Sumallika Morakul

Jean-Roch Mouret

Pamela Nicolle

Cristian Trelea

Jean- Marie Sablayrolles

Violaine Athes
email: vathes@grignon.inra.fr

Modelling of the gas-liquid partitioning of aroma compounds during wine alcoholic fermentation and prediction of aroma losses

Keywords: gas-liquid transfer, online GC measurement, wine, aroma, dynamic modelling

A model was elaborated to quantify the gas-liquid partitioning of four of the most important volatile compounds produced during winemaking fermentations, namely isobutanol, ethyl acetate, isoamyl acetate and ethyl hexanoate. Analyses of constant rate fermentations demonstrated that the partitioning was not influenced by the CO 2 production rate and was a function of only the must composition and the temperature. The parameters of the model were identified in fermentations run at different temperatures, including anisothermal conditions.

The prediction of the partition coefficient (k i ) by the model was very accurate for isobutanol, isoamyl acetate and ethyl hexanoate. The technological potential of the model was confirmed by using it to calculate the losses of volatiles in the gas phase during fermentation and comparing them with experimental data. Up to 70% of the produced volatile compounds were lost. The difference between observed losses and losses estimated from predicted k i values never exceeded 3%.

Introduction

The synthesis of higher alcohols and esters during fermentation makes an important contribution to wine quality and the control of the production of these volatile compounds is one of the major ways to control the organoleptic characteristics of wine. The higher alcohols are undesirable at high concentrations, but in smaller quantities they are thought to contribute positively to overall wine quality. Esters have a significant effect on the fruity flavour in wine. The esters making the largest olfactory impact are ethyl acetate, isoamyl acetate, isobutyl acetate, ethyl hexanoate and 2-phenylethyl acetate [START_REF] Swiegers | Yeast and bacterial modulation of wine aroma and flavour[END_REF]. Varietal aromas -volatile compounds derived from non-volatile precursors in the grape which are released by the yeast during fermentation, such as thiols-also play an essential role in wine aroma but they are usually present at very low concentrations and are therefore more difficult to quantify.

The concentrations of volatiles at the end of fermentation depend primarily on their synthesis by the yeasts but may also be significantly modified by losses into the exhausted CO 2 . Therefore, understanding and modelling the transfer of aroma compounds between the gas and liquid phases would be extremely useful, and the calculation of balances differentiating the microbiological process of production and the physicochemical process of transfer into the exhausted CO 2 is central to this issue. The online monitoring of volatile compounds in the tank headspace, as recently proposed by Mouret et al. [START_REF] Mouret | On-line measurement of 'quality markers' during winemaking fermentations[END_REF], allows online estimation of volatile concentrations in fermenting musts, provided that reliable models for gas-liquid partitioning are available for all phases of the fermentation process. Finally, such models could subsequently be coupled to predictive models of volatile compound synthesis, based on knowledge of the biochemical pathways involved. Indeed, some authors have already proposed such models in beer making conditions [START_REF] Gee | A flavour model for beer fermentation[END_REF][START_REF] Trelea | Reliable estimation of the key variables and of their rates of change in alcoholic fermentation[END_REF][START_REF] Trelea | Dynamic optimisation of the aroma production in brewing fermentation[END_REF].

Several models have been developed to quantify the transfer of volatile molecules between aqueous solutions and gas phases [START_REF] Banavara | Modeling dynamic flavor release from water[END_REF][START_REF] Marin | Volatile release from aqueous solutions under dynamic headspace dilution conditions[END_REF][START_REF] Nahon | Modeling flavor release from aqueous sucrose solutions, using mass transfer and partition coefficients[END_REF]. However, none of them is directly applicable to winemaking conditions. Indeed, unlike the conditions considered in these established models, the concentrations of volatile molecules, as well as the overall composition of the fermenting must, are continuously changing during alcoholic fermentations. Another difference is the production and release of CO 2 , bubbles of which increase the transfer from the liquid to the gas, by stripping. Finally, only 3 molecules (isobutyl acetate, acetaldehyde and ethyl acetate) out of 21 were of interest in wine fermentations.

Several authors have studied flavour release in the context of oenology but mostly focused on the partitioning properties of volatiles in final wines [START_REF] Robinson | Interactions between wine volatile compounds and grape and wine matrix components influence aroma compound headspace partitioning[END_REF][START_REF] Tsachaki | Effect of ethanol, temperature, and gas flow rate on volatile release from aqueous solutions under dynamic headspace dilution conditions[END_REF][START_REF] Tsachaki | Aroma release from wines under dynamic conditions[END_REF] and did not consider their behaviour during fermentation. Recently, Morakul et al. [START_REF] Morakul | Comprehensive study of the evolution of gas-liquid partitioning of aroma compounds during wine alcoholic fermentation[END_REF] evaluated the effect of the matrix changes (mainly corresponding to the consumption of sugar and the production of ethanol) and of the temperature on gas-liquid partitioning in model conditions simulating fermenting musts. Ferreira et al. [START_REF] Ferreira | Losses of volatile compounds during fermentation[END_REF] assessed volatile compound losses due to the CO 2 production and showed that up to 80% of some molecules could be blown off; however, the experimental conditions used in [START_REF] Ferreira | Losses of volatile compounds during fermentation[END_REF] were not completely representative of the fermentation conditions, because changes in the matrix composition were not considered and the stripping rate was much higher than usually observed in winemaking.

In this paper, the objective was to develop a model of the evolution of the partition coefficient between the gas and liquid phases of four major volatile molecules, (ethyl acetate, isoamyl acetate, ethyl hexanoate and isobutanol) in winemaking fermentations. The partition coefficient k i is expressed as the ratio between the mass concentration of the compound in the gas phase [ gas i C in mg/L] and that in the liquid phase [ liq i C in mg/L] at equilibrium.

The work was focused on these four molecules because they are representative of higher alcohol and ester families. Isobutanol is one of the major fusel alcohols whose concentrations in wines are several tens of mg/L. It is synthesized by the yeasts from amino acids, in particular valine, and from keto-acids. As most higher alcohols are weakly volatile, its partition coefficient (k i ), expressed as a mass concentration ratio, at 25°C in grape musts is around 6.810 -4 [START_REF] Morakul | Comprehensive study of the evolution of gas-liquid partitioning of aroma compounds during wine alcoholic fermentation[END_REF]. Despite its high concentration in the liquid phase, it is often below its perception threshold in gas [START_REF] Swiegers | Yeast and bacterial modulation of wine aroma and flavour[END_REF]. Ethyl acetate, isoamyl acetate, and ethyl hexanoate are well known for their contribution to the fruity aroma of wines [START_REF] Francis | Determining wine aroma from compositional data[END_REF]. Their concentrations in wines are usually low (20 -60 mg/L for ethyl acetate and less than 10 mg/L for isoamyl acetate and ethyl hexanoate) but nevertheless always above their perception thresholds [START_REF] Swiegers | Yeast and bacterial modulation of wine aroma and flavour[END_REF]. The k i values at 25°C in grape musts are around 1.010 -2 for ethyl acetate, 2.910 -2 for isoamyl acetate and 4.510 -2 for ethyl hexanoate [START_REF] Morakul | Comprehensive study of the evolution of gas-liquid partitioning of aroma compounds during wine alcoholic fermentation[END_REF].

