Modeling VaporâLiquidâLiquid Phase Equilibria in FischerâTropsch

Article pubs.acs.org/IECR

Modeling Vapor−Liquid−Liquid Phase Equilibria in Fischer−Tropsch Syncrude Braden D. Kelly and Arno de Klerk* Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Alberta T6G 2 V4, Canada S Supporting Information *

ABSTRACT: Vapor−liquid−liquid equilibrium (VLLE) during product recovery and separation after Fischer−Tropsch synthesis affects the efficiency of downstream processing. Proper prediction of the VLLE is necessary to improve this processing step in the Fischer−Tropsch process; however, there is little guidance on what thermodynamic models to use. A similar problem presents itself in processes related to biomass conversion. The selection of an appropriate thermodynamic model to describe the nonideal VLLE of water−oxygenate−hydrocarbon mixtures was investigated. Cubic equations of state, virial equations of state, activity coefficient models, and equations of state with advanced mixing rules were considered. The evaluation was conducted using both default and optimized parameters. Predictive performance was improved when binary interaction parameters were optimized using experimental data, but parameter optimization is onerous and it is not always practical. It was found that cubic equations of state should not be used for nonideal systems, and even when combined with advanced mixing rules, there is a risk of poor predictive performance. Although the nonrandom two-liquid (NRTL) activity coefficient model is often considered for polar compounds, this investigation found that the predictive performance of NRTL degraded as the nonideality of the system increased. The universal quasi-chemical (UNIQUAC) activity coefficient model was the best all-around model for predicting the phase behavior of water−oxygenate−hydrocarbon systems. The Hayden−O’Connell virial equation of state predicted the vapor− liquid phase equilibrium of hydrogen bonding materials well. UNIQUAC in tandem with the Hayden−O’Connell equation of state is recommended for the modeling of Fischer−Tropsch syncrude VLLE when the partitioning of oxygenates between phases is important.

1. INTRODUCTION

of unrecoverable product loss, corrosion problems, refining challenges, and increased wastewater treatment cost.1 Design engineers who want to improve the design of syncrude cooling and phase separation require an accurate thermodynamic description of the phase equilibria. A similar problem is encountered in the design of phase separation for biomass conversion processes.2,3 There is little guidance in the literature with regard to what thermodynamic description to employ and what is available in process simulation software, in order to accurately predict the vapor−liquid−liquid equilibrium (VLLE) resulting from the condensation of mixed hydrocarbons, oxygenates, and water. Modeling of phase equilibria related to Fischer−Tropsch is discussed in the literature, but usually in a more limited context. There is a body of phase equilibrium modeling work published on the vapor−liquid equilibrium (VLE) in the Fischer− Tropsch reactor (Figure 1) under typical low-temperature Fischer−Tropsch synthesis conditions.4−8 In related investigations, the VLE of synthesis gas in the liquid phase was studied.9,10 All of these studies are concerned with describing the phase behavior in the synthesis reactor. Under lowtemperature Fischer−Tropsch synthesis conditions, with an operating temperature upward of 170 °C and operating pressure below 3 MPa, water is a vapor phase product and

Fischer−Tropsch synthesis is an indirect liquefaction technology that is industrially applied for the conversion of synthesis gas to syncrude. The composition of the syncrude is dependent on the Fischer−Tropsch technology and its operation; however, in all cases, the syncrude contains a mixture of hydrocarbons, oxygenates, and water. Cooling and condensation of the hot gaseous syncrude leaving the reactor after Fischer−Tropsch synthesis produces a three-phase mixture consisting of an organic phase, an aqueous phase, and a gas phase product (Figure 1). The impact of phase separation on downstream processing is far reaching, and it can be the origin

Received: Revised: Accepted: Published:

Figure 1. Vapor−liquid equilibrium (VLE) and vapor−liquid−liquid equilibrium (VLLE) of Fischer−Tropsch reaction products, as illustrated by a typical low-temperature Fischer−Tropsch process. © 2015 American Chemical Society

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July 16, 2015 September 17, 2015 September 25, 2015 October 5, 2015 DOI: 10.1021/acs.iecr.5b02616 Ind. Eng. Chem. Res. 2015, 54, 9857−9869

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Industrial & Engineering Chemistry Research

