UNIQUAC model for wax solution with pour point depressant

Fluid Phase Equilibria 280 (2009) 9–15

Contents lists available at ScienceDirect

Fluid Phase Equilibria journal homepage: www.elsevier.com/locate/fluid

UNIQUAC model for wax solution with pour point depressant夽 W.H. Chen, X.D. Zhang, Z.C. Zhao ∗ , C.Y. Yin Research Institute of Chemical Engineering, Dalian University of Technology, 158 Zhong Shan Road, Dalian, 116012, PR China

a r t i c l e

i n f o

Article history: Received 25 September 2008 Received in revised form 17 January 2009 Accepted 4 March 2009 Available online 19 March 2009 Keywords: UNIQUAC model Pour point depressant Wax precipitation DSC

a b s t r a c t It had been shown that after adding pour point depressant (PPD), the diffraction line intensities of paraffin mixtures progressively decreased without any significant variation of the Bragg angle values. This phenomena is due to the structure of paraffin mixture is partly transformed from orthorhombic into hexagonal form. Owing to the crystal lattice transformation, the amount of wax precipitated from oil treated with PPD in the experimental range is lower than that from untreated oil and the wax precipitated from treated oil is richer in the higher melting point paraffins than that from untreated oil. A thermodynamic model is established in this work to predict these experimental results. The liquid phase behavior is described by the LCVM mixing rule and an equation of state-GE model while the solid-phase non-ideality is represented by the UNIQUAC equation, respectively. New correlations for the melting points and solid–solid transition temperatures of treated paraffins are established based on the experimental results by differential scanning calorimeter (DSC). The experimental results indicated that the melting points and solid–solid transition temperatures of treated paraffins were both decreased. The calculation results for the amount and composition of wax precipitated from treated and untreated solutions at different temperatures have been compared with experimental observations. It has been shown that the predicted results agree well with the experimental ones. © 2009 Elsevier B.V. All rights reserved.

1. Introduction Crude oil is a complex mixture of light and heavy hydrocarbons. The heavy hydrocarbons tend to precipitate in the form of wax and asphalt when the temperature of the crude oil falls below the wax appearance temperature [1]. The amount of solid deposit precipitated from crude oil increases with the decreasing of temperature. Finally, these solids flock together and accumulate at the bottom of the well bores, production facilities and gathering-system pipelines, leading to the decrease in the operating efficiency. Many methods [2,3] have been attempted for the prevention of the crystals mating together. Wax inhibitors are usually added into waxy oil to minimize the transport problems. Therefore many theoretical and experimental studies [4–17] have been continually performed in order to reveal the PPD mechanism. Inhibition of wax crystallization is considered to occur in the presence of PPD by nucleation, adsorption or co-crystallization. It is generally believed that the PPD function by disrupting or preventing the formation of three-dimensional wax networks, leaving the amount of crystalline wax unaffected. However, according to

夽 Supported by the National Natural Science Foundation of China (No.: 10272029). ∗ Corresponding author. Tel.: +86 411 39893626; fax: +86 411 83633080. E-mail address: [email protected] (Z.C. Zhao). 0378-3812/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.fluid.2009.03.003

the experimental results carried out in our laboratory, the amount of wax precipitated from treated oil at different temperatures is lower than that from untreated oil and the wax precipitated from treated oil is richer in the higher melting point paraffins than that from untreated oil. It was also shown that these effects are due to the crystal lattice structure of paraffin mixture is transformed from orthorhombic into hexagonal form by pour point depressant [18]. In order to predict the experimental results, an UNIQUAC thermodynamic model is established in the present work. New correlations for the melting points and solid–solid transition temperatures of treated paraffins are established based on the DSC experimental results. 2. Experimental 2.1. Chemicals The waxes were supplied by the Dalian Petrochemical Corporation. The melting points of waxes estimated from differential scanning calorimetric measurements are 57.2 ◦ C and 67 ◦ C, respectively. The compositions of waxes measured by gas chromatography are listed in Figs. 1 and 2. Two different pour point depressants were studied in this work, the derivative of polyalkyl methacrylate (CE) was supplied by the Shanghai Kunshan Company and the alkyl naphthalene copolymer (T801) was supplied by the Dalian Petrochemical Corporation.

