Fluid Phase Equilibria 388 (2015) 182–187

A thermodynamic consistency test for experimental isobaric data ofwax solubility in gaseous systems

Javad Kondori a, Hamed Hashemi b, Saeedeh Babaee b, Jafar Javanmardi a,Amir H. Mohammadi b,c,*, Deresh Ramjugernath b,**aDepartment of Chemical Engineering, Shiraz University of Technology, Shiraz, Iranb Thermodynamics Research Unit, School of Engineering, University of KwaZulu-Natal, Howard College Campus, King George V, Avenue, Durban 4041, SouthAfricac Institut de Recherche en GénieChimiqueetPétrolier (IRGCP), Paris Cedex, France

A R T I C L E I N F O

Article history:Received 3 May 2014Received in revised form 27 December 2014Accepted 31 December 2014Available online 3 January 2015

Keywords:Thermodynamic consistency testWax solubilityIsobaric experimental dataGibbs–DuhemSupercritical fluids

A B S T R A C T

The ever-increasing demand for natural gas as an energy source has led to a great deal of interest andnumerous studies being undertaken by researchers in the field. The efficient production of natural gasfrom deep well reservoirs has always been an area of intense research in the gas production industry,with immense efforts to understand and mitigate issues which can affect this efficiency. The solubility ofthe waxy compounds in some natural gases can be regarded as one of these issues that may affectproduction efficiency. In order to fully understand the phenomenon of wax solubility in natural gas,reliable experimental data are required. This study aims to investigate the reliability of such data using athermodynamic model. For this purpose, the wax solubility in supercritical constituents of natural gas,such as carbon dioxide and ethane, has been estimated using the Peng–Robinson equation of state andtwo-fluid van der Waals (vdW2) mixing rules. The residual enthalpies were evaluated using the resultsobtained. The Gibbs–Duhem equation at constant pressure was applied for evaluation of the consistencyof the experimental data. From the analysis, the data were classified as thermodynamically consistent(TC), not fully consistent (NFC), and thermodynamically inconsistent (TI).

ã 2015 Elsevier B.V. All rights reserved.

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1. Introduction

Natural gas, until the middle of the 20th century, was dismissedas an impractical by-product of crude oil production. This haschanged significantly with natural gas now accounting forapproximately 22% of the world’s energy consumption, with thepercentage likely to increase with every larger reserves beingdiscovered. It has been predicted by the International EnergyAgency that the demand for the natural gas will increase nearly43% by 2035. Natural gas is regarded as the cleanest and mosteconomical conventional fuel compared to hydrocarbon fuels suchas oil and coal which produce high levels of greenhouse emissions.

The temperature depression in petroleum pipelines conveyingwaxy crudes may result in the formation of solid compounds

* Corresponding author at: Institut de Recherche en GénieChimiqueetPétrolier(IRGCP), Paris Cedex, France.** Corresponding author.

E-mail addresses: a.h.m@irgcp.fr, amir_h_mohammadi@yahoo.com(A.H. Mohammadi), ramjuger@ukzn.ac.za (D. Ramjugernath).

http://dx.doi.org/10.1016/j.fluid.2014.12.0480378-3812/ã 2015 Elsevier B.V. All rights reserved.

which are comprised mainly of paraffin hydrocarbons (C18—C36),known as paraffin wax and naphthenic hydrocarbons (C30—C60).The presence of such compounds may be expected in some naturalgas production fields [1,2]. The extraction of these compounds bysupercritical constituents of natural gas, such as carbon dioxideand ethane, in gas production from deep well or acid gas fields mayhave catastrophic repercussions [1,2]. Therefore, the measurementof solubility of such compounds in supercritical fluids is animportant area of research [2]. Hence, before design of the relatedfacilities for natural gas production from gas reservoirs, thesolubility of waxes should be taken into account to avoid anypossible failure in the system (lost production, or failure of pipingsystem) [2]. For this purpose the knowledge of natural gas + waxphase behavior is inevitable [2]. Accordingly, developing a reliablemodel for predicting this phase behavior is necessary [2].Unfortunately, there are a scarcity of experimental data in theopen literature which have considered this phenomenon [2]. Thereliability of the model depends on the accuracy of theexperimental data which are employed for the fitting of modelparameters. The use of inaccurate or incorrect measured experi-mental data would result in parameters which produce a model