After assessing the effects of the main factors involved, and in particular the impact of stripping by CO 2 , the model for the prediction of the partition coefficient (k i ) was developed and then validated in different winemaking situations. The model was then used to estimate the losses of volatile compounds in several winemaking situations.

Material and methods

Fermentations

Yeast strains

The Saccharomyces cerevisiae strains EC1118 and K1 were used. These commercial wine yeasts are produced as active dry yeast by Lallemand SA. Each fermentation tank was inoculated with 0.2 g/L of active dry yeast previously rehydrated for 30 minutes at 35 °C.

Musts

Various grape musts from the South of France were used. They were flash-pasteurised and stored under sterile conditions. Their sugar concentrations were between 180-200 g/L and their assimilable nitrogen concentrations were 40, 120, 140 and 240 mg/L.

Tanks

Fermentations were run at pilot scale in stainless steel tanks. The tanks contained 90 L of must and the headspace represented 30% of the total volume.

Control of fermentation

The CO 2 released was automatically and continually measured with a gas mass flow meter and the rate of CO 2 production (dCO 2 /dt) was calculated with a high level of precision. The fermentations were controlled in different ways:

(i) Constant rate fermentations (CRF): to control the stripping effect, constant rate fermentations were run at 20°C. In these experiments, the rate of CO 2 production was kept constant by a feedback control system involving the addition of ammoniacal nitrogen via a peristaltic pump (Ismatec Reglo) [START_REF] Manginot | Use of constant rate alcoholic fermentations to compare the effectiveness of different nitrogen sources added during the stationary phase[END_REF].

(ii) Isothermal fermentations (IF): the temperature was maintained at a constant value (20 and 30°C), with a precision of 0.1°C.

(iii) Anisothermal fermentations (AF): the temperature was regulated according to the CO 2 production, which is proportional to the sugar degradation, with a slope of 0.2°C/(g/L) of evolved CO 2 . This evolution of temperature simulated anisothermal conditions observed in industrial-size tanks when the temperature rises freely until the final setpoint is reached [START_REF] Sablayrolles | Kinetics of alcoholic fermentation under anisothermal conditions.2. Prediction from the kinetics under isothermal conditions[END_REF].

Two anisothermal fermentations were run between 15 and 30°C, thus covering the maximum range of temperatures used in winemaking. Another fermentation was conducted between 20 and 30°C, simulating a common temperature profile for red winemaking. All parameters and control conditions for the fermentation experiments in this study are summarized in Table 1.

Analysis of volatile compounds 2.2.1. Online measurements in the gas

The gas was pumped at a flow rate of 14 mL/min from the tank headspace through a heated transfer line and concentrated in a cold trap (Tenax TM) for 6 min (desorption at 160°C for 1 min), and injected into a ZBWax (60 m  0.32 mm  0.5 µm, Phenomenex Inc.).

The injector was kept at 200°C. Helium was used as the carrier gas at a constant pressure of 120 kPa. The oven temperature program was 38°C for 3 min, 3°C/min up to 65°C, then 6°C/min to 160°C, held for 5 min, then 8°C/min up to 230°C and held for 5 min. A flame ionisation detector (FID) was used at 260°C. The on-line GC system was calibrated by using a Sonimix 6000C1 (LNI Schmidlin SA). This equipment generates standard gases by dilution from standard gas bottles or permeation tubes. Standard gas bottles (Air Product) containing 4004, 85.1 and 100 mmol/Kmol of ethyl acetate (CAS number 141-78-6), isoamyl acetate (CAS number 123-92-2) and isobutanol (CAS number 78-83-1), respectively, were used. A permeation tube with a permeation rate of 4831 ng/min at 45°C (LNI Schmidlin SA) was used to calibrate ethyl hexanoate (CAS number 123-66-0) concentration. The permeation tube was placed in an oven at 45°C, and diluted with air at 51 mL/min.

Measurements in the liquid

NaCl (1 g) was added to 3 mL of the fermentation sample in a 20 mL vial. To standardise the equilibrium conditions between the liquid and the headspace, the ethanol concentration in the vial was adjusted to 11% by adding 2 mL of a mixture of 12 g/L tartaric acid solution diluted either in water or a ethanol/ water mix (30% v/v). Fifty µL of 4-Methylpentan-2-ol at a concentration 3 g/L was added to the vial as an internal standard. The sample vial was heated and agitated for 5 min at 50°C in a headspace autosampler HT200 equipped with a gastight syringe, preheated to 60°C. One mL of headspace gas was analysed by using a HP6890 GC coupled with a FID detector. The injector temperature was 240°C. The GC oven was equipped with a BP20 column (30 m  0.53 mm  1.0 µm, SGE). H 2 was used as the carrier gas at a constant flow rate of 4.8 mL/min. The oven temperature programme was 40°C for 3 min, 3°C/min to 80°C, 15°C/min to 160°C held for 1 min, then 30°C/min to 220°C and then held at 220°C for 2 min. The detector was set at 250°C. Peak areas were acquired with Agilent Chemstation software.

Determinations of gas-liquid partition coefficients (k i )

The gas-liquid partition coefficients (k i ) during fermentation were followed by dividing the volatile concentrations in the tank headspace by the concentrations in the liquid at various times. Several k i were also determined in samples taken at different stages of fermentation by using the Phase Ratio Variation (PRV) method in static conditions as previously described [START_REF] Morakul | Comprehensive study of the evolution of gas-liquid partitioning of aroma compounds during wine alcoholic fermentation[END_REF][START_REF] Athes | Comparison of experimental methods for measuring infinite dilution volatilities of aroma compounds in water/ethanol mixtures[END_REF].

Modelling

The equations of the mathematical model (listed in the section Results) were implemented in a program written under Matlab 7 (The Matworks Inc., Natick, MA). The parameters were identified by nonlinear regression under Matlab, using the Statistic Toolbox.

Results and discussion

Model development

Effects of CO 2 stripping and of must composition

Morakul et al. [START_REF] Morakul | Comprehensive study of the evolution of gas-liquid partitioning of aroma compounds during wine alcoholic fermentation[END_REF] used synthetic solutions with increasing ethanol concentrations and decreasing sugar concentrations to simulate the evolution of the composition of must during fermentation. They showed that the gas-liquid partition coefficients (k i ) of higher alcohols and esters continuously decreased as the composition of a model wine fermentation medium changed because the sugar induces 'salting out' of volatile compounds (at the beginning of a fermentation) whereas the ethanol increases their solubility, and thereby decreases their volatility. The authors also observed a decrease of the relative gas-liquid ratio of these molecules during fermentation. However, the ratios were expressed in arbitrary units and could not be directly compared to the values of k i obtained in synthetic solutions, without any release of CO 2 .

