Influence of pressure on the LLLE in water+n-alkyl polyoxyethylene ether+n-alkane systems

Fluid Phase Equilibria 163 Ž1999. 259–273 www.elsevier.nlrlocaterfluid

Influence of pressure on the LLLE in water q n-alkyl polyoxyethylene ether q n-alkane systems J.G. Andersen, N. Koak 1, Th.W. de Loos

)

Laboratory of Applied Thermodynamics and Phase Equilibria, Delft UniÕersity of Technology, Julianalaan 136, 2628 BL Delft, Netherlands Received 12 October 1998; accepted 7 June 1999

Abstract The influence of pressure and temperature on the phase behavior of the systems H 2 O q C 4 E 1 q C 8 and H 2 O q C 4 E 2 q C 8 is investigated. At constant pressure and increasing temperature, a 2 ™ 3 ™ 2 type phase behavior was observed for both the systems, while at constant temperature and increasing pressure, a 2 ™ 3 ™ 2 type phase behavior was found. The systems H 2 O q C 4 E 1 q C 10 , H 2 O q C 4 E 1 q C 8 and H 2 O q C 7 E 5 q C 12 are modeled with the SAFT HS equation of state. Although the model gives qualitatively the correct phase behavior, the quantitative match with the experimental data is found to be unsatisfactory. q 1999 Elsevier Science B.V. All rights reserved. Keywords: Data; Liquid–liquid–liquid equilibria; Equation of state; Water; Alkane; Surfactant

1. Introduction Surfactant flooding is one of the more promising tertiary oil recovery processes w1,2x. However, surfactants are generally expensive chemicals and in order to make surfactant flooding a profitable process, one has to minimize the consumption of surfactant and at the same time maximize the recovery of residual oil. In other words, it is important to know how to reach the optimal conditions of the surfactant flooding process. Since the reservoir conditions differ from reservoir to reservoir, and even with time in the same reservoir, the influence of a change in, for instance, pressure, temperature, oil, composition, surfactant, etc., on the phase behavior of waterŽ brine. q surfactantq oil mixtures has to be known in order to choose a suitable surfactant and surfactant concentration for the flooding process. A considerable amount of work has been done by several research groups to ) 1

Corresponding author. Tel.: q31-15-2782667; fax: q31-15-2788047; e-mail: [email protected] Current address: 300 Hyprotech Centre, 1110 Centre Street North, Calgary, Alberta, Canada T2E 2R2.

0378-3812r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 8 - 3 8 1 2 Ž 9 9 . 0 0 2 3 6 - 8

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investigate the phase behavior of water q surfactantq oil systems w3x. However, most of these measurements were performed at atmospheric conditions. Exceptions to these are the works of Kahlweit et al. w4x, Kim and O’Connell w5x and Sassen et al. w6–8x, who investigated the influence of pressure on the phase behavior of systems with water, oil, nonionic surfactants, ionic surfactants and electrolytes. This work reports results of experimental measurements on the two systems H 2 O q C 4 E 1 q C 8 and H 2 O q C 4 E 2 q C 8 for pressures up to 30 MPa. Further, an attempt is made to model the phase behavior of the systems H 2 O q C 4 E 1 q C 10 , H 2 O q C 4 E 1 q C 8 and H 2 O q C 7 E 5 q C 12 with SAFT HS equation of state w9x following up the work of Garcia-Lisbona et al. w10,11x. These researchers report success at describing the phase behavior of binary water q surfactant mixtures with SAFT HS EOS.

