Implementation and performance evaluation of different cubic ...

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Implementation and performance evaluation of different cubic equations of

state for the estimation of properties of organic mixtures

Auteur Welliquet Jonathan

Promoteur(s) Quoilin Sylvain

Faculteacute Faculteacute des Sciences appliqueacutees

Diplocircme Master en ingeacutenieur civil eacutelectromeacutecanicien agrave finaliteacute approfondie

Anneacutee acadeacutemique 2015-2016

URIURL httpsgithubcomCoolPropCoolProp httphdlhandlenet226822013

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Implementation and performance evaluation of different cubic equations ofstate for the estimation of properties of organic mixtures

Jonathan WelliquetUniversity of Liegravege Faculty of Applied Sciences

Aerospace and mechanical engineering departmentThermodynamic Laboratory

Abstract

The thermodynamic properties of organic mixtures is a really important aspect for the development ofthe new thermodynamic cycles However mixtures are not all yet well known and a model that could givea good approximation of the properties in a fast way could help

The cubic equations of states provide a simple way requiring minimal information to approximate thestate of a fluid This provide an interesting tool with enough flexibility to improve the accuracy as moreexperimental data become available The results for vapour-liquid equilibrium of mixtures are particularlygood

Keywords CoolProp Cubic EOS Mixtures

URL httpwwwfacsaulgacbe (Jonathan Welliquet)

Preprint submitted to Thermodynamic Laboratory August 20 2016

Contents

1 Introduction 3

2 State of the art 421 Cubic Equations of State 4

211 Soave-Redlich-Kwong 4212 Peng-Robinson 4213 Volume translation 5214 VTPR 6

22 Mixing rules 823 Software 8

231 RefProp 8232 CoolProp 8

3 Volume translation implementation 931 Solving the cubic equation 932 Preparing for the other thermodynamic properties 9

4 Comparison 1141 Pure fluid 1142 Binary mixtures 2243 Ternary mixtures 29

5 Acknowledgements 32

6 Conclusions 33

2

1 Introduction

The improvements in thermodynamic cycles relies on the possibility to chose the most suitable fluid andto model it accurately

Thermodynamic libraries likes RefProp FluidProp and CoolProp provides efficient models for sufficientlywell known fluids (mainly through Helmholtz equation of state or interpolation from experimental data)However there are still a lack of data for less studied fluids particularly mixtures which usually need exper-imental data to evaluate the interaction parameters required for the models These interaction parameterare often approximated or not used at all

Accurate models like the Helmholtz equations of state (HEOS) usually require a consequent numberof experimental data whereas the cubic equations of state are simpler model that can already gives goodresults with very few experimental data (critical pressure and temperature pcrit Tcrit and acentric factor ω)Being simpler models they also have the benefit from being faster Of course these advantages comes at thecost of a lower accuracy These cubic models can be enhanced by some parameters (approximated or fittedto experimental data) to increase their accuracy

The cubic equations of state are thus a good candidate to have a fast model to approximate the behaviourof non yet well studied fluids This is extremely helpful in the research field where this allows to quicklyevaluate a lot of potentials fluids and select the one worthy of interest before running expensive experimentalsetup to evaluate more accurately their behaviour

The scope of this work is to evaluate what can be expected from these Cubic equations of state A focuswill be set on organic mixtures relevant for refrigeration and heat pump applications The implementationa simple volume translation model has also been proceed and is explained in this report

3

2 State of the art

21 Cubic Equations of StateThe thermodynamic state of a fluid can be defined by two independent state variables An equations

of state (EOS) is a relation between state variables generally aiming to compute a third variable from twoother known ones

Cubic equations of state have of cubic that they can be expressed as a cubic equation of the molarvolume v

The first cubic equation of state was the so called Van der Waals equation of state and of the form(p +

av2

)(v minus b) = RT (1)

With the a and b parameters depending on the critical pressure and critical molar volumeThis equation 1 is linking the pressure p the molar volume v and the temperature T Theses kind of

equations are generally referred as PVTEOS and have the advantage to provide both the liquid and vapourphases with a single equation (Frey et al 2007)

With time some improvements have been added to improve the quality of the approximation in boththe general formula and in the way to compute the attraction parameter a and the repulsion parameter (oreffective molecular volume) bThe attractive parameter is often separated in a constant part ac multiplied by a temperature dependantone α(TR ω) such as a = acα(TR ω)

The most common equations of state used in process simulation are mainly based on the Soave-Redlich-Kwong and Peng-Robinson EOS (Frey et al 2007)

211 Soave-Redlich-KwongThe Soave-Redlich-Kwong (SRK) is an improved Redlich-Kwong equation of state and has the original

form (Soave 1972)

p =RT

v minus bminus

acα(TR ω)

v(v + b)(2)

With the parameters

ac = 042747

(R2T2

c

Pc

)b = 008664

(RTc

Pc

)α(TR ω) =

[1 + m(ω)

(1minus

radicTR

)]2m(ω) = 0480 + 1574ω minus 0176ω2

(3)

212 Peng-RobinsonThe Peng-Robinson (PR) equation is a modification of the SRK that allows better molar volume for

liquids and better representation of liquid-vapour equilibrium for many mixtures (Valderrama 2003) How-ever when considering the entire family of EOS derived from the SRK and PR neither has a clear advantagein the accuracy of itrsquos property predictions (Frey et al 2007) It has the original form (Peng and Robinson1976)

p =RT

v minus bminus

acα(TR ω)

v(v + b) + b(v minus b)(4)

4

With the parameters

ac = 045724

(R2T2

c

Pc

)b = 007780

(RTc

Pc

)α(TR ω) =

[1 + m(ω)

(1minus

radicTR

)]2m(ω) = 037464 + 154226ω minus 026992ω2

(5)

213 Volume translation

10minus3 10minus2 10minus1 100

200

250

300

350

400

P=

10times

104

Pa

P=

10times

104

Pa

P=

32times

104

Pa

P=

32times

104

Pa

P=

10times

105

Pa

P=

10times

105

Pa

P=

32times

105

Pa

P=

32times

105

Pa

P=

10times

106

Pa

P=

10times

106

Pa

P=

32times

106

Pa

P=

32times

106

Pa

P=

60times

106 P

a

P=

60times

106 P

a

P=

10times

107 P

a

P=

10times

107

Pa

P=

10times

108

Pa

P=

10times

108

Pa

Specific volume [m3kg]

Tem

pera

ture

[K]

REFPROPSRK

Figure 1 Isobar curves and saturation curve (dashed) on temperaturevolume plot comparison of SRK with REFPROP fluidR407C

A correction to the molar volume of the form vc = v + c can be applied to the cubic equations of stateThis correction is particularly interesting for mixtures as the molar volume of the pure fluid is different fromthe molar volume of the mixture

The need for such correction can be seen in the Figure 1 A constant translation would correct most ofthe error on the liquid side while having nearly no impact on the gaseous phase (the volume being order ofmagnitude higher)

Densities are usually known from experiments for the majority of pure fluids (an similarly for knownmixtures) and tabulated in databases Molar mass is constant for a given material and also generally knownfor pure fluids So when molar volume is not directly known density and molar mass are generally availableto compute itIt is common to use the molar volume at the reduce temperature Tr = 07 to compute the translationparameter (Schmid and Gmehling 2012)

c = (vEOS minus vexp)∣∣∣Tr=07

(6)

This constant volume translation can significantly improve the results for the saturated liquid densitiesin the low temperature range (Tr lt 08) but fail near the critical temperature (Ahlers and Gmehling 2001)

5

A solution to this can be to have a temperature dependant volume correction Ji and Lempe (1997) suggesta dependency of the form

c = (vEOS minus vexp)∣∣∣T=Tc

035

035 + η∣∣∣α(TR ω) minus TR

∣∣∣γ (7)

Where α(TR ω) is the same as in the one of the cubic equation of choice and η and γ are obtained bymatching experimental data For SRK Ji and Lempe (1997) propose the general formulation

η = 23010eminus38267(13minuszc

)+ 0950

γ = 15458eminus57684(13minuszc

)+ 0635

(8)

With zc being the compressibility factor at the critical pointA volume translated Peng-Robinson (VTPR) would be written (Schmid and Gmehling 2012)

p =RT

v + c minus bminus

acα(TR ω)

(v + c)(v + c + b) + b(v + c minus b)(9)

214 VTPRDespite its name the VTPR model is more than just a Volume Translated Peng-Robinson It generally

refers to a combination of the UNIFAQ group contribution mixture and a volume translation (Schmid andGmehling 2012 Schmid et al 2014)

The equations of the model are developed in the Figure 2

Figure 2 Diagram of the VTPR equations From source Schmid and Gmehling (2012)

The group contribution model discompose the different functional groups of the organic molecules and setinteraction parameters between each of them This gives a very interesting way to evaluate the interactionany mixture will have without the need to specifically test this mixture This however has the cost to requireto evaluate the interaction between all the functional groups and gives a slower model to solve

This model is currently in development for CoolProp (VTPR)

6

Table 1 Mixing and combining rules in two-constant cubic EOS (Valderrama 2003 Chen and Liu 2007 Wong and Sandler1992)

Van der Waals a =sum

i

sumj

xi x jai j ai j =radic

aia j b =sum

i

sumj

xi x jbi j bi j =bi + b j

2

One parameter ai j =radic

aia j (1 minus ki j) bi j =bi + b j

2

two parameters ai j =radic


2(1 minus Ii j)

Panagiotopoulos-Reid (PR)


aia j [1 minus ki j + (ki j minus k ji xi)] bi j =bi + b j

2

three parameters ai j =radic


2(1 minus Ii j)

General nonquadratic (GNQ)


aia j (1 minus ki j) ki j = δi xi + δ j x j bi j =bi + b j

2

four parameters ai j =radic

aia j (1 minus ki j) ki j = δi xi + δ j x j bi j =bi (1 minus βi) + b j (1 minus β j)

2

Kurihara et al (KTK)

three parameters a =sum

i

sumj

xi x jradic

aia j minus(τ minus φ) gE

RES

ln(

bminusφbminusτ

)]

b =sum

i

sumj


2

gERES = RT x1x2

[η1 + η2 (x1 minus x2) + η3 (x1 minus x2)

2]

Huron-Vidal a = b

sumi

xiai

bi+

gE(x)Clowast

b =sum

i

sumj


2

Wong-Sandler a = b

sumi

xiai

biminus AE

infin(x)

b =

sumisum

j xi x j

(b minus a

RT

)i j

1 minussum

i xiaibiminusAEinfin(x)

RT

one parameters V1(b minus

aRT

)i j=

(bi minus

aiRT

)+

(b j minus

a jRT

)2

(1 minus ki j)


aRT

)i j=

bi + b j

2minus

radicaia j (1 minus ki j)

RT

three parameters(b minus

aRT

)i j=

bi(1 minus li) + b j

2minus


RT

7

22 Mixing rulesA summary of the most common mixing rules for two constants EOS can be found in the Table 1It worth noting that it is possible to simplify the b constant in the basic Van der Waals mixing rule

b =sum

isum

j xix jbi j

=sum

isum

j xix jbi+b j

2

=sum

isum

j xix jbi2 +

sumisum

j xix jb j

2

= 2(sum

isum

j xix jbi2

)=

sumisum

j xix jbi

=sum

i(sum

j x j)xibi

=sum

i xibi

(10)

23 Software231 RefProp

RefProp is a commercial software developed by NIST (Lemmon et al 2013)It has different models such as Helmholtz equations of state and translated Peng-Robinson equation

(PRT)This software is used as a reference value to compare the accuracy of the different models

232 CoolPropCoolProp is an open-source software CoolProp (2016)It has different models such as the Helmholtz equations of state IF97 Incompressible models and

different cubic equations of statesThe Soave-Redlich-Kwong (SRK) and Peng-Robinson (PR) models are used with the general form

p =RT

v minus b+

a(T )(v +∆1b)(v +∆2b)

(11)

For SRK ∆1 = 0 ∆2 = 1For PR ∆ = 1 plusmn

radic2

This allows to have a single implementation to cover both casesThis equation is used to define the residual non-dimensional Helmholtz energy and its derivatives as

explained in ()The residual non-dimensional Helmholtz energy and its derivatives are afterwards used to compute the

other thermodynamic properties

8

3 Volume translation implementation

In this work the volume translation is considered as a constant value cThe cubic equations of states for Soave-Redlich-Kwong and Peng-Robinson are implemented in Cool-

Prop in the general form seen in equation 11The volume translation can be added in this general form as

p =RT

v + c minus b+

a(T )(v + c +∆1b)(v + c +∆2b)

(12)

31 Solving the cubic equationThe cubic equation is solved in the function rho_Tp_cubic who uses the temperature and pressure to

solves the cubic and give back the density solution(s)The equation 12 is thus rewritten in term of density

p =RT

1ρ+ c minus b

+a(T )(

1ρ+ c +∆1b

) (1ρ+ c +∆2b

) (13)

This equation can be simplified by introducing

d1 = c minus b (14)d2 = c +∆1b (15)d3 = c +∆2b (16)

p =RTρ

1 + d1ρ+

a(T )ρ2

(1 + d2ρ) (1 + d3ρ)(17)

Then expresses as a polynomial of the density ρ

0 = minusp (18)+ ρ (RT minus p (d1 + d2 + d3)) (19)+ ρ2 (RT (d2 + d3) minus p(d1d2 + d1d3 + d2d3) minus a(T )) (20)+ ρ3(RTd2d3 minus pd1d2d3 minus d1a(T )) (21)

The coefficients of this 3rd order polynomial are then sent to an analytic cubic equation solver to givethe one to 3 solutions for density

32 Preparing for the other thermodynamic propertiesTo compute the other values CoolProp uses the residual non-dimensional Helmholtz energy and itrsquos

derivatives First the equation 13 is reformulated as a function of the non dimensional density δ = ρρr

andreciprocal reduced temperature τ = Tr

T Further explanation on the choice of the reducing parameters ρr

and Tr are available in ()This leads to

p =Tr

τ

R1δρr

+ c minus b+

a(τ)(1δρr

+ c +∆1b) (

1δρr

+ c +∆2b) (22)

or

p =Tr

τ

δρrr1 + (c minus b)δρr

+δ2ρ2r a(τ)

(1 + (c +∆1b)δρr) (1 + (c +∆2b)δρr)(23)

9

The derivative with respect to δ of the residual non-dimensional Helmholtz energy is given by ()(partαr

partδ

)τ

=pτ

δ2ρrRTrminus1

δ(24)

Inserting equation 23 into equation 24 leads to(partαr

partδ

)τ

=(b minus c)ρr

1 minus (b minus c)δρrminusτa(τ)RTr

ρr

(1 + (b∆1 + c)δρr) (1 + (b∆2 + c)δρr)(25)

The value of the residual non-dimensional Helmholtz energy can be obtained by integrating this equa-tion 25 The result can be decomposed to the form

αr = ψ(minus) minusτa(τ)RTr

ψ(+) (26)

With the two integrals

ψ(minus) =

int δ

0

(b minus c)ρr

1 minus (b minus c)δρrdδ (27)

= minus ln (1 minus (b minus c)δρr) (28)

ψ(+) =

int δ

0

ρr

(1 + (b∆1 + c)δρr) (1 + (b∆2 + c)δρr)dδ (29)

