

.62100

.91800

.68200

.53700

.85400

.78800

.93500

.79300

.08600

.68200

.87500

.83600

.84500

. 19300

.04700

.90100

.34300

.81800

.38200

.92400

.66100

.93800

.15200

.47700

242.

233.

222.

212.

207.

206.

242.

231 . 219.

206.

198.

243.

231 . 217.

200.

183.

246.

233.

217.

196.

251 . 237.

220.

195.

258.

244.

226.

200.

159.

269.

255.

236.

210

185

283

269

251

228

210

300

287

271

250

237

232

229

321

308

294

278

268

264

260

255

96637

20910

53074

61726

56345

26015

43162

731 17

41685

62650

22676

43902

73573

.53422

.81873

.61327

.27168

.61840

.48606

.59337

.28200

.86640

.05862

.83742

.86428

.99916

. 1 1204

.24903

.84390

.40842

.48741

.41878

.94564

. 19053

.23791

.55179

.43107

.09131

.31 108

.54494

. 18976

. 101 14

.98933

.89592

.02923

.76267

.34499

.21270

.77895

.32151

.41720

.00546

.84041

.96340

-4

-8

12

.05637

.27710

.09726

.45126

.05145

.39815

.85862

.15717

.09615

.78250

. 13576

.66702

.00427

.23978

.63573

.62427

.52068

. 14460

.40794

.29587

.39600

. 19260

.51638

. 19258

.36228

. 18784

.58496

.64 697

.51010

.36542

. 13359

.49922

.73636

.34647

.38391

.23621

.50393

.70169

.22508

. 13706

.68524

.73486

.85567

.29708

.98223

.86167

.99801

60530

60305

1 .60249

1 .24380

.93254

.31159

3.48640

-2

-4

1

1

- .4367

- . 1 1 90

.0437

- .2127

- .9982

-2. 1788

- .3554

- .0679

.0438

- .3801

1308

- .2748

.0018

.1101

- .3176

4.9285

- .21 19

.0619

. 1872

- . 1507

- . 1578

.0809

.2341

.0962

- .1401

.0766

.2580

.3220

7.2584

- .1358

.0523

.2107

.3479

. 1867

- . 1 357

.0876

.2000

.3067

- . 1071

.0456

.2380

.2703

.3398

. 1247

- .4251

2.1617

.3096

.5161

.5409

.5725

.4612

.3520

.1193

1 .3809

30
APPENDIX C

Tables of Thermodynamic Properties

31
1- Z

-i Z3 oo u o \

o oo s

> o

onoxroinoT'-iooTsoiowMnwi-

(O^mMjiocNniDoo-ninsociiaxNio ooooO'-'-'-'-'-fVMMnnoifio'jT

CNCNCNC\CNCMCNOJCNC\ICNCMC\ICN<N<NCNCNC<0<

CO£O

•r—

4-> O

C

=3

CO

<U

a

o

s

>

>- SC aO -i a- o

I- E

Z ^

UJ \

coi><3- a>*j-LOi>-roOf-oococoi>cooo<NiN<0(0 ui'-CNioiooiinw'-iOLOcvnn-oi'-cnr)

»-iD <- Win 7 r;a3ror--C7>'3-ooaorocNcr)'g-0(N

tn rTncNr^rr-oocN<DCNOOinoO'^a)<D<Toj

'-oDoo^-cncor-r^oour. ^r^Tcocococo<\cNCNCM

O* 1- T- T- oitNotoiONOuia)'-tNinajooooininio^(3)0)TCNN<-M nnotincvnfoomtJiaiocNiDoai'-Tootianit-ajaanT

0(N^co^co^^t^ioinin ,3-roco.-^ocT>c»cDoocot*-i>coiQ

iDU3(DtDt^r-coLninir)u-»ininir»ininir)in^r«T<T>3-'3-'r'T'j-^r

cO'i-'i-C)'i-coooir>t--a)a>C'--cococMifiir>cN(Dt,»u)oococM*r'-<n iom<Tfoif)tDCDOOOOOoa)a)i^ir)root^'T--t^'j-ioa)cn

oiir>»-t^<y)<Da>co>Ttf)iDc~coaoai'^roif)t^cDO<N(oir)GO»-^r

Tinm<D^NNCD(Doo(DflDa)tDa)0)oio)cnoiooooO'- »- ODtOlOtOlOl0lOtOO3COU>(OlOvO(OtDlQ<OtDlOt"»f»t--r^f^-^t>«

UJ

0)

00 SCD o

•r— -C

4-> o

S- o

C1J 00 c•r— o

s- cr> Q_ c

o

a r—

•rTM fO E

fO cu c s_ >> 3

•o 4-> o (O E SS- 0) O) Ol

.c E

I— a> +>

a> j= Hl— o

0J

«3

UJao

X

o

o

CO

>-

el-

'sX

< >- z a

UJ UJ

t- z z UJ

uj > a —, ^ O t- ~~v X < <

o > a. O ~" S

</> cc

1-4 uia

_i SUO a: > 2

lu •-< \ X t- <

i- < a O > 2

oo —i • >— a. n

uj 2

q a

UJ

ccD <

oo o. oo 2

UI

a:

a.

t>.ojrocn^roioicNOO'-o>^oicofooooo((j»ooot^<rt^'TOoo

t^tot>«»- T-ooaot^rooin--ino^r'-t^cot<-cNLOOO'-fot>-o»-

ajiDTrocM'-'-r-incDCNtocncotDrocniDCNCDLnt-oo'TLOOiTcoLnt~-ai'-cNro<3-^-TmLr)ir)iooot^t--cocr)cr)0'-'-cNco<Tco

CNCNCNOJOiCNOJCMOJOJCNCXCNCMCNCargCNCNCNCNCMCMCMCVCNOI

CJ)C0C0"3-0Ot^COCMCNCy)'-C0(N'-CD(Na)0Dt^r0'J-'<-"T'3-LO(£)00

iDcO'-toaiNcoMO^'nooDm'-q-iniiKoiDinTtNOinmw wcoinr-mMDi/iO'-'j-MJiodnoinoinoinoiflOOiaiiii

(Ot^ci'-<Nro>TinintotDoooots-t^aoootD(T)00'-»-oJCMco^f

•-^-•^(NCMCNCNCNCNCNCNtNOJfNCMOJCNCNCNCOCOrOrOfOCOOOn

CMCNOJCNCNCVCNCNCgCNCNCNCNCNOJCNCgCNCNtNOJCNCMOIOJOJO)

Ttooo-^moo«-r-r»»- totNaomo((X)LOc\(T>cD«3tnoo<Ni-ocn r^aiT-rriot^aiajr-t^cDtoooiiiin'T^r'rconnoorooocorooi a)0)OOOOOooa>coa}cocooocoa3cx>oocoa3ma)coaoa>oo(9 00'-'-'-'--r-00000000000000000000

oooooooNnoooim(D(V(0<ro<noo)oocoMno)Ooo OOOOOOO'-'-OOKOMDT'-COIOfflNCO^O'-nn oooooooofintnioMiai'-c^riONOiorefNon ooooooooooooooO'-'-'-'-'-'-oioKNoinn

cocDtDt^r~^tDa3ooootnotn'-cM<Nr^'rcofincO'-oO'-o

Lororoinot^oicriaiiDOCMT-oiLOcocDiDCNiot^oorooococNco

^co^it>-ntoo^'a3(NtDCDoi"3't^fMtDO ,5'r--ontDcurot>-o

l>-t^t^l>QOOOCD'J-OOror>«-OOOTrO^OOOlOLOCO'>-oD(DCNO> coTinoo^cDoocrcnoo«-'-cgcM(o<rinLOoot^oooDa>t-(»)^r

wwTwwinifliflininininiftinininiflinininioioio

in ui

in i-<

UI

o.2

oooootnoinomowomooooooooooooo

(Oi>a)0>oO'-*-cMc\icoco*r<rin<Di>a}o>o*-ciico<Ttocoo

toi>tot^coooa5oococooocDCDcoa)cooocoa)cncna>cncncTiO)0 «M(NCIMM«OIO(«PI«OIOIOIM«CIPIMOI(N(NCMnOIP)

32
>- Q

H- Z

o o \

O CO s _l

UJ u. > o

0«-cr)int^C}0<TiocncN*rtDCT>'-c)cocNco OOOOOO — >--'-(NOJCN<NC'000 00*]'3- OICNCNCN(NC\IC'gCNCNCNCNOJCNC>^C^^C^J<NCNC\

ao

^r-rocNt^ocNfcor^i-i.DoO'-iDcoootnco

cocor^-ociooo^Troo — i.nh-t^'-cncoiQtn (DncncNCNoocoiN^'jananoT'-CDinco ODOmn^-CTicjr-tDinT^rocororocNojcN

C. <N -- *- t-

> -(DiDooMOincNooitioDTiDO'Tuini/nDin'-iNSNano

T-a)<TO)<T)nocNG)io^cocDCT)CN<jicT)'-'a'(X)roa)if)'-inoto

(nt^oroo, noicDOCTicD(£iir)'3-«3-cM'r-'-ociaiooo3oor>-t^io

>- ^ O -J cc o

(- s

Z w

UJ \

ON'-n0[)<TMOlfiO((flMCq-ONO(JllDOlOl(D<T0)^W(fl

cDoiooo^asaicNinujustDajiritD^roocriincNCTiiDCNint^cD

cNoo<TCDinQO'^-i/)c^cna)o»-cNcnLr)i>aiocN^rir)t--o>cNma)

<j-^inunDiDM^Nr--MiicocDcocoooa)aio)oima)CTiooo

a. _i

-i O

< s

I— "3 z

Ojr^t^OOlOtO^T'-OOCOOCMOTlDOOCNO'-CDOCD'a-CDC)

(Nui'-'-uioiuJN'-anDcMDnaDiDnoiinofN'-noO'-'r

cntDTCMOcnoicnt^o^rcO'-LncotncNCDLncNcriT'-t^cDOi'r '-rnint^cncnO'-cMnron'g-^^-LniDcDt^aDcocrioO'-n^'

CNCNCNCNCNCNncococ')cocorocr>cTcororococoror')sT'T<3''3' ,3' CNCMCNJ<NCNOJCNCN<NOJCN<N<NC\CNCMCNOJOJOJCNCM(NCMCNOIOI

-Moo

< > _l Z 13 O

a dt s

'-«-ro'3'CDir)U"i»-iv)ir)CT)(DCDir)Qoooco<T)'-cN<iicnt^ot^T'-

roocT)'-i^-n^cococot--io^-cNCTnir)r~cocx5t^i£iLi)^-ai'rco

(Dojr^«3-oa>cor--roir)CT)CNLOcr)0(X)"-i.O'-tD'-tD'>-uDinin^T <Ttor^cT)T-'-ojnTT^rir)Lr)LOi£)tDt--t^aoooaia)00'-cNco

•-•<-i-»-tNCNC\CMCNCNCNOJCNCNCNCNCNCNCNOJC\ICN00C0nnC>J CNCNCNCNCNCNCNCNCNOJCNOJCNCVOJCNCNCMCNCNCNCNOJtNCNCNCJ

CD _Q

UJ >

cc "* x

O i— \ X < < u > a. o »—

•

S

CO a.

1—1 UJQ

_i 5 LL) o

cr > >

UJ i—

<

-V X 1— <

UJ 1— < Q.

QL o > 2

O CO *-* X t~i <x n o UJ 2 o a Q

CO

1-1 UJ co cr ? 3 «a a CO o. ^ CO F

UJ UJ

-j a. o a

2

O UJ o

3

ID t-< 5C <r

UJ

a.

r^cnT-i-yDt^oocN — *-oocna>cT>cDaococot^r'-c^^-t--r-c-- GioiooooO'-OKDOiaioimaicocDajaoajcocDCDcoiDaja) OO^- — r-'-^-OOOOOOOOOOOOOOOOOOO

ooooooooonnaxfm'-iDoniDNmoO'-OMs OOOOOOOOtfKNOOlMDnfllin'-MIOlDM'nnN ooooooooojOTmLniDt^aiocN^rtnr-cDOcNincD'- OOOOOOOOOOOOOOOO'-'-'-'-'-'-CNCNCNCNO

rOCDUDt^t^--r-(£ltDrOcT)(D'TCOCMCOir'^-ir)t^(NOJ'-r-rJ-«TOO Lnroroinot^Gicooot^^cNCNCDOt^criaDLnai-^-^oi'-ooo

Tn<Tr^nioomt^naoTCT)<TaD<x>tO"0-cNor^if>csia>cN<Tt"- t^t^f^t^cococn'j-cnTcocot^cNCDin^'OCMT-aioot^mroo^

ro>3-inu3t^coaocDcrioO'-'-ojcNco<3-ir)iot~i^ajoo<N^Tin

T^rT<g-«T'T"3'«T'Tinmir)ir)u')LOifiLnuiuiif)ifiir)LOco(D«Dio

oooootnomoinoinotnooooooooooooo

cor^<DG>oo*-'-c*eNcoreTTij->cot~coa>o*-pjpo'r<oa)0

r~t^r-t~-oocoQO(j)QooooococDcocoaDcocoocnCT)a)a>o)0)0>o

CNOJCNCNCNCNCNOICNCNOiCNCNCNICNCNCNCMJNCSOJOJ CJOJOJOJOO

33
> Q

t- Z

•-h 3 (/) O O \

O V) 2 —i

uj u. > O

tnintDCNinu3(D'<-cnro-^cooocDCMir)0^r«>

mmoioooO'-'-»-(M(N(NPinofi)^<j

'-'-•-OJCNCNCNCNOJCNCNCNCNCNCNCMCNCNtN

a

wai'-^'-inooinnaacDinMDCDccui

c~cNf»cD<j>rr)cr>*j-CT>r-.-nr*-ooinc\ii-r-« o^rmor~-Lnco<D-^'-^Ta3roO(OiOi^T o n cn »- «- — •<-

>

N(DiD<}'CV(Onoioin(jiO'-a3ron(D(,)(OOKi<0<T(Dr«0)(0

wn(flonraj^ncN(\OflOMomncMT-ooo)oia)(DNMO

>- -x. aO -i a o

aDi-ot-t^-mot^ojir)"3-ocMCNO'-r-cD(D'r-ron»-ioncooo 0(DwoomoMDNn<nnininin^cMOO)iDooNn(OiiiO)

U3'-t^<NCD«- ,^'r^»-CM(r)<Tm(Ot^O>'-00<3-(£)CDO'^-n(D(TlC<

lOlOlO(O(OlO<D<l)U>lOlOlOl0lOCQ(OlOlOCQlQtOl0COlOlQtQ^

"O

oj3

£

•r~C

oo

I—

>

Q.

< >- -I ZOO <x tx S

UJ UJ \ (- Z "3 z uj

UJ

uj >

a: « *

O h- s

X < < O > Q. -• 5

toM^rooioiCM'-iflr-Nr-MDOuiiDmioofOoo^N'-wp)

cN^cNcomh-cNOnn^oiini-r-uJTT-t^rot^^inoo^raO'r-

'-ooLDCNOCDCTicrioint^O'a-oO'-cDLncMooinr-ooTOooinoo

O-^cnLnr^t^mcno-'-'^cNojCNcopisj-ininiot^r^oocnO'-CM

OJCNCNCNCNCNC^CNCNCNCNCMCMOJOJCNCMCNOJCNC^CgCNCN'NCMCN

^rTinm(DOU3c--cNCNOOiti)ncNa)OCNU")'-'-tot^co(or^co

cNLnocoOT(T)cocnu-)ioir)<g-n«-incni-csinn<NT-ocoT-if) r-tDrMt^-g-CNOcncDCNLrico^^rt^cNr^ncoroooncDncMCNTr-'-T-'^^CNCNCNCNCNrMOJCNCNCNCMCNCNCNOJCNCNCNCNClnn

WOJCNCNCNOJCgCNCNCMOJOgCMCNCNCNCNCNCNCNCNCNCNCNCNCJCN

Ttoaj'-inaj-'j-Mn^coi-ONOONintoot'-oooiaxJ)

r-aiT-«3-tor--criot^iX)Lr)"^^T'TnnfOfNCNCNCNCNCNCN'-^T- 0)01OOO0O'-010l0)010'ilJI010>tJ10101(J101010)010)(JIO 00^----'-'-0000000000000000000

UJao

X

o

o

CO

COa

UJ_lo

S UJ O

CC > S

LU •-! "\

X I- <

h- < a o > s

CO -< • Manuj S

a a

UJa

3 <

(/) a

UJK

a.

OOOOOOOOf10)'-P)<fq-lOMI)OM<rifl(OOtCOO oooooooO'-otDMnin^t-ciflniKNmfl-ONO)'-^ OOQOOOOO'-CJCN(T)«3-in<0r~<T>OCNTU1l>CX)O(y)t-»O ooooooooooooooooO'-'-'-r-r-T-cNCNcin

cntocDt^r>--r-tDionoM(j)»-tDOtDir)cr. iDOinLDt^cNojoit^n

ir)rofoifiOh-CT)CDror^in»-r)TOMtr)(r)cooa>uD^Lnr~-t^cNT VCTrNrnDOUI'-OlMnoiOHDJlOIIStDOOIOTflOCOOl

r~t^r»isaoroo)TO ,3"(J>^ra>rocot^r~{r>ir)'T>T(T)cN'-a)f^in

o ,Tin(DMDa)roooO'-'-piP(n^ui(flr>ooo)0'-onno

in

CM

ID

<X<

a.UJ

a.

oooooinomoinouiomooooooooooooo

<or-cocnoO'-'-CMoiroro'T'Tin(Ot^cDO)0'-cjfo^-(OCDO

ivt^-t^t^ajcDCDCDODcococooooococDooooaDcnaicDcnoaioio

OICMOIC^C^OtCNCNC^OICNCgOJtNtNCNCJCNCNCgCJCNICJOIOIOICO

34
> Q

t- Z

-" 13 l/> O O ^l/) S

> O

m'-t^io»-<TU'>*-'T<Tcn»-f~or»ir>»-ir>

oina)^<i(CO<TNon(r)a)'-ncons fflooiooO'-'-'-cMOKNoiconoT^ »-»-»-CNC\CNCNCNCNCNCNOgCNCNCNCNCNCN

a

<_> —

c\iTCMo<t^T-«T<T(N--otot^a>cn<a-o>c)

MncNOOooiD'rvooinwa'Dmina)

ti n t\ '---'- >-

>

rotot^n'-'-cDrouj^cDoaicDinaiiDCNt^minrnooooomo

ir)CNma>mmt^cNcoO'-t^a)«Tootr)<NCNroiooif>oioo<TO

(DOfMino ,5-CT)a3U3t^oooaor~(r)<a-cooj^ooCT)CT)CDOot^r~

^•ir)inir)a)tDtot^cnu3iD(i>LnininmLnir)ir)inir)^- "Ti'"Ti- t

>- iC

a.O -J oe O

t- E

z ~

uj \"3

lD(0CMinr-^(DNNOin ,TOCMCMUTM^nU)MOO(O'-N

O^Tcn^-^oCT)OtT)cn^-ir)u:a)a)ir)<Tojoa)iocN<j)U3a»'-o» Oinou3CNi/)t^-'-<3-<of^oocr)0»-<,)ioc^(j)ocN'Tinr»0'Tis- (C(£(£COv£)tQOCQOlDO(DvDCOCDOt0OOOOO(DCO(0(OCO

•o

<L) £

•i—

+-> C

oo

a

< > -i zoo c: k 5»

C0OCDt^'^CDint^CNa3OOOOOOC0«TOCDCT)Lf)ir)'r--r-00<0

cDOt^-t^-CN'-ncDOcNO^aiui'-cNOaDmoi/iO'Tcon-CDCN

^•^c^-TCN'-ocDoiDO^Tt^'-incNaiLnojaiLficNCD^Tr^cDCN coO'-ninot^t^criCTiooo-^'-cNCNn^T^TtnoiDt^aja)'^

CNCNC\CNCNC>4CNCNCNOJCNCNC\ICNCNCNCNC\IOJCN01CNCNCNCNCNOJ

ro f- o cNinofflcD^aiui>u^N(OintNOon'-^'C')(j)<rtD

rocN'c-a)oi---^t^OLr)r^cocor--iX)'-ir)coO'-'--^OCTiin'^ir)

-(TJIOMDOIO" CNCNCNfOMn^J-^rintDlDf^t^r-QOCDO

*-t-i-t-^^-^CNOICNCNCNCNCNCNCN<NCNCNC'JCNCNCNCNCNCNC0

CNCNCNOJCNCNCNCNCNCNCNCNCNCNCNOJOJCNCNCNCNCNCNCNOJCNOI

CD -Q

ro

LLl cro

Xo

o

V)

UJ

UJ >

(X. —• KC O »- \

X < < o > Q. O — s

(/) or. .-c uja

_i S UJ O

oi > 2 UJM\

X t- <l i- < a o > s

f-< cr ro

uj 2 a q

UJ

cr=3

CO

LLl OSa.

a

"TOQO'-inaj'-'a-cn^-LncnT'-aj'j- — air-tooLn'r«3- «T«rin t^a>-r-TOr^(T)O'-O<T)CX)00C0t^C^r^LD(iDOO(£lOLDOCD'J5

CT)CTOOOOO^^O01CT)OTCr)CT)01CTlCT)CT)OTLT)CT)CT)01CJ1CJ)0^ OO-- — <- — --~*---00000000000000000

OOOOOOOOOLnTT-CDLncNCDt^t^aDOrOOOLO'T'TrO OOOOOOOOO'-cnr^^TCNOLn'-t^no'DojoiLnaj-^-^r ooooooooO'-'-tNnfininaKD'-o'noMiiciico) OOOOOOOOOOOOOOOOOO'---"-*-*--'-<N0JCM

rocDiDr^t^-^cDOLnfor-ooooOLOOLri^-nnCTirMoococoT- LOCOrOLnOt^CTlCOTOLO'-O'TrMOlDCNCDCDaDO'TOCDLOCO ^•roq-t^-nuDOLO'-oimrocMT-ot^<Ti-t^fr)cj)LO'>-r^t-~coao r-t^r-t^oDroOTTOLnoifiOinocncDCDcocot^t^t^tDLOTro nTiniDMDtooioO'-'-MCMnfO'TifiiDt^axJiO'-ninN

^^^^^^^^inLOLOLOLOLnLOLOinLOLOLOLnintocotoioto

o

in

UJ

cr3

»-<a

UJ

a.2

UJ

oooooinotnoinoinomooooooooooooo

<Dt^ooCT»oO'-'<-CNCNroco^r'TLr)(ot^cocr(0'-cNcn>3-cDooo

^t^t^r^CD0D00CDCDCDCDQ000CDCDCDCD00000>CJ)a5CJ)(J)CT)CTIO C4CJCNCMCNCNCNCNCNCNCNCNCNCJCNCNCNCJCNCNCNCMCNCNCNCNO

35
>- o

»- z MJU)

O O *s. O CO s _l

LU U. > o

a-C0CMC»C»tDf»JOItD«-C)«O<D!TSrtnt»

cooioimooO'-'-wpiPiNnntO'rT

*-'-»-'^CNCNCN<NOJCNCNCN<NCNCNCNC*C«

a. n<fno(OPnn<rcoocDMDOooo)(nin QOTCNi-c^-tDin'T'-ocDaJOcoinoT^o

OCNCDOLnaoinroifiT— co en oo in <r 10 r» — in n oj -r- .- i-

>

t^wt^'-^c^ncnnajcOf-tooir-t^'-f^cDOiO'-ocNciinci*

'-ajOCMOtOlDC^t^CDt^'T'-'T'-^tvtntOCJlCJt^CNOO'-lOO

incoa)CMr--oijr)roT-T-tncJocDh-ir)cT5CM-r-oocDa)a5cx)t^t>.