To complete this previous preliminary study, the first aim of the present work was to clarify the effect of stripping on gas-liquid partitioning of aroma compounds. The stripping effect is complex because, in usual fermentations, both the rate of CO 2 production and other factors vary throughout the fermentation process. The problems associated with this complexity were overcome by controlling the rate of CO 2 release. The effect of stripping was indeed isolated by running defined fermentations, in which the rate of CO 2 production was kept constant by perfusion of ammoniacal nitrogen controlled. By modifying the amount of assimilable nitrogen initially present in the must i.e. 40 mg/L or 120 mg/L (no addition or addition of 80 mg/L of ammoniacal nitrogen), it was possible to set up two fermentations (CRF-0.3 and CRF-0.6) in which the rates of CO 2 production were kept constant at 0.3 g /L.h and 0.6 g /L.h respectively. The rate of CO 2 production was regulated between 10 and 85% of the fermentation progress. Fig. 1 compares the evolution of the CO 2 production rate (i) in these two fermentations and in (ii) an isothermal fermentation at 20°C, without any control of the CO 2 production rate (IF-20-B).

Changes in gas-liquid concentration ratios of ethyl acetate, isoamyl acetate, ethyl hexanoate and isobutanol were compared in these three different fermentation conditions.

They were also compared to the values of k i calculated by the static headspace PRV method in samples taken during fermentation. In these samples, k i was measured at equilibrium, in the absence of CO 2 release. Fig. 2 shows the results obtained for isobutanol and isoamyl acetate, the following observations being also valid for the other volatile molecules (data not shown).

A very remarkable result was that (i) almost identical decreases in k i with increasing ethanol concentration were observed whatever the CO 2 production rate and (ii) values of the partition coefficients were close to those obtained at equilibrium without any CO 2 release. It can therefore be concluded that stripping did not significantly change the gas-liquid partitioning of aroma compounds during fermentation and that the two phases always remained at equilibrium throughout the process in spite of the CO 2 flux. Therefore, at constant temperature, the values of k i which reflect changes in the gas-liquid partitioning of aroma compounds in fermenting musts only result from changes in the composition of the liquid phase, that is the decreasing sugar concentration and increasing ethanol concentration.

Consequently, at constant temperature, the evolution of k i can be written as follows:

 k i  A  E  B (Equation 1)
where A and B are constants depending on the considered compound i, and E is the ethanol concentration (g/L) in the liquid phase, which is proportional to the sugar consumption and CO 2 production. E is therefore representative of the whole matrix effect corresponding to the modification of the ethanol and sugar concentrations.

Effect of temperature

Gas-liquid partitioning not only depends on the composition of the liquid phase; it is also strongly affected by the temperature. For a constant medium composition, the Clausius-Clapeyron law is usually applied to the changes in partition coefficient (k i ) with temperature [START_REF] Meynier | Partition of five aroma compounds between air and skim milk, anhydrous milk fat or full-fat cream[END_REF]:

  d(ln k i ) d(1 T)   vap R or  ln k i  C   vap R  T (Equation 2)
Where H vap is the phase change enthalpy of the volatile compound expressed in J/mol, T is the absolute temperature (K), R is the perfect gas constant (8.413 J/mol.K) and C is a constant.

Nevertheless, Morakul et al. [START_REF] Morakul | Comprehensive study of the evolution of gas-liquid partitioning of aroma compounds during wine alcoholic fermentation[END_REF] showed that, in synthetic media, the value of the parameter H vap is not constant. For example, the H vap of isobutanol was 71.4 kJ/mol in a synthetic medium simulating a grape juice and 37.8 kJ/mol in a synthetic medium simulating a wine. As a consequence, the effect of the temperature on the gas-liquid partitioning not only depends on the temperature but is also a function of the composition of the liquid phase. So, the classical Clausius-Clapeyron expression was modified to introduce the dependence of the values C and H vap on the medium composition:

 ln k i  D1 D2  E  D3 D4  E R  T (Equation 3)
Where T is the absolute temperature and D1, D2, D3 and D4 are constants. To give a clearer physical meaning to the parameters of the model, we modified the previous equation by including a reference temperature (T ref ), so the model expression became:

 ln k i  F1 F2  E  F 3  F 4  E R 1000 T  1000 T ref         (Equation 4)
Where T is the current absolute temperature, T ref corresponds to the absolute reference temperature, i.e 293 K (20°C) in this study and F1, F2, F3 and F4 are constants. F1 is the logarithm of the partition coefficient (lnk i ) at the reference temperature in the initial must (E = 0). F2 represents the sensitivity of the partition coefficient to medium composition at the reference temperature. F3 corresponds to the value of H vap in the initial must (E = 0), H vap giving the sensitivity of k i to changes in temperature. F4 represents the sensitivity of H vap to changes in medium composition, described here as the ethanol concentration. The arbitrary factor 1000 was introduced for numerical convenience, to have numeric parameter values (F1-F4) of order of one. This generally favours reliable identification with nonlinear regression software. This factor can be of course absorbed into the values of F3 and F4.

The mathematical expression detailed in Equation 4was then used in the subsequent steps to model the evolution of the k i values for ethyl acetate, isoamyl acetate, ethyl hexanoate and isobutanol throughout the wine fermentation as a function both of the ethanol production and of the temperature. 2).

Model identification

Model parameters in

The estimated values of F1 were consistent with the values of lnk i measured by the PRV method [START_REF] Morakul | Comprehensive study of the evolution of gas-liquid partitioning of aroma compounds during wine alcoholic fermentation[END_REF] in static conditions in the must at the beginning of fermentation (-5.11, -3.94, - The values of F3 representing the sensitivity of k i to the temperature, were compared to previously reported H vap values [START_REF] Morakul | Comprehensive study of the evolution of gas-liquid partitioning of aroma compounds during wine alcoholic fermentation[END_REF]. The H vap was 39, 39.4, 67.5 and 71.4 kJ/mol for ethyl acetate, isoamyl acetate, ethyl hexanoate and isobutanol, respectively. Although the values are in the same order of magnitude as our F3 values, there are differences of about 20% for isoamyl acetate, ethyl hexanoate and isobutanol. These differences between F3 and H vap may be a consequence of the differences in the matrix used, as the F3 values were identified using the natural must whereas H vap were calculated using a synthetic medium which contained only sugar and weak acids to simulate the must at the start of the fermentation. The difference between F3 and H vap for ethyl acetate is higher than 40%, and this might be due to an atypical behaviour of this compound. Indeed, temperature had little influence on the value of k i of ethyl acetate and therefore, it is difficult to determine precisely the values of F3 and F4.

A sensitivity analysis of the model was conducted to assess the effect and the relative importance of the model parameters. Average conditions (T=25°C and ethanol concentration E=45g/L) were selected and each parameter (F1-F4) was arbitrarily increased by 30%. As expected, parameter F1 (directly related to the partition value) had the higher sensitivity, comprised between 64% for ethyl hexanoate and 92% for isobutanol. Its knowledge is thus the most important for accurately predicting k i . The second most important parameter (between 10 and 16% sensitivity) was F3, confirming the usually reported fact that temperature has a significant effect on volatility. The effect of the medium composition expressed via F2 was similar (between 4% for ethyl acetate and 17% for ethyl hexanoate).

Finally, parameter F4 was found to have some effect only for ethyl acetate (4%), and less than 1% for the other compounds studied; this is consistent with the model identification results

indicating that a significantly different from zero value of F4 could only be determined for ethyl acetate.

Model validation

After parameter identification, the variation of k i as a function of ethanol concentration and temperature, according to equation 4, was plotted. Fig. 3 shows the plot for fermentations used for parameter identification and Fig. 4 that for independent fermentations: (i) isothermal fermentation at 20°C (IF-20-B) and (ii) anisothermal fermentation between 20 and 30°C (AF-20-30).