2. Experimental procedure 2.1. Equipment The high pressure experiments were carried out in the experimental setup described in detail by Sassen et al. w8x. The core of the apparatus is the sampling autoclave which is a modified Ruska through-window PVT cell with an inner volume of 100 ml. The cell can be used up to a pressure of 69 MPa and a temperature of 422 K. The coexisting liquid phases can be observed visually through the glass windows of the cell and are sealed by mercury at the bottom of the vessel. Mercury also acts as the pressure transmitting fluid and the pressure in the system is generated by compressed nitrogen. Sampling is carried out by pushing the coexisting phases upward with mercury through a sampling valve. The pressure in the cell was maintained constant to within "0.1–0.2 MPa during the sampling of phases. The pressure in the cell could be measured with an accuracy of "0.01 MPa with a digital pressure indicator. The sampling autoclave is placed in thermostated water bath. The bath water temperature could be maintained at a constant value within "0.02 K. The temperature of the water bath could be measured with an accuracy of "0.01 K using a Pt resistance thermometer. 2.2. Materials The water used was double distilled, and had a conductivity of less than 10y6 S cmy1. The n-octane and the nonionic surfactant C 4 E 1 were products of Merck Schuchardt and were both GC quality Ž) 99 wt.%.. The nonionic surfactant C 4 E 2 was also a Merck Schuchardt product of GC quality Ž) 98 wt.%.. Before use, the surfactants were stored over molecular sieve 3A. Both the surfactants and n-octane were used without further purification. 2.3. Method In the case of high pressure measurements, the sampling autoclave was filled with an overall composition of the mixture in the three-phase region. Then the pressure and temperature were adjusted to the desired set points. The mixture was then stirred for 30 min. Following this the stirring was stopped and the system was allowed to separate and settle in the present liquid phases. Normally,

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a satisfactory phase separation was obtained after approximately 1 h. Samples were then taken from different phases. This was done by slowly emptying the entire autoclave at constant pressure and temperature using the sampling valve at the top of the autoclave. The first amount of each liquid phase collected was thrown away and then samples of about 10 ml were taken from each phase. The large pressure drop over the sampling valve resulted in a flash of the liquid phases into two or three liquid phases. It was therefore necessary to homogenize the samples by quantitatively adding surfactant before analysis of the phases. The samples were analyzed by the use of a gas chromatograph. 3. Experimental results Prior to performing measurements at high pressures, the phase behavior of the two ternary systems system H 2 O q C 4 E 1 q C 8 and system H 2 O q C 4 E 2 q C 8 was determined at pressures at or close to atmospheric pressure. The experiments were performed at a constant H 2 O:C 8 ratio of 50:50 mass% which resulted in a pseudo-binary cross-section in the shape of a fish when the temperature of phase transitions was plotted vs. the mass fraction of nonionic surfactant g w8x. Tables 1 and 2 contain the results of these measurements. The symbol 2 refers to a two-phase system with the surfactant primarily in the bottom water rich phase. The symbol 2, on the other hand, refers a two-phase system with the surfactant mainly in the upper oil rich phase. The numbers 3 and 1 refer to three-phase and one-phase systems, respectively. In Figs. 1 and 2 the temperatures of the phase transitions 2 ™ 3, 3 ™ 2, 2 ™ 1 and 1 ™ 2 are plotted against gamma. Both systems show a transition of type 2 ™ 3 ™ 2 on increasing temperature. The ‘‘X-point’’ in the tail of the fish represents the highest mutual solubility of water and oil in the presence of a minimum amount of surfactant. These points are estimated to be T s 293.15 K and g s 0.53, and T s 362.15 K and g s 0.6 for the systems H 2 O q C 4 E 1 q C 8 and H 2 O q C 4 E 2 q C 8 , respectively. Table 1 Results of low pressure Ž ; 0.1 MPa. experiments for the system H 2 OqC 4 E 1 qC 8 a is the surfactant free mass fraction of octane. g denotes the mass fraction of C 4 E 1. TL is the temperature of the phase transition 2™3 and 2™1. TU is the temperature of the phase transitions 3™ 2 and 1™ 2.

a

g

TL wKx

TU wKx

0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

0.150 0.174 0.200 0.250 0.300 0.350 0.400 0.500 0.522 0.525 0.549

287.6 285.9 285.9 286.06 286.38 287.32 288.44 292.7 292.84 293.35 284.17

290.6 294.55 295.3 296.41 296.52 296.45 295.85 293.68 – 294.1 300.35

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Table 2 Results of low pressure Ž ; 0.1 MPa. experiments for the system H 2 OqC 4 E 2 qC 8 a is the surfactant free mass fraction of octane. g denotes the mass fraction of C 4 E 1. TL is the temperature of the phase transition 2™3 and 2™1. TU is the temperature of the phase transitions 3™ 2 and 1™ 2.