10

W.H. Chen et al. / Fluid Phase Equilibria 280 (2009) 9–15

Fig. 3. DSC curves of wax 1 with T801blends.

Fig. 1. Composition of paraffin mixture 1.

2.2. DSC experiment Differential scanning calorimetry (DSC) of samples sealed in aluminum capsules were performed during the heating cycle at a scanning rate of 10 ◦ C/min and in a temperature range of +80 ◦ C to −30 ◦ C. IR spectroscopy did not show any evidence of interactions between ethylene-vinyl acetate (EVA) and C24 D50 in CCl4 solution at room temperature, however, there were quite drastic modifications of IR spectra of EVA–paraffin blends in the dry state [7]. So the samples used in DSC experiment were paraffin–PPD dry blends. The dry samples could be prepared by using the vacuum technique. The paraffin mixture was mixed with certain proportion PPD in CCL4 solvent and then the solvent was removed by heating and vacuum-pumping. Figs. 3 and 4 show the thermograms of dry blend of paraffin mixture 1 with T801 and paraffin mixture 2 with CE, respectively. From the DSC thermograms it can be seen that after the waxes were treated with additives, the DSC curves of waxes were all shifted to lower temperature. The phase transition temperatures and energies obtained from the prominent peaks in thermograms are given in Tables 1 and 2. The experimental data show that the transition enthalpies had little changes especially the sum of solid–solid transition enthalpy and melting enthalpy. It means that the PPD has little effect on the total amount of wax which would completely precipitate at very low temperature. However, the melting points and the solid–solid transition temperatures of paraffin mixtures were both decreased

Fig. 4. DSC curves of wax 2 with CE blends.

Table 1 Effect of T801 PPD on transition temperatures (◦ C) and energies (J/g) of wax 1. Additive

0

1%

Melting temperature Melting enthalpy S–S transition temperature S–S transition enthalpy

57.2 135.9 39.0 15.41

51.2 134.4 35.7 20.89

while they were being treated with PPD. All of the results indicated that PPD do not completely prevent the paraffin mixture from precipitating; but just shift the precipitation toward a lower temperature. 3. Thermodynamic modeling The amount of PPD in wax solution is so little that its contribution to the molar composition of the original paraffin solution can be neglected. In other words, the molar composition of solution with and without PPD is the same. The effect of PPD on the thermodynamic behavior of waxy oil is modeled as a reduction in the melting points of the waxes and solid-phase transitions. In this Table 2 Effect of CE PPD on transition temperatures (◦ C) and energies (J/g) of wax 2.

Fig. 2. Composition of paraffin mixture 2.

Additive

0

1000 ppm

5000 ppm

Melting temperature Melting enthalpy S–S transition temperature S–S transition enthalpy

67 135.6 43.5 22.35

61.2 134.1 41.2 23.97

60.3 129.3 39.7 24.25

W.H. Chen et al. / Fluid Phase Equilibria 280 (2009) 9–15

case, the approaches which are used to describe wax precipitation in waxy oil are suitable for wax-pour point depressant system. When the liquid and solid phases are in thermodynamic equilibrium, the fugacity of component i in these phases must be the same, i.e.: fiL

=

fiS

(1)

11

Whereas for the parameter a, the LCVM mixing rule is used [22]. a = bRT



1− + Av Am

  GE  RT

1 −  xi ln Am

+

i

b bi

+

i

xi

ai bi RT (10)

fiL = xiL PϕiL

(2)

where Am , Av and  are constant, then the fugacity coefficient of component i in a mixture, for the PR EOS is given by the following equation:

√

PV  V + (1 + 2)b P (V −b) ˛ ¯i L bi (11) −1 − ln − √ ln ln ϕi = √ RT b RT 2 2 V + (1 − 2)b

fiS

(3)

with

where ϕiL represents the fugacity coefficient of component i in a liquid phase and P is the system pressure. The fugacity fiOS of component i in the pure solid reference state can be related to the pure subcooled liquid fugacity fiOL from the change of energy between the pure solid and the liquid at temperature T [19].