Nomenclature

A Area (m2)ARD Absolute relative deviationd Derivative operatorE ErrorEoS Equation of statek Binary interaction parameterf FugacityG Gibbs energyH Molar enthalpyl Binary interaction parameterNDP Number of experimental data pointsP Pressure (MPa)PR Peng–RobinsonR Universal gas constant (MPa m3/molT Temperature (K)TC Thermodynamically consistent dataV Molar volume (m3/mol)vdW2 van der Waals 2 fluid mixing ruley Mole fraction in gas phaseZ Compressibility factor

Greek symbolsf Fugacity coefficientD Difference valuev Acentric factor

SubscriptsA Areac Critical propertyi ith component in a mixture or ith experimental data setj jth component in a mixture or jth individual calculated

areaT Refers to experimental P–T–y dataf Refers to calculated parameters of the model for evalua-

tions of the integrals in Eqs. (8)–(10)1 Refers to supercritical CO2 or ethane2 Refers to paraffin wax

Superscriptscal Calculatedexp Experimentals SolidR Residual propertysat Saturation (sublimation) pressure (MPa)

J. Kondori et al. / Fluid Phase Equilibria 388 (2015) 182–187 183

which is inaccurate or incorrect. Analyzing the reliability ofexperimental data has become an area of interest for manyresearchers.

The “Slope Test”, the “Integral Test”, the “Differential Test” andthe “Tangent-Intercept Test” are among the well-knownapproaches which have been developed so date for evaluatingthe consistency of experimental data [3–8]. Comprehensivereviews of these methods can be found in literature [4,5].

Valderrama can be regarded one as the pioneers of thermody-namic consistency testing of experimental data [8–13]. The Gibbs–Duhem [3,6,7] equation has been adopted by Valderrama for thispurpose at constant temperature. In a previous study, a newapproach for assessing the water content of methane experimentaldata at constant pressures was developed [14]. Hence dependingon experimental data being considered, and whether the data areat constant pressure or temperature, either the constant pressureor constant temperature approach can be employed.

In this study, the consistency of isobaric wax solubilityexperimental data in carbon dioxide and ethane have beenthermodynamically evaluated. The Gibbs–Duhem [3,6,7] equation,in terms of residual molar enthalpy and molar volume, has beenapplied for this purpose. The thermodynamic consistency, partialconsistency (not fully consistent), and thermodynamic inconsis-tency of data have been determined.

2. Thermodynamic consistency test

The “Gibbs–Duhem” [3,6,7] relation can be written in terms ofresidual molar enthalpy (HR) and residual molar volume (VR) for ahomogeneous mixture as follows [6,14]:

Siyid

GRi

RT

" #¼ �HR

RT2 dT þ VR

RTdP (1)

where yi stands for the mole fraction of species i in the mixture, GRi

is the residual Gibbs energy, R represents the universal gasconstant, and P and T are the pressure and temperature of the

system, respectively. Residual Gibbs energy “GRi ” can be expressed

by the following equation [5–7]:

GRi ¼ RTln’i (2)

in which fi represents the fugacity coefficient of component i inthe mixture. Substitution of Eq. (2) into Eq. (1) gives:

Siyid½ln’i� ¼ �HR

RT2 dT þ VR

RTdP (3)

For the case of study (wax solubility in the gaseous system) only

two components are involved and Eq. (3) considering hR ¼ HR=RTcan be simplified as follows [3,6,7]:

� hR

T

" #dT ¼ y1dðln’1Þ þ y2dðln’2Þ (4)

where y1 and y2 are the mole fraction of supercritical fluid andsolute (wax) in the gas phase, respectively and f1, f2 represent thefugacity coefficients of the components in the gas phase. Thefollowing equation is used for evaluation of hR:

�hR ¼ TZV1

ð@Z@T

ÞdVV

þ ðZ � 1Þ (5)

where Z indicates the compressibility factor of the gas phase, and Tand V are temperature and molar volume of the system,respectively. A mathematical re-arrangement of Eq. (4) in termsof the wax composition in the gas phase (y2 = 1 � y1) gives:Z

1Ty2

dT ¼Z

1

ð�hRÞ’2

d’2 þZ ð1 � y2Þ

ð�hRÞy2’1

d’1 (6)

in which the parameters, hR, f1, f2, and Z can be calculated using anaccurate thermodynamic model for the wax–gas equilibria.Further simplifications can also be made by designating the leftand right hand sides of Eq. (6) by AT and Af, respectively, as follows[8,14]:

AT ¼Z

1Ty2

dT (7)

A’ ¼ A’1þ A’2

(8)

where

A’1¼

Z ð1 � y2Þð�hRÞy2’1

d’1 (9)

Yes

Yes

Is ARD% within [0 -25]%? Change the correla�ng model

Are all ∆A% in the range of [0 -18]%? Yes The data are thermodynamicallyconsistent

No

No

Are the data outside the range of [0 -18]% greater than 25% of the whole

dataset?

