A new method for phase equilibrium measurements in reacting mixtures

Fluid Phase Equilibria 203 (2002) 31–51

A new method for phase equilibrium measurements in reacting mixtures Frank Alsmeyer a,∗ , Wolfgang Marquardt a,1 , Günter Olf b a

Lehrstuhl für Prozesstechnik, RWTH Aachen, Templergraben 55, D-52056 Aachen, Germany b Bayer AG, Zentrale Technik–Technische Entwicklung, D-51368 Leverkusen, Germany Received 22 August 2001; accepted 24 May 2002

Abstract We propose a new method for phase equilibrium measurements where zero net mass flux over the phase boundary is obtained even at chemical non-equilibrium. Thus, physical equilibrium can be guaranteed irrespective of (potentially slow) mass transfer. We have used this method for the experimental determination of vapor–liquid equilibria (VLE) for a reactive transesterification system in a new type of flow-through still where compositions of both phases are observed in situ by infrared spectroscopy to avoid disturbance of the steady state. The design circumvents limitations of conventional apparatus and allows measurements for promising but demanding applications like reactive distillation. Besides, the data obtained with this method can be used to develop kinetic information. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Experimental method; Vapor–liquid equilibria; Reactive systems; Spectroscopy; Mixture

1. Introduction Combined reaction/separation processes have received much attention recently [1]. One important example is reactive distillation [2] where several processes are commercially applied, e.g. for the production of fuel ethers. Design and operation methods for reactive separation processes are being constantly improved, but they rely on accurate physical property data that are often not available for candidate systems [2]. This is particularly true for phase equilibria like vapor–liquid equilibria (VLE), liquid–liquid equilibria (LLE) or vapor–liquid–liquid equilibria (VLLE). Under process conditions, reaction and phase separation for such systems occur simultaneously and on a similar time scale. If the reaction is autocatalytic or non-catalytic, it is, therefore, impossible to separate the measurement of phase equilibria and reaction rates, which would be the conventional approach in ∗

Corresponding author. Tel.: +49-241-809-4668; fax: +49-241-809-2326. E-mail addresses: [email protected] (F. Alsmeyer), [email protected] (W. Marquardt). 1 Co-corresponding author. 0378-3812/02/$ – see front matter © 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 8 - 3 8 1 2 ( 0 2 ) 0 0 1 7 0 - X

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Table 1 Existing experimental work on reactive VLE, for the categories (1)–(3) see text

(1) Da  1

Static cells

Circulation stills

Flow-through stills

Siddiqi et al. [3]

Hirata and Komatsu [4,5], Hirata et al. [6] Nishi [10] Kang et al. [12] Wang and Zhao [13] Lee and Kuo [14], Lee and Liang [15], Lee and Lin [16] Lee et al. [17]

Maurer [7], Maurer and co-workers [8]

Heintz and Verevkin [9]

(2) Da  1

Grünert et al. [18] Arlt [20]

(3) Intermediate Da

Hasse and Maurer [11]

Carvoli and Delogu [19] Lee et al. [17] Sawistowski and Pilavakis [21] Reichl et al. [22] Roederer et al. [23] Roederer [24]

process design. New experimental procedures to determine physical properties are, therefore, required for such combined reaction/separation processes. Table 1 lists references concerned with the experimental determination of reactive VLE. We discuss in the next section why most of the approaches are of limited use for multifunctional reactors. We then propose a new general method where zero net mass flux over the phase boundary can be obtained even if one phase is not in chemical equilibrium, which guarantees attainment of the phase equilibrium. As an application of this method, we describe our experimental setup for isothermal reactive VLE measurements, called the zero flux still (ZFS). Experiments and results obtained in this apparatus are presented for both the reactive quaternary transesterification system n-butanol/ethyl acetate/ethanol/n-butyl acetate (BuOH/EtOAc/EtOH/BuOAc) and its non-reactive binary reactant system BuOH/EtOAc. 2. Classification of existing approaches Phase equilibrium experiments can be divided into synthetic and analytical methods. This classification is common for LLE (e.g. [25]), but useful for VLE as well. Clearly, synthetic methods, i.e. methods where a phase transition is approached by changing a state variable at a fixed composition, cannot be used for reactive phase equilibria because the phase composition changes over time due to conversion. Any method for reactive phase equilibria will be analytical in that it has to rely on some analysis of the phase composition, most often accomplished via gas chromatography (GC). Moreover, because conversion is unavoidable, one is concerned with multicomponent mixtures. As we are not aware of experimental setups designed especially for reacting systems involving two liquid phases (except if they are in chemical equilibrium), the following discussion of previous experimental work is limited to VLE. Table 1 lists all experimental studies of VLE in reacting systems that we have found in the literature. We distinguish three common types of experimental setups: static cells, circulation