(d) The performance of each of the thermodynamic models was evaluated. The objective was not a numeric analysis (that is included irrespective), but an analysis of the underlying reasons for the performance of the model. By doing so more generalized statements could be made about the suitability of classes of thermodynamic model descriptions.

there is no second liquid phase. Furthermore, the contribution of oxygenates is usually ignored in the VLE calculations, because the more-polar short-chain oxygenates are also vaporphase products under the synthesis conditions in the Fischer− Tropsch reactor. Investigations that involve the VLLE of Fischer−Tropsch syncrude are less common. The need to have better description of the VLLE was realized early on in the industrial development of Fischer−Tropsch refining processes.11 Considerable effort was expended to gather distillation and separation data experimentally, little of which was published. The same situation was faced decades later for the development for processes dealing with hydrocarbon, oxygenate, and water separations.12 For process development, some piloting is inevitable, but this is not tenable for the development and evaluation of conceptual designs. Previously, the VLLE of syncrude during product cooling and separation after Fischer−Tropsch synthesis was considered, and a limited evaluation and validation of thermodynamic models was presented.13 It highlighted the need for guidance in the selection of a credible thermodynamic description of the VLLE of hydrocarbon−oxygenate−water systems. It is the objective of this study to provide guidelines for the selection of suitable thermodynamic models for this purpose.

3. THERMODYNAMIC MODEL SELECTION At equilibrium, it is a necessary and true condition for each component in a mixture to have equal chemical potentials in each phase. It is equivalent to say that each component in a mixture must have the same fugacity in each phase. As applied in process simulation software, thermodynamic models are used to calculate the fugacities of each component in each phase. Appropriate algorithms are applied to ensure that mole and energy balance constraints, as well as stability requirements, are also met. The degree to which the equilibrium calculation matches the reality is dependent on how accurately the thermodynamic model describes the fugacity of each component in each phase. This is not an easy task for nonideal mixtures. Many models poorly predict equilibrium compositions. The reason for poor predictions can often be found in the theoretical derivation of the model that included simplifications and assumptions that are invalid for nonideal mixtures. Therefore, many models in process simulation software are at least semiempirical in nature. There are four types of commonly used models: (a) classical cubic equations of state, (b) advanced mixing rule cubic equations of state, (c) activity coefficient models, and (d) virial equations of state. Advanced mixing rule cubic equations of state are cubic equations of state that incorporate activity coefficient models in their mixing rules. Newer models, such as the statistical associating fluid theory (SAFT), and cubic-plus-association (CPA), are slowly gaining acceptance. These models are more complex but, in principle offer better predictive capability.3 However, SAFT and CPA models are not yet widely found in major process simulation software. Part of the reason is the computation effort required, since these models are quite complicated compared to cubic, virial, or activity coefficient models. One model of each type was selected for evaluation (see Table 1).14,15 The Peng−Robinson equation of state was

2. METHODOLOGY Thermodynamic models for the description of the VLLE of hydrocarbon−oxygenate−water systems were evaluated. The following methodology was employed: (a) Representative thermodynamic models of each class of model description were selected for evaluation. In order to make the work as generally useful as possible, the models that were selected, were models typically found in commercial process simulation software. The different classes of thermodynamic models and the selection made will be justified in Section 3. (b) The next step was to gather published experimental liquid−liquid equilibrium (LLE)/VLLE data on representative ternary systems, and the necessary VLE and mutual solubility data for the constituent binary systems of each ternary. These ternary systems are simpler than the mixtures produced during Fischer−Tropsch synthesis, which is a shortcoming. Being simpler, the ternary systems made it easier to analyze the results to determine why thermodynamic models do (or do not) provide an adequate description. Data selection is discussed in Section 4. (c) The selected thermodynamic models were employed to predict the LLE/VLLE data. The difference in the calculated values (xcalc) from the experimental values (xexp) were expressed as an absolute average percentage difference (AAPD) of the number of data points (n) by eq 1: AAPD =

