Mutual Solubility of Water and Hydrocarbons - Journal of Chemical

Article pubs.acs.org/jced

Mutual Solubility of Water and Hydrocarbons Published as part of The Journal of Chemical and Engineering Data special issue “Proceedings of the 19th Symposium on Thermophysical Properties” Carl Landra*,† and Marco A. Satyro‡ †

Virtual Materials Group, Inc., Calgary, Alberta T2L 2K7, Canada Clarkson University, Potsdam, New York 13699, United States

‡

ABSTRACT: The accurate modeling of systems containing water and hydrocarbons is important to support key decisions related to the design, simulation, and optimization of a variety of industrial processes, ranging from refineries, to gas plants and liquified natural gas processing facilities. Processes of interest for the production of hydrocarbons now include widely different temperatures and pressure ranges, making the use of empirical models to simulate the behavior of water and hydrocarbon mixtures awkward and prone to inconsistencies. In this work we show that the use of the Peng−Robinson equation of state using the Huron−Vidal mixing rule combined with the nonrandom two-liquid model and temperature-dependent interaction parameters provide an accurate platform to correlate mutual solubility data for a variety of hydrocarbons. Moreover, the interaction parameters were correlated on the basis of simple molecular descriptors such as molecular weight and the paraffin, iso-paraffin, olefin, naphthene, and aromatic (PIONA) chemical family classification and Watson-K factor. The model shows an absolute average error in water mole fraction in the hydrocarbon phase equal to 34% and an absolute average error in the hydrocarbon mole fraction in the aqueous phase equal to 98% using the PIONA-based parameters and an absolute average error in water mole fraction in the hydrocarbon phase equal to 34% and an absolute average error in the hydrocarbon mole fraction in the aqueous phase equal to 148% using the Watson-K factor based parameters. The method can be used for systems defined using pure or pseudocomponents and is easily integrated within the structure of existing process simulators.

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INTRODUCTION In the dawn of process simulation as applied to hydrocarbon processes, it was fundamental to ensure that reasonable estimates for the solubility of water in hydrocarbons could be provided using simple equations of state. A simple solution was suggested by Heidemann,1 and it is still widely used. A quadratic mixing rule for the attractive term for the cubic equation of state is used as shown in eq 1, and the interaction parameter between water and hydrocarbon is set to approximately 0.5. nc

a=

values between water and hydrocarbons depending on the hydrocarbon chemical family. Solubility models based on eq 1 have an inherent problem related to the number of adjustable parameters. Since only one adjustable parameter is available per binary pair, we can use eq 1 to model only the solubility of water in the hydrocarbon-rich phase or the solubility of hydrocarbon in the water phase. For example, using the interaction parameter determined to model the solubility of water in hydrocarbons will correspond to an estimation of the solubility of hydrocarbon in the water-rich phase. The estimated hydrocarbon solubility in the aqueous phase based on an interaction parameter determined based on the solubility of water in hydrocarbon is usually not good as shown in Figure 1. This inaccuracy is not a significant problem when performing material and energy balances around a crude tower but are important if we wish to perform environmental studies in the wastewater since the amount of hydrocarbons in the water phase is usually severely underestimated.4

nc

∑∑

aiaj xixj(1 − kij) (1)

i=1 j=1

where a is the attractive term from a cubic equation of state, x is the mole fraction, kij is the interaction parameter and i and j are the component indexes. This approach was widely adopted for use in process simulators since it provides reasonable estimates for the solubility of water in liquid hydrocarbons over modest but important temperature ranges of interest for refining and natural gas processing.2 This idea was further developed by Tsonopolous and Heidman3 through the use of different kij © XXXX American Chemical Society

Received: August 11, 2015 Accepted: November 11, 2015

A

DOI: 10.1021/acs.jced.5b00685 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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MODEL DESCRIPTION The Peng−Robinson equation of state28 is defined by eq 2, expressed in the form made popular by Møllerup and Michelsen:29 acα(T ) RT − v−b (v + δ1)(v + δ2)

P=

(2)

In this equation P is the pressure, R is the gas constant, v is the molar volume, b is the covolume, ac is the attractive term, calculated at the critical point, α(T) is an empirical correction to the attractive term to ensure good vapor pressure prediction, and δ1 and δ2 are numerical constants. The constants δ1 and δ2 are defined by eqs 3a and 3b. Figure 1. Calculated and experimental mutual solubility of benzene and water from 298 to 423 K at saturation pressure using the advanced Peng−Robinson equation of state. Experimental data from ref 7.