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and flow-through stills. An overview of these experimental methods for the non-reactive case can be found, for example, in Hála et al. [26]. Whether one of them can, in principle, be applied for a given reactive system depends on • the chemical reaction rate constant(s) of the system, k (which can always be defined to be of pseudo-firstorder [27]), • the physical (phase) equilibration time, τVLE , depending on both the system and the apparatus, • the (mean) residence time, τ of the reacting phase(s) in the apparatus and • the target compositions for the VLE measurement. Note that for some apparatus/system combinations τ can be smaller than τVLE . In such a case, accurate VLE measurements cannot be made in the given experimental setup. The dimensionless product, kτ can be defined as the Damköhler number Da = kτ . In terms of this number, the limiting cases for the attainable composition in the apparatus are chemical equilibrium (Da  1) and no reaction (Da  1). Most of the references in Table 1 can be attributed to one of these limits: 1. For large Da  1, simultaneous chemical (reaction) and physical (phase) equilibrium is the only state that can be attained. This is a common situation for, but not limited to, fast reacting systems, such as electrolyte systems [3], and there is no fundamental difficulty to experimentally determine the VLE using any one of the three established methods, e.g. an Othmer type still (i.e. with circulation of the vapor phase) [4–6,10,12–17], or a static cell [9]. A flow-through apparatus is an option if one can make sure that both chemical and physical equilibrium are attained within the apparatus. These designs require larger amounts of chemicals than recirculating stills or static cells, but in special cases, they can be useful. As an example, for systems with a more volatile component, Maurer [7], and Maurer and his co-workers [8] used phase separation via a thin-film evaporator large enough to ensure physical equilibration. In a third paper of the same research group, deviations from chemical equilibrium were explicitly avoided by evaporating only small amounts of sample using a gas saturation technique [11]. 2. In case of Da  1, phase equilibrium can be attained, while the residence time of the apparatus is too small to reach chemical equilibrium. A quasi-steady state is attained for slow or moderately fast reactions. The character of such methods is approximative by definition. In one variation that one encounters, physical equilibrium is assumed, and all the reaction products are considered in the analysis. The binary parameters are then estimated from polynary data. Carvoli and Delogu [19] used a circulation technique for such a study. A second variation is to account for product formation by an extrapolation of the measured properties to the beginning of the experiment. An example is the work of Grünert et al. [18], who was able to determine VLE for slowly reacting olefin oxides in a static apparatus. More recently, it has been attempted to push the applicability of this method further towards faster reactions by reducing τ . The apparatus of Arlt [20] is specifically designated for reactive distillation applications and suited for half-life periods around 30 min. It is basically a static cell, but includes injection of the second component through a circulation stream favouring mixing. Pressure is measured as a function of time after injection, at (assumed) constant temperature, and then extrapolated to the injection time. There is some disadvantage to it in that error bounds cannot be given because this extrapolation to the unreacted binary is used during analysis. 3. Regardless of the actual Da number, a strict steady state can be accomplished in stills of the flowthrough type. This is the more rigorous and more widely applicable approach for reactive VLE

