Experimental measurements and thermodynamic modeling ofwax disappearance temperature for the binary systems n-C14H30  + n-C16H34, n-C16H34 + n-C18H38 and n-C11H24 + n-C18H38

Fluid Phase Equilibria 388 (2015) 93–99

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Fluid Phase Equilibria j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / fl u i d

Experimental measurements and thermodynamic modeling of wax disappearance temperature for the binary systems n-C14H30 + nC16H34, n-C16H34 + n-C18H38 and n-C11H24 + n-C18H38 S. Parsa a , J. Javanmardi a, * , S. Aftab a , K. Nasrifar b a b

Department of Chemical Engineering, Shiraz University of Technology, 71555-313 Shiraz, Iran Department of Chemical Engineering, University of Nizwa, Nizwa PC 313, Oman

A R T I C L E I N F O

A B S T R A C T

Article history: Received 4 August 2014 Received in revised form 19 December 2014 Accepted 22 December 2014 Available online 25 December 2014

The current work investigates the wax disappearance temperature (WDT) of three binary systems including n-tetradecane + n-hexadecane, n-hexadecane + n-octadecane and n-undecane + n-octadecane as a function of temperature at local atmospheric pressure. Verifying the uncertainties of the measurements, the WDT of pure n-hexadecane and the system n-tetradecane + n-hexadecane are compared with available experimental data reported in literature. Good agreement between the measured experimental data in the present study and those reported previously in literature is observed. Finally, by modeling the paraffin systems with different combinations of ideal solution behavior, regular solution theory, predictive Wilson, predictive UNIQUAC and UNIFAC, the solid–liquid equilibria of the binary systems were described to find the most accurate model without using any adjustable parameter. ã 2015 Published by Elsevier B.V.

Keywords: Solid–liquid equilibria Solid solution Paraffin hydrocarbon Wax disappearance temperature Activity coefficient model

1. Introduction Paraffin waxes are often precipitated from petroleum fractions. Formation of solid waxes is undesirable and considered a main problem in petroleum industry. Changing in environmental temperature may lead to wax deposition. Plugging of pipelines, production well damage, fuel filters and process equipment are repercussions of wax precipitation [1–4]. Temperature, pressure and fluid composition are the main factors affecting wax deposition. Wax deposit constituents lie between pure paraffins to asphaltenes. In this broad range, many compounds can be found in the wax deposits such as microcrystalline paraffins, asphaltenes, resins and etc. [5]. The importance of paraffins in the crystallization behavior of waxy mixtures is originated from its majority in petroleum fractions. Hence, paraffins are regarded as major potential wax formers. The wax appearance temperature (WAT), also known as cloud point, is the temperature at which the first crystal of paraffin forms. WAT is a key parameter in oil industry because wax crystals will deposit if the temperature is lower than the WAT. The wax disappearance temperature is the temperature at which the last precipitated paraffin re-dissolves in the oil [6]. Wax appearance

* Corresponding author. Tel.: +98 713 7354520/917 7133450; fax: +98 713 7354520. E-mail address: [email protected] (J. Javanmardi). http://dx.doi.org/10.1016/j.fluid.2014.12.036 0378-3812/ ã 2015 Published by Elsevier B.V.

temperature is not necessarily an equilibrium temperature. Experimental studies reveal that different techniques detect different WAT [7]. For instance, WAT measured using visual microscopy can be 10–20
C higher than those determined using techniques such as differential scanning calorimetry, laser-based solid detection systems, and viscometry [7,8]. In addition to detection technique, WAT strongly depends on cooling rate [9,10]. Fast cooling rates often lead to a lower measured WAT [9]. Determination of the melting temperature of last crystal is easier and more reproducible than the formation temperature of first crystal [11]. In contrast to WAT, the wax disappearance temperature represents a true solid–liquid equilibrium point [9,12]. Using equilibrium step heating and a proper measurement technique, WDT can be accurately detected [13–15]. Considering the problems caused by wax precipitation, many researchers have measured WAT and WDT of different systems to generate reliable experimental data. Researchers not only have investigated the effect of different parameters on the WDT and WAT, but also proposed thermodynamic models to accurately predict the thermodynamic behavior of multi-component systems [6,9,12,16–21]. For example, Wang et al. [6] measured WAT and WDT of n- C24H50 and n-C36H74 in n-decane solutions both with and without wax inhibitors using light transmittance method. Their results exhibited the effect of inhibitors on the values of WAT and WDT. Ji et al. [9] proposed a thermodynamically consistent model to predict the phase boundary, amount and composition of wax