100 n

n

∑ i=1

Table 1. Thermodynamic Models and Model Types Evaluated model Peng−Robinson Gibbs excess Peng−Robinson NRTL UNIQUAC Hayden−O’Connell

model type cubic equation of state advanced mixing rule cubic equation of state activity coefficient activity coefficient virial + chemical theory

ref 14 14 14 14 15

(xexp)i − (xcalc)i (xexp)i

chosen to represent cubic equations of state. In the literature, Peng−Robinson is commonly used for hydrocarbons, as well as for VLE calculations in Fischer−Tropsch reactors. Because of its common use, the Peng−Robinson equation of state was included in the evaluation, although it was anticipated that it would not perform well for VLLE. The implementation of the Peng−Robinson model that was used included a correction for liquid volume estimation.16 The Huron−Vidal Peng−Robinson plus nonrandom two-liquid description was chosen as the

(1)

The calculations were performed using the implementation of the different thermodynamic models in the VMGSim process modeling software. In principle, other software implementations should give the same results; however, in practice, there sometimes are differences in results between different process modeling software packages. The study was not repeated using other commercial process modeling software. 9858

DOI: 10.1021/acs.iecr.5b02616 Ind. Eng. Chem. Res. 2015, 54, 9857−9869

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Industrial & Engineering Chemistry Research advanced mixing rule model to show the influence modification of mixing rules can have on cubic equation of state phase equilibria predictions. The description of association is important for compounds such as carboxylic acids (acetic acid in the datasets employed for this study). The nonrandom two-liquid (NRTL) and universal quasi-chemical (UNIQUAC) activity coefficient models are the two most common models used for nonideal liquid calculations. 14 The Hayden− O’Connell equation was chosen as the vapor-phase virial equation of state, because it combines the virial equation with chemical theory to account for association. The equations describing the thermodynamic models and mixing rules have been outlined in Appendix A at the end of this article.

Table 2. Origin of Experimental Data Employed for Optimizing and Modelling Measurement Range Covered compound

temperature (K)

pressure (kPa)

Binary Systems water−acetic acid 373.15− 391.65 water−ethanol 351.26− 373.15 water−hexane 273.15− 313.15 water−heptane 273.15− 318.15 acetic acid−hexane 313.2− 391.25 ethanol−heptane 344.15− 371.15 Ternary Systems water−acetic acid−hexane 298.15 and 304.15 water−ethanol−heptane 341.87− 352.39

4. VAPOR−LIQUID−LIQUID EQUILIBRIUM (VLLE) OF HYDROCARBON−OXYGENATE−WATER SYSTEMS 4.1. Equilibrium Data Selection. Generally, the models used in process simulators are either semiempirical or entirely empirical; there are no models that are entirely theoretical. All of the chosen models (Table 1) were semiempirical and ideally required empirical optimizing prior to being used for ternary LLE and VLLE calculations. Despite Fischer−Tropsch being a mature and significant industry, published data that involve hydrocarbon−oxygenate− water systems is limited. The data that are available and relevant have been collected at ambient pressure. This is an unfortunate limitation of the current evaluation, since the intended application of the work is for VLLE calculations at elevated pressure. Furthermore, in an actual Fischer−Tropsch reaction product, there are many components and it is impractical to obtain equilibrium data for each possible binary pair. Out of necessity, and to make this a practical endeavor, only the types of data likely to be available in a larger context was used, i.e., VLE data for miscible pairs and mutual solubility data for immiscible pairs. VLE data was employed to fit binary interaction parameters for the miscible pairs of components (see Table 2),17−24 and mutual solubility data was used for the water−hydrocarbon (immiscible) pairs (Table 2).25,26 The ternary datasets that were employed for model evaluation also are summarized in Table 2.27−29 The data were used as published. 4.2. Regression of Fitting Parameters. Optimizing models can become very time-consuming and gets more complicated with each component added to the mixture. The very basic necessity is VLE data for the miscible pairs, followed by mutual solubility data for the immiscible pairs (typically, the water−hydrocarbon pairs in the case of Fischer−Tropsch reaction products). In addition to these basic requirements for fitting, binary interaction parameters can also have experimental tielines from other ternaries that include their pair added into the regression routine. When available, experimental tielines help to increase the accuracy of binary interaction parameters significantly. While, in the case of the selected ternaries, it would be possible to increase accuracy by including experimental tielines into the regression routine, too few are available for the vast majority of components. The VMGSim process modeling software included parameter estimation routines. The Nelder−Mead simplex method was chosen as the regression algorithm, with an absolute difference minimization as the objective function, similar to eq 1. The quality, type, and conditions of the available data (Table 2) affected the quality of fitting parameters that were regressed.