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apart from the chemical equilibrium limit. The flow-through method allows for short residence times (Da < 1), but the drawback of these designs is their high product consumption. Sawistowski and Pilavakis [21] were the first authors to publish reactive VLE data obtained under steady state conditions, using a conventional flow-through still. More recently, two special designs of this type have been proposed for reactive VLE. Roederer and co-workers [23,24], used a specialized flow-through still to determine the VLE and reaction kinetics of an isomerization reaction at three different temperatures. The reaction was relatively slow, with a half-life period of about an hour in the fastest case. Another flow-through still with mean residence times of 0.5–1 min was presented by Reichl et al. [22]. Pseudo-binary data, i.e. with negligible product formation, were determined for two esterification/hydrolysis reactions at isobaric conditions. Several non-reactive systems were also examined for the purpose of validation. The authors point out that inspite of the short residence time, the systems may not react too quickly. The VLE of methanol/formic acid, having a half-life period of about 2 min, could not be determined. It is noted that this conclusion is based on the premise of the authors to measure only binary interactions. In both setups, there is a potential danger that VLE is not entirely reached, because the residence time in the still might not be sufficient. To sum up, the experimental approaches based on methods (1) and (2) are of limited use in conjunction with the design of multifunctional reactors. We, therefore, propose a new general method for reactive phase equilibrium measurements that is also based on method (3) but, in contrast to the existing stills, guarantees attainment of the VLE. 3. Measuring reactive phase equilibria under steady state conditions To introduce the general method, we first discuss the case of reactive VLE measurements in this section. To obtain a strict steady state, flow-through designs are the only possible choice, as discussed in the previous section. This still type also has the advantage of short residence times leading to low Da numbers, which is necessary to cover a large composition region for not too slowly reacting systems. Within this short time, one has to make sure that physical equilibrium is actually reached, i.e. τVLE < τ . In conventional VLE stills, the best solution is the use of a Cottrell tube in combination with separate feeds of preheated liquid and superheated vapor [26]. This avoids any disturbing influence by partial condensation or evaporation on the experimental results, especially the measured temperature. In principle, these stills can be used for reacting systems [22]. However, it is not trivial to test if mass transfer is sufficient in such an apparatus: if the residence time or flow and mixing conditions are varied, conversion varies as well. Thus, one has no means to vary mass transfer for a fixed composition. To overcome this possible limitation of existing stills, we propose to complement the flow-through method with an important modification. As usual, the thermostated (premixed) inlet stream enters the still, where the mixture is allowed to physically equilibrate. However, whereas in usual designs both vapor and liquid phase are continuously removed, we enclose the vapor phase in the still. The principle is depicted in Fig. 1 for a three component system A ↔ B + C. When the liquid level is held constant and thorough mixing is ensured, the liquid phase composition will finally attain a steady state that can be influenced by variation of the mean residence time τ in the still as shown in Fig. 2. For τ → 0, the composition will be close to the reactant A, in the case of a mixture, e.g. A + C or B + C, close to the

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Fig. 1. Measurement principle.

respective binary subsystem (dashed margins of the shaded attainable region). For τ → ∞, chemical equilibrium compositions (solid line) can be obtained. Intermediate τ yield compositions inbetween these two extremes (e.g. on the dotted lines). Note that we are not limited to feeding reactants. By adding products to the feed, almost any liquid composition can be established in the still, even in cases with simultaneous reactions. Whatever the residence time, the vapor is exposed to a constant composition at the phase boundary. The significant advantage of this procedure is that we can allow the phases to equilibrate as long as we keep providing new material. Physical equilibration is not hindered by possibly slow mass transfer, whereas all existing designs must reach the physical equilibrium state within the residence time of the apparatus. In our still, under steady state conditions, the net mass flux via the phase boundary (interface) is effectively zero, and we will, therefore, call it ZFS. One might ask what residence times can be achieved in such a still. It is obvious that the construction of the still (Fig. 4) takes up the idea of a continuous stirred tank reactor (CSTR). The limitation then lies in the time that is needed to ensure homogeneous mixing. One drawback of this method is that, just like in static cells, we must degass the inlet streams thoroughly prior to mixing in order to avoid accumulation of dissolved, inert gases in the enclosed vapor phase. Secondly, we cannot investigate mixtures with chemical reaction in the vapor phase.

Fig. 2. Attainable region.

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In the parameter estimation procedure following the experimental program, we take account of the polynary nature of the data, i.e. a multicomponent model is fitted to the data. The approach conventionally used for non-reactive VLE to measure only binary interactions and assemble these to multicomponent models can simply be no longer used in the case of noticeable conversion. On the one hand, this means that one may lose the general applicability of the binary or, in this case, pseudo-binary parameters in conjunction with other systems. On the other hand, the primary goal here is to obtain data and a corresponding VLE model valid in the composition regions that are attained within the application at hand. Typically, commercially applied reactive distillation processes lie in the kinetic regime (intermediate Da) and thus, well within the regions [2] attainable with this method. Other researchers, e.g. [15], have estimated binary model parameters for reactive systems solely based on VLE data at simultaneous chemical equilibrium. The risk to obtain models that are physically meaningless apart from chemical equilibrium is high because of the inverse nature of the parameter estimation problem, where small errors in the data can lead to large errors in composition regions where no data are available. Because in our still we extend the experimentally attainable region as far as possible towards the unreacted binary systems, this risk is considerably reduced. The steady state method at zero flux is not limited to VLE measurements, but can potentially be applied in all cases where homogeneous mixing of the coexisting phases is possible, and where there is no (significant) reaction in at least one phase. For the sake of completeness, we would like to mention that the principle of enclosing one phase has been applied by Colburn et al. [28] before, but not in conjunction with reactive systems. In his apparatus, the phases are however reversed, and a steady vapor stream flows over the enclosed liquid phase until liquid temperature and composition remain constant.