•O

dJ

=3C

•i-

!-> C

o

c_>

CD -Q

> x

a.o _i a. o

V- s z -_-• LU

"3

>

a. _1

-i o

< > X •v

t- 3

z

LU

_J< >- _J z a o

cc cr p

UJ LU \ K- z "D z UJ

*-H UJ LU >

£K *—

>c O (- \ X < < o > a. o HH S

CO crUJQ

_j s uj O

a > S

LU M \ I h- <

UJ - < Q.

Q-. o > s o to hh X H-l m n a LU s o a q

tO

l~* LU

oo a

5 r> < a LO a \ co s= tu LU _j a. o a. s

tn LU

t^ a:3

u> »-< si a:

LU

a.£

O)t«»O'-01C0C0t>-01t^00'-0101LO4-«-CDCD^rCDt71CDLO'J-tDOI Tr~T-Lnocof^t^-cT)'j-cooocoa)cnt7)OOLO'TO(CT)tDoocoLor^

TCJiL0OC0C0'-'3-t«-O'-CNt»)'TL0t>cn^-C0Lr<C0C0OCNL000iT

CNCNCo^r>r<TLOLOincocDcocDcocDcocor~r^t^t~r>-a3oooocDO>

cdcocococdcocococdcocdcocococococococdcocococococococo

l0OJO0)0>PIMn<I<TO0)T-nN00CVPi(M'7fl0(0 0)00I,)lDa)

oirnO'-'-aiaj'-ocoooKOini-cNNONncoroi^'-oooN

aiLO'-ajLnncNCNCNOi^Tt^^LricDcDcooconaicDCNcTit-Tto (CcoO'-roTmiOM^tDoooioioiO'-tNoincTTininNCDO)

^»-C^CNOJO(CNI(^OJO(C^OIC\ICNICNI(^C^C0C0<T)00C0r0r0C001C»)

CNCNCNMOJCNCNOICNCgCNCNCNICNOaCNCNCNCVIC^C'JCNCNCMCNC'JM

Lf)LO^cT>rot^T-cD^j''3-(DcocNa3cocr)t'i^Lr)condQOoot^"^o

^OcomntN^-ffloicnninioin^oinsjO'-iNiN'-ONna) ^•mnco^rcNOa3r^<5- QO'r-'^t^ocD'-tocNr~ojt^c\t^<x)cDLO O-OTTlONOXDaiOO'-'-'-OIOIfOtTT'TininiDlDMDO)

*-»-»-«--»-'-*-»-t-CNCNCN<NC\IOJCNOI<NCVOJCMCNCN<N<NC>IO»

CNCNCNCNCNCNCNCNCNCNCMCNCNtNCJCNCNCNCNCgCNCNCMCNCNCNOJ

TtooO'-inco — TcDfOCNiDcscnt^'roj^ooicncDcncnO'-CN

(-^ai'-«Tcor^a)o»-*J"co<Noj'-T--^-»--^-T-ooooO"-'-»- CTiaiOOOOO'-'-OOOOOOOOOOOOOOOOOO

OOOOOOOOOOO'-i,!lD'-fO0j(Il(VlD<-S!rOlDT OOOOOOOOOcOnOI^-TCN^-rr)CD'^-'-t^TOr>-^"q-00 OOOOOOOOOO'-CNCVCO^TCOt^OOOCNntOt^CDCNLOO) OOOOOOOOOOOOOOOOOO'-'-*-'-»-«-0l0<0l

fOtDcot^r~-^tocOLf)cDr~-cDOtocoa)Or~cD'- <3

- t^cNCT)toncM LOncoLOOt^cT>co^r-Lna)'-ocO'-ojO)LOOooLOt^f^t^LO»- Tn<Tt--ncoOLn'-mr--ooO'-'-0'^-^rmcDcocDcococococo

r^t^t^t^ajotDTOinOLO'^-cO'-'-'-'-'-'-'-'-'-'--'-'-'^ CO^-LOCOr-OOOOCTiOO'-'-tNCNrO'TLOCDt^OOOO'-CNTtOOO

T'a-'3-'T"3-^r^r'rLOiniOlOlOLOlOLOLOLOLOLOLOCDtOtOtOCOlO

oooootnOLOOLOoinoLoooooooooooooo

C0t»00<nOO'-'-<NOJ<nC0<r'TL0t0t<-a)0>O'-CNC0'T«)C0O

r»r^r>-t^<i»mcx3tomooaocnooc3CDa)ojo3cx)c7>cnc7>cT)t7)OTc7)0 CJtNCNCM<NCNCMCNtNCNCN<NCNCNO»CNCNOJtN<NtNCNO4CMCNO<C0

36
> Q

h- Z

(J O \

O t/> 2

> O

t^cocx(o-<-ojoocot*-coi^-coa>t>Lncoo>co

inuDCNiDOfococMtDococooicNinoioo MDOimooO'-'-oioiMCNonTiin

'-'-•-'-CNCNCNCNCNOrfCNCNCNCNCNtNCMCN

a

XL

>

o(t^inocor^«rooincMC^<Noio>ooif)a)in aiLnioooroiDojcomLOcocNn^rcNCO'-

MTirnnioniO'-indnoiLOoninn cvindTTOOiOoioiooNnoxtos

Oi ^j-ir)'r-mcDCNOt^t«-tro«TOOfotna)t~-'-cM«oo»-oor^a>CM oiDCDa3<ToioocDa>cNO^'-cMt^tna)r^ooonoocna)T-in«- v <r v t in in id (do NaxDiDininminiflintninvT'j-'T^f

>•Q.o

CC

cNOOoooimaicot^t^TQCDincotot^cM^r-cDt^t^TroincN

0'?r--a)cO'-aicr)OcO'-cNro'T ,T^-rocMOcoincNO)too>'-o oi<ioi<rO(,)incon<iiOM)0(3)Ocv<tiDa)oi<-(<)<T(oo)(>)(o

T-cNCNco'Tq-'q-q-mtnmmininiDiDujtoioiot^f^t^h-roooa}

(01OO(O(01D(0(£IOLO(O(O(O(OIO(OO(OOLO(£)(O(C)(0(O(0(O

-O

a>C

4-> c

oo

a. -i

-» O

< 2

I -^

t- -o z

oocDmcooi'-inonnconoiincffflinm'-in-wioMONa)

a)iDif)(^na)iot^<r)oro'j-c\or--cDooio«J- OcD'-ino>cocNto

TO(£iojCT)t^iDir)ir)'g-(i)r>jcooooo(-~T'-oo<3-»-r~-c»)4oa>-<- Lnt^coO'-cNnq-m(£>iDr-r^oocoCT>(nO'-'-cNnro<3-ir)tflco •^'-T-CNCNCNCNCNCNCNCNCNCNCMCNCNCNrOCOrOCOnrOCOnCOO

OJCM(NOJCNtNCNCM(NC\CNCSC<CgCJCMCNCNCNCMCN<NOJCNr>iCN<N

O) -Q

A3

< > -J ZOO

LU UJ \ I- Z "3 Z UJ

cnr-«3-cD(£»'-t^«ToocTit^int^oooir)(T)ioa)(,)o^or^(s-uicN ^r-oj0iocot--ocDt^ncDt^t^r^(T)CDT-roincpioio^T«-t^<N

CNO'-ir)'-coOLr)(T)'-ina3»-^Tr--nQOM'cr)^-a)^T<T><?<TPr)o

cnocjoif)ir>iDt^a3a)aia)OOO'-'-cNCNrif0«T«TiniDt>-cD

O'-'-'-'-'-'-'-'-'-T-'-CNCNCJOiCNCNCMCNCNCNCNOiCNtNCW

CNCgCN<NCNCNO»CNOJ(N<NOgCNCNCNO(<NCNCN<N(N(NCNtNCJ<NCN

LU >

cc -. sc OH\ X < < O > Q. Oh2 to a

>-* LUa

_i S UJ O

X t- <

LU y- < Q. CC O > s O to H* X •—

a co o LU s o a a

4/1

1-1 LU

co CC

Ji 3 < o to a. \ to 2

UJ LU _

i

CC o a

so UJ o ce3

t> H-< x

CC

UJas

UJ

rrtoco«-LOoo-^TcninLn»-ootDLf)rtfNtNCNooco^r'TintDcoo

r~CT)T-'»uDr~cr)0'-r-ooLOLf)LnLr)LOLOininLOLf)LOLOLOLr)tD cncnooooO'-'-oooooooooooooooooo 00'-<-'-<-«-'--<-*-'-'>-i-'-'-<-T-i-.n-T-*-r-r-T-T-T-*-

oooooooooo*-to<ro-t~-io->-cn^-Ln*-a>cocncNr-*r ooooooooocotntocMaiOT-r-cNCDLOCNOomojt^i-fo o o o o o O-O ooooT-nnnm id oo o» n 'trio co <- in a OOOOOOOOOOOOOOOOOOO'-'-'-'-^-CNCNCJ

C0(Dl0t^r^*-lDl0Lr>L0<T)a>OC0tD<T00''-OC0'-f~O'-OL0(^ incocoLfioi^CTicDTajcNcoooot^OTaiooocootDoooi^cNco IflfM'UDOlll'-IDOfKIIOl'-lO'-lD'-IO'-lflO'T'jnM

r^t^i>t^oococr)q-OLOi-tO'-tocycNcoco«3-^-LnLncotor»coo) coTintor«-cococnoO'<-'-cxcNco'TLOtDt^cocnO'-cN'T<oco

^TTSTT^r^T^rLOlOlOLOlOLOLOLOLOinLOlOLOlOtOJOtOtOtO

oooooLOOLOomoiooioooooooooooooo

«oi>cocnoo-^-'-oioicoro«T«TLOtDt>-cocno»-cjco'!r(Ocoo t^^t^t^oooococococococDcocDcocooocococncncncROcncno

OJOJCNOJtNCNOiCNOJCNOjCJCNC^CJCNCNCNOIOgCNCJCNtNWOICO

37
>- Q

I- Z — zi in o o v. OU)£

> o

too>o>cnoe>«-a}CM»-t^o<Nooaco«-oi

C0C\ia>*r00CMC0C\lt^'-<Ta0'-<J-C'>-(NCOe) iDoofflcioioO'-'-tNtvNootoi'rm

•-'-'-'-'-CMCNOICNCNCNtNCMCNCNCNCNC*

a.

5C

COCOinONTOlOMJli-COOjT-t-OKDV

in<j!ifla--NC. niDNOo^rmoiooow

occo*roocr>f~ir> tncNCN*rcr><3-o<3-or^

»- Gi S. <*5 CNi T- T- y-

> nooioiOPiroo'XfoinNOTMDKi'-noiinooonD'fN'-

^(or^i^cMincNaoifi(j>coinioiii(T><oocoooocor--cNa)'i-in'r-

(DONinOCOOJIDCN'-Ol'T'-OIMn'TOIr-^OOXriOOOSN

a

=3

§O

CD I—

-Q

> 1C ao _j

CC o

t- s z —

UJ

"3

>-a _1

_i o

< ?

X V »- "3 z

UJ

_l< v _l z a o

a: or :> UJ LU n.

f- z. -D z UJ

»-H UJ UJ >

or •— >£ o »— V

X < < o > a. o HH £

to cc

1—

UlQ

_

S UJ c a. > Si UJ 1—1 \

X t- <

UJ t- < a a o > s O (/) »-H X HH cr ro o UJ £

o a a m

*—

UJ n a. s 3 < a (/) a

>x UJ £

UJ UJ

_j tr o a. £

in UJ

CM 3

t^ »-< 2C a

UJ

a.£

otot^mcn'JT'-cnmooicnoc^oooiDt^moi'-ot^cocoin mmiooO'-ano'nninoofli'-'-M'-'-oiMnNOMnaooo TOiq-cDini^onujcno — cn«Tint^CTiooj<^(ococn«-«Tt*T-

•»-T-ojcNc»)cT)'3'^r^T^, if)inininir)mir)cDio<o(OiDCDr^t^r»co

(O(O(O(0(0t0t0(0(O(0(O(O(0(OtO(£<0(0tQ(0(OCO(O(0<0(0(0

o>'TO'3-a)0'Tcooocoin'T'Tcj'-oot^'-inoir~a)'rintDio<r

(00(0'3- iooir)ni^conTn'-ooo)oioom-^t^cjf«.^oo<TO)

•»-t>-cNoo ,Tn'-ocoont^'-incDincNCT)iDnc3itDCNO>>-T«) Tint^ooo-'-cNcncoTininiototor^cDaDaioO'-cNCMTinu)

T-'-»-'>-CVCNCMCM<NCNCNCNCMCNOJCN(\(NCNr0<v)nr000n00C»)

OICNCNCJOICNCNOJCNOJCNOJCMOJCMCNCNCNOJCNCNCNOJCNOIOgW

inf»-MOO)tDlDOnVMM7CO(D^OD'-inoi[OCOO)0)U,)W

conmait^cNO'-cO'-oO'-nncNcnTt-O'-cNoi'-ot^na) -inairoajiOTCNOOKNiDrnwinoifl-scNNMNoir-r-o

©<nocNcoTm(or>-r*cococoa)aioO'>-'r-ojojno')fin<or*

OO'-'-'-'-»-'-t-'-»-'-»-'^'-CN<NCNCN0J0JCJ0JC>JCMCMCJ CNCJCMOJCMCMC<OICMCN<MCMCMCMCVC\OJOJOJ<NCNOJCN01CJCNOI

Ttooo — ir)CD — Ta)CNinncNCj<NCNoi^rmcooocnoc>4^rt^o>

t^o>»-"TU3r~0)0'-ocj)<7)dCJ)cr>o)a>aio>a5CT)a)ooooo QOOOOOO — '-'-OOOOOOOOOOOO'-'-'- — «-

oooooooootooiomTinTOOT'-ocMinooiooio OOOOOOOOO'-tDCOailDCOOO^-OlOOOOt^^rCNt^CMtD ooooooooooO'-'-nn^iDaioi'-nTfflflOr-ino) OOOOOOOOOOOOOOOOOOO'-'-'-'-'-CMOICM

<ntO'^)r~t^T-iD(Di/)0)r^^rncjDt^ir)DCM^-t-c>jt^f^cNTC4in innninOM3)a)TfO(NO)inocninininunoNCDO(oo)MO

T(T)Tr»fOlOOin»-f--OJlD>-(DOa>CO[^tDir)'3-flOO<NO<T>00

r^t>-t^t>-eocoo)<rotnt-<DCMt>»nn'Tin(Di^cDa)0'-c»)t«) p)<jiO(OMDa)0>oO'-'-e<oi(')^ifliONa)0)OMninM)>

^rc«r<T9^r^r^-iou)inLnininm(nix)Lomtntn(ou>(£>u>u>(0

oooooiooinomouioiflooooooooooooo

<ot*-ooo»oo»-'-cwci(»)cn*r'Tincot>-oocnO'-cM(n"*cocoo

t^t»r>r«coaococooocoa>a)cocoooccicococDa)a)o>a>(7>cna>o CJCJCNOJWCMC^CMCJCVOICNCJCNCJCNCJCJCNCNCNCMOJCMOICMCO

38
>- o

t- Z •-> 3 </> u o v. O CO 5

> o

a

(j —

it

>o

(DeoNOKDninNn'rtneocM'iinTOt'-

coooo^-oocNooootncNLDcnntocTiLOOto

tDOOCDtDCDOO'-'-CNCNCNrOnrOTLOLn

^'-r-'r-^CNCNCNCNCNCNCNCNCNCNCMCNCN

«(0(Nno(<TS(o<rooo)CDcoa)i/)inT (C3>-iDcnu3Oir>c\ciuia)i0cN^rNC0'-

<j-CT>^-CNt^msro<Tsr<rcr>^int--oir--ic

rocor^ — r~cNor^cDCNrj<TtT>TO<3- or~ Oir;nLomofOcoN(i)L'iii^nn(N

C- O ID ro CM CJ t- *- to *- '-ninoicifoi/iONTnocotDiotNOJOonMDioioo'r

«Dp-oic\r-0"ToJoo^ron<4-'-cT)t-LOoooj-^oocT)OCDQor»t^ cnronTTLnLneDr-ootoiDtDLnLOLnLOLOLOiDin^-^r^'T'J-'T

D(I) 3

C

•p-

-!-> C

O

CJ>

>- s: a.o -i a o

i- s

z -'

LU \"3

5-

Q. —I

-J o

< £

X \

h- "3

•r-t^r-inrocoO'-'-cncNO'-t^ocnOLntont^ooh-'J-oi'^O O01(DO(Nmi0<T^r0NO)OO'-OOC0a)1'-C0in(NU)M3) O^'OiinocNinco^TiniDcocriooi^inMji'-ot'KDOKNin

••-'-•-CNronronT'T'T'g-^rrrLOLOLOLOLOLntoiDcDcoiDf^t^ OOOCOOOOCOOCOOOOC0(£OO<£CDOOCOOOCO(OC0

cNroif)0(J>0'TOCN'Tcno<T>r-'TLr)Lncr)'-t^rocDCNt^«3-oiri aiTOiinoroMDinTmniooT'-ooincNmin'-cD^NOoi tNTifiNOioiO'-cNnn^^ininiDiDNOotDOioO'-ot^rin

T-r-T-r-T-.r-C^OJCNOJCMCMOJCNCMCNOJCMCNCNCNnOOOOCOnn

CNOJCNCNCNCNCNCNCNCNlNCNCNCNCJCNCN04CNCNOJ<N04CNCN(N<N

-Q

< V -1 zoo a o: 5

LU LU \

t- Z "3

LOt^oait^OCO<3-OOOCOOLOOO»-COLOt-CTlC\IODI^T-T-cn^rCT>

micmiO'-iowT-inoN'-otMNainincDOOoooiin'-in

oyoocNi-~q-c\iocot^OTt^onco<3-cr)s3-0'/)OLoaiaicTico

t^oocn-r-o(n'3-LOLOLOt^t--i-»oooooocncnO'-'-cN<N04n^rLO OOO'-'-'-'-'-'-'-'-'-'-'-'-'-'-'-nNOKNWOtCinW

CNCNOJCNCNCNCNCNCNCMCNCNCNCNCNCNCMtMCNCNCNCNCNCNOJCNCJ

LU >

CC -• ^ Ol-\

X < < O > Q. O — S

co a:

^rooO'-LnoO'-'TCD'r'a-LOLOt^ai-^Tt^tTi^ooiDooocit^Tr^CT>'-«TL0r--01O'-CNCNCNCNCNCNC0C0C0rr)T^l-T^-L0L0L0L0 OlUOOOOO'-'-'-'-'-'-'-'-'-'-'-'-'-'-'-'-'-rr^ OO^T"-'-'-'-'-— — -*-— t- -r- -r- _T-,-,-,-,--r-^,-TO

XO

O

CO

COa

SlUO

CE > £ LJM\ Ih< i- < a o > s

CO >-> • — cc co

LU S a a

LU

cc

co

CO

LU

cca.

<

Q.

OOOOOOOOO--OO<TC0L0r-L0ait'-<T>r0OCT>a>r0*-''- ooooooooo-^-cotNcoLOCNt^rocncoco^cnto^T'-ooLO ooooooooooO'-'-cNroTcor^(T>^co>q-cDoocNina) OOOOOOOOOOOOOOOOOOO'-'-'-'-'-CNOJOl

COOOt^r^--COCOLO^r~"3-CD^TCOI-~CO'TCX)OOCNCT)COOCOfOCO innroinONcnoo^NcoorNmcDifliDcO'-iDnooiOfooo <jntM^iDoin>-MioiDtM(Di-iN'-icooiinotDMD

t^r-t^f^cDroa5^rOLn'<-t^cNcDroiocDt^cDO'-coq-cooO'-'a' ro^rLOcoc^cooocDOO'-'-ojcNco'TLOcot^aiO'-cNcoLOOoo

T^r«3-'T^-Tf'3-LOLOininLOLOLOLOLr)LOLOLOcotocotocDcot^

o

in

LU

cc<

a.LUa

oooooinoinoLOoinotnooooooooooooo

cDr^oooioO'-'-cMCMroco'r'a-LOiof^oocDO^fNcottoajo

^t^r^t^coooroaDcx)cT>mcoa)coa3cx>cT>a)ooa>a)cT^ MC^C^C\ICNO)CNCNCNCNO4CNC4O(CNCNC>JOJCNCJCNCNO(rgCNOIC0

39
> Q

H- Z MOW

O O v. o to s _l

LU U. > o

CJCOCOinCMCVOOCncNtncDOCTlCN'STCOClOO

cNOooTairooiinoTcocNiricDCNQo^TO) tDcooocDCTioO'-cNCMOjnnroT^rinin

'-'-'-'-'-CNOJCNCNCNCNCNCNCNCNCNCJtN

a

o —

o

>o

U3^in(J)CDOlT-r~CT)U)Ot-C»5CD'>--^inQO <\D0nriNC3CM(NOjyj01CMM00)NOa)

^<j--(\a)N(,)(Nnm<-oioiso'rno(

tDOJl0C0C0L'")O ,3'<TO'-nc0(T>O<TOr~. CD'-'-fT^oinoajMDinq-^'jnnn

o o li n pi >- •- <- in —

N<TOl0lOMJlOe)O^"TC0OHi)OO0)'rffl'-IOaiC0O(fl«

oocoooocNnt-»a)ir)"TOOOO^Tcj(oco^TioOTa>inCT)coo)

roirif^o^rt^T-ooTmcriT *-cnt^-u-)rocN«-oocr>cocct^r,»co rec^co^^^inint^cooioioiriLOir>ininir>ifiin<Tsr'i-<j-<3-<T

>-ao

a.