The mean relative error between model prediction values and the measured values was calculated as follows: 5)

   1 n  k ij measured  k ij predicted k ij measured  100% (Equation
Where n is the number of k i measurements used for model validation. Table 3 indicates that (i) the average differences between the experimental and the calculated values were less than 10% for isoamyl acetate, ethyl hexanoate and isobutanol and (ii) the precision of the k i estimations was comparable for data from experiments not used for parameter identification.

These results demonstrate the value of the model to predict k i with a good accuracy for these 3 compounds. The prediction was much less satisfactory for ethyl acetate with differences up to 33%, due to an atypical behaviour of this compound.

One of the main reasons why predicting k i is valuable is that it allows calculation of the concentrations of volatiles in the gas phase from measurements in the liquid, and the reverse.

It is therefore possible to calculate the global production by adding the volatile concentration in the liquid to the amount lost in the gas phase (Equation 6): The relative amount of volatiles lost, i.e the ratio of losses to total production, is of particular technological interest. Table 4 compares measured (using concentrations in the gas) and predicted (using k i values and concentrations in the liquid) loss values. The predicted losses were very close to the values measured, illustrating the accuracy of the model. The amounts of lost volatile in the gas phase varied with the volatility of the compounds: it was negligible in the case of isobutanol but was 70% for ethyl hexanoate at 30°C.

 Losses  C gas (t)  Q(t

Conclusion

The gas-liquid partitioning of the main aroma compounds produced during winemaking fermentations, namely isobutanol, isoamyl acetate, ethyl hexanoate and to a lesser extent ethyl acetate, was accurately predicted by the model. The model, based on the effects of changes to the matrix and temperature during fermentation, allowed estimation of the partition coefficient (k i ) with less than 10% error, except for ethyl acetate. The benefits of predicting k i include allowing the calculation of the total production of the volatile compounds from a single measure (concentration in the gas or in the liquid phase). This is particularly advantageous in the case of on-line monitoring of the main aroma compounds in the gas, as described by Mouret et al. [START_REF] Mouret | On-line measurement of 'quality markers' during winemaking fermentations[END_REF]. The ability to calculate the total production and to differentiate between the amounts remaining in the liquid and those lost in the CO 2 are major issues for improving our understanding of yeast metabolism and optimising fermentation control. From a microbiological point of view, the total amount produced needs to be considered whereas, from a technological point of view, the concentration remaining in the wine is more important. For some molecules, such as isobutanol, the losses in the gas are negligible but for more volatile compounds, in particular esters, such losses can represent a very significant proportion of the total production. Minimising these losses, by optimizing the fermentation control, particularly the temperature profile, is a significant challenge. The objective is to find the best compromise between fermentation kinetics and aroma production. The development of metabolic models predicting the synthesis of aroma compounds [START_REF] Charnomordic | Two modelling approaches of winemaking: first principle and metabolic engineering[END_REF], in combination with the model of gas-liquid partitioning and with a kinetic model [START_REF] Malherbe | Modeling the effects of assimilable nitrogen and temperature on fermentation kinetics in enological conditions[END_REF] represents a complex but very promising prospect. Comparison with k i measured in static conditions by the PRV method (). Temperature:

Figure captions

20°C.

  Equation 4 were determined simultaneously by nonlinear regression based on the values of the k i (in concentration ratio) obtained from three experiments (i) isothermal fermentation at 20°C (IF-20-A) (ii) isothermal fermentation at 30°C (IF-30) and (iii) anisothermal fermentations between 15 and 30°C (AF-15-30). All k i measurements (41 values, including 14 from IF-20-A, 11 from IF-30 and 16 from AF-15-30) were used to determine the parameters F1-F4 together with their standard errors (Table

Fig 1 - 1 .

 11 Fig 1-1. Evolution of the CO 2 production rate as a function of ethanol concentration, for a

Fig 2 .

 2 Fig 2. Changes in gas-liquid ratio (k i ) as a function of ethanol concentration for isoamyl

Fig 3 .

 3 Fig 3. Comparison of predicted and measured k i for isoamyl acetate (B) and isobutanol (C) in

Fig 4 .

 4 Fig 4. Comparison of predicted and measured values for k i for isoamyl acetate (B) and

Fig 1 Figure1Fig 2 .

 12 Fig 1

  Figure2

  Figure4

  3.68 and -7.72 for ethyl acetate, isoamyl acetate, ethyl hexanoate and isobutanol, respectively). Among the volatile compounds studied, ethyl hexanoate had the highest lnk i consistent with the higher volatility of this compound whereas isobutanol, which had a lower value of lnk i , is always less volatile than esters. F2 values were negative, indicating that k i decreased as the ethanol concentration increased. The most negative value indicates the greatest sensitivity of k i to the changes in liquid composition. Ethyl hexanoate was the molecule most affected by the liquid composition (F2=-1.3910 -2 ) and ethyl acetate and isobutanol were less sensitive with F2

values of -2.9010 -3 and -4.1010

-3

, respectively. This sensitivity is seemingly related to the hydrophobicity of the molecule. Indeed, the hydrophobicity constant values (LogK ow at 25°C), i.e. 0.76, 0.73, 2.25 and 2.83, for isobutanol, ethyl acetate, isoamyl acetate and ethyl hexanoate, respectively (SRC Interactive PhysProp database, Syracuse), are in the same order as F2.

Table 3 .

 3 Mean relative errors (%) between predicted and measured k i calculated according to equation 5, with n: number of k i measurements per fermentation.

	Table3
	Fermentations	Ethylacetate	Isoamylacetate	Ethyl hexanoate	Isobutanol
		%	n	%	n	%	n	%	n
	Fermentations used for model identification
	Anisothermal 15-30°C	12.8	16	4.13	16	4.1	16	3.28	16
	Isothermal at 20°C	13.5	14	5.15	14	6.5	14	6.23	14
	Isothermal at 30°C	14.5	11	3.47	10	7.0	12	4.63	12
	Mean	13.5		4.25		5.7		4.65
	Independent fermentations used for model validation only
	Anisothermal 20-30°C	17.2	11	9.07	11	6.6	11	7.94	11
	Isothermal at 20°C	32.8	10	5.77	10	4.2	10	4.92	10
	Mean	24.7		7.42		5.4		6.50

Table 4 .

 4 Volatile compound losses (%). Comparison of predicted* (pred.) and measured** (meas.) values for losses, in %. Predicted losses were calculated from k i values and concentrations of the volatiles in the liquid.

	Experiments	Ethyl acetate	Isoamyl acetate	Ethyl hexanoate	Isobutanol
		pred.	meas.	pred.	meas.	pred.	meas.	pred.	meas.
	Anisothermal 15-30°C	7.48	6.87	33.3	33.7	54.2	54.3	0.66	0.65
	Isothermal at 20°C	5.86	6.02	25.2	25.6	44.6	44.4	0.55	0.54
	Isothermal at 30°C	13.6	13.0	44.1	42.2	70.9	71.0	1.33	1.33
	Anisothermal 20-30°C	10.5	12.5	45.0	46.7	66.3	64.7	0.93	1.01
	Isothermal at 20°C	5.59	8.73	27.1	26.2	46.2	45.3	0.63	0.63

***Measured losses were calculated from concentrations of the volatiles in the gas.

Acknowledgements

This research was funded by the European Union Seventh Framework Programme (FP7/2007-2013), under grant no. KBBE-212754.