4. The zero flux still for VLE 4.1. Flowsheet A flowsheet of our VLE apparatus based on the steady state method with zero flux is given in Fig. 3. Two reactants A and B are separately degassed following a suggestion of van Ness and Abbott [29] both several hours before and during the VLE experiment. Volumetric high pressure liquid chromatography (HPLC) pumps guarantee highly accurate and constant flows to fix mean residence times in a range of 30 s to several hours. Thermostat 1 preheats the streams prior to mixing. It is used to control the temperature of the mixed streams, by means of manipulating the thermostat’s temperature. This is to compensate for mixing effects. By keeping the mixed stream’s temperature below or above that of the still, reactions with significant exotherm or endotherm can be handled. To this end, an additional controller (not depicted) can be used to control the still’s temperature via the inlet temperature. The stream then passes the ZFS thermostat 2 and enters the still from below. The liquid level in the still is measured by a capacitive level sensor and held constant by manipulating the valveless piston pump at the exit. However, because the dielectric constant of the mixture depends on its composition, this controller can only be used if the system is already close to the desired steady state. The mass flow can be double-checked with an electronic scale. Some details of the ZFS are shown in Figure 4. The total volume of the still is 735 ml, where the liquid takes up less than 90 ml. A cylindrical glass wall permits visual observation of the phase boundary. Both phases are thoroughly mixed by a magnetically coupled stirrer. All parts in contact with chemicals are made of stainless steel, glass, teflon or kalrez, except the crystal windows for infrared access which are

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Fig. 3. Flowsheet of the zero flux still (ZFS).

made of zinc selenide. Liquid and vapor temperatures are measured with platinum resistance thermometers to an accuracy of 0.1 K. The piezoelectric pressure sensor is accurate to within 2 mbar. Operation of the ZFS is currently possible in the range of about 0.05–8 bar and 20–230 ◦ C. The still can be evacuated and purged with, e.g. nitrogen.

Fig. 4. Construction Details of ZFS and IR Access.

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4.2. IR access Both phases are analyzed in situ and online by Fourier transform infrared (FT-IR) spectroscopy in the mid infrared region, in a wavenumber range of 700–4000 cm−1 . The vapor phase is accessed by two adjustable insertion tubes (see front view in Fig. 4) to be measured in transmission. To avoid condensation on the crystal windows, the tubes are purged with preheated nitrogen. Optical path length and nitrogen temperature were optimized in preliminary experiments to give good signal-to-noise ratios. The tubes are connected to a BioRad Excalibur FTS 3000 IR spectrometer through an optical bench. For the liquid phase, we use the attenuated total reflection (ATR) technique with a standard immersion probe with two reflections (side view of Fig. 4). It is mounted in the sample rack of the spectrometer. Spectra can alternatively be recorded in the liquid using the internal deuterated triglycine (DTGS) detector of the spectrometer or in the vapor with an external mercury–cadmium–telluride (MCT) detector. Both spectral and all remaining data are recorded by means of two synchronized PCs. By applying in situ analysis, sampling errors and the addition of inhibitors are avoided, but we can nevertheless take GC samples for validation purposes. 4.3. Experimental procedure For illustration of the reactive experiments in the ZFS, Fig. 5 shows the constituent concentrations over time for a typical experiment. The following sequence has been carried out:

Fig. 5. Transient and steady states in the ZFS.

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(1) The still is evacuated, and the reactants are degassed for several hours. (2) At t = 0, data acquisition is started and the pumps are turned on at appropriate flowrates to obtain the desired reactant ratio. Of course, product formation (EtOH and BuOAc) starts instantly. (3) When the ATR probe crystal is covered with liquid, the outlet pump is started. Liquid spectra are now recorded on a regular basis starting, in this case, at t = 1.4 min. In the system at hand, due to stoichiometry and because the vapor holdup is negligible, the mole fractions of both products are equal during the whole experiment. This is confirmed by GC analysis. The more frequently recorded compositions inferred by spectral analysis deviate slightly from equimolarity because the calibration is of limited accuracy (cf. Section 5.1). The level is observed visually, and the outlet flow is adjusted, if necessary. (4) When the liquid composition approaches a steady state at about t = 50 min in Fig. 5, the level controller is turned on for better stabilisation of the residence time. (5) The most adequate property to observe when the steady state is reached is the measured pressure, because it is extremely sensitive to changes in temperature and composition. In our experiments, we define the steady state as the point in time where the pressure change falls below 10 mbar/h. At this point, high quality IR spectra are recorded with more scans as compared to normal observation. Samples are taken for GC analysis at t = 74 min. Note that spectra with fewer scans yield less accurate compositions due to spectral noise, as can be seen at around t = 80 min, for example. At this point, noise in the liquid compositions is not an indication of transient behavior of the system. (6) The flow rate or flow rate ratio can be changed to reach a different steady state. This can be repeated as long as fresh reactant is available. Steps (4) and (5) are repeated accordingly. Two such changes have been applied at t = 75 and 118 min. (7) The pumps are stopped and the inlet/outlet valves are closed to allow for chemical equilibration at t = 138 min. (8) After chemical and physical equilibration at around t = 174 min, the composition is once again analysed via IR and GC. This gives an additional VLE data point without further reactant consumption and at the same time information about the chemical equilibrium. (9) The liquid content in the still is determined volumetrically. With this additional piece of information, the data can be analysed with respect to the chemical reaction rate.