=

ln(1 + (b∆1 + c)δρr

1 + (b∆2 + c)δρr

)b(∆1 minus∆2)

(30)

∆1 minus∆2 0 is required but satisfied for PR and SRKSeveral derivatives with respect to τ and δ at constant composition are required in CoolProp Some of

them are not impacted by the volume translation and can be found in () and the one affected are developedin the supplementary material

10

4 Comparison

To evaluate the accuracy of the cubic equation of state models is done by comparing with recognisedthermodynamic software and experimental data All the fluids studies here are already quite well studiedfluids this will allows to compare the models with a known reference This gives an overview of what canbe expected for fluids that have not been yet studied enough to have an accurate state model

Only a small portion of the studied fluids are displayed here You will find many other graphics in thesupplementary material

41 Pure fluidA large data set of experimental data has been collected by NIST for pure fluid who gracefully allowed

its use for this workThe part in use here are temperature-pressure-density data and temperature-quality-density data The

experimental density is compared to the one computed from the different equations of state by the pressureand temperature input or temperature-quality input The density deviation is defined by

Eρ =ρdata minus ρcalc

ρdata(31)

In order to enhance data displaying any deviation bigger than 100 has been caped to 100 Thisapproximation was considered reasonable as a magnitude of 100 deviation is already not acceptable

The box plot (as in Figure 3) indicate the repartition of the deviation values The lower bar representthe minimal deviation value the first bar of the rectangle represent the first quartile the middle bar themedian the upper bar of the rectangle the third quartile and the upper bar the maximal value

This allows to know that for instance in Figure 3 for fluid R134A 75 of the data for RefProp andHEOS are under 02 of deviation to the experimental data and half of the data under 004 of deviation

In order to have a general overview of where the differences occurs isobars in temperature volume plothave also been done These plots however do not include the experimental data

10minus4

10minus3

10minus2

10minus1

100

101

102

REFPROP HEOS PR SRK PR kij SRK kij10minus1110minus910minus7

Den

sity

rela

tive

devi

atio

n[

]

Figure 3 Relative density deviation to experimental data for fluid R134A

11

160 180 200 220 240 260 280 300 320 340 360 380 400 420 440 460 480 500

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus01 0 01 02 03 04 05 06 07 08 09 1 11

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

Figure 4 Density dependence on the temperature and pressure for fluid R134A

12

For a lot of pure fluids it can be observed as in Figures 3 and 4 that RefProp and the HEOS model ofCoolProp gives very similar results It however happens that the model differs slightly as can be observedin the Figure 5 and 6

The maximal deviation with fluid R134A tops at least 100 (Figures 3) for all EOS but it can beobserved in Figure 4 that this is the case for only one point at a bit more than 400 K and 15 MPa This isprobably an invalid data point If we exclude this outlier the deviations for fluid R134A are under 3 forall HEOS

10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]

Figure 5 Relative density deviation to experimental data for fluid R41

For these pure fluid density comparison the Cubic models give significantly worst deviations comparedto the Helmholtz equations of state

When looking at the isobars (Figure 7) it can be seen that a big part of the difference between theHEOS and the cubics looks like a translation in volume in the liquid phase

A volume translation parameter has been computed by making the difference between the volume of therespective cubic and RefProp at a reduced temperature of 07Tcrit This introduce RefProprsquos own errorbut correct most of the translation error

We can see in the Figures 3 4 5 and 6 that the effect is generally positive reducing significantly thedeviation This effect depends of course on the actual translation which is not the same for al fluid and alsodepend on the cubic equation in use (PR or SRK)

The specific effect of this translation can be seen on the Figures 8 and 9The constant translation parameter correct a big part of the volume translation issue but do not correct

it entirely Near critical values still have a significant deviation (see Figures 8 and 9) A more complextemperature dependant parameter could potentially improve the behaviour in that area

For some fluids the Peng-Robinson model gives better results than the Soave-Redlich-Kwong (as canbe seen for R134A 3 and R41 5) but this is not always the case Carbon monoxide for instance is betterrepresented by the SRK model than PR as can be seen in Figure 10 and 11 but the PR becomes moreaccurate with volume translation Some others like the MethylPalmitate have quite good volume translatedSRK (12 and 11)

13

100 150 200 250 300 350 400 450 500 550 600

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus02 0 02 04 06 08 1 12 14 16 18 2 22 24 26 28 3 32

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

Figure 6 Density dependence on the temperature and pressure for fluid R41

14


200

250

300

350

400

450

P=

100times

104

Pa

P=

100times

104

Pa

P=

100times

104

Pa

P=

100times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

100times

107 P

a

P=

100times

107 P

a

P=

100times

107 P

a

P=

100times

107

Pa

P=

100times

108

Pa

P=

100times

108

Pa

P=

100times

108 P

a

P=

100times

108

Pa


Tem

pera

ture

[K]

REFPROPHEOS

PRSRK

Figure 7 Isobar curves and saturation curve (dashed) on temperaturevolume plot fluid R134A


200

250

300

350

400

450

P=

100times

104

Pa

P=

100times

104

Pa

P=

100times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

100times

107 P

a

P=

100times

107 P

a

P=

100times

107 P

a

P=

100times

108

Pa

P=

100times

108 P

a

P=

100times

108 P

a


Tem

pera

ture

[K]

REFPROPPR

PR VT

Figure 8 Isobar curves and saturation curve (dashed) on temperaturevolume plot comparison of PR with REFPROP fluidR134A

15


200

250

300

350

400

450

P=

100times

104

Pa

P=

100times

104

Pa

P=

100times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

100times

107 P

a

P=

100times

107

Pa

P=

100times

107

Pa

P=

100times

108

Pa

P=

100times

108

Pa

P=

100times

108

Pa


Tem

pera

ture

[K]

REFPROPSRK

SRK VT

Figure 9 Isobar curves and saturation curve (dashed) on temperaturevolume plot comparison of SRK with REFPROP fluidR134A

10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]

Figure 10 Relative density deviation to experimental data for fluid Carbon Monoxide

16

50 100 150 200 250 300 350 400 450 500 550 600

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus05 0 05 1 15 2 25 3 35 4 45 5 55 6 65

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

Figure 11 Density dependence on the temperature and pressure for fluid Carbon Monoxide

17

10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]

Figure 12 Relative density deviation to experimental data for fluid MethylPalmitate

It can also be noted that sometimes some EOS do not gives results when other ones gives or givesunacceptable deviations (ge 100) where others gives more reasonable results as for the fluid n-Dodecane(14 and 15)

In a general manner the relative deviations do not seem to be much affected by the temperature nor thepressure value 4 6 11 13 and 15 This means that the absolute deviation (the deviation in Pa or K) willincrease proportionally with the pressure and the temperature

18

310 320 330 340 350 360 370 380 390

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus05 0 05 1 15 2 25 3 35 4 45 5 55

middot107

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

Figure 13 Density dependence on the temperature and pressure for fluid MethylPalmitate

19

10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]

Figure 14 Relative density deviation to experimental data for fluid n-Dodecane

20

250 300 350 400 450 500 550 600 650

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus05 0 05 1 15 2 25 3 35 4 45 5 55 6 65 7 75

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

Figure 15 Density dependence on the temperature and pressure for fluid n-Dodecane

21

42 Binary mixturesAn other data set of experimental data has been collected by NIST for mixtures but only containing

vapour-liquid equilibrium (VLE) dataThese data consist of the molar fraction of each component and the temperature and pressure The

molar fraction at a given temperature and pressure are specified to be either liquid or gaseous which allowsto define the quality (0 or 1)

Two values where computed thanks to the state models the temperature from the pressure and thequality and the pressure from the temperature and quality The deviation between the computed valuesand the experimental data where then computed as following

ET =Tdata minus Tcalc

Tdata(32)

Ep =pdata minus pcalc

pdata(33)

The effect of the volume translation has not been evaluated here as no densityvolume data whereprovided

As these are mixtures there is the possibility to use an interaction parameter The one currentlyimplemented in CoolProp is the Van der Waals mixing rules with one parameter ki j For this work theinteraction parameter was fitted to minimize the deviation to experimental data with Brentrsquos method Theerror to minimise was expressed as follow

E =sum∣∣∣ET + 01Ep

∣∣∣ (34)

were ET and Ep are from equations 32 and 33The difference of results between pure temperature or pure pressure errors where not significant The

pressure term has been weighted by 01 as itrsquos magnitude was around 10 times bigger than the deviation interm of temperature

With the mixture the differences between RefProp and CoolProprsquos HEOS are a bit more marked as canbe seen in Figure 16 Depending on the fluid RefProp can be better than CoolProprsquos HEOS especiallywhen it comes to near critical data where the later tend to gives very wrong values (see Figure 18) but theFigure 19 is a good example where CoolProprsquos HEOS is far better

On the cubicrsquos side the results for the liquid-vapour equilibrium seems extremely good and comparablewith RefProp and CoolProprsquos HEOS It is interesting to notice that the volume translation problem occurringwith density and volume value do not seem to be a weight for these VLE data

A very important thing to notice with the mixture R1234YF-R134A is the influence of the molar fractionon the deviation (Figure 20) RefProp and the two cubics (without the binary interaction parameter ki j)have a deviation that considerable increases (around 10 times bigger) when mixing the two fluid comparedto the pure fluids with a maximum around equimolar composition This is the kind of behaviour that isexpected when using two sufficiently different fluids the way they interact together is different to the waythey interact with themselves

This effect is reduced with the interaction model and it appears that CoolProprsquos HEOS have a goodinteraction model for this mixture This is also corrected for the cubic by the ki j interaction parameterThis explains the better behaviour of CoolProprsquos HEOS and the cubics with interaction parameter for thisparticular mixture

Other mixtures like R134A-R32 are more similar and donrsquot benefit that much from a better mixing rule(Figure 17) This lead to more homogeneous deviations between the EOS

Again the variation of temperature and pressure on the relative deviation seems minimal except whenapproaching to the critical point

The temperature deviations are significantly smaller than the pressure deviations for all EOS

22

10minus4

10minus3

10minus2

10minus1

100

101

102

REFPROP HEOS PR SRK PR kij SRK kij10minus11

10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]

(a) Temperature deviation

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]

(b) Pressure deviation

Figure 16 Relative deviation to experimental saturation data for mixtures based on R125 and R134A

23

0 01 02 03 04 05 06 07 08 09 110minus4

10minus3

10minus2

10minus1

100

Molar fraction of R134A [minus]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 01 02 03 04 05 06 07 08 09 110minus3

10minus2

10minus1

100

101


Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

Figure 17 Dependence on the molar fraction for the binary mixture R134A-R32

24

190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 36010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 05 1 15 2 25 3 35 4

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

Figure 18 Dependence on the temperature and pressure for the binary mixture R134A-R32

25

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]


Figure 19 Relative deviation to experimental saturation data for mixtures based on R1234YF and R134A

26

0 01 02 03 04 05 06 07 08 09 110minus4

10minus3

10minus2

10minus1

100

Molar fraction of R1234YF [minus]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 01 02 03 04 05 06 07 08 09 110minus3

10minus2

10minus1

100

101


Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

Figure 20 Dependence on the molar fraction for the binary mixture R1234YF-R134A

27

270 275 280 285 290 295 300 305 310 315 320 325 330 335 34010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

02 03 04 05 06 07 08 09 1 11 12 13 14 15 16 17 18

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

Figure 21 Dependence on the temperature and pressure for the binary mixture R1234YF-R134A

28

43 Ternary mixturesThe ternary mixtures are from the same data set as the binaries The binary interaction parameters ki j

where fitted with the binary mixture and reused hereThe results for the ternary mixtures are similar to the ones from the binaries

29

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]


Figure 22 Relative deviation to experimental saturation data for mixtures based on R125 R32 and R134A

30

200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 35010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

minus02 0 02 04 06 08 1 12 14 16 18 2 22 24 26 28 3 32 34 36 38

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

Figure 23 Dependence on the temperature and pressure for the ternary mixture R125-R32-R134A

31

5 Acknowledgements

I would like to thank the professor Sylvain Quoilin for having given to me the opportunity to make thismaster thesis abroad This was a very interesting experience which allowed me to practice English and meetan other culture

I have a big thank to give to the DTU team who took care of me in Denmark the professor FredrikHaglind and the two post doctorates Maria E Mondejar Montagud and Jorrit Wronski It was a realpleasure to work with them

I also thanks Ian Bell our contact at NIST who manage to provide us with the database and withoutwho CoolProp would not exist

32

6 Conclusions

The simple cubic equations of state do not always gives satisfying results to compute density This canhowever be mostly corrected with a simple translation coefficient requiring a single measurement of saturatedliquid and more complex translation models could potentially give more accurate results

The cubic equations of states are very effective at modelling the liquid vapour equilibrium competingwith well recognise software

Depending on the interaction between the fluid constituting the mixtures all models benefit from binaryinteraction knowledge This is sometimes integrated in the software but would generally be an issue withnot yet well studied mixtures A simple coefficient (to be determined experimentally or approximated) canbe used to improve greatly the results of cubic equations when the interaction between the fluids is signif-icant An alternative would be to approximate the interaction with the UNIFAQ model as it is done withthe VTPR Determination of models to approximate the binary interaction parameters depending on thetype of fluid used would be an interesting subject for complementary study

More complex models can be used for the attractive parameter like the Mathias-Copeman and the TWUequations They both require 3 supplementary parameters and are already implemented in CoolProp Theirimpact could be interesting for a further study

The speed of the models are not compared in this work The comparison would be interesting butit is useful to notice CoolProp also provide a tabular interface which allows for extremely fast propertiescomputation when the tables have been generated (with a small loss of accuracy)

The cubic equations of states gives a wide range of possibilities from the simplest and fast model butslightly lacking accuracy to more complex and accurate models They provide a great tool for evaluation offluids when few data are available

33

Ahlers J Gmehling J 2001 Development of an universal group contribution equation of state Prediction of liquid densitiesfor pure compounds with a volume translated Peng-Robinson equation of state Fluid Phase Equilibria 191 (1-2) 177ndash188URL httpwwwsciencedirectcomsciencearticlepiiS0378381201006264pdfftmd5=86daea9e53bace87587e62b056b3007eamppid=1-s20-S0378381201006264-mainpdf

Bell I Jaumlger A 2016a Helmholtz energy transformation of common cubic equations of state for use with pure fluids andmixtures Journal of Research of the National Institute of Standards and Technology 121 (July) 238ndash263URL httpswwwresearchgatenetpublication304186500_Helmholtz_Energy_Transformations_of_Common_Cubic_Equations_of_State_for_Use_with_Pure_Fluids_and_Mixtures

Bell I H Jaumlger A 2016b Intermediate Terms 1ndash14Bell I H Jaumlger A 2016c Supplementary Information to accompany Helmholtz energy transformations of common cubic

equations of state for use with pure fluids and mixtures No 5Chen W-Y Liu J 2007 Mathcad Modules for Supercritical Fluid Extraction based on Mixing Rules Appendix A - Mixing

Rules (662) 1ndash10URL httphomeolemissedu~cmchengsExtractionAppendixA_MixingRulesdoc