ref(s)

101.325

17−20

101.325

24 (DECHEMA)a 25 (IUPACNIST)a 26 (IUPACNIST)a 21, 23 (DECHEMA)a 22 (DECHEMA)a

101.325 101.325 10.5− 101.325 101.325

101.325

27, 28

101.325

29

a

Multiple sources included in each data collection. Data from NIST was smoothed data from multiple sources provided by NIST. Data from DECHEMA was all sources at the temperatures and pressure listed.

The binary interaction parameters for the energy of interaction of component i with component j were optimized for all of the models. The optimized values for the fitting parameters and the default values in the process simulator are given for various thermodynamic models: Peng−Robinson (Table 3), Gibbs excess Peng−Robinson (Table 4), NRTL (Table 5), UNIQUAC (Table 6), and virial (Table 7). Table 3. Optimized and Default Binary Parameter (k12) for the Peng−Robinson Cubic Equation of State k12

a

binary system

optimized

defaulta

water (1)−acetic acid (2) water (1)−ethanol (2) water (1)−hexane (2) water (1)−heptane (2) heptane (1)−ethanol (2) hexane (1)−acetic acid (2)

−0.1521 −0.0875 0.4479 0.4491 0.0600 0.0760

0 −0.0911 0.4669 0.4606 0 0

Default parameters in the VMGSim process simulator.

There are theoretical bounds in which some parameters should be limited during optimization, such as the Peng− Robinson interaction parameter being between a negative one and a positive one. In the NRTL model, a third parameter, the nonrandomness parameter (αij) is supposed to be equal to 2/Z, where Z is the coordination number and is generally between 8 and 12. The parameter αij is typically set to a constant value of 0.2 or 0.3, thus making the NRTL a two-parameter model, rather than a three-parameter model.14 However, it was found that, by allowing the nonrandomness parameter value to be free to take on any value, better fits were predicted. Therefore, the NRTL model was treated as a threeparameter model in this work. Whenever possible the value of the nonrandomness parameter was kept positive to retain 9859


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Table 4. Optimized and Default Binary Interaction Parameters (τij) and Nonrandomness Parameter (αij) for the Gibbs Excess Advanced Mixing Rule Cubic Equation of State (Huron−Vidal Peng−Robinson + NRTL) Defaulta

Optimized

a

description

b12b

b21b


465.780 765.948 631.445 5899.55 897.665 −774.570

298.770 161.814 1535.50 2501.18 811.418 1668.11

α12

b12b

b21b

α12

0.7371 0.3100 −0.3388 0.1527 0.3583 0.0175

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

Default parameters in the VMGSim process simulator. bbij see Appendix A.

Table 5. Optimized and Default Binary Interaction Parameters (τij) and Nonrandomness Parameter (αij) for the NRTL Activity Coefficient Model Defaulta

Optimized

a

description

b12b

b

b21


588.870 704.435 300.920 5891.68 716.773 639.220

−269.100 −85.009 392.948 2031.30 615.327 631.090

α12

b12b

b21b

α12

0.2000 0.2637 −1.7827 0.2054 0.4965 0.5054

575.678 683.406 1955.30 2158.74 719.492 470.965

−434.089 −71.3683 1552.14 1519.13 −566.693 −470.965

0.0077 0.2981 0.3 0.3 0.3 0.3616


Table 6. Optimized and Default Binary Interaction Parameters (τij) for the UNIQUAC Activity Coefficient Model Defaulta

Optimized

a

b

description

b12


−387.953 −114.651 −571.384 −461.143 −586.574 −284.317

b21b

b12b

b21b

347.839 −35.1894 −1246.53 −1304.15 77.4075 −38.6999

−307.772 −114.386 −300.026 −300.031 −601.794 −354.661

288.142 −25.0915 −1318.01 −1308.01 93.2960 −0.2408


Table 7. Optimized and Default Binary Interaction Parameters (aij) for the Hayden−O’Connell with NRTL and UNIQUAC Models Defaulta

Optimized

a

description

a12 (NRTL)

a12 (UNIQUAC)

a12 (NRTL)

a12 (UNIQUAC)


3.06 1.129 0 0 0 0

3.47 0 0 0 0 0

2.5 1.55 0 0 0 0

2.5 1.55 0 0 0 0

Default parameters in the VMGSim process simulator.