^r~-coiD<3-^TOiDO^nooir)ooin^rcr)a3ir)ooa)r-coO'-to coiDinuiifloganfliniflaiO'-'-'-'-oooiDT'-aiinninMa moinoinooociiooioo(r,)^in^cnocN<f(Bt»0)'-<it»o

COtOCOCOlOLOCDtOtDOtOOtOOOtOOOOOOtDlDCOCOtOlO

<uC

•r"

+-> C

o

c_>

>-

Q. ocMirxTOODint-oxDNfflinoiooxnrnooiinmT-w^inN

_io lOTnin'-onMOiD'-'-oco'nntnp'ioiDOJNCMionaif

S r~ojt^cNooiDTCM'r-oincDoi(Dor^^-^oo'3-'-r--"TOroinoo \ •^nTtor^oocnO'-cNCNc^conT^rinuDtDr^oocDcno-^r^co

"3 T-r--i-^T--r-T-CNCNCNCNCNCNCNCNCNJCNCNCNOJCNCNCNC0nnO

OJCNOJCNCNCNCNCNCNCNCgCMCMCNCMCNCNCNCJOJCNCNCNCNCNCNOI

CU JQ

(0

< > -I ZOO iras u uj \ t- Z "3 Z UJ

TOi<Nooar.r--<Ta)tDOCNrotDcDt^a)cocN»-cNir)CM^rcNt-a)CN

^inn^niri^cD'-'TT-q-inin'a-oincoO'-'-'-ooiinotn

^•^ODCNUsrO'^aot^iDcnoiLncD'-f-cNt^roconcDrot^r-t^d) «ot~-cao-^cNron>3-mina)cDU3r~t^cDCDai(j)00'-T-cNn«3- OOO'-'-'-'-'-'-'-'-'-'-'-'-'-'-'-'-'-CVPKVPKNClPI

CNCNCNCMCNCNCNCMCNCgCMCMCMCMCNCNCMCMOJOJOJtNOlOiOJCNCN

CCO

I

cjo

CO

UJ >

cc -• se o i- \ X < < o > a. -• s

co ce

.-. u

a

S uj O

ce > S

uj >-< \ 1 t- <

t- < Q. O > S

</) l-H • nanuj 5 a a

CC

</> to

UJ

CC

Q.

tioaj'-inaj^Tcnioih-O'rNonoO'J'tD'-fNOi^OT'j'

t^cD'- ,^tDr-cnO'-"a-LOLf)tDeotDt^t>-cocococncr>a)cnoO'- oifflOdooO'-'-'-'-'-'-'-'-'-'-'-'-'-'-'-'-'-wwo 00»-'r-r- T-^-^-.r-^-r-T-T-^-r--r-^^-^-^-n- T-r-^r- T-^

ooooooooO'-cNn'-cMt^q-coQoco-^cMcocMcnt^ain- OOOOOOOOO'-tOCMtDtDrOCDLnCNOCOtO^Tm-r-tDt^tO ooooooooooO'-'-<Nfo^TtocoO'~coinr»cf)0(too OOOOOOOOOOOOOOOOOO*-^-'-*-*-»-CN<N00

rootDt^h--r-tDcOLr)r~-t^to^cr)r-ococNojcr)T-Lr)OLO"3-cn"3' Lnrontnot-crico^rcrioocncnT-cnOLonoot^oiocncococo TroM-t^rocooLO'-t^LnroocDi^ro^cocOTCN-^-ocot^tOLO

r--t>-t^t^cocoer)'3-OLO'r-t^nco<TtDcocr)'-nir)f^cno^rcocM C0Tint0t--C0C0CnoO'-'-CNCNC0^Tlf)tDC0Cr)O'-CN«Tt0C0T-

^r^r'T'T«s-"iT^r«TLOininininLOinif)inif)LnLOtD(oioiototot^

in

»-<

CCUJ

a.5

UJ

ooooomoinotnoinomooooooooooooo

coiNcocnoO'-'-wcMnco^j-^Tintot^cocnO'-cNco'rtocoo

t^r~t^t^<Dcocoa3a5(nQoa5coa)a3a3a3roa)CT)cncncno)o>tT»o (NCNCNCMC>40<CMtN<NCMCN(N<NCNCN<NrjCJCNCN<NCMO(C*CNOgO

40
V Q

I- Z

•-• 3 </> O O -v O l/) S

> O

a.o —

>

t'~CO'-»-O'-Oa3O<3-CO(0C)CO»-LO<T«-

^TT-OCD-^inCMf-CNt^^-inaiOitDCNCDT ujmoioioO'-'-tNiNnnnTTinKHi)

•-•^'-•-CNCNCNCNICNCNCNCNCNCNCNCNCNCN

PIO(3)OO«Ol0rt(NWOia)0<Dl0«T

^co^cr><3-ooiot^CT>t^-cO'«-coojcOP'>aiio

LO co v <\ CM •- r- n

0)CNCNOr~-ct)(DinoO'^c^ooofr)OcT)if)"3-T-oit--cNna)a3cO ^•CTJCDi/iLninaor^cDCNncD^^-t^tooaioootO'-r^couD'-t^

*- cn ^r t*- — "3-QOLnoair--cNOcD(D^rro»-»-oc7)C7icx)a3i^t^(D

T3

CD3

C

•r-

•4-> C

oo

CD

> 2C

O.o _J

CE o

1- s

z >^

LU \"3

>-a _1

_i o

< s

X \

t- "3 z

LU

_i< >- -J z o o

o: c: s

cDTt--in^raiooooir)roi^Lr)cnoir)ojLr)^-cTiT-ocDmcaoocN (D(flinocoiri«oa3'-Nroo<io(Moo3innoiO(,)inNO)

»-tO'r-tD'-n(£ioicN<TtDt>-a3<T)OCNTCDt^a)'-ro^rcoa)CNin

oO'-'-cvojooinnnfonnT^T'T'r'Tinifiminirnoco

U)L0CD(£)(£>C0(0^C0l0U>C0(0(OC0(£IC0(£)U3CDU3(O(0l0(X)CD(O

0(DOOinNcoMO'-<Toj^<nflnnT-cDmn-(D(D^a)0

aDwaicoococo'-aiLnaDooiDoiaioait^naiLOO^ooin'^t^ ffl'-lno^DW'-OlI)^'-lno^nlo^•o^to^to^olJ)^^'it

ocMnmtDt^oQcricnO'-'-r-cNCNro'g-TLOuDiDt^cDcacTi'-oi ^T-<-r-^»-r-r-r-MOI(N(MCMOJOIIMCNC\CNC\OIOI(NO(nn

CNCNCN04 0]OJCNCNCNOJ04CNCNrjOJCMCNCNCNCNOJCMCMCNCNCN(N

CN^rcMrot-ojLn<d-ir)CDCDCNcn«T'-r~LnO!/)CNCNtDLnooo)a3

cNLncocN(DnocotD^Tt^-^'g-f~-OLOOtD-^iD'-(j3'-(Dtr)inT intot^aiO'-oicNro^rTinLOLOuDcot^-t^oooocnaioo^ojfo OOOO'-«-'"-*-*-»-'-'-'-*-'-t-«-»-»-.-i-*-c\|<N0J0J0I

CNCNCNCNCNCNCNCMCNCNCMCNCNCNCNrjCNCMCNOiCMCNCNCJCNtOJCN

LU

CEo

X

CJo

10

UJ >

ce -- sc OK\ I < <

cj > a o >->s.

to cr

.-! LUa

S LU O

CE > 2 U)H\ IH< i- < a. O > 2

to i-< • Maniu 2

a a

^rtocO'-LncD'-'TCT)f~-cNor^cNt~-^T-^-to-^(i)0^rcD — moo) I^Olr-inOMJlO'-lDCOOlOlOO'-tNtNOKTT'TTinuiaiO

CT>CDOOOOO'-»--^'-'-»-CNCNCNCNCNOJOICNOiCNCNCNCNCM

OOOOOOOOOMOOinN'-CO'-O^'-'-nNtOOlMD OOOOOOOOO'-t~-'a-'-CDr--nT-cf)r-.i0L0^-cT)r0CNCNCN OOOOOOOOOOO'-CNCNnLflt^COOCN^-tDCOOfCDCN OOOOOOOOOOOOOOOOOO-^'^'- — '-CNCNCNCO

CE3

to

to

LU

CEa.

oiiDtDt>-r~T-tDtDiriot^tDOCNLn(T)tDco»-cD(X)cr)'-cT)U)r^a) LncocoLnot-cDCDTroonocDOconncDcDooncMCN'-CDCN < sj-oTstniDocn'-coNcouDiniDiDcootNintocMiDOcncDO)

a. t^t^f»t^corocr)^rOLf>»-t^ncT)tr)r^oicN^rcocO'-rotooino 2 coq-LOtDt^cDCDaioO'-'-ONcgro'TLrit^oocDOCNcnTr-ooi

^<T^T^r^r^r"3-TiOLnintr»LOLOLOLnLnLOLr)LOtototDiototorO uj

CC3

00 H-< X

CEUJ

a.s

UJ

oooootootooiootooinooooooooooooo

(ONCocnoO'-'-cNoinnc^iniDMDCRO'-wnq-tficoo

t^t^t^t^cooocooDmcDcoromrocucDajajcocricncTiaicncncno

CNCNCNCNCNCNCaCNCNCNCNCNC\CNCNCNCNC4CNCNC\OJCNMCgOIP)

41
>- Q

t- Z «3W

o o \

O V) s

_lUJ u. > o

ino--'-o«ncnin(\iOMn'-<0'-(,)t-

-"---CjCNCNCMCNCNCNCNCNCNCNCVCNCM

a

oaDirir-tnointDincNOcnTT-cNi-^t^

<NOCNrotDcnr-<X)CNmcO(£)ai'-cr)T-ir)oo

t*- lo n cn t- t- »-

> in^Qm^NCNoanooooo'jfT-oiooTiooiooKNnuxo

cNUDTOoa>'-oo'TCNCDor~-ot^a3TnLnoocNoocoo ,Ta)in

CTiocNioai'-uDCMr^n^r^oor-inrocN'-oaicDcocDCDt^coto

-a

CD3

C

Oo

a.O -J

a: o

i- s

z —

UJ \~3

>•

a.

lDCOOOOOt^-CN^TOOCDCr)int^liDI^-cnnOC»)<TCM<DOJ(DCO«> --ootD^TcocDnoQooinujc^t^t^cDinco-r-ooincNCDint^cno

ooojt^(Nt-»a>CNir)t^O'-oin^-int^a>r-co«TiDCDCT)'r-ff^TcnoO'-'-'-cvtvpinnnoooon'Tf'jTfTinininio LncOCOCOCDOOOCOOCDU30000(OCOOOCOOtOCOCOlQCO

OONIfiNT'-MJl'-OOCNOICOinq-CO'-inCNCOOlPli-OOOl

int^-'-t^r^T<NCOOCDO<J)lDCNCDa)(D1-OlD^inOT»-t^OI

a)OincD ,*cNOcDr^^T(DcNi£)onot^'T'^r^«3-ot--cna)CD'-

<D'<-cNnmiDr^r^coa)(noo-'-'-cNCNroT<rini£>iDr^ooc>*- O'-'-'-'-'-i-'-'-'-'-CNCNCNOJOJOJCNCNOJCNCNOJCNCNCMn

CNCMCNCNCNCMCNCNCNCNCNCNCNCNCNCNCNCMCN04CNCNCNCNCNCNO*

aj jQ

< > _i zoo a: o: s

uj ui \

t- Z "3 Z UJ

t-H UJ

UJ >

a: ~< *: o t- v. i < < u > a. O m S

co a;

»-< uja

u^inor~o<J)0)^rco<X)r-'-ocT)'~cDCT)CDr~-a)ir)inT-roQ3T-iD

inLnr--ot^r--a)'3-roLf)cn^^-aioocNir)i-~oooocor^co<3-cri'srr~ otDOiroiDnocownioonmco^CD^cn^ffi'joi^nnPi TinocDcno^'-CNcoc^^'T^-^iniooiot^t^oocDCDO'-w

CNOJCNCNOJCNC^CNC^C^CNCNCNrjCNCNCNOJCNCNCNCNCJOJCNOJCN

fcooO'-inoo — ^r<Dt^r~cDcDrocT)cr)ODin»-t«-cvr^-^tDcoo<0 t^a>'--*Toc-~a)0'-oi'-<Nro<j-<3-ir>or^oocoCT>a)00'-cNCN CDCDOOOOO'-'-'-CMOiCNOiOitNCJCNCNCNCNOanMOOClCO

OO'-'-'-*-*- — — ,-,-,-t-^,-t-,-t-^,-,-t-,-t-,-»-*-

o

I

o

o

CO

eno

sUJ

_lo

S UJ O

a: > s

uj « \

X t- <

i- < a O > s

CO 1-H • •- a o

ui s

a a

ui

a:3 <

co a

co s

ooooooooocoLnojcoocorocnoinooncDT-tocNOcn ooooooooocnoaoo<3-coi~c7>a>cooo<x>ooCT>o">*-(T)

,T oooooooooo-^'-<Nro«3-cot>-cr>'-coLOt^a)'r-cDOt OOOOOOOOOOOOOOOOOO'-'-'-'-'-CNCMCOO

0(Dor~t^^cDOLna)0)cncDO'3-a)t-~LOCNOif)oiLnrocT)'-LO innoifiONOioD^cotNnaicn'-niNioiiicoiot^cNOOco

TcT)"Tt^ncoom'-aDCT>0'-roO'-r--^T-^-a)t^cDinif)tr)ior^ t^t^t^r^ajnoi^TOifi'-cDi'Ococn-r-'^t^aicMincD'-h-cocn co<TLOcDt^oocoa)00'-^o(nro'T(ot^cDa)'«-<Ncoint^ocM

T«T"sj-i- 'T«r ,T«TininLOLOLOLOincoir)ir)LOLOcococococot^i>

in

CM Uia:3

<

crui

a.s

LU

oooootooinoinoinoinooooooooooooo

(OiNcocnoO'-'-cMojoro'T'rLOcot-cooiO'-cNfOTaJcoo

f^t^^^O)CDCDCDQOCr)OOCOCOCOCOCDC300COC31CT)CnaiCnCJ10)0 CNNO|{NOinM«MOiC*CMCNMP({MCNtNCMCMOICMPIOIOIOin

42
> a

\- z

-i 3 to

CJ O v. O 00 s

> o

t»<rc>toini£):oaocNOif>c^<ocoa>i0oa>

(DONnCDOimiri'-lOO'TIDCNIfltNflDI

f- — — CNCNCNCNCNCNOJCNCNOJCNCNCNOJOl

a.

it:

inoiD>-oo<NTinoiiD(Dncjis<TPnO'r

L<">cn<TCNCDCOcr>:^coir>cn<TC'ocr><Nm(Of^ ocn — tNT-rnrirot^cD^ocjsincDTojr^

nir)0"Tir)CTir~cD^tDOLnor--'TOr^<T c ro cn *- — »-

>o

TOiocM(o»- ,5TioiNaj'-ooo(D(Din'-iono(NOifflcNajo)

'-Tcooo(Dif)uTOcNCNCDO'-tDLnaouDr»-cnocDnaitD'-iD<o

MDONlDOinOTN'-OlMn^N'-OOlOlCOCDNNMOlO

oa>3

C

•i—

4-> co

> it: Q.O -J

<x o

I- s z —

LU \"3

a

OTOiocooiDcocoinir>aoinr^ioc')*-cr>'i-ir>t^(OCNC,»0'-CN-oo a3na5tDir)oi"TOODO'-<NojojcNT-cT)t^^r'-a3ir)«-ooO'-«N TaicoooromcO'-rouDt^ooaiO'-ro^ooooO'-coinioocoto

ci0)OO'-'-'-tM(NCMCNWwnnnnnn>T^<T ,Ttuiuiin

tniniOlOlDiO(OU3tDlOlDlOlD(Ol0CO<D(DlOU)lOlOlOODOOl0lD

t-f-coaimcNinomincDinoooaiciincNt-'TCNtDt^^r'-oo*

oioionOfflnnMDinnoinooiNTOi/iOTOOttfflKio

CDO'-oj^rininiDt^cDocicriaicnoO'-csitNcoT'a-inioc^ooa) O*-*-'-'-'-'-'-*- — '-'-'-'-CNCNCNCNtNCNCNCNCNCNCNCNCN

C\CNCNC^CNCN010<C\CNI(NCNCNCNCNCN<NCNOJCNCNCNCNCN01CNCN

0)

A3

<3 >- _l ZOO o: as UJ LU \

I- Z "3

O00'-lDCNCNtDCN'-CNCN«T«Tir)CM0D'-CNCDCNn00OC0O'T<3- inoinncDNN'-tJi'-noooiocO'-'nninin^Tj^nnNO

loco — Tt^q-'-cT)iDcricocT)CNLnf^rocDncoroaDcoaD<N04'-^ Di^MooioO'-cvtNtNnnoi^minioioNNoooiO'- 0OOOOO-"--"'-rn^-^-^T-^^T-ri.0|0| C\CNC\C\CNOJOiOJCNCNCSCNCNOJCNCN<NCN(NCNCNCNOJCNCNCNCN

O

X

o

o

CO

roO

>s. LU_lO

LU >

CC — X Oi-\

x < < O > CL O -> s

lo a:

i-i LUa

2 LU O

cr > 2 W-iN

X I- <

t- < Q. O > 2

CO •-< • i-i CC CO

LU 2

a a

co a

CO 2

CCa.

tcocdt-loco — <toisn- — cnococcc^^r'-r-oicococNO^

t^CJ)'-^-lDt^cnO'-fOLOt^COCOOO'-CNrO<T'TU)LO(nt~-COCO (JioiooooO'-'-n«oi(N(Noinnonnnnnnn(oco QO-'-'-'--T---r---^'-^'-^ — *-,-T-,--r-,-»-,-,-TOOOOOOOOO'-COCDO'TOLOCOCOCNrOLO'-r-LOCNCNCN ooooooooor^LOTTcorocMCNco'CLncococn^Lficnco OOOOOOOOOO'-cNn^-Lor-CD — roLOt^o>T-Tcooir^ OOOOOOOOOOOOOOOOO'-*-'-*-»-CNCNCN00C">

MOor^c^-^coOLO^-cjCNOLO^LD'-'-cocoaiCTiLOCNCDt^co innnmOM!ico ,5

, -if)NinDoiNn«(DOoO'-oi<-inwo

^•cr)'g't--r)tDOL0'-ocNL0CT)r)rocDai'-nt~-OL0cnLf)oai(T) t>-t^t>-t^CD00CTl«3-OC0CNC0T'>-t^OC0t^OC0t~-OCr)t^<TT-O) COTLOLDt^COCOCnOO'-'-CNfOCOLOcOt^cDO'-COTLOCOT-CO

^^^^'T'T'T'TLOLOLnLOLOLOLOLOLOLOLncDLOlOCOtOCOt^t^

o

in <

CCLUas

LU

oooooiooLooinoLOomooooooooooooo

lOt-OOCDOO'-'-CNCNCOCO'T'TLOCD^CDCnO'-CNn'iriDCOO

r»r»t^t^oocDcococoQDci)cococDcococDCDcocT)cnaicT)Oicncr)0

OICNOlCNOICNCNWOICNC^CNCNCNCNtNOICNCNCNCNIOIOllOIOICICO

43
I- Z

-> 13 in OON OU1S _l

UJ u. > o

oor--^ro)'Tooin'-iO'-iDO^rcocNCT)ir)»- ooo500»-'-ojroc,i«T<TLnLf)Lr)iDuDt^a) — *-CNCNCNCNCNCNOJCNCN<NCNCNCNCNCNCN

a.

toinoocNiooicNTt*-a>cnio<j-c4<j't^cj>in Otnt^oiinncoTcoo^tncDTinr-cNO

Or~tOCNtnrooiCT)OCT)T'-UDX<3-'Xi(DCD

tNcor^oo(MiX)<Nr>-cDOir)'-t^'TCNaDLf)0

<T CN *- «- «- t-

>a

inr-foo>cNCDO'-u3inooT-tNooinmQOiDOino>ocDtDooo>t^

'-TCNCo«Tf-'>-'^CN'r-<Daoro^cgcDt«-0)cnr-.ojO)ir)CNr~no

m<oaDO'3-t*-*-r--'r-cNa)ioir><3-c»)^oa>aiaooor--t^c-~co<o<o

CLO

a: O

OTfot^T-poT-t^oo^ooocnincnncNt^o^QOinO'a-in'Tt^t^ cooitD'-cjinoDnocDCDOCDQOt^uDrr'-oomoiaiin^n^j-m

^ir)Oir>o>cN<Tt>-0'-cNd'g-ir)u>coocNof>int^ooor<ina)»-

moiooO'-'-'-oiNPiNOJNWrtnonntoniTf^in

UT)lJ1lOlDOOlOlOlOO<l>lOlOlOlOlOlOlOlOlO<OlOlOlOlOtDlO

XI

<u3

C

•i—

4-> £

OO

>-a

ooo>'-mineNm<TT-r^,-r-f»cNog*-'-in<Ta>oa)«Tco<ot-

<ni0TU3OTOC0'>-t,*<r''-u3'>-<D«yT-t<-ojt-»«-(OCT>f»)a>ir>o t^'r-maiT'-aiuDi/iO'ToO'-incoiricNCDin'-oo^roc^cntNin i^aiOT-coT^-incot^r^r-QooocoaiooT-cMCNco^-'j-int^oo OOf^'-'-'-'--'--'-'-'-'-'-MCN(NWWMMOIWO(W

CNCgCNCNCMCNCXCNCNCNCMOJCMCNCNCJCiCNCNCNOJCNCNCgCNCNCN

JO

<T3

< >- -I ZOO o: cc 2

UJ UJ "v. t- Z "3 Z UJ

omr-i/ioiconntoinMOiooooniDOioffl'-cvoo'rino

cn^oi'-n^^coaicocDt^inrooicNro^rrocN-i-oTt^q-QO'-'T t~-oroocnto<r)ot^cNmoo^<TOCNr~fNt^tNt^^cD'-oocn «<rm(ON(DOioO'-'-'-Pio)CNn(TT'nnifnD<ONaia)cn OOOOOOO'-'- — '--•'-<-'-'- — '-••-'-''-'-'- — '-'-'- (NCNCNCNCNCNOJCNOJOJCNCNCNCNCVCNCNOJC^CNJOICNOJOlC^OrfCN

UJ >

oc — it: OH\ I < < O > Q. o •-> s

(/) q:

TCOCD'-inCD'-^rcntOCDO'-OOOCNrocl^-OltDCNOO'T^J-n'- t^O)--^rior^cno^cDOoin"^'TOt^coaic7)0'-'-oiO'^in cioiooooO'-'-Nnnrinoncitonn'r'ntT^^^ OO^T-^--^r-T-^T-^T-r--^^^-T-T-^^-^^^T-^To

I

o

o

in

_l S ul O

CC > s

UJ M \

I t- <

t- < a O > s

i-i q; 01

UJ 5 O Q

UJ

Ql

<

a.

ooooooooooainoo^oioiocotMOiioinuiinffl'-in OOOOOOOOO'TTtfilDlDt^COOOJlDl^OcnuDOlinCNCO OOOOOOOOO'-CNOTintOCO'-COint'^OCN'TlO'-tOO 0000000000000000'-'-»-'-0<CNCNC<a<")<T

niDOt^t^^(jDtoir>o)<Tr~ocMif)cDnr»ncNOh-oa>f^cNin

tnfOPOinot^O)a3«3't^in»-"T'-cMir)O^Tr^t--c«5if)cO'T'-rot^ <jo<iM>HDOin'-(NNnanDncoinNO(JiO)(JiO'-inoio

f~r>»f~f»coooa>TO<DCNa>tncNOCN<ao^"t--*-u')0^>'CN'«~o> n<Tir)tDr~03oooioO'-^ojncoiniDooo)OCNc»>uitoo>cj«T

"Tsr^rfT^rTTininminmintntninininajiDtotDtotot^t^

in iu

Z3

CO I-<

UJas

UJ

ooooomotnomoinoinooooooooooooo

<ot^<ncnoO'-»-o»oi{»)(n<a->rin<Dt>.oDO>0'-c<co'j-«ocoo t^f^t^r^cDosoooocoooajajoooococDaocooDaiooicDooioio

OJCNCNCNCSCNCNCNCNCNCSOJCNCNCNOJCNCMCNOrfOJCMOICNOIOtPJ

44
> o

»- z •-• 3 </> O O V. o tO s _lOJ u. > o

"-Tcont^ciDinincDaDooiot^incjcNcoo

cDiflcNt^T-mcNcoooooror^^inaicocNO

a>o>---c\icNcooo<T<TmLOcocotot--ooco

>-CNCNCNCMCNOJ<NCNCNC\CNCNCNCNCN(NC<

a

(J — NOKNOMDN'-Ol'-'-nMOOOIPIOairodoror-r^CNt^'-t^cNfOOr^ old

0«-Trt(3<TCDCt)0U)ON ,J0IO(D<Tf«

> (DNco^orooO'-ioco^n'jO'jioiooonroaxO'-MJ) WinodflnaiCOOXTOOlDiniDOl^OO'-lD'-MOOOOION

ro^rcDoooiTCD^rooa3cD^-roc\T-oCT)cr>aDoor--t^t^cO(OcDin

rgcNCNOJcnron*i-inininininininin«T*T*j;«3-«a, '3- <T«i- «j-*r'T

"O3

C

Oo

> ic cnt^aicocN'f-'TiDro'TincNOOT-cocMoooaif^'-intDtDCNcora. • cNt^cNoomoincDinio^iiDmin^-cNcnt^not^coomt^ooo) O -i ooojoi-(D<D'-ooiot^coa)0'-c\isi-ir>t^a>^oj<TLnr~oo')co

a: o

i- S tooi(j)000'-'-'->-'->-cNwwoioioi(Nntooi,)r,)f<T<T Z —

if)[jlLTCOOtDlO(OU30tDOOOOOOOOtOtQlOlDtOtOtOtQ

UJ \ ,-_,- T-_ r- T-,_,__,_._,_,_,_,_,_,_,_ T_,_,_,_,_,_,_ r-

"3

Z

UJ

c5cxoot-~t"-Loa>cocNOoa> a>'-oO'-in<3-a>-^a>inaoo<flco

rocD^Tnir)oocNCT)'-oiin'-inO'3- '-t-~ojc~-^cooicoiDcocDn CDoitDOT'-cntDLnoocNiDOirotflnaiiDojcnLn'-co'Tt^oicN

u3coa)'-cNron^rLni/)U)toiDt^t^cDcocj)00'-cNCNn'3-mt>. 000'-'->-'-»-t-»-i-i-T-T-^^T-i!-tVWNMCJMW««

OJOJCNOICMCNCNOJCNCNOJCMOJCNOICMCNCNCMCNCNC^CNOJCNOJOI

Qi -Q

CEO

X

o

o

tO

< >—

zoo CC CC S

UJ UJ \

H- Z "3 Z UJ

UJ

UJ >

£X -< *

t- \ 1 < < O > Q. O - S

CO CC

t-< UJa

_i S UJ O

a: > 2

UJ >-l -v. X t- <

(- < Q- O > S

CO -" • >-> CC C)

uj S a a

CC

to

to

ID

CC

a.

<

a.

co^incnco^^cNLOoooooiOLOtooicjt^tDoiai^rtotooorocN

N-inoT'-oioin^iiKNOioptn^noiotoiDnoniooo

ooiincO'-oo^rcNCJicNLnoO'-rocD'-cD'-tD'-LOOLnotTioot^

cNro^rLf)t-»t^ootDa>ooO'-'-'-c>jcNfoo«T«TtnLOto<or>-a) OOOOOOOOO-- — '-"-'- — '-<- — »-•-'-'--'-'-'-*-

CNCVOJCNCMOJCMCNCNCNOJCNCVCNCMCNOJCNCNCNCMCNOJCNCNCNCY

<5-iocD'-LOoO'-'rcDTCNtDa)t--too<Y,)cvi(T)->-o)cocNooa>a>QO t^cri'-'TtDr^cDO'-TOr^oocnocNooTintotDt^oocDtDO'- ffioiooooO'-'-nnfonn'TTitT'jf'iiT'nnin OO-^^'^'-'-'-'-'-'-T-'-^^'-'-^'-'-'-'-T-^^^^-

OOOOOOOOO(DOO0)MD<tifll^OnMNM0l£l<t 00000000000)T-(NTOO'3-CDCNt>-'r-inO ,TrOOJr- ooooooooootniniOMOr-oinmofimaioinoin ooooooooooooooo — '-'- — c\io4cno4coco<3-<t

coiotot^i^'-cDcoLnTcwt^nO'-^rcMt^cMooLOcoLor-oj^Tif) ifiooromoMiicDTN"Tcommm(00<Tffl(Jia)fo<TONOtD "TroirsoiflOin- smooinoiniDOioitD'j'-coiOcvr-o

t^t^t^r^cococn^rotoooot^T^inoicocDCNt^CMto^T-'-'-

n«j-if)tot^oDcoo)00'-o4CNc»)"q-intDCDa)'»-cM<Tini>on«o

TT'j-'T'T^Tii-inmLOinininmiDinLOintoiDiocDtDt^r^t*

o UJ o sr

CD H- oooootnoinoinoinomooooooooooooo

(ONoooioO'-'-NMnnT'nniDMBOiO'-MnviofflO

t^t^r^^tt>coc)a5CDa)(iicocoooa3(DCDCDoocT)tT)a50ia>a>cj)0

CNCNC<CMCNCNCNOJCNCNCNCJCJ<NCMC<CN<NC>JCN<NCMCNCMCMOIC»)

45
> Q

I- Z

-• =J C/) o o ^ oms

> o

^NMon'?--Moo)anr(OMonnoo

^TOlO^-CDOTOOD'-lD^inairOt^rrr-t^

CJCNOiCNCNCNCNCNCNCNtNCNCNCNCNCJCNCNCN

a.(J —

TinotouicNOitoCT)ojp«-t-cDinot^ooooo

cO'-or^iDr^:DO"3't^t^cot-io*-rocNO'-

coiDrontNLnocNiDONnintMrniooitDTCM *- i-

>

ocDooo30CNroai'-cio»-on(DTcoinooooir)co-r-o>oito mN^-MOOXDinotDiDiooj'-iniDciinfflT «- 00 to en o r- in T-CM"3-tOOCNCDCMU3^roiCM»--r-OCT)OOOOt^-r-t^lO<fltOOmill

c

•r—

+-> C

oo

>- X. ir)t>-CNn(Nt^t^^-CNOl0OCN04CNh-C7)CDinOC0'TTCNmT0>

a. • nr-.ojt^niOOinuiiD'T^-cooj'-oDiocMcncDCMOOTO'-cNCN

a: O

i- s ajmoioooO'-'-'-'-'-'-'-'-'-oKNCNPioiwndnn'r

"3

a

i

n'-inwomcDTNOcO'-oiDCDOnwujMnotioiDr-pi

CMir>CT>lDlOt^OU30D'3-00nf^Or0Oir)O'T00CNtD(T><N00^TCJ> »-Tt^'-if)CNor^rot^OTt^»-'T^-r-^roiDcooiir)CN^rt>-o> (DMDO'-MnnT^ifiminiDioNNcooimoO'-Nco^in

OOO'-'-'-'-'-'-'-'-'-'-'-'-'-'-'-'-'-tVtVCiMPIWM

C^CNCVCNCNCNCNCNOICNCNCNCVICNCNCNCNCNCNCNCNCNCNCNOICNCN

UJcco

xa

o

to

< >- -i zoo o: a s

UJ UJ \ »- Z "3

UJ

UJ >

cc -• s: O t- \ X < < O > Q- o«s I/) <x. M UJQ

_l S UJ O

a: > S UJM\

X I- <

t— < a. O > 2 W >-< • Mirn

UJ S

o a

UJ

a:

=3 <

to a w S

UJ

a.

Tir)oino)t^ot-»Lnojroa)a>r~'-<N'T'>-ojcDCNC4Cj)'3-ooinco

Olr-lfiOCO'JCN'-MfiCMCD^OICHDinq-CNaiNTONOlT-M ntDrO'-root^^cj)CMLnr~0(T)ir)OmoLOCDTCT)^root^c-(D '-ojrointDf-c^cococncDaiooO'-'-cwcNCNcon'j-Tintot^ 000000000000*-*-*-*-'-i-'-'-T-T-»-.r-T-,-rCNCNCNOJCNIOJCNOJC^OICNCNCNCNCNOICNCNCNCNCNCNCNCNCNCNCN

*rtoco — moo — <rog — i^O'-'-OinajOKTKDiocoo^cnaioi

t^<D^<TtDf-cf)oaiT-cN>Tir)tDr>-cocr. O'-cNco^inintot^cD (jioiooooO'-nTTfT'J^'r'Ti/iinininininininuiin

OO'"'-'-'-'-^'-'-'-'-'--'-'-'---'^^'----'-'---'-'-

oooooooooocvommO'-n'nniniflNNNMOPiN oooooooO'-ioonioonoiin'-MKJun'-Mii'-oi OOOOOOOOC)<T(DMDO'-OlOO)'-^(0(DP('ifOimO ooooooooooooO'-'-'-'-'-oKVPKvnnniTin

rotD(Dr^r~'-tocO(NT-r~^roif)inotocMtoiDojt^ino«3- oo<D uinninONfficoiflMDnioroini-cioicoaioiTncDoi^M

*T rOT>n(DOlf)lOlOM31'-^Mnn(,)<JlOOiniDO<-ON

r-t^t^r~oofocr)^TOr^'3, -^05UjrooDrooonooncn'3;0»-c>ic») (nTiniot^a3oaoioo»-cN04ro^rtr)t~-CDO'»-ro«TtDco»-'Tr^

in

en 3>-<

a:UJ

a.s

UJ

ooooomoinoinoinoinooooooooooooo

cot^ooOTOO'-'-tNCNCoo'ij-'Tincor-oooiO'-cNfo^rtoooo

r-t^t-t^-oooooocooDCDcoooajajoooooDooajcncnoncncDcncno (NCNCNOICNCNCNCNC^CNCNCNC^CNCNCNCNOICYCNCNMCNfNCNOfC)

46
>- Q

1- Z

•- =) t/) u o \ OW5 —

UJ U- > O

NocotMioonoif)'-mo<Tco[NiDnoio

'-CNCNcoro^T"Tinma)aDc^r»-c^oooocnoo CNCNCNCNCNOJCNCNCNCNC^CNCNCNCNCNCNOn

u —

o

>

ooincDf^niDooitDcoTcoocniiicMCNt^O)

LnooLnaD<Dot^co«Nonr-n^-n — noo ooonnmCTimt^cNooincNOootDLnn^-a)

oiina)inoinNa)Mniooi'-cNOih<-<nD<nD(NCNO(ioo

oooiooiTOiir)no<N<3-r~cNt^cNif)Oir)'-a)ir)co^cn^D'TOj

0>T-cN^rar)o^rocT)<N'-ooa5aiaDQ0t^t^ictDCDU?if>Lf)inir)

CLO

r-CN'-CDCDOCOOLr)(DO'-Or-<TUD<TO'Tt^t^t^ir)CNCMOO'-

CNlD'-inOCN<3-t^C0O>O'-CNCNr0tnt^C0OCNf,0ir)lDCD»-'Tt^

COCDQOlOOOOOO'-'-'-'-^'-'-'-nOieMtNMMOnO L0LnL0unOOOLQuDOOOOOiX>LQOOcDc0CQOtQOOl0C0

-D

0)3

c

•p4-> £

o

>-

a. —i

-I o

< s I \ »- -3 z

Ul

mnooT'-inincDCNco^-inoooocDQOinooooinofoininc'oajo

miDCD(T)'-'-cot^ina)r,)(£>cn(Nir)oi/>a5<T)t^T-q-t^oto»-r»

rou3CTi(v)c^q-»-cxicNir)aicNir)Oi(Maicn'-ooT»-r~nocNinr>- intDt^a>0'-cNoiroc»)co'T'T>g-ir)miot^t--ooa)aiO'-oMn'T OOOO'-'-'-'-'-'-'-'-'-'-'-'-'-'-'-'-'-'-NWMWW

WCNCVCNCVCNCNCNCNOJOJCNCNCNCNCMCNOjrMCJOJOJCNCMCNCNCM

CD

(T3

< >- _l ZOO a o: 5

LLI UJ >

ce « s: O t- \

x < < o > a o -" s

to cea

'-incoocjDTt-coooocNoooooo^or-'-'-CDC'j'TLnootfl

iniDt^-'-t^cMoor^r~-na)'3, Oir)CT)a3t^^rc\CT)incMQOTiDt^r» siTi'-TiDnoiiiiaiNTNOCNTOiq-tjiq'OjncooiMOini' o>-n<iunD(DNMDcocD(j)<Jioi(JioO'-'-o((Nnnq, in(0 OOOOOOOOOOOOOOOO'-'-T----'-'-'-*-*-'- —

CNCNOJCMCNCYOJCNICNOlCNOrfOJCNOICNCNCNCNCMOIOJCNOICNOJCX

<Ti0co*-incO'-'3-a>ootNCN<NOir><x>oocncoiDcoocMO«T

M3)'-<], fflMJiO(Da)0'-oin^inioa30)OiO'-CN(TTin(0

rooiooooO'-i'rinini/iininuiin^uiiniixflfflioioioifl

o

Iu

o

S UJ O

ce > s

UJ -i \ X t- <

I- < Q. o > s

</) «-l • •-< cc n

UJ S o a

ooooooootO'riOf'-iDOirKDOOOiajinNmNPio ooooooooaj'Joi^ointDio^n'-toiii'a'Noxjoin ooooooooint^ooO'-ir)^Tt^O(T)OCD'-Tt^o')ir)o«) ooooooooooO'-'-'-'-'-wpinoincinnfiiiio

UJ

cc

CO

LUa

a.

ntoor--r~T-totooonaDciooocDcn'Taicot^<3-tDCT)oocT>to innninONOicoMOCM^rcMinrocDMDtDannO'-cDoiaiiD

< ^•n-g-r^noOLnt^-^0'>-r~roo^3'Ot~~LO'T ,3-LOtDc--cNCna3

a. t^t>-r--r~corocT)'3- '-cT)0 ,a''-tDt^oja3rocDir)r-r-.oa)oi'rr»> 2 roTintoh-cocoaioO'-CNfoco'TiDt^aiocMq-in^cooiina)

C'TT^TTfTLnmLninwminminuitDOtototocDr^t^t'*

o

If!

O)

HI

cc^-<

ccUJa

2

ooooomoinoinoinoinooooooooooooo

iot^cocftoo*-'-MCMnof<3-ir>iQf»cocno»-e>(o*rcoa>o

t^t>-^l>.COCOCOOOCOa3COCOCDCOCOCOOOCOCDCn01Cr)CT)C7)010>0

CNCNCNCMCNOJCNCMCSCYOlCNOJCNOJOrfejCYCVCNOgOICNCSCNOIPJ

47
> Q

t- Z ~ => CO uos O CO 2 > o

r^*-COO<TCO'-Ln*-CO»-(DO<3-COC\IOrOOCO

cNroro^-<TTLf)ir)tD(Dt^r~cococoa)CT)0'-'- CNCNOJCNCNCNCNCNOiCNCNOJCNCNCNCMCNOOOOCO

a.

CJ ~

OiO'-cnr^'-r^roinifiLOor'^cocncNOTT-*-

oocot^cNtDOCN^'-nrooiao'-to^Tn^rcnt^ lOiOKNiocMcoinoiDnotDMnTn^aico

>u

nrocN^rocD^t^-r-comoococNOiocNootoocDCDcncoTtoo

CN<3- OCNtDOCDOt>-T-(0'-t^>3-T-m^t^^C4Cr)t^lDTCNOa)

oooi'-oocDaicN'-oocDdiQococDr^f-uDtoiOLnmininifiinvr

o

o

>- ic nn^T-^aiT-f^ajf^ificjai^-OTiocMintoioinrocn^-cNtoto

a. • oiMinoiTiDoi'noj'-ocoMncMoiin'-Nnai^O'-'-'- O -> CD^TCDCNt^a>CNOO>Tir)OOr-t^OO(J>'-CN«J-(Or»0>OCN«Tt~OCl) cc o

t- 5 MDOOlOlOlOOOOOOOOO'-'-'-'-'-'-nCttNPinP)

Z ^ lOLnLOinifiLOOOOOOOOOO«>OCOlOl0lOCOlOCOCDlOCD

~3

>-

z

LU

r~OOCNCDTCDOOCDCN'T«3-CMCr)TCOnq-CNCOCMlf)(OlDtDMt^O

o*'-cN^rocr)Ocooiina)«-rou5CD<r)r-T-^r(D»-<T^O(0»-t>-

too)CNinaiinnr~-T-^-h-'r-^rr~.or~coou504a)ir)'i-cooc»)ir) ^Lnt^cooiO'-'-cNCNCNcorooT^miDiDt^r^aDOiai'-cNcn OOOOO'-'-'-'-»-f'->-<-i-'-'->-'-TT.T-^^0tPI(M

CJCNCMCNCNtNOJtNOJCNCMCNCMCNCNCNCNCNCMCNCNCNCNCMCNCNCM

cco

X

o

o

CO

a

LU

_io

< >- -I zoo

LU LU \ t- Z "3 Z LU

LU

LU >

a: — x. O t- \

X < < o > a. O •-« 2

co cc i— LUo

_l S LU O

CC > S

LU >-i \

X tr <

i- < a O > s

CO "-H • wanLU S

o a

cc

co a

to s

LU

cca.

OcoO'-cnoO'-'-cDcof--^rcnoi<TCNifiin^>iTir)>Ti-(D^-ioco

^tMnmainoioinoino^mn^coiricMroq-oiD'-NMN

^rotnt-~cntDtNt^aicN<Tr^cn--^TairoQoror~-r>jt^-T-u3Ln^Tco O'-cNroTLOcDcocot^r^t^t^cococDOicnoO'-'-cNcgfoq-m OOOOOOOOOOOOOOOOOO'-'-t-'-t-^-t-^-^

CNCNtNCJ04CNCNCN<NCNOIOJO(CWCNCNCNCNOJC>l<NCNC\)CJC>JC>JCi

^(OoO'-tncc-^Gicot^cnoooit^ojinot^tomcoT-coocNco

cDO)OOOOOuiLOLOLOLncococooocDOCD«3cor~c^t^r~c^ 00"-"-t---*-'-<-'-'-'-'-'--'--*-'-t-'-'-'--«-'-*-'-

oooooooToot^oiTreoomcnoacMOr^cMuit^r^cN*- ooooooocom(N(iiiii'-N(Mnn<i<T'jntooi'-oiN<r OOOOOOOt^cn^cgTcot^cncNUicO'-^Tt^Ofoco^-t^n ooooooooo-'-'-'-^'-npi(\nnn<TTsrinin(D

roiocots-t^.^iO'Tir)0'-'-CNjcoLO'-cDcDcDt^ot-~CMO'Tcr)to mnniriot^cn^-t^f^'g-uDnTOrocoLncNQDroTcooo'TOT

^rr>Tt^ncDOCDtD^T<v)ojojcNnina)r'')a)Lr)roT-ocnocot-» t^t^t^r^-cococninco'^-cnt^inro^-t^cooconot-'TOincnco coTincot^ajoocnO'-'-cNooq-LOcoQOO'-ooiniocooncoo

^rTTTn-TTTLOLnminminiDLOLOcotococotDcot^t^t^co

in tu

t^ cc<

CCLUa

S

LU

oooootnoinomomoLoooooooooooooo

cot,~coa)00'-'-CNC>icocoT<TLOcor»cocr)0'-cMro^rcoooo

r^i^t^t^oococooococococDcocococococococncncncncncncno

CN<N<NCNCJCNCNCJ«O«0aCNCNCN<NCSO<OJCN(NCNCN<NOICMCNt»)

48
> Q

I- Z

-• 3 tO O O v. ows

> o

OIC)V"T'-SOC(MfflOO>'TNaiQOlOCJM<J>C(

n^TTir)ir)LniDcou)r~r^oocoCT)<T)CT>oo-^o<c>j OlOiCNCNCNCNOiOiCNCNCNCNCNICNlNCNCOCOCOCOCO

a.

2C

ocxDOiootinMOin^-ino^NcitDooo)'-

LOcNincoojcooioir>»-<3-cN<rcr>Lr)coro<rcDcDto

Mflinini^TnnnncNCvwoicMcvoi'-'-'-

>

•^0)^T'-o>o(»-i^rotO'^(T)i-incNCNOCNO)cncoa)in<iT(Ooio r~00Tt000C0<N'-00T»-l^lf)(NOU3f0Ot^ir)'TCN'^OCDt^l0

tot^a>i->3-f^a>a>aocoa)r--r,»f~t^(ocoioinir>ir>ininLr>'5r*T»T

•o3

c

•I— c

oo

CLo

x cor^^r^r»cN^^co^o^cocN*rcoO'-ocoinoincocoLOco

TO)oiojioCT)tf)'3-cN'-ooo(Dinna)iocNooroa)inoif)U3<ouj

-J t^»-inO'TU500O)O'-CNCNr0>TiniD00O'-CO<TlOa)CT)CJU100 o

S SCOIDOKDCIOlOlOOOOOOOOO'-'-'-'-'-'-'-CIMn

mN^cgoi«noN«so«n<TO(DPHDooo)aio)Nno)r» _iO mo0>orocN'3-t--a>cN*rt--cr>'-ror--o*rr^oc'oiocncNooroai s a>CMT03'-oocoiDoinioa>cNiDa)ir)CNoo>g-T-r^rooicooO'-co — cotDiot-aicDOOO'-'-'-ojcNCNjn^-^rintDtDt^t^oooi'-rj 3 000000'-t-'-'-'-'-'-'-'-'-'-'-'>--^'-^'-'^'-CNCN

CgCNC4CNCNtNCNCMOJCJCMCNCNCNCMCMOJCNCNOICN<NCNCNC4CMC<

0) .a

< v -i ZOO a: cc S

lu uj s t- Z "3 Z Ui

i-noTaifloiinOfowinnointfflooiifl'-'noMOoiin

orocNCNir)coroa3rot~-T-in(D(T)cDroCT)(£>'-t^rocDnoococor^ int^-cD'-roijiTCDOT'-^iccoO'-cococNP-CN'ri-^inO'^rocN'-

cn o — roT'rinir)ir)<DCDOiDt^r~r~aooocDa)00'-'-cNn'r 01OOOOOOOOOOOOOOOOOOO'-'-'-'-'-'-'- «-<NCN04i^CJO<{NCNrgtNCNCMCNCJOJCNCMCN<NCN<NCMCMCNCMCJ

UJ >

a "H ic I < < o > a o >-• s

co a:

iiDOO'-inooiDon'rininTnoinMJioiraMnoofiiino

t^cri'-'Tcor^'-ro'jLntDr^ootDO'-CNfO'TLOor-ajcTiO'-CN c7)<jiOOOOtototoioocotDcor~r^i^t^t^t--r^r^r^r-ooaoa} OO'"'-'-'-'-'-'-'-'--^'-'-'-'-'-'-'-'-^-^^-^^^^

LU

cc. o

xo

o

to

COsa-^

UJ

_JO

S LU O

a. > s

x - <

t- < a o > s

co •-• • nanuj s

o a

UJ

cc

z>to

to

LU

cc

a.

OOOOOOi>roa)t^fr-a)r«'rLOT-q-coOLOt^cDtot-CNO) ooooooMDTiNONf'-cO'-TioooO'-oin^inioin OOOOOOOCN^rtOCDtD^fOTCD'-Tt^^TI^-OCOCnin-^- oooooO'-'-'-'-'-'-rtrtNPinroni-tiiniJiintos

COtDLOt^t--'-CDO>rO(D<3-CNtO'-LnOO'-eN'Tt^LOCNCOt^LOCV LOrontoot>-'TtOLoa)a)'Tror>-^rocDr^tDTO'TLOCNroir)in Tto'Tt-ntoro^rtocD'-LntTincDaiont^cMcoT'-aitOLOto

t~t>-r-i>a)foott)tD'rco»-0>ootDcoT-cDLOrooootocoa)LO«- n"TLOtor~roa>aio»-cNcoco'Tint^a>oc>(<Toc^o>»-«Tajc>t

TTT^TTT^rTLOLOinLOLOLOLOLOLOtOtDtOtOtOLOlNININa)

o

o

UJ

cc< oooooLOOLOOLOomoLoooooooooooooo

«0INC0CnOO'-'-C<CMC»)(0^-<Tin<Ol>00CI)O'-CNC0'TlD00O

iNi>r«t^cocococococococotococDtT}cocococricncncncncncno WWCNCgCNCNCNtNOJOJCNMCNCWCNCNCJC^CNCNC^CJtNCMCJCNCO

49
> a

*- z

-< =J CO uo\ O CO s _JLU u. > o

LOcoc7>cO'-LOr>-t^co^rr«-coc»)t^cntDr~in-^oiooo

*-«rt^'»-ina)'-<Tt'"-OLnOLr>a>nr-i-Loa>cocvco incnLncDcotDt^t^r^cococDcncnoO'-T-r-oioon

OICNCNOJCNCNCNCNCNOJCNCNCNCNCOCOCOrOCOCOC'lrl

CJ —

5£

•oroinoTnLOLOLOtocncDCNt^cO'-rot^t^'ij-to^ t^Ocnr^ts-Tto^ocDcO'-co«TLOcDc\oa)inocoa)

LOO)TCDOCOLr)(^'-t^«T<TCO«3-(NO<Cv)'Tt^LO'TLO t--'-t^rO'-cDcri'Tn'^-o^r~Ln<Tr)CNT-oa)CDt^to

!_oinT<T>g-fororororoc\CNCx(NCNCNCvcN-^-»-»-T-

> NN^«3incnwoi"j'-<j>o<Ninsnp)io(NOO)Ow<jimp( CNTCDOC\tDt^LOCNOCOLnT<NOt^inco^001t^t-»CO'TdCO

mtor^ooot^t^t^t^t^cDcOtototOLnLOLnLnLn^-rr'j-^rT'T'jo

<U3

C

•i— 4JC

oo

> ^ ^rcoLOCNt^cMt^cNcooroir)r~QD(j>ocT>r~'TOino)CM'rcDmo(

a. ocNTi^otD^rn^oa)co"^rcNOt~-cMoo^rOLOOco»-T--r-»- O -I L0Cnr0t^CMP0^J-L0CDf-t^-a3CT>O'-£N<3-ini^c7)OCNC*)t0 00«- ,3' cc O

1- 2 NMDCDOKIICIIOIOKJIOKDOOOOOOOO'-'-'-t-'-OIW

z ^ LnLnuiLnLOLnLOinLOLnLnuiLococDCDcocococococococotDcoco

~3

a. —i -J O

< s x v.

I- ~3 z

LU

r--cNCNcgocN<Tcoa3a5a)CDf~-LOcof«.0'^ojc,iv-oo)t^<j-or*'

t»-r)Oa>'-'-nLf)t~-ai»-foinr^cr)CNtocntNLOCD'-ncocNa)n

cNLnaDO>3-a)CNLnooT-ir)cD»-<3-r~TOcoc50iLncN(D^-i^-a)c< ncinMamoiaioiooO'-'-'-oion^'TmioiOMiiO)'- OOOOOOOOOt-<-i-*--^^t-*-^t-,-t-t-t-,-,-,-cn

OJCNCNtNOJCJCNCNCNCNCNCVCNCNCNCNtNOICNCNiCSO)C^CNC\ICNP4

r—

LU

cco

I

o

o

CO

COsa\LU

-Io

<t >- -J zoo cr or S

UJ LU \ t- z -o Z LU

I—

LU LU >

cc >-• >c O I v X < < o > a O -i £

CO cc

i-i LUo

-i S LU O

a. > s

LU l-i \ lK<t

I- < O- O > 2

CO M • HanLU 5 a a

LU

CS3

CO

to

LU

CC

a.

<

a.2

a)a)a)oo^coi^LOc\corotocnO'-ocD'-(y)'3- ^rcNOcoiNco<n

otoncM^N^inaicMiDoiwiDoiinoui'-iO'-iO'-inq-nM

O'-roinr^-'-^iDcO'-coLnaoooji^cNcO'r-LOO^cnrocN-r-o

cno^cNco^<T»r^-LOLnLOLOtocD'i)c>-ivcococna)cno»-CN<,j CnOOOOOOOOOOOOOOOOOOOOOO-^'-'-'- x-CNCNCNOJCNCNC^CNC\IC\IC^OJC^C^04C^C^CNOICNCNlNCN(NCNcN

^rcocO'-LomLntot^cor-couicNOcointotococonoco^O'it^O'-'TCDO'-CNfOfLOcoc-cocr)0'-cN(TJ«rLncot--t^cnO'-

cncnooot^t^r^i^^r^i^t>.r^i>a)coooa3cococococococncn

OOOOOG)IN'3-h-t^«TINCnCniNCOLOt^LOOC)CMO>'J-t«-OtO

OCOOOt-t^-t--CDL0'3-CJOC0CDT-tDO^rC0T-^rt0Cnc0t>0) oooooiioooocN'nocooi'-intDCNmcocvijKxi'-oofO

OOOOO'-'-'-CNCNCNCNCMCNncOCOI-T'TLOLOLOtOtOlNCO

PltDt0t^l>CMT»-f0C0r>C0T-h-C0'-"T"TCNI>'^Lf) ,3

- ININOIC0 LncocoLnocri^Ln^cNcocn^cN^tTiLncNcn'Tcocrit^'^iN^rco

^rro^rt-.oi-^t^cooi^M'CNir-ocncocn'-ror^'r-cooiaioooco

^r^tvt>-cOLOrocN'-cr>cor»(OLOfO'-cncocO'Tcn^ooocO"ir'-

co>TLOtots-cocno»-'-oJco'rLOcocoo)'-coLor~o)'-o(too<r

«T ,q-"T'T"T'3-'TLOLOLOLOLOLOinLOLOLOlOtOtO(DlOt<-l>t^C000

in

CM <

ccLU

Q.s

LU

oooooinotooiooinoinooooooooooooo

to^rocnoO'-'-cNCNciro^-vLOcoiNCOcnO'-cNco^-tocoo

r«f^t^r^cocDcoa)a)ooa)coa5coa)cococococna>t7»<j>cno)0)0 WCNWCMCNCMCNOgCMCNCNCNCNtNCNOIcNtNCNCMOIOICMCNCMeiCO

50
>- Q

1- Z

1—

1

3 CO u o \

o CO S _lUJ LI. > O

ooiocD'r-<3-LOcoincnocDLOOitDcDC)CDir)cjr--LnocN

^[^-OTt^orocotDCNTCD^rcooiccO'j-cD'-flOLO'-

iQcor^t^t^aDoorococncnaioO'-'-cNCNcNcoroTin ojcNCNCNCNCNojcNCNiNCNiNconronnnntoronn

ao

>

o

oicoioooor~0)CDt--t^-1-0"5-cM»-a)<3- cocont~-LOO LOLoaoor^n — t--co — in r~ in <r cr, to in cn r~ co in cri o

CD^-LnCN'-^TCT-/LOrOrO'OtDCNOcDO'MLnOO(NCNCr)'r) LOCNCDt^LOn^-OCT, 03r^LO"g-rO-^--OCTlCO<X>r^COLO I'jnnoonfoocNOinioirvwojncN'-^'-^T-TOCNT-CD^TODtDCDCNCOOcDCNOCTlCnricnaDCOOfOr^CNTQO'T CTiOLOin^r^rn^ooot^Ln'j-rO'-aiQOcOLO'T^rcocNCNT-oo

coin(Ocooooocoinininininin<Tsrsr <3- ,T ,3-<3-'3'^r<r<T'3'

-a

O)

Oo

>- 1C O -I

or o

t- s

z —

LU \

>•

Qr^^mO^^t^cn^0IO^^^C0^to"tfC0C\linr^LT>CT>CT>l£>-i- r-aiOrot^LOrO-^OCDCD^OJOCD^TCDLOOCD'-CO'-tDCDCDCD

£NCDT-LD00C7)O'-CNCN00'TL0i0CDCD01^00>TCDt^<T>O00c0<T)

t^r^ooooaocDOioicDcDCDcTiGicDaiaiOTOOOOOO'-'-'-'-

LninuiinLnLnLOLnLnLnLOLnLOinLOLOLntDcotDcocococDcoioio

001CM(OP)'-OtD©C)0^00)lfilDlD(Oli1TPI'-00)Mn<)-

inaj'T'-ai'-n^nocoO'-n'T^oitMinooT-crsortauro

cDCD'-^i-<TC0-^Tf~O'Tr--onc0(MCDLn'r-ctiq-ot^<10L000»- tNniriiDNNCDCDCDOioioiooO'-'-cMnnq'LniniDMBO 000000000000»-*- — »-»-'-*-'-'-'-'-'-'-*-«

CM<NCMCNC\lNCN(NCNCNCMCNtNCNtNOiCJCNCMOJCNCNtNCNCNICNOJ

O) .O

03

< >- -I ZOO a a s

LU LU \ H- Z O

Z LU

LU

LU >

CC -. 2£ O t- ^

X < <t o > a. O "-" S

to at

^rc7>cD'-Lnt^al•»-^•-ooOLncNcT>^J)alcDCNa, cNOCD'-LOt^cD

cocNaDco^^-r^^q-t^ocNLncoOLnOLno^raint~-CNOcoto

<y;or--ai<TiT-r)ocoocriLO[--CT>cNcD'-Lno^rcorot^-cN'-cr)aD cDcnO'-CNOoo(r)OT^-<3-^-^-LnLOcocDr^c^f^cocDcDOO»- 0)010000000000000000000000'-*-'- T-^C^CNCNCNCNCNCNCNCNCNCNOJC^CMOiCNCMCNCNCNCNCNCNCNICJ

q-cDoo — aor-aicot^iDLon — qdlo t»-cnoo'>CT>r--mooorointr-cD'-TOO-'-fNroTLOcor^r^cotDOcNCNnTLntoc^aDCDO

oiaioot^cocoaocococoLXicocDcocacnaienoiaioicnoiaioio OO — '-'-'-•^'-'-'-•^'-'-'-'-^'^'-'-'-'-'-'-'-'-'-Oi

LU

ccO

XoO

to

5 UJ O

at > S UJM\

X t- <

i- < a O > s

to i-i • —> QL CO LU S O Q

or

to

LO

LU

CC

oooo<fP)^iotDiofV(DNS"j-ir)i-^oo»-oioooniflo ooooO'-riiwcNMCNT-ooimincNconaivconNi-oiD ooooorvfiiiiiDOcj'jioNfflnNOfN'-fai'-fflmr- OOOOCNrMotcMCNnnonnniTiriininiDioiONMBO)

C0C0tDr~tDTOJCT>^T^-c0CTiCT)'TCN'»-<3-00CDOCNf^Cn^rt0CNCn LnroroLncN'3'T-c\criOLO<Ti--q-'3-orororocNOD^-^oooooir^ Tooft^c^r-CDcno(r)LnaDT-LOCT)a3QDcr)-r-'srr^rgt--(NLr)Otv- r^r^t^r--OLT)Cor~t^LDLO'Tq-ocN-r-ocna>cor^t^tou3LOLO^i- covLOcocDa3a)0'-csro ,q-iniDr^Oi-r-cN'acocDOCN>TCDCNU3

TTfT^TT^rLOLOLOLOLOLOLriLOLOtCLDCDlDtDt^OC^t^OOa)

o

m EC3<

a.S

UJ

oooooLooinomoinoinooooooooooooo

«Dt^00O)OO'-'-CNCMC0r0T«3-Lni0r«-CDCr/O'-CNC0'T<0C0O r^r^^^mcocorocDroaDcococDajcocococooiO)^

CNCNtNOJWCNCNC^CNCNCNCNCNOtCNCNtNCNCNOgCNCNCNCNlNOICO

51
£» > Q

f- Z

»—

=5 10

u

O \ O to ?

_i

IXl u. > o

tnin^rcN'-cotocoO'D— tDOTf-coc30r~coc^cT>t-«-cotocN'T o

in<

T)'-CT>t^q-cMCCDir)rooa)incNCT)toi

T30t^foo)ir)»-LOCi'^-u3 o

tctDci3Lntr)miriir) <TT^r^rnnroojcNCNCN'-'-oooa>cooo(0

CNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCN'-'-'-'-

10

ro

0)

S_

n3

S-<Da.E

I—

+-> I—3

CDC

cu

+-> UJ

a.>

>-ax

(OoocioonnnmcinDioaiiDn'KDOffiO'r'-toiOTno)

t- «t ^r c, t- -r- co o id id t- to co— i^- 03 o n cn to en r> o to a) cd cd in Ln>-cotDi^cnr,)OcicNC")'-ai'?-:^-cN^(roiD'- — cncNicn^rT — scnorN<j(!)cnw^x^fflo^!Noaia)o(3)^oot\n^(M>-

<T ^J LO lO lO LO JTi CD tO '"D r- t-- CO CD CT!

O

C «- C3 "T Is- O "J"

O

O

O CN a.

t-— i —— CMr-j'^rrtO'r-Cf)

»- "T •^cnt^tDr^coococD^roiCN'Tcnt^conrocnrotDrot^t^t^oooo

0^cou3t^a>CN^toa>cNtncD'-incr><3-cO'3-*-tot-~r^Oi^cNCNto

cotDtDcDU3tD^^r^r^cocncocnCT)cr>oO'-cNCNco ,3-iDt^o ,3''3- <:j''3, f'T'Ti'T^:-^r"3, ^T<T^r«3-<5-\j-inminLOiri m in to trs to to c>- > it o^cot^cNcr>maioiroiDr--'r-cocT)LnLr)CN'^LniDcDincNcocT)CN-r- r- o. • (D^(\ocriMomin^'TVi/)irnocoonuDOi/>'-cnaiT-co<Tn cn O -i NcooioO'-rvrKrintONcocnO'-tTTiPNcoO'-fHOffliNa) »- a o

i- 2 coajcDOioioioimoioicDcncncnooooooO'-'-'-'-'-OKN <r z ~- mmuiwtfiir>mmmmir)inir)miDiDioiDioio<DtoioiDiDcoioiD to

t-^TfOicncotocnocn^-oO'-coiDwtNco^r'-iOLniDuiTOOco <r ^incrirooo^rotD'T'-oaiO'^ror-CNcot^cD'-cocncO'-cjior^ cn T-COincD003tOCB^^O-CT>COlOOCNa3OTCOt---OltD''-r--<ri-CNCO to r-r~t^r~cocorococncncricT!000-' •-oirNnfTJ-'j-^CNco cn OOOOOOOOOOOO'-'-'-'-'-'-'.-T-.r-T-,-,-,-,-,-.,- CN CNCNCNCNCNCNICNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNtgCNCNCNCN CN

Z5O

to

CU

a>Q.o

S- Q_o

•I—

+-> CO

s-

+->

(O

CD < > -J ZOO o: a S

UJ uj \ t- Z ~3 z uj Z t- o

UJ < 5 3o

•->

a

to \ a UJ O cr cr 13 a to <

to a. UJ IXl S

10 cc < a. Xa u

C3 cr z 3

ft-4 »-

1- <

to CL- x.

t—1

UJ

X 0. UJ s o UJ

CJ 1-

^^t^n^cncDr\j-i-a3cotoc\i(Daio3CTJCT!tD'-cT!tDCc-jn'--t~-tr)

T-cNntni^cTicNtDO^cT!Lnc\cnr^i^r--cT)ncT)tDt--cNt-t^<i3-oro iricoooi'jtDO'-^iacO'-'jiDaxNDcccMinoiroQoneou'ii'co

cNCNrorocococo^v^^ininu"jintotQtor~r^^cococr>cT>0'-cN OOOOOOOOOOOOOOOOOOOOOOOOO'----*- CNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCN

Oi.ocD^j-cD'r-^c--aiir)«T'?CNCOt-t^'Troh-a)co'rt

v300^ ,>T03 co^coininincoa>^cooocorO!Dtoroto^^^cocNooificocoto

^OCOC>3C003COCNr-^tDOC<3r--OCOtDCDO'-C\CN-^CO'

_.ft~-^rt-- cNc\»-T-oocncncocDt^r-tDmu3T03CNCN^oo3cotomcO'r-tCOCOCOCOCOCOCNCNCNCNCNCNCNCNCNCNCNCNCNCNCN'r-i-'-i--'--'-

u3LD-^Lr)mtococT)cr)t-oo)r~cot!3r~coincNcDt^^--^P3— cn cn co 0)coci)LncN(xin(DtDCNrotoo^''3'23CNCN:rj'Tcr)^rci)^r'-tDU3Ln t^cor^tD"TOtoocnmino30TiomcNin^cDtDcoO'-incNCNco CNCo^otonc^najcicoocoaaof^ocNTLritoincMM^n

U3<3''^'^rr303CNCN-^'r-OOC33CT)COa3t~tDtDLfi^rC'3CN-^OCOtD03

oooocooooooocnaicDrooioiaicnoiQmoimcDcoco

cncoa>cNt^Lf)tDcoo3T-T-rocotDtocr)"3- c\cNtDCN^ror^ir)tD'<-(J> u3«-o-^ot^^-^-cnr--Lno3r-ocr)CDCocoa3cocr)0'-tN^TtDCT)^ O'-'-cNroro'crLriLntDt^cocnoO'-fNnq-LOtDcocnO'-iNrom

'TintDt^cocrio-^cNco'TintococnO'-cNro^intDt^cnO'-cNco

t^^t^^r~r^(DCDCOCOCOQ3COCO(DCnOr)CT>CT)C33(33CT)CT)030000

oooooooooooooooooooooooooooo

tDt>-COO)0'-CNrO<Tir)tD«^CD<nO'-CNCO'3-UltOt^CDOlO-r-CNCO

OlOlOldiOOOOOOOOOO-'-'-^-'-'-'-'-'-nOOIPI

l^t^t^t^COCOCDCDCOCOCOCDCOODCOCDCOCOCDCOCOCOCOCOCOCOCOCO

CNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCN

CN

in

CNoooo

*rco

CDo

COoo

in

CO

CN

CO

CN

52
£ > Q

I- Z

—i Z> CO o o \ O CO s _JLU LL. > o

CMCDCDT— aDLO'-aJTOtO'-CD'-LOOJT-CO'TCSO'TLOaiPO'TCO o

LO<T<TT5J-fOCnC

T>OJOJC^-^-^OOCT>COa3[^tOLnTCNOC^ ,5'CD'T

O '-'-'-^'-^^^^-'-^^^^•^-OOOOOOOOOCDCTiCDtCNCNOICMCNCNCNCNCNCNCMCMCMCNCNCNCNCMCNCMCMCMCMCN'-*-'-'-

LU

to

fO

O)i4-> fOS0)cE

(Uo

D.

fO

Q.O

—o2 >

>- ^ O -J

ce

O

i- £ z —

lu \"3

mCTlOCD^t^OCncDCDCOCO^C^CDCOCOCn^COCM'T'-COOCMCMCn

<TCH0H1Nn->T'-<T^-MfiMDa]OO'!'O,r-(3i^ocv«O r»oc\LOcocNcOLnotDroocjicr. — _-, nTOionoiincvTm C50r--i^f^scDcncT)00'-cgf\oiuitDccotT)j:-^:^iDCNCNCor^ — to LOTcon^TtDcnncDt^-tDt^^aat^ocDOOtDai^-ooaj'T'T'TO

(OLOr*CTl'-i7)LOa30COUDtT)fOcDOLn01Ln'-r--LO"TLOQOtO-^-CNtO

oooO'-'-'-'-cKNCNtNnnT^q-inifliDNajaiooiinmo)

LninLnLOLnLrLnLOLOLOLnLnLOLOLnLOLnLOLOLniriLnLriLDtDtDtDc^

cn^j-OMCDcOLOLncNLntD<r)c^(D'-o^O<T)CT)cotoeotoot~-tDOJO »- ODtDOO'-'-'-'-OCDCDeD^CNtTiLn-^LntDCN^r'TOgCDCDLO'r-CO CM oooooocDtDOTcntDaioioicocoajcDajcncot^t-t^t^tocoLr) t

f»t^f~f»^t^cDtDtDtDlDU3COtDtDLOtOtDLDCOtOtDtDU3COLDCOtD «0

a;c

x:

+-> LUo

00

a> •f

4J

S-cuco

s_

+-> fO

s-3

4-> CO CO

CD z

LU< > -I ZOO

LU LU \ t- z s

LU < S

(- LU \ < X "D —1

cco

a. *• ro < <r- > >

oQ

a - z _i CO LU o

LU

a s

*-H -a

LUa LU o CC

ce 13

a. co <

CO

a

LU LU E

co a. < a. X

a. LU o ce z 3 *-* tt- <

CO CC iC

t~l LU X a

LU £ o LU u tt»-cO'T^rr~-TTtDcn^'QOCNfO'-'TOt^-^ocn»Ta5cnLO>T>- ,q'co t

oncnci'joiniocDOOOcoinOTiniiioiirnD'-'-^nDtNmn cm couD^^cnixi^^cDi^iriocDrnouDCNCD^rcri'TcncocDcocriuDCD in crimaicnoocDcom^r^^t^aJUDcDLOiri'T'TcorocNCN'-ocncocD cm corororocorocorococococorocorococorororotococooococNCMCM cm CNCNCMCNCMCMCNCMCNCNCMCMCNCNCNCMCNCNCNCNCNCNCMOJCMrMCMCM CM

coQO^TLO'-'-LororocD'-t--cMt^cr)t^cocM^rocnLnt^LOLOcoLoro cm nLOt^a3CT)cncot^LOCMCr)^TCnrM«TLO^Tojc^ocr)LOtD'-t--a)r~r>. cm -CDMnrO'-ciMnnoffiinnON'r'-N'TCunointDOon en Ocncncricncricocomcocot^r^r^t^cococDLOLO^-v^rtocMCM'-a) in nCMCMCMCMCMrMCNCMCMCMCMCNCMCMOJCNCMCMCMCMCMCMCNCMCMCMT- »- CMCMCMCMCMCMrMCMCNCMCMCMCMCMCNCNCNCNCMCMCMCMCMCMCMCMCMCM CM

OLoai«TOD»--^t^aiLO'T'rcMa5r^h-Toot^co<xiq-noO'-'rco o

m^coLnLOincocn^cooocococDtDOLO'^'c^'rcocNcOLOcococo o

t^COaJCOCOCOCOCMr-'-CDOCOt^OCOcOCOO-^CN CM-t- co gN <T >

cMCN^^oocncncocor^r^uDLOLn'TtocNrM'^-ocncocOLncO'-r»

ntOCOCOCOrOCMCMCMCNCMCMCNCMCMCNCNCMCMCMCM'-'-'^'-'-'-

cNai^cocM^cocn-^LOCMcncMCNCotDLncDtocD'TrocO'-'-'-cMcn o

coa3cotocncNiDCNCNLO^rcr)^-cr)r--'-LOcO'-cDcoO'-cNOCocMO

O

r^cMCntDTT^'cDcncoCTicDcor^'-cot^oc^cOLOOfocooc^cocM ^- LOcncNLDO'5"COCMi£i'-LOOLOOcD--r^'g-or~Lnq-(T)roiX)OOco co mcocncTiooO'-'-CMCMCoco<?^-LOLncDc^t~-cocnO'-cN'Tcocf) <0 ^^^^LOinLOLnLOLOLnLOLOLnLOLnLnLOLnLnLOLOcococDtococo r»

cnco<T)CM^ui<£a5co

— ^rococDtocT)rrrMCMcocN^ror^LOco»-cn

O

LO^r^^o^^^crir^LnroT-ocTicocDcocDcocTiO'-cN'Tcocj)'- co O — ^CMnroM'LnLOtD^cocnoO'-cNro^LntDCOCnO'-CNicoLO o

^Lnio^cDCPO^CNco^incococnO'-cNco^TLOtDt^cnO'-CMfO «r t^t^t^t^^f^cocommmmmcococncncricncTiaiaicncnoooo O

in o o o o o o o o o o o o o o o o o o o o o o o o o o o o <r tot^cocnO'-cMco'TLOcDt~cDa>0'-cMco'rLOtot^coaio--cMco co aioioiooooooooooO'-'--- — '--•-•-'-cmcmcmcm cm t^c^c^r^cDcoaDaajcDa^caaDCDcocccocococDQDCOcococococDco co CMCMCMCMCMCMCMCMCMCMCMCMCMCMCMCMCMCMCMCMCMCMCMCMCMCMCMCM CM

53
re

at

i-=5

t/) to

cu

s- > Q

t- Z U O "V o </> s > o a

2C >

aiMnO'-oii^^oio^inoiON^oioiiflfNm'/i'-cO'-q-^'iDOi o tr)Lf)uiLf)ir)^T ig-TT^T(r)<T)<T)cr)CNOJoj'r-'^--^-oooc')cr)oor^toco CNCNCNCJCNCNCNCN<NOJC\CNC\CNCNCNCMCN<NCNCNCNCN'-'-'~»-«-»-

cMT-iDM^r-OTtooioiirKKDn^cvnoioiinNi-inoioiin

to+

CO CD cv-'-wiDtN'-nairnn-cDoajmcootTfmTCMCDoia

rj<J-CDSO>OlDCr)CNd'-lOCJCDCDir)lDOr~CDtD tCOr~GlCOCD

'---•r-'-T-T-cNCJ(

Y)05-'(Xlin ^ • 00 »- T 2

-^ cM^O'-cNTootncnr^t^cncDO'-io^-oocDcnocontNcorrTcot^ \ ir)t~-a>'-roif)t^oojinoO'-tr)cnnr~<Nt^(Y)Ocr)oooir)inir)T-tN«T

"3 tOcocor^t^t^t^oooocDooa)tT)cnoO'-'-cNooro>criot^a)ojco<3

p QO TTTTTTTTTT^-^'a-'TminioiDinintoininininiocot^o

•r"

(Uc

>- it oor^cni-iOT-oooocnrocRoooiin'a-t^iooiocriooot^t^oiotoioco •»- a. • tDto^O'-ocoMoioininifiiiiNCDOCMiDoi^'-cDajcNOO'-ai cn o -i cno^cNco^r^-inujt^oocnO'-iNroiniot^cDOcjcoinoo-r-inoain »-

a: o

t- s mmo'/OioimaioioioioimoooooooO'-'-'-'-'-oKNCNO <r z — mmminmmmminir>mmioioioioio<ococoiocoiQ<o(o<oioco<o to

LU3

4-o

(/> <u

•r— +J

s-<DQ-O

i- Q.

S4-> ra

c/j

A3

-O

az

LU< > -I ZOO a: a S

LU UJ \ H- Z -o Z UJ z i- _j UJ < o 1- uj S < X -\

_J "3

a

i—

=3O > n »—

1- s

-J 1—

o

to \ - z —I

to UJ o

LU

a 5

*-H 1-

CC UJ

UJ cc a 3 o 1— a < a CCUJ 5C

LU a. to £ < UJ X la.O UJ z cc

H-t 3 <

(- to a. lO to s •-* UJ X ce UJ a. ou

ciM'i'rooinin'-iT'-MnofflCNCMi-nnoio^T-^O'-'- »?• (D'-ificnTai^ON'rcN^O'-ooinoiofiM'jincNoir-iniTi- <n r-ocN^t^cnr^irit^oocoaiojLncDCNLnCTirot^cNr^ocncaaiooo to t^rocDoocooDCTicnaioooO'-'-'-oicNr'joO'T^inLntDt^oD'- oi OOOOOOOOO'-^'-^'-'-'-'-'-'-^'-'-'-'-'-'-'-'-CN OI CNCNCNCNCNCNCNOirgOICNCNlNOICNCNOiOJOiCNCNOgiNCJC'JCNCNCNCS Oi

<ro<T>c\o3cnrocNt^ocN^^cNOTOOOOcncT)coOLncr>oococn''- <n 0^^o^oaicNuicn^cT)incN(T<coo30m[^uiLna)ci)(ot--«3-crit^ cn n^coroocNiNOi'- TtocncN'g-f-O'rrt^OTcoodr^rooot-'o cr> norooTT^r'r^riOLnLOLntDoiot^t^t^cDCDcocncnO'-cNoiT 10 OOOOOOOOOOOOOOOOOOOOOOOO*-'---*-'- i- C^CNC^C^C^C^CNOlC^OICNOJCNCNOICNJCNCJCNCNCNtNOICNCJCNOICNOI CN

lOtNOOMTKDOt^oiin'-NOcocooiDtoir'n'-cNOjO'-nMji o

ujoc^^iOLnm^coooo'q-cNcncNOr-^coi^'q-rO'-'^-t^inT-ioin o TOinQinomO'JfflnN'-Tco^'f^moiooonD^wmiDO '-'-ooaioicomMOCDLriifl'ToocNT-ooioicDioin'j-cNQNP)

(n<,)(,)CY)(NCNP(CMCNCNCMCNCNtNCNtNCN(NCN'-T-^T-^i-T-

«TOCM<TCNCnr^OL0^O'>T(OCMtO<Ot~-Cn'TCNC000t^00t~OCN^}-CN

O

OLOCNOOi^inojiOLnaii^oioocncDcNcO'-cDr^ojiocncricriOLO o

u3cooLno(oiuionLnio^^oa)ci3inaioro'-tN^Toi-r-c)CNt^oj t

^c^ocninoiooit^cNt^oir^'r-LfiaicncociicN^-iriiovr'-^cN'TT- co ^cncocvcNCN^^oocncriQOCDt^iotoin^'q-cooiT-ocnr-.LnoitT) <o oooooooooooiaifl)Oioioio)0>o)Ciocnoio)a)coa>to^ r»

N'-tnoooiinooonincooir-n'jintoh-NtDcoiDcoMoini-con in r^[^oiiitn^oooi^oaiCf)cx)t^OLr)<3-cocN^-ocT)ODC~-ioiocT) ,3- >r cocno^cNc^^incot^oDcocnor-CNjfo^rincot^oococnO'-cvicNO') o

01(l)OOOOOOOOOOO"'-'-'-'-'-'-'-'-'-nN(VK0l CN I^t^CDCDO0O0Q0O3COaDO0C0a)O3Q300Q0CO0000mCOCOC0ODC0O3COa) CO CNCNCJCNOiCNCNCNOICSlCNCNCNOJCNCNICNC^OJOlCNCNCNCNCNCNCNOIOJ CI OOOOOOOOOOOOOOOOOOOOOOOOOOOOO f) OOOOOOOOOOOOOOOOOOOOOOOOOOOIOO o i>-cocT)0'-cMcn»TLniot^cocnO'-cMco^-iocot-oooiO'>-ojioo^r T

t^c^f-oocococococococococoocncncnoicncnoioicnoooooo o

^T ,!TT'T'T'T"TT^r'T^r ,T'T'J"'^" ,T"5r ,5" ,3''J''J"Tir>LOlOtOLOin 10

54
re

0)sto

to

s- Q.

—•3 V)

C_> O ^

O to 5

> O

a.o —

>

«TCMOtDroou3coo)m»-cD<xcoo^rr^ooa)t^<omcococDOcNO o

i^nnoncNtM'-'-T-oomaimMiKa'rncMominonin'r •----'-'>-••- o

— —«-—•— T-ooooooooooa>a>o>cot*T CNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCN'-'-'-'-'i--'-

(0+

cn t- n

*t ro o • "T

CO 0) ro to • 01 o r- CD CO cn to ooocDOicMincjicococN^rr^cocNin'-coOTcocNCj'j'aoLncNcDcoco C0OCM^>01'-<Tl^OC,)IDO<TCDnC0<TOC0l0(DC0C1^iXlT-MlD o '-'-'- •»- '-<NCNCNcococoT^r>Tir)uicot^t^cDaiocN^-c--coocj

inuiinifiininir)Lnininif)ir)inif)if)inir)inir)ifiintniDcotocot>-cs-«-

t^omcooiotocDc*^-cjcoiD — oo<3"cot-»coinco<rinco<NC^ Jl^n^CNOOOCO.T^OCCOilDCOENOCN'-Kh.OlOlOl

CECDOLncoin — CNCDojcomt^^Tcr. tDcNCDCNinoocN^rcto

<Tr^'-Tc:cNr--cNr-<T»-~-cDO'-'j3'TLr)OJir)OO^cnoin r»t*acscciGOO'-CMC\ficiDi^<j)»-vt^cNCD(0(jin»-

i '-•---'-t-^t-cmcnw-. n<rtnmco

S-O

D.

CO

> 5£

a.O -J ce o

t- s

2 -~

uj \"3

O — Ot--CN"TinCNt^crit~-r-CNQOCDCOOO'-CNaOCOf^lD^TCOCNO)0> •- co^TLf)tr)cD<x)cDcoin^rcoo(Ot^T»-t-c\cDa)OOcDco<3-cooDa)t^ cn CM»-oa)CDt^cDir)«j-coc\>-ocot^co^rcO'-inoocDco — oo^roimco »-, ooocj)oiaia)CJiaicj)CT)oa)cDCDCDcrici)CDr~t--r^r~t>-cDc£)if)ir)'T ^

C^t^t^tDU3lDCOy3lOCDCDCDCOCOcDlOCDlDC£iCDCDCDCOCOCDtDCOCOCO CD

C

4->

<

X

oicji^cocflcocotnooc^cOc'Oin^rooLOCNOor^eDcoaicNco'TCNcooocj) «r «t»- CD'rcT)<rcD'-coinLr)if)cooir)CT)--ot~-r-^tDcot--cDcDcocDcn cm cNOr^incNor~LncNCTia)cooc^cocTicDCNt-coa)CNcDa)T-T-t^iDO in aiaicDoocDcoc>-c^r~cocDcDc£)Lr)Lr)'T'g-'TcorocNCN'-oocnf~io^- cn COCOCOCOCOCOCnCOCOCOCOCOCOCOCOCOCOCOCOCOCOCOCOCOCOCNCNCNCN CN CNCNCNCNCNWCNCNCNC^CJCNCNCNCNCNCNOICNCNCNCNCNCNCNOJCNCNCN CN o

C/» 0)

•r4-> S-

<uQ.O

S- O.C

o

•I—

+->

s-=5

4-> CO

o

a.<>

UJ

< > —

i

zoo cc ce s

uj < o

> co

i- s ~ Q

to \ Z -J ul O a 2

cDr-cN^iDinaicDcocDcoQO'a-aDOr^aicNcoO'-cooi^cri'r-'i-inr^ cn ojTcor^r^.i^ipmcoot^cNt^ocococNOincDi-cNCNtDait^'- »- <r cn cD^cNOcoco^cNOQOir)coocriincNCTicDc\cr)^-OLr)aicN^-co<3'CN o> aio)OTO)CDCDCDajcDr^i>r^i>u3(0<J3ir)inir)'T«3-^TcocNCN'<-oo)r* in CNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCN»-»- *- CNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCN CN

CDCN001^COa50^0)lf)'-t^OCDCj30COU)ir)CO'-CNCOCO'-COt>»C) o

ccoco'S-LnincO'-ccoco'TCNCDCNco — <tcoc-<tcO'— srt^ir)-— mm o TOuioinoi/ioioioN-'jco-'JocomooaitD^ncocoo — r-ooa)CT)CDCDc^tocDir)tjOTcococN'-ooia)a)(CLf)TCNO)r».co

COCOCOCOCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNt-'— — f- -r- t- rt^a> — ocotoo)r~coc3 — •g-ocof^cNf-cncocrjOOcDcoco^rcNco-'- co o

Oc^coc^ocoococNTCNcoa>cNCDT-cooco<3-oa)^rocoir)'-t^cD o

cDcoor--ii)inif)t^O'^ot^tDcr)'-CD>-ocDcocDOir)coc7it^ocoin «r ir)cncocDOTcocNt^ — cdoliocd — c^^ot^ifi^rcoTcocNtncNin co cnooO'- «-— CNCNcoco^Tmm<£<£r~-cDCDa)0'-c\!cotr>r»a>co co TT^iiiifiinu^ini/)ifiinininir>ininininininininioiocoiocococot-» t»»

Oi

ro

or

UJ

a.o

cr

o.Ul

to<

X

Q.O

X

Ulo

a

3

ce

c/j to

Ul

cea.

Q.

t^-- inaDCNinasocoiricocTiT-n^iiiajt^r-cDcxjcDCD^coin^-coco in f^i>cDLnin^rcococN'-oa)a)cric~-coin^-cocN-— ocdcomdi/kdi *r coa^o^cNco"Tinu3t^cocDcnO'-cNcoq-incot^-cr)cocnO'-cNCNco co OlOOOOOOOOOOOO— *-'-'-'-*-•"-*- — - — CNCNCNCNCN CN f^C^COCDCDCDOOQOCDCDCDCDOOCOObCOQOCDCDODQOOOCOOOCDOOODODOO 00 CNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCN CN

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O P) o o o o o o o o o o o o o o o o o o o o o o o o o o o m o o msoio^ CNcoTincot^cDa)0'-cNcorrLr)cDt^cDcj)0»-CNcoco^ ^

l>^t^O3a}COCOCOCDCOCOCOCOO)C7)0)CJ>C7>O)O)G)CJ)O)OOOOOO O

vri?T"Ti<rT<nrT"T |T7<i>rT^^i^'rwininininin in

55
56
APPENDIX D

Listing of Computer Program for Table Generation

57
C MAIN PROGRAM FOR GENERATION OF TABLES IN THIS REPORT. COEFFICIENTS

C ARE OBTAINED FROM BLOCKDATA.

IMPLICIT REAL^B (A-H.O-Z)

REAL TT.ANAME5.QNAMES

COMMON /COEFS/ A ( 20 ) . Q ( 20 ) . ANAMES ( 20 ) . QNAMES( 20)

COMMON /OTHER/ COMP . DPDRHO . DPDTCK

DIMENSION TT(27)/2 76. .277. ,278. ,279. ,280. ,280.5,281 . .281 .5,282.

1 .282.5,283. ,283.5,284. ,284.5.285. .286. ,287. .283. ,289. .290. ,291

.

2.292. ,293. .294. ,296. .298. ,300./

159 FORMAT (5X.2HA( . I2,2H)= , F1 2 . 6, 5XA6 , 8X2HQ( . I2,2H)=, F12.6.5XA6)

CALL CONGEN

WRITE (6. 159)( I ,A(I ) ,ANAMES(I ) , I .0(1 ) ,ONAMES( I ) .1 = 1,20)

66 READ(5.800,END=99) DENSIN

800 FORMAT( ) WRITE(6,44) DENSIN

44 F0RMAT(F12.2, ' MOLE/LITER ISOCHORE ' /1 11 X1H . /

' TEMPERATURE PRESSUR

1E ISOTHERM ISOCHORE INTERNAL ENTHALPY ENTROPY ' 5X 'CV ', 7X'CP'

2.4X8HVEL0CITY/24X'DERIVATIVE DERIVATIVE ENERGY '. 41X 'OF SOUND'/

3 5X'DEG K' ,7X'MPA' , 5X ' L-MPA/MOL MPA/K' . 4X' J/MOL' 5X5HJ/M0L

,

4 4X'd/M0L-K J/MOL-K' , 8X 'M/SEC /1

1

1X1H. ) PO 64 111=1 .27

TEMK=TT(III)

CALL THERMO (R2KT.R1 ,TH1 . DENSIN . TEMK . PRESS , DVD . CPS . ENTROP . ENTHAL

.

1 CVOL. ENERGY, SOUND)

DPDRH0=1 ./DENSIN/COMP

IF(DABS(TH1 ) .E0.1 . ) GO TO 22

WRITE (6, 55) TEMK, PRESS . DPDRHO. DPDTCK. ENERGY, ENTHAL, ENTROP

1 .CVOL. CPS. SOUND

55 F0RMAT(F10.1 . F12.5,F11.4,F10.4,2F10.1,~10.2.2F9.2.F9.1,2F10.5)

GO TO 64

22 WRITE (6. 55) TEMK , PRESS . DPDRHO, DPDTCK . ENERGY . ENTHAL , ENTROP , CVOL

64 CONTINUE

GO TO 66

99 STOP

END

C ALTERNATIVE MAIN PROGRAM WHICH ENABLES THE USER TO CHOOSE THE SYSTEM

C OF UNITS FOR THE TABLE. CALCULATION IS ALONG ISOCHORES. WITH THE

C INPUT BEING DENSITY, INITIAL TEMPERATURE. FINAL TEMPERATURE AND

C TEMPERATURE INCREMENT.

IMPLICIT REAL'8 (A-H.O-Z)

REAL ANAMES. QNAMES

DOUBLE PRECISION NT.ND.NP.NH

COMMON /UNITS/ IT . ID . I P , IH , NT , ND . NP . NH , FT . FD , FP , FH COMMON /COEFS/ A ( 20 ) , ( 20 ) , ANAMES( 20 ) ,ONAMES( 20)

COMMON /OTHER/ COMP . DPDRHO , DPDTCK

159 FORMAT (5X,2HA( , I2,2H)= . F1 2 . 6 . 5XA6 , 8X2H0( . 12 . 2H) = . F1 2 . 6 , 5XA6)

CALL CONGEN

WRITE (6.159HI ,A(I) .ANAMES(I) . I ,Q( I ) ,QNAMES( I ) .1 = 1.20)

CALL UNIT

66 WRITE(6.799)

799 FORMAT(' INPUT DENSITY. INITIAL T. FINAL T AND T INCREMENT:')

800 FORMAT ( ) READ(5.800,END=99) DENS.T1 .T2.TI

WRITE (6. 44) DENS,ND.NT,NP.NP.ND.NP,NT.NH,NH.NH.NT.NH,NT

DENSIN=DENS+FD

58
44

64

55

22

99

F0RMAT(F12.2,2X, A6, ' ISOCHORE'/ 111X1H./' TEMPERATURE PRESSUR

1E ISOTHERM ISOCHORE INTERNAL ENTHALPY ENTROPY ' 5X ' CV '. 7X ' CP

2' ,4X8HVEL0CITY/24X'DERIVATIVE DERIVATIVE ENERGY '. 42X ' OF SOUND'/

3 6X, A6.4X.A6.3X.A4, '/' .A6. 1X.A4, '/' .A1 .4X.A6.4X.A6,

4 4X.A5, '-

' .A1 .7X.A5. '-' .A1 ,8X, 'M/SEC'/M 11X.1H. ) TT=T1-TI

TT=TT+TI

IF(TT.GT.T2) GO TO 66

TEMK=TTT(TT)

CALL THERMO(R2KT.R1 ,TH1 . DENSIN, TEMK, PRESS . DVD. CPS, ENTROP . ENTHAL.

1 CVOL. ENERGY, SOUND)

DPDRHO=FP/DENS/COMP

POUT=PRESS*FP

E=ENERGY*FH

H=ENTHAL*FH

S=ENTROP*FH*FT

CV=CVOL*FH*FT

CP=CPS*FH*FT

DPDTsDPDTCK*FP*FT

IF(DABS(TH1 ).E0.1 • ) GO TO 22

WR I T E ( 6 . 55 ) TT . POUT . DPDRHO . DPDT .E.H.S.CV.CP, SOUND

FORMAT(F10.2.F12.5.F1 1.4.F10.4.2F10.1.F11.3.2F9.2.F9.1.2F10.5)

GO TO 64

WR I T E ( 6 , 55 ) TT . POUT . DPDRHO . DPDT , E . H . S , CV

GO TO 64

STOP

END

BLOCKDATA

DOUBLE PRECISION A.Q

COMMON /COEFS/A(20) .0(20) ,ANAMES(20) ,QNAMES(20)

DATA A/-.007833D0.2*0.D0. - 1 6 . 96B6D0 . 5 . 3439D0 , .325D0. 1 .3761 7D0.0.D0

1 . 1 .67472D0.23.9809D0.4.82D0. .7662D0. -36.4812D0, -27.35945D0

2. -12.5003D0. -10.5742D0.4*0.D0/

DATA 0/- .008369D0. - . 001 21 8D0 . 28 . 0541 DO . 282 . 3452D0 , 7 . 634D0 . 5 . 0403D0

1 . .1 1309D0.- .777D0. 12*0. DO/

DATA ANAMES/6HC .6HC0T3 , 6H .6HC0T2 .6HDPDT .6HBETA

1.6HK0 ,6H ,6HB*B ,6HA .6HDELTA .6HK1 , 6HMUC

2.6HMU1 .6HMU2 , 6HMU3 .6HS00 .6HS20 .6HS01 .6HS21 /

DATA QNAMES/2*6H .6HM0L WT.6HTC .6HRH0C .6HPC

1 .6HDPCDTC.6HSL0PDI .6HP11 .6HALPHA .6HP00 .6HP20 .6HP40

2.6HDELTAI .6HALPHAI ,6HBETA I , 6HGAMMAI . 6HP01 .6HP21 .6HP41 /

END

SUBROUTINE CONGEN

C THIS SUBROUTINE CALCULATES ALL QUANTITIES NOT DEPENDENT ON R OR THETA

IMPLICIT DOUBLE PRECISION (A-H.O-Z)

COMMON /COEFS/ A (20). 0(20)

DATA DELPP.DELPM.DE LP PH.DF.LPMH/1 .D-6.-1 .D-6.1 .000001 DO, .999999D0/

EQUIVALENCE ( DELI . Q ( 1 4 ) ) . (DRH0C,A(3) ) . (BETA.A(6) ) . ( DELTA , A (1 1 )

)

1 , (C0TEE2.A(4) ). (DPDT,A(5) ) . ( DELTC , A( 8 ) ) . (BESQ,A(9)

)

2.(CC,A(1)).(AA.A(10)) . (TCK.Q(4)).(RH0C.Q(5)),(PC.Q(6)) . (XK0.A(7))

3.(ALHI.Q(15)),(BETI.Q(16) ) . (GAMI , Q( 1 7 ) ) . ( P01 . Q( 1 8 ) ) . ( P21 . Q( 1 9 )

)

4. (ALPHA.Q(IO) ). (P00,0(11 ) ). (P20.0(12) ). (P40,0(13) ). (P41 .0(20)

)

5. (S00,A(17)) ,(S20,A(18)) , ( S01 . A( 1 9) ) . ( S21 , A (20)

)

ALPHA = 2. DO - A(6)*(A(11) + 1 . DO ) IF(DA6S(ALPHA) . LT. 1 .D-6) ALPHA=1 .D-6

GAf/iMA = BETA*(DELTA - 1.D0)

59
DELI * 0.50D0

IF (DELI.LT. -BETA)DELI=-BETA

ALHI = ALPHA - DELI

BETI = BETA + DELI

GAMI * GAMMA - DELI

IF( ALHI

.

LE.DELPPH. AND. ALHI .GE.DELPMH) ALHI = 1 .000001 DO

IF (ALHI .LE.DELPP. AND. ALHI .GE.DELPM) ALHI * .000001D0

DELPC = Q(7)*DELTC

ERR = 2.D0*BtTA*DELTA - 1 . DO

POO = (BETA*(DELTA-3.D0)-BESQ*ALPHA*GAMMA)/(2.D0*

1 BF.SQ*BESQ*(2.D0-ALPHA)*( 1 . DO- ALPHA) * ALPHA

)

P20=-( BETA* (DELTA- 3. ) - BESO* ALPHA* ERR )/( 2

. *BESQ* ( 1

. -ALPHA)

(ALPHA) ) P40=(ERR-2. )/2. /ALPHA

SOO = (2. -ALPHA)*POO

S20 = -BETA*(DELTA-3. )/2 . /BESQ/ALPHA

IF (XKO. LE.0.D0)XK0 = .0001D0

DA » 0(1)

DB = Q(2)

RA • DA/(1 .DO - BESO)

RB * DB/(1 .DO - BESO)

SWO « S00+S20

SS1 = AA*XK0*SW0+RA**(1 . ALPHA)

SS2 = AA*XKO*SWO*RB**( 1

.

ALPHA)

D1 = CC*(SS1-SS2)

P01 « (BETA*(DELTA-3.D0)-3 DO*DELI- A(9)* ALHI*GAMI)

/(2 .D0*A(9)*A(9)*(2.D0-ALHI)*(1 .DO- ALHI) ALHI)

P21 = -( (BETA*(DELTA-3.D0) 3.D0*DELI-A(9 )*ALHI*'ERR)/

1 p

1 (2.D0*A(9)*(1 .DO-ALHI )*ALHI )

)

P41 « ( .5*ERR - 1

.

)/ALHI

SOI = (2. -ALHI )*P01

S21 = -{BE7A*DELTA-3.*BETI)/2./BESQ/ALHI

PTW * P01 + P21 + P41

SW1 « S01+S21

SSW1 « AA*A( 12)*(RA**(1 . DO- ALPHA+DELI

)

)*SW1

SSW2 = AA+A( 12)*(RB**(1 . DO- ALPHA+DELI ) )*SW1

D2 = CC*(SSW1 -SSW2)

0(9) = Q(8)*.9905D0 + (D1 +D2 )/( DB-DA

)

RETURN

END

SUBROUTINE THERMO ( RH02KT , R1 , TH1 . D , T , PRESS , DVDPT . CP

.

2 ENTROP , ENTHAL , CV . ENERGY . SOUND)

CALCULATES ALL THERMODYNAMIC PROPERTIES, BOTH IN 1- AND 2-PHASE

REGION, FOT GIVEN DENSITY AND TEMPERATURE.

IMPLICIT D0U3LE PRECISION (A-H.O-Z)

COMMON /OTHER/ COMP , DPDRHO . DPDTCK

COMMON /COEFS/ A(20),Q(20)

DIMENSION S(2) ,SD(2)

EQUIVALENCE (C0T3,A(2) )

,

(DRhOC,A(3)) , (BETA.A(6)) .( DELTA , A( 1 1 )

)

1 , (C0T2,A(4)) ,(DPDT.A(5)) . (XMWT , Q( 3) ) ,

(

DELTC . A(8 ) )

.

(BESQ,A(9))

2. (CC.A(1)).(AA.A(10)) , (TCK,0(4)).(RHOC.0(5)),-(PC.Q(6))

3, ( ALPHA. 0( 10) ),(XK1 , A( 1 2 ) ) ,

(

DELI ,Q( 1 4 ) ) . ( FAC ,Q( 7 ) ) . ( XKO, A( 7) ) 4, (ALHI,Q(15)),(P11 ,0(9)). (P1W,Q(18)) . ( P2W,Q( 1 9) ) , ( P4W,Q( 20 )

)

5. (P00.Q(11)) ,(P20,Q(12)),(P40.Q(13)).(S00.A(17)) . (S20,A(18))

IFLAG « XK(1 )=A(7)

XK(2)>A(12)

8 TER » 2.D0*BETA*DELTA - 1 . DO

60
TEE=(T-TCK)/TCK

TSTAR=TEE+1 .DO

DTSTIN=1 .DO-( 1 .DO/TSTAR)

RHO=D/RHOC

CALL CONVER(RHO,TEE,AMU,TH1 ,R1 ,RH01 , S.RHODI ,ER)

TT1=TH1*TH1

PTW=P1W+P2W*TT1+P4W+TT1*TT1

P1=AA*XK0*(R1**(2.D0-ALPHA) )+(POO+TT1 * ( P20+TT1 + P40)

)

P3=RH0DI*AMU+PTW + AA*XK1*(R1 ** ( 2 . DO- ALPHA+DELI )

)

P4=DTSTIN*(DPDT+DTSTIN*(C0T2+DTSTIN*(C0T3) )

)

PBAR=TSTAR*(P1+P3+P4+1 .DO)

PRESS=PBAR+PC

IF(IFLAG.EQ. 1 ) RETURN

PT=DPDT+2.D0*C0T2*DTSTIN+3.D0*C0T3*DTSTIN*DTSTIN

UD=A(14)+2.D0*A( 1 5

) +DTST IN+3 . DO* A ( 1 6) *DTSTIN*DTSTIN

UFUNCT=S( 1 )+P11 *AMU+PT-RHO + UD+S(2)

ENERGY=1 . D3* ( PC*UFUNCT )/RHO/RHOC

CALL AUX(R1 ,TH1 . D2PDT2 , D2PDMT , RH02KT , AA . XK , SD . CVCOEX)

IF(DABS(TH1 ) .EO. 1 .DO) RH02KT=1 . D30

DVDPT=- ((RH02KT*RHOC**2)/( ( D**3 ) * PC* T STAR )

)

C0MP=RH02KT/PC/RH0+*2

DPDRHO=1 . /D/COMP

CV1 =2 . DO*P1 1 *D2PDMT/RH02KT

CV2=(D2PDMT*D2PDMT )/RH02KT

D2PZER=2.DO*COT2+6*COT3*DTSTIN

D2MZER=2.D0*A(15)+6.D0*A( 16)*DTSTIN

CV3=RHO*D2MZER

CV4=P1 1+P11/RHC2KT

CVS=(D2PZER-CV3-CV1 -CV2-CV4+D2PDT2 )/TSTAR* *2

CVCOEX=(CVCOEX*AA)/( ( 1 . DO- BESQ ) **2

)

IF(DABS(TH1 ) .EO.-DO) CVS= ( D2PZER-CV3+CVC0EX)/TSTAR**2

CV=1 .D3*PC*CVS/D/TCK

TAU=( -1 .DO)/TSTAR

DPDTR = PT+P1 1 * (AMU- ( RHO/RH02KT) )+S( 1 )+S( 2

) - RHO*D2PDMT/RH02KT

DPDTR=PBAR-(TAU*DPDTR)

DPDTCK=DPDTR*PC/TCK

CP=(RH02KT*DPDTR + *2/RHO**2+CVS)*PC*1 . D3/D/TCK

ENHOL=PRESS/PC/TSTAR- (TAU+UFUNCT)

ENTHAL=1 .D3 + PC*TSTAR*ENHOL/RHOC/RHO

UZER0=A(13)+DTSTIN*(A(14)+DTSTIN*(A(15)+DTSTIN*A( 16))

)

IF(DABS(TH1 ) .EO. 1 .DO) GO TO 44

SOUND=-CP/CV/D/D/DVDPT/XMWT

SOUND=DSQRT ( DABS ( SOUND ) ) * 1 . D3

44 ENTROP=(ENHOL-RHO* (UZERO+AMU) )*PC*1 . D3/RHO/RHOC/TCK

20 CONTINUE

RETURN

ENTRY PRES(R1 ,TH1 .D.T, PRESS)

IFLAG = 1 GO TO 8

END

61
SUBROUTINE AUX(R1 ,TH1 , D2PDT2 . D2PDMT . D2PDM2 . AA , XK , SD . CVCOEX

C CALCULATES SECOND DERIVATIVES. IS CALLED BY THERMO

IMPLICIT REAL*8 (A-H.O-2)

COMMON /COEFS/ A(20).Q(20)

DIMENSION XK(2).S(2). SD( 2 ) . W( 2) . Y( 2 ) , Z ( 2 ) , COEX( 2

EQUIVALENCE (CC.A(1 ) ) . ( BETA , A( 6 ) ) . ( BESQ . A( 9 ) ) . ( DELTA . A( 1 1 )

1,(ALPHA.Q(10)),(S00.A(17)).(S20,A(18)).(S01 . A( 1 9) ) . (S21 . A( 20)

DELI = O.DO

S(1 )=S00+S20*TH1+TH1

S(2)=S01+S21*TH1*TH1

SD(1) = 2. *TH1*S20

SD(2) = 2.*TH1*S21

WW = O.DO

YY = O.DO

ZZ = O.DO

GAMMA = BETA* (DELTA - 1 .DO)

TT1 = TH1+TH1

TER = : 2.D0*BETA*DELTA 1 .DO

G = (1I .+(BESQ*TER-3. )* TT1 - BESO* (TER'2. )*TT1 *TT1 ) CVCOEX = O.DO

DO 30 I = 1 .2 ALHI = ALPHA - DELI

BETI = BETA H- DELI

GAMI = GAMMA - DELI

W( I)=(1 . -ALHI)*(1 . -3.*TT1 )*S(I )-BETA*DELTA*(1 .-TT1 )*TH1*SD(I)

W( I ) = (W( I) *(R1**( -ALHI) ) )/G

W( I ) = W( I )*XK( I)

WW = WW + W( I ) Y(I) = BETI*( 1 .D0-3.D0*TT1 )*TH1 - BETA*DELTA* ( 1 . DO- TT1 ) *TH1

Y(I) = (Y(I) *(R1**(BETI - 1 .DO) ) )*XK( I)/G

YY = YY + Y( I ) Z(I) = 1.D0 - BESQ*(1.D0 - ( 2 . DO'EETI ) ) *TT1

Z(I) = (Z(I) +(R1**(-GAMI))-)*XK(I)/G

ZZ = ZZ + Z( I

A1 = (BETA*(DELTA-3.D0)-3.D0*DELI-BESQ*ALHI*GAMI)

1 /( 2. DO* BE SO* BESQ* (2. DO- ALHI ) * ( 1 . DO- ALHI ) * ALHI

A2 = 1+(BETA*(DELTA-3.D0)-3.D0*DELI-BESQ*ALHI*TER)/

1 (2.D0*BESQ*(1 .DO-ALHI)*ALHI)

A2 = - A2

A4 = 1 .D0+( (TER-2.D0)/(2.D0*ALHI )) F1 = A1 + A2 + A4

COEX(I) = ((2. DO - ALHI)*(1.D0 - ALHI ) * ( R1 **( - ALHI )

) *F1 *XK( I )

CVCOEX = CVCOEX + COEX(I)

DELI = 0.5D0

30 CONTINUE

D2PDT2 = AA*WW

D2PDMT = YY + AA*CC*WW

D2PDM2 = ZZ/AA + 2.D0*CC*YY + (CC+ *2 ) *AA*WW

RETURN

END

SUBROUTINE SS ( R . TH , S , SD)

C CALCULATES THE PARAMETRIC PART OF THE ENTROPY FUNCTION

C FOR GIVEN R AND THETA.

IMPLICIT DOUBLE PRECISION( A-H . 0-Z

DIMENSION S(2),SD(2)

COMMON /COEFS/ A(20).Q(20)

EQUIVALENCE ( ALPHA , Q( 1 0) ) , (BETA.A(6) ) . (BESQ.A(9)) . ( DELTA . A ( 1 1 )

1 , (DELI. 0(1 4)) .( ALHI.,0(1 5) ) , ( BET I ,Q( 1 6 ) ) , ( GAMI , Q( 1 7) ) . ( POO ,Q( 1 1 )

2. (P01 .0(18) ) . (S00.A(17)) , (S20.A(18)) . ( SOI . A( 1 9 ) ) , ( S21 . A (20)

TT = TH*TH

S(1 )= SOO + S20*TT

SD( 1 ) = 2. *S20*TH

S(2) = S01 + S21+TT

SD(2) = 2.*S21*TH

S(1)=S(1)*A(10)*A(7)*R**(1. -ALPHA)

S(2)=S(2)*A(10)*A(12)*R**(1.-ALHI)

RETURN

END

62
SUBROUTINE CONVER(RHO.TEE.AMU.TH1 ,R1 . RH01S.S1 . RHODI , ERROR 1

)

IMPLICIT REAL*8 (A-H.O-Z)

COMMON /COEFS/ A(20).0(20)

DIMENSION S1 (2) ,SD(2)

EQUIVALENCE(BETA,A(6) ) , (DELTA, A(1 1)),(XK1,A(12)),(CC,A(1))

1 . (ALH1 ,Q( 15) ) , (ALPHA,Q( 10) ) , (BESQ,A(9) ),(P11.Q(9))

2 .( DELI. 0(14)), (P1W,Q(18)). (P2W,0(19) ) , (P4W,Q(20) ) 3, (AA,A( 10) ) , (XK0,A(7) ) , (SOO,A( 17) ) , (S20.A( 18)) , (BET I, 0(1 6))

TSTAR = TEE+1 .DO

( 1 .DO/TSTAR)

R1=DTSTIN/( 1

. -BESQ)

1 . DO

LT.O. )

DTSTIN = R1=DTSTIN

IF(DTSTIN.

TH1=0.

IF(DTSTIN. LT.O. ) TH1=1 . CALL SS(R1 ,TH1 ,S1 ,SD)

RHODI = 1 .DO + P11 "DTSTIN

RHODIT = RHODI + CC* ( S1 ( 1 )+S1 ( 2 ) ) DRHO = RHO - RHODIT

AMU = O.DO

IF(DTSTIN.GT.O.DO) GO TO 1 RH01C0 = XK0*R1**BETA + XK1*R1**BETI

TWOFAZ = RH01C0

IF (DABS( DRHO) . GT . TWOFAZ) GO TO 1 RH01S = DSIGN(RH01CO,DRHO) + CC*S1 ( 1

)

TH1 = DSIGN( 1 .DO, DRHO)

ERR0R1 = 1 .DO

GO TO 999

1 CONTINUE

IF(DRHO.NE.O.DO) GO TO 2 TH1 = O.DO

R1 = DTSTIN

RH01S = CC»S1 ( 1

)

2 CONTINUE

C RULE FOR FIRST PASS

Y1 = DTSTIN

DEN1 = RHO - RHODIT

CALL RTHETA(R1 , TH1 , DEN1 , Y1 ) TT=TH1 *TH1

AMU = AA* R1**(BETA+DELTA)+TH1*(1 .DO-TT)

Y1 = DTSTIN + CC*AMU

CALL SS(R1 ,TH1 ,S1 ,SD)

RHOWEG = XK1*(R1**(DELI+BETA) )+TH1 + CC*S1(2)

RH01S = DEN1 + CC*S1(1) + RHOWEG

ERR0R1 = RHO - RHODI - RH01S

IF( DABS(ERR0R1 ) . LT.1 .D-5 ) GO TO 999

C RULE FOR SECOND PASS

DEN12 = RHO - RHODI - CC*S1 ( 1 ) + RHOWEG

IF (DEN12.EQ.DEN1 ) DEN12 = DEN1 - 1.D-06

CALL RTHETA(R1 ,TH1 .DEN12, Y1

)

TT = TH1+TH1

AMU = AA- R1 **(BETA*DELTA)+TH1*(1 .DO-TT)

Y1 = DTSTIN + CC'AMU

CALL SS(R1 ,TH1 ,S1 ,SD)

RHOWEG

RH01S2 = ERR0R2 = IF( DABS

ERR0R1 = RH01S =

= XK1 +R1 **(DELI+BETA)*TH1 + CC*S1(2)

DEN12 + CC+S1(1) + RHOWEG

RHO - RHODI

(ERR0R2) .GT.1

ERR0R2

RH01S2

RH01S2

,D-5 ) GO TO 998

GO TO 999

998 CONTINUE

C RULE FOR NTH PASS

DEN2 = DEN12

DO 44 ISIG =1,10

SLOPE = ( ERR0R2-ERR0R1 )/(DEN2 -DEN1)

HOLD = DEN2

DEN2 = DEN1 - ( ERR0R1 /SLOPE

)

CALL RTHETA(R1 ,TH1 ,DEN2.Y1

)

TT = TH1*TH1

63
AMU = AA" R1 **(BETA*DELTA)*TH1 *( 1 .DO-TT)

Y1 = DTSTIN + CC*AMU

CALL SS(R1 ,TH1 ,S1 ,SD)

RHOWEG = XK1 *R1**(DELI+BETA)*TH1 + CC*S1(2)

RH01S = DEN2 + CC*S1(1) + RHOWEG

ERROR1 = ERROR2

ERROR2 = RHO - RHODI - RH01S

IF( DABS(ERROR2) . LT.1 .D-6 ) GO TO 999

DEN1 = HOLD

44 CONTINUE

IF(DABS(ERROR2) .GT. 1 .D-6) WRITE (6,66) ERROR2 , RHO , DTST IN , DEN2 ,CC

66 FORMATf 1X.8F9.5)

999 CONTINUE

RETURN

END

SUBROUTINE RTHETA( R , THETA , RHO. TEE ) CC THIS VERSION WILL FIT DATA FOR THETA GT 1.0 AND LT 1.000001 AS IF M CC SOLVES RHO = EM'THETA* (

+ * BETA

CC AND TEE = R* ( 1 . DO- BESQ " THETA*THETA

IMPLICIT REAL+8 (A-H.O-Z)

COMMON /COEFS/ A( 20 ) , Q( 20 ) , QQ( 20

EQUIVALENCE ( BETA , A ( 6 ) ) , ( EM . A ( 7 ) ) . (BESQ.A(9)

IF(EM. LE.O.DO .OR. BESO . LE . 1 . DO ) GO TO 600

ABSRHO = DABS( RHO ) IF(A3SRH0 .LT. 1.D-12 ) GO TO 600

BEE = DSQRT(BESQ)

IF(DABS(TEE) .LT. 1.D-12) GO TO 495

IF( TEE .LT. O.DO ) Z = 1 . DO- ( 1 . DO- BEE ) *TEE/( 1 . DO- BESQ

1 *(EM/ABSRHO)**( 1 .DO/BETA)

IF(TEE.GT.O.DO) Z = ( 1 . DO+TEE* ( EM/BEE/ABSRHO) *+ (1 . DO/BETA ))** -BETA

IF( Z.GT. 1 .00234D0+BEE ) GO TO 496

C = -RHO*BEE/EM/DABS(TEE)**BETA

Z = DSIGN(Z.RHO)

100 DO 500 N = 1 , 16

Z2 = Z*Z

Z3 = 1 .DO - Z2

DZ = Z3*(Z+C*DABS(Z3)**BETA)/(Z3+2.D0*BETA*Z2)

Z = Z - DZ IF(DABS(DZ/Z) .LT. 1.D-12) GO TO 498

500 CONTINUE

601 WRITE(6.450) R. THETA. RHO . TEE , BETA . EM , BESQ

I F( DABS (THETA) . GT . 1 .0001 ) THET A=THET A/DABS ( THETA

RETURN

498 THETA = Z/BEE

R = TEE/( 1 .DO-Z+Z)

R = DABS(R)

RETURN

495 THETA = DSIGN ( 1 . DO . RHO)/BEE

R = (RHO/I EM'THETA) )**(1 .DO/BETA)

RETURN

496 THETA = DS IGN ( 1 . . RHO)

R = TEE / ( 1 .ODO - BESQ ) R = DABS(R)

RETURN

600 IF(DABS(TEE) .LT. 1.D-12) GO TO 601

IF(TEE. LT.O.DO) GO TO 496

THETA = 1 . D- 1

R = TEE

450 F0RMAT(2X. 'RTHETA DOES NOT CONVERGE' . 7(1X. E12.6) ) RETURN

END

64
C SUBROUTINE SATDEN CALCULATES THE VAPOR PRESSURE AND THE

C SATURATED LIQUID AND VAPOR DENSITIES AT THE INPUT TEMPERATURE

SUBROUTINE SATDEN( T . DL , DV . PRESS)

IMPLICIT DOUBLE PRECISION (A-H.0-2)

COMMON /OTHER/ COMP , DPDRHO . DPDTCK

COMMON /COEFS/ A(20).Q(20)

DIMENSION S(2) .SD(2)

EQUIVALENCE (COT3.A(2) ) . (DRHOC,A(3) ) . (BETA.A(6) ) . ( DELTA , A( 1 1 )

1 , (C0T2.A(4)) , (DPDT,A(5)) , (XMWT ,Q( 3) ) . (DELTC . A(8) ) . (BESQ.A(9))

2 . ( CC . A ( 1 ) ) . ( AA . A ( 1 ) ) . ( TCK . ( 4 ) ) . ( RHOC . Q ( 5 ) ) . ( PC , Q ( 6 )

3. (ALPHA.QOO) ). (XK1 ,A( 12) ). ( DELI . Q( 1 4 ) ) ,(FAC,Q(7)), (XKO,A(7))

4,(ALHI,Q(15)),(P11.Q(9)).(P1W.Q(18)).(P2W.Q(19)), (P4W,Q(20))

5, (POO.Q(11 ) ) , (P20.QM2)) , (P40,Q(13)) . (S00.A(17)) , (S20.A(18))

6, (S01 ,A(19) ) , (S21 ,A(20)) . (BET I ,Q( 16)

ERR * 2.DO*BETA*DELTA - 1 . DO

TEE=(T-TCK)/TCK

TSTAR=TEE+1 .DO

DTSTIN=1 .DO-(1 .DO/TSTAR)

D1=1 .+P11*DTSTIN

RR=DTSTIN/( 1

. -BESQ)

D2=XKO*RR**BETA + XK1*RR**BETI

D3=CC*AA*(XK0*(S00+S20)*RR**(1 . -ALPHA) + XK1 * ( S01 +S21 )

1 RR+*(1 . -ALHI )) RHOL=D1+D2+D3

RHOV=D1 -D2+D3

DL=RHOL*PHOC

DV=RHOV*RKOC

CALL CONVER(RHOL.TEE,AMU.TH1 ,R1 .RH01 .S.RHODI ,ER)

PTW=P1W+P2W+P4W

P1=AA*XKO*(R1**(2.DO-ALPHA) ) * ( POO+P20+P40

P3=RH0DI*AMU+PTW V AA*XK1*(R1 ** ( 2 . DO- ALPHA+DELI )

P4=DTSTIN*(DPDT+DTSTIN*(COT2+DTSTIN*(COT3) )

P6AR=TSTAR*(P1+P3+P4+1 -DO)

PRESS=PBAR*PC

RETURN

END

SUBROUTINE DFIND( D , P , DGUESS , T , DVDPT

C THIS SUBROUTINE WILL CALCULATE BY ITERATION THE DENSITY FOR A C GIVEN PRESSURE AND TEMPERATURE. AN INITIAL GUESS FOR THE

C DENSITY ("DGUESS") IS ALSO REQUIRED.

IMPLICIT DOUBLE PRECI S10N( A-H . 0-2

DIMENSION S(2) ,SD(2) ,XK(2)

COMMON /COEFS/ A(20).Q(10)

XK( 1 )=A(7)

XK(2)=A(12)

DD = DGUESS

VOL I = 1 ./DD

TT = T DYLIM = .0001

DO 10 d=1 . 12 CALL PRESf R1 ,TH1 .DD.TT, PRESS)

DY=( P-PRESS)

CALL AUX(R1 ,TH1 , D2PDT2 , D2PDMT , RH02KT , A( 10) , XK . S . SD . CVCOEX

TSTAR=T/(0(4)+A(8)

DVDP=- ( (RH02KT*(Q(5)+A(3) )**2)/( ( DD* *3 ) * ( Q(6 ) -i-Q( 7 ) *A( 8 ) ) *TSTAR )

IF(DVDP.LT. -2.D0) DVDP=-2.D0

IF(DVDP.GT. 1 .0-2) DVDP=1.D-2

DELV = DVDVDP

VOL = VOLI + DELV* .6D0

DD = 1 .DO/VOL

VOLI = 1 .DO /DD

IF(DABS(DY) . LT. DYLIM) GO TO 81 10 CONTINUE

WRITE (6.1 ) P. PRESS, DGUESS. DD.DVDP. DELV

1 FORMAT(' NO CONVERGENCE :', 6F1 2 . 5)

81 D = DD

RETURN

END

65
C THE FOLLOWING £ SUBROUTINES FORM A PACKAGE ALLOWING THE USER TO

C OPERATE IN A SYSTEM OF UNITS OF HIS CHOICE.

SUBROUTINE UNIT

C THIS SUBROUTINE QUERIES THE USER AS TO HIS CHOICE OF UNITS AND SETS

C INTERNAL PARAMETERS APPROPRIATELY. THE INTERNAL UNITS OF THE PROGRAM

C ARE TEMPERATURES IN K, DENSITIES IN MOL/DM3. ALL OTHER QUANTITIES

C CALCULATED IN DIMENSIONLESS UNITS AND DIMENSIONED AT OUTPUT TIME.

IMPLICIT DOUBLE PRECISION (A-H.O-Z)

DOUBLE PRECISION NT , ND . NP . NH , NNT . NND , NNP , NNH

COMMON /UNITS/ I T , I D . I P , IH , NT , ND . NP . NH , FT . FD . FP . FH DIMENSION FFD(4).FFP(5),FFH(6) ,NNT(4) ,NND(4) . NNP(5) .NNH(6)

DATA FFD/. 03564541 DO, 35. 64541 DO, 1 . DO , .5709853D0/

DATA FFP/1 .D0,10.D0,9.869232667D0.145.037738D0, 10. 1971 DO/

DATA FFH/2+. 03564541 DO, 1 . DO . 8 . 51 379D- 3 , .2388459D0. .01532476D0/

DATA NNT/1HK. 1HC1HR, 1HF/

DATA NND/6HKG/M3 .6HG/CM3 .6HM0L/L .6HLB/FT3/

DATA NNP/6H MPA , 6H BAR , 6H ATM , 6H PSI .6HKG/CM2/

DATA NNH/6HKJ/KG . 6H J/G .6HJ/M0L .6HCAL/G . 7HCAL/M0L . 6HBTU/LB/

DATA A1 ,A2,A3,A4/8HTEMPERAT.7HDENSITY

30

31

32

33

1 .8HPRESSURE, 8HENERGY /

WRITE(6,11) A1 WRITE(6.12)

READ(5. 10,END=99) IT IF(IT.EQ.O) STOP

IF' IT. GT. 41 GOTO 30

NT=NNT(IT)

WRITE(6.11) A2

WRITE(6,13)

READ(5. 10,END=99) ID IF(ID.GT.4 .OR. ID.LT.1) GOTO 31

ND=NND(ID)

FD=FFD(ID)

WRITE(6,11) A3

WRITE(6,14)

READ(5.10,END=99) IP IF(IP.GT.5 .OR. IP.LT.1) GOTO 32

NP-=NNP( IP)

FP=FFP( IP)

WRITE(6,11 ) A4

WRITE(5. 15)

READ(5, 10.END=99) IH IFUH.GT.6 .OR. IH.LT.1) GOTO 33

NH=NNH( IH)

FH=FFH(IH)

RETURN

99

10

1 1 12

13

14

15

ENTER UNITS

CHOOSE FROM

CHOOSE FROM

CHOOSE FROM

CHOOSE FROM

6=BTU/LB'

CHOSEN FOR ' ,A8)

1=DEG K. 2=DEG C 3=DEG R, 4=DEG F'

*KG/M3. 2=G/CM3. 3 = M0L/L. 4=LB/FT3')

=MPA, 2=BAR, 3=ATM, 4=PSIA. 5=KG/CM2')

=Kd/KG. 2=J/G, 3=J/M0L, 4=CAL0RIES/G . 5=CAL0

FH

STOP

FORMAT( ) FORMAT (

FORMAT ( FORMAT ( FORMAT (

FORMAT (

1RIES/M0L,

END

FUNCTION TTT(T)

FUNCTION TO CONVERT INPUT TEMPERATURES IN EXTERNAL UNITS TO DEG K DOUBLE PRECISION T . TTT . FT . FD , FP , FH . NT . ND , NP , NH

COMMON /UNITS/ I T , ID . I P , IH . NT . ND. NP , NH , FT , FD, FP GO TO (1 .2, 3. 4). IT TTT=T

FT=1 . RETURN

TTT=T+273.15D0

FT=1 . RETURN

TTT=T/1 .ODO

FT= . 5555555555556D0

RETURN

TTT=(T+459.67D0)/1 . 8D0

FT= . 5555555555556D0

RETURN cc

END UU

1
Appendix E. Units and Conversion Factors

Units used in the tables

Pressure - MPa Temperature - K Density - mo! /dm 3 Energy, Enthalpy - J/mol

Entropy - J/(mol-K)

Specific heat - J/(mol-K)

Speed of sound - m/s

Molecular weight of ethylene

Gas constant*

M = 28.0541

R = 8.31434 J/(mol

Reduction Factors

Pressure

MPa to Multiply table value by

Pabar

atmosphere

psi, lbf/in 2

10 6 10 9.869233

145.037738

Density

mo! /dm 3 to Multiply table value by

kg/m 3 lbm/ft 3 28.0541

1.7513585

Energy, Enthalpy

J/mol to Multiply table value by

kJ/kg

BTU/lbm

0.0356454

0.01532476

Entropy, Specific heats

J/(mo1.K) to Multiply table value by

kJ/(kg.k)

BTU/(lbm.R)

0.0356454

0.00851375

Temperature

K to

°C°F

Transform table value by

(T,°C)

(T,°F)

(T.R)

(T,K) - 273.15

9

5

9

5

C(T,K) - 273.15] + 32

(T,K)

Speed of sound

m/s to Multiply table value by

ft/s 3.28083

*The actual value of the gas constant is not required for the programs in this

Tech Note. The value given here is that used in reducing the oriqinal Burnett

PVT data (ref. 3, 18) and in NBS Tech Note 1045 (ref. 5).

67
Temperature, K

ro IO

00 CO o o

CO

o

Pressure, MPa

Fig. 1 Range of validity of the present formulation. Left: in

temperature - density space. Right: in pressure-temperature

space.

68
-9

.3-

.2-

.1

-.1

-.2

Density Deviations

T = 298.15 K

* DH

TWW

HLSB

o TZ —MJ

O

Density, mol/dm'

Fig. 2

.2r

-.1

-.2

Density deviation, in %, between the experimental PVT data

and the present formulation, if compared at the same pressure

at 298.15 K. A DH [10]; x TWW [11 ]; + HLSB [3], 99.993% pure;

Y HLSB [3], 99.999% pure; o TZ [12,13]; MJ [5].

Pressure Deviations

T = 298.15 K

-.3

Fig. 3

Density, mol/dm3

- DH

. TWW

v + HLSB

o TZ

MJ

11

Pressure deviations, in %, between the experimental PVT data

and the present formulation, if compared at the same density

at 298.15 K. Symbols as in Fig. 2.

69
Density Deviations

T = 293.15 K

-.2

-.4

A DH

X TWW

Y + HLSB

O TZ

-MJ

<3

-.1

-.2

Fig. 4 As in Fig. 2, but at 293.15 K.

Pressure Deviations

T = 293.15 K

A DH

X TWW

Y + HLSB

o TZ

-MJ

Fig. 5 As in Fig. 3, but at 293.15 K.

70
.2-

<1

-.2-

-.4 L

.3

X

Y +

DH

TWW

HLSB

Density Deviations

287<T<290 K

o TZ

Density, mol/dm 3

6 x7 8 x 9

v X 10

, 1

X

11

l X X Y

X

X Y

X

X

+ 4- + +

Y

x

X A

A

A

-tA

<D A X A A A

A

A A A A

Fig. 6 As in Fig. 2, but for temperatures from 287-290 K.

Pressure Deviations

287<T<290 K

* DH

* TWW

Y * HLSB

o TZ

MJ

Density, mol/dm

Fig. 7 As in Fig. 3, but for temperatures from 287-290 K.

71
<i

.25

+

i X i

Density Deviations

284<T<287K

+

1 ir 6 7

* + 8 9 + + * X a10 11

X

+

3 Density, mol/dm

A

A

-.25

X

A

A

A

X

X - •

A

X

-.5 X * A

A

A

X Y +

DH

TWW

HLSB

-.75 - O TZ

Fig. 8 As in Fig. 2, but for temperatures from 284-287 K.

.06

.04-

.02-

-.02 L

Pressure Deviationsi 284<T<287K

* DH

A

x TWW

r* HLSB

o TZ X

X

A A

A

X *

X

CD A * * .

X X * y

+ Y X

Y

1 V I **

+

.

"tK X

1

1 x ^ 1_ ... 6 ^ 8 9 10 11

Density, mol/dm 3

+

Fig. 9 As in Fig. 3, but for temperatures from 284-287 K.

72
Density Deviations

278<T<284 K

1**z*J? S*i ** ^ 8 10 11

-5

-10

-15

^A A I* Va^*

Density, mol/dm

:

-DH

xTWW

Y * HLSB

°TZ

Fig. 10 As in Fig. 2, but for temperatures from 278-284 K, i.e.,

spanning the critical temperature. The large density departures

between the different data sets are caused by the divergence

of the compressibility and the exDansion coefficient.

Pressure Deviations

278<T<284 K * DH

x TWW

04 r+ HLSB

° TZ

02 X

1

*

t

O A. A

A

Y

1

X

1 1 1 i i 5.5 +•

4- 6.0 6.5 7.0

Density, mol/dm 3

4-

02

Fig. 11 Pressure deviations, in %, between experimental PVT data and

the present formulation, if compared at the same density. The

comparison is for the subcritical densities, 5.5-6.5 mol/dm 3

, and for the temperatures from 278-284 K. Symbols as in Fig. 2.

73
.04

o .02

*DH

xTWW

Y + HLSB

Pressure Deviations

278<T<284K

tx i

* X

* i

V

i

*-§*-

Density, mol/dm'

8

Fig. 12 As in Fig. 11, but for densities from 6.5-8.5 mol/dm 3

, spanning the critical density.

i.e.,

Pressure Deviations

278<T<284 K

* DH

.08 —

x TWW

Y + HLSB A

1

X A* A

.04

4*

* A

A A A

A * ^ A ft +

* + tx

1 III '1 it

+

+

1 8 9

T 10+

T

11

Density, mol/dm3 x X

nA

Fig. 13 As in Fig. 12, but for liquid-like densities from 8.5 - 10.5

mol/dm 3

.

74
CO Q_

X

CDCO Q_

CDo

.002r

.001 -

^-.001

-002 L

VAPOR PRESSURE DEVIATIONS

*DH -- HLSB

TEMPERATURE, K

* A 279

A 280 281: * 282*

• *4I

'**

283

Fig. 14 Departures of the vapor pressures from the present formulation

x DH [10]; HLSB [3], 99.993% pure sample; A HLSB [3],

99.999% Dure sample.

002-

co 0.01

o

E

rau

-0.01

-0.02 -

-0.03

?

279

o SAMPLE AP

o SAMPLE B

DOUSLIN AND

HARRISON

280 281 282

T/K

Fig. 15 Departures of the coexisting densities from the present formulation.

Upward-pointing line segments denote vapor, downward-pointing

ones liquid densities.

%DH [10]; o HLSB, 99.993% pure sample [3], o HLSB, 99.999%

pure sample [3].

75
SPEED OF SOUND

-j 1 1 i_

7 8

Density, mol/dm 3

Fig. 16 The speed of sound as measured by Gammon [4], o, compared with

full curves. systematic differences exist.

Only below T very near the phase boundary do

1 1 \r

298.15 K o 289.35 K 7%

x 293.15 l< v 281.65 K a 288.15 l< 281.15 l< + 284.15 K * 280.15 K

SPEED OF SOUND DEVIATIONS

DATA OF GAMMON

<

X+

A

-X- + n+

A .A+ Jb

A-K

D ~a^o'r-D

* AQD

Q.

10 DENSITY, mol/dm

Fig. 17 Departures of the speed of sound data [4], in %, from the

prediction of our surface. Some points have very large departures:

their estimated error, however, is also quite large. Near the

phase boundary, however, the departures of 1-2% are systematic

and significant.

76
+50

_ +20

O

5 o

T=283.15 K

H.D. T=288.15 K

M.J.

IUPAC

+20

-50-

H.D.

M.J.

T=298.15 K

IUPAC

8

p

, mol/dm

10

Fig. 18 Comparison of the enthalpies of ethylene according to various

formulations. M.J. [5]; IUPAC [14]; HD [17]. The base line

is the present formulation, which was anchored to that of M.J. at the state point 6 mol/dm 3

, 298.15 K.

77
Fig. 19 The difference between the prediction of McCarty and Jacobsen

for several thermodynamic properties and the present formulation.

Top: enthalpy difference aH; center: energy difference AS.

The M.J. formulation has a somewhat different density dependence

than the present one. Substantial differences occur near the

critical density and within a few K from the critical temperature.

78
+20%-

+10%

-20%"

-40% J

-20%

-40%

Fig. 20

AC;

AC\

6 8

| 298.15 I 293.15

288.15

283.15

The percentage difference between second- derivative values

according to the McCarty-Jacobsen formulation and the present

one. Top: speed of sound difference AC ; center: difference

in specific heat at constant volume AC ; bottom: difference

in specific heat at constant pressure AC . The differences

between the two formulations are substantial within the range

of 5 K from the critical point. The analytic formulation M.J.

will have a non-zero thermodynamic speed of sound and a finite

C at the critical point, while it underestimates the strength

of the divergence of C .

79
10.0-

P,MPa

300 310

T, K

Fig. 21 The region of P-T space that should be avoided in custody

transfer if the pressure is measured to, respectively, 0.1%,

0.05% or 0.02% and an accuracy of 0.1% is desired in density.

80
Fig. 22 The region of P-T space that should be avoided in custody

transfer if the temperature is measured to, respectively,

0.1%, 0.05% and 0.02% and an accuracy of 0.1% is desired in density.

81
Fig. 23 The region of P-T space that should be avoided in custody

respectively, 0.005%, 0.01% or 0.02% (in mole fraction) of an impurity very different in volatility from ethylene, is present,

and an accuracy of 0.1% is desired in density.

82
NBS-114A (rev. 2-eo

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions)

PUBLICATION OR

REPORT NO.

NRS TO HfiS

2. Performing Organ. Report NoJ 3. Publication Date

OrfohP.r 198?

4. TITLE AND SUBTITLE

A Thermodynamic Surface for the Critical Region of Ethylene

5. AUTHOR(S)

J. M. H. Levelt Sengers r ,T. S. Gallagher,. F. W. Ra1fonr r agri .1 . V. Spngprc

6. PERFORMING ORGANIZATION (If joint or other than NBS, see instructions)

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

7. Contract/Grant No.

8. Type of Report & Period Covered

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City, State, ZIP)

Celanese Chemical Co., Cities Service Co., Continental Oil Co., Gulf Research and

Development, Mobil Chemical Co., Monsanto Polymers and Petrochemicals Co.,

Phillips Chemical Co., Union Carbide Corp., and the National Bureau of Standards.

10. SUPPLEMENTARY NOTES

J

Document describes a computer program; SF-185, FlPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here)

Tables are presented of thermodynamic properties of ethylene in the range

279-300 K in temperature, 5.75-10.5 mol/dm3 in density, which range includes the

critical point. The tables presented here are based on the critical-point scaling

laws and incorporate the critical anomalies in a proper fashion. The tables thus

complement the formulation of the equation of state of fluid ethylene by McCarty

and Jacobsen (NBS Tech. Note 1045, 1981) which does not claim accuracy near the

critical point. The predictions of the present formulation are compared with

four sets of recent PVT data, and with speed-of-sound data. Tables are presented

of pressure, energy, enthalpy, entropy, specific heats and speed of sound as function of temperature along finely-spaced isochores. The computer program

required for table generation is included. Even if the surface were perfect, the

reliability of densities calculated at experimental pressures and temperatures of

limited accuracy declines rapidly as the critical point is approached. Contour

plots in P-T space are presented of reqions to be avoided in custody transfer for

given uncertainties in pressure, temperature and sample composition,

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

critical region; custody transfer; density; enthalpy; ethylene; equation of state;

impurity; scaling laws; specific heat; speed of sound; tabular values;

thermodynamic properties.

13. AVAILABILITY

[_XJ Unlimited

| | For Official Distribution. Do Not Release to NTIS

fx] Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402.

2] Order From National Technical Information Service (NTIS), Springfield, VA. 22161

14. NO. OF

PRINTED PAGES

85

15. Price

$5.00

USCOMM-DC 6043-P80 frU.S, GOVERNMENT PRINTING OFFICE] 19 8 2-360-997/2257

NBS TECHNICAL PUBLICATIONS

PERIODICALS

JOURNAL OF RESEARCH—The Journal of Research of the National Bureau of Standards reports NBS research and develop- ment in those disciplines of the physical and engineering sciences in which the Bureau is active. These include physics, chemistry,

engineering, mathematics, and computer sciences. Papers cover a broad range of subjects, with major emphasis on measurement

methodology and the basic technology underlying standardization. Also included from time to lime are survey articles on topics

closely related to the Bureau's technical and scientific programs. As a special service to subscribers each issue contains complete

citations to all recent Bureau publications in both NBS and non- NBS media. Issued six times a year. Annual subscription: domestic

$18; foreign $22.50. Single copy, $4.25 domestic; $5.35 foreign.

NONPERIODICALS

Monographs—Major contributions to the technical literature on

various subjects related to the Bureau's scientific and technical activities. Handbooks—Recommended codes of engineering and industrial practice (including safety codes) developed in cooperation with in- terested industries, professional organizations, and regulatory

bodies. Special Publications—Include proceedings of conferences sponsored by NBS, NBS annual reports, and other special publications

appropriate to this grouping such as wall charts, pocket cards, and

bibliographies. Applied Mathematics Series—Mathematical tables, manuals, and

studies of special interest to physicists, engineers, chemists,

biologists, mathematicians, computer programmers, and others engaged in scientific and technical work.

National Standard Reference Data Series—Provides quantitative data on the physical and chemical properties of materials, compiled from the world's literature and critically evaluated. Developed under a worldwide program coordinated by NBS under

the authority of the National Standard Data Act (Public Law

90-396).

NOTE: The principal publication outlet for the foregoing data is the Journal of Physical and Chemical Reference Data (JPCRD)

published quarterly for NBS by the American Chemical Society

(ACS) and the American Institute of Physics (AIP). Subscriptions,

reprints, and supplements available from ACS, 1 155 Sixteenth St., NW, Washington, DC 20056.

Building Science Series—Disseminates technical information developed at the Bureau on building materials, components,

systems, and whole structures. The series presents research results,

test methods, and performance criteria related to the structural and

environmental functions and the durability and safety characteristics of building elements and systems.

Technical Notes—Studies or reports which are complete in themselves but restrictive in their treatment of a subject. Analogous to monographs but not so comprehensive in scope or definitive in treatment of the subject area. Often serve as a vehicle for final reports of work performed at NBS under the sponsorship of other government agencies.

Voluntary Product Standards—Developed under procedures

published by the Department of Commerce in Part 10, Title 15, of

the Code of Federal Regulations. The standards establish nationally recognized requirements for products, and provide all concerned interests with a basis for common understanding of the

characteristics of the products. NBS administers this program as a supplement to the activities of the private sector standardizing

organizations. Consumer Information Series—Practical information, based on N BS research and experience, covering areas of interest to the con- sumer. Easily understandable language and illustrations provide

useful background knowledge for shopping in today's tech- nological marketplace. Order the above NBS publications from: Superintendent of Documents. Government Printing Office, Washington, DC 20402. Order the following NBS publications—FlPS and NBSIR's—from

the National Technical Information Services, Springfield, VA 22161

Federal Information Processing Standards Publications (FIPS

PUB)—Publications in this series collectively constitute the Federal Information Processing Standards Register. The Register

serves as the official source of information in the Federal Govern- ment regarding standards issued by NBS pursuant to the Federal Property and Administrative Services Act of 1949 as amended,

Public Law 89-306 (79 Stat. 1127), and as implemented by Executive Order 1 1717 (38 FR 12315, dated May II, 1973) and Part 6 of Title 15 CFR (Code of Federal Regulations).

NBS Interagency Reports (NBSIR)—A special series of interim or

final reports on work performed by NBS for outside sponsors

(both government and non-government). In general, initial dis- tribution is handled by the sponsor; public distribution is by the National Technical Information Services, Springfield, VA 22161,

in paper copy or microfiche form.
U.S. Department of Commerce

National Bureau of Standards

Washington, D.C. 20234

Official Business

Penalty for Private Use $300

POSTAGE AND FEES PAID

U S DEPARTMENT OF COMMEFj

COM-215

THIRD CLASS BULK RATE