F4 (kJ mol/g.L) -4.410 -1 ± 1.510 -1 -1.710 -3 ± 5910 -3 * 8.610 -2 ± 6.110 -2 * 6.410 -3 ± 6010 -3 * * A standard error leading to the value zero being included in the 95% confidence interval means that the parameter is not significantly different from zero.

Table2


W Shen

H Benyounes

L Dong

S Wei

J Li

V Gerbaud

CONCEPTUAL DESIGN OF NON-IDEAL MIXTURE SEPARATION WITH LIGHT ENTRAINERS

Keywords: Conceptual design, Feasibility study, Extractive distillation, Azeotropic mixture, Light entrainer

A method is proposed to study the separation of minimum-, maximum-boiling azeotropic, and low volatility mixtures with a light entrainer, to investigate feasible regions of the key operating parameters reboil ratio (S) and entrainer -feed flowrate ratio (F E /F) for continuous processes. The thermodynamic topological predictions are carried out for 1.0-2, 1.0-1a, and 0.0-1 Serafimov's class diagrams. It relies upon the knowledge of residue curve maps, along with the univolatility line, and it enables the prediction of possible products at the bottom of the column and limiting values of F E /F. The profiles of the stripping, extractive, and rectifying sections are calculated by equations considering S and F E /F, and they bring information about the location of singular points and possible composition profile separatrices that could impair process feasibility. Providing specified product composition and recovery, the approximate calculations are compared with rigorous simulations of extractive distillation processes. Separating non-ideal mixtures using a light entrainer provides more opportunities for the case when it is not easy to find an appropriate heavy or intermediate entrainer.

INTRODUCTION

In extractive distillation, a suitable entrainer commonly should be a miscible, heavy boiling component. It should form no new azeotrope, and interact differently with the components to be separated, causing the changes of relative volatilities, and thereby ease the separation. However, there are some cases when its use is not recommended, such as for a heat sensitive, high boiling component mixture to be separated. Different entrainers can cause different components to be recovered as bottom product or recovered overhead in extractive distillation. Poten-tial entrainers are critical since an economically optimal design made with an average design using the best entrainer could be much less costly [START_REF] Laroche | Homogeneous azeotropic distillation: Comparing entrainers[END_REF]. Theoretically, any candidate entrainer satisfying the feasibility and optimal criteria can be used no matter if it is a heavy, light, or intermediate entrainer. Literature studies on intermediate or light entrainers validate this assumption. [START_REF] Laroche | Homogeneous azeotropic distillation: Comparing entrainers[END_REF] investigated the use of heavy, intermediate, and light boiling entrainers to separate minimumboiling azeotropes. In a batch operation, a recently published paper reviewed the use of these three kinds of entrainers to separate maximum-boiling azeotropes and low relative volatility mixtures (Rodriguez-Donis et al., 2009a,b;Rodriguez-Donis et al., 2012a,b;Shen et al., 2013aShen et al., ,b,2015)). However, Rodriguez-Donis et al. (2012a) mainly focused on thermodynamic topological insight of how knowledge of the location of univolatility lines and residue curve analysis help in assessing the feasibility of batch extractive distillation. It was not further tested for continuous operation.

In this study, we extended our previous work (Shen et al., 2013b) on the design of thermodynamic feasibility insight for a conceptual batch and continuous extractive distillation. The separations of some new ternary systems, including a low relative volatility mixture with light entrainer, are explored. The UNIQUAC Thermodynamic model is used instead of the UNIFAC model to provide more reliable VLE calculations. After a brief analysis of the topological features of the system, profiles of the different sections are calculated. We focus on a sensitivity analysis of key operational parameters: entrainer -feed flow rate ratio and reboil ratio. The influences of the key operational parameters on profiles of different sections are studied. The composition profiles of the stripping, extractive and rectifying sections are calculated. The interaction relationships of key operational parameters have been explored. The rigorous simulation using the UNIQUAC model has been carried out to validate the thermodynamic insights and sensitivity analysis.

STATE OF THE ART WITH LIGHT ENTRAINER

After studying more than 400 couples of azeotrope -entrainer systems, [START_REF] Laroche | The curious behavior of homogeneous azeotropic distillation -implications for entrainer selection[END_REF] concluded that: (1) light entrainers, even though rare in industrial practice, could be as common as heavy entrainers theoretically since it is as easy to find a potential light entrainer as a heavy one; (2) light entrainers often represent the only viable alternative when a heavy entrainer cannot be used; and (3) light entrainers can perform as well or better than heavy entrainers.

Compared to extractive distillation using a heavy entrainer, very few literature studies focus on light entrainers. The minimum-boiling azeotropic mixture ethanol and water with the light entrainer methanol was first tested by [START_REF] Hunek | Separation of an azeotropic mixture by reverse extrac-tive distillation[END_REF] in a pilotplant experiment; this process is called reverse extractive distillation. Using the light entrainer acetone in the separation of ethanol (A) -water (B), [START_REF] Laroche | Homogeneous azeotropic distillation: Comparing entrainers[END_REF] showed that the univolatility curve location could be used to determine the product. [START_REF] Lang | Feasibility studies for batch extractive distillation with a light entrainer[END_REF] assessed the feasibility of the extractive distillation of ethanol (A)-water (B) with the light entrainer methanol in a batch rectifier and of a mixture of n-butanol (A) -n-butylacetate (B) with npropylformate and di-propylether as light entrainers in a batch stripper. Concerning a batch rectifier and a batch stripper, [START_REF] Varga | Batch extractive distillation with light entrainer[END_REF] studied the separation of three types of mixtures: ethanol-water (minimum-boiling azeotrope) with the light entrainer methanol, water -ethylene diamine (maximum-boiling azeotrope) with the light entrainer methanol, and chlorobenzene -ethylbenzene (close boiling mixture) with the light entrainer 4-methylheptane. More recently, applying thermodynamic insights with the knowledge of the location of univolatility lines and residue curve analysis, Rodriguez-Donis et al. (2012a) published a study on the feasibility of extractive distillation for possible separation of azeotropic mixtures with a light entrainer that belongs to Serafimov's class 1.0-2 and 1.0-1a. Some azeotropic and low relative volatility mixture separations using light entrainer studied in the literature are summarized in Table 1. Light entrainer is denoted as E, the higherboiling component recovered at the bottom is defined as B, the lower-boiling component obtained as top distillate is denoted as A, and azeotropic point are denoted by Az. This paper aims to investigate thermodynamic feasibility insight for the continuous extractive distillation process of three types of typical mixtures with light entrainers.