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S. Parsa et al. / Fluid Phase Equilibria 388 (2015) 93–99

Nomenclature Cn Cp d f H i j k MW n P q r R T Tc

v

x Z

Carbon number Specific heat capacity Density Fugacity Enthalpy Counter of component Counter of component Counter of component Molecular weight Number of components Pressure Structural parameter Structural parameter Gas universal constant Temperature Critical temperature Molar volume Mole fraction Coordination number

Greek letters Solubility parameter Average solubility parameter Activity coefficient Interaction energy parameter in Eq. (19) Molar volume Acentric factor Volume fraction Area fraction Difference Characteristic energy parameter Segment fraction

d d g l t y v f u D L F

Superscripts cal Calculated comb Combinational exp Experiment f Fusion l Liquid res Residual s Solid sub Sublimation tot Total tr Transition vap Vaporization Subscripts i Component j Component k Component n Component

number number number number

precipitated. They used UNIQUAC equation to describe the solid phase and the SRK and PR equations of state to calculate the vapor– liquid fugacities. Also, they developed correlations for fusion properties and heat capacities of n-parrafins and modified term m in SRK and PR equation of state. Furthermore, they proposed a correlation for calculation of fusion temperatures at increased pressure conditions to consider the effect of pressure. In that work, WDTs of C6H14–C16H34 and C6H14–C17H36 were measured and used to check the validity of their proposed correlations for fusion

properties and heat capacity. Finally, they examined the reliability of their thermodynamic model by measured WDTs of C16H34– C18H38, C16H34–C20H42, C15H32–C19H40, C6H14–C16H34–C17H36 [9] and WDTs of C17H36–C19H40 [22], C14H30–C15H32–C16H34 and C18H38–C19H40–C20H42 [23]. Bhat et al. [12] measured WDT, WAT, and pour point temperature (PPT) of prepared wax-solvent mixtures using visual observation method at atmospheric pressure. The examined mixtures were prepared by dissolving 6–22 mass % of a paraffinic wax (n- C20H42–n-C40H82) in n-hexadecane (C16H34) and a paraffinic solvent with C11H24-C15H32 and C13H28 and C14H30 being the two predominant constituents. Finally, the obtained results were thermodynamically modeled using Flory free-volume and predictive UNIQUAC to bring into account the non-ideality of the liquid phase and solid phase, respectively. In addition, Milhet et al. [21] investigated two binary systems C14H30–C15H32 and C14H30–C16H34. They measured the WDT and observed that these two systems show eutectic like behavior. For thermodynamic modeling of the investigated systems, the PR equation of state was used for calculation of the liquid fugacity coefficient and the volumetric properties were corrected using volume translation proposed by Peneloux et al. [24]. The activity coefficient of the solid phase was described by means of the Chain Delta Lattice Parameter (CDLP) model, developed by Coutinho et al. [25]. In the present work, the WDT of three binary systems including n-tetradecane + n-hexadecane, n-hexadecane + n-octadecane and n-undecane + n-octadecane are measured using a visual observation method at local atmospheric pressure (0.9 bar). The measurements are then verified with two known systems. Later, for prediction of the measured WDT, the liquid and solid phases are modeled by ideal behavior, predictive Wilson [26], predictive UNIQUAC [27], regular solution theory [28,29] , and UNIFAC activity coefficient models [30]. Finally, the predicted results are compared with the experimental WDTs and the best combination of activity coefficient models is found and reported. 2. Experimental 2.1. Materials The chemicals (paraffins) and their purities used in this work are shown in Table 1. 2.2. Experimental procedure Known compositions of binary mixtures were prepared by gravimetric method. The mixture was then fed to an equilibrium cell with 5 cm3 volume. Shown in Fig. 1, the equilibrium cell was equipped with a magnetic stirrer to keep the liquid phase well mixed. An ethanol-cooling bath was used to control and keep the temperature constant. To reach the initial equilibrium temperature, the mixture was cooled to a temperature significantly lower than the wax disappearance temperature. The temperature was then kept constant for an hour by a controllable circulator (TCS-1) with ability of scheduling (Julabo TP-50). Subsequently, the mixture was Table 1 The suppliers and purities of the chemicals used in this work. Chemical name