The data are ThermodynamicallyInconsistent (TI)

The data are Not Fully Consistent(NFC)

NO

Fig. 1. Flowchart diagram of the thermodynamic consistency test used in this study[8].

Table 2Sublimation pressures of the investigated paraffin waxes at different temperatures[2].

Compound T/K Sublimation pressure/MPa

n-C25H52 308 1.58 � 10�11

313 5.39 � 10�11

n-C28H58 308 1.71 �10�13

318 2.67 � 10�12

325 1.68 � 10�11

n-C30H62 308 1.50 � 10�14

313 6.46 � 10�14

n-C32H66 308 1.02 � 10�15

313 4.74 �10�15

318 2.12 �10�14

319 2.86 � 10�14

n-C33H68 308 1.15 �10�15

313 5.43 � 10�15

318 2.44 �10�14

184 J. Kondori et al. / Fluid Phase Equilibria 388 (2015) 182–187

A’2¼

Z1

ð�hRÞ’2

d’2 (10)

In this study, the Simpson 3/8 integration method was used fordetermination of AT and Af. The equivalency of AT and Afwithin anacceptable deviation will determine the consistency of the datasetconsidered. This deviation is defined using a percent area deviationbetween experimental and calculated values [1,14]:

DAi ¼ 100jA’ i � ATij

AT i

� �(11)

where i indicates the number of the dataset. The error propagationmethod [15] has been used for the evaluation of the boundaries forthese deviations at constant pressure. Considering mole fraction ofwax in the gas phase as the independent measured variable and Afas the dependent measured variable, the error in the calculatedareas, EA, and the percent error, %EA can be obtained usingfollowing equations [16,17]:

EA ¼ @A’@P

� �DP þ @A’

@y

� �Dy (12)

%EA ¼ 100j EAA’ j

j (13)

where subscript j indicates the jth calculated area. In this study, amaximum uncertainty of 0.1 MPa for the experimental pressure

Table 1Experimental datasets used for the consistency test in this study.

System NDPa P range/MPa

T range/K y2�106 range/molefractionb

Ref.

CO2 + n-C25H52

4 10.35–20.5 308–313 215–952 2

CO2 + n-C28H58

2 20 308–318 435–689 2

CO2 + n-C28H58

2 11 308.15–318.15 54.6–76 21

Ethane + n-C30H62

8 6.57–13.64 308.1–313.1 486–1710 2

Ethane + n-C32H66

16 6.57–20.2 308.1–319.1 149–2180 2

Ethane + n-C33H68

16 6.47–20.2 308.1–318.1 183–2970 2

a Number of data points.b Wax solubility.

and 5% for experimental solubility data of wax in carbon dioxideand ethane are assumed. It should be noted that theseuncertainties are dependent on the experimental measurementmethods, for example the method which was used by Teja et al.was based on dynamic method [2]. The relative average absolutedeviations range between [0–18]% for the solubility data of theinvestigated waxes in supercritical carbon dioxide and ethane wasobtained applying the central finite difference method [18] in twopreceding equations. This range has been considered as themaximum acceptable error for areas (DAi) in Eq. (11). A flowchartfor the procedure used for the checking of the thermodynamicconsistency of the investigated dataset is shown in Fig. 1.

3. Thermodynamic model

In this study, the equality of the fugacities of solutes (wax) inadjacent phases (pure solid and gas phase) has been used as theequilibrium criteria [1,2]:

f solidi ¼ f gasi (14)

where f stands for the fugacity of component i in the mixture. Inthis study, the following assumptions have been made for themodeling of the wax–gas system [1,2]:

1 The supercritical fluid is not soluble in the solid (solute-containing) phase.

2 The fugacity of the pure solid i represents the fugacity of thesolute i in the mixture.

3 The pressure dependency of the solute molar volume has beenneglected.

4 The solid phase is incompressible.5 The saturated fugacity coefficient of the solute is assumed to beunity.

Table 3Solid molar volumes (Vs) of the paraffin waxes [2] investigated.

Solute vs� 103/m3/mol

n-C25H52 0.4513n-C28H58 0.4894n-C30H62 0.5222n-C32H66 0.555n-C33H68 0.5714

Table 4Acentric factors (v) and critical properties (Tc: critical temperature and Pc: criticalpressure) of the pure compounds investigated.

Compound Tc/K Pc/MPa v

C2H6 305.32 4.872 0.099CO2 304.19 7.382 0.2276n-C25H52 818.56 1.0256 1.066n-C28H58 842.11 0.9694 1.163n-C30H62 856.17 0.9421 1.226n-C32H66 869.12 0.9208 1.287n-C33H68 875.22 0.9119 1.317

J. Kondori et al. / Fluid Phase Equilibria 388 (2015) 182–187 185

Considering the preceding assumptions and using Eq. (14), thefollowing equation will be obtained for calculation of the solidsolubility in the supercritical fluid:

Table 5Model predictions for the paraffin waxes (2) solubility in CO2 and ethane (1).

System P/Mpa T/K yexp2 � 106

CO2 + n-C25H52 10.35 308.00 215

313.00 321

20.50 308.00 602

313.00 952

CO2 + n-C28H58 20.00 308.00 689

318.00 435

11.00 308.15 54.6

318.15 76

Ethane + n-C32H66 6.57 308.10 216

313.10 177

319.10 149

10.10 308.10 713

313.10 933

319.10 1280

12.02 308.10 801

313.10 1150

319.10 1440

13.64 308.10 959

313.10 1440

319.10 2140

16.67 308.10 1260

313.10 1730

20.20 308.10 1810

313.10 2180

Ethane + n-C33H68 6.47 308.10 371

313.10 288

318.10 183

10.20 308.10 963

313.10 1540

318.10 1540

12.12 308.10 1140

313.10 1470

318.10 1960

13.64 308.10 1360

313.10 1720

318.10 2970

16.67 308.10 1640

313.10 2240

20.20 308.10 2370

313.10 2930

Ethane + n-C30H62 6.57 308.10 549

313.10 486

10.10 308.10 1240

313.10 1450

12.02 308.10 1450

313.10 1450

13.64 308.10 1710

313.10 1710

a Data out of model predictions criteria (doutful data).b Interaction parameters between the ith and jth compounds in the mixture, which

yi ¼Psati exp½vsi ðP � Psat

i Þ=RT�’iP

(15)

Th Peng–Robinson equation of state [19] and the two-fluid vander Waals (vdW2) [20] mixing rules have been used for calculationof the solid, solutes, and supercritical fluids fugacity coefficients(fi) in the mixture and also other required parameters. Moredetails in this regard are given elsewhere [1].

4. Consistency criteria

The accuracy of the model used for correlation / representationof the experimental data is crucial in the thermodynamicconsistency test. In other words, the average absolute deviationsbetween the model predictions and the experimental data shouldbe within the acceptable margin of errors. In this study, the range

ycal2 � 106 ARD% kijb lij

b

236.2 9.90 0.194 0.418 [2]324.0 1.00 [2]663.0 10.20 [2]

1043.0 9.60 [2]

751.1 8.90 0.035 �0.32 [2]439.5 1.00 [2]82.3 50.73a [21]69.3 8.82 [21]

258.4 19.70 0.057 �0.19 [2]208.9 18.00 [2]196.8 32.10a [2]855.6 20.00 [2]1110.1 19.00 [2]1675.1 30.90a [2]962.9 20.20 [2]1370.8 19.20 [2]1889.3 31.20a [2]1140.5 18.90 [2]1709.7 18.70 [2]2818.0 31.70a [2]1527.1 21.20 [2]2062.2 19.20 [2]2184.7 20.70 [2]2581.1 18.40 [2]

441.4 18.98 �0.35 �0.151 [2]344.4 19.58 [2]239.2 30.71a [2]1155.6 20.00 [2]1844.9 19.80 [2]2005.1 30.20a [2]1359.7 19.27 [2]1754.9 19.38 [2]2565.6 30.90a [2]1627.1 19.64 [2]2062.1 19.89 [2]3890.7 31.00a [2]1966.9 19.93 [2]2658.2 18.67 [2]2846.4 20.10 [2]3508.4 19.74 [2]

667.0 21.49 �0.06 0.06 [2]610.8 25.68a [2]

1483.7 19.65 [2]1801.0 24.211744.1 20.28 [2]1832.8 26.40a [2]2066.4 20.80 [2]2171.4 27.00a [2]

are consistent with those reported in Ref. [2].

186 J. Kondori et al. / Fluid Phase Equilibria 388 (2015) 182–187

of [0–25]% has been chosen as the acceptable range for the absoluterelative deviations (ARD) of the model predictions which is definedas follows:

ARD% ¼ 100 � jycali � yexpi jyexpi

(16)

where superscripts “cal” and “exp” stand for calculated andexperimental values, respectively.

According to what has been discussed so far, the followingprocedure has been adopted for determination of thermodynami-cally consistent (TC), thermodynamically inconsistent (TI), and notfully consistent (NFC) determination of experimental data:

1 Initially, the ARD% of the model should lie between 0 and 25%,otherwise the poor prediction should be eliminated and thecorrelating model changed. In these cases, the related experi-mental data are regarded as doubtful data and they are not usedin the test.

2 A dataset is deemed to be thermodynamically consistent (TC) ifthe model provides acceptable error ranges (ARD%) and the areatest is met for all data points in the dataset.

3 Thermodynamically inconsistent (TI) experimental datasets aredefined as the datasets in which that the area test is not fulfilledfor most of the data (more than 25% of the areas) even thoughthe thermodynamic model correlates the experimental datacorrectly (with ARD% between 0 and 25%).

4

Table 6Results of the thermodynamic consistency test for the experimental paraffin waxes (2

System P/MPa T/K Z f1 f2

CO2 + n-C25H52 10.35 308 0.264 0.5210 1.210 � 1313 0.292 0.5527 3.650 �

20.5 308 0.401 0.3310 1.010 � 1313 0.417 0.3493 2.810 �

CO2+ n-C28H58 20 308 0.397 0.3337 0.050 �318 0.420 0.3770 0.087 �

Ethane + n-C32H66 6.57 308.1 0.254 0.5282 0.037 �

313.1 0.285 0.5610 0.085 �10.1 308.1 0.326 0.3880 0.029 �

313.1 0.343 0.4165 0.044 �12.02 308.1 0.378 0.3503 0.032 �

313.1 0.386 0.3728 0.049 �13.64 308.1 0.415 0.3244 0.040 �

313.1 0.422 0.3456 0.059 �16.67 308.1 0.484 0.2900 0.094 �

313.1 0.491 0.3095 0.093 �20.2 308.1 0.5652 0.2646 0.040 �

313.1 0.5695 0.2824 0.059 �

Ethane + n-C30H62 10.1 308.1 0.333 0.3919 0.416 �

313.1 0.343 0.4164 0.631 �

Ethane + n-C33H68 6.47 308.1 0.251 0.5343 1.56 � 1313.1 0.279 0.5630 0.127 �

10.2 308.1 0.328 0.3861 0.244 �313.1 0.337 0.4101 0.65 �1

12.12 308.1 0.372 0.3450 0.196 �

313.1 0.379 0.3670 0.485 �13.64 308.1 0.407 0.3211 0.186 �

313.1 0.413 0.3418 0.435 �16.67 308.1 0.475 0.2860 0.206 �

313.1 0.482 0.3057 0.446 �20.2 308.1 0.555 0.2610 0.283 �

313.1 0.561 0.2784 0.585 �

Not fully consistent (NFC) experimental datasets are defined asdata which are predicted by the model correctly, however lessthan 25% of the data are outside the defined margin of errors, i.e.[0–18]%.

Fig. 1 shows the procedure schematically [8].

5. Experimental data

48 isobaric experimental datasets were considered in thisstudy, most of which were taken from GPA research report 171 [2],and are summarized in Table 1. These datasets include solubility ofparaffin waxes (alkanes from n-C24 to n-C33) in CO2 and ethane.Tables 2 and 3, show the sublimation pressures and solid molarvolumes of the paraffin waxes, respectively. Acentric factors andcritical properties of the investigated compounds are reported inTable 4.

6. Result and discussion

The consistency check procedure adopted in this study can bedivided in two parts: first obtaining the thermodynamic modelpredictions of the wax solubility data, and second evaluating theexperimental data using the obtained results. The results obtainedfrom the model for the prediction of the paraffin wax solubility insupercritical CO2 and ethane, as well as adjusted interactionparameters of the model are reported in Table 5. As can been seen,

) solubility data in supercritical fluids (1).

HR AT Af DAi% Test result

0�6 �3.465 69.788 62.635 10.2 TC 10�6 �3.1260�6 �4.006 21.873 19.036 14.9 TC10�6 �3.779

10�6 �3.976 59.707 60.852 1.88 TC 10�6 �3.564

10�6 �3.496 42.077 46.598 9.70 TC10�6 �3.167

10�6 �3.883 12.236 14.308 14.47 TC10�6 �3.942

10�6 �3.907 17.073 17.393 1.83 TC 10�6 �3.736 10�6 �3.959 14.000 14.269 1.84 TC 10�6 �3.80310�6 �4.0324 11.055 11.336 2.48 TC

10�6 �3.8809 10�6 �4.0794 8.1457 8.2785 1.61 TC 10�6 �3.9376

10�7 �3.832 12.05 12.27 1.82 TC10�7 �3.644

0�12 �3.496 49.596 46.955 5.62 TC10�12 �3.13910�12 �3.901 13.611 12.890 5.58 TC0�12 �3.72810�12 �3.988 12.550 12.648 0.15 TC10�12 �3.82310�12 �4.039 10.609 10.625 4.71 TC10�12 �3.883

10�12 �4.111 8.512 8.933 4.72 TC 10�12 �3.96010�12 �4.168 6.149 6.203 0.86 TC

10�12 �4.022

J. Kondori et al. / Fluid Phase Equilibria 388 (2015) 182–187 187

the ability of the model used for prediction of the experimentaldata is acceptable and for most of the data, absolute deviationvalues lie within the range of [0–25]%. For some cases, thethermodynamic model criteria was not met (model predictionswere not within the range of [0–25]%); in these cases the poorpredictions were eliminated and the data were not considered inthe consistency test. The results of the thermodynamic consistencytest for the datasets investigated are reported in Table 6. As can beobserved, all the datasets considered (the datasets which are wellcorrelated by the thermodynamic model) are thermodynamicallyconsistent. The same result was found in the previous study [1] atconstant temperature which confirms the reliability of theproposed thermodynamic consistency test in this study. Severalfactors should be taken into consideration when evaluating thereliability or accuracy of an experimental dataset, such as theprocedure or technique used for the measurement of theexperimental dataset; the accuracy of the calibration methods;the ability of the researcher performing the experiments; theaccuracy of the low solubility measurements; and so on. It can beinferred from the thermodynamic consistency check of thedatasets analyzed in this study that researchers have taken greatcare in the measurement of the experimental data. The results ofthis study would confirm the reliability of experimental data whichcan then be used with confidence for the tuning of thermodynamicmodel parameters. Thermodynamically inconsistent data or notfully consistent data will result in erroneous predictions of themodel for further applications and the reason of such deviationsmay not be identified easily.

It should be note that the proposed thermodynamic consistencytest is only applicable to isobaric experimental data and thedeveloped equations in this study are based on this assumption. Ina previous study [1] an isothermal procedure was performed forthe evaluation of the thermodynamic consistency of the experi-mental data. Hence, depending on the way in which theexperimental data has been presented (isothermal or isobaric)either procedure (temperature constant or pressure constant) canbe applied. Looking for isobaric or isothermal experimental data isone of the limitations of the proposed consistency tests. Onesolution to this problem is generating pseudo experimental datausing statistical software. However, in generating such datathermodynamically tested data are required.

7. Conclusions

A new thermodynamic consistency test based on calculation ofthe residual enthalpies was applied at constant pressure for 48experimental data of paraffin wax solubilities in supercritical CO2

and ethane. The original Gibbs–Duhem [3,6,7] equation was usedto relate the calculated residual enthalpies to solubility andfugacity coefficients of the components. The PR EoS [19] coupledwith vdW2 [20] mixing rule was used for the prediction of theparaffin wax solubilities in supercritical CO2 and ethane. Theresults show that all the considered datasets which are within themodel capability seem to be thermodynamically consistent. Theseresults are in good agreement with the results obtained from aprevious study [1] in which the datasets were tested thermody-namically at constant temperature. Since all the datasets

considered in this study are thermodynamically consistent, theprocedure applied by Teja et al. [2] in their measurements can beconcluded as reliable.

Given the importance of solubility data of paraffin waxes insupercritical fluids and the fact that these kinds of data are indeedrare, the results obtained in this study can be used for furtherapplications in natural gas systems.

Acknowledgements

This work is based upon research supported by the SouthAfrican Research Chairs Initiative of the Department of Science andTechnology and National Research Foundation.

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