a

g

TL wKx

TU wKx

0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

0.176 0.200 0.251 0.301 0.350 0.399 0.453 0.500 0.600

– 341.67 340.9 – – 345.755 348.23 – 359.5

358.75 362.7 365.5 368.38 366.84 366.61 366.66 365.81 366.95

A comparison of Figs. 1 and 2 shows that the three-phase region widens up and moves to higher temperatures as the nonionic surfactant is changed from C 4 E 1 to C 4 E 2 . This is consistent with the results presented by Kahlweit et al. w3x. These researchers have shown that for a given oil ŽC k ., the larger the j-value of the surfactant ŽC i E j . at fixed i, the higher the temperature position and larger the width of the three-phase region. The elevated pressure measurements for both the systems investigated in this work were performed at a H 2 O:C 8 ratio of 50:50 mass% and the mass% of the nonionic surfactant was either 25 or 35 mass%. The temperatures at which the high pressure measurements were performed were chosen partly using the results of ‘‘fish measurements’’ described above, and partly by considering the pressure influence on the phase behavior of the ternary water q surfactantq oil system described by Sassen et al. w8x. The results of the elevated pressure measurements are contained in Tables 3 and 4 for the systems H 2 O q C 4 E 1 q C 8 and H 2 O q C 4 E 2 q C 8 , respectively. Fig. 3 shows the influence of pressure at constant temperature and the influence of temperature at constant pressure on the three-phase region for the system H 2 O q C 4 E 1 q C 8 . From Fig. 3a, it can be

Fig. 1. Pseudo-binary cross-section for the system H 2 OqC 4 E 1 qC 8 Ž P ; 0.1 MPa, a s 0.5..

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Fig. 2. Pseudo-binary cross-section for the system H 2 OqC 4 E 2 qC 8 Ž P ; 0.1 MPa, a s 0.5..

seen that at a temperature of 296.15 K, the three-phase region turns counterclockwise on increasing pressure. In other words, the solubility of water in the middle surfactant rich phase increases and that of octane decreases. Fig. 3b shows the reverse trend at a pressure 15 MPa on increasing temperature. At a constant pressure, on increasing the temperature, the solubility of octane in the middle surfactant rich phase increases. Fig. 4 shows similar trends for the system H 2 O q C 4 E 2 q C 8 . The trends for the two systems investigated in this work are in accordance with those reported by Sassen et al. w8x for the system H 2 O q C 4 E 1 q C 10 . Also, Kahlweit et al. w3x report that at constant pressure, for the same surfactant, an increase in the carbon number of the alkane moves the temperature location of the three-phase region to higher temperatures. A comparison of the experimental results of Sassen et al. w8x for the system H 2 O q C 4 E 1 q C 10 and the system H 2 O q C 4 E 1 q C 8 investigated in this work shows this trend. The evolution of the three-phase region at constant temperature and varying pressure, and at constant pressure and varying temperature, can be partially explained by formation or decomposition of hydrogen bonds between the surfactant and water. At a constant temperature, an increase in pressure corresponds to an increase in the hydrogen bonding between water and surfactant. In other words, the hyrophilicity of the surfactant increases. As a consequence, the solubility of water in the surfactant rich middle phase increases and that of the alkane decreases. On the other hand, an increase in temperature at constant pressure results in disruption of hydrogen bonds between water and surfactant and, as a consequence, the surfactant becomes more hydrophobic. This results in an increased solubility of the alkane in surfactant. However, a complete explanation of the observed experimental trends would also require consideration of the micellar structure of the mixtures w12x. 4. Modeling 4.1. Model and computations As mentioned above, in this work, an attempt was also made to model the phase behavior of a few water q surfactantq oil mixtures with the SAFT HS equation of state. The choice of the model was influenced by the recent work of Garcia-Lisbona et al. w10,11x in which these researchers report success at modeling a number of binary mixtures of water q surfactant with the SAFT HS model.

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Table 3 Results of high pressure measurements for the system H 2 OqC 4 E 1 qC 8 wt w , wt o and wt s denote the mass percentages of water, octane and C 4 E 1, respectively Ž a s 0.5.. T wKx

P wMPax

g

Phase

wt w

wt o

wt s

Upper Middle Lower Upper Middle Lower Upper Middle Lower Upper Middle Lower Upper Middle Lower Upper Middle Lower Upper Middle Lower Upper Middle Lower Upper Middle Lower Upper Middle Lower Upper Middle Lower Upper Middle Lower

1.08 34.71 84.29 0.85 38.96 82.76 0.70 46.19 77.68 2.25 22.52 85.86 2.33 22.55 85.98 1.31 30.10 85.34 1.35 30.74 85.56 0.75 45.19 79.80 0.76 46.09 77.70 4.45 18.34 86.27 1.88 27.01 86.25 1.48 29.44 85.34

84.17 13.16 0.43 85.88 11.80 0.52 86.68 8.58 0.94 76.86 25.95 0.60 76.36 26.09 0.78 82.04 17.15 0.49 81.92 16.85 0.38 86.36 8.49 0.79 86.57 8.68 0.96 69.31 31.80 0.45 78.89 21.30 0.27 81.52 17.71 0.30

14.75 52.13 15.28 13.27 49.24 16.73 12.63 45.22 21.39 20.89 51.52 13.54 21.31 51.36 13.24 16.65 52.76 14.17 16.73 52.40 14.06 12.89 46.32 19.41 12.67 45.24 21.33 26.24 49.86 13.27 19.23 51.69 13.48 17.00 52.85 14.36

293.15

5

0.25

293.15

15

0.25

293.15

20

0.25

296.15

5

0.25

296.15

5

0.25

296.15

15

0.25

296.15

15

0.25

296.15

30

0.25

296.15

30

0.25

300.15

15

0.25

300.15

20

0.25

300.15

30

0.25

Although the SAFT HS EOS does not account for the micellar structure of mixtures involving water and surfactant, it does explicitly take into account the formation of hydrogen bonds in these systems. The SAFT HS equations are not presented here and the reader is referred to the papers of Garcia-Lisbona et al. w10,11x for a detailed description of the SAFT HS EOS. The hydrogen bonding models for water and surfactant used in this work are the same as those used by Garcia-Lisbona et al. w10,11x. The hydrogen bonding models are described briefly below and again the reader is referred to the paper of Garcia-Lisbona et al. w10,11x for a detailed description. Water is modeled as having four

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Table 4 Results of high pressure measurements for the system H 2 OqC 4 E 2 qC 8 wt w , wt o and wt s denote the mass percentages of water, octane and C 4 E 1, respectively Ž a s 0.5.. T wKx

P wMPax

g

Phase

wt w

wt o

wt s

Upper Middle Lower Upper Middle Lower Upper Middle Lower Upper Middle Lower Upper Middle Lower Upper Middle Lower Upper Middle Lower Upper Middle Lower Upper Middle Lower Upper Middle Lower Upper Middle Lower Upper Middle Lower

0.37 39.71 86.66 0.35 45.73 86.26 0.32 50.02 79.63 1.54 26.08 89.59 1.27 29.49 88.12 1.31 28.88 87.35 0.48 36.97 78.83 2.44 18.96 90.04 1.09 22.53 89.75 1.53 24.73 90.06 1.60 25.76 87.48 1.55 25.39 88.33

86.32 7.77 2.21 86.98 5.95 0.45 87.54 5.72 0.73 78.59 14.92 0.08 81.22 12.60 0.12 80.45 12.19 0.49 86.53 7.49 0.14 71.54 22.46 1.09 79.41 17.91 1.36 77.82 19.00 0.16 76.47 14.50 0.37 76.95 16.19 0.06

13.31 52.52 11.13 12.67 48.32 13.28 12.14 44.26 19.64 19.87 58.99 10.32 17.50 57.91 11.76 18.23 58.92 12.16 12.99 55.53 21.03 26.02 58.58 8.87 19.50 59.56 8.89 20.66 56.26 9.78 21.96 59.73 12.15 21.50 58.42 11.61

348.15

5

0.25

348.15

15

0.25

348.15

20

0.25

358.15

5

0.25

358.15

15

0.25

358.15

15

0.35

358.15

20

0.25

363.15

5

0.25

363.15

15

0.25

363.15

15

0.25

363.15

15

0.35

363.15

20

0.25

hydrogen bonding sites: two positive Ž H . sites and two negative Ž e . sites. Only H–e bonding is allowed. The surfactant is modeled as having one positive site H Žowing to the terminal –OH group. , one negative site of type e Žowing to the terminal –OH group., a negative site eU Žcorresponding with the terminal –OH group. and three negative sites O per oxyethylene group. For the pure surfactant, only H–e bonding is allowed. In a mixture, the surfactant eU and O sites can cross-associate with H sites of molecules other than the surfactant, in this case water. The pure component parameters are

266

J.G. Andersen et al.r Fluid Phase Equilibria 163 (1999) 259–273

Fig. 3. LLLE triangles for the system H 2 OqC 4 E 1 qC 8 . Ža. T s 296.15 K: Žv . P s 5 MPa, ŽB. P s15 MPa, Ž'. P s 20 MPa. Žb. P s15 MPa: Žv . T s 293.15 K, ŽB. T s 296.15 K, Ž'. T s 300.15 K. Compositions are in mass fractions.

contained in Table 5. From Table 5, it can be seen that the only difference between the parameters for the various surfactants is in the number of alkyl and oxyethylene groups. This results in a different chain length m for different surfactants. Similarly, for n-alkanes, only m changes with a change in the carbon number of the alkane. Phase equilibrium calculations with the SAFT HS equation of state required calculation of implicit quantities such as a mole fraction not bonded at a site and its derivatives with respect to the molar amounts and the total volume. These were obtained numerically by an iterative solution of the corresponding implicit equations. The constant temperature and pressure two-phase computations were carried out by a combination of the conventional successive-substitution method for equilibrium calculations w13,14x with a Newton approach. In many cases, the convergence was quite slow for the successive-substitution method. Therefore, in order to speed up the computations, the Newton method was resorted to after a

Fig. 4. LLLE triangles for the system H 2 OqC 4 E 2 qC 8 . Ža. T s 358.15 K: Žv . P s 5 MPa, ŽB. P s15 MPa, Ž'. P s 20 MPa. Žb. P s 5 MPa: Žv . T s 348.15 K, ŽB. T s 358.15 K, Ž'. T s 363.15 K. Compositions are in mass fractions.

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Table 5 SAFT HS EOS pure component parameters m is the number of spherical segments, s is the diameter of each hard sphere segment, ´ the integrated mean-filed energy per spherical segment, ´ hb is the energy of the site–site hydrogen bond and K the bonding volume for the site–site interaction. C is the number of carbon atoms and O is the number of oxygen atoms per oxyethylene unit.

H 2 O w11x Surfactant w11x Alkane w26x

m

˚x s wA

Ž ´ r k . wKx

Ž ´ hb r k . wKx

˚ 3x K wA

1 Ž C q O y1.r3q1.2 Ž C y1.r3q1

3.60 3.855 3.86

4452 3135 3135

1558 3448 0

1.3578 0.391 0

sufficient convergence was achieved with the successive-substitution method. At constant temperature and pressure, the Newton method requires solving the following set of equations. m i II mi I g Ži. s y s 0; i s 1,2, . . . ,nc Ž1. RT RT where nc is the number of components and m i is the chemical potential of component i. I and II refer to the two phases. The Newton strategy for solving these equations is as follows. Let nIi be the molar amount of component i in phase I, and nIIi the molar amount of component i in phase II. The total molar amount of component i is constant and is given by the equation:

ž / ž /

nTi s n Ii q n IIi . Treating

n IIi

Eg Ži. En IIk

Ž2.

to be the independent molar amount, we have: s

1

nT E  m Ž i . rRT 4

nTII

En k

II

q

1

nT E  m Ž i . rRT 4

nTI

En k

I

Ž3.

where n T is the total molar amount of a phase. The derivatives in the previous equation are evaluated at constant temperature and pressure. With an EOS, it is more convenient to work with derivatives at constant temperature and total volume V. The relation between derivatives of chemical potential at constant temperature and pressure and the corresponding derivatives at constant temperature and total volume is given by the following equation: n T Em irRT En k

1 s T,P

n T Ž EPrEn i .

T ,V

n T Ž EPrEn k .

Ž n T EPrEV . T

RT

T ,V

q

n T Em irRT En k

.

Ž4.

T ,V

These derivatives are used in the following equation representing the iterative process: JD ns yg

Ž5.

Where the Jacobian matrix is given by: Js

Eg Ži. En IIk

Ž6. nc=nc

and, the correction vector is given by: D ns Ž D n1 ,D n 2 , . . . ,D n nc .

T

Ž7.

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268

The molar amounts are updated as follows: n IIi s n IIi q D n i

Ž8.

and n Ii s nTi y n IIi . Ž9. Deiters w15x and, recently, Michelsen w16x, have also presented Newton algorithms for performing phase equilibrium calculations. The Newton algorithm used in this work for two-phase constant temperature and pressure phase equilibrium calculations is very similar to that used by Michelsen w16x. The constant temperature and pressure multi-phase flash calculations were carried out using the multi-phase flash program of Heidemann w17x. This program uses the multi-phase successive-substitution scheme of Abdel-Ghani et al. w18x. 4.2. Modeling results In this section, the parameter subscripts 1, 2 and 3 always refer to water, surfactant and alkane, respectively. The cross-segment diameter si j was taken as Ž sii q sj j .r2 and the cross-bonding volume for site–site interaction K 12 was calculated as wŽ K 11r3 q K 21r3 .r2x 3. The first system considered is H 2 O q C 4 E 1. Garcia-Lisbona et al. w11x recommend the crossparameters w ´ 12rk s 3469.63 K, ´ hbrk Ž H–e and H–eU . s 1803 K, ´ hbrk Ž H–O . s 1874 Kx for this system. With these parameters, the calculated T y x sections for this system at pressures of 1 and 20 MPa are compared with the experimental data of Schneider w19x in Fig. 5a. At 1 MPa, the match with the experimental data is good in terms of lower and upper critical solution temperatures. The calculated closed-loops are much narrower than the experimental ones. The closed-loop at 20 MPa is much smaller than the experimental data and shows that the pressure influence is too strong. In order to get a better representation of the experimental data, the three cross-parameters were refitted to the upper and lower critical solution temperatures at 1 and 20 MPa and the values of the cross-parameters obtained were w ´ 12rk s 3486.28 K, ´ hbrk Ž H–e and H–eU . s 1760 K, ´ hbrk Ž H–O . s 1869 Kx. The calculated curves obtained by using the new cross-parameters are compared with the experimen-

Fig. 5. Temperature-composition sections for the system H 2 OqC 4 E 1. Ža. Cross-interaction parameters from Ref. w11x. Žb. Cross-interaction parameters estimated in this work. Experimental data from Ref. w19x.

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269

tal data in Fig. 5b. Although the match is still semi-quantitative, the overall representation is better. In the subsequent calculations involving the components H 2 O and C 4 E 1, the new cross-parameters were used. One of the reasons why the calculated slope Ž EPrET . critical of the lower critical solution behavior, regardless of the cross-parameters used, is smaller than the experimental values is the large magnitude of the calculated V E Žmolar excess volume. in comparison with the experimental values w20x. The sign of the calculated V E is negative as observed experimentally, but its magnitude is much larger. To an approximation, Ž EPrET . critical is inversely proportional to V E w21x. The system H 2 O q C 4 E 1 has been correlated by Knudsen et al. w21x using the SRK EOS in combination with the UNIQUAC G E model. These researchers were able to get an excellent correlation of this system although that required a fairly large number of temperature-dependent binary parameters. Also, of note is the work of Schneider w22,23x. Schneider used Porter and Flory–Huggins approaches and found that these equations gave the correct dependencies of thermodynamic excess functions. Fig. 6Ža,b. contains a comparison of the correlation results for the binary systems H 2 O q C 7 E 5 and C 7 E 5 q C 12 with the experimental data of Sassen et al. w24x. Fig. 6a is for the system C 7 E 5 q H 2 O and to generate this figure, the cross hydrogen bonding parameters from the H 2 O q C 4 E 1 system were used. The integrated mean-field energy parameter was fitted to the lower critical solution temperatures at various pressures and the value obtained was ´ 12rk s 3040 K. The model gives the correct qualitative trends although the match with the experimental data is semi-quantitative at best. Fig. 6b contains the correlation for the system C 7 E 5 q C 12 with ´ 23rk s 3087 K. Again, the model gives qualitatively the correct results but the calculated curves are much narrower than the experimental ones. Next, we present the modeling results for the ternary system H 2 O q C 7 E 5 q C 12 . All binary parameters except for H 2 O q C 12 system are reported above. The integrated mean-field energy parameter for this binary sub-system was obtained by a fit to the high pressure vapor–liquid critical curve data of Brunner w25x and a value of 3325 K was obtained for ´ 13. Fig. 7 contains the calculated three-phase ŽLLLE. triangles at a pressure of 20 MPa for a number of temperatures. It can be seen that as expected, the three-phase region opens up with increasing temperature, turns clockwise and then closes. So the qualitative trend is correct. However, we do not have any experimental data for the phase compositions. The only available data for this ternary system are the sealed tube measurements

Fig. 6. Ža. Temperature-composition sections for the system H 2 OqC 7 E 5. Žb. Temperature-composition sections for the system C 7 E 5 qC 12 . Experimental data from Ref. w24x.

270

J.G. Andersen et al.r Fluid Phase Equilibria 163 (1999) 259–273

Fig. 7. Calculated LLLE triangles for the system H 2 OqC 7 E 5 qC 12 . P s 20 MPa: Žv . T s 345 K, ŽB. T s 375 K, Ž'. T s 405 K, Žinverted triangle atop another triangle. T s 435 K, Ž%. T s 465 K, Ž=. T s 470 K, ŽI. T s 475 K. Compositions are in mass fractions.

reported by Sassen et al. w24x. Their experimental results indicate that the three-phase regions opens at approximately 340 K and closes at approximately 395 K. The calculated three-phase triangles open at approximately the correct lower temperature, but the three-phase region extends to much higher temperatures than observed experimentally. Next, we present the model three-phase Ž LLLE. results for the system H 2 O q C 4 E 1 q C 10 . For Fig. 8Ž a,b. ´ 13rk s 3325 K was used in the calculations. Since there is no LLE data available for the sub-system ŽC 4 E 1 q C 10 . , ´ 23rk was taken to be Ž ´ 22rk .Ž ´ 33rk . s 3135 K. The results of calculations at a constant pressure of 0.1 MPa and varying pressures are shown in Fig. 8a. Fig. 8b shows the influence of pressure at a temperature of 345 K. The qualitative trend is correct but in comparison with the experimental data of Sassen et al. w8x, the three-phase region opens up at much

(

Fig. 8. LLLE triangles for the system H 2 OqC 4 E 1 qC 10 . Ža. P s 0.1 MPa: Žv . T s 325 K, ŽB. T s 345 K. Žb. T s 345 K: ŽI. P s 0.1 MPa, Žq. P s10 MPa. Compositions are in mass fractions.

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Fig. 9. LLLE triangles for the system H 2 OqC 4 E 1 qC 10 . Ža. P s 0.1 MPa: Ž=. T s 300 K, Žv . T s 303 K, ŽB. T s 305 K, Ž'. T s 315 K, Žinverted triangle atop another triangle. T s 325 K, Ž%. T s 335 K. Žb. T s 305 K: ŽB. P s 0.1 MPa, Žq. P s10 MPa. Compositions are in mass fractions.

higher temperatures and seems to be persisting to much higher temperatures also. Knudsen et al. w21x report similar results while modeling the three-phase triangles for the system H 2 O q C 4 E 1 q C 8 with SRK EOS in combination with UNIQUAC G E model. In order to obtain the three-phase region at approximately the correct temperatures, ´ 13rk and ´ 23rk were treated as adjustable parameters. Fig. 9 shows the correlation for the system H 2 O q C 4 E 1 q C 10 with ´ 13rk s 3773.27 K and ´ 23rk s 3197.90 K. Fig. 9a is at a constant pressure of 0.1 MPa. Although the correlation is still semi-quantitative in comparison with the experimental data, some progress were made. The three-phase region opens up at lower temperatures at approximately the correct temperature but still persists to higher temperatures Žapproximately 20 K. . The experimental three-phase region at a pressure of 0.1 MPa opens at approximately 297 K and closes at approximately 318 K. Perhaps one reason why the calculated three-phase region opens up at lower temperatures is that ´ 13rk has been increased to artificially increase the attraction between water and oil. Based on a fit to binary sub-systems only, the model is not able to account for the enhanced mutual solubility of water and oil in the presence of the surfactant. It was mentioned before that the SAFT HS as used in this work does not account for the micellar structure of the mixtures. It is believed w12x that this feature of the water q surfactantq oil mixtures is an important consideration in phase separation phenomenon. Perhaps this is one area where the model can be improved to give better agreement with experimental data. Fig. 9b shows the influence of pressure at a temperature of 305 K. At this temperature, the qualitative trend with an increase in pressure is correct. However, as compared with the experimental data w8x, the pressure influence is not strong enough. The final system investigated in this work is the system H 2 O q C 4 E 1 q C 8 . The modeling results obtained for this system were similar in qualitative trends and quantitative accuracy to that for the system H 2 O q C 4 E 1 q C 10 . Hence, the results are not shown here.

5. Conclusions From the measurements performed, it is clear that pressure and temperature can have a significant influence on the phase behavior of water q nonionic surfactantq oil systems. For both the systems

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studied, the qualitative effect of a change in pressure or temperature on the phase behavior of the systems was found fully consistent with what was reported earlier by Kahlweit et al. w4x and Sassen et al. w8x. Consequently, we observed a phase behavior of type 2 ™ 3 ™ 2 with increasing temperature Žconstant pressure. in both systems, and a 2 ™ 3 ™ 2 behavior upon increasing pressure at constant temperature. The change in nonionic surfactant from C 4 E 1 to C 4 E 2 caused the three-phase region to widen up and shift to higher temperatures. Also, this is in accordance with the results of Kahlweit et al. w3x, namely that for a given oil ŽC k ., the larger the j-value of the surfactant Ž C i E j . at fixed i, the higher the temperature position and width of the three-phase region. Our modeling results show that although the SAFT HS EOS in its present form is able to give qualitatively the correct phase behavior for waterq nonionic surfactantq oil systems, the quantitative agreement with the experimental data is unsatisfactory. Perhaps the agreement between model results and the experimental data can be made better by incorporating the micellar structure of such systems in the model. A description of complex system such as waterq surfactantq alkane with its complicated dependencies on temperature, pressure and composition requires a model of the liquid state where delicate interactions with the exhibition of micelles, micro-emulsions and hydrogen bonds are considered.

Acknowledgements We are grateful to Dr. A. Galindo for information regarding the modeling research work on water and surfactant mixtures at Sheffield University, UK.

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