From basic mass balance analysis, feasibility of an extractive distillation under a finite reflux ratio (reboil ratio in reverse extractive distillation) condition requires that the top and bottom product compositions are connected each other through the liquid composition profiles x i in each section. The calculation requires choosing a target product composition and depends on many parameters. In azeotropic distillation, or a common distillation process with two column sections, the relevant parameters to be considered are the heat condition of the feed variable q, the feed stage location, total number of stages, column holdup, flow rates, condenser cooling duty, boiler heat duty, and reflux ratio. Not all are independent because the distillation column model has only two degrees of freedom (Widgado and Seider, 1996). Extractive distillation further adds the entrainer feed flow rate ratio to the list of the parameters as another degree of freedom. We focus only on the influence of the reboil ratio and entrainer -feed flow rate ratio on feasibility. Finding the ranges of reboil ratio and entrainer -feed flow rate ratio values that enable a feasible extractive distillation is the main issue of extractive distillation. Applying a light entrainer for separating a maximum-boiling azeotrope, the corresponding ternary diagram belongs to the Serafimov class 1.0-1a (occurrence 21.6%). The separation of a minimum-boiling azeotrope with a light entrainer corresponds to the 1.0-2 class (occurrence 8.5%). The extension of thermodynamic insight to other mixture classes with light entrainers was systematically studied by Rodriguez-Donis et al. (2012a), who combined knowledge of the thermodynamic properties of residue curve maps and of the univolatility and unidistribution curve locations. Rodriguez-Donis et al. (2012a) explored thermodynamic insights for extractive distillation of non-ideal mixtures with light entrainer, not only for well-studied cases (e.g., 1.0-1a class), but also for other possible feasible classes found in a batch processes study. For suitable classes, the general criterion under infinite reboil ratio could explain the product to be recovered and the possible existence of limiting values for the entrainer -feed flow rate ratio for batch operation: there exists a minimum entrainer feed ratio for the Serafimov class 1.0-1a with univolatility curve AB =1 that reaches the A-E (B-E) edge; there exists maximum entrainer flow rate to recover A(B) and no limit for B (A) recovery in the bottom product for the class 1.0-2 with univolatility curve AB = 1 that reaches the A-E (B-E), etc. The behavior at finite reboil ratio could be deduced from the infinite behavior and properties of the residue curve maps, and some limits on the reboil ratio were found. However precise determination of the limiting values of reboil ratio or of the entrainerfeed flow rate ratio required other techniques, summarized as follows.

For separating azeotropic mixtures, besides the conventional batch rectifier (Lelkes et al., 1998a;[START_REF] Stéger | Feasibility of extractive distillation process variants in batch rectifier column[END_REF], both batch stripper [START_REF] Varga | Batch extractive distillation with light entrainer[END_REF] and middle vessel columns [START_REF] Davidyan | Batch distillation in a column with a middle vessel[END_REF] have also been suggested and discussed in the literature, even though the use of a light entrainer would be recommend for use at a batch stripper, since the product expected to be a heavy boiler could still be removed from the boiler [START_REF] Varga | Batch extractive distillation with light entrainer[END_REF]. Extractive distillation can be operated either in a batch or in continuous mode. In the present work, we consider a continuous column configuration. Because we consider a light entrainer (boiling temperature below that of both A and B), the entrainer stream is fed below the main feed, these two feeds leading to three column sections: stages above the azeotropic mixture feed are called the rectifying section, stages between the azeotropic mixture feed and entrainer feed named the extractive section, with the stages below the stripping section (Figure 1).

FEASIBILITY STUDY METHODOLOGIES

Our methodology for the investigation of the extractive process feasibility relies on a short-cut method to compute the extractive distillation liquid column profiles, derived from differential Equation (1) [START_REF] Lelkes | Batch extractive distillation: The process and the operational policies[END_REF]:

i i i dx y y dh
(1) y i * and y i are the equilibrium composition with x i and the operating composition computed from material balance for a given tray, respectively. This equation is solved as an initial value problem during the feasibility study [START_REF] Varga | Batch extractive distillation with light entrainer[END_REF]. The model calculates the liquid composition profile in each column section based on the following assumptions:

(1) theoretical plates; (2) saturated liquid feed of mixture to be separated; (3) saturated vapor entrainer feed; (4) constant molar flow rate ratio of liquid and vapor in the three respective sections of the column;

(5) the liquid is an incompressible fluid.

Depending on Equation (1), Shen and Gerbaud (2013) published Equations ( 2), (3), and (4) for section profiles by considering a boiling liquid main feed F (feed physical state q=0) and defining the reboil ratio S. The rectifying profile for the saturated vapor entrainer is:

1 1 * 1 E i E E i F W i E F S dx F F F W x S x x x y F F dh W W W S S W W (2)
and the extractive profile for the saturated vapor entrainer

1 * 1 * 1 E i E i E W i E F S dx F W S x x x y F dh S W S W (3)
For the stripping profile:

1 1 1 * 1 i i w i dx S x x y dh S S S (4)
Under the infinite reboil ratio, the equations are identical whatever the entrainer feed state q value is, as was recalled by Rodriguez-Donis et al. (2012): "the extractive liquid composition maps are similar and the process limiting entrainer -feed flow rate ratio under infinite reboil ratio is identical considering the entrainer as a saturated liquid or vapor". This will hold for the assessment of the limiting flow rate ratio values. Then, as the entrainer is fed below the main feed (Figure 1), all the entrainer readily goes up into the extractive section. Consequently, we use Equations ( 2), ( 3) and (4) to compute each section composition profile. The second section of this work tries to continue validating these equations, and study the influence of the reboil ratios on profiles of different sections. Rigorous simulation validation is then carried out with ProSim Plus software for continuous column.

RESULTS AND DISCUSSION

Thermodynamic Topological Feasibility Insights

The thermodynamic topological ternary diagram is introduced to illustrate the feasibility of azeotropic mixture separation with light entrainer. Filled circles represent stable node SN rcm , empty circles represent unstable node UN rcm , and empty down triangles represent residue curve saddle points S rcm . For all illustrated mixtures, the diagram is obtained at 1 atm and the UNIQUAC thermodynamic model is used. For simplicity, three component abbreviations are used: A represents the lightest component with lower boiling point than B in the mixture to be separated, B represents the component with higher boiling point in the mixture of A and B, and E represents the entrainer. Based on the general feasibility criterion proposed in Shen and Gerbaud (2013):"Component A or B can be drawn as first bottom product using a stripper configuration if there is a residue curve going from the entrainer E towards A or B and following an increasing temperature in the region in which A or B is the least volatile component of the ternary mixture." In other word, the general feasibility criterion is valid for either component A or B in the mixtures of 1.0-1a, i.e., either of them can be drawn as first bottom product using a stripper configuration that depends on the univolatility line location at A-E side or B-E side. If the AB =1 curve intersects the binary side A-E, A is the expected product in the distillate because it is the most volatile in the region ABE where it is connected to E by a residue curve of decreasing temperature from E to A. If the AB =1 curve intersects the binary side B-E then B is the expected product. Thermodynamic topological feasibility analysis is carried out for the following categories of mixtures.