5. Analytical methods VLE measurements require accurate composition measurements over the entire attainable composition region. To achieve this in a multicomponent mixture is not a standard IR spectroscopical task. Therefore, we are using optical and classical GC techniques in parallel. 5.1. IR spectroscopy Vapor phase compositions are obtained by a least squares fit of previously measured pure component spectra to the unknown mixture spectra (an introduction to the method can be found in, e.g. Saarinen and Kauppinen [30] or Martens and Naes [31], pp. 168). Because of potential detector non-linearities, spectral regions with absorbance values greater than 1.4 must be disregarded in that analysis. We have obtained even better results when only absorbances below 0.8 were considered. This might be due to the special

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characteristics of the Fourier transform technique, where non-linearities can appear for narrow bands starting at absorbance values of 0.7 [32]. This procedure has been validated in preliminary experiments. Accuracies of about 1 mole% are possible in the case considered. As a side result, this analysis yields the sum of the partial pressures of the absorbing components. When compared to the directly measured pressure, this is useful to detect inerts in the apparatus. These inerts can appear in the still due to insufficient degassing or evacuation or because of leakages. A set of 60 calibration spectra was used to build a PLS (partial least squares) model [31] for the evaluation of the liquid phase spectra. According to the calibration results, compositions should be accurate to within 1 mole%. In practice, however, we obtained accuracies of only about 2.5 mole% in some cases. The reason for this is not quite clear. In contrast to the situation in the vapor phase, it is not a trivial task to set up an accurate calibration model for the entire composition region in a liquid mixture, even for a two component system. The situation becomes more difficult for a four component system, especially in our case, where structural groups are the same for the reactant and the product pair and thus produce similar spectral responses. The overall change in the liquid spectra during the reaction is, therefore, small. The IR analytical results for the liquid are still useful for monitoring of the reaction, but not sufficiently accurate for VLE measurements. Therefore, GC samples were additionally taken at the steady states. For the general case of reactive systems, it might not be possible to collect calibration data for a PLS model at all, because calibration standards cannot be prepared due to conversion. In this case, one has to rely on some alternative method to infer compositions from the spectral information. One possibility might be to model the spectra based on physical knowledge and to use this for the purpose of analysis. 5.2. Gas chromatography GC analysis has been performed on a Varian Star 3400 with autosampling unit AS 8100 and a Delta Optima 6-235 column at 200 ◦ C, using hydrogen as the carrier gas and a flame ionisation detector. Different
calibrations were used for the binary and the quaternary case. The standard errors of calibration  SEC = (1/(n − f )) ni=1 (xi − xˆi )2 , where xˆi are the predicted mole fractions of n calibration samples and f the number of parameters in the model, were 0.4 mole% for both components in the binary system and better than 0.6 mole% for all constituents in the four component system. 6. Material For validation of the experimental method, we have looked at the binary reactant system of the transesterification reaction BuOH + EtOAc ↔ EtOH + BuOAc,

(1)

and then at the reaction itself. It combines easy handling, a chemical equilibrium constant close to unity and a reaction rate that can be tuned by addition of different (small) amounts of an appropriate catalyst, in our case 150–250 ppm of potassium-tert-butanolate. Without catalyst, the material does not react which facilitates validation of the method as well as calibration of the spectroscopic model. There are no interfering side or consecutive reactions.

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Table 2 Purity ξ and water content ξw,max of the chemicals used in the experiments and parameters for the Antoine equation pi0 = exp(a − b/(T + c)), corresponding valid temperature range (pi0 in mbar, T in ◦ C) Component

ξ (wt.%)

ξw,max (wt.%)

a

b

c

Tmin (◦ C)

Tmax (◦ C)