˛i =

At atmospheric pressure, the fugacity of component i in the liquid and solid phases can be calculated by using the following equations:

=

fiOL fiOS

iS xiS fiOS



= exp

f

Hi



1−

RT



1 − RT

f i

T



T

+

f

Ti

1 Cpi dT + R

T

Hit



RT



T 1− t Ti



Cpi T

T

(4)

dT

The pure liquid fugacity of component i at atmospheric pressure can be calculated by the following equation: OL fiOL = Pϕipure

(5)

Then the equilibrium constant can be written as follows: KiSL =

xiS xiL

=

1 − RT

ϕiL OL iS ϕipure

 T

f i

T



exp

f

Hi



1−

RT

1 Cpi dT + R





Tt

T

i

T

Cpi T

f

Ti

+

Hit RT

 1−

T Tit





dT

(6)

where Tf (K) and Hf (J mol−1 ) represent the fusion temperature and the enthalpy of fusion, respectively, whereas Tt (K) is the transition temperature and Ht (J mol−1 ) the enthalpy of the solid–solid transitions. Heat capacity changes between phase transitions, Cpi (J mol−1 K−1 ), were analyzed in the literature and found to be a linear function of temperature and proportional to the molecular weight. It can be written in the form [20]: L S Cpi = Cpi − Cpi = 1.2739MWi − 1.9467 × 10−3 MWi T

(7)

3.1. Liquid-phase non-ideality The fugacity coefficient of component i in the liquid phase is calculated by an EOS/GE model. Among the EOS models available, the modified PR equation of state is used. P=

RT a − V −b V (V + b) + b(V − b)

(8)

The parameters a and b of pure component are described by the conventional critical parameters approach. The critical properties and acentric factor required in the evaluation of equation of state parameters are obtained from the Gasem’s correlations [21]. For mixtures, the conventional linear mixing rule is kept for the parameter b: b=

i

xi bi

Av

+

1− Am



ln i +

1− Am





ln

b b ai + i −1 + bi b bi RT

(12)

The activity coefficient of component i is calculated using the UNIQUAC method. 3.2. Solid-phase modeling



f i

T



(9)

For describing the non-ideality of the solid phase, the Wilson equation was used to describe the non-ideality of the wax and satisfactory representation of narrow paraffin distribution was obtained at first. When paraffin distributions widen out, the non-ideality of solutions increase and the model over-estimates the precipitation of the lightest components. To overcome this problem, assuming that the high non-ideality between the heaviest and the lightest paraffins leads to the coexistence of several solid solutions, Coutinho [19] used the UNIQUAC model instead of Wilson equation. He also presented alternative methods of fixing parameters in the UNIQUAC model, which has been used to compute wax formation in diesel fuels [23], cloud points in fuels [24], and wax formation in crude oils at atmospheric pressure. The UNIQUAC equation is used to describe the activity coefficient in solid phase. The general UNIQUAC equation in terms of molar excess Gibbs energy is given as GE = RT



xi ln i =

n

xi ln

˚ 

i=1

i

xi

Z  qi xi ln i 2 ˚i n

+

i=1

⎡ ⎤   n n ij − ii ⎦ − xi qi ln ⎣ j exp − i=1

qi RT

j=1

(13)

with ˚i =

x ri

i

xr j j j

i =

x qi

i

xq j j j

(14)

The symbols ri and qi represent the dimensionless molecular structural parameters of pure component and have been given in the following correlations [19]: ri = 0.1Cn + 0.0672

(15)

qi = 0.1Cn + 0.1141

(16)

The predictive local composition concept allows the estimation of the interaction energies, ii which is used by the local composition models. The pair interaction energies between two identical molecules are estimated from the heat of sublimation of an orthorhombic crystal of the pure component i: 2 ii = − (Hisblm − RT ) Z

(17)

where Z is the coordination number and taken as 6 in the UNIQUAC model. The heats of sublimation are considered to be temperature independent and calculated at the melting temperature of the

12

W.H. Chen et al. / Fluid Phase Equilibria 280 (2009) 9–15

normal alkanes. They are equal to the sum of the heats of vaporization, melting and solid–solid transition. The heats of melting and solid–solid transition have been given in Ref. [25]. The heats of vaporization are given by Gopinathan and Saraf [26]. vap

Hi

3

= 1.081 × 10

 ×

(−1.418×10−2 ) + (Sgi Tbi )