Source

Purity (mole fraction)

Purification method

n-undecane n-tetradecane n-hexadecane n-octadecane

Merck Merck Merck Merck

0.99 0.99 0.99 0.99

None None None None

S. Parsa et al. / Fluid Phase Equilibria 388 (2015) 93–99

95

4.1. Regular solution theory According to regular solution theory, activity coefficient is related to the molar volume, vi, and solubility parameter, d, by [28,29]: vi ðd  di Þ2 RT

lng i ¼

(5)

where the solubility parameters in the liquid and solid phases are functions of carbon number. These parameters were expressed by Pedersen et al. [32]

dli ¼ 7:41 þ 0:5194ðlnCni  ln7Þ

(6)

dsi ¼ 8:5 þ 5:763ðlnCni  ln7Þ

(7)

and the average value of solubility parameter, d, is given by:

d¼

n X

f i di

(8)

i¼1

Fig. 1. Schematic diagram of experimnetal apparatus.

heated gradually by increasing the bath temperature. The increasing rate of temperature was selected quite low so that the mixture reached to equilibrium in each step. The increasing rate of temperature was about 0.2 K/h. WDT was detected visually by observing the disappearance of the last crystal and the temperature was measured by a thermocouple (Pt-100) with a gradation of 0.1 K.

where n is the number of components, fi is the volume fraction of component i which can be calculated for each phase from

fli ¼

fsi ¼

xli vli

(9)

n

Si xli vli xsi vsi

(10)

n

Si xs vsi

3. Thermodynamic modeling In this work, the molar volumes of the two phases were taken equal

Solid–liquid equilibrium can be described by: l

s

fi ¼ fi

(1)

where f i is the fugacity of component i and s and l stand for the solid and liquid phases, respectively. The fugacities for solid and liquid phases are expressed by s

s

ZP

f i ¼ xsi g si f purei

vsi dp RT

(2)

vli ¼ vsi ¼ vi ¼

MWi di;25

(11)

where di,25 is the liquid density at 25
C. The liquid density at 25
C can be calculated from the following correlation [32]: di;25 ¼ 0:8155 þ 0:6272  104 MWi 

13:06 MWi

(12)

P0

l

l

ZP

f i ¼ xli g li f purei

4.2. Predictive Wilson model vli dp RT

(3)

P0

where xi and g i represent the mole fraction and activity coefficient of component i, respectively. R is the gas constant, T is the temperature, P is the pressure and v is the molar volume. The relation between pure solid and liquid component fugacity can be obtained from [31]: 2 3 f f ! ZT i ZT i l f 6D H i f purei T 1 1 DC pi 7 (4) dT 7 ¼ exp6 DCpi dT þ s 4 RT 1  f  RT 5 R T f purei T i

T

T

Another investigated activity coefficient model is predictive Wilson [26] (p.Wilson) which is presented as follows 0 1 X xk Lki X lng i ¼ 1  ln@ xj Lij A  (13) X xj Lkj j k j

where Lij is the characteristic energy parameter. The characteristic energy parameters were calculated from   L  Lii Lij ¼ exp  ij (14) RT

where Cpi is the heat capacity and Tif and DHif are the fusion temperature and fusion enthalpy of pure component i, respectively. Correlations used for calculation of these parameters are provided in Appendix A.