Ethanol Ethyl acetate 1-Butanol n-Butyl acetate

99.8 99.5 99.0 99.5

0.2 0.05 0.2 0.1

18.9666 16.6401 18.3352 16.4712

3667.70 2866.60 3587.87 3151.09

226.184 217.881 196.881 204.00

20 16 0 22

93 144 118 162

Potassium-tert-butylate

99.8

0.01

For sampling purposes, the reaction can be stopped by adding water, because then the catalyst reacts instantly to yield tert-butanol and KOH (potassium hydroxide). The catalytic effect of this base is much weaker, so further conversion can be neglected during GC analysis. To avoid phase separation, an excess of acetone was added to the samples. The purity of the chemicals used (Merck) are listed in Table 2. For the reactive experiments, BuOH and EtOAc were dried on a Bayer TE-144 zeolite packing to avoid partial catalyst deactivation. The water content was reduced to less than 20 ppm as determined by Karl–Fischer titration. 7. Reference data For all subsequent calculations, we used Antoine parameters for the pure component vapor pressures pi0 given in Table 2. They were fitted to data from [33] in the given temperature ranges. For the binary system BuOH/EtOAc, we have found six VLE data sets in the open literature [33], all isobaric between 0.705 bar and atmospheric pressure. With these data, it is possible to estimate parameters for some adequate g E -model (e.g. [34]), for example the Wilson model. However, all our experiments were carried out isothermally at 60 ◦ C yielding total pressures as low as 0.08 bar. Such g E calculations would, therefore, constitute an extrapolation with unknown error bounds. Alternatively, as there are mixing enthalpies available at 20–35 ◦ C, a different extrapolation to these conditions is possible using the Gibbs–Helmholtz equation for excess properties [35]. We preferred to conduct reference measurements at this temperature in a standard circulation still of the Gillespie type [26] (circulation of vapor and liquid phase) as manufactured by Fischer. The separated phases were analyzed with the same GC method that was used for the ZFS measurements. The experimental results are presented in Table 3. For the Wilson model in the formulation [36]   xk Λki  ln γi = 1 − ln xj Λij − , (2) j xj Λkj j k where the temperature dependence is given by   bij , Λij = exp aij + T /K

(3)

parameters b12 and b21 were fitted to the data (all aij =0). For this purpose, we used the maximum likelihood objective function [37] with the Britt–Luecke algorithm [38] included in the Aspen Plus [39] software package. For (1) BuOH and (2) EtOAc, this yielded b12 = −197.24 and b21 = −121.02.

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Table 3 Experimental T –p–x–y data for the binary system BuOH (1)/EtOAc (2) at about 60 ◦ C, circulation still (all compositions in mole%) No.

T (◦ C)

p (mbar)

x2 (%)

y2 (%)

1 2 3 4 5 6 7 8 9 10 11

60.1 60.0 60.0 60.2 60.1 59.9 60.0 60.2 60.0 60.1 60.0

80 142 205 269 302 366 414 454 488 518 558

0.0 4.5 13.3 24.6 31.7 46.8 57.1 69.6 79.0 88.3 100.0

0.0 45.7 62.2 75.0 79.2 86.0 89.3 91.7 93.9 96.2 100.0

Table 4 Experimental T –p–x–y data for the non-reacting quaternary system EtOH/EtOAc/BuOH/BuOAc at about 60 ◦ C, circulation still (all compositions in mole%) No.

1 2 3 4 5 6 7 8 9 10

T (◦ C)

60.1 60.1 60.2 59.9 60.0 59.9 60.1 59.8 59.9 59.9

p (mbar)

351 372 380 323 324 319 383 419 374 395

EtOH

EtOAc

BuOH

BuOAc

x (%)

y (%)

x (%)

y (%)

x (%)

y (%)

x (%)

y (%)

13.4 15.8 25.7 5.0 9.6 13.1 47.7 48.5 41.1 35.5

23.1 26.5 42.7 9.0 18.1 24.8 66.1 62.5 58.0 49.8

31.2 32.5 23.6 33.0 27.3 24.6 9.5 14.7 13.8 20.2

61.3 59.7 43.9 73.8 62.8 56.4 21.3 28.1 30.2 39.4

39.8 35.9 26.1 55.0 49.6 40.3 21.0 18.1 29.4 30.2

10.9 9.3 6.3 14.9 14.4 12.3 4.8 3.6 6.2 6.2

15.6 15.8 24.6 7.1 13.6 19.0 21.8 18.7 15.7 14.1

4.7 4.5 7.1 2.2 4.7 6.5 7.8 5.9 5.6 4.5

The capability of the Wilson model to describe the quaternary system has also been validated. Nonreactive measurements were carried out in the same Fischer circulation still. Experimental results are summarized in Table 4. The interaction parameters included in Aspen Plus [39] for the corresponding binary subsystems were slightly adjusted for better representation of the measured data. Table 5 presents Table 5 Wilson parameters for the quaternary system EtOH (1)/EtOAc (2)/BuOH (3)/BuOAc (4) Component i