31.98 log10 Tbi +

−1.573 22.12 Tbi



MWi

(18)

The parameter Sg is the specific gravity of component i and can be calculated by the following correlation: Sgi = 0.843593 − 0.128624 ni − 3.36159n3i − 13749.5n12 i

(19)

with ni = 1 −

Tbi Tci

(20)

where Tb (K) and Tc (K) represent the boiling point and the critical temperature, respectively and they can be obtained from the Gasem’s work [20]. The intermolecular acting forces between two n-alkanes are mainly London dispersion forces and arise along the contact surface of the molecules. In the solid phase, chain molecules act, to a large extent, as stiff rods. In this case the contact surface would be only dependent of the length of the short molecules. This means that the interaction energy between a long and a short molecule is the same as the one between two identical short molecules [27]: ij = ji = jj

(21)

where j represents the shorter chain n-alkane between molecules i and j. With this model, the phase behavior of complex hydrocarbon mixtures can be adequately predicted by using pure component properties only. 3.3. Properties of solid–liquid and solid–solid transitions The fusion temperatures of normal paraffins are estimated using the correlations proposed by Won [28]. f

Ti = 374.5 + 0.02617MWi − f

Ti = 411.4 −

32, 326 MWi

20, 172 MWi

(MWi ≤ 450 g/mol)

(MWi > 450 g/mol)

(22) (23)

Table 3 Amount of wax precipitated form solution 1 treated with T801. Temperature (◦ C)

Untreated oil

0.1%

25 20 15 10 5

0.610 0.890 2.035 3.856 5.436

0.223 0.598 1.267 2.659 4.364

Table 4 Amount of wax precipitated form solution 2 treated with CE. Temperature (◦ C)

Untreated oil

100 ppm

500 ppm

25 20 15 10 5

1.670 3.150 4.813 6.527 7.796

0.703 1.132 2.446 4.235 5.769

0.775 1.185 2.388 4.169 6.209

case, the fusion temperatures of treated paraffins are established in the following relational expression. f

Ti = 368.5 + 0.02617MWi − f

Ti = 405.4 −

32, 326 MWi

20, 172 MWi

(MWi ≤ 450 g/mol)

(26)

(MWi > 450 g/mol)

(27)

The solid–solid transition temperatures of treated alkanes are established as follows. n-paraffins with odd carbon number: 9 ≤ Cn ≤ 43 Tit = 0.0039Cn3 − 0.4249Cn2 + 17.28Cn + 89.80

(28)

n-paraffins with even carbon number: 22 ≤ Cn ≤ 42 Tit = 0.0032Cn3 − 0.3249Cn2 + 12.78Cn + 153.9 (29) The same hypothesis is adopted for the paraffin mixture 2 with CE copolymer. The DSC results show that the transition enthalpies had little changes, so the correlations previously proposed by authors [25] are used in evaluating the melting and solid–solid transition enthalpies of both normal and treated paraffins. 4. Modeling results and discussion The experimental data for the amount and composition of wax precipitated from treated and untreated oils at different temperatures previously proposed by authors [18] are listed in Tables 3–6,

The solid–solid transition temperatures of normal paraffins are calculated from the following correlations previously proposed by authors [25]. n-paraffins with odd carbon number:

Table 5 Composition (mass%) of wax from untreated solution 2.

9 ≤ Cn ≤ 43 Tit =0.0039Cn3 −0.4249Cn2 + 17.28Cn + 93.10

Com.

25 ◦ C

20 ◦ C

15 ◦ C

10 ◦ C

5 ◦C

C19 C20 C21 C22 C23 C24 C25 C26 C27 C28 C29 C30 C31 C32 C33 C34 C35 C36

0.357 1.078 2.476 4.250 6.701 7.146 7.539 6.870 7.401 6.900 8.225 7.873 8.270 7.785 6.576 4.902 3.428 2.222

0.275 1.150 2.861 5.086 7.989 8.230 9.211 8.168 8.718 8.308 8.980 7.722 7.194 5.748 4.488 2.916 1.904 1.053

0 1.187 2.922 5.195 8.164 8.405 8.333 8.467 8.742 8.018 8.363 7.498 7.438 5.566 4.084 2.867 1.896 0.985

0 1.188 2.974 5.228 8.286 8.841 10.29 9.433 9.889 9.739 8.905 7.151 6.359 4.466 3.272 2.067 1.241 0.674

0.402 1.374 3.394 6.041 9.724 10.12 10.56 10.11 10.13 8.535 8.300 6.419 5.313 3.640 2.623 1.671 1.098 0.549

(24)

n-paraffins with even carbon number: 22 ≤ Cn ≤ 42 Tit =0.0032Cn3 −0.3249Cn2 + 12.78Cn + 157.2

(25)

The DSC results indicated that the melting points and solid–solid transition temperatures of paraffin mixtures were both decreased while they were being treated with PPD. Therefore, the correlations for the melting points and solid–solid transition temperatures of normal paraffins mentioned above are not suitable for the present case. It is necessary to establish new correlations for these properties of treated paraffins. For paraffin mixture 1, it can be seen that the melting point dropped 6 ◦ C and the solid–solid transition temperature dropped 3.3 ◦ C from the DSC experimental data while it was treated with 1% T801 copolymer. It is assumed that the melting point depression of each alkane in wax 1 is 6 ◦ C and the solid–solid transition temperature depression of each alkane is 3.3 ◦ C. In this

W.H. Chen et al. / Fluid Phase Equilibria 280 (2009) 9–15

13

Table 6 Composition (mass%) of wax from solution 2 treated with 100 ppm CE. Com.

25 ◦ C

20 ◦ C

15 ◦ C

10 ◦ C

5 ◦C

C19 C20 C21 C22 C23 C24 C25 C26 C27 C28 C29 C30 C31 C32 C33 C34 C35 C36

0 0.390 0.892 2.147 3.082 5.495 4.295 6.500 6.763 8.924 8.695 10.66 9.865 9.905 7.756 6.539 4.703 3.390

0.237 0.833 1.576 3.164 4.396 5.579 5.988 7.057 8.147 9.849 9.214 10.40 9.313 7.719 6.553 4.744 3.259 1.966

0.333 0.862 1.948 3.348 5.173 5.737 6.534 8.397 9.128 11.14 10.69 10.46 9.284 6.649 4.302 2.927 1.972 1.112

0.284 0.998 2.479 4.438 7.124 9.301 7.641 8.808 9.853 9.411 10.36 8.021 7.233 5.335 3.849 2.451 1.553 0.858

0.442 1.013 2.534 4.528 7.372 8.065 9.839 10.46 9.601 9.577 9.536 8.015 6.802 4.665 3.398 2.159 1.310 0.684

Fig. 6. The weight percentage of wax precipitated from solution 2.

respectively. Two different solutions were studied in the experiment. The first solution is composed of a 10 wt% solution of the wax 1 in isooctane. The second one is constituted by a 10 wt% solution of the wax 2 in isooctane as a matrix. Consider 1 mol of sample and let S be the moles of solid phase with mole fraction of component i is xi S , zi represents the mole fraction of component i in original paraffin solution. And then at a given temperature, the amount of wax precipitated from oil is calculated from the following equation:

N S wax weight percentage (%) =

i=1

N

MWi xiS S

i=1

(30)

MWi zi

In the dry blends of paraffin mixture and PPD, the amount of PPD is 10 times higher than that in paraffin solutions and it is brought about to completion because the mass concentration of paraffin solution is 10%. The calculated and experimental results for the amount of wax precipitated from treated and untreated solutions are presented in Figs. 5 and 6. It can be seen that the predicted results for the amount of wax precipitated from treated oil is lower than that from untreated oil, which is consistent with the experimental observations. The predicted results for the untreated oils agree well with the experimental ones. Unfortunately, there are small differences between theoretical and experimental results for the treated solutions. This may be due to the sensitivity of each alkane to pour point depressant is not the same, then the melting point depression of each alkane is different and the solid–solid

Fig. 5. The weight percentage of wax precipitated from solution 1.

Fig. 7. The composition of wax precipitated form solution 2 without and with 100 ppm CE at 10 ◦ C.

transition temperature depression of each alkane is also unequal. However, it is suggested that the effect of PPD on each alkane is the same in this work. That may be the reason for the small differences of treated solutions. Generally speaking, the results obtained by the UNIQUAC local composition model show a good agreement with those of the experiments. The compositions of wax precipitated from solution 2 without and with 100 ppm CE copolymer at 10 ◦ C as well as 5 ◦ C are plotted in Figs. 7 and 8 to verify the feasibility of the approach adopted in

Fig. 8. The composition of wax precipitated from solution 2 without and with 100 ppm CE at 5 ◦ C.

14

W.H. Chen et al. / Fluid Phase Equilibria 280 (2009) 9–15

transformation, the amount of wax precipitated from treated oil is lower than that from untreated oil meanwhile the wax precipitated from treated oil is richer in higher melting point paraffins in the experimental range. The thermodynamic properties of phase equilibrium between solid and liquid for waxy oils are changed by PPD. So a model is established to simulate the influence of PPD on the thermodynamic behavior of wax crystallization. The LCVM mixing rule combined with an equation of state-GE model and the UNIQUAC equations are used to describe the liquid phase and the wax phase, respectively. New correlations for the melting points and solid–solid transition temperatures of treated paraffins are established based on DSC experimental results. Experimental results indicated that the melting points and solid–solid transition temperatures of wax were decreased duo to adding PPD. The predicted results for the amount and composition of wax precipitated at different temperatures agree well with the experimental ones.

Fig. 9. The composition of wax precipitated from solution 2 with 500 ppm CE at different temperatures. () Exp. data (25 ◦ C) (—) UNIQUAC (25 ◦ C); () Exp. data (15 ◦ C) (- - -) UNIQUAC (15 ◦ C); (夽) Exp. data (5 ◦ C) (–·–·–) UNIQUAC (5 ◦ C).

this work. It can be seen that the wax precipitated from treated oil is richer in the higher melting point paraffins than that from untreated oil. It had been shown that after adding pour point depressants, the diffraction line intensities of the paraffin mixture, progressively decreased without any significant variation of the Bragg angle values. This phenomenon is similar to the work of Dirand and co-workers [29] who studied the structure behavior changes of paraffin mixtures by XRD with increasing temperature. This decrease is the result of partial transformation of paraffin mixture from orthorhombic into hexagonal structure. The orthorhombic lattice is an ordered phase at lower temperature and the hexagonal lattice is a disordered phase at higher temperature. The wax with PPD will prefer to crystallize in a less ordered state which is more akin to the liquid phase. The addition of PPD in paraffin mixture makes the mixture maintain the similar structure to liquid phase. Thus the melting points of paraffin mixtures are lowered. This is means that the wax precipitated from treated oil at a given temperature is corresponds to the wax precipitated from untreated oil at a higher temperature, so the experimental phenomenon can be observed. The compositions of wax precipitated from solution 2 with 500 ppm CE PPD at different temperatures are also plotted in Fig. 9 in order to demonstrate the predictive capacity of the model using UNIQUAC. As the temperature of waxy oil is just lower the wax appearance temperature, the paraffins with higher melting point will precipitate first, followed by the lower melting point paraffins. So the solid phase becomes richer in light components with the decreasing temperature. This migration of components from the heavy to the lower component is well described in this figure. It can also be seen that the calculated values are in agreement well with the experimental ones. The model presented in this work shows a good performance at the composition of the wax precipitated from solution with and without PPD in the entire temperature range studied. All of the results indicate that the UNIQUAC model provides a good prediction for the thermodynamic properties of waxy solution with PPD. 5. Conclusions It had been shown that PPD changes the structure of wax from orthorhombic into hexagonal form. Due to the crystal structure

List of symbols a EOS attractive term parameter b EOS covolume parameter Cn carbon number Cp heat capacity (J mol−1 K−1 ) f fugacity GE excess Gibbs free energy (J mol−1 ) H enthalpy (J mol−1 ) K solid–liquid equilibrium constant MW molecular weight (g mol−1 ) P atmospheric pressure (Pa) q UNIQUAC structural parameter r UNIQUAC structural parameter R ideal gas constant (J mol−1 K−1 ) Sg specific gravity (kg m−3 ) S the moles of solid with the total feed of unity T temperature (K) V molar volume (m3 mol−1 ) x mole fraction for both phases z feed composition in mole fraction Greek letters ˛ EOS parameter ϕ fugacity coefficient  activity coefficient ii interaction parameters of UNIQUAC equation Superscripts f fusion L liquid phase S solid phase Sblm sublimation t solid–solid transition vap vaporization Subscripts b boiling property c critical property i component i Acknowledgements The authors would like to thank Chinese natural science foundation committee for supporting the project of rheological and breakage dynamics of oil drops in oil/water emulsion below the solidification point of oil drops and in turbulent flow field (No.: 10272029).

W.H. Chen et al. / Fluid Phase Equilibria 280 (2009) 9–15

References [1] A.M. Elsharkawy, T.A. Al-Sahhaf, M.A. Fahim, Fuel 79 (2000) 1047–1055. [2] A. Hunt, Oil Gas J. 7 (1996) 96–103. [3] M.G. Bernadiner, SPE Paper no. 25192 Presented at the International Symposium on Oilfield Chemistry, New Orleans, LA, 1993, pp. 2–5. [4] J. Hu, L.G. Zhang, Y.C. Dai, Acta Petrolei Sinica 12 (1996) 73–79. [5] X.Z. Ding, G.R. Qi, S.L. Yang, Polymer 40 (1999) 4139–4142. [6] K.S. Pedersen, H.P. Ronningsen, Energy Fuels 17 (2003) 321–328. [7] E. Marie, Y. Chevalier, F. Eydoux, L. Germanaud, P. Flores, J. Colloid Interface Sci. 290 (2005) 406–418. [8] S.P. Srivastava, R.S. Tandon, P.S. Verma, A.K. Saxena, G.C. Joshi, S.D. Phatak, Fuel 71 (1992) 533–537. [9] F.S. Zhang, B. Wang, Oilfield Chem. 12 (1995) 347–352. [10] G.A. Holder, J. Winkler, Nature 207 (1965) 719–721. [11] A.D. Randolphaph, M.A. Larson, Theory of Particulate Processes, Analysis and Techniques of Continuous Crystallization, Academic Press, New York, 1988, pp. 129–132. [12] I.D.M. Rubin, P.R.D. Munmaya, SAE Technical Paper Series, 1991, pp. 1–10. [13] J.W. Qian, G.R. Qi, X.Z. Ding, S.L. Yang, Fuel 75 (1996) 307–312.

[14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29]

15

J.W. Qian, G.R. Qi, D.L. Han, S.L. Yang, Fuel 75 (1996) 161–163. B. Wang, H.B. Zhang, F.S. Zhang, ACTA 19 (1998) 97–102. J.L. Zhang, C.J. Wu, W. Li, Y.P. Wang, Z.T. Han, Fuel 82 (2003) 1419–1426. H.S. Ashbaugh, X.H. Guo, D. Schwahn, R.K. Prudhomme, D. Richter, L.J. Fetters, Energy Fuels 19 (2005) 138–144. W.H. Chen, Z.C. Zhao, C.Y. Yin, Fuel, Submitted for publication. J.A.P. Coutinho, Ind. Eng. Chem. Res. 37 (1998) 4870–4875. K.S. Pedersen, P. Skovborg, H.P. Ronningsen, Energy Fuels 5 (1991) 924–932. W.Z. Gao, L.R.J. Robert, K.A.M. Gasem, Fluid Phase Equilib. 179 (2001) 207–216. C. Boukouvalas, N. Spiliotis, P. Coutsikos, N. Tzouvaras, D. Tassios, Fluid Phase Equilib. 92 (1994) 75–106. J.A.P. Coutinho, C. Dauphin, J.L. Daridon, Fuel 79 (2000) 606–616. F.I.C. Mirnate, J.A.P. Coutinho, Fluid Phase Equilib. 180 (2001) 247–255. W.H. Chen, Z.C. Zhao, L.J. Wang, Fluid Phase Equilib. 255 (2007) 31–36. N. Gopinathan, D.N. Saraf, Fluid Phase Equilib. 179 (2001) 277–284. J.A.P. Coutinho, K. Knudsen, S.I. Andersen, E.H. Stenby, Chem. Eng. Sci. 51 (1996) 3273–3282. K.W. Won, Fluid Phase Equilib. 30 (1986) 265–279. V. Chevallier, D. Petitjean, M. Bouroukba, M. Dirand, Polymer 40 (1999) 2129–2213.