We note that polar compounds such as water also require special handling to ensure that accurate vapor pressures are calculated.5,6 Accurate vapor pressures for pure components ensure that accurate multicomponent vapor−liquid equilibrium can be calculated. We can also see why such a simple model has found wide applicability when modeling refining processes where reasonable estimates for the solubility of water in hydrocarbons is a key design consideration. The weakness of quadratic mixing rules was recognized and addressed early by Kabadi and Danner8 and further developed by Twu9 and Michel et al.10 Kontogeorgis and co-workers11−14 obtained good results when a statistical associating fluid theory (SAFT)-like association term was added to a cubic equation of state15,16 (CPA). A more conventional approach is to use a Gibbs Excess mixing rule for the construction of a thermodynamic model based on the original idea by Huron and Vidal.17−21 This class of mixing rule provides a robust platform for data correlation and extrapolation as long as the covolume is not allowed to be temperature dependent.22,23 Matsuda et al.24 demonstrated the applicability of this approach for water/hydrocarbons and hydrocarbon/methanol systems while Kristensen et al.25 and Shimoyama et al.,26 demonstrated the ability of Huron−Vidal type mixing rules to accurately model the distribution of methanol between water and methanol phases as long as temperature dependent parameters are used. The need to model defined as well as undefined hydrocarbons, easiness to extend the model to other polar systems without the need to extensively re-evaluate pure component properties to include association parameters, the existence of models that can reasonably estimate the solubility behavior of water/hydrocarbon and hydrocarbon/water systems,27 and the ability to incorporate these and other estimation methods for robust estimation of interaction parameters in a process simulation environment are conditions met by Huron−Vidal type mixing rules. Given the time scale required for the development of industrially robust property package systems and the number of derived works that are based on this development−hydrates and hydrate inhibition computation, waxes, and solid phase formation and replacement of activity coefficient models in general, a Gibbs excess approach was deemed the most adequate. This is not to say that quality property packages based on other models such as CPA cannot be constructed.

δ1 =

1 (2 + 2 2 ) 2

(3a)

δ2 =

1 (2 − 2 2 ) 2

(3b)

The use of the van der Waals conditions at the critical point define the attractive term and covolume for each component, eqs 4 and 5 ac, i = 0.4572355289210

bi = 0.0777960739039

(RTc, i)2 Pc, i

(4)

RTc, i Pc, i

(5)

The covolume term b for a mixture is calculated using eq 6. nc

b=

∑ xibi

(6)

i=1

In eq 6, bi represents the covolume of component “i” calculated using eq 6 and xi represents the mole fraction of component “i” in the phase of interest. The attractive term for a mixture is defined by eqs 7, and α is calculated such as to reproduce accurate pure component vapor pressures and Tr,i is the reduced temperature of component i. ai = ac, iα(Tr, i)

(7)

The mixing rule used for the attractive term is defined by eq 8: ⎛ nc a ⎞ E⎟ a = b⎜⎜∑ xi i + σG∞ ⎟ ⎝ i = 1 bi ⎠

(8)

Any excess Gibbs free energy expression can be used in eq 8. The numerical constant σ is defined by δ1 and δ2 as shown in eq 9. σ=−

1 1+δ 1 ln 1 + δ1 δ1 − δ2 2

(9)

The Gibbs excess model is defined by eq 10, based on the nonrandom two-liquid (NRTL) model30 as modified by Huron and Vidal:16 E G∞

nc

=

∑ xi i=1

n

∑ j =c 1 GjixjτjiRT n

∑ j =c 1 Gjixj

(10)

The remaining NRTL terms are defined using eqs 11 and 12: B



τji = aji +

bji T

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+ cji

simplifications were used. The majority of the data used in this work came from the IUPAC solubility data series.35−40,41 While solubility data for the hydrocarbon and/or water rich phases was available for all of these binary component sets, there were times when there was no mutual solubility data. In such instances, the method suggested by Satyro et al.27 was used to estimate the missing experimental data. Table 2 shows an example of a typical data set using cyclohexene as an example. The data are shown as a series of

(11)

Gji = bj exp( −αjiτji)

(12)

The terms aji, bji, cji, and αji are the so-called interaction parameters and are used to fit experimental VLE and VLLE data. The terms aji, bji, and cji are usually not symmetric. The term αji is symmetric in this work.