The interaction energies between identical molecules i, lii, is related to the heat of sublimation and temperature. The value of this parameter is given by

4. Investigated activity coefficient models

Lii ¼ ðDHsub  RTÞ i

The non-ideality of the solid wax and liquid hydrocarbon phase can be described using activity coefficient models. The investigated activity coefficient models in this work are regular solution theory, predictive Wilson, predictive UNIQUAC and UNIFAC.

where Z is the coordinating number. The value of this parameter is set to 6 due to orthorhombic behavior of solid crystals [26,33]. Sublimation enthalpy is related to fusion, transition and vaporization enthalpy. Morgan and Kobayashi correlated the enthalpies of

2 Z

(15)

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S. Parsa et al. / Fluid Phase Equilibria 388 (2015) 93–99

sublimation for paraffins [34]. The interaction energy parameters lij or lji is equal to the interaction energy parameter of the nalkane with the shorter chain (j) of the pair ij

lij ¼ lji ¼ ljj

(16)

4.3. Predictive UNIQUAC model Predictive UNIQUAC (p. UNIQUAC) model which is originated from the original UNIQUAC consists of two parts, namely, combinatorial and residual. The former is due to entropic effects, size difference and free volume. The latter is attributed to the energetic interactions of dissimilar molecules which lead to enthalpy of mixing [27,35]. The predictive UNIQUAC reads lng i ¼ lng comb þ lng res i i

(17)

        Fi Fi Z Fi F ¼ ln þ1  qi ln þ1 i lng comb i 2 xi xi ui ui

(18)

2

lng res i

0 0 1 6 BX u t X j ij 6 ¼ qi 61  ln@ ui t ji A  B B X 4 @ ut j¼1 j¼1

i kj

13 C7 C7 C7 A5

(19)

k¼1

  l  lii t ji ¼ exp  ji qi RT

x qi

(21)

xj qj

j

xi ri Fi ¼ X n xj r j

The reliability of the performed method was established by measuring the WDTs of pure n-C14H30, pure n-C16H34, pure nC18H38 and WDTs of n-tetradecane + n-hexadecane binary system previously reported by Milhet et al. [21]. In addition, it must be mentioned that the n-hexadecane + n-octadecane system was previously investigated by Ji et al. [9] and Smith [36] but with different compositions. In the present study, the following compositions (% wt) of n-C18H38 were studies – that is, 0.00, 0.11, 0.20, 0.35, 0.49, 0.5, 0.68, 0.83, 0.91 and 1. Comparing the measured experimental values in this study with those reported in literature for pure n-C14H30, pure n-C14H30, pure n-C16H34, pure nC18H38 and the binary system n-tetradecane + n-hexadecane as given in Tables 2 and 3 revealed the validity of the measurements. The measured WDTs for the two systems n-hexadecane + noctadecane and n-undecane + n-octadecane are provided in Table 4. As can be seen in Fig. 2, the n-hexadecane + n-octadecane binary system shows eutectic like behavior which is consistent with what was reported by Ji et al. [9] and Smith [36] before. Also, it is observed that WDT increases when the weight percent of the Table 2 Comparison between the data measured in this work for pure n-C14H30, pure nC16H34 and pure n-C18H38 with those reported in NIST data archive. Compound

Average melting temperature (K) This work

NIST data Archive: SRD 69

Refs.

n-C14H30 n-C16H34 n-C18H38

279.4 291.5 301.6

278.7  0.9 291  1. 0 301  0.7

[21], [37–51] [21], [47–49], [52–61] [49], [50,51], [60–71]

(20)

Area and segment fraction (ui, Fi) are defined by i ui ¼ X n

5. Results and discussion

(22)

j

where r and q are the structural parameters which are affected by size and external surface. These parameters can be calculated from [27] ri ¼ 0:1C ni þ 0:0672

(23)

qi ¼ 0:1C ni þ 0:1141

(24)

Table 3 Experimental wax disappearance temperature in K measured at local atmospheric pressure (0.9 bar) for the system (1  w) n-C14H30 + w n-C16H34, w is weight fraction of n-C16H34. w of C16H34