Cubic equations of state, as well as activity coefficient models and hybrids of both, are capable of having additional parameters added through the use of temperature-dependent interaction parameters. The use of temperature-dependent parameters can increase the accuracy of models, but it requires that more time be spent on data regression. More importantly, it makes it harder to distinguish the capabilities of the models on a fundamental level, although it improves the ability of models to fit data. To allow for a meaningful investigation of model capabilities, aside from the built-in temperature dependence of the activity coefficient models, no additional

physical meaning, as originally designed by Renon and Prausnitz. However, Marina and Tassios30 found that, by allowing this parameter to be treated as purely empirical, improved fits could sometimes be found by allowing the nonrandomness parameter to have a negative value. They further found that (i) αij = −1 has almost the same effect as αij = 0.3 and (ii) with αij = −1, better predictions were made for immiscible binary components. In this work, for the hexane− water system, allowing a negative value for the NRTL αij (Table 5) led to the best fit when dealing with the LLE of the acetic acid−water−hexane ternary system. 9860


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system28 can be found in the Supporting Information (Figure S1).

temperature-dependent parameters were used. This is an option that could be employed in practice, similar to using additional forms of data such as experimental tielines in regression routines, but does not aid in the current evaluation of different models for the purposes of Fischer−Tropsch VLLE.

5. MODELING OF HYDROCARBON−OXYGENATE−WATER VAPOR−LIQUID−LIQUID EQUILIBRIUM (VLLE) The industrial process simulation software VMGSim was used to model the published experimental equilibrium data (Table 2) of two ternary LLE systems and one VLLE system. The evaluation was performed with the optimized fitting parameters, as well as the VMGSim default fitting parameters, because it is not always practical to optimize fitting parameters for complex systems, such as the Fischer−Tropsch reaction product. The evaluation using default fitting parameters is an indication of the quality of predictions that can typically be anticipated. The evaluation with optimized parameters is a measure of how well the thermodynamic model can predict nonideal systems. In these evaluations, a systematic deviation from the experimental data indicates a fundamental shortcoming of the model. 5.1. Peng−Robinson. The phase equilibria calculated by the Peng−Robinson cubic equation of state is shown for the water−acetic acid−hexane system27 (Figure 2) and the water− ethanol−heptane system29 (Figure 3). The calculation of the LLE using the second dataset for the water−acetic acid−hexane

Figure 3. Peng−Robinson calculation of the VLLE for the water− ethanol−heptane system using (top) default parameters and (bottom) optimized parameters. Calculated values are solid lines; experimental values29 are dashed lines.

Large errors of prediction were found using both default and optimized values in each phase of every system. Two things are immediately clear: (i) the Peng−Robinson equation of state is vastly improved with parameter optimization, showing its importance, and (ii) even after parameter optimization, the Peng−Robinson equation of state is still a very poor model for systems containing water and oxygenates, in addition to hydrocarbons, showing the importance of a model’s theoretical foundation. The Peng−Robinson equation of state was developed specifically for the oil and gas sector and is not designed for polar components. Using the Peng−Robinson equation of state with default settings led to spectacular failure in predictions for all LLE. The absolute average percentage difference (AAPD), as well as the maximum deviation, between the calculated and experimental data is shown in Table 8. While not as bad, the calculated multicomponent vapor-phase compositions involving oxygenates were still poor. While it is a simple model and quick to optimize, not enough was gained through optimization in these systems to make it viable for use as a thermodynamic model to calculate VLLE data for water−oxygenate−hydrocarbon systems. 5.2. Gibbs Excess Peng−Robinson. The addition of the NRTL model into the mixing rules of the Peng−Robinson cubic equation of state greatly increases its ability to predict the phase behavior of oxygenates. The calculated phase equilibria

Figure 2. Peng−Robinson calculation of the LLE for the water−acetic acid−hexane system using (top) default parameters and (bottom) optimized parameters. Calculated values are solid lines; experimental values27 are dashed lines. 9861