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Table 2. Sample Data for Cyclohexene

DATABASE DEVELOPMENT With the equation of state and mixing rule defined, the next step is the definition of the pure components and the experimental database to be used for the calculation of interaction parameters. The component definition was based on the need to support a newly created oil characterization method based on the PIONA31 (paraffin, iso-paraffin, olefin, naphthene and aromatic) hydrocarbon chemical family classification. This classification captures in an approximate way the basic chemistry of oils and is used to model reactive and nonreactive hydrocarbon mixtures encountered in conventional oil production and refining as well as other important hydrocarbon fluids such as shale oil.32−34 The components used in this study are shown in Table 1. The majority of the data was selected to be between 298 and 398 K, mostly at atmospheric pressure. If the data did not provide a measured pressure, the data was assumed to be at the calculated bubble pressure. We note that all calculations were performed using a rigorous multiphase flash engine and no

Temp, T/K 278.3 288.4 293.2 296.7 296.7 298.2 298.3 308.4 318.4 293.2 303.2 313.2

Watson-K

component

chemical family

MW/g/(g mol)

Kw/°R1/3

n-hexane n-heptane n-octane n-nonane n-decane n-undecane n-dodecane 2,3-dimethylbutane cyclohexene 1-hexene 1-heptane 1-octene 1-decene cyclopentane cyclohexane methylcyclohexane methylcyclopentane ethylcyclohexane o-xylene m-xylene p-xylene toluene benzene ethylbenzene styrene p-cymene n-butyl benzene anthracene

paraffin paraffin paraffin paraffin paraffin paraffin paraffin paraffin olefin olefin olefin olefin olefin naphthene naphthene naphthene naphthene naphthene aromatic aromatic aromatic aromatic aromatic aromatic aromatic aromatic aromatic aromatic

86.18 100.20 114.23 128.26 142.28 156.31 170.33 86.18 82.14 84.14 98.19 112.21 140.27 70.13 84.16 98.19 84.16 112.21 106.17 106.17 106.17 92.14 78.11 106.17 104.15 134.22 134.22 178.23

12.95 12.81 12.80 12.77 12.77 12.81 12.86 12.78 10.69 12.67 12.55 12.53 12.58 11.11 11.12 11.43 11.44 11.47 10.37 10.50 10.54 10.21 9.84 10.43 10.10 10.93 10.91 9.50

6.140 6.550 5.000 6.160 6.270 4.670 6.560 6.630 6.810 1.440 1.930 2.560

× × × × × × × × × × × ×

10−05 10−05 10−05 10−05 10−05 10−05 10−05 10−05 10−05 10−03 10−03 10−03

selected component cyclohexene cyclohexene cyclohexene cyclohexene cyclohexene cyclohexene cyclohexene cyclohexene cyclohexene water water water

temperatures and equilibrium phase compositions of the selected component. For the first point, this would mean that at 278.3 K, at the bubble point pressure, that the composition of cyclohexene in the aqueous phase would be 6.140 × 10−05 mole fraction. We note that lighter hydrocarbons, notably the initial paraffin series from methane to n-pentane require a different approach for model construction since not only mutual solubility in liquids are important, but also the solubility of water in a gas phase is a key consideration33 for the correct estimation of water content in natural gases,34 as shown in Figure 2.

Table 1. Selected Components for Binary Solubility molecular weight

phase composition/mole fraction

Figure 2. Methane water content at 366 K compared to GPA RR 210.44

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BINARY DATA REGRESSION With the data sets defined for the different binaries of interest formed by the combination of components listed in Table 1 and water, it was now possible to proceed to regress the necessary data into useful interaction parameters for the Gibbs excess mixing rule defined by eq 11. On the basis of previous experience25,27 it was known that the interaction parameters C



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Table 3. Binary Solubility Regression Results component

ai‑water

awater‑i

bi‑water/K

bwater‑i/K

temp range/K

ref

n-hexane n-heptane n-octane n-nonane n-decane n-undecane n-dodecane 2,3-dimethylbutane cyclohexene 1-hexene 1-heptene 1-octene 1-decene cyclopentane cyclohexane methylcyclohexane methylcyclopentane ethylcyclohexane o-xylene m-xylene p-xylene toluene benzene ethylbenzene styrene p-cymene n-butyl benzene anthracene