WDT (K)a

WDT (K)b

0.00 0.04 0.10 0.14 0.30 0.42 0.58 0.75 0.90 1.00

279.2 NA 277.5 NA NA NA NA 288.3 290.3 291.5

279.4 278.7 277.3 275.9 277.6 280.2 284.3 288.3 290.3 291.5

a

4.4. UNIFAC model Using UNIFAC activity coefficient model, the combinatorial term is used for describing the non-ideality of the systems containing normal paraffin and the residual term is omitted [30]         Fi Fi Z Fi F þ1  qi ln þ1 i (25) lng i ¼ ln 2 xi xi ui ui where area and segment fraction (u i, Fi) are defined by Eq. (21) and (22)with ri ¼ 0:6744C ni þ 0:4534

(26)

qi ¼ 0:54C ni þ 0:616

(27)

b

Experimental data from Ref. [21]. This work.

Table 4 Experimental wax disappearance temperature in K for the systems (1  w) n-C16 + w n-C18 and (1  w) n-C11 + w n-C18, w is weight fraction of n-C18 at local atmospheric pressure (0.9 bar). n-C16 + n-C18

n-C11 + n-C18

w of C18H38

WDT (K)

w of C18H38

WDT (K)

0.00 0.11 0.20 0.35 0.49 0.50 0.68 0.82 0.91 1.00

291.5 289.7 290.4 292 293.9 293.48 296.4 299.4 300.6 301.6

0.15 0.21 0.36 0.53 0.59 0.75 0.91 1.00

276.8 279.6 286.6 291.6 293.4 297.5 300.2 301.8

The expanded uncertainty Uc is Uc (T) = 0.1 K, Uc (w) = 0.01, Uc (P) = 0.1 bar (0.95 level of confidence).

S. Parsa et al. / Fluid Phase Equilibria 388 (2015) 93–99

304

97

305 Exp. this work Exp. [9] Exp. [36]

302 300

300 295

T (K)

T (K)

298 296 294

290 Exp. for C16+C18 system this work

285

C16+C18: Regular liquid- p.Wilson solid C16+C18: Ideal liquid- p. Wilson solid

280

292

Exp. for C11+C18 system this work

290

275

288

270 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

C11+C18: Regular liquid- p. Wilson solid C11+C18: Ideal liquid- p. Wilson solid

0

n - C16H34 mole fraction

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

n -C18H38 weight fraction

Fig. 2. Comparison between the data measured in this wotk for n-C16H34-n-C18H38 system with those reported in the litearture.

heavy component for n-undecane + n-octadecane system increases. Predicting WDT, different activity coefficient models comprising regular solution theory, predictive Wilson, predictive UNIQUAC, UNIFAC and ideal solution behavior were used to describe the solid phase. Liquid phase was described by ideal solution behavior, regular solution theory and predictive Wilson equation. In Table 5, using different combinations of activity coefficient models for the liquid and solid phases led to different accuracies. Comparing the first and second applied combinations of activity coefficient models for solid and liquid phases in Table 5 revealed that there is no significant difference between using regular solution model and ideal solution model for liquid phase while the solid phase was modeled by p. Wilson activity coefficient model for all three systems. This can be seen in Fig. 3 for the systems n-C11H24 + n-C18H38 and n-C16H34 + n-C18H38 and in Fig. 4 for the system n-C14H30 + n-C16H34. The point worth mentioning is that similar to reported data by Milhet et al. for n-C14H30 + nC16H34, the eutectic like behavior was observed as in Fig. 4 which is due to the fact that when a liquid binary mixture crystallizes, it first turns into a translucent solid phase so-called rotator phase in most cases. If the mole fraction of n-C16H34 is between the eutectic and the peritectic compositions, crystals are stable and remain in this

Fig. 3. Comparison between ideal and regular solution models for the liquid phase while the solid phase is described by predictive Wilson for the two systems nC11H24 + n-C18H38 and n-C16H34-n- C18H38.

state. Otherwise, crystals are metastable and end up by turning into an opaque triclinic phase. When the mole fraction of n-C16H34 is between 0.175 and 0.40, crystals are in rotator phase and in other composition the triclinic phase exists [21]. The point must be considered is that using ideal solution for the solid phase led to overestimation of the WDTs of the three systems. For instance, see the system n- C16H34 + n-C18H38 as shown in Fig. 5. This trend was similar to what reported by Ji et al. [9] investigating the binary systems n-C16H34 + n-C18H34, n-C16H34 + n-C20H42 and nC15H32 + n-C19H40. This suggests that the solid solution acts like a non-ideal phase showing positive deviation. In addition, a closer look in Figs. 6–8 showed that when liquid phase was predicted by ideal solution model while solid phase was described by p. Wilson, p. UNIQUAC and UNIFAC models, p. Wilson and p. UNIQUAC can predict the WDTs of all investigated systems accurately but UNIFAC gives the least accuracy for all the investigated systems. Finally, as shown in Table 5, for cases that p. Wilson model was used for considering the non-ideality of the liquid phase while the solid phase was modeled by different predictive models, this model was not a proper model to describe the liquid phase. The similar trend was reported by Esmaeilzadeh et al. [72] .

Table 5 Predictive capability of different predictive models for calculating the wax disappearance temperature of the investigated binary mixtures. No.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 a

AARD% ¼

AARD%a

Activity coefficient Liquid phase

Solid phase

n-C14 + n-C16

n-C16 + n-C18

n-C11 + n-C18

Ideal solution Regular solution Ideal solution Regular solution Ideal solution Regular solution Ideal solution Ideal solution Regular solution Regular solution p. Wilson p. Wilson p. Wilson p. Wilson p. Wilson

p. Wilson p. Wilson p. UNIQUAC p. UNIQUAC Regular solution Regular solution UNIFAC Ideal solution UNIFAC Ideal solution p. Wilson p. UNIQUAC Regular solution Ideal solution UNIFAC

0.125 0.128 0.313 0.321 0.791 0.798 0.809 0.812 0.820 0.810 1.110 1.210 1.520 1.861 2.251

0.152 0.154 0.100 0.110 0.403 0.404 0.400 0.431 0.405 0.439 1.911 1.490 1.173 1.610 2.950

0.107 0.115 0.090 0.092 0.259 0.284 0.136 0.190 0.140 0.258 2.001 1.941 1.375 1.970 1.780

exp 100Snj jWDTcal j j WDTj

n

WDTexp j

98

S. Parsa et al. / Fluid Phase Equilibria 388 (2015) 93–99

294

304 Exp. in this work

Exp. this work

292

302

Regular liquid- p. Wilson solid

290

Ideal liquid- p. Wilson solid

288

Exp. [21]

T (k)

286

T (K)

284 282

Ideal liquid- UNIFAC solid

300

Ideal liquid- p. Wilson solid

298

Ideal liquid- p. UNIQUAC solid

296 294

280

292

278

290

276

288

274 0

0.1

0.2

0.3 0.4 0.5 0.6 0.7 n -C16H34 weight fraction

0.8

0.9

0

1

Fig. 4. Comparison between ideal and regular solution models for the liquid phase while the solid phase is described by predictive Wilson model for the n-C14H30 + nC16H34 system.

0.1

288

T (K)

304

0.9

1

286 284 282

300

280

298

T (K)

278

296

276

294

274 0

292

0.1

290

0

0.1

0.2

0.3 0.4 0.5 0.6 n -C18H38 weight fraction

0.7

0.8

0.9

1

Fig. 5. Experimental and predicted WDT for the binary system n-C16H34 + n-C18H38 using ideal model for both liquid and solid phases.