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Industrial & Engineering Chemistry Research Table 8. Error Analysis of Calculated Compared to Experimental Equilibrium Data of Ternary Systems Using the Peng−Robinson Equation of State with Default and Optimized Parameters AAPD (%) description water−acetic acid−hexane (25 °C) organic phase aqueous phase water−acetic acid−hexane (31 °C) organic phase aqueous phase water−ethanol−heptane organic phase aqueous phase vapor phase

Maximum Error (%)

default

optimized

default

optimized

107 198

53 37

785 1606

99 100

316 83

42 34

1313 166

293 100

98 78 18

70 46 9

400 709 57

327 100 24

Figure 5. Gibbs excess Peng−Robinson calculation of the VLLE for the water−ethanol−heptane system using optimized parameters; default parameters failed to predict LLE. Calculated values are solid lines; experimental values29 are dashed lines.

Table 9. Error Analysis of Calculated, Compared to Experimental, Equilibrium Data of Ternary Systems Using the Gibbs Excess Peng−Robinson Model with Default and Optimized Parameters

using the Gibbs excess Peng−Robinson model with optimized parameters is shown for the water−acetic acid−hexane system27,28 (see Figure 4, as well as Figure S2 in the Supporting Information), and water−ethanol−heptane system29 (Figure 5).

AAPD (%) description water−acetic acid−hexane (25 °C) organic phase aqueous phase water−acetic acid−hexane (31 °C) organic phase aqueous phase water−ethanol−heptane organic phase aqueous phase vapor phase a

Figure 4. Gibbs excess Peng−Robinson calculation of the LLE for the water−acetic acid−hexane system using optimized parameters; default parameters failed to predict LLE. Calculated values are solid lines; experimental values27 are dashed lines.

Maximum Error (%)

default

optimized

default

optimized

a a

39 36

a a

93 100

a a

27 33

a a

160 100

a a 32

32 97 6

a a 74

81 1349 16

Failed to predict LLE.

providing reasonable results for the VLLE (Figure 5). The quality and type of data used to regress parameters have a significant role in the accuracy of a model, and the Gibbs excess model seems to be the most sensitive of the models tested in this regard. 5.3. NRTL and Hayden−O’Connell. Similar to the application of the NRTL as mixing rule in the Gibbs excess Peng−Robinson model, the NRTL requires nonzero interaction parameters to function with the Hayden−O’Connell virial equation of state. The main difference in the application with the virial equation of state is that the unknown default parameters of the NRTL were automatically estimated using the UNIFAC model, whereas this was not the case for the software implementation of NRTL in the Gibbs excess function. The default settings for the NRTL used UNIFAC for the water−hexane, water−heptane, and heptane−ethanol pairs. The remainder were calculated by VMGSim, using VLE data. Comparisons of the experimental and calculated LLE of the water−acetic acid−hexane system using the NRTL and Hayden−O’Connell equation of state are shown in Figure 6,27 as well as in Figure S3 in the Supporting Information.28 In

The Gibbs excess Peng−Robinson model with default parameters failed to predict LLE. This was a consequence of the default parameters that were all zero in the process simulation software employed for this study (see Table 4). Zero values for the interaction parameters are not realistic for the NRTL model. The specific implementation in the process modeling software did not implement an estimation of the NRTL parameters. The poor performance of the Gibbs excess Peng−Robinson equation of state with default parameters was not an inherent shortcoming of the model. The optimized Gibbs Excess mixing rules improved the performance of the Peng−Robinson equation of state to predict the aqueous and organic phase for every component in the LLE systems (Table 9). Both the average error and the maximum error decreased significantly, compared to that of the Peng− Robinson equation of state on its own (recall Table 8). While showing great improvement in the LLE systems, the Gibbs excess calculation failed, even qualitatively, with regard to 9862


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Figure 7. NRTL with Hayden−O’Connell calculation of the VLLE for the water−ethanol−heptane system using (top) default parameters and (bottom) optimized parameters. Calculated values are solid lines; experimental values29 are dashed lines.

Figure 6. NRTL with Hayden−O’Connell calculation of the LLE for the water−acetic acid−hexane system using (top) default parameters and (bottom) optimized parameters. Calculated values are solid lines; experimental values27 are dashed lines.

Table 10. Error Analysis of Calculated Compared to Experimental Equilibrium Data of Ternary Systems Using the NRTL with Hayden−O’Connell with Default and Optimized Parameters

both default LLE systems, the NRTL failed to predict LLE at high concentrations of acetic acid. As a general consideration, this is a major error. The VLLE comparison for the water− ethanol−heptane system29 is shown in Figure 7. There was a general improvement in the prediction of the phase equilibria when optimized parameters were employed (see Table 10). The NRTL predicted the existence of each tieline, using default settings in the water−ethanol−heptane ternary system, with good fits at low concentration of ethanol and large errors at high concentrations of ethanol (as shown in Figure 7). Optimizing the NRTL led to increased accuracy in the low-concentration tielines but did not help at high concentrations, even failing to predict the last two tielines entirely. The Hayden−O’Connell equation of state improved after optimization. 5.4. UNIQUAC and Hayden−O’Connell. Modeling of the two water−acetic acid−hexane ternary systems27,28 using the Hayden−O’Connell virial equation of state with UNIQUAC is shown in Figure 8 and in Figure S4 in the Supporting Information. The modeling of the VLLE data of the water− ethanol−heptane system29 is shown in Figure 9. The development of UNIQUAC led to the group contribution method known as UNIFAC, and it is not surprising that, by default, several parameters for UNIQUAC are estimated using UNIFAC. In the present evaluation, the process modeling software VMGSim used UNIFAC to estimate the water−hexane, water−heptane, and hexane−acetic acid binary pairs. VLE data sets were used for the rest of the

AAPD (%) description water−acetic acid−hexane (25 °C) organic phase aqueous phase water−acetic acid−hexane (31 °C) organic phase aqueous phase water−ethanol−heptane organic phase aqueous phase vapor phase a

Maximum Error (%)

default

optimized

default

optimized

554 521

34 30

a a

92 100

434 407

18 32

a a

74 100

63 428 8

43 89 3

a a 22

a a 7

Failed to predict some LLE tielines.

parameters. Surprisingly, in the case of UNIQUAC, there was little difference in the accuracy of LLE and VLLE results (see Table 11) in the organic phase when using default parameters, compared to using optimized parameters. However, there was significant improvement in prediction in the aqueous phases. Another difference between UNIQUAC predictions and the other models was that, while the most dilute tieline had the highest error using default UNIQUAC and the other models, this was not the case for the optimized UNIQUAC. For 9863


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Figure 9. UNIQUAC with Hayden−O’Connell calculation of the VLLE for the water−ethanol−heptane using (top) default parameters and (bottom) optimized parameters. Calculated values are solid lines; experimental values29 are dashed lines.

Figure 8. UNIQUAC with Hayden−O’Connell calculation of LLE for water−acetic acid−hexane using (top) default parameters and (bottom) optimized parameters. Calculated values are solid lines; experimental values27 are dashed lines.

Table 11. Error Analysis of Calculated Compared to Experimental Equilibrium Data of Ternary Systems Using the UNIQUAC with Hayden−O’Connell with Default and Optimized Parameters

UNIQUAC with optimized parameters, the highest deviation from the experimental occurred for more oxygenate-rich mixtures. Regardless of whether default or optimized UNIQUAC was used, both results were more accurate than the other models for the water−acetic acid−hexane systems, with respect to the entire system. UNIQUAC also always predicted the correct number of tielines in LLE and VLLE.

AAPD (%) description water−acetic acid−hexane (25 °C) organic phase aqueous phase water−acetic acid−hexane (31 °C) organic phase aqueous phase water−ethanol−heptane organic phase aqueous phase vapor phase

6. SUITABILITY OF MODELS FOR HYDROCARBON−OXYGENATE−WATER VLLE 6.1. Aqueous-Phase Solutions with 0−10 wt % Oxygenates. The evaluation of the selected models over the entire composition space is not an application-specific evaluation, but rather provides a general assessment of the performance of the models for hydrocarbon−oxygenate−water mixtures. In reality, Fischer−Tropsch mixtures are not oxygenate-rich, and they almost always contain

Modeling VaporâLiquidâLiquid Phase Equilibria in FischerâTropsch

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