−4.608 −6.247 −4.608 −4.024 −3.806 −3.227 −6.077 −2.992 −5.346 −1.712 −3.086 −1.126 −1.786 −6.801 −5.000 −4.440 −6.196 −3.261 −3.169 −1.824 −2.893 −0.957 −2.720 −1.297 −2.293 −1.033 −1.674 −1.025

−1.846 −3.048 −4.500 −5.323 −7.045 −8.567 −1.510 −9.755 −2.605 −2.610 −1.862 −4.595 −7.072 0.521 −1.058 −3.024 −1.189 −5.108 −0.284 −2.819 −2.778 −1.202 −1.914 −1.963 −2.683 −5.285 −3.884 −5.706

4165.784 4649.912 4102.082 3935.216 3995.508 3804.563 4543.838 3739.685 3886.297 2894.677 3339.471 2786.946 3089.606 4568.807 4337.030 4165.037 4444.912 4041.510 3099.836 2734.736 3095.595 2371.203 2860.192 2577.500 2743.979 2561.877 2774.889 2500.000

3236.106 3998.289 4695.360 4841.716 5638.856 6219.994 2987.495 6649.430 2390.891 2761.485 2645.428 4069.243 4944.220 1815.847 2675.104 3500.234 2664.205 4450.662 1496.427 2289.570 2298.171 1546.772 1592.902 2032.594 2064.300 3602.936 3138.586 4819.469

273.2−477.6 273.2−423.6 273.2−422.7 298.0−373.2 298.2−398.2 298.2−398.2 298.2−398.2 273.2−422.8 278.3−313.2 293.2−494.3 278.3−318.4 298.2−549.8 288.2−475.2 298.2−426.3 278.3−482.2 283.2−410.5 283.2−303.2 310.9−561.4 273.2−318.2 273.2−473.4 273.2−461.3 273.2−524.3 273.1−511.3 273.2−536.1 280.2−338.2 283.2−473.0 280.2−373.2 273.2−348.2

38 39 41 28 28 28 28 38 37 37 28 41 42 36 37 39 37 41 40 40 40 39 45−48 40 40 42 42 43

important, and in this work the temperatures are defined between 298.15 and 398.15 K. The initial trends are shown in Figures 3 to 6 as a function of the logarithm of the molecular

had to be temperature dependent. To reduce the number of adjustable parameters, facilitate the interpretation of results, and eventually generalize the interaction parameters to support solubility calculations for oils cij and cji were set to zero and αji was set to be 0.2. This leaves four parameters available for regression per binary pair aij, aji, bij, and bji as defined in eq 11. The results of this regression for each component are in Table 3. The recommended data in the IUPAC data series35−42 were individually examined, and it is believed that their uncertainty is in the order of 30% in liquid mole fraction. In this work only recommended or tentative data from the IUPAC data series were used as suggested by Satyro et al.27 The actual uncertainty of the individually reported data points by IUPAC are not available, and therefore no proper statistical weighting is possible at this time when regressing data. A more detailed examination of the original data is available in Satyro et al.27 The data used for the benzene regression46,47 reported uncertainties in composition ranging from 0.000008 mole fraction to 0.0104 mole fraction. The solubility of anthracene in water was included to provide a prototype component representing the aromatic fraction of heavy oils. Therefore, only the aij and bij for anthracene−water were used for the generalizations, omitting the water− anthracene aij and bij terms. With the binary interaction parameters defined for the different hydrocarbons with water we can now attempt to generalize the hydrocarbon−water interaction parameters. The generalization process is performed by calculating the value of τij and τji at different temperatures as defined in eq 13 and Table 3. The selection of an appropriate temperature range is

Figure 3. τi‑water for each component calculated at 298.15 K.

weight, which is a simple molecular identifier and a crude measure of the size of molecules. We note that a group contribution could have been used but that would limit the usefulness of the method for mixtures of defined chemical compounds while our objective is to support mixtures with defined as well as undefined compounds. In general, τij increases with molecular weight, but there is still a significant amount of scatter. To reduce the scatter we need to add additional chemistry information to the model. This was done through the development of correlations based on PIONA chemical type or through the use of a parameter D



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available from oil characterization procedures will always be approximate.

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PIONA GENERALIZATION With the τij at 298 and 398 K defined, we impose the functional form used for equilibrium data correlation commonly used for activity coefficient models, eq 13: τij = aij +

bij (13)

T

The aij and bij parameters are then generalized for each chemical family using eq 14: aij , bij = αij ln(MWHC) + δij

Figure 4. τwater‑i for each component calculated at 298.15 K.