305 Exp. this work

300

Ideal liquid- p. UNIQUAC solid Ideal liquid- p.Wilson solid

295

Ideal liquid- UNIFAC solid

290 285 280 275 270 0

0.1

0.2

0.3 0.4 0.5 0.6 n -C18H38 weight fraction

0.7

0.8

0.9

0.2

0.3 0.4 0.5 0.6 0.7 n-C16H34 weight fraction

0.8

0.9

1

Fig. 8. Comparison between predictive UNIQUAC, predictive Wilson and UNIFAC models for the solid phase while the liquid phase is described by ideal solution model for n-C14H30 + n-C16H34 system.

288

T (K)

0.8

Exp. this work Ideal liquid- p. UNIQUAC solid Ideal liquid- p. Wilson solid Ideal liquid- UNIFAC solid Exp. [21]

290

Ideal liquid-Ideal solid

0.7

294 292

302

0.3 0.4 0.5 0.6 n -C18H38 wt %

Fig. 7. Comparison between predictive UNIQUAC, predictive Wilson and UNIFAC models for the solid phase while the liquid phase is described by ideal solution model for n-C16H34 + n-C18H38 system.

Totally, based on the obtained results, it can be concluded that using ideal solution theory for the liquid phase and p. UNIQUAC and p. Wilson for the solid phase activity coefficient models led to the best predictive results for the studied systems.

Exp. this work

0.2

1

Fig. 6. Comparison between predictive UNIQUAC, predictive Wilson and UNIFAC models for the solid phase while the liquid phase is described by ideal solution model for n-C11H24 + n-C18H38 system.

6. Conclusions In this work, the WDTs for three binary systems including ntetradecane + n-hexadecane, n-hexadecane + n-octadecane and nundecane + n-octadecane have been experimentally measured using a visual observation method. The WDTs have been modeled using single solid solution theory for the solid phase. Different activity coefficient models including ideal solution, regular solution theory, p. Wilson. UNIFAC and p. UNIQUAC have been used to find the most accurate combination of models to predict the measured WDTs of the systems. The obtained results have revealed that generally there is no significant difference between the regular solution theory and ideal model for the liquid phase. In addition, the obtained results have revealed that among the examined activity coefficient models used for the solid phase p. UNIQUAC combined with ideal solution theory led to the most accurate predictions for n- C11H24 + n-C18H38 (0.09% AAD) and nC16H34 + n-C18H38 (0.08% AARD) systems and for n-C14H30 + nC16H34 system, combination of p. Wilson for the solid phase and ideal solution theory for the liquid phase gave the most accurate result (0.13% AARD). Finally, the results have demonstrated that p. Wilson and UNIFAC are not proper models to catch the non-ideality of the liquid phase and the solid phase, respectively.

S. Parsa et al. / Fluid Phase Equilibria 388 (2015) 93–99

Acknowledgement Financial support from Shiraz University of Technology is greatly acknowledged. Appendix A. Calculation of heat capacity difference of component i in solid and liquid phase [32]   cal ¼ 0:3033MWi  4:635  104 MWi T DCpi (A-1) g mol K Calculation of heat of sublimation difference for component i [28]   cal DHfi (A-2) ¼ 0:1426MWi T fi g mol

DHsub ¼ DHvap þ DHfi þ DHtr i i i

(A-3)

vaporization enthalpy is calculated using Morgan and Kobayashi correlation [34]:

DHvap i RTc

ð1Þ ð2Þ 2 ¼ DHð0Þ v þ vDHv þ v DHv

(A-4)

0:3333 DHð0Þ þ 12:865x0:8333 þ 1:171x1:2083 v ¼ 5:2804x

 13:116x þ 0:4858x2  1:088x2

(A-5)

0:3333 DHð1Þ þ 273:23x0:8333 þ 465:08x1:2083 v ¼ 0:80022x

 638:51x  145:12x2 þ 74:049x3

(A-6)

0:3333 DHð2Þ  346:45x0:8333  610:48x1:2083 v ¼ 7:2543x

þ 839:89x þ 160:05x2  50:711x3

x¼1

T Tc

DHtr ¼ DHtot  DHf 

DHtot

 KJ ¼ 3:7791Cn  12:654 g mol

(A-7)

(A-8)

(A-9)

(A-10)

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