Minimum-Boiling Azeotropic Mixture Separation Using Light Entrainer

Four cases of separation of minimum-boiling azeotropic mixtures using light entrainers are illustrated in Figure 2. Using light entrainer, the ternary system belongs to the 1.0-2 class. The volatility order is E>Az>A>B. The cases ethanol/water/methanol (Fig. 2a denoted as case a), ethanol/toluene/acetone (Fig. 2b denoted as case b), and n-butanol/n-butyl-acetate/npropyl-formate (Fig. 2c denoted as case c) belong to the sub-case of class 1.0-2 with a univolatility curve AB =1 that reaches the A-E edge. In the volatility order region indicated, both A and B are the least volatile in the respective regions, where there exists a residue curve with increasing temperature from E to their locations; either component A or B is a possible bottom product of the extractive distillation process depending on the overall feed composition When B is the desired bottom product, it can be recovered without any limit for the entrainer feed ratio, whereas when A is the desired bottom product, the entrainer candidates will strongly depend on the extractive stable range SN extr,A , as there exists a minimum entrainer feed ratio to get A. If the upper limit for the feed flow rate is not a concern for industrial practice of continuous extractive distillation, the lower limit should be as low as possible to keep the energy demand low. The location of the univolatility line is the closest to E for case b, then for case a, and finally for case c. This expands the extractive stable range SN extr,A range, which also means an increase in the upper limit for the feed flowrate; case b has indeed the highest upper limit for the feed flowrate. Overall, Fig. 2b indicates that acetone exhibits the largest feasible extractive region for the separation of ethanol and toluene, targeting ethanol as product, which can result in a better operational stability. That may become critical at low reflux ratio when the range of feasible feed flowrate is narrowed. For the case of the benzene -MEK (i.e., methyl ethyl ketone) separation using the entrainer acetone (Fig. 2d). The univolatility line AB =1 ends at the binary B-E side at about 10% benzene and defines two feasible regions. Since the azeotropic components can be distillated only if the boundary is curved enough, however, extractive distillation is a worthy alternative process, as the feeding of the entrainer at an intermediate column tray generates extractive profiles that are able to cross the distillation boundary of the residue curve map [START_REF] Bernot | Patterns of composition change in multicomponent batch distillation[END_REF]). The rectifying stable separatrix is slightly curved, i.e., concave shape, in the region that contains component A, which makes it hardly possible to obtain MEK in azeotropic distillation, but feasible to get MEK as a bottom product in extractive distillation, while the other examples in Figure 2 have the convex shape in the region that contains component A.

Maximum-Boiling Azeotropic Mixture Separation Using Light Entrainer

The separations of the maximum-boiling azeotropes using light entrainers are illustrated by three cases in Figure 3. From Fig. 3a for separation of water (A) and ED (i.e., ethylenediamine) (B) using the light entrainer MeOH (E), the univolatility line AB =1 ends at the B -E sides at about 20 mol% ED, defining two different volatility regions. The feasible region EBA lies above the univolatility line. Water (A) can be recovered as bottom product above a minimum entrainer -feed flow rate ratio, so it can intersect a stripping profile which can reach x W,A , whereas no corresponding flow rate restrictions are placed on recovering B. Fig. 3b shows the acetone (A) and chloroform (B) separation using the light entrainer DCM (i.e., dichloromethane) (E). The point where the univolatility line intercepts the DCM-acetone edge is near to a dichloromethane vertex, located at x E =0.88 (88% DCM). The stable extractive node SN ext,A give rise to a minimum entrainer flow rate ratio. Below the minimum values, SN ext,A is located on the univolatility line; thus, the extractive profile cannot reach a stripping profile that approaches the expected product A. Similarly, Fig. 3c interprets the topological features for the separation of the maximum-boiling azeotropic mixture propanoic acid -DMF (i.e., dimethylformamide) using the light entrainer MIBK (i.e., methyl isobutyl ketone). The univolatility line starts at the maximumboiling azeotrope, intersects one triangle side and divides the composition graph into two volatility order regions, EBA and EAB. The point where the univolatility line intercepts the A-E edge is near to a MIBK corner, located at x E =0.97 (97% MIBK), and decides if apex A can be recovered from the bottom as x P,A lies on the A-E side (Fig. 3b). A is less vola- tile than E and B in the region EBA where it is connected to E by a residue curve of increasing temperature from E to A. The separation of ethyl acetate (131.9 °C) (A)benzene (136.2 °C) (B) with low relative volatility using the light entrainer acetone (56.5 °C) (E) belong to the 0.0-1 class. Figure 4 displays the thermodynamic features of the second case of ethyl acetate -benzene using acetone as entrainer. The univolatility line AB =1 intersects the A-E edge very close to the A apex and the B-E edge closer to the B apex. Then the two components A and B are products in the EBA and EAB volatility order regions, respectively. A requires a minimum entrainer flow rate ratio value, whereas B recovery is limited by a maximum entrainer flow rate ratio value.

The Influence of the Reboil Ratio on Composition Profiles of Different Sections

A detailed calculation of the profile map shows that when the reboil ratio gets smaller the feasible region of the stripping profiles gets smaller until the stripping profiles can no longer intersect the extractive profile region. This is shown in Figure 5. For x WA ={A, B, E}= {vary, vary, 0.01}, where the composition of component E is kept constant at the value 0.01 while varying the composition of components A and B, Fig 5a displays three stripping profiles computed as the result of varying the expected purity in component A from 0.98 to 0.7. The shape of the stripping profiles follows that of the residue curves typical for a 1.0-1a mixture. For an A content of 98 mol % or 70 mol %, the profiles are near the AE edge. For an A content of 30 mole%, it goes to the BE edge. Fig. 5b shows the evolution of the stripping profile computed from x WA with a purity of 98% in A, while changing the other component concentrations under various reboil ratios. Under an entrainerfeed flow rate ratio F E /F=1, the shaded region in Figure 5b shows all the possible stripping profiles while varying the composition of B and E. Accordingly, the three different parts of these shaded regions are obtained by changing reboil ratios. Figure 5b also indicates that the stripping profile gets shorter in length as the reboil ratio decreases from 10 to 1. This will affect the feasibility because a smaller stripping profile may not intersect an extractive profile. In other words, changing the reboil ratio with the entrainer -feed flow rate ratio, we can state that the desired product specification can be maintained over a wider range of reboil ratios as the entrainerfeed flow rate ratio increases. Figure 6a, b, c, concerning the separation of MEK (i.e., methyl ethyl ketone) and benzene using acetone as entrainer, illustrates the evolution of the fixed points and separatice locations as the reboil ratio S decreases. The extractive unstable node UN extr moves toward apex A parallel to the binary edge AB. The saddle node S extr moves toward the SN extr,A on the extractive separatrix, which results in the shrinking of the extractive feasible region when the boilup ratio S decreases from 30 to 1. The extractive separatrix location remains the same. At the boilup ratio S=1, this stresses the need for a large reboil ratio for the process to be feasible, whose consequence is a large heat duty.

Rigorous Simulation

In this section, rigorous simulation is performed with ProSim Plus 3.1. For all illustrated mixtures, the thermodynamic UNIQUAC model is used. These simulations provide compositions and temperatures profiles for different entrainer-feed ratio, reboil ratio, and composition. Table 2 displays the corresponding extractive distillation column specifications. The number of trays in the extractive section is set at a proper value so that the terminal point of the extractive section composition profile reaches near to the extractive section stable node. The rigorous simulation operation specifications for the acetone -chloroform -dichloromethane mixture are summarized in Table 2. Under conditions of S=20 and F E /F=20, Figure 7, concerning acetonechloroform mixture separation using dichloromethane as light entrainer, displays the rigorous composition profile, along with the simplified extractive profile from Equations (3). The feed mixture is assumed to be in a boiling liquid state and the entrainer in a saturated vapor. In the physical states (e.g., saturated vapor, saturated liquid, etc) and properties (e.g., tempaerature, and pressure) of the feed mixture settings, we set the operating saturated liquid temperature to 423 K for the feed mixture and the saturated vapor temperature to 389.3 K for the entrainer at 1 atm. The specification for this column is somewhat unusual, as the reboil ratio is fixed instead of the common tray using reflux ratio and distillate rate.

The extractive column has two design degrees of freedom left once the total number of stages and feed plate location are fixed: reboil ratio and entrainerfeed flow rate ratio. Given a composition of x F = {A; B; E} = {0.7; 0.3; 0.0}, it is feasible to recover A from the azeotropic mixture. With F E /F = 20, both the top and bottom of column are heavily polluted by the entrainer. However, the bottom of column is almost absent of B and, at the top of column, is almost free of A, thus enabling an effective separation of A and B in the next simple distillation column. The simulated extractive profiles agree well with simplified calculated profiles. Most important, by the extractive section profile reaches the SN ext , which is located as expected on the A-E edge. Therefore, it can intersect a stripping profile moving towards A near the A-E edge.

FE/F=1 S=30

MEK (A)

[SNextr]

[SNextr]

[UNextr] 8b shows the cases of separation of MEA (A) and benzene using the entrainer acetone to recover benzene (B) (product x WB from x F2= {A; B; E} = {0.225; 0.70; 0.075}). Each section of the rigorous profiles matches well with the simplified profiles. The process enables the recovery of MEK with a purity of 0.99901 or benzene with a purity of 0.99903. For both simulations, the rectifying and the extractive separatrices have close locations, and extractive profiles are only an extension of rectifying profiles. However, the profiles of these two sections have different curvature. For both cases, the rectifying profile is bounded on its left by the rectifying separatrix. Then the extractive section profile is bounded on its right by the extractive separatrix.

From the initial average feed point x F3 = {A; B; E} = {0.225; 0.275; 0.500} (see Fig. 8c) , located between the boundary and the univolatility line, one would expect to obtain benzene as a bottom product by using azeotropic distillation. However by the extractive distillation process we recover a bottom product whose composition lies in the neighborhood of the MEK vertex.

CONCLUSIONS

A method to study the separation with a light boiling entrainer E of minimum-azeotropic (Serafimov class 1.0-2), and maximum-azeotropic (Serafimov class 1.0-1a), as well as low-volatility (Serafimov class 0.0-1) mixtures has been proposed, so as to investigate the potential feasible region of the operating parameters: reboil ratio (S) and entrainer -feed flow rate ratio (F E /F) for continuous processes. First, prediction under infinite reboil ratio conditions is illustrated. It relies on the knowledge of the residue curve map topology and classification, along with the computation of the univolatility line, and enables the prediction of possible products at the bottom of the column and the values of the entrainerfeed flow rate ratio. Second, the approximate composition profiles also bring information about the location of pinch points and possible composition profile separatrices that could impair the process feasibility. We have considered for the continuous process a column configuration with the entrainer fed below the main azeotropic mixture feed, giving rise to three column sections: stripping, extractive and rectifying. Third, the approximate calculations are validated with rigorous simulations of continuous extractive distillation processes at specified values of product composition and recovery.

Under the infinite reboil ratio, the univolatility line AB =1 ends at the binary sides. This determines two different volatility order regions. We conclude that for maximum boiling azeotrope using light entrainer, class 1.0-1a with univolatility curve AB =1 that reaches the A-E (B-E) edge, there exists a minimum entrainer feed ratio which corresponds to SN ext,A (SN ext,B ) to get A(B). The SN ext,A (SN ext,B ) lies near A-E (B-E) edge where it can intersect the stripping profile which reaches A (B) in the bottom product. For a minimum boiling azeotrope using light entrianer, class 1.0-2 with univolatility curve AB = 1 that reaches the A-E (B-E), there exists a maximum entrainer flow rate to recover A(B) and no limit for B (A) recovery in the bottom product. This can be explained by the fact that SN ext,B (SN ext,A ) to get B (A) can be situated in any location on the edge B-E (A-E). For the separation of low relative volatility mixtures using light entrainers (0.0-1 diagram), feasibility depends on the univolatility line AB existence. When it does not exist, B is the unique possible product at the bottom of the column. When it exists, both original components A and B can be recovered, B below a maximum value of the entrainer feed flow rate and A above a minimum value. In perspective, using a light entrainer could provide more appropriate and economic alternatives to a heavy or intermediate entrainer for separating non-ideal mixtures.

Figure 1 :

 1 Figure 1: Configurations of typical extractive distillation with light entrainer.

Figure 2 :

 2 Figure 2: Minimum-boiling azeotropic mixture separations using light entrainer (1.0-2 class).

Figure 3 :

 3 Figure 3: Maximum-boiling azeotropic mixture separations using light entrainer (1.0-1a class).

Figure 4 :

 4 Figure 4: Low relative volatility mixture separation with light entrainer (0.0-1 class).

Figure 5 :

 5 Figure 5: Influences of the reboil ratio on composition profiles of the stripping section.

Figure 6 :

 6 Figure 6: Influences of the reboil ratio on composition profiles of the extractive section.

Table 1 : The study case related to extractive distillation separation of azeotropic and low relative volatility mixtures with light entrainers. Classification: 1.0-2; Azeotropic type: Minimum; Volatility order: E>Az>A>B

 1

	A	ethanol	ethanol/propanol	MEK	n-butanol
	B	water	toluene	benzene	n-butyl-acetate
	E	MeOH	acetone	acetone	n-propyl-formate
					/dipropyl-ether
	References	Hunek et al. 1989	Laroche et al. 1992	Rodriguez-Donis	Lang et al. 1999
				et al. 2012a
		Laroche et al. 1992	Rodriguez-Donis	Shen and Gerbaud
			et al. 2012a	2013
		Lang et al. 1999
		Varga et al. 2006b
		Rodriguez-Donis et al. 2012a
		Shen and Gerbaud 2013
	Classification: 1

.0-1a; Azeotropic type: Maximum; Volatility order: E>A>B>Az

	A	water	acetone	propanoic acid
	B	ethyl-enediamine	chloroform	Dimethyl-formamide
	E	MeOH	Dichloromethane	MIBK
	References	Varga et al. 2006b	Rodriguez-Donis et al. 2012a	Rodriguez-Donis et al. 2012a
		Rodriguez-Donis et al. 2012a		Shen and Gerbaud 2013
		Shen and Gerbaud

2013 Classification: 0.0-1; Azeotropic type: low alpha; Volatility order E>A>B

	A	chlorobenzene	ethyl acetate
	B	ethylbenzene	benzene
	E	4-methylheptane	acetone
	References	Varga et al. 2006b	Rodriguez-Donis et al. 2012a

ACKNOWLEDGEMENT

Weifeng Shen appreciates the guidance and valuable comments by Dr. Ivonne Rodríguez-Donis at LGC of Université de Toulouse, INP, and UPS. We gratefully acknowledges financial support from the National Natural Science Foundation of China (No. 21606026, 21206174) and Natural Science Foundation of Chongqing, China (No.cstc2016jcyjA0474).

APPENDIX

The UNIQUAC model is used to calculate vapor liquid equilibrium (VLE) properties. The binary parameters have been taken from DECHEMA. The model parameters are listed in Table A1.