Component j

bij (K)

bji (K)

aij

aji

1 1 1 2 2 3

2 3 4 3 4 4

−266.87647 −174.84054 −217.03329 −113.95 202.514719 −492.46895

−724.07336 113.495328 −159.7495 −170.11 −383.3091 −708.7945

0.5856 0 0 0 0 2.1615

1.133 0 0 0 0 −0.6088

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Table 6 Experimental minus calculated properties for the non-reacting quaternary system EtOH/EtOAc/BuOH/BuOAc, circulation still (all compositions in mole%) No.

p (mbar)

y EtOH (%)

y EtOAc (%)

y BuOH (%)

y BuOAc (%)

1 2 3 4 5 6 7 8 9 10

−4.82 −2.78 2.25 −1.39 8.98 −1.51 0.52 0.78 −4.13 −1.37

0.00 0.44 0.27 0.32 0.41 −0.63 −0.99 0.37 0.30 0.80

−0.35 −0.61 −0.09 0.35 −0.28 0.37 0.75 −0.33 −0.06 −0.56

0.37 0.19 −0.09 −0.29 0.01 0.27 0.09 −0.10 −0.36 −0.31

−0.02 −0.01 −0.09 −0.36 −0.14 −0.01 0.15 0.06 0.13 0.08

the adjusted parameters. Table 6 shows the differences between experiments and model correlations. Good agreement can be obtained.

8. Experimental results All ZFS experiments were performed at about 60 ◦ C. 8.1. Non-reactive system BuOH/EtOAc ZFS data are given in Table 7 for BuOH/EtOAc. They are compared to the Wilson model predictions using the adjusted interaction parameters in Fig. 6. For the liquid composition x, both the GC and the IR results are shown. In the non-reactive case, it is furthermore possible to calculate x from the pump settings and liquid densities, provided the pumps run Table 7 Experimental T –p–x–y data for the binary system BuOH (1)/EtOAc (2) at about 60 ◦ C, ZFS (all compositions in mole%) No.

T (◦ C)

p (mbar)

x2 (%)

y2 (%)

1 2 3 4 5 6 7 8 9 10 11

60.0 60.3 60.0 60.0 60.2 60.1 60.2 60.1 60.1 60.0 60.1

79 170 240 304 332 382 416 448 481 514 556

0.0 10.0 20.7 30.5 36.2 50.0 58.5 68.4 78.3 87.7 100.0

0.0 56.4 72.6 80.6 83.5 87.6 90.2 92.5 94.8 96.9 100.0

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F. Alsmeyer et al. / Fluid Phase Equilibria 203 (2002) 31–51

Fig. 6. VLE of the binary system butanol/ethyl acetate at 60 ◦ C.

at their nominal value. Although all three sets of concentration measurements agree with the calculated dew point curve within experimental accuracy, the GC results are probably the most reliable. 8.2. Reacting system The first prerequisite for reliable reactive VLE measurements in the ZFS is a stable steady state. Fig. 7 shows discrete liquid compositions in a validation experiment. Here, after the chemical equilibrium was

Fig. 7. Transient and steady states in the ZFS.

F. Alsmeyer et al. / Fluid Phase Equilibria 203 (2002) 31–51

45

Fig. 8. Measured y (small symbols) and y calculated from xGC (+) vs. time.

nearly reached at t = 01:20 h, the pumps were restarted at the same nominal flow. The measured mass flow versus time is given in the upper part of the diagram. Both steady states are identical to within experimental accuracy in all measured variables. To assess the efficiency of mixing, the stirrer speed was varied during one steady state in a different experiment. A significant change in any of the measured variables was only observed when the stirrer was turned off, and even then, the deviation from the thoroughly mixed state was only minor with about 2 mole% in the liquid phase. We conclude that the design of the inlet and outlet favors mixing. Fig. 8 shows the vapor composition over time for the experiment with the liquid composition transient already shown in Fig. 5. GC samples were taken at three steady states and at the chemical equilibrium composition. The corresponding compositions y calculated from the Wilson model are also shown. They do not deviate significantly from the measured values. Table 8 lists the complete VLE results for the reacting system. Compositions in chemical equilibrium are marked by an asterisk (∗). Liquid compositions x are usually GC results, but in experiments 4, 6, 9 and 10 no samples were taken and thus, the IR results are given. In experiments 4 to 10, due to temporary problems with a valve, larger amounts of inert gases entered the still, and no reliable pressure measurements are available. Pressures in brackets are also somewhat too high. In these cases, inerts were detected by comparison with the pressures inferred from the vapor spectra. It is noted that we have listed the compositions for all four components, which of course sum up to one, to show that the product concentrations in the liquid (EtOH and BuOAc) comply with the stoichiometric condition to within analytical accuracy.