CoolProp 2016 Cubic Equations of StateURL httpwwwcoolproporgcoolpropCubicshtml

Fauacutendez C a Valderrama J O 2009 Low pressure vaporndashliquid equilibrium in ethanol+congener mixtures using theWongndashSandler mixing rule Thermochimica Acta 490 (1-2) 37ndash42URL httpwwwsciencedirectcomsciencearticlepiiS0040603109000999pdfftmd5=65533f85d53569eeebae29e565402cc4amppid=1-s20-S0040603109000999-mainpdf

Frey K Augustine C Ciccolini R P Paap S Modell M Tester J 2007 Volume translation in equations of state as ameans of accurate property estimation Fluid Phase Equilibria 260 (2) 316ndash325URL httpwwwsciencedirectcomsciencearticlepiiS0378381207004591pdfftmd5=c750d4ea93f662a13b87183c76a8654eamppid=1-s20-S0378381207004591-mainpdf

Ji W-R Lempe D 1997 Density improvement of the SRK equation of state Fluid Phase Equilibria 130 (1-2) 49ndash63URL httpwwwsciencedirectcomsciencearticlepiiS0378381296031901

Lemmon E W Huber M L McLinden M O 2013 Reference Fluid Thermodynamic and Transport Properties-REFPROPversion 91URL httpwwwnistgovsrduploadREFPROP9PDF

Loacutepez J A Cardona C A 2006 Phase equilibrium calculations for carbon dioxide+n-alkanes binary mixtures with theWongndashSandler mixing rules Fluid Phase Equilibria 239 (2) 206ndash212URL httpwwwsciencedirectcomsciencearticlepiiS0378381205004565

Martin J J 1967 Equations of StatemdashApplied Thermodynamics Symposium Industrial amp Engineering Chemistry 59 (12)34ndash52URL httpdxdoiorg101021ie50696a008$delimiter026E30F$nhttppubsacsorgdoipdf101021ie50696a008

Martin J J 1979 Cubic Equations of State-Which Industrial amp Engineering Chemistry Fundamentals 18 (2) 81ndash97URL httpdxdoiorg101021i160070a001

Meng L Duan Y Y Wang X D 2007 Binary interaction parameter kij for calculating the second cross-virial coefficientsof mixtures Fluid Phase Equilibria 260 (2) 354ndash358URL httpwwwsciencedirectcomsciencearticlepiiS0378381207004323pdfftmd5=e3b19d08e08099003d28392a4450f768amppid=1-s20-S0378381207004323-mainpdf

Peng D-Y Robinson D B 1976 A New Two-Constant Equation of State Industrial amp Engineering Chemistry Fundamentals15 (1) 59ndash64URL httppubsacsorgdoiabs101021i160057a011

Schmid B Gmehling J 2012 Revised parameters and typical results of the VTPR group contribution equation of stateFluid Phase Equilibria 317 110ndash126URL httpdxdoiorg101016jfluid201201006

Schmid B Schedemann A Gmehling J 2014 Extension of the VTPR group contribution equation of state Groupinteraction parameters for additional 192 group combinations and typical results Industrial and Engineering ChemistryResearch 53 (8) 3393ndash3405

Soave G 1972 Equilibrium constants from a modified Redlich-Kwong equation of state Chemical Engineering Science 27 (6)1197ndash1203URL httpacels-cdncom00092509728009641-s20-0009250972800964-mainpdf_tid=cd3fc6c8-1dbd-11e6-a8de-00000aacb35dampacdnat=1463661351_8f1dbe034b52854e2d97cd6d80b7b56b

Valderrama J O 2003 The State of the Cubic Equations of State Industrial amp Engineering Chemistry Research 42 (8)1603ndash1618URL httppubsacsorgdoiabs101021ie020447b

Valderrama J O Marambio L E Silva A a 2002 Mixing rules in cubic equations of state applied to refrigerant mixturesJournal of Phase Equilibria 23 (6) 495ndash501URL httpdownloadspringercomstaticpdf558art3A1013612F105497102770331181pdforiginUrl=httplinkspringercomarticle101361105497102770331181amptoken2=exp=1463652668~acl=staticpdf558art253A101361252F105497102770

Wong D S H Sandler S I 1992 A Theoretically Correct Mixing Rule for Cubic Equations of State 38 (5)URL httponlinelibrarywileycomdoi101002aic690380505epdf

34

Implementation and performance evaluation of different cubic equations ofstate for the estimation of properties of organic mixtures

Jonathan WelliquetUniversity of Liegravege Faculty of Applied Sciences

Aerospace and mechanical engineering departmentThermodynamic Laboratory

Abstract

The thermodynamic properties of organic mixtures is a really important aspect for the development ofthe new thermodynamic cycles However mixtures are not all yet well known and a model that could givea good approximation of the properties in a fast way could help

The cubic equations of states provide a simple way requiring minimal information to approximate thestate of a fluid This provide an interesting tool with enough flexibility to improve the accuracy as moreexperimental data become available The results for vapour-liquid equilibrium of mixtures are particularlygood

Keywords CoolProp Cubic EOS Mixtures

URL httpwwwfacsaulgacbe (Jonathan Welliquet)

Preprint submitted to Thermodynamic Laboratory August 20 2016

Contents

1 Introduction 3








6 Conclusions 33

2

1 Introduction






3

2 State of the art





av2







form (Soave 1972)

p =RT

v minus bminus

acα(TR ω)

v(v + b)(2)

With the parameters

ac = 042747

(R2T2

c

Pc

)b = 008664

(RTc

Pc

)α(TR ω) =

[1 + m(ω)

(1minus

radicTR

)]2m(ω) = 0480 + 1574ω minus 0176ω2

(3)



p =RT

v minus bminus

acα(TR ω)


4

With the parameters

ac = 045724

(R2T2

c

Pc

)b = 007780

(RTc

Pc

)α(TR ω) =

[1 + m(ω)

(1minus

radicTR

)]2m(ω) = 037464 + 154226ω minus 026992ω2

(5)



200

250

300

350

400

P=

10times

104

Pa

P=

10times

104

Pa

P=

32times

104

Pa

P=

32times

104

Pa

P=

10times

105

Pa

P=

10times

105

Pa

P=

32times

105

Pa

P=

32times

105

Pa

P=

10times

106

Pa

P=

10times

106

Pa

P=

32times

106

Pa

P=

32times

106

Pa

P=

60times

106 P

a

P=

60times

106 P

a

P=

10times

107 P

a

P=

10times

107

Pa

P=

10times

108

Pa

P=

10times

108

Pa


Tem

pera

ture

[K]

REFPROPSRK






(6)


5



035


∣∣∣γ (7)



)+ 0950


)+ 0635

(8)


p =RT

v + c minus bminus

acα(TR ω)

(v + c)(v + c + b) + b(v + c minus b)(9)







6



i

sumj


aia j b =sum

i

sumj


2



2



2(1 minus Ii j)




2



2(1 minus Ii j)




2



2



i

sumj

xi x jradic


RES

ln(

bminusφbminusτ

)]

b =sum

i

sumj


2

gERES = RT x1x2


2]

Huron-Vidal a = b

sumi

xiai

bi+

gE(x)Clowast

b =sum

i

sumj


2

Wong-Sandler a = b

sumi

xiai

biminus AE

infin(x)

b =

sumisum

j xi x j

(b minus a

RT

)i j

1 minussum


RT


aRT

)i j=

(bi minus

aiRT

)+

(b j minus

a jRT

)2

(1 minus ki j)


aRT

)i j=

bi + b j

2minus


RT


aRT

)i j=


2minus


RT

7


b =sum

isum

j xix jbi j

=sum

isum

j xix jbi+b j

2

=sum

isum

j xix jbi2 +

sumisum

j xix jb j

2

= 2(sum

isum

j xix jbi2

)=

sumisum

j xix jbi

=sum

i(sum

j x j)xibi

=sum

i xibi

(10)






p =RT

v minus b+

a(T )(v +∆1b)(v +∆2b)

(11)


radic2




8




p =RT

v + c minus b+

a(T )(v + c +∆1b)(v + c +∆2b)

(12)



p =RT

1ρ+ c minus b

+a(T )(

1ρ+ c +∆1b

) (1ρ+ c +∆2b

) (13)


d1 = c minus b (14)d2 = c +∆1b (15)d3 = c +∆2b (16)

p =RTρ

1 + d1ρ+

a(T )ρ2

(1 + d2ρ) (1 + d3ρ)(17)









p =Tr

τ

R1δρr

+ c minus b+

a(τ)(1δρr

+ c +∆1b) (

1δρr

+ c +∆2b) (22)

or

p =Tr

τ


+δ2ρ2r a(τ)

(1 + (c +∆1b)δρr) (1 + (c +∆2b)δρr)(23)

9


partδ

)τ

=pτ

δ2ρrRTrminus1

δ(24)


partδ

)τ

=(b minus c)ρr


ρr

(1 + (b∆1 + c)δρr) (1 + (b∆2 + c)δρr)(25)



ψ(+) (26)


ψ(minus) =

int δ

0

(b minus c)ρr



ψ(+) =

int δ

0

ρr

(1 + (b∆1 + c)δρr) (1 + (b∆2 + c)δρr)dδ (29)

=

ln(1 + (b∆1 + c)δρr

1 + (b∆2 + c)δρr

)b(∆1 minus∆2)

(30)



10

4 Comparison







ρdata(31)





10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]


11

160 180 200 220 240 260 280 300 320 340 360 380 400 420 440 460 480 500

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus01 0 01 02 03 04 05 06 07 08 09 1 11

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


12



10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]









13

100 150 200 250 300 350 400 450 500 550 600

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus02 0 02 04 06 08 1 12 14 16 18 2 22 24 26 28 3 32

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


14


200

250

300

350

400

450

P=

100times

104

Pa

P=

100times

104

Pa

P=

100times

104

Pa

P=

100times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

100times

107 P

a

P=

100times

107 P

a

P=

100times

107 P

a

P=

100times

107

Pa

P=

100times

108

Pa

P=

100times

108

Pa

P=

100times

108 P

a

P=

100times

108

Pa


Tem

pera

ture

[K]

REFPROPHEOS

PRSRK



200

250

300

350

400

450

P=

100times

104

Pa

P=

100times

104

Pa

P=

100times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

100times

107 P

a

P=

100times

107 P

a

P=

100times

107 P

a

P=

100times

108

Pa

P=

100times

108 P

a

P=

100times

108 P

a


Tem

pera

ture

[K]

REFPROPPR

PR VT


15


200

250

300

350

400

450

P=

100times

104

Pa

P=

100times

104

Pa

P=

100times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

100times

107 P

a

P=

100times

107

Pa

P=

100times

107

Pa

P=

100times

108

Pa

P=

100times

108

Pa

P=

100times

108

Pa


Tem

pera

ture

[K]

REFPROPSRK

SRK VT


10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]


16

50 100 150 200 250 300 350 400 450 500 550 600

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus05 0 05 1 15 2 25 3 35 4 45 5 55 6 65

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


17

10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]




18

310 320 330 340 350 360 370 380 390

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus05 0 05 1 15 2 25 3 35 4 45 5 55

middot107

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


19

10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]


20

250 300 350 400 450 500 550 600 650

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus05 0 05 1 15 2 25 3 35 4 45 5 55 6 65 7 75

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


21






Tdata(32)


pdata(33)




∣∣∣ (34)










22

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



23

0 01 02 03 04 05 06 07 08 09 110minus4

10minus3

10minus2

10minus1

100


Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 01 02 03 04 05 06 07 08 09 110minus3

10minus2

10minus1

100

101


Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


24

190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 36010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 05 1 15 2 25 3 35 4

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


25

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



26

0 01 02 03 04 05 06 07 08 09 110minus4

10minus3

10minus2

10minus1

100


Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 01 02 03 04 05 06 07 08 09 110minus3

10minus2

10minus1

100

101


Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


27

270 275 280 285 290 295 300 305 310 315 320 325 330 335 34010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

02 03 04 05 06 07 08 09 1 11 12 13 14 15 16 17 18

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


28



29

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



30

200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 35010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

minus02 0 02 04 06 08 1 12 14 16 18 2 22 24 26 28 3 32 34 36 38

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


31

5 Acknowledgements




32

6 Conclusions







33






















34

Contents

1 Introduction 3








6 Conclusions 33

2

1 Introduction






3

2 State of the art





av2







form (Soave 1972)

p =RT

v minus bminus

acα(TR ω)

v(v + b)(2)

With the parameters

ac = 042747

(R2T2

c

Pc

)b = 008664

(RTc

Pc

)α(TR ω) =

[1 + m(ω)

(1minus

radicTR

)]2m(ω) = 0480 + 1574ω minus 0176ω2

(3)



p =RT

v minus bminus

acα(TR ω)


4

With the parameters

ac = 045724

(R2T2

c

Pc

)b = 007780

(RTc

Pc

)α(TR ω) =

[1 + m(ω)

(1minus

radicTR

)]2m(ω) = 037464 + 154226ω minus 026992ω2

(5)



200

250

300

350

400

P=

10times

104

Pa

P=

10times

104

Pa

P=

32times

104

Pa

P=

32times

104

Pa

P=

10times

105

Pa

P=

10times

105

Pa

P=

32times

105

Pa

P=

32times

105

Pa

P=

10times

106

Pa

P=

10times

106

Pa

P=

32times

106

Pa

P=

32times

106

Pa

P=

60times

106 P

a

P=

60times

106 P

a

P=

10times

107 P

a

P=

10times

107

Pa

P=

10times

108

Pa

P=

10times

108

Pa


Tem

pera

ture

[K]

REFPROPSRK






(6)


5



035


∣∣∣γ (7)



)+ 0950


)+ 0635

(8)


p =RT

v + c minus bminus

acα(TR ω)

(v + c)(v + c + b) + b(v + c minus b)(9)







6



i

sumj


aia j b =sum

i

sumj


2



2



2(1 minus Ii j)




2



2(1 minus Ii j)




2



2



i

sumj

xi x jradic


RES

ln(

bminusφbminusτ

)]

b =sum

i

sumj


2

gERES = RT x1x2


2]

Huron-Vidal a = b

sumi

xiai

bi+

gE(x)Clowast

b =sum

i

sumj


2

Wong-Sandler a = b

sumi

xiai

biminus AE

infin(x)

b =

sumisum

j xi x j

(b minus a

RT

)i j

1 minussum


RT


aRT

)i j=

(bi minus

aiRT

)+

(b j minus

a jRT

)2

(1 minus ki j)


aRT

)i j=

bi + b j

2minus


RT


aRT

)i j=


2minus


RT

7


b =sum

isum

j xix jbi j

=sum

isum

j xix jbi+b j

2

=sum

isum

j xix jbi2 +

sumisum

j xix jb j

2

= 2(sum

isum

j xix jbi2

)=

sumisum

j xix jbi

=sum

i(sum

j x j)xibi

=sum

i xibi

(10)






p =RT

v minus b+

a(T )(v +∆1b)(v +∆2b)

(11)


radic2




8




p =RT

v + c minus b+

a(T )(v + c +∆1b)(v + c +∆2b)

(12)



p =RT

1ρ+ c minus b

+a(T )(

1ρ+ c +∆1b

) (1ρ+ c +∆2b

) (13)


d1 = c minus b (14)d2 = c +∆1b (15)d3 = c +∆2b (16)

p =RTρ

1 + d1ρ+

a(T )ρ2

(1 + d2ρ) (1 + d3ρ)(17)









p =Tr

τ

R1δρr

+ c minus b+

a(τ)(1δρr

+ c +∆1b) (

1δρr

+ c +∆2b) (22)

or

p =Tr

τ


+δ2ρ2r a(τ)

(1 + (c +∆1b)δρr) (1 + (c +∆2b)δρr)(23)

9


partδ

)τ

=pτ

δ2ρrRTrminus1

δ(24)


partδ

)τ

=(b minus c)ρr


ρr

(1 + (b∆1 + c)δρr) (1 + (b∆2 + c)δρr)(25)



ψ(+) (26)


ψ(minus) =

int δ

0

(b minus c)ρr



ψ(+) =

int δ

0

ρr

(1 + (b∆1 + c)δρr) (1 + (b∆2 + c)δρr)dδ (29)

=

ln(1 + (b∆1 + c)δρr

1 + (b∆2 + c)δρr

)b(∆1 minus∆2)

(30)



10

4 Comparison







ρdata(31)





10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]


11

160 180 200 220 240 260 280 300 320 340 360 380 400 420 440 460 480 500

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus01 0 01 02 03 04 05 06 07 08 09 1 11

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


12



10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]









13

100 150 200 250 300 350 400 450 500 550 600

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus02 0 02 04 06 08 1 12 14 16 18 2 22 24 26 28 3 32

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


14


200

250

300

350

400

450

P=

100times

104

Pa

P=

100times

104

Pa

P=

100times

104

Pa

P=

100times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

100times

107 P

a

P=

100times

107 P

a

P=

100times

107 P

a

P=

100times

107

Pa

P=

100times

108

Pa

P=

100times

108

Pa

P=

100times

108 P

a

P=

100times

108

Pa


Tem

pera

ture

[K]

REFPROPHEOS

PRSRK



200

250

300

350

400

450

P=

100times

104

Pa

P=

100times

104

Pa

P=

100times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

100times

107 P

a

P=

100times

107 P

a

P=

100times

107 P

a

P=

100times

108

Pa

P=

100times

108 P

a

P=

100times

108 P

a


Tem

pera

ture

[K]

REFPROPPR

PR VT


15


200

250

300

350

400

450

P=

100times

104

Pa

P=

100times

104

Pa

P=

100times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

100times

107 P

a

P=

100times

107

Pa

P=

100times

107

Pa

P=

100times

108

Pa

P=

100times

108

Pa

P=

100times

108

Pa


Tem

pera

ture

[K]

REFPROPSRK

SRK VT


10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]


16

50 100 150 200 250 300 350 400 450 500 550 600

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus05 0 05 1 15 2 25 3 35 4 45 5 55 6 65

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


17

10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]




18

310 320 330 340 350 360 370 380 390

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus05 0 05 1 15 2 25 3 35 4 45 5 55

middot107

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


19

10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]


20

250 300 350 400 450 500 550 600 650

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus05 0 05 1 15 2 25 3 35 4 45 5 55 6 65 7 75

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


21






Tdata(32)


pdata(33)




∣∣∣ (34)










22

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



23

0 01 02 03 04 05 06 07 08 09 110minus4

10minus3

10minus2

10minus1

100


Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 01 02 03 04 05 06 07 08 09 110minus3

10minus2

10minus1

100

101


Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


24

190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 36010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 05 1 15 2 25 3 35 4

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


25

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



26

0 01 02 03 04 05 06 07 08 09 110minus4

10minus3

10minus2

10minus1

100


Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 01 02 03 04 05 06 07 08 09 110minus3

10minus2

10minus1

100

101


Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


27

270 275 280 285 290 295 300 305 310 315 320 325 330 335 34010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

02 03 04 05 06 07 08 09 1 11 12 13 14 15 16 17 18

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


28



29

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



30

200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 35010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

minus02 0 02 04 06 08 1 12 14 16 18 2 22 24 26 28 3 32 34 36 38

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


31

5 Acknowledgements




32

6 Conclusions







33






















34

1 Introduction






3

2 State of the art





av2







form (Soave 1972)

p =RT

v minus bminus

acα(TR ω)

v(v + b)(2)

With the parameters

ac = 042747

(R2T2

c

Pc

)b = 008664

(RTc

Pc

)α(TR ω) =

[1 + m(ω)

(1minus

radicTR

)]2m(ω) = 0480 + 1574ω minus 0176ω2

(3)



p =RT

v minus bminus

acα(TR ω)


4

With the parameters

ac = 045724

(R2T2

c

Pc

)b = 007780

(RTc

Pc

)α(TR ω) =

[1 + m(ω)

(1minus

radicTR

)]2m(ω) = 037464 + 154226ω minus 026992ω2

(5)



200

250

300

350

400

P=

10times

104

Pa

P=

10times

104

Pa

P=

32times

104

Pa

P=

32times

104

Pa

P=

10times

105

Pa

P=

10times

105

Pa

P=

32times

105

Pa

P=

32times

105

Pa

P=

10times

106

Pa

P=

10times

106

Pa

P=

32times

106

Pa

P=

32times

106

Pa

P=

60times

106 P

a

P=

60times

106 P

a

P=

10times

107 P

a

P=

10times

107

Pa

P=

10times

108

Pa

P=

10times

108

Pa


Tem

pera

ture

[K]

REFPROPSRK






(6)


5



035


∣∣∣γ (7)



)+ 0950


)+ 0635

(8)


p =RT

v + c minus bminus

acα(TR ω)

(v + c)(v + c + b) + b(v + c minus b)(9)







6



i

sumj


aia j b =sum

i

sumj


2



2



2(1 minus Ii j)




2



2(1 minus Ii j)




2



2



i

sumj

xi x jradic


RES

ln(

bminusφbminusτ

)]

b =sum

i

sumj


2

gERES = RT x1x2


2]

Huron-Vidal a = b

sumi

xiai

bi+

gE(x)Clowast

b =sum

i

sumj


2

Wong-Sandler a = b

sumi

xiai

biminus AE

infin(x)

b =

sumisum

j xi x j

(b minus a

RT

)i j

1 minussum


RT


aRT

)i j=

(bi minus

aiRT

)+

(b j minus

a jRT

)2

(1 minus ki j)


aRT

)i j=

bi + b j

2minus


RT


aRT

)i j=


2minus


RT

7


b =sum

isum

j xix jbi j

=sum

isum

j xix jbi+b j

2

=sum

isum

j xix jbi2 +

sumisum

j xix jb j

2

= 2(sum

isum

j xix jbi2

)=

sumisum

j xix jbi

=sum

i(sum

j x j)xibi

=sum

i xibi

(10)






p =RT

v minus b+

a(T )(v +∆1b)(v +∆2b)

(11)


radic2




8




p =RT

v + c minus b+

a(T )(v + c +∆1b)(v + c +∆2b)

(12)



p =RT

1ρ+ c minus b

+a(T )(

1ρ+ c +∆1b

) (1ρ+ c +∆2b

) (13)


d1 = c minus b (14)d2 = c +∆1b (15)d3 = c +∆2b (16)

p =RTρ

1 + d1ρ+

a(T )ρ2

(1 + d2ρ) (1 + d3ρ)(17)









p =Tr

τ

R1δρr

+ c minus b+

a(τ)(1δρr

+ c +∆1b) (

1δρr

+ c +∆2b) (22)

or

p =Tr

τ


+δ2ρ2r a(τ)

(1 + (c +∆1b)δρr) (1 + (c +∆2b)δρr)(23)

9


partδ

)τ

=pτ

δ2ρrRTrminus1

δ(24)


partδ

)τ

=(b minus c)ρr


ρr

(1 + (b∆1 + c)δρr) (1 + (b∆2 + c)δρr)(25)



ψ(+) (26)


ψ(minus) =

int δ

0

(b minus c)ρr



ψ(+) =

int δ

0

ρr

(1 + (b∆1 + c)δρr) (1 + (b∆2 + c)δρr)dδ (29)

=

ln(1 + (b∆1 + c)δρr

1 + (b∆2 + c)δρr

)b(∆1 minus∆2)

(30)



10

4 Comparison







ρdata(31)





10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]


11

160 180 200 220 240 260 280 300 320 340 360 380 400 420 440 460 480 500

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus01 0 01 02 03 04 05 06 07 08 09 1 11

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


12



10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]









13

100 150 200 250 300 350 400 450 500 550 600

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus02 0 02 04 06 08 1 12 14 16 18 2 22 24 26 28 3 32

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


14


200

250

300

350

400

450

P=

100times

104

Pa

P=

100times

104

Pa

P=

100times

104

Pa

P=

100times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

100times

107 P

a

P=

100times

107 P

a

P=

100times

107 P

a

P=

100times

107

Pa

P=

100times

108

Pa

P=

100times

108

Pa

P=

100times

108 P

a

P=

100times

108

Pa


Tem

pera

ture

[K]

REFPROPHEOS

PRSRK



200

250

300

350

400

450

P=

100times

104

Pa

P=

100times

104

Pa

P=

100times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

100times

107 P

a

P=

100times

107 P

a

P=

100times

107 P

a

P=

100times

108

Pa

P=

100times

108 P

a

P=

100times

108 P

a


Tem

pera

ture

[K]

REFPROPPR

PR VT


15


200

250

300

350

400

450

P=

100times

104

Pa

P=

100times

104

Pa

P=

100times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

100times

107 P

a

P=

100times

107

Pa

P=

100times

107

Pa

P=

100times

108

Pa

P=

100times

108

Pa

P=

100times

108

Pa


Tem

pera

ture

[K]

REFPROPSRK

SRK VT


10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]


16

50 100 150 200 250 300 350 400 450 500 550 600

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus05 0 05 1 15 2 25 3 35 4 45 5 55 6 65

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


17

10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]




18

310 320 330 340 350 360 370 380 390

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus05 0 05 1 15 2 25 3 35 4 45 5 55

middot107

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


19

10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]


20

250 300 350 400 450 500 550 600 650

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus05 0 05 1 15 2 25 3 35 4 45 5 55 6 65 7 75

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


21






Tdata(32)


pdata(33)




∣∣∣ (34)










22

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



23

0 01 02 03 04 05 06 07 08 09 110minus4

10minus3

10minus2

10minus1

100


Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 01 02 03 04 05 06 07 08 09 110minus3

10minus2

10minus1

100

101


Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


24

190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 36010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 05 1 15 2 25 3 35 4

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


25

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



26

0 01 02 03 04 05 06 07 08 09 110minus4

10minus3

10minus2

10minus1

100


Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 01 02 03 04 05 06 07 08 09 110minus3

10minus2

10minus1

100

101


Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


27

270 275 280 285 290 295 300 305 310 315 320 325 330 335 34010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

02 03 04 05 06 07 08 09 1 11 12 13 14 15 16 17 18

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


28



29

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



30

200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 35010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

minus02 0 02 04 06 08 1 12 14 16 18 2 22 24 26 28 3 32 34 36 38

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


31

5 Acknowledgements




32

6 Conclusions







33






















34

2 State of the art





av2







form (Soave 1972)

p =RT

v minus bminus

acα(TR ω)

v(v + b)(2)

With the parameters

ac = 042747

(R2T2

c

Pc

)b = 008664

(RTc

Pc

)α(TR ω) =

[1 + m(ω)

(1minus

radicTR

)]2m(ω) = 0480 + 1574ω minus 0176ω2

(3)



p =RT

v minus bminus

acα(TR ω)


4

With the parameters

ac = 045724

(R2T2

c

Pc

)b = 007780

(RTc

Pc

)α(TR ω) =

[1 + m(ω)

(1minus

radicTR

)]2m(ω) = 037464 + 154226ω minus 026992ω2

(5)



200

250

300

350

400

P=

10times

104

Pa

P=

10times

104

Pa

P=

32times

104

Pa

P=

32times

104

Pa

P=

10times

105

Pa

P=

10times

105

Pa

P=

32times

105

Pa

P=

32times

105

Pa

P=

10times

106

Pa

P=

10times

106

Pa

P=

32times

106

Pa

P=

32times

106

Pa

P=

60times

106 P

a

P=

60times

106 P

a

P=

10times

107 P

a

P=

10times

107

Pa

P=

10times

108

Pa

P=

10times

108

Pa


Tem

pera

ture

[K]

REFPROPSRK






(6)


5



035


∣∣∣γ (7)



)+ 0950


)+ 0635

(8)


p =RT

v + c minus bminus

acα(TR ω)

(v + c)(v + c + b) + b(v + c minus b)(9)







6



i

sumj


aia j b =sum

i

sumj


2



2



2(1 minus Ii j)




2



2(1 minus Ii j)




2



2



i

sumj

xi x jradic


RES

ln(

bminusφbminusτ

)]

b =sum

i

sumj


2

gERES = RT x1x2


2]

Huron-Vidal a = b

sumi

xiai

bi+

gE(x)Clowast

b =sum

i

sumj


2

Wong-Sandler a = b

sumi

xiai

biminus AE

infin(x)

b =

sumisum

j xi x j

(b minus a

RT

)i j

1 minussum


RT


aRT

)i j=

(bi minus

aiRT

)+

(b j minus

a jRT

)2

(1 minus ki j)


aRT

)i j=

bi + b j

2minus


RT


aRT

)i j=


2minus


RT

7


b =sum

isum

j xix jbi j

=sum

isum

j xix jbi+b j

2

=sum

isum

j xix jbi2 +

sumisum

j xix jb j

2

= 2(sum

isum

j xix jbi2

)=

sumisum

j xix jbi

=sum

i(sum

j x j)xibi

=sum

i xibi

(10)






p =RT

v minus b+

a(T )(v +∆1b)(v +∆2b)

(11)


radic2




8




p =RT

v + c minus b+

a(T )(v + c +∆1b)(v + c +∆2b)

(12)



p =RT

1ρ+ c minus b

+a(T )(

1ρ+ c +∆1b

) (1ρ+ c +∆2b

) (13)


d1 = c minus b (14)d2 = c +∆1b (15)d3 = c +∆2b (16)

p =RTρ

1 + d1ρ+

a(T )ρ2

(1 + d2ρ) (1 + d3ρ)(17)









p =Tr

τ

R1δρr

+ c minus b+

a(τ)(1δρr

+ c +∆1b) (

1δρr

+ c +∆2b) (22)

or

p =Tr

τ


+δ2ρ2r a(τ)

(1 + (c +∆1b)δρr) (1 + (c +∆2b)δρr)(23)

9


partδ

)τ

=pτ

δ2ρrRTrminus1

δ(24)


partδ

)τ

=(b minus c)ρr


ρr

(1 + (b∆1 + c)δρr) (1 + (b∆2 + c)δρr)(25)



ψ(+) (26)


ψ(minus) =

int δ

0

(b minus c)ρr



ψ(+) =

int δ

0

ρr

(1 + (b∆1 + c)δρr) (1 + (b∆2 + c)δρr)dδ (29)

=

ln(1 + (b∆1 + c)δρr

1 + (b∆2 + c)δρr

)b(∆1 minus∆2)

(30)



10

4 Comparison







ρdata(31)





10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]


11

160 180 200 220 240 260 280 300 320 340 360 380 400 420 440 460 480 500

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus01 0 01 02 03 04 05 06 07 08 09 1 11

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


12



10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]









13

100 150 200 250 300 350 400 450 500 550 600

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus02 0 02 04 06 08 1 12 14 16 18 2 22 24 26 28 3 32

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


14


200

250

300

350

400

450

P=

100times

104

Pa

P=

100times

104

Pa

P=

100times

104

Pa

P=

100times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

100times

107 P

a

P=

100times

107 P

a

P=

100times

107 P

a

P=

100times

107

Pa

P=

100times

108

Pa

P=

100times

108

Pa

P=

100times

108 P

a

P=

100times

108

Pa


Tem

pera

ture

[K]

REFPROPHEOS

PRSRK



200

250

300

350

400

450

P=

100times

104

Pa

P=

100times

104

Pa

P=

100times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

100times

107 P

a

P=

100times

107 P

a

P=

100times

107 P

a

P=

100times

108

Pa

P=

100times

108 P

a

P=

100times

108 P

a


Tem

pera

ture

[K]

REFPROPPR

PR VT


15


200

250

300

350

400

450

P=

100times

104

Pa

P=

100times

104

Pa

P=

100times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

100times

107 P

a

P=

100times

107

Pa

P=

100times

107

Pa

P=

100times

108

Pa

P=

100times

108

Pa

P=

100times

108

Pa


Tem

pera

ture

[K]

REFPROPSRK

SRK VT


10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]


16

50 100 150 200 250 300 350 400 450 500 550 600

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus05 0 05 1 15 2 25 3 35 4 45 5 55 6 65

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


17

10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]




18

310 320 330 340 350 360 370 380 390

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus05 0 05 1 15 2 25 3 35 4 45 5 55

middot107

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


19

10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]


20

250 300 350 400 450 500 550 600 650

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus05 0 05 1 15 2 25 3 35 4 45 5 55 6 65 7 75

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


21






Tdata(32)


pdata(33)




∣∣∣ (34)










22

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



23

0 01 02 03 04 05 06 07 08 09 110minus4

10minus3

10minus2

10minus1

100


Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 01 02 03 04 05 06 07 08 09 110minus3

10minus2

10minus1

100

101


Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


24

190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 36010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 05 1 15 2 25 3 35 4

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


25

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



26

0 01 02 03 04 05 06 07 08 09 110minus4

10minus3

10minus2

10minus1

100


Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 01 02 03 04 05 06 07 08 09 110minus3

10minus2

10minus1

100

101


Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


27

270 275 280 285 290 295 300 305 310 315 320 325 330 335 34010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

02 03 04 05 06 07 08 09 1 11 12 13 14 15 16 17 18

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


28



29

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



30

200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 35010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

minus02 0 02 04 06 08 1 12 14 16 18 2 22 24 26 28 3 32 34 36 38

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


31

5 Acknowledgements




32

6 Conclusions







33






















34

With the parameters

ac = 045724

(R2T2

c

Pc

)b = 007780

(RTc

Pc

)α(TR ω) =

[1 + m(ω)

(1minus

radicTR

)]2m(ω) = 037464 + 154226ω minus 026992ω2

(5)



200

250

300

350

400

P=

10times

104

Pa

P=

10times

104

Pa

P=

32times

104

Pa

P=

32times

104

Pa

P=

10times

105

Pa

P=

10times

105

Pa

P=

32times

105

Pa

P=

32times

105

Pa

P=

10times

106

Pa

P=

10times

106

Pa

P=

32times

106

Pa

P=

32times

106

Pa

P=

60times

106 P

a

P=

60times

106 P

a

P=

10times

107 P

a

P=

10times

107

Pa

P=

10times

108

Pa

P=

10times

108

Pa


Tem

pera

ture

[K]

REFPROPSRK






(6)


5



035


∣∣∣γ (7)



)+ 0950


)+ 0635

(8)


p =RT

v + c minus bminus

acα(TR ω)

(v + c)(v + c + b) + b(v + c minus b)(9)







6



i

sumj


aia j b =sum

i

sumj


2



2



2(1 minus Ii j)




2



2(1 minus Ii j)




2



2



i

sumj

xi x jradic


RES

ln(

bminusφbminusτ

)]

b =sum

i

sumj


2

gERES = RT x1x2


2]

Huron-Vidal a = b

sumi

xiai

bi+

gE(x)Clowast

b =sum

i

sumj


2

Wong-Sandler a = b

sumi

xiai

biminus AE

infin(x)

b =

sumisum

j xi x j

(b minus a

RT

)i j

1 minussum


RT


aRT

)i j=

(bi minus

aiRT

)+

(b j minus

a jRT

)2

(1 minus ki j)


aRT

)i j=

bi + b j

2minus


RT


aRT

)i j=


2minus


RT

7


b =sum

isum

j xix jbi j

=sum

isum

j xix jbi+b j

2

=sum

isum

j xix jbi2 +

sumisum

j xix jb j

2

= 2(sum

isum

j xix jbi2

)=

sumisum

j xix jbi

=sum

i(sum

j x j)xibi

=sum

i xibi

(10)






p =RT

v minus b+

a(T )(v +∆1b)(v +∆2b)

(11)


radic2




8




p =RT

v + c minus b+

a(T )(v + c +∆1b)(v + c +∆2b)

(12)



p =RT

1ρ+ c minus b

+a(T )(

1ρ+ c +∆1b

) (1ρ+ c +∆2b

) (13)


d1 = c minus b (14)d2 = c +∆1b (15)d3 = c +∆2b (16)

p =RTρ

1 + d1ρ+

a(T )ρ2

(1 + d2ρ) (1 + d3ρ)(17)









p =Tr

τ

R1δρr

+ c minus b+

a(τ)(1δρr

+ c +∆1b) (

1δρr

+ c +∆2b) (22)

or

p =Tr

τ


+δ2ρ2r a(τ)

(1 + (c +∆1b)δρr) (1 + (c +∆2b)δρr)(23)

9


partδ

)τ

=pτ

δ2ρrRTrminus1

δ(24)


partδ

)τ

=(b minus c)ρr


ρr

(1 + (b∆1 + c)δρr) (1 + (b∆2 + c)δρr)(25)



ψ(+) (26)


ψ(minus) =

int δ

0

(b minus c)ρr



ψ(+) =

int δ

0

ρr

(1 + (b∆1 + c)δρr) (1 + (b∆2 + c)δρr)dδ (29)

=

ln(1 + (b∆1 + c)δρr

1 + (b∆2 + c)δρr

)b(∆1 minus∆2)

(30)



10

4 Comparison







ρdata(31)





10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]


11

160 180 200 220 240 260 280 300 320 340 360 380 400 420 440 460 480 500

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus01 0 01 02 03 04 05 06 07 08 09 1 11

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


12



10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]









13

100 150 200 250 300 350 400 450 500 550 600

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus02 0 02 04 06 08 1 12 14 16 18 2 22 24 26 28 3 32

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


14


200

250

300

350

400

450

P=

100times

104

Pa

P=

100times

104

Pa

P=

100times

104

Pa

P=

100times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

100times

107 P

a

P=

100times

107 P

a

P=

100times

107 P

a

P=

100times

107

Pa

P=

100times

108

Pa

P=

100times

108

Pa

P=

100times

108 P

a

P=

100times

108

Pa


Tem

pera

ture

[K]

REFPROPHEOS

PRSRK



200

250

300

350

400

450

P=

100times

104

Pa

P=

100times

104

Pa

P=

100times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

100times

107 P

a

P=

100times

107 P

a

P=

100times

107 P

a

P=

100times

108

Pa

P=

100times

108 P

a

P=

100times

108 P

a


Tem

pera

ture

[K]

REFPROPPR

PR VT


15


200

250

300

350

400

450

P=

100times

104

Pa

P=

100times

104

Pa

P=

100times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

100times

107 P

a

P=

100times

107

Pa

P=

100times

107

Pa

P=

100times

108

Pa

P=

100times

108

Pa

P=

100times

108

Pa


Tem

pera

ture

[K]

REFPROPSRK

SRK VT


10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]


16

50 100 150 200 250 300 350 400 450 500 550 600

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus05 0 05 1 15 2 25 3 35 4 45 5 55 6 65

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


17

10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]




18

310 320 330 340 350 360 370 380 390

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus05 0 05 1 15 2 25 3 35 4 45 5 55

middot107

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


19

10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]


20

250 300 350 400 450 500 550 600 650

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus05 0 05 1 15 2 25 3 35 4 45 5 55 6 65 7 75

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


21






Tdata(32)


pdata(33)




∣∣∣ (34)










22

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



23

0 01 02 03 04 05 06 07 08 09 110minus4

10minus3

10minus2

10minus1

100


Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 01 02 03 04 05 06 07 08 09 110minus3

10minus2

10minus1

100

101


Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


24

190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 36010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 05 1 15 2 25 3 35 4

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


25

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



26

0 01 02 03 04 05 06 07 08 09 110minus4

10minus3

10minus2

10minus1

100


Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 01 02 03 04 05 06 07 08 09 110minus3

10minus2

10minus1

100

101


Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


27

270 275 280 285 290 295 300 305 310 315 320 325 330 335 34010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

02 03 04 05 06 07 08 09 1 11 12 13 14 15 16 17 18

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


28



29

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



30

200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 35010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

minus02 0 02 04 06 08 1 12 14 16 18 2 22 24 26 28 3 32 34 36 38

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


31

5 Acknowledgements




32

6 Conclusions







33






















34



035


∣∣∣γ (7)



)+ 0950


)+ 0635

(8)


p =RT

v + c minus bminus

acα(TR ω)

(v + c)(v + c + b) + b(v + c minus b)(9)







6



i

sumj


aia j b =sum

i

sumj


2



2



2(1 minus Ii j)




2



2(1 minus Ii j)




2



2



i

sumj

xi x jradic


RES

ln(

bminusφbminusτ

)]

b =sum

i

sumj


2

gERES = RT x1x2


2]

Huron-Vidal a = b

sumi

xiai

bi+

gE(x)Clowast

b =sum

i

sumj


2

Wong-Sandler a = b

sumi

xiai

biminus AE

infin(x)

b =

sumisum

j xi x j

(b minus a

RT

)i j

1 minussum


RT


aRT

)i j=

(bi minus

aiRT

)+

(b j minus

a jRT

)2

(1 minus ki j)


aRT

)i j=

bi + b j

2minus


RT


aRT

)i j=


2minus


RT

7


b =sum

isum

j xix jbi j

=sum

isum

j xix jbi+b j

2

=sum

isum

j xix jbi2 +

sumisum

j xix jb j

2

= 2(sum

isum

j xix jbi2

)=

sumisum

j xix jbi

=sum

i(sum

j x j)xibi

=sum

i xibi

(10)






p =RT

v minus b+

a(T )(v +∆1b)(v +∆2b)

(11)


radic2




8




p =RT

v + c minus b+

a(T )(v + c +∆1b)(v + c +∆2b)

(12)



p =RT

1ρ+ c minus b

+a(T )(

1ρ+ c +∆1b

) (1ρ+ c +∆2b

) (13)


d1 = c minus b (14)d2 = c +∆1b (15)d3 = c +∆2b (16)

p =RTρ

1 + d1ρ+

a(T )ρ2

(1 + d2ρ) (1 + d3ρ)(17)









p =Tr

τ

R1δρr

+ c minus b+

a(τ)(1δρr

+ c +∆1b) (

1δρr

+ c +∆2b) (22)

or

p =Tr

τ


+δ2ρ2r a(τ)

(1 + (c +∆1b)δρr) (1 + (c +∆2b)δρr)(23)

9


partδ

)τ

=pτ

δ2ρrRTrminus1

δ(24)


partδ

)τ

=(b minus c)ρr


ρr

(1 + (b∆1 + c)δρr) (1 + (b∆2 + c)δρr)(25)



ψ(+) (26)


ψ(minus) =

int δ

0

(b minus c)ρr



ψ(+) =

int δ

0

ρr

(1 + (b∆1 + c)δρr) (1 + (b∆2 + c)δρr)dδ (29)

=

ln(1 + (b∆1 + c)δρr

1 + (b∆2 + c)δρr

)b(∆1 minus∆2)

(30)



10

4 Comparison







ρdata(31)





10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]


11

160 180 200 220 240 260 280 300 320 340 360 380 400 420 440 460 480 500

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus01 0 01 02 03 04 05 06 07 08 09 1 11

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


12



10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]









13

100 150 200 250 300 350 400 450 500 550 600

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus02 0 02 04 06 08 1 12 14 16 18 2 22 24 26 28 3 32

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


14


200

250

300

350

400

450

P=

100times

104

Pa

P=

100times

104

Pa

P=

100times

104

Pa

P=

100times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

100times

107 P

a

P=

100times

107 P

a

P=

100times

107 P

a

P=

100times

107

Pa

P=

100times

108

Pa

P=

100times

108

Pa

P=

100times

108 P

a

P=

100times

108

Pa


Tem

pera

ture

[K]

REFPROPHEOS

PRSRK



200

250

300

350

400

450

P=

100times

104

Pa

P=

100times

104

Pa

P=

100times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

100times

107 P

a

P=

100times

107 P

a

P=

100times

107 P

a

P=

100times

108

Pa

P=

100times

108 P

a

P=

100times

108 P

a


Tem

pera

ture

[K]

REFPROPPR

PR VT


15


200

250

300

350

400

450

P=

100times

104

Pa

P=

100times

104

Pa

P=

100times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

100times

107 P

a

P=

100times

107

Pa

P=

100times

107

Pa

P=

100times

108

Pa

P=

100times

108

Pa

P=

100times

108

Pa


Tem

pera

ture

[K]

REFPROPSRK

SRK VT


10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]


16

50 100 150 200 250 300 350 400 450 500 550 600

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus05 0 05 1 15 2 25 3 35 4 45 5 55 6 65

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


17

10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]




18

310 320 330 340 350 360 370 380 390

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus05 0 05 1 15 2 25 3 35 4 45 5 55

middot107

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


19

10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]


20

250 300 350 400 450 500 550 600 650

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus05 0 05 1 15 2 25 3 35 4 45 5 55 6 65 7 75

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


21






Tdata(32)


pdata(33)




∣∣∣ (34)










22

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



23

0 01 02 03 04 05 06 07 08 09 110minus4

10minus3

10minus2

10minus1

100


Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 01 02 03 04 05 06 07 08 09 110minus3

10minus2

10minus1

100

101


Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


24

190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 36010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 05 1 15 2 25 3 35 4

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


25

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



26

0 01 02 03 04 05 06 07 08 09 110minus4

10minus3

10minus2

10minus1

100


Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 01 02 03 04 05 06 07 08 09 110minus3

10minus2

10minus1

100

101


Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


27

270 275 280 285 290 295 300 305 310 315 320 325 330 335 34010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

02 03 04 05 06 07 08 09 1 11 12 13 14 15 16 17 18

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


28



29

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



30

200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 35010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

minus02 0 02 04 06 08 1 12 14 16 18 2 22 24 26 28 3 32 34 36 38

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


31

5 Acknowledgements




32

6 Conclusions







33






















34



i

sumj


aia j b =sum

i

sumj


2



2



2(1 minus Ii j)




2



2(1 minus Ii j)




2



2



i

sumj

xi x jradic


RES

ln(

bminusφbminusτ

)]

b =sum

i

sumj


2

gERES = RT x1x2


2]

Huron-Vidal a = b

sumi

xiai

bi+

gE(x)Clowast

b =sum

i

sumj


2

Wong-Sandler a = b

sumi

xiai

biminus AE

infin(x)

b =

sumisum

j xi x j

(b minus a

RT

)i j

1 minussum


RT


aRT

)i j=

(bi minus

aiRT

)+

(b j minus

a jRT

)2

(1 minus ki j)


aRT

)i j=

bi + b j

2minus


RT


aRT

)i j=


2minus


RT

7


b =sum

isum

j xix jbi j

=sum

isum

j xix jbi+b j

2

=sum

isum

j xix jbi2 +

sumisum

j xix jb j

2

= 2(sum

isum

j xix jbi2

)=

sumisum

j xix jbi

=sum

i(sum

j x j)xibi

=sum

i xibi

(10)






p =RT

v minus b+

a(T )(v +∆1b)(v +∆2b)

(11)


radic2




8




p =RT

v + c minus b+

a(T )(v + c +∆1b)(v + c +∆2b)

(12)



p =RT

1ρ+ c minus b

+a(T )(

1ρ+ c +∆1b

) (1ρ+ c +∆2b

) (13)


d1 = c minus b (14)d2 = c +∆1b (15)d3 = c +∆2b (16)

p =RTρ

1 + d1ρ+

a(T )ρ2

(1 + d2ρ) (1 + d3ρ)(17)









p =Tr

τ

R1δρr

+ c minus b+

a(τ)(1δρr

+ c +∆1b) (

1δρr

+ c +∆2b) (22)

or

p =Tr

τ


+δ2ρ2r a(τ)

(1 + (c +∆1b)δρr) (1 + (c +∆2b)δρr)(23)

9


partδ

)τ

=pτ

δ2ρrRTrminus1

δ(24)


partδ

)τ

=(b minus c)ρr


ρr

(1 + (b∆1 + c)δρr) (1 + (b∆2 + c)δρr)(25)



ψ(+) (26)


ψ(minus) =

int δ

0

(b minus c)ρr



ψ(+) =

int δ

0

ρr

(1 + (b∆1 + c)δρr) (1 + (b∆2 + c)δρr)dδ (29)

=

ln(1 + (b∆1 + c)δρr

1 + (b∆2 + c)δρr

)b(∆1 minus∆2)

(30)



10

4 Comparison







ρdata(31)





10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]


11

160 180 200 220 240 260 280 300 320 340 360 380 400 420 440 460 480 500

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus01 0 01 02 03 04 05 06 07 08 09 1 11

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


12



10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]









13

100 150 200 250 300 350 400 450 500 550 600

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus02 0 02 04 06 08 1 12 14 16 18 2 22 24 26 28 3 32

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


14


200

250

300

350

400

450

P=

100times

104

Pa

P=

100times

104

Pa

P=

100times

104

Pa

P=

100times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

100times

107 P

a

P=

100times

107 P

a

P=

100times

107 P

a

P=

100times

107

Pa

P=

100times

108

Pa

P=

100times

108

Pa

P=

100times

108 P

a

P=

100times

108

Pa


Tem

pera

ture

[K]

REFPROPHEOS

PRSRK



200

250

300

350

400

450

P=

100times

104

Pa

P=

100times

104

Pa

P=

100times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

100times

107 P

a

P=

100times

107 P

a

P=

100times

107 P

a

P=

100times

108

Pa

P=

100times

108 P

a

P=

100times

108 P

a


Tem

pera

ture

[K]

REFPROPPR

PR VT


15


200

250

300

350

400

450

P=

100times

104

Pa

P=

100times

104

Pa

P=

100times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

100times

107 P

a

P=

100times

107

Pa

P=

100times

107

Pa

P=

100times

108

Pa

P=

100times

108

Pa

P=

100times

108

Pa


Tem

pera

ture

[K]

REFPROPSRK

SRK VT


10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]


16

50 100 150 200 250 300 350 400 450 500 550 600

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus05 0 05 1 15 2 25 3 35 4 45 5 55 6 65

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


17

10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]




18

310 320 330 340 350 360 370 380 390

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus05 0 05 1 15 2 25 3 35 4 45 5 55

middot107

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


19

10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]


20

250 300 350 400 450 500 550 600 650

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus05 0 05 1 15 2 25 3 35 4 45 5 55 6 65 7 75

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


21






Tdata(32)


pdata(33)




∣∣∣ (34)










22

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



23

0 01 02 03 04 05 06 07 08 09 110minus4

10minus3

10minus2

10minus1

100


Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 01 02 03 04 05 06 07 08 09 110minus3

10minus2

10minus1

100

101


Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


24

190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 36010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 05 1 15 2 25 3 35 4

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


25

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



26

0 01 02 03 04 05 06 07 08 09 110minus4

10minus3

10minus2

10minus1

100


Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 01 02 03 04 05 06 07 08 09 110minus3

10minus2

10minus1

100

101


Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


27

270 275 280 285 290 295 300 305 310 315 320 325 330 335 34010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

02 03 04 05 06 07 08 09 1 11 12 13 14 15 16 17 18

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


28



29

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



30

200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 35010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

minus02 0 02 04 06 08 1 12 14 16 18 2 22 24 26 28 3 32 34 36 38

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


31

5 Acknowledgements




32

6 Conclusions







33






















34


b =sum

isum

j xix jbi j

=sum

isum

j xix jbi+b j

2

=sum

isum

j xix jbi2 +

sumisum

j xix jb j

2

= 2(sum

isum

j xix jbi2

)=

sumisum

j xix jbi

=sum

i(sum

j x j)xibi

=sum

i xibi

(10)






p =RT

v minus b+

a(T )(v +∆1b)(v +∆2b)

(11)


radic2




8




p =RT

v + c minus b+

a(T )(v + c +∆1b)(v + c +∆2b)

(12)



p =RT

1ρ+ c minus b

+a(T )(

1ρ+ c +∆1b

) (1ρ+ c +∆2b

) (13)


d1 = c minus b (14)d2 = c +∆1b (15)d3 = c +∆2b (16)

p =RTρ

1 + d1ρ+

a(T )ρ2

(1 + d2ρ) (1 + d3ρ)(17)









p =Tr

τ

R1δρr

+ c minus b+

a(τ)(1δρr

+ c +∆1b) (

1δρr

+ c +∆2b) (22)

or

p =Tr

τ


+δ2ρ2r a(τ)

(1 + (c +∆1b)δρr) (1 + (c +∆2b)δρr)(23)

9


partδ

)τ

=pτ

δ2ρrRTrminus1

δ(24)


partδ

)τ

=(b minus c)ρr


ρr

(1 + (b∆1 + c)δρr) (1 + (b∆2 + c)δρr)(25)



ψ(+) (26)


ψ(minus) =

int δ

0

(b minus c)ρr



ψ(+) =

int δ

0

ρr

(1 + (b∆1 + c)δρr) (1 + (b∆2 + c)δρr)dδ (29)

=

ln(1 + (b∆1 + c)δρr

1 + (b∆2 + c)δρr

)b(∆1 minus∆2)

(30)



10

4 Comparison







ρdata(31)





10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]


11

160 180 200 220 240 260 280 300 320 340 360 380 400 420 440 460 480 500

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus01 0 01 02 03 04 05 06 07 08 09 1 11

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


12



10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]









13

100 150 200 250 300 350 400 450 500 550 600

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus02 0 02 04 06 08 1 12 14 16 18 2 22 24 26 28 3 32

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


14


200

250

300

350

400

450

P=

100times

104

Pa

P=

100times

104

Pa

P=

100times

104

Pa

P=

100times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

100times

107 P

a

P=

100times

107 P

a

P=

100times

107 P

a

P=

100times

107

Pa

P=

100times

108

Pa

P=

100times

108

Pa

P=

100times

108 P

a

P=

100times

108

Pa


Tem

pera

ture

[K]

REFPROPHEOS

PRSRK



200

250

300

350

400

450

P=

100times

104

Pa

P=

100times

104

Pa

P=

100times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

100times

107 P

a

P=

100times

107 P

a

P=

100times

107 P

a

P=

100times

108

Pa

P=

100times

108 P

a

P=

100times

108 P

a


Tem

pera

ture

[K]

REFPROPPR

PR VT


15


200

250

300

350

400

450

P=

100times

104

Pa

P=

100times

104

Pa

P=

100times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

100times

107 P

a

P=

100times

107

Pa

P=

100times

107

Pa

P=

100times

108

Pa

P=

100times

108

Pa

P=

100times

108

Pa


Tem

pera

ture

[K]

REFPROPSRK

SRK VT


10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]


16

50 100 150 200 250 300 350 400 450 500 550 600

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus05 0 05 1 15 2 25 3 35 4 45 5 55 6 65

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


17

10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]




18

310 320 330 340 350 360 370 380 390

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus05 0 05 1 15 2 25 3 35 4 45 5 55

middot107

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


19

10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]


20

250 300 350 400 450 500 550 600 650

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus05 0 05 1 15 2 25 3 35 4 45 5 55 6 65 7 75

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


21






Tdata(32)


pdata(33)




∣∣∣ (34)










22

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



23

0 01 02 03 04 05 06 07 08 09 110minus4

10minus3

10minus2

10minus1

100


Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 01 02 03 04 05 06 07 08 09 110minus3

10minus2

10minus1

100

101


Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


24

190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 36010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 05 1 15 2 25 3 35 4

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


25

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



26

0 01 02 03 04 05 06 07 08 09 110minus4

10minus3

10minus2

10minus1

100


Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 01 02 03 04 05 06 07 08 09 110minus3

10minus2

10minus1

100

101


Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


27

270 275 280 285 290 295 300 305 310 315 320 325 330 335 34010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

02 03 04 05 06 07 08 09 1 11 12 13 14 15 16 17 18

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


28



29

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



30

200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 35010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

minus02 0 02 04 06 08 1 12 14 16 18 2 22 24 26 28 3 32 34 36 38

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


31

5 Acknowledgements




32

6 Conclusions







33






















34




p =RT

v + c minus b+

a(T )(v + c +∆1b)(v + c +∆2b)

(12)



p =RT

1ρ+ c minus b

+a(T )(

1ρ+ c +∆1b

) (1ρ+ c +∆2b

) (13)


d1 = c minus b (14)d2 = c +∆1b (15)d3 = c +∆2b (16)

p =RTρ

1 + d1ρ+

a(T )ρ2

(1 + d2ρ) (1 + d3ρ)(17)









p =Tr

τ

R1δρr

+ c minus b+

a(τ)(1δρr

+ c +∆1b) (

1δρr

+ c +∆2b) (22)

or

p =Tr

τ


+δ2ρ2r a(τ)

(1 + (c +∆1b)δρr) (1 + (c +∆2b)δρr)(23)

9


partδ

)τ

=pτ

δ2ρrRTrminus1

δ(24)


partδ

)τ

=(b minus c)ρr


ρr

(1 + (b∆1 + c)δρr) (1 + (b∆2 + c)δρr)(25)



ψ(+) (26)


ψ(minus) =

int δ

0

(b minus c)ρr



ψ(+) =

int δ

0

ρr

(1 + (b∆1 + c)δρr) (1 + (b∆2 + c)δρr)dδ (29)

=

ln(1 + (b∆1 + c)δρr

1 + (b∆2 + c)δρr

)b(∆1 minus∆2)

(30)



10

4 Comparison







ρdata(31)





10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]


11

160 180 200 220 240 260 280 300 320 340 360 380 400 420 440 460 480 500

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus01 0 01 02 03 04 05 06 07 08 09 1 11

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


12



10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]









13

100 150 200 250 300 350 400 450 500 550 600

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus02 0 02 04 06 08 1 12 14 16 18 2 22 24 26 28 3 32

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


14


200

250

300

350

400

450

P=

100times

104

Pa

P=

100times

104

Pa

P=

100times

104

Pa

P=

100times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

100times

107 P

a

P=

100times

107 P

a

P=

100times

107 P

a

P=

100times

107

Pa

P=

100times

108

Pa

P=

100times

108

Pa

P=

100times

108 P

a

P=

100times

108

Pa


Tem

pera

ture

[K]

REFPROPHEOS

PRSRK



200

250

300

350

400

450

P=

100times

104

Pa

P=

100times

104

Pa

P=

100times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

100times

107 P

a

P=

100times

107 P

a

P=

100times

107 P

a

P=

100times

108

Pa

P=

100times

108 P

a

P=

100times

108 P

a


Tem

pera

ture

[K]

REFPROPPR

PR VT


15


200

250

300

350

400

450

P=

100times

104

Pa

P=

100times

104

Pa

P=

100times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

100times

107 P

a

P=

100times

107

Pa

P=

100times

107

Pa

P=

100times

108

Pa

P=

100times

108

Pa

P=

100times

108

Pa


Tem

pera

ture

[K]

REFPROPSRK

SRK VT


10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]


16

50 100 150 200 250 300 350 400 450 500 550 600

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus05 0 05 1 15 2 25 3 35 4 45 5 55 6 65

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


17

10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]




18

310 320 330 340 350 360 370 380 390

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus05 0 05 1 15 2 25 3 35 4 45 5 55

middot107

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


19

10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]


20

250 300 350 400 450 500 550 600 650

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus05 0 05 1 15 2 25 3 35 4 45 5 55 6 65 7 75

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


21






Tdata(32)


pdata(33)




∣∣∣ (34)










22

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



23

0 01 02 03 04 05 06 07 08 09 110minus4

10minus3

10minus2

10minus1

100


Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 01 02 03 04 05 06 07 08 09 110minus3

10minus2

10minus1

100

101


Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


24

190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 36010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 05 1 15 2 25 3 35 4

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


25

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



26

0 01 02 03 04 05 06 07 08 09 110minus4

10minus3

10minus2

10minus1

100


Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 01 02 03 04 05 06 07 08 09 110minus3

10minus2

10minus1

100

101


Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


27

270 275 280 285 290 295 300 305 310 315 320 325 330 335 34010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

02 03 04 05 06 07 08 09 1 11 12 13 14 15 16 17 18

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


28



29

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



30

200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 35010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

minus02 0 02 04 06 08 1 12 14 16 18 2 22 24 26 28 3 32 34 36 38

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


31

5 Acknowledgements




32

6 Conclusions







33






















34


partδ

)τ

=pτ

δ2ρrRTrminus1

δ(24)


partδ

)τ

=(b minus c)ρr


ρr

(1 + (b∆1 + c)δρr) (1 + (b∆2 + c)δρr)(25)



ψ(+) (26)


ψ(minus) =

int δ

0

(b minus c)ρr



ψ(+) =

int δ

0

ρr

(1 + (b∆1 + c)δρr) (1 + (b∆2 + c)δρr)dδ (29)

=

ln(1 + (b∆1 + c)δρr

1 + (b∆2 + c)δρr

)b(∆1 minus∆2)

(30)



10

4 Comparison







ρdata(31)





10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]


11

160 180 200 220 240 260 280 300 320 340 360 380 400 420 440 460 480 500

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus01 0 01 02 03 04 05 06 07 08 09 1 11

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


12



10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]









13

100 150 200 250 300 350 400 450 500 550 600

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus02 0 02 04 06 08 1 12 14 16 18 2 22 24 26 28 3 32

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


14


200

250

300

350

400

450

P=

100times

104

Pa

P=

100times

104

Pa

P=

100times

104

Pa

P=

100times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

100times

107 P

a

P=

100times

107 P

a

P=

100times

107 P

a

P=

100times

107

Pa

P=

100times

108

Pa

P=

100times

108

Pa

P=

100times

108 P

a

P=

100times

108

Pa


Tem

pera

ture

[K]

REFPROPHEOS

PRSRK



200

250

300

350

400

450

P=

100times

104

Pa

P=

100times

104

Pa

P=

100times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

100times

107 P

a

P=

100times

107 P

a

P=

100times

107 P

a

P=

100times

108

Pa

P=

100times

108 P

a

P=

100times

108 P

a


Tem

pera

ture

[K]

REFPROPPR

PR VT


15


200

250

300

350

400

450

P=

100times

104

Pa

P=

100times

104

Pa

P=

100times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

100times

107 P

a

P=

100times

107

Pa

P=

100times

107

Pa

P=

100times

108

Pa

P=

100times

108

Pa

P=

100times

108

Pa


Tem

pera

ture

[K]

REFPROPSRK

SRK VT


10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]


16

50 100 150 200 250 300 350 400 450 500 550 600

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus05 0 05 1 15 2 25 3 35 4 45 5 55 6 65

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


17

10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]




18

310 320 330 340 350 360 370 380 390

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus05 0 05 1 15 2 25 3 35 4 45 5 55

middot107

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


19

10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]


20

250 300 350 400 450 500 550 600 650

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus05 0 05 1 15 2 25 3 35 4 45 5 55 6 65 7 75

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


21






Tdata(32)


pdata(33)




∣∣∣ (34)










22

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



23

0 01 02 03 04 05 06 07 08 09 110minus4

10minus3

10minus2

10minus1

100


Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 01 02 03 04 05 06 07 08 09 110minus3

10minus2

10minus1

100

101


Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


24

190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 36010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 05 1 15 2 25 3 35 4

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


25

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



26

0 01 02 03 04 05 06 07 08 09 110minus4

10minus3

10minus2

10minus1

100


Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 01 02 03 04 05 06 07 08 09 110minus3

10minus2

10minus1

100

101


Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


27

270 275 280 285 290 295 300 305 310 315 320 325 330 335 34010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

02 03 04 05 06 07 08 09 1 11 12 13 14 15 16 17 18

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


28



29

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



30

200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 35010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

minus02 0 02 04 06 08 1 12 14 16 18 2 22 24 26 28 3 32 34 36 38

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


31

5 Acknowledgements




32

6 Conclusions







33






















34

4 Comparison







ρdata(31)





10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]


11

160 180 200 220 240 260 280 300 320 340 360 380 400 420 440 460 480 500

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus01 0 01 02 03 04 05 06 07 08 09 1 11

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


12



10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]









13

100 150 200 250 300 350 400 450 500 550 600

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus02 0 02 04 06 08 1 12 14 16 18 2 22 24 26 28 3 32

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


14


200

250

300

350

400

450

P=

100times

104

Pa

P=

100times

104

Pa

P=

100times

104

Pa

P=

100times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

100times

107 P

a

P=

100times

107 P

a

P=

100times

107 P

a

P=

100times

107

Pa

P=

100times

108

Pa

P=

100times

108

Pa

P=

100times

108 P

a

P=

100times

108

Pa


Tem

pera

ture

[K]

REFPROPHEOS

PRSRK



200

250

300

350

400

450

P=

100times

104

Pa

P=

100times

104

Pa

P=

100times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

100times

107 P

a

P=

100times

107 P

a

P=

100times

107 P

a

P=

100times

108

Pa

P=

100times

108 P

a

P=

100times

108 P

a


Tem

pera

ture

[K]

REFPROPPR

PR VT


15


200

250

300

350

400

450

P=

100times

104

Pa

P=

100times

104

Pa

P=

100times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

100times

107 P

a

P=

100times

107

Pa

P=

100times

107

Pa

P=

100times

108

Pa

P=

100times

108

Pa

P=

100times

108

Pa


Tem

pera

ture

[K]

REFPROPSRK

SRK VT


10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]


16

50 100 150 200 250 300 350 400 450 500 550 600

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus05 0 05 1 15 2 25 3 35 4 45 5 55 6 65

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


17

10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]




18

310 320 330 340 350 360 370 380 390

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus05 0 05 1 15 2 25 3 35 4 45 5 55

middot107

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


19

10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]


20

250 300 350 400 450 500 550 600 650

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus05 0 05 1 15 2 25 3 35 4 45 5 55 6 65 7 75

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


21






Tdata(32)


pdata(33)




∣∣∣ (34)










22

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



23

0 01 02 03 04 05 06 07 08 09 110minus4

10minus3

10minus2

10minus1

100


Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 01 02 03 04 05 06 07 08 09 110minus3

10minus2

10minus1

100

101


Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


24

190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 36010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 05 1 15 2 25 3 35 4

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


25

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



26

0 01 02 03 04 05 06 07 08 09 110minus4

10minus3

10minus2

10minus1

100


Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 01 02 03 04 05 06 07 08 09 110minus3

10minus2

10minus1

100

101


Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


27

270 275 280 285 290 295 300 305 310 315 320 325 330 335 34010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

02 03 04 05 06 07 08 09 1 11 12 13 14 15 16 17 18

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


28



29

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



30

200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 35010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

minus02 0 02 04 06 08 1 12 14 16 18 2 22 24 26 28 3 32 34 36 38

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


31

5 Acknowledgements




32

6 Conclusions







33






















34

160 180 200 220 240 260 280 300 320 340 360 380 400 420 440 460 480 500

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus01 0 01 02 03 04 05 06 07 08 09 1 11

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


12



10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]









13

100 150 200 250 300 350 400 450 500 550 600

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus02 0 02 04 06 08 1 12 14 16 18 2 22 24 26 28 3 32

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


14


200

250

300

350

400

450

P=

100times

104

Pa

P=

100times

104

Pa

P=

100times

104

Pa

P=

100times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

100times

107 P

a

P=

100times

107 P

a

P=

100times

107 P

a

P=

100times

107

Pa

P=

100times

108

Pa

P=

100times

108

Pa

P=

100times

108 P

a

P=

100times

108

Pa


Tem

pera

ture

[K]

REFPROPHEOS

PRSRK



200

250

300

350

400

450

P=

100times

104

Pa

P=

100times

104

Pa

P=

100times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

100times

107 P

a

P=

100times

107 P

a

P=

100times

107 P

a

P=

100times

108

Pa

P=

100times

108 P

a

P=

100times

108 P

a


Tem

pera

ture

[K]

REFPROPPR

PR VT


15


200

250

300

350

400

450

P=

100times

104

Pa

P=

100times

104

Pa

P=

100times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

100times

107 P

a

P=

100times

107

Pa

P=

100times

107

Pa

P=

100times

108

Pa

P=

100times

108

Pa

P=

100times

108

Pa


Tem

pera

ture

[K]

REFPROPSRK

SRK VT


10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]


16

50 100 150 200 250 300 350 400 450 500 550 600

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus05 0 05 1 15 2 25 3 35 4 45 5 55 6 65

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


17

10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]




18

310 320 330 340 350 360 370 380 390

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus05 0 05 1 15 2 25 3 35 4 45 5 55

middot107

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


19

10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]


20

250 300 350 400 450 500 550 600 650

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus05 0 05 1 15 2 25 3 35 4 45 5 55 6 65 7 75

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


21






Tdata(32)


pdata(33)




∣∣∣ (34)










22

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



23

0 01 02 03 04 05 06 07 08 09 110minus4

10minus3

10minus2

10minus1

100


Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 01 02 03 04 05 06 07 08 09 110minus3

10minus2

10minus1

100

101


Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


24

190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 36010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 05 1 15 2 25 3 35 4

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


25

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



26

0 01 02 03 04 05 06 07 08 09 110minus4

10minus3

10minus2

10minus1

100


Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 01 02 03 04 05 06 07 08 09 110minus3

10minus2

10minus1

100

101


Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


27

270 275 280 285 290 295 300 305 310 315 320 325 330 335 34010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

02 03 04 05 06 07 08 09 1 11 12 13 14 15 16 17 18

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


28



29

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



30

200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 35010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

minus02 0 02 04 06 08 1 12 14 16 18 2 22 24 26 28 3 32 34 36 38

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


31

5 Acknowledgements




32

6 Conclusions







33






















34



10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]









13

100 150 200 250 300 350 400 450 500 550 600

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus02 0 02 04 06 08 1 12 14 16 18 2 22 24 26 28 3 32

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


14


200

250

300

350

400

450

P=

100times

104

Pa

P=

100times

104

Pa

P=

100times

104

Pa

P=

100times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

100times

107 P

a

P=

100times

107 P

a

P=

100times

107 P

a

P=

100times

107

Pa

P=

100times

108

Pa

P=

100times

108

Pa

P=

100times

108 P

a

P=

100times

108

Pa


Tem

pera

ture

[K]

REFPROPHEOS

PRSRK



200

250

300

350

400

450

P=

100times

104

Pa

P=

100times

104

Pa

P=

100times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

100times

107 P

a

P=

100times

107 P

a

P=

100times

107 P

a

P=

100times

108

Pa

P=

100times

108 P

a

P=

100times

108 P

a


Tem

pera

ture

[K]

REFPROPPR

PR VT


15


200

250

300

350

400

450

P=

100times

104

Pa

P=

100times

104

Pa

P=

100times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

100times

107 P

a

P=

100times

107

Pa

P=

100times

107

Pa

P=

100times

108

Pa

P=

100times

108

Pa

P=

100times

108

Pa


Tem

pera

ture

[K]

REFPROPSRK

SRK VT


10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]


16

50 100 150 200 250 300 350 400 450 500 550 600

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus05 0 05 1 15 2 25 3 35 4 45 5 55 6 65

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


17

10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]




18

310 320 330 340 350 360 370 380 390

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus05 0 05 1 15 2 25 3 35 4 45 5 55

middot107

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


19

10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]


20

250 300 350 400 450 500 550 600 650

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus05 0 05 1 15 2 25 3 35 4 45 5 55 6 65 7 75

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


21






Tdata(32)


pdata(33)




∣∣∣ (34)










22

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



23

0 01 02 03 04 05 06 07 08 09 110minus4

10minus3

10minus2

10minus1

100


Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 01 02 03 04 05 06 07 08 09 110minus3

10minus2

10minus1

100

101


Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


24

190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 36010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 05 1 15 2 25 3 35 4

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


25

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



26

0 01 02 03 04 05 06 07 08 09 110minus4

10minus3

10minus2

10minus1

100


Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 01 02 03 04 05 06 07 08 09 110minus3

10minus2

10minus1

100

101


Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


27

270 275 280 285 290 295 300 305 310 315 320 325 330 335 34010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

02 03 04 05 06 07 08 09 1 11 12 13 14 15 16 17 18

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


28



29

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



30

200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 35010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

minus02 0 02 04 06 08 1 12 14 16 18 2 22 24 26 28 3 32 34 36 38

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


31

5 Acknowledgements




32

6 Conclusions







33






















34

100 150 200 250 300 350 400 450 500 550 600

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus02 0 02 04 06 08 1 12 14 16 18 2 22 24 26 28 3 32

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


14


200

250

300

350

400

450

P=

100times

104

Pa

P=

100times

104

Pa

P=

100times

104

Pa

P=

100times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

100times

107 P

a

P=

100times

107 P

a

P=

100times

107 P

a

P=

100times

107

Pa

P=

100times

108

Pa

P=

100times

108

Pa

P=

100times

108 P

a

P=

100times

108

Pa


Tem

pera

ture

[K]

REFPROPHEOS

PRSRK



200

250

300

350

400

450

P=

100times

104

Pa

P=

100times

104

Pa

P=

100times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

100times

107 P

a

P=

100times

107 P

a

P=

100times

107 P

a

P=

100times

108

Pa

P=

100times

108 P

a

P=

100times

108 P

a


Tem

pera

ture

[K]

REFPROPPR

PR VT


15


200

250

300

350

400

450

P=

100times

104

Pa

P=

100times

104

Pa

P=

100times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

100times

107 P

a

P=

100times

107

Pa

P=

100times

107

Pa

P=

100times

108

Pa

P=

100times

108

Pa

P=

100times

108

Pa


Tem

pera

ture

[K]

REFPROPSRK

SRK VT


10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]


16

50 100 150 200 250 300 350 400 450 500 550 600

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus05 0 05 1 15 2 25 3 35 4 45 5 55 6 65

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


17

10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]




18

310 320 330 340 350 360 370 380 390

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus05 0 05 1 15 2 25 3 35 4 45 5 55

middot107

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


19

10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]


20

250 300 350 400 450 500 550 600 650

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus05 0 05 1 15 2 25 3 35 4 45 5 55 6 65 7 75

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


21






Tdata(32)


pdata(33)




∣∣∣ (34)










22

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



23

0 01 02 03 04 05 06 07 08 09 110minus4

10minus3

10minus2

10minus1

100


Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 01 02 03 04 05 06 07 08 09 110minus3

10minus2

10minus1

100

101


Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


24

190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 36010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 05 1 15 2 25 3 35 4

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


25

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



26

0 01 02 03 04 05 06 07 08 09 110minus4

10minus3

10minus2

10minus1

100


Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 01 02 03 04 05 06 07 08 09 110minus3

10minus2

10minus1

100

101


Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


27

270 275 280 285 290 295 300 305 310 315 320 325 330 335 34010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

02 03 04 05 06 07 08 09 1 11 12 13 14 15 16 17 18

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


28



29

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



30

200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 35010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

minus02 0 02 04 06 08 1 12 14 16 18 2 22 24 26 28 3 32 34 36 38

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


31

5 Acknowledgements




32

6 Conclusions







33






















34


200

250

300

350

400

450

P=

100times

104

Pa

P=

100times

104

Pa

P=

100times

104

Pa

P=

100times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

100times

107 P

a

P=

100times

107 P

a

P=

100times

107 P

a

P=

100times

107

Pa

P=

100times

108

Pa

P=

100times

108

Pa

P=

100times

108 P

a

P=

100times

108

Pa


Tem

pera

ture

[K]

REFPROPHEOS

PRSRK



200

250

300

350

400

450

P=

100times

104

Pa

P=

100times

104

Pa

P=

100times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

100times

107 P

a

P=

100times

107 P

a

P=

100times

107 P

a

P=

100times

108

Pa

P=

100times

108 P

a

P=

100times

108 P

a


Tem

pera

ture

[K]

REFPROPPR

PR VT


15


200

250

300

350

400

450

P=

100times

104

Pa

P=

100times

104

Pa

P=

100times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

100times

107 P

a

P=

100times

107

Pa

P=

100times

107

Pa

P=

100times

108

Pa

P=

100times

108

Pa

P=

100times

108

Pa


Tem

pera

ture

[K]

REFPROPSRK

SRK VT


10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]


16

50 100 150 200 250 300 350 400 450 500 550 600

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus05 0 05 1 15 2 25 3 35 4 45 5 55 6 65

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


17

10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]




18

310 320 330 340 350 360 370 380 390

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus05 0 05 1 15 2 25 3 35 4 45 5 55

middot107

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


19

10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]


20

250 300 350 400 450 500 550 600 650

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus05 0 05 1 15 2 25 3 35 4 45 5 55 6 65 7 75

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


21






Tdata(32)


pdata(33)




∣∣∣ (34)










22

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



23

0 01 02 03 04 05 06 07 08 09 110minus4

10minus3

10minus2

10minus1

100


Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 01 02 03 04 05 06 07 08 09 110minus3

10minus2

10minus1

100

101


Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


24

190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 36010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 05 1 15 2 25 3 35 4

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


25

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



26

0 01 02 03 04 05 06 07 08 09 110minus4

10minus3

10minus2

10minus1

100


Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 01 02 03 04 05 06 07 08 09 110minus3

10minus2

10minus1

100

101


Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


27

270 275 280 285 290 295 300 305 310 315 320 325 330 335 34010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

02 03 04 05 06 07 08 09 1 11 12 13 14 15 16 17 18

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


28



29

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



30

200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 35010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

minus02 0 02 04 06 08 1 12 14 16 18 2 22 24 26 28 3 32 34 36 38

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


31

5 Acknowledgements




32

6 Conclusions







33






















34


200

250

300

350

400

450

P=

100times

104

Pa

P=

100times

104

Pa

P=

100times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

320times

104

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

100times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

320times

105

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

100times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

320times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

600times

106

Pa

P=

100times

107 P

a

P=

100times

107

Pa

P=

100times

107

Pa

P=

100times

108

Pa

P=

100times

108

Pa

P=

100times

108

Pa


Tem

pera

ture

[K]

REFPROPSRK

SRK VT


10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]


16

50 100 150 200 250 300 350 400 450 500 550 600

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus05 0 05 1 15 2 25 3 35 4 45 5 55 6 65

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


17

10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]




18

310 320 330 340 350 360 370 380 390

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus05 0 05 1 15 2 25 3 35 4 45 5 55

middot107

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


19

10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]


20

250 300 350 400 450 500 550 600 650

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus05 0 05 1 15 2 25 3 35 4 45 5 55 6 65 7 75

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


21






Tdata(32)


pdata(33)




∣∣∣ (34)










22

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



23

0 01 02 03 04 05 06 07 08 09 110minus4

10minus3

10minus2

10minus1

100


Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 01 02 03 04 05 06 07 08 09 110minus3

10minus2

10minus1

100

101


Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


24

190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 36010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 05 1 15 2 25 3 35 4

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


25

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



26

0 01 02 03 04 05 06 07 08 09 110minus4

10minus3

10minus2

10minus1

100


Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 01 02 03 04 05 06 07 08 09 110minus3

10minus2

10minus1

100

101


Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


27

270 275 280 285 290 295 300 305 310 315 320 325 330 335 34010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

02 03 04 05 06 07 08 09 1 11 12 13 14 15 16 17 18

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


28



29

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



30

200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 35010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

minus02 0 02 04 06 08 1 12 14 16 18 2 22 24 26 28 3 32 34 36 38

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


31

5 Acknowledgements




32

6 Conclusions







33






















34

50 100 150 200 250 300 350 400 450 500 550 600

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus05 0 05 1 15 2 25 3 35 4 45 5 55 6 65

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


17

10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]




18

310 320 330 340 350 360 370 380 390

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus05 0 05 1 15 2 25 3 35 4 45 5 55

middot107

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


19

10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]


20

250 300 350 400 450 500 550 600 650

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus05 0 05 1 15 2 25 3 35 4 45 5 55 6 65 7 75

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


21






Tdata(32)


pdata(33)




∣∣∣ (34)










22

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



23

0 01 02 03 04 05 06 07 08 09 110minus4

10minus3

10minus2

10minus1

100


Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 01 02 03 04 05 06 07 08 09 110minus3

10minus2

10minus1

100

101


Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


24

190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 36010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 05 1 15 2 25 3 35 4

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


25

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



26

0 01 02 03 04 05 06 07 08 09 110minus4

10minus3

10minus2

10minus1

100


Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 01 02 03 04 05 06 07 08 09 110minus3

10minus2

10minus1

100

101


Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


27

270 275 280 285 290 295 300 305 310 315 320 325 330 335 34010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

02 03 04 05 06 07 08 09 1 11 12 13 14 15 16 17 18

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


28



29

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



30

200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 35010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

minus02 0 02 04 06 08 1 12 14 16 18 2 22 24 26 28 3 32 34 36 38

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


31

5 Acknowledgements




32

6 Conclusions







33






















34

10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]




18

310 320 330 340 350 360 370 380 390

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus05 0 05 1 15 2 25 3 35 4 45 5 55

middot107

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


19

10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]


20

250 300 350 400 450 500 550 600 650

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus05 0 05 1 15 2 25 3 35 4 45 5 55 6 65 7 75

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


21






Tdata(32)


pdata(33)




∣∣∣ (34)










22

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



23

0 01 02 03 04 05 06 07 08 09 110minus4

10minus3

10minus2

10minus1

100


Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 01 02 03 04 05 06 07 08 09 110minus3

10minus2

10minus1

100

101


Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


24

190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 36010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 05 1 15 2 25 3 35 4

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


25

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



26

0 01 02 03 04 05 06 07 08 09 110minus4

10minus3

10minus2

10minus1

100


Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 01 02 03 04 05 06 07 08 09 110minus3

10minus2

10minus1

100

101


Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


27

270 275 280 285 290 295 300 305 310 315 320 325 330 335 34010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

02 03 04 05 06 07 08 09 1 11 12 13 14 15 16 17 18

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


28



29

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



30

200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 35010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

minus02 0 02 04 06 08 1 12 14 16 18 2 22 24 26 28 3 32 34 36 38

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


31

5 Acknowledgements




32

6 Conclusions







33






















34

310 320 330 340 350 360 370 380 390

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus05 0 05 1 15 2 25 3 35 4 45 5 55

middot107

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


19

10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]


20

250 300 350 400 450 500 550 600 650

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus05 0 05 1 15 2 25 3 35 4 45 5 55 6 65 7 75

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


21






Tdata(32)


pdata(33)




∣∣∣ (34)










22

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



23

0 01 02 03 04 05 06 07 08 09 110minus4

10minus3

10minus2

10minus1

100


Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 01 02 03 04 05 06 07 08 09 110minus3

10minus2

10minus1

100

101


Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


24

190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 36010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 05 1 15 2 25 3 35 4

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


25

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



26

0 01 02 03 04 05 06 07 08 09 110minus4

10minus3

10minus2

10minus1

100


Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 01 02 03 04 05 06 07 08 09 110minus3

10minus2

10minus1

100

101


Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


27

270 275 280 285 290 295 300 305 310 315 320 325 330 335 34010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

02 03 04 05 06 07 08 09 1 11 12 13 14 15 16 17 18

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


28



29

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



30

200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 35010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

minus02 0 02 04 06 08 1 12 14 16 18 2 22 24 26 28 3 32 34 36 38

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


31

5 Acknowledgements




32

6 Conclusions







33






















34

10minus4

10minus3

10minus2

10minus1

100

101

102


Den

sity

rela

tive

devi

atio

n[

]


20

250 300 350 400 450 500 550 600 650

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus05 0 05 1 15 2 25 3 35 4 45 5 55 6 65 7 75

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


21






Tdata(32)


pdata(33)




∣∣∣ (34)










22

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



23

0 01 02 03 04 05 06 07 08 09 110minus4

10minus3

10minus2

10minus1

100


Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 01 02 03 04 05 06 07 08 09 110minus3

10minus2

10minus1

100

101


Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


24

190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 36010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 05 1 15 2 25 3 35 4

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


25

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



26

0 01 02 03 04 05 06 07 08 09 110minus4

10minus3

10minus2

10minus1

100


Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 01 02 03 04 05 06 07 08 09 110minus3

10minus2

10minus1

100

101


Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


27

270 275 280 285 290 295 300 305 310 315 320 325 330 335 34010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

02 03 04 05 06 07 08 09 1 11 12 13 14 15 16 17 18

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


28



29

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



30

200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 35010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

minus02 0 02 04 06 08 1 12 14 16 18 2 22 24 26 28 3 32 34 36 38

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


31

5 Acknowledgements




32

6 Conclusions







33






















34

250 300 350 400 450 500 550 600 650

10minus3

10minus2

10minus1

100

101

102

Temperature [K]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT

minus05 0 05 1 15 2 25 3 35 4 45 5 55 6 65 7 75

middot108

10minus3

10minus2

10minus1

100

101

102

Pressure [Pa]

Den

sity

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR VTSRK VT


21






Tdata(32)


pdata(33)




∣∣∣ (34)










22

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



23

0 01 02 03 04 05 06 07 08 09 110minus4

10minus3

10minus2

10minus1

100


Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 01 02 03 04 05 06 07 08 09 110minus3

10minus2

10minus1

100

101


Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


24

190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 36010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 05 1 15 2 25 3 35 4

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


25

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



26

0 01 02 03 04 05 06 07 08 09 110minus4

10minus3

10minus2

10minus1

100


Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 01 02 03 04 05 06 07 08 09 110minus3

10minus2

10minus1

100

101


Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


27

270 275 280 285 290 295 300 305 310 315 320 325 330 335 34010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

02 03 04 05 06 07 08 09 1 11 12 13 14 15 16 17 18

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


28



29

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



30

200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 35010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

minus02 0 02 04 06 08 1 12 14 16 18 2 22 24 26 28 3 32 34 36 38

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


31

5 Acknowledgements




32

6 Conclusions







33






















34






Tdata(32)


pdata(33)




∣∣∣ (34)










22

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



23

0 01 02 03 04 05 06 07 08 09 110minus4

10minus3

10minus2

10minus1

100


Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 01 02 03 04 05 06 07 08 09 110minus3

10minus2

10minus1

100

101


Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


24

190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 36010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 05 1 15 2 25 3 35 4

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


25

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



26

0 01 02 03 04 05 06 07 08 09 110minus4

10minus3

10minus2

10minus1

100


Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 01 02 03 04 05 06 07 08 09 110minus3

10minus2

10minus1

100

101


Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


27

270 275 280 285 290 295 300 305 310 315 320 325 330 335 34010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

02 03 04 05 06 07 08 09 1 11 12 13 14 15 16 17 18

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


28



29

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



30

200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 35010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

minus02 0 02 04 06 08 1 12 14 16 18 2 22 24 26 28 3 32 34 36 38

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


31

5 Acknowledgements




32

6 Conclusions







33






















34

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



23

0 01 02 03 04 05 06 07 08 09 110minus4

10minus3

10minus2

10minus1

100


Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 01 02 03 04 05 06 07 08 09 110minus3

10minus2

10minus1

100

101


Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


24

190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 36010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 05 1 15 2 25 3 35 4

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


25

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



26

0 01 02 03 04 05 06 07 08 09 110minus4

10minus3

10minus2

10minus1

100


Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 01 02 03 04 05 06 07 08 09 110minus3

10minus2

10minus1

100

101


Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


27

270 275 280 285 290 295 300 305 310 315 320 325 330 335 34010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

02 03 04 05 06 07 08 09 1 11 12 13 14 15 16 17 18

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


28



29

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



30

200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 35010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

minus02 0 02 04 06 08 1 12 14 16 18 2 22 24 26 28 3 32 34 36 38

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


31

5 Acknowledgements




32

6 Conclusions







33






















34

0 01 02 03 04 05 06 07 08 09 110minus4

10minus3

10minus2

10minus1

100


Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 01 02 03 04 05 06 07 08 09 110minus3

10minus2

10minus1

100

101


Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


24

190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 36010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 05 1 15 2 25 3 35 4

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


25

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



26

0 01 02 03 04 05 06 07 08 09 110minus4

10minus3

10minus2

10minus1

100


Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 01 02 03 04 05 06 07 08 09 110minus3

10minus2

10minus1

100

101


Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


27

270 275 280 285 290 295 300 305 310 315 320 325 330 335 34010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

02 03 04 05 06 07 08 09 1 11 12 13 14 15 16 17 18

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


28



29

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



30

200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 35010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

minus02 0 02 04 06 08 1 12 14 16 18 2 22 24 26 28 3 32 34 36 38

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


31

5 Acknowledgements




32

6 Conclusions







33






















34

190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 36010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 05 1 15 2 25 3 35 4

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


25

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



26

0 01 02 03 04 05 06 07 08 09 110minus4

10minus3

10minus2

10minus1

100


Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 01 02 03 04 05 06 07 08 09 110minus3

10minus2

10minus1

100

101


Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


27

270 275 280 285 290 295 300 305 310 315 320 325 330 335 34010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

02 03 04 05 06 07 08 09 1 11 12 13 14 15 16 17 18

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


28



29

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



30

200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 35010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

minus02 0 02 04 06 08 1 12 14 16 18 2 22 24 26 28 3 32 34 36 38

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


31

5 Acknowledgements




32

6 Conclusions







33






















34

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



26

0 01 02 03 04 05 06 07 08 09 110minus4

10minus3

10minus2

10minus1

100


Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 01 02 03 04 05 06 07 08 09 110minus3

10minus2

10minus1

100

101


Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


27

270 275 280 285 290 295 300 305 310 315 320 325 330 335 34010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

02 03 04 05 06 07 08 09 1 11 12 13 14 15 16 17 18

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


28



29

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



30

200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 35010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

minus02 0 02 04 06 08 1 12 14 16 18 2 22 24 26 28 3 32 34 36 38

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


31

5 Acknowledgements




32

6 Conclusions







33






















34

0 01 02 03 04 05 06 07 08 09 110minus4

10minus3

10minus2

10minus1

100


Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

0 01 02 03 04 05 06 07 08 09 110minus3

10minus2

10minus1

100

101


Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


27

270 275 280 285 290 295 300 305 310 315 320 325 330 335 34010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

02 03 04 05 06 07 08 09 1 11 12 13 14 15 16 17 18

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


28



29

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



30

200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 35010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

minus02 0 02 04 06 08 1 12 14 16 18 2 22 24 26 28 3 32 34 36 38

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


31

5 Acknowledgements




32

6 Conclusions







33






















34

270 275 280 285 290 295 300 305 310 315 320 325 330 335 34010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

02 03 04 05 06 07 08 09 1 11 12 13 14 15 16 17 18

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


28



29

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



30

200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 35010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

minus02 0 02 04 06 08 1 12 14 16 18 2 22 24 26 28 3 32 34 36 38

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


31

5 Acknowledgements




32

6 Conclusions







33






















34



29

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



30

200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 35010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

minus02 0 02 04 06 08 1 12 14 16 18 2 22 24 26 28 3 32 34 36 38

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


31

5 Acknowledgements




32

6 Conclusions







33






















34

10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7Tem

pera

ture

rela

tive

devi

atio

n[

]


10minus4

10minus3

10minus2

10minus1

100

101

102


10minus9

10minus7

Pres

sure

rela

tive

devi

atio

n[

]



30

200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 35010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

minus02 0 02 04 06 08 1 12 14 16 18 2 22 24 26 28 3 32 34 36 38

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


31

5 Acknowledgements




32

6 Conclusions







33






















34

200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 35010minus4

10minus3

10minus2

10minus1

100

Temperature [K]

Tem

pera

ture

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j

minus02 0 02 04 06 08 1 12 14 16 18 2 22 24 26 28 3 32 34 36 38

middot106

10minus3

10minus2

10minus1

100

101

Pressure [Pa]

Pres

sure

devi

atio

n[

]

REFPROPHEOS

PRSRK

PR ki jSRK ki j


31

5 Acknowledgements




32

6 Conclusions







33






















34

5 Acknowledgements




32

6 Conclusions







33






















34

6 Conclusions







33






















34






















34

Implementation and performance evaluation of different cubic ...

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