(14)

The results are summarized in Table 4. Table 4. Generalized Values for a and b in eq 13 Based on eq 14 chemical family paraffins olefins naphthenes aromatics

Figure 5. τi‑water for each component calculated at 398.15 K.

a or b

αHC‑H2O

δHC‑H2O

αH2O‑HC

δH2O‑HC

a b a b a b a b

3.948 −1042.43 4.302 −867.83 7.531 −1165.13 1.779 −297.12

−29.329 9102.45 −22.482 7207.37 −38.915 9536.62 −10.281 4133.47

−11.589 5074.58 −8.576 4725.19 −12.027 5580.83 −6.043 4373.24

50.224 −19485.53 35.859 −18460.56 51.966 −22006.68 25.652 −18140.08

Figures 7 to 10 show how well these regressed aij, aji, bij, and bji reproduce the original τij and τji.

Figure 6. τwater‑i for each component calculated at 398.15 K.

Figure 7. τi‑water for each component calculated at 298 K with fit values for τi‑water.

that captures the aromaticity for different hydrocarbons such as the Watson-K.28 It is important to stress that even if we are using different chemical species to help us characterize the oil the different species are not enough to completely capture the chemical behavior of a hydrocarbon. For example, looking at the solubility behavior of aromatics in water as a function of molecular weight we would have to consider situations where the increase in molecular weight comes from the addition of more aromatic rings to the molecule or addition of paraffinic segments. Further we would have to provide additional details about the aromatic rings−fused or not−and the type of paraffin segments−linear or branched. It is clear that a simple solution for use in process simulation coupled with information usually

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WATSON K GENERALIZATION A more approximate way to distinguish between the different hydrocarbon chemical families is to use the Watson K factor which provides a measure of a molecule’s aromaticity. We started by plotting the interaction parameters as a function of Watson K as shown in Figures 11 and 12. From that we see that there is an approximate linear relationship between the parameters, and we use eq 15 for the correlation. We proceed by generalizing the aij, aji, bij, and bji values from eq 13 in terms of both molecular weight and Watson K factor using eq 15. The parameters for eq 15 are shown in Table 5. E



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Figure 8. τwater‑i for each component calculated at 398 K with fit values for τwater‑i.

Figure 12. τ values for all components at 398 K compared to Watson K.

aij , bij = σ ln(MWHC) + ωK w + δ

(15)

Table 5. Generalized Values for a and b in eq 13 Based on eq 15 generalized parameter

σ

ω

δ

ai‑water awater‑i bi‑water/K bwater‑i/K

4.05 −9.07 −1178.82 3799.75

−0.65 −0.52 391.62 722.59

−14.73 44.89 4481.90 −22758.53

The comparison of the τij using eq 15 and the experimentally determined τij can be seen in Figure 13.

Figure 9. τi‑water for each component calculated at 398 K with fit values for τi‑water.

Figure 10. τwater‑i for each component calculated at 398 K with fit values for τwater‑i.

Figure 13. Comparison to experimentally determined τij and the τij calculated using eq 15.

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RESULTS AND DISCUSSION The two solubility models, one based on the PIONA chemical families and the other based on the use of the Watson-K parameters were compared using the solubility data collected by Satyro et al.27 based on the IUPAC solubility series. Using this data set provides a larger background to test the accuracy of the model and the results are summarized in Figures 14 to 19. Figures 14 and 15 were calculated using the parameters from Table 3 and PIONA-based parameters for all components not included in Table 3, while Figures 16 and 17 use the PIONA-based parameters for all of the components and Figures 18 and 19 use the Watson-K-based parameters for all of the components. These figures show that the PIONA parameter based results give a very similar estimate for the

Figure 11. τ values for all components at 298 K compared to Watson K.

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Figure 17. Water composition in hydrocarbon phase using PIONAbased parameters. This is based on eq 14. Percent error is 34%.

Figure 14. Hydrocarbon composition in water phase using regressed parameters and PIONA-based parameters. This is based on eqs 13 and 14. Average absolute percent error is 63%.

Figure 18. Hydrocarbon composition in water phase using Watson-Kbased parameters. This is based on eq 15. Average absolute percent error is 148%. Figure 15. Water composition in hydrocarbon phase using regressed parameters and PIONA-based parameters. This is based on eqs 13 and 14. Percent error is 30%.

Figure 19. Water composition in hydrocarbon phase using Watson-Kbased parameters. This is based on eq 15. Average absolute percent error is 42%.

Figure 16. Hydrocarbon composition in water phase using PIONAbased parameters. This is based on eq 14. Average absolute percent error is 98%.

To further test the model, the predicted water solublity in kerosene was compared to experimental results.49 The kerosene is modeled as a series of pseudocomponents as summarized in Table 6, and the results are shown in Figure 22. The molecular weight of the kerosene is 173 g/g mol and its density is 814.8 kg/m3. The kerosene was characterized using a standard oil characterization and therefore no PIONA data were available. The calculations were done using the Watson-K generalization.

water composition in the hydrocarbon phase as the specific component regressed values does. The Watson-K-based parameters give slightly worse results. Using a PIONA-type characterization for a hydrocarbon feed can give a significant improvement in mutual solubility with water than using pseudocomponents obtained from a typical distillation curve characterization. More detailed comparisons are shown for cyclopentane and toluene in Figures 20 and 21.

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CONCLUSIONS AND RECOMMENDATIONS The use of a Gibbs excess mixing rule equation of state based on the NRTL activity coefficient model can provide reliable estimates for mutual hydrocarbon and water solubilities for a G



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variety of components, either characterized as pure components or characterized through the use of pseudocomponents. It is important to select a Gibbs excess model that supports asymmetric parameters for the construction of a reasonable model for the solubility of water in the hydrocarbon-rich phase and for the solubility of hydrocarbon in the aqueous phase. The interaction parameters also must be a function of temperature. We found that the NRTL model as cast by Huron and Vidal to be a good platform for data correlation and extension, as well as straightforward to implement for process simulation calculations. The interaction parameters were generalized to be used with a PIONA or conventional oil characterization using chemical families or the Watson-K factor. Both methods provide substantial improvements over symmetric mixing rules conventionally used in process simulation. The PIONA chemical family prediction tends to provide more accurate results than the Watson-K generalization. The absolute average percent errors when using the specific binary interaction parameters as well as the generalized parameters are summarized in Table 7.

Figure 20. Results for cyclopentane using PIONA generalization parameters based on eq 14. Average error for cyclopentane in water is 2.82%. Average error for water in cyclopentane is 1.75%.

Table 7. Summary of Absolute Average Percenter Errors (AAPE/%) for Each Correlation Method solubility

boiling point/K 476 487 491 494 498 501 503 506 510 515 529

Watson-K (eq 15)

Satyro et al.27

30

34

34

28

63

98

148

83

The key advantage of this method over the method proposed by Satyro and co-workers is that it can be used directly in an equation of state instead of relying on further regressions based on estimated solubility data. The model is as accurate as models based on association theories but does not require the solution of a noncubic equations of state, and it is easily adapted for use in process simulators.

Table 6. Kerosene Distillation Data IBP 10 20 30 40 50 60 70 80 90 97.5

PIONA (eq 14)

water in hydrocarbon hydrocarbon in water

Figure 21. Results for toluene using PIONA generalization parameters based on eq 14. Average error for toluene in water is 25.7%. Average error for water in toluene is 14.3%.

percent distilled/%

binary specific (Table3)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors are grateful to Virtual Materials Group, Inc. for the permission to publish this work. REFERENCES

(1) Heidemann, R. A. Three-Phase Equilibria Using Equations of State. AIChE J. 1974, 20 (5), 847−855. (2) GPSA Engineering Data Book, 13th ed. (electronic) FPS; Gas Processors Supplier Association: 2012; Vol. II, section 20. (3) Tsonopolous, C.; Heidman, J. L. High-Pressure Equilibria with Cubic Equations of State; 4th Conference on Fluid Properties and Phase Equilibria for Chemical Process Design, Helsignor, Denmark, 1986. (4) Satyro, M. A. The Role of Thermodynamic Modeling Consistency in Process Simulation; 8th World Congress of Chemical Engineering, Palais des Congres, Montreal, August 23−27 2009. (5) Mathias, P. M. A Versatile Equation Of State. Ind. Eng. Chem. Process Des. Dev. 1983, 22, 385−391.

Figure 22. Experimental and calculated water content in kerosene vs temperature.49 Parameters estimated using eq 15. H



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