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Table 8 Experimental T –p–x–y data for the reacting quaternary system EtOH/EtOAc/BuOH/BuOAc at about 60 ◦ C, ZFS (all compositions in mole%) No.

1 2 3 4 (IR) 5 6 (IR) 7∗ 8∗ 9∗ (IR) 10∗ (IR) 11 12 13∗ 14 15 16 17∗ 18 19 20 21∗ 22 23∗ 24 25 26 27 28∗ 29 30∗ 31 32 33∗

T (◦ C)

60.1 59.8 59.1 59.9 59.0 54.3 60.8 59.5 60.5 60.8 60.0 60.0 59.9 59.8 59.8 59.9 59.9 60.2 59.9 60.1 59.9 59.8 59.9 59.8 59.8 59.9 59.9 59.9 59.9 59.8 59.9 60.0 59.9

p (mbar)

381 379 370 – – – – – – – (417) (404) (401) 422 420 416 422 418 399 395 388 (339) (324) (250) (250) (236) (225) (200) 537 545 456 424 434

EtOH

EtOAc

BuOH

BuOAc

x (%)

y (%)

x (%)

y (%)

x (%)

y (%)

x (%)

y (%)

20.8 16.4 15.7 13.8 6.9 1.0 25.2 25.3 24.3 20.4 10.0 10.2 25.2 15.7 13.3 10.9 24.4 7.1 6.2 4.5 25.0 10.3 24.1 4.3 4.6 5.6 7.3 15.2 7.6 10.8 9.5 4.8 24.0

33.4 25.9 24.4 20.5 11.6 3.2 41.5 40.0 39.2 30.5 16.8 17.6 40.3 25.1 21.3 16.7 38.4 12.5 10.5 9.0 40.2 19.6 43.5 10.5 10.5 13.8 18.5 43.6 14.0 19.3 16.4 8.8 37.3

29.3 33.8 34.1 37.5 42.8 46.0 24.8 25.0 26.5 38.8 41.4 40.3 26.2 43.5 45.6 47.5 33.9 47.6 46.5 46.9 26.3 27.5 14.7 16.4 16.2 14.1 11.1 3.2 80.1 76.9 57.9 55.5 37.7

52.8 61.9 63.4 66.2 75.9 83.9 44.7 47.5 46.8 60.1 70.9 70.0 46.4 64.8 68.6 73.0 51.0 77.1 78.1 78.9 46.0 63.0 36.8 61.6 61.6 55.9 48.4 16.3 83.3 78.6 75.8 81.8 53.0

29.6 34.0 35.0 35.5 43.9 51.1 24.9 24.7 24.4 19.7 38.6 39.5 23.5 25.1 27.6 30.5 16.9 37.9 40.9 44.2 23.1 51.7 37.0 75.1 75.2 74.7 74.5 66.4 5.0 1.9 23.0 34.9 14.7

6.7 8.1 7.4 9.1 9.9 11.8 5.8 5.3 6.0 3.9 9.9 9.0 5.7 6.0 6.5 7.4 3.8 9.1 10.0 9.7 5.7 13.2 10.4 25.2 25.2 26.4 27.2 27.0 1.0 0.3 5.1 8.4 3.3

20.4 15.8 15.2 13.4 6.3 1.7 25.1 25.0 24.7 21.0 9.9 10.1 25.2 15.7 13.5 11.1 24.7 7.3 6.3 4.5 25.6 10.5 24.2 4.2 4.0 5.6 7.3 15.2 7.3 10.4 9.6 4.8 23.7

7.1 4.0 4.8 4.2 2.6 1.2 8.0 7.2 7.9 5.5 2.4 3.4 7.7 4.1 3.6 3.0 6.8 1.3 1.5 2.5 8.1 4.2 9.2 2.7 2.7 3.9 6.0 13.1 1.6 1.9 2.7 1.0 6.4

In Table 9, the quaternary VLE results are compared to calculations with the Wilson model based on the reference data. Root mean squared errors (RMSEs) of compositions and pressure are also listed. The agreement in the vapor compositions (about 1 mole%) is excellent considering that y represents analysis errors in both phases and a possible systematic error in the Wilson model. The experimental pressures show similar accuracies as those obtained in the circulation still. The pressure deviations do not show any systematic dependence on the absolute compositions, so we suspect that there is no significant model error for the given Wilson parameters.

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47

Table 9 Experimental minus calculated pressures and vapor compositions for the reacting quaternary system EtOH/EtOAc/BuOH/BