Flash points of partially miscible aqueous–organic mixtures predicted by UNIFAC group contribution methods

Fluid Phase Equilibria 345 (2013) 45–59

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Flash points of partially miscible aqueous–organic mixtures predicted by UNIFAC group contribution methods Horng-Jang Liaw a,b,∗ , Tsung-Pin Tsai b a b

Department of Safety, Health and Environmental Engineering, National Kaohsiung First University of Science and Technology, 2 Jhuoyue Road, Kaohsiung, Taiwan Department of Occupational Safety and Health, China Medical University, 91 Hsueh-Shih Road, Taichung, Taiwan

a r t i c l e

i n f o

Article history: Received 26 November 2012 Received in revised form 7 February 2013 Accepted 15 February 2013 Available online 26 February 2013 Keywords: Flash point UNIFAC Partially miscible mixtures Aqueous–organic mixtures Prediction

a b s t r a c t This work predicts the flash points of partially miscible aqueous–organic mixtures using the flash point prediction model of Liaw et al. (J. Chem. Eng. Data 55 (2010) 3451–3461) handling non-ideal behavior through liquid phase activity coefficients evaluated with UNIFAC-type models, which do not need experimentally regressed binary parameters. Validation of this entirely predictive model is conclusive with the experimental data over the entire flammable composition range for 10 aqueous–organic binary and ternary mixtures. Overall, the model describes the experimental data of flash point well when using UNIFAC-type models to estimate the activity coefficient. If the LLE UNIFAC parameters are not accessible, a model based upon the VLE UNIFAC parameters provides an acceptable means of predicting flash point for partially miscible aqueous–organic mixtures, as revealed by a comparison between predicted and experimental data. © 2013 Elsevier B.V. All rights reserved.

1. Introduction In 2012 in Taiwan, an explosion resulted in damage to a waste water tank during hot work, defined by the US Occupational Safety and Health Administration (OSHA) as electric or gas welding, cutting, brazing, or similar flame or spark-producing operations [1]. The incident investigation indicated that flammable liquids partially miscible with water were present in the waste water. The fire and explosion hazards of liquids are primarily characterized by their flash points [2]. The flash point is defined as the temperature at which a liquid emits sufficient vapor to form a combustible mixture with air [3]. Because the cost of deriving flash point data from test instruments is very high, NT$20,000 (US$600) per sample in Taiwan, several alternative models for predicting the flash points of different type of mixtures are proposed. Most of the models were developed for miscible mixtures [2,4–15]. The models developed for partially miscible mixtures are only those proposed by us [16–19]. The partial miscibility of the mixtures is attributed to the strong non-ideality of the liquid phase; thus, models handling the non-ideality of the solution, testing for partial miscibility span and computing the flash point in a predictive manner, requiring a binary

∗ Corresponding author at: Department of Safety, Health and Environmental Engineering, National Kaohsiung First University of Science and Technology, 2 Jhuoyue Road, Kaohsiung, Taiwan. Tel.: +886 7 6011000x7606. E-mail address: [email protected] (H.-J. Liaw). 0378-3812/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.fluid.2013.02.013

interaction parameter from the literature. The non-ideality of the liquid phase is accounted for by liquid-phase activity coefficients computed by means of thermodynamic models. The frequently used NRTL and UNIQUAC thermodynamic models, require binary interaction parameters regressed on experimental data, and are, thus, often missing due to the vast combinations of possible mixtures. In contrast, predictive models such as the UNIFAC models [20,21] do not need experimental binary interaction parameters. Instead, chemical group contributions obtained from a large database are summed to evaluate the interaction parameters, and can be used to compute mixture flash points [13,22–25]. The original UNIFAC model [20,21] splits the activity coefficient into combinatorial and residual parts. To improve the performance of the original UNIFAC model for the prediction of vapor–liquid equilibrium (VLE), liquid–liquid equilibrium (LLE), and excess enthalpies, many modifications are suggested [26–33]. However, the studies on the modifications of the UNIFAC model to estimate LLE are still very scarce, as are data for UNIFAC group interaction parameters, e.g., the cyclic compounds are not included in literature. The modification developed by Hooper et al. for LLE of water–organic systems [31] is limited to few mixtures, and the aqueous–alcohol mixtures are not included at all. The group interaction parameters are very limited for the A-UNIFAC model developed for VLE and LLE [32,33]. The mixtures applicable to Hooper’s study [31] and A-UNIFAC model [32,33] are fewer than those applicable to the modification by Magnussen et al. [30]. Gmehling and Rasmussen were the first to calculate the flash points of mixtures using the UNIFAC model to estimate the liquid

46

H.-J. Liaw, T.-P. Tsai / Fluid Phase Equilibria 345 (2013) 45–59

phase activity coefficients and Zabetakis’s correlation [34] to estimate the lower flammability limits [13]. They considered mixtures of flammable solvents such as chloroform with methyl ethyl ketone or methyl acetate, isobutanol + toluene and methanol + methyl acetate, and aqueous–organic mixtures, water with methanol, ethanol, or 2-propanol. Vidal et al. combined the flash point prediction models of Liaw et al. [4,5] with the UNIFAC model to predict the minimum flash point behavior of highly non-ideal solutions such as octane + ethanol and octane + 1-butanol, and estimated the flash points of aqueous–ethanol mixtures [22]. Recently, the general flash point prediction model for miscible mixtures proposed previously [6] was combined with the UNIFAC-type models to predict the flash points of miscible mixtures systematically for 24 flammable solvents and aqueous–organic binary and ternary mixtures, including ideal mixtures as well as mixtures both Raoult’s law-negative and positive [23]. Moghaddam et al. assessed the models by Liaw et al. [4,6], Wickey and Chittenden [15], and Catoire et al. [12] for the estimations of flash points for six mixtures of flammable solvents, and concluded that the model by Liaw et al. combined with the UNIFAC model predicted the flash points of mixtures with good accuracy [24]. All four of these works focused on miscible mixtures; application of UNIFAC-type models to predict the flash points of partially miscible mixtures was only our previous study for binary aqueous–organic solutions, which only gave brief results for four aqueous–alcohol solutions [25], in the literature search. The flash point estimation for ternary partially miscible mixtures is quite different from that of binary analogs [16,19], and application of UNIFAC-type models to such ternary systems was not found in our literature review. To our knowledge, the models developed for partially miscible mixtures to date are only the four proposed in our previous studies, which are for flammable solvents and aqueous–organic binary and ternary mixtures [16–19]. The general model for partially miscible mixtures [19] is reducible for flammable solvents and aqueous–organic binary and ternary mixtures. In this work, we apply it to investigate the flash points of binary and ternary partially miscible aqueous–organic mixtures, presenting some experimental data for the first time. Short chain alcohols, such as butanol, are commonly used solvents in chemical and pharmaceutical processes [35]. Ndodecyl-␤-d-glucopyranoside + water + n-dodecane + 1-pentanol and n-decyl-␤-d-glucopyranoside + water + n-octane + 1-butanol are two microemulsions that have been well studied [36,37]. Butyl acetate and butyl propionate are used as entrainers to separate azeotropic mixtures such as water + acetonitrile and water + ethanol, respectively, in chemical processes [38,39]. Cyclohexanone has the potential to be an organic solvent for recovery of butyric acid and propionic acid from water [40,41]. The partially miscible binary aqueous solutions of 1-butanol, 2-butanol, isobutanol, 1-pentanol, butyl acetate, butyl propionate, octane, cyclohexanone, and the ternary mixtures of water + ethanol + 1butanol and water + butyl acetate + 1-butanol were, thus, selected as samples for study in this work.

2. Experimental protocol An HFP 362-Tag Flash Point Analyzer (Walter Herzog GmbH, Germany), which met the requirements of the ASTM D56 standard [42], was used to measure the flash points of a variety of partially miscible aqueous–organic mixtures (water + butyl acetate, water + butyl propionate, water + cyclohexanone, and water + butyl acetate + 1-butanol) with different compositions, using a closed cup method. The apparatus consisted of an external cooling system, test cup, heating block, electric igniter, sample thermometer, thermocouple (sensor for fire detection), and indicator/operating

display. The apparatus incorporates control devices that program the instrument to heat the sample at a specified rate within a temperature range close to the expected flash point. The literature data and the estimated data based on our previously proposed model [19] were used as the expected flash points for pure substances and mixtures, respectively. The flash point was automatically tested using an igniter at specified temperature test intervals. If the expected flash point was lower than or equal to the change temperature, heat rate-1 was used and the igniter was fired at test interval-1. If the expected flash point was higher, heat rate-2 was used and the igniter was fired at test interval-2. Using the standard method, the change temperature is laid down by the standard and cannot be changed. The first flash point test series was initiated at a temperature equivalent to the expected flash point minus the start-test value. If the flash point was not determined when the test temperature exceeded the sum of the expected flash point plus the end-of-test value, the experimental iteration was terminated. The instrument operation was conducted according to the standard ASTM D56 test protocol [42] using the following parameters: start test, 5 ◦ C; end of test, 20 ◦ C; heat rate-1, 1 ◦ C/min; heat rate-2, 3 ◦ C/min; change temperature, 60 ◦ C; test interval-1, 0.5 ◦ C; and, test interval-2, 1.0 ◦ C. The liquid mole fraction was determined from the mass measured using a Setra digital balance (EL-410D: sensitivity, 0.001 g; maximum load, 100 g). The prepared mixtures were stirred by a magnetic stirrer for 30 min before the flash point test. A Milli-Q plus was used for water purification. n-Butyl acetate (99.5%), and cyclohexanone (99.5%) were sourced from Panreac (Spain). n-Butyl propionate (99%) was purchased from Alfa Aesar (Lancaster, England), and 1-butanol (99.9%), from J.T. Baker (USA). 3. Flash point prediction model 3.1. General model for predicting the flash point of partially miscible mixtures Within the mutual-solubility region, the flash point was evaluated by the method for a multi-component i miscible analog, including the modified equation of Le Chatelier (Eq. (1)), the Antoine equation (Eq. (2)), and a model for estimating activity coefficients  i [19]: 1=

sat  xi i Pi,T i= / kl

sat Pi,fp

sat log Pi,T = Ai −

Bi T + Ci

(1)

(2)

where the summation runs over all flammable components, kl is the sat , the vapor presnon-flammable components of the mixture. Pi,fp sure of the pure flammable component, i, at its flash point, Ti,fp , can be estimated using the Antoine equation. Within the partially miscible region, the two liquid phases are in equilibrium with compositions defining a so-called tie line. A property of vapor–liquid–liquid equilibrium is that any liquid composition located on this tie-line, in particular, the composition of both liquid phases in equilibrium, is in equilibrium with a single vapor composition located on the so-called vapor line [43,44]. As the flash point is related to the vapor composition, it should keep constant whatever the liquid composition on the LLE tie line. For a binary mixture, a single tie line exists and the flash point is constant for the whole composition range within the partial miscibility region [17,18]. For a ternary mixture several tie lines lead to several flash point values within the partial miscibility region [16,19]. For two liquid phases in equilibrium in which the reference fugacity is the same, the equilibrium compositions can be estimated by the

H.-J. Liaw, T.-P. Tsai / Fluid Phase Equilibria 345 (2013) 45–59

equilibrium equality of the compound fugacities in each phase, and such an equality is reducible as [19]: (xi i )˛ = (xi i )ˇ

i = 1, . . . , N

(3)

47

The group interaction parameter,  mn , is given by:

 a mn

mn = exp −

(13)

T (i)

where ˛ and ˇ refer to the two coexisting liquid phases. The flash point within each tie line can be calculated by substituting into Eqs. (1) and (2) the value of the equilibrium composition estimated by Eq. (3) in an iterative procedure. 3.2. UNIFAC-type models Recently, the predictions of our previously proposed model for miscible mixtures combining the original UNIFAC and modified UNIFAC-Dortmund 93 models gave good agreement with the measured flash points [23]. Thus, the original UNIFAC model and the modified UNIFAC-Dortmund 93 model were used to describe the liquid phase activity coefficient in the estimation of the flash points in this study. The tie lines were estimated using Eq. (3) in combination with the UNIFAC model as modified by Magnussen et al. [30], whose interaction parameters were obtained by fitting to the LLE data. 3.2.1. Original UNIFAC The original UNIFAC model [20,21] expresses the activity coefficient as the sum of the combinatorial and residual parts:

Eqs. (10)–(13) also hold for ln k , except that the group composition variable, k , is now the group fraction group k in pure fluid i. 3.2.2. The modified UNIFAC-Dortmund 93 In this modified model, the combinatorial term is given as [26,27]: ln iC = ln

i xi

+1−

i xi

−



z   q ln i + 1 − i 2 i i i



(14)

where 3/4

i =

xi ri



(15)

3/4 xr j j j

and the interaction parameter,  mn , in the residual part is given by:



mn = exp

−

amn + bmn T + cmn T 2 T



(16)

(4)

The group contributions of these parameters are systematically improved by being regressed using an ever larger experimental data set within the UNIFAC consortium [45].

accounts for differences in size The combinatorial part, ln and shape of the molecules, and the residual part, ln iR , accounts mainly for the effects that arise from energetic interactions between the groups. The combinatorial part is expressed as:

3.2.3. Original UNIFAC for LLE calculation Magnussen et al. modified the original UNIFAC model for LLE application by regressing the interaction parameters with LLE experimental data [30].

ln i = ln iC + ln iR iC ,

i z    + qi ln i + li − i xj lj xi 2 xi i N

ln iC = ln

(5)

j

where z li = (ri − qi ) − (ri − 1); 2

z = 10

(6)

i , the segment fraction of component i, and  i , the surface area fraction of component i, are defined as: x ri

i =

i

i =

i

(7)

xr j j j

x qi

(8)

xq j j j

where ri and qi are the pure component volume parameter and pure component area parameter, respectively. The residual part is obtained using the following relations: ln iR =



(i)

(i)

k (ln k − ln k )

(9)

k

where



ln k = Qk 1 − ln

  m

m =

 m mk

−

 m  km  m

n

Q Xm

m n

Qn Xn

(10)

(11)

and the fraction of group m in the mixture, Xm , is given by:



Xm =

(i)

m xi

i  i

(i)  x n n i

4. Results and discussion 4.1. Parameters and data used in this manuscript



n nm

3.2.4. Binary interaction parameters used to estimate the activity coefficient Determining the flash point of a partially miscible mixture is a problem that involves issues related to LLE and VLE: the flash point definition of “sufficient vapor to become a combustible mixture” is related to VLE (Eqs. (1) and (2)), while partial miscibility concerns LLE as shown by Eq. (3). Thus, LLE parameters are used in Eq. (3) to estimate the tie line equilibrium liquid compositions, and VLE parameters are used in Eqs. (1) and (2) to compute the flash point. The flash point in the mutual solubility region is estimated by the VLE parameters. The span and the constant flash point within each tie line are estimated using the VLLE model, as suggested in previous studies [16,18,19], where LLE parameters are used in Eq. (3) and VLE parameters are used in Eqs. (1) and (2), with Eqs. (1)–(3). The constant flash point within each tie line was estimated based on the estimated span approaching flammable component. In our study, the VLE model, in which only VLE parameters are used in Eqs. (1)–(3), was also used to estimate the flash points for comparison.

(12)

The general flash point prediction model for partially miscible mixtures, as described in Section 3.1, was used for water + 1-butanol, water + 2-butanol, water + isobutanol, water + 1pentanol, water + butyl acetate, water + butyl propionate, water + octane, water + cyclohexanone, water + ethanol + 1butanol, and water + butyl acetate + 1-butanol. The VLE activity coefficients were estimated using the original UNIFAC and UNIFAC-Dortmund 93 models [20,21,26,27], and the LLE analogs were estimated using the UNIFAC model as modified by Magnussen et al. [30]. The prediction results were compared with the

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H.-J. Liaw, T.-P. Tsai / Fluid Phase Equilibria 345 (2013) 45–59

Table 1 Measured flash points for binary mixtures. x1

Tfp (◦ C) Water (1) + butyl acetate (2)

0.0 0.01 0.025 0.04 0.041 0.042 0.045 0.047 0.05 0.06 0.065 0.067 0.068 0.069 0.07 0.075 0.08 0.085 0.095 0.1 0.19 0.2 0.25 0.28 0.29 0.3 0.32 0.4 0.5 0.6 0.7 0.8 0.9 0.95 0.97 0.98 0.985 0.986 0.987 0.99 0.992 0.995 0.998 0.9983 0.9985 0.9987 0.999 0.9991 0.9992 0.9993 0.9994 0.9995 0.9996 0.9997

Table 2 Measured flash points within the mutual solubility region for water (1) + 1-butanol (2) + butyl acetate (3).

27.5 28.1 28.9 – – – – – 29.3 28.6 28.6 28.6 28.6 28.9 28.8 29.0 28.4 28.9 28.2 29.3 – 29.4 – – – 29.0 – 29.1 29.1 29.0 28.5 28.6 28.6 28.4 – – – – – 28.1 – – 28.4 29.5 29.1 36.4 39.9 – 41.0 50.0 51.0 54.5 – –

Water (1) + butyl propionate (2) 40.8 – – 41.7 41.6 41.0 41.5 41.5 42.2 41.6 – – – – – – – – – 41.7 – 41.6 – – – 41.7 – 41.5 42.2 41.6 41.6 41.6 41.5 41.3 – – – – – 41.8 – 41.0 41.7 – – – 41.4 41.4 41.3 41.6 – 41.4 46.0 46.5

Water (1) + cyclohexanone (2) 43.8 – – – – – – – – – – – – – 45.2 – – – – 45.5 47.8 47.6 48.3 48.7 48.4 48.3 48.7 48.3 48.1 48.0 48.3 48.7 48.2 47.8 48.7 47.8 47.6 49.4 50.3 53.6 60.7 – – – – – – – – – – – –

corresponding new and previously published [18,19] experimental data. New data are provided in Tables 1–3. The new flash point for butyl acetate, 27.5 ◦ C, is close to that of Mallinckrodt Baker, 26 ◦ C [46], and Dow, 29 ◦ C (84 ◦ F) [47], although it differs from that of DIPPR [48], NIOSH [49], both at 22 ◦ C, and Merck [50], the Chemical Database of the University of Akron, both at 25 ◦ C [51]. The new data for butyl propionate, 40.8 ◦ C, is close to that of Alfa Aesar [52], Fisher Scientific [53], and Dow [47], all at 38 ◦ C (100 ◦ F), although it differs from that of Merck, at 32 ◦ C [50]. In addition, the measured flash points (27.5 ◦ C and 40.8 ◦ C) are also both close to the flash points estimated by Saldana et al. (27.6 ◦ C and 38.3 ◦ C) for butyl acetate and butyl propionate, respectively [54]. The pure compound flash point data are listed in Table 4. Pure chemical flash points were measured using the flash point analyzer,

x1

x2

Tfp (◦ C)

x1

x2

Tfp (◦ C)

0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.010 0.025 0.050 0.060 0.065 0.067 0.068 0.100 0.100 0.100 0.100 0.100 0.100 0.100 0.100 0.100

0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900 0.950 1.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900

27.5 27.2 27.2 27.4 27.6 28.2 28.8 29.8 30.9 33.3 35.4 36.9 28.1 28.9 29.3 28.6 28.6 28.6 28.6 28.7 27.4 28.0 28.2 29.3 29.8 31.1 34.5 38.3

0.200 0.200 0.200 0.200 0.200 0.200 0.300 0.300 0.300 0.300 0.400 0.400 0.500 0.530 0.985 0.990 0.992 0.993 0.994 0.995 0.996 0.9987 0.9990 0.9992 0.9993 0.9994 0.9995

0.300 0.400 0.500 0.600 0.700 0.800 0.400 0.500 0.600 0.700 0.500 0.600 0.500 0.470 0.015 0.010 0.008 0.007 0.006 0.005 0.004 0.000 0.000 0.000 0.000 0.000 0.000

29.3 29.3 31.1 32.2 35.5 40.3 31.5 32.6 34.7 41.6 36.2 42.1 43.1 44.0 44.9 50.7 54.2 55.6 58.5 63.6 68.1 36.4 39.9 41.0 50.0 51.0 54.5

Table 3 Measured flash points within the two-liquid-phase region for water (1) + 1-butanol (2) + butyl acetate (3). x1 Tie line #1 0.069 0.070 0.075 0.080 0.085 0.095 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900 0.950 0.990 0.998 0.9983 0.9985 Tie line #2 0.1107 0.1195 0.3391 0.5588 0.7784 0.9892 0.9936 0.9962 Tie line #3 0.1739 0.1819 0.1902 0.3915 0.5930 0.7945 0.9880 0.9920

x2

Tfp (◦ C)

0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

28.9 28.8 29.0 28.4 28.9 28.2 29.3 29.4 29.0 29.1 29.1 29.0 28.5 28.6 28.6 28.4 28.1 28.4 29.5 29.1

0.0741 0.0734 0.0555 0.0375 0.0196 0.0023 0.0020 0.0017

28.5 28.3 28.0 28.6 28.6 28.3 28.5 28.7

0.1805 0.1787 0.1772 0.1336 0.0903 0.0470 0.0053 0.0045

28.6 28.8 28.3 28.2 28.5 28.7 28.1 28.6

x1 Tie line #4 0.2679 0.2748 0.3000 0.3087 0.4801 0.6513 0.8224 0.9867 0.9901 0.9914 Tie line #5 0.3397 0.3766 0.5303 0.6841 0.8378 0.9884 0.9890 Tie line #6 0.4287 0.4391 0.4693 0.5990 0.7280 0.8570 0.9808 0.9834 0.9845 Tie line #7 0.540 0.550 0.600 0.700 0.800 0.900 0.950 0.980 0.982 0.983

x2

Tfp (◦ C)

0.3134 0.3105 0.3000 0.2964 0.2235 0.1511 0.0786 0.0090 0.0076 0.0070

30.5 30.2 30.5 29.8 29.5 29.8 29.5 29.7 29.9 29.8

0.3758 0.3555 0.2683 0.1816 0.0949 0.0099 0.0096

31.3 30.8 31.8 30.7 31.1 30.8 30.9

0.4655 0.4571 0.4324 0.3275 0.2229 0.1184 0.0180 0.0159 0.0151

35.8 35.8 35.3 35.6 34.8 35.1 35.5 35.9 36.3

0.460 0.450 0.400 0.300 0.200 0.100 0.050 0.020 0.018 0.017

43.5 44.0 43.2 43.3 43.8 43.0 43.1 43.2 43.7 43.9

H.-J. Liaw, T.-P. Tsai / Fluid Phase Equilibria 345 (2013) 45–59

49

Table 4 Antoine coefficients and experimental flash points of the solution components. Substance

Antoine coefficients

1-Butanola 2-Butanola Ethanola Isobutanola 1-Pentanola Butyl acetateb Butyl propionateb Octanea Cyclohexanonea a b c

A

B

C

7.83800 7.47429 8.11220 8.53516 7.39824 6.15145 6.7566 6.93142 7.47050

1558.190 1314.188 1592.864 1950.940 1435.570 1368.0510 1871.62 1358.800 1832.200

−76.269 −86.650 −46.966 −36.003 −93.352 −69.2202 −26.583 −63.295 −28.950

Reference

Tfp,exp (◦ C)c

[55] [55] [55] [55] [55] [56] [57] [58] [59]

36.9 22.0 13.0 28.5 49.5 27.5 40.8 14.5 43.8

± ± ± ± ± ± ± ± ±

2.8 2.4 0.6 1.0 1.2 0.8 0.6 1.4 1.2

log(P/mmHg) = A − B/[(T/K) + C]. log(P/kPa) = A − B/[(T/K) + C]. The uncertainty is represented by the value of double standard deviation.

Table 5 Pure component volumes and surface areas used in the UNIFAC-type models. UNIFAC Dortmund

Magnussen et al.’s UNIFAC

ri

qi

ri

qi

ri

qi

3.9243 3.9235 2.5755 3.9235 4.5987 4.8274 5.5018 4.1433 5.8486 0.9200

3.668 3.664 2.588 3.664 4.208 4.1960 4.7360 3.340 4.936 1.400

3.7602 3.5930 2.4952 3.7602 4.3927 3.800 4.4325 4.5592 5.0600 1.7334

4.0778 4.0514 2.6616 4.0778 4.7859 4.8137 5.6687 5.0082 6.3702 2.4561

3.9243 3.9235 2.5755 3.9235 4.5987 4.8274 5.5018 – 5.8486 0.9200

3.668 3.664 2.588 3.664 4.208 4.1960 4.7360 – 4.936 1.400

with the Antoine coefficients sourced from the literature [55–59]. The group volume and surface area parameters, and the UNIFAC group interaction parameters for different UNIFAC-type models were obtained from the literature [20,27,30,60], the pure component volume parameters and pure component area parameters are listed in Table 5, but for some mixtures, group contributions were not available in the literature, such as the LLE UNIFAC parameters for cyclohexanone. Finally some non-ideal simulations using the NRTL or UNIQUAC equations were used as references to elucidate the predictive capability of the model based on the UNIFAC equation, with the binary interaction parameters of NRTL or UNIQUAC equation obtained from the literature [55,57,38,61–69] and listed in Tables 6 and 7. Evidence of non-ideality was assessed by computing activity coefficients for the various models used. Activity coefficient calculations were done at the flash point temperature and in the solubility region. Activity coefficient behavior helps us understand the flash point behavior. As shown in earlier articles [16–19,70] and by Eqs. (1) and (3), flash point is strongly connected to VLE and LLE behavior.

100

γ2

1-Butanol 2-Butanol Ethanol Isobutanol 1-pentanol Butyl acetate Butyl propionate Cyclohexanone Octane Water

Original UNIFAC

10

1 80

70

Tfp/ºC

Compound

60

50

40

4.2. Binary aqueous–organic mixtures Experimental flash point data for the eight binary aqueous–organic mixtures covering their entire flammable composition ranges are displayed in Figs. 1–8. Mutual solubility regions in both water-rich and water-lean regions exist for the partially miscible aqueous–organic mixtures investigated in this study: water + 1-butanol, water + 2-butanol, water + isobutanol, water + 1-pentanol, water + butyl acetate, water + butyl propionate, and water + cyclohexanone. Octane is almost immiscible with water, and the reverse also holds. For the seven mixtures with two mutual solubility regions studied, the flash points of which increase smoothly along with the quantity of water in the water-lean region, increase sharply in the water-rich region,

30

0

0.2

0.4

x1

0.6

0.8

1

Fig. 1. Comparison of predicted flash point and experimental data for water (1) + 1butanol (2). () Experimental data, (—) original UNIFAC (VLLE), (- - - -) UNIFAC Dortmund 93 (VLLE), (– · –) NRTL (VLLE); (– – –) original UNIFAC (VLE), and (– - -) UNIFAC Dortmund 93 (VLE).

and are almost constant in the two liquid phase regions for each (Figs. 1–6 and 8). In contrast to these mixtures, the flash point of water + octane is almost constant over the whole test range from molar fraction of water 0–0.99975 (Fig. 7). By inspection of

50

H.-J. Liaw, T.-P. Tsai / Fluid Phase Equilibria 345 (2013) 45–59

Table 6 VLE parameters of the NRTL and UNIQUAC equations for the binary and ternary solutions.a Mixtures

A12

A21

˛12

Reference

Water (1) + 1-butanol (2) Water (1) + 2-butanol (2) Water (1) + isobutanol (2) Water (1) + 1-pentanol (2) Water (1) + butyl acetate (2) Water (1) + butyl propionate (2) Water (1) + cyclohexanone (2) Water (1) + ethanol (2) Ethanol (1) + 1-butanol (2) 1-Butanol (1) + butyl acetate (2)

1332.336 891.640 1109.011 252.687 2363.474 74.525 548.566 611.735 38.072 485.277

193.464 133.786 114.185 77.061 −560.729 75.559 100.654 47.240 −32.941 −160.712

0.4056 0.4406 0.3155 – 0.1 0.2 0.3 0.4500 0.3038 0.3024

[55] [55] [55] [55] [38] [61] [62] [63] [63] [64]

a

NRTL: Aij = (gij − gjj )/R; UNIQUAC: Aij = (uij − ujj )/R.

the activity coefficients (upper parts of Figs. 1–8), the flammable components of such aqueous–organic mixtures reveal positive deviations from that of an ideal solution, with highly positive deviation and near ideality in the water-rich and water-lean regions, respectively. Because of the existence of two liquid phases (aqueous and organic) and the compositions of the two liquid phases being in equilibrium within the partially miscible region, two different activity coefficient curves with constant values present in such a region. The activity coefficient curves of the aqueous and organic phases are continuous with that in the water-rich and water-lean regions, respectively. Except for the mutual solubility region of water-rich, which is very narrow, the flash point values of the studied binary, partially miscible, aqueous–organic mixtures do not increase significantly as the quantity of water increases (see Figs. 1–8). This is the extreme behavior of flash point variation where the liquid phases are in equilibrium. Another extreme behavior was observed in our previous study [70] in which the flash point of a binary, partially miscible, aqueous–organic mixture within the entire flammable range, excluding the water-rich mutual solubility region, is close to that of its flammable component where such a mixture is not stirred, and the flash point of such a mixture is less than that of being in equilibrium. In the waste water of industry, partially miscible mixtures are always present and are not usually stirred, thus the flash point of waste water is close to that of the

flammable component, which explains the occurrence of explosive events such as the waste water tank explosion in Taiwan in 2012. Table 8 compares experimental values for equilibrium composition between liquid phases and measured invariant flash point averages in the two liquid phase regions with the corresponding predictions. The results estimated by the VLLE model shown in Table 8 for the aqueous solutions of 1-butanol, 2-butanol, isobutanol, and 1-pentanol were obtained from our previous study [25], with data for water + 1-butanol being recalculated and revised in the current study. The measured span of twoliquid phase region is close to the estimations, based on either the NRTL or UNIFAC-type models for water + 1-butanol when using VLLE model, where the VLE and LLE parameters are used. However, there are some deviations in the analogous estimated values for water + 2-butanol, water + isobutanol, water + 1-pentanol, water + butyl acetate, and water + butyl propionate when using UNIFAC VLLE model. This deviation in the estimated span of the two-liquid phase region is attributed to the predictive capability of the liquid–liquid equilibrium by use of the UNIFAC model as modified by Magnussen et al., which is not as accurate. This deviation in LLE application for the UNIFAC model as modified by Magnussen et al. has also been reported in the literature [71,72]. In contrast, the measured invariant flash point averages in the two-liquid phase region are close to the estimated

Table 7 LLE parameters of the NRTL and UNIQUAC equations for the studied systems. Model

A12 = a12 + b12 T + c12 T 2 a12

Water (1) + 1-butanol (2) −2610.15 NRTL (˛12 = 0.45) Water (1) + 2-butanol (2) −2744.73 NRTL (˛12 = 0.45) Water (1) + isobutanol (2) 3.770 NRTL (˛12 = 0.3)b Water (1) + 1-pentanol (2) 242.413 UNIQUAC Water (1) + butyl acetate (2) 1651.50 NRTL (˛12 = 0.2) Water (1) + butyl propionate (2) 2107.5 NRTL (˛12 = 0.2) Water (1) + octane (2) −169.718 NRTL (˛12 = 0.2) Water (1) + cyclohexanone (2) −4114.53 NRTL (˛12 = 0.3) Water (1) + ethanol (2) 537.780 NRTL (˛12 = 0.45) Ethanol (1) + 1-butanol (2) −191.792 NRTL (˛12 = 0.45) 1-Butanol (1) + butyl acetate (2) 133.122 NRTL (˛12 = 0.3) a b

NRTL: Aij = (gij − gjj )/R; UNIQUAC: Aij = (uij − ujj )/R. Aij = ij .

A21 = a21 + b21 T + c21 T 2

a

b12

c12

a21

a

Reference b21

c21

19.4473

−0.0237040

−3884.30

30.3191

−0.0527519

[63]

19.1484

−0.0228962

−3871.43

25.0760

−0.0393948

[63]

0

0

0.025

0

0

[65]

0

0

90.395

0

0

[66]

0

0

410.28

0

0

[67]

−1.0017

0

271.74

0.3983

0

[57]

12.5591

0

4197.06

−7.5243

0

[68]

26.3914

−0.0303981

54.8557

2.9021

−0.0077349

[69]

0

0

991.132

0

0

[63]

0

0

492.973

0

0

[63]

0

0

0

0

[67]

−5.62806

H.-J. Liaw, T.-P. Tsai / Fluid Phase Equilibria 345 (2013) 45–59

51

Table 8 Comparison of estimated values for equilibrium composition between liquid phases, x1,2LP , and its flash point, Tfp,2LP , with corresponding experimental data. System

Model

Estimated value Original UNIFAC

Water + 1-butanol

VLLE a VLE

Water + 2-butanol

VLLE a VLE

Water + isobutanol

VLLE a VLE

Water + 1-pentanol

VLLE

a

VLE Water + butyl acetate

VLLE VLE

Water + butyl propionate

VLLE VLE

Water + octane

VLLE VLE

Water + cyclohexanone

VLLE c VLE

a b c

Experimental data UNIFAC Dortmund 93

NRTL/UNIQUAC

x1,2LP

Tfp,2LP (◦ C)

x1,2LP

Tfp,2LP (◦ C)

x1,2LP

Tfp,2LP (◦ C)

x1,2LP

Tfp,2LP

0.542 0.979 0.526 0.978 0.535 0.981 0.519 0.980 0.538 0.981 0.522 0.980 0.426 0.993 0.420 0.992 0.0845 0.9996 8.3 × 10−4 0.9992 0.0639 0.9999 0.0013 0.9998 7.1 × 10−4 0.999996 7.0 × 10−4 0.999993 0.041 0.998 0.106 0.996

44.52

0.542 0.980 0.373 0.972 0.535 0.981 0.390 0.966 0.537 0.981 0.364 0.972 0.426 0.993 0.289 0.992 0.0854 0.9996 0.0861 0.9986 0.0644 0.9999 0.0727 0.9997 7.1 × 10−4 0.999996 5.6 × 10−3 0.999975 0.041 0.998 0.038 0.976

43.12

0.541 0.985

44.38

0.54 0.983

44.2 ± 0.7

0.673 0.957

30.17

0.67 0.95

29.7 ± 0.5

0.463 0.975

34.43

0.46 0.98

34.1 ± 1.1

0.374 0.994

55.69

0.37 0.995

55.8 ± 0.4

0.0524 0.9985

28.39

0.069 0.9985

28.8 ± 0.8

0.0588 0.9987

41.94

0.047 0.999

41.6 ± 0.6

3.8 × 10−6 0.999996

14.49

4 × 10−6 0.99975

14.5 ± 0.7

0.297 0.985

48.89

0.29 0.985

48.2 ± 0.7

44.34 29.22 29.04 36.31 36.11 55.81 55.72 27.28 27.49 40.91 40.82 14.50 14.50 44.49 45.25

b

(◦ C)

42.01 27.75 26.88 34.67 33.53 55.52 53.95 28.83 28.84 41.98 42.13 14.50 14.58 44.47 44.42

Data are adopted from previous study [25]. The uncertainty is represented by the value of double standard deviation. Modified method by replacing cyclic CH2 group with the single CH2 group to estimate the flash point.

flash point averages determined using the UNIFAC VLLE model, except for those of water + butyl acetate and water + isobutanol estimated using original UNIFAC model, with about 1.5 ◦ C and 2 ◦ C differences, respectively, and that of water + 1-butanol and water + 2-butanol based on UNIFAC-Dortmund 93 model, with about 1 ◦ C and 2 ◦ C differences, respectively. The contrariness of the estimated deviations in equilibrium compositions between liquid phases, but good agreement in flash points in the two liquid phases for water + 2-butanol, water + isobutanol, water + 1pentanol, water + butyl acetate, and water + butyl propionate when using the UNIFAC VLLE model can be attributed to two factors. One is that the variation of flash point in the water-lean mutual solubility region is not significant, and the other is that the estimated deviation in equilibrium composition between liquid phases is not so remarkable. The phenomenon of slight variation of flash point in the water-lean region has also been observed in miscible aqueous–organic mixtures [5,6,23], and in such a region, the flammable component follows the ideal solution behavior, with the activity coefficient of the flammable component close to unity for the studied mixtures displayed in Figs. 1–6 and 8. In contrast, the predictions, irrespective of using NRTL or UNIFAC-type models, all indicated that octane and water are almost immiscible with each other, which is consistent with the observation (Table 8). Overall, the NRTL- and UNIQUAC-based predictions are superior to those based on UNIFAC-type models for the estimation of the two-liquid phase region, and the predictive capability of flash point in such a region for the former is comparable to those of the latter.

The flash points predicted by the VLLE model for the seven studied partially miscible aqueous solutions and the corresponding measured values are compared in Figs. 1–7. Predictions are in good agreement with the experimental data over the entire flammable range, when the NRTL/UNIQUAC, original UNIFAC or UNIFAC-Dortmund 93 is used to estimate the flash point. Table 9 demonstrates that predictions are excellent over the entire flammable range, excluding the water-rich mutual solubility region for water + butyl acetate, with the deviations being 0.4 ◦ C, 1.4 ◦ C, and 0.3 ◦ C using NRTL, original UNIFAC, or the UNIFAC-Dortmund 93 equation, respectively. However, there are remarkable deviations between the predictions and measurements in the water-rich mutual solubility region, with flash point deviations of 28.7 ◦ C, 18.2 ◦ C, and 16.6 ◦ C for NRTL, original UNIFAC, and UNIFAC-Dortmund equations, respectively. This phenomenon of greater deviation in the water-rich region was also observed in miscible aqueous–organic solutions [5,6,23] and the other partially miscible aqueous–organic mixtures in this study and previous paper [25], water + 1-butanol, water + 2-butanol, water + isobutanol, water + 1-pentanol, and water + butyl propionate (Table 9), and can be explained by the model’s failure to consider the effect of inert concentration on the lower flammable limit of a mixture [34,73]. In the estimation of flash point for an aqueous–organic mixture, Eq. (1) uses Le Chatelier’s rule [74], which assumes that an inert substance such as water has no effect on the lower flammable limit of a mixture. For the aqueous solutions of 2-butanol and 1-pentanol, the NRTL and UNIQUAC predictions, with the sets of binary-parameter

52

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Table 9 Average temperature deviation between calculated and experimental flash points, Tfp a , for the studied solutions, comparing models. Mixture

Model

Tfp (K) NRTL/UNIQUAC

Water + 1butanol

2.9 9.8d 0.7e –

VLLEb

1.3c 3.6d 0.3e –

VLLE

VLE

Water + 2-butanol

VLE

VLLEb

Water + isobutanol

VLE

Water + 1-pentanol

VLLEb

VLE

VLLE

Water + butyl acetate

VLE

VLLE

Water + butyl propionate

VLE

Water + octane

VLLE VLE VLLE

Water + cyclohexanone

c

b

VLE

Water + ethanol + 1butanol

VLLE

Water + 1-butanol + butyl acetate

VLLE

 Tfp,exp − Tfp,pred /N.

Original UNIFAC c

1.6 2.7d 0.8e 1.5c 2.7 0.7e 2.8c 11.0d 0.9e 2.9c 11.0d 1.0e 1.1c 0.7d 1.2e 1.0c 0.7d 1.1e 1.3c 5.8d 0.3e 1.3c 5.8d 0.3e 4.3c 18.2d 1.4e 3.6c 14.5d 1.2e 0.9c 2.1d 0.6e 1.0c 2.2d 0.7e 0.3c 0.3c 3.7c,f 6.6d,f 3.2e,f 3.0c 5.9d 2.5e 1.0c 2.5g 0.5h 2.8c 9.7g 2.0h

0.7c 2.0d 0.3e –

0.8c 3.5d 0.2e –

5.4c 28.7d 0.4e –

65.6c 267.3d 10.7e –

0.3c – 5.0c 34.9d 0.5e –

1.3c 6.9g 0.5h 2.7c 19.0g 0.9h

a

Deviation of the flash point: Tfp =

b

Data are adopted from previous study [25]. Tfp over the entire flammable range. Tfp for the water-rich mutual solubility region. Tfp over the entire flammable, excluding the water-rich mutual solubility region. Modified method by replacing cyclic CH2 group with the single CH2 group to estimate the flash point. Tfp for the water-rich mutual solubility region with xwater ≥ 0.9. Tfp over the entire flammable, excluding the water-rich mutual solubility region with xwater ≥ 0.9.

UNIFAC Dortmund 1.4c 3.0d 0.3e 1.9c 3.1d 1.0e 2.8c 6.8d 1.8e 3.0c 6.8d 2.1e 0.5c 0.9d 0.4e 0.7c 0.9d 0.6e 1.1c 4.0d 0.4e 1.9c 4.0d 1.5e 3.2c 16.6d 0.3e 1.3c 5.6d 0.3e 0.7c 1.8d 0.4e 0.7c 1.8d 0.4e 0.3c 0.3c 3.7c,f 6.6d,f 3.2e,f 3.6c 6.0d 3.3e 1.2c 2.1g 0.9h 1.5c 9.3g 0.7h

N c d e f g h

values used for the former aqueous solution selected from several of our previous study [18], have the best agreement with the experimental data, better than the already good predictions based on the UNIFAC-type models (Table 9). Table 9 demonstrates that for the aqueous solution of isobutanol, the modified UNIFAC Dortmund 93 based predictions are superior to the NRTL-based predictions; the predictive capability of original UNIFAC model is also very good. For the water + 1-butanol mixture, NRTL predictions are acceptable, but less accurate than predictions based on the UNIFAC models (Table 9). Because of poor predictive capability in the water-rich

mutual solubility region for the cases of butyl acetate and butyl propionate aqueous solutions, the NRTL-based predictions are not in as good agreement with the measurements as any of the two UNIFAC-based predictions. The predictions based on UNIFAC-type models are comparable to the analog of the NRTL-based model for water + octane. Overall, the prediction results of the flash point prediction model based upon the VLLE UNIFAC model agree well with the measured flash points corresponding to an aqueous–organic solution.

H.-J. Liaw, T.-P. Tsai / Fluid Phase Equilibria 345 (2013) 45–59

53

1000

100

γ2

γ2

100

10

10

1

1

80

80

70

Tfp/ºC

Tfp/ºC

60

40

20

60

50

40

0

0.2

0.4

x1

0.6

0.8

1

Fig. 2. Comparison of predicted flash point and experimental data for water (1) + 2butanol (2). () Experimental data, (—) original UNIFAC (VLLE), (- - - -) UNIFAC Dortmund 93 (VLLE), (– · –) NRTL (VLLE); (– – –) original UNIFAC (VLE), and (– - -) UNIFAC Dortmund 93 (VLE).

Fig. 3. Comparison of predicted flash point and experimental data for water (1) + isobutanol (2). () Experimental data, (—) original UNIFAC (VLLE), (- - - -) UNIFAC Dortmund 93 (VLLE), (– · –) NRTL (VLLE); (– – –) original UNIFAC (VLE), and (– - -) UNIFAC Dortmund 93 (VLE).

0

0.2

0.4

x1

0.6

0.8

1

Fig. 4. Comparison of predicted flash point and experimental data for water (1) + 1pentanol (2). () Experimental data, (—) original UNIFAC (VLLE), (- - - -) UNIFAC Dortmund 93 (VLLE), (– · –) NRTL (VLLE); (– – –) original UNIFAC (VLE), and (– - -) UNIFAC Dortmund 93 (VLE).

Fig. 5. Comparison of predicted flash point and experimental data for water (1) + butyl acetate (2). () Experimental data, (—) original UNIFAC (VLLE), (- - - -) UNIFAC Dortmund 93 (VLLE), (– · –) NRTL (VLLE); (– – –) original UNIFAC (VLE), and (– - -) UNIFAC Dortmund 93 (VLE).

54

H.-J. Liaw, T.-P. Tsai / Fluid Phase Equilibria 345 (2013) 45–59

Fig. 6. Comparison of predicted flash point and experimental data for water (1) + butyl propionate (2). () Experimental data, (—) original UNIFAC (VLLE), (- - -) UNIFAC Dortmund 93 (VLLE), (– · –) NRTL (VLLE); (– – –) original UNIFAC (VLE), and (– - -) UNIFAC Dortmund 93 (VLE).

4.3. Predictive results for binary aqueous–organic mixtures using only VLE parameters Because the UNIFAC group interaction parameters for LLE application are not as complete as for VLE application, the application of the VLLE UNIFAC method to estimate the flash point of partially

Fig. 7. Comparison of predicted flash point and experimental data for water (1) + octane (2). () Experimental data, (—) original UNIFAC (VLLE), (- - - -) UNIFAC Dortmund 93 (VLLE), (– · –) NRTL (VLLE); (– – –) original UNIFAC (VLE), and (– - -) UNIFAC Dortmund 93 (VLE).

Fig. 8. Comparison of predicted flash point and experimental data for water (1) + cyclohexanone (2). () Experimental data, (—) original UNIFAC (VLLE), (- - - ) UNIFAC Dortmund 93 (VLLE), (– · –) NRTL (VLLE); (– – –) original UNIFAC (VLE), and (– - -) UNIFAC Dortmund 93 (VLE).

miscible mixtures is constrained to limited mixtures. The VLE UNIFAC parameters were used in Eqs. (1)–(3) to estimate the flash points of binary aqueous–organic mixtures, and the predictions were then compared with measurements (Figs. 1–8). Table 8 shows that the predictive capability of the two-liquidphase region and the invariant flash point in such a region using VLLE UNIFAC parameters was superior to the analog using VLE UNIFAC parameters for 1-butanol, 2-butanol, 1-pentanol, and butyl propionate aqueous solutions, although the predictive capability of the former is comparable with the latter for isobutanol, butyl acetate, and octane aqueous solutions. However, except for water + 1-butanol and water + octane, where the VLLE model for the former and VLLE and VLE models for the latter gave excellent estimations, there are some deviations in the estimated spans of the two-liquid-phase region, irrespective of using VLLE or VLE UNIFAC parameters, although it was acceptable. Table 9 indicates that the flash points computed from VLE UNIFAC parameters are as good as those calculated using VLLE UNIFAC parameters for above mentioned seven mixtures. Since the purpose of this manuscript is to predict the flash point rather than to estimate the two-liquid-phase region, the prediction results using VLE UNIFAC parameters seem to be acceptable, at least for the seven mixtures mentioned above. Since group volume and surface area parameters for cyclic groups is lacking in the LLE UNIFAC model reported by Magnussen et al., the flash point of water + cyclohexanone cannot be estimated by the VLLE UNIFAC parameters. In order to verify the applicability of the VLE UNIFAC model for flash point estimation of partially miscible aqueous–organic mixtures, the VLE UNIFAC parameters were used in Eqs. (1)–(3) here to estimate the flash point of cyclohexanone aqueous solution. Fig. 8 and Table 8 show that there are some deviations between the predicted flash point and corresponding experimental data within the two-liquid-phase region when using VLE UNIFAC parameters. This deviation can be attributed to the estimated span of the two-liquid-phase region around the waterlean region far from the measurement, 0.106 and 0.038 for the

H.-J. Liaw, T.-P. Tsai / Fluid Phase Equilibria 345 (2013) 45–59

55

Fig. 9. Binodal curves of water + ethanol + 1-butanol. (䊉) Partially miscible, () miscible, (—) original UNIFAC, (- - - -) UNIFAC Dortmund 93, and (– · –), NRTL.

estimated values of water composition using the original UNIFAC and UNIFAC-Dortmund 93 vs. 0.29 for the measurement (Table 8), and that resulted in deviation of the flash point. Since the LLE UNIFAC method by Magnussen et al. has no specific CH2 groups for cyclic compounds, but a single CH2 group contribution, the VLLE method was modified by replacing the cyclic CH2 group with the single CH2 group to estimate the flash point of the cyclohexanone aqueous solution in this study. As the case of VLE UNIFAC model, Fig. 8 and Table 8 show that the modified VLLE UNIFAC-type models cannot accurately describe the flash point within the twoliquid-phase region. It appears reasonable to conclude, therefore, that the single CH2 group is not adequate for cyclic compounds from the perspective of flash point prediction. However, the VLLE NRTL model, with LLE parameters being regressed on solubility data, described the measured flash point data and two-liquid-phase region well in comparison with experimental data as shown in Fig. 8 and Table 8. These results reflect the predictive capability of the NRTL-based flash point prediction over the entire flammable range, excluding the water-rich mutual solubility region, is much superior to that of the UNIFAC-based model, although the predicted flash point of the NRTL-based estimates were far from the measurements in the water-rich mutual solubility region (see Table 9). It seems that the flash point predictive capability for binary, partially miscible, aqueous–organic solutions using the UNIFAC model depend upon the accuracy of the LLE prediction. The prediction is good for the case of not significant estimated error in the span of the two-liquid-phase region nearing the water-lean mutual solubility region, but has greater flash point deviation for the case of substantial analogous error. Since even a rough flash point trend is better than nothing at all, a model based upon VLE UNIFAC parameters is suggested to predict the flash points for binary partially miscible aqueous–organic mixtures if the VLLE parameters regressed on experimental data are not accessible. 4.4. Ternary aqueous–organic mixtures By analogy with common liquid–liquid equilibrium ternary diagram classification, the water + ethanol + 1-butanol mixture exhibits a single partially miscible binary mixture and is a type-I mixture (see Fig. 9). The NRTL-based predicted region of the water + ethanol + 1-butanol mixture is slightly less than the experimental measurements; however, it is very close to the corresponding measurements (Fig. 9 and Table 10). The predicted regions and tie lines almost overlap with each other when using original UNIFAC or UNIFAC-Dortmund 93 models combined with UNIFAC model modified by Magnussen et al. (Fig. 9 and Table 10).

Fig. 10. Binodal curves of water + butyl acetate + 1-butanol. (䊉) Partially miscible, () miscible, (—) original UNIFAC, (- - - -) UNIFAC Dortmund 93, and (– · –), NRTL.

These two predicted regions are both larger than the measurements in comparison with the predictions and measurements (Fig. 9). For water + butyl acetate + 1-butanol, a type-II mixture with two partially miscible binary mixtures, Fig. 10 shows LLE predictions for several tie-lines with NRTL, the original UNIFAC, and the UNIFACDortmund 93 parameter sets. The predicted tie lines almost overlap with each other for the two UNIFAC group contribution methods, and both equations predict well the tie line slopes, but they do not have the same extended length, which are both slightly less than the measurements (Fig. 10 and Table 11). The NRTL-based predicted region is much greater than the measurement, although its predicted tie lines have slopes similar to those of the UNIFAC-based model and corresponding measurements (Fig. 10). According to theory, the flash point on a given tie-line should be constant. Predictions and measurements of spans for some tie lines and flash points in such tie lines are compared in Tables 10 and 11 for water + ethanol + 1-butanol and water + butyl acetate + 1-butanol mixtures. For the case of water + ethanol + 1butanol, the estimated tie lines, irrespective of NRTL-based or UNIFAC-based estimations, have slopes similar to the measured slopes, although the extended lengths are different (Fig. 9). Table 10 indicates that the average measured flash point is in best agreement with the NRTL-based constant predicted flash point, which subsequently is the original UNIFAC-based prediction. The predicted constant flash points based on the original UNIFAC model agree with the average measurements for tie lines #1–3, and with some deviation for tie line #4. Compared with those based on NRTL or original UNIFAC model, the differences between predicted flash points and average measured values are relative greater for the UNIFAC-Dortmund 93 based predictions. The relatively greater deviation based on the UNIFAC-type model is attributed to the relative poor estimation of two-liquid-phase region. Table 11 shows that the average measured flash point is in agreement with the NRTL-based and UNIFAC-Dortmund 93-based constant predicted flash point value, with the flash point deviation for tie lines #2–4 being relative greater than those of other tie lines. The original UNIFAC-based prediction showed greater deviation in the predicted constant flash point. Table 8 also shows that the predicted flash point within the two liquid phase region based on the original UNIFAC model has greater deviation for water + butyl

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Table 10 Comparison of predicted flash point values, Tfp,pred , in the estimated tie lines with corresponding experimental data, Tfp,exp , for water (1) + ethanol (2) + 1-butanol (3). Tie line

Prediction Activity coefficient model

#1

NRTL Original UNIFAC UNIFAC Dortmund

#2

NRTL Original UNIFAC UNIFAC Dortmund

#3

NRTL Original UNIFAC UNIFAC Dortmund

#4

NRTL Original UNIFAC UNIFAC Dortmund

a

Measurement Tfp,pred (◦ C)

Span of tie line x1

x3

0.9850 0.5411 0.9795 0.5422 0.9797 0.5416 0.9800 0.5658 0.9750 0.5483 0.9750 0.5481 0.9600 0.6474 0.9600 0.5765 0.9600 0.5765 0.9300 0.7344 0.9400 0.6123 0.9400 0.6123

0.0150 0.4589 0.0205 0.4578 0.0203 0.4584 0.0166 0.4213 0.0223 0.4396 0.0220 0.4388 0.0240 0.3029 0.0247 0.3650 0.0244 0.3640 0.0373 0.1938 0.0284 0.2880 0.0281 0.2868

44.40

Tfp,exp (◦ C) a

Span of tie line x1

x3

0.983 0.540

0.017 0.460

44.2 ± 0.7

0.959 0.547

0.037 0.439

43.5 ± 0.5

0.960 0.616

0.024 0.331

41.3 ± 0.7

0.940 0.705

0.030 0.217

39.3 ± 0.4

44.52 43.12 43.76 43.69 42.24 41.66 40.64 39.20 39.52 38.00 36.45

The uncertainty is represented by the value of double standard deviation.

acetate. Thus, we suspect that the relatively poor prediction capability of flash point for water + butyl acetate when using the original UNIFAC model, which implies less accuracy in the binary interaction parameters of VLE, makes the predicted flash point in the tie lines of water + butyl acetate + 1-butanol to behave with greater deviation from the measurements.

Figs. 11 and 12 depict the measured and the NRTL-based or UNIFAC-based predicted flash points for water + ethanol + 1-butanol and water + butyl acetate + 1-butanol mixtures, respectively. As in the case of binary aqueous–organic solutions mentioned above, the agreement is excellent over the entire flammable range, except near the water-rich mutual solubility

Fig. 11. Comparison of predicted flash point with experimental data for water (1) + ethanol (2) + 1-butanol (3) (complete data sets are available from the authors upon request). () Experimental data; blue ( / ), original UNIFAC; red ), UNIFAC Dortmund 93; and green ( / ), NRTL. ( /

Fig. 12. Comparison of predicted flash point with experimental data for water (1) + butyl acetate (2) + 1-butanol (3) (complete data sets are available from the ), original UNIauthors upon request). () Experimental data; blue ( / / ), UNIFAC Dortmund 93; and green ( / ), FAC; red ( NRTL.

H.-J. Liaw, T.-P. Tsai / Fluid Phase Equilibria 345 (2013) 45–59

57

Table 11 Comparison of predicted flash point values, Tfp,pred , in the estimated tie lines with corresponding experimental data, Tfp,exp , for water (1) + 1-butanol (2) + butyl acetate (3). Tie line

Prediction Activity coefficient model

#1

NRTL Original UNIFAC UNIFAC Dortmund

#2

NRTL Original UNIFAC UNIFAC Dortmund

#3

NRTL Original UNIFAC UNIFAC Dortmund

#4

NRTL Original UNIFAC UNIFAC Dortmund

#5

NRTL Original UNIFAC UNIFAC Dortmund

#6

NRTL Original UNIFAC UNIFAC Dortmund

#7

NRTL Original UNIFAC UNIFAC Dortmund

a

Measurement Tfp,pred (◦ C)

Span of tie line x1

x3

0.9985 0.0524 0.9996 0.0845 0.9996 0.0854 0.9970 0.0591 0.9980 0.1191 0.9980 0.1195 0.9950 0.0707 0.9960 0.1940 0.9960 0.1902 0.9920 0.0983 0.9940 0.2980 0.9935 0.3087 0.9900 0.1307 0.9920 0.3733 0.9915 0.3766 0.9870 0.2677 0.9860 0.4737 0.9860 0.4693 0.9850 0.5411 0.9795 0.5422 0.9797 0.5416

0.0015 0.9476 0.0004 0.9155 0.0004 0.9146 0.0014 0.8514 0.0004 0.8057 0.0004 0.8071 0.0013 0.7200 0.0004 0.6220 0.0004 0.6325 0.0012 0.5156 0.0003 0.4138 0.0004 0.3949 0.0010 0.3750 0.0003 0.2731 0.0003 0.2679 0.0007 0.1432 0.0002 0.0892 0.0002 0.0983 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

28.39

Tfp,exp (◦ C) a

Span of tie line x1

x3

0.9985 0.069

0.0015 0.931

28.8 ± 0.8

0.9962 0.1107

0.0020 0.8152

28.4 ± 0.4

0.9920 0.1739

0.0036 0.6457

28.5 ± 0.5

0.9914 0.2679

0.0016 0.4187

29.9 ± 0.7

0.9890 0.3397

0.0014 0.2845

31.0 ± 0.7

0.984 0.4287

0.0005 0.1058

35.5 ± 0.9

0.983 0.54

0.00 0.00

44.2 ± 0.7

27.28 28.83 28.77 26.96 29.06 29.39 26.46 29.82 30.64 26.00 30.99 31.82 26.37 31.82 35.29 31.38 35.19 44.38 44.52 43.12

The uncertainty is represented by the value of double standard deviation.

region (Table 9). Again, this can be attributed to the failure of the constant lower flammable limit assumption in the mutual solubility water-rich region. If the mutual solubility water-rich region was not taken into account, the NRTL and the modified UNIFAC-Dortmund 93 models gave the best prediction for water + ethanol + 1-butanol and water + butyl acetate + 1-butanol mixtures, respectively (Table 9). Since the flash point predictive capability of the mutual solubility water-rich region for UNIFACtype models is much superior to that of NRTL, and any of the two UNIFAC-type model predictions give lower average deviations than with NRTL model over the entire flammable range for both water + ethanol + 1-butanol and water + butyl acetate + 1-butanol mixtures, except for the original UNIFAC model being comparable to that of NRTL for the latter mixture (Table 9). Overall, the predictions are consistent with the experimental data, as confirmed by the low average deviations reported in Table 9. In this manuscript, the predicted flash points were in good agreement with the experimental data when using UNIFAC-type models to estimate the liquid phase activity coefficient, although there are still deviations in the two-liquid-phase regions between predictions and measurements. Since the purpose of this model is to predict the flash point rather than to estimate the two-liquid-phase region, the prediction results are acceptable.

5. Conclusions We investigated the ability of activity coefficients derived from UNIFAC-type models, which do not need any experimental binary interaction parameters, to predict the flash points of partially miscible aqueous–organic binary and ternary mixtures using the non-ideal flash point model proposed by Liaw et al. [19]. Predictions were systematically compared with NRTL or UNIQUAC activity coefficient model-based predictions and new experimental data or data from previous studies [18,19]. Good flash point predictions were observed for the case of nonsignificant estimated error in the span of the two-liquid-phase region, while relatively greater deviations were observed for the case of substantial analogous error. Overall, the flash point is well represented by the combined model over the entire flammable composition range for all of the binary and ternary mixtures studied, although there are some deviations in the estimated region of two liquid phases. For some mixtures, the predictions based on UNIFAC-type models were superior to the predictions based on NRTL model. In the estimation of flash point with this proposed method, we suggest that if the LLE UNIFAC parameters for a solution are not accessible, the analogous VLE parameters may be used.

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H.-J. Liaw, T.-P. Tsai / Fluid Phase Equilibria 345 (2013) 45–59

List of symbols

A, B, C Aij g l N sat Pi,T

Antoine coefficients binary parameter (K) binary parameters of the NRTL equation (J/mol) UNIFAC parameter, defined in Eq. (5) number of experimental data saturated vapor pressure (kPa)

Q qi R ri T u X x z

saturated vapor pressure of component, i, at flash point (kPa) group area parameter pure component area parameter gas constant (8.314 J/mol K) pure component volume parameter temperature (K) binary parameters of the UNIQUAC equation (J/mol) liquid-phase group fraction liquid-phase composition coordination number

sat Pi,fp

Greek letters ˛ij NRTL parameter deviation of flash point Tfp i the segment fraction of component i k activity coefficient of group k (i) activity coefficient of group k in pure component i k  activity coefficient (i) k number of groups of kind k in a molecule of component i k the surface area fraction of group k the surface area fraction of component i i  defined in Eq. (13) Superscripts combinatorial part C R residual part Subscripts experimental data exp fp flash point i species i k, m, n group k, m, n predictive value pred Acknowledgements The authors thank the National Science Council of Taiwan, ROC for supporting this study financially under Grant #NSC 97-2221-E039-002-MY3. References

[12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42]

[43] [44] [45] [46] [47] [48] [49] [50]

[51] [52] [53]

[54] [55] [56] [57] [58] [59]

[1] Regulations, 29 CFR 1910.119, Process Safety Management of Highly Hazardous Chemicals, 7-1-04 ed., Occupational Safety and Health Admin., Department of Labor, 2004. [2] D.A. Crowl, J.F. Louvar, Chemical Process Safety: Fundamentals with Applications, 2nd ed., Prentice Hall PTR, New Jersey, 2002. [3] CCPS/AIChE, Guidelines for Engineering Design for Process Safety, 1st ed., American Institute of Chemical Engineers, New York, 1993. [4] H.-J. Liaw, Y.-H. Lee, C.-L. Tang, H.-H. Hsu, J.-H. Liu, J. Loss Prev. Proc. 15 (2002) 429–438. [5] H.-J. Liaw, Y.-Y. Chiu, J. Hazard. Mater. 101 (2003) 83–106. [6] H.-J. Liaw, Y.-Y. Chiu, J. Hazard. Mater. 137 (2006) 38–46. [7] W.A. Affens, G.W. McLaren, J. Chem. Eng. Data 17 (1972) 482–488. [8] D. White, C.L. Beyler, C. Fulper, J. Leonard, Fire Safety J. 28 (1997) 1–31. [9] R.W. Garland, M.O. Malcolm, Process Saf. Prog. 21 (2002) 254–260. [10] H.-J. Liaw, C.-L. Tang, J.-S. Lai, Combust. Flame 138 (2004) 308–319. [11] H.-J. Liaw, T.-A. Wang, J. Hazard. Mater. 141 (2007) 193–201.

[60] [61] [62] [63] [64] [65] [66] [67] [68] [69] [70]

L. Catoire, S. Paulmier, V. Naudet, J. Phys. Chem. Ref. Data 35 (2006) 9–14. J. Gmehling, P. Rasmussen, Ind. Eng. Chem. Fundam. 21 (1982) 186–188. S.-J. Lee, D.-M. Ha, Korean J. Chem. Eng. 20 (2003) 799–802. R.O. Wickey, D.H. Chittenden, Hydrocarbon Process 42 (1963) 157–158. H.-J. Liaw, V. Gerbaud, C.-Y. Chiu, J. Chem. Eng. Data 55 (2010) 134–146. H.-J. Liaw, W.-H. Lu, V. Gerbaud, C.-C. Chen, J. Hazard. Mater. 153 (2008) 1165–1175. H.-J. Liaw, C.-T. Chen, V. Gerbaud, Chem. Eng. Sci. 63 (2008) 4543–4554. H.-J. Liaw, V. Gerbaud, H.-T. Wu, J. Chem. Eng. Data 55 (2010) 3451–3461. A. Fredenslund, R.L. Jones, J.M. Prausnitz, AIChE J. 21 (1975) 1086–1099. A. Fredenslund, J. Gmehling, M.L. Michelsen, P. Rasmussen, J.M. Prausnitz, Ind. Eng. Chem. Process Des. Dev. 16 (1977) 450–462. M. Vidal, W.J. Rogers, M.S. Mannan, Process Saf. Environ. Prot. 84 (2006) 1–9. H.-J. Liaw, V. Gerbaud, Y.H. Li, Fluid Phase Equilibr. 300 (2011) 70–82. A.Z. Moghaddam, A. Rafiei, T. Khalili, Fluid Phase Equilibr. 316 (2012) 117–121. T.-P. Tsai, H.-J. Liaw, Adv. Mater. Res. 560–561 (2012) 1178–1183. U. Weidlich, J. Gmehling, Ind. Eng. Chem. Res. 26 (1987) 1372–1381. J. Gmehling, J. Li, M. Schiller, Ind. Eng. Chem. Res. 32 (1993) 178–193. B.L. Larsen, P. Rasmussen, A. Fredenslund, Ind. Eng. Chem. Res. 26 (1987) 2274–2286. J.C. Bastos, M.E. Soares, A.G. Medina, Ind. Eng. Chem. Res. 27 (1988) 1269–1277. T. Magnussen, P. Rasmussen, A. Fredenslund, Ind. Eng. Chem. Process Des. Dev. 20 (1981) 331–339. H. Hooper, S. Michel, J.M. Prausnitz, Ind. Eng. Chem. Res. 27 (1988) 2182–2187. A.C. Mengarelli, E.A. Brignole, S.B. Bottini, Fluid Phase Equilibr. 163 (1999) 195–207. O. Ferreira, E.A. Macedo, S.B. Bottini, Fluid Phase Equilibr. 227 (2005) 165–176. M.G. Zabetakis, Flammability Characteristics of Combustible Gases and Vapors, U.S. Dept of the Interior, Bureau of Mines, Washington, 1965. A. Cháfer, E. Lladosa, J.B. Montón, J. dela Torre, Fluid Phase Equilibr. 317 (2012) 89–95. M. Kahlweit, G. Busse, B. Faulhaber, Langmuir 11 (1995) 3382. H. Kahl, K. Quitzsch, E.H. Stenby, Fluid Phase Equilibr. 139 (1997) 295–309. J. Acosta, A. Arce, E. Rodil, A. Soto, Fluid Phase Equilibr. 203 (2002) 83–98. H.-M. Lin, G.-B. Hong, C.-E. Yeh, M.-J. Lee, J. Chem. Eng. Data 48 (2003) 587–590. H. Ghanadzadeh, A. Ghanadzadeh, S. Asgharzadeh, M. Moghadam, J. Chem. Thermodyn. 47 (2012) 288–294. S. Cehreli, B. Tatli, P. Bagman, J. Chem. Thermodyn. 37 (2005) 1288–1293. ASTM D 56, Standard Test Method for Flash Point by Tag Closed Tester, American Society for Testing and Materials, West Conshohocken, PA, 1999. H.C. Van Ness, M.M. Abbott, Classical Thermodynamics of Nonelectrolyte Solutions: with Applications to Phase Equilibria, McGraw-Hill, New York, 1982. H.N. Pham, M.F. Doherty, Chem. Eng. Sci. 45 (1990) 1823–1836. The UNIFAC Consortium, http://unifac.ddbst.de/ (accessed 2010). Mallinckrodt Baker, http://www.avantormaterials.com/ (accessed 2012). Dow, http://www.dow.com/ (accessed 2012). AIChE, DIPPRO® , DIPPR Project 801 Pure Component Data, Public Version, American Institute of Chemical Engineers, New York, 1996. NIOSH, http://www.cdc.gov/niosh/npg/ (accessed 2012). Merck, http://www.merckmillipore.com.tw/chemicals;sid=-APWa4wW9nXZa 8Oh5gS7PCTWf4DEm-axwC3IPT-7LUjApQKY1OO1wYoo71hb1hxi6SHGd4 PB Tv bAXfWofHyUPq2ffPL0DGy5luSjQPTeu6PQXfWofBMAGr (accessed 2012). Chemical Database, http://ull.chemistry.uakron.edu/erd/ (accessed 2012). Alfa Aesar, http://www.alfa.com/ (accessed 2012). Fisher Scientific, http://www.fishersci.com/ecomm/servlet/cmstatic?href= index.jsp&store=Scientific&segment=scientificStandard&&storeId=10652 (accessed 2012). D.A. Saldana, L. Starck, P. Mougin, B. Rousseau, L. Pidol, N. Jeuland, B. Creton, Energy Fuels 25 (2011) 3900–3908. J. Gmehling, U. Onken, W. Arlt, Vapor–Liquid Equilibrium Data Collection, Part 1a, DECHEMA, Frankfurt, Germany, 1981. J.A. Riddick, W.B. Bunger, T.K. Sakano, Organic Solvents, 4th ed., Wiley, New York, 1986. M.-J. Lee, L.-H. Tsai, G.-B. Hong, H.-M. Lin, Fluid Phase Equilibr. 216 (2004) 219–228. J. Gmehling, U. Onken, W. Arlt, Vapor–liquid Equilibrium Data Collection, Part 6a, vol. 1, DECHEMA, Frankfurt, Germany, 1980. J. Gmehling, U. Onken, W. Arlt, Vapor–liquid Equilibrium Data Collection, Parts 3 + 4, vol. 1, DECHEMA, Frankfurt, Germany, 1979. S. Skjold-Jørgensen, B. Kolbe, J. Gmehling, P. Rasmussen, Ind. Eng. Chem. Process Des. Dev. 18 (1979) 714–722. W.-T. Liu, C.-S. Tan, Ind. Eng. Chem. Res. 40 (2001) 3281–3286. A. Vetere, Fluid Phase Equilibr. 99 (1994) 63–74. H. Kosuge, K. Iwakabe, Fluid Phase Equilibr. 233 (2005) 47–55. J. Gmehling, U. Onken, W. Arlt, Vapor–Liquid Equilibrium Data Collection, Part 2b, vol. 1, DECHEMA, Frankfurt, Germany, 1978. Y. Tang, Z. Li, Y. Li, Fluid Phase Equilibr. 105 (1995) 241–258. J.M. Resa, J.M. Goenaga, M. Iglesias, R. Gonzalez-Olmos, D. Pozuelo, J. Chem. Eng. Data 51 (2006) 1300–1305. J. Liu, J. Zhang, J. Chem. Ind. Eng. 3 (1988) 111–123. M. Klauck, A. Grenner, J. Schmelzer, J. Chem. Eng. Data 51 (2006) 1043–1050. T. Hauschild, H. Knapp, J. Solution Chem. 23 (1994) 363–377. H.-J. Liaw, V. Gerbaud, C.-C. Chen, C.-M. Shu, J. Hazard. Mater. 177 (2010) 1093–1101.

H.-J. Liaw, T.-P. Tsai / Fluid Phase Equilibria 345 (2013) 45–59 [71] E. Lladosa, A. Cháfer, J.B. Montón, N.F. Martínez, J. Chem. Eng. Data 56 (2011) 1925–1932. [72] A. Cháfer, E. Lladosa, J.B. Montón, J. de la Torre, Fluid Phase Equilibr. 317 (2012) 89–95.

59

[73] H.-J. Liaw, C.-C. Chen, C.-H. Chang, N.-K. Lin, C.-M. Shu, Ind. Eng. Chem. Res. 51 (2012) 2747–2761. [74] H. Le Chatelier, Ann. Mines 19 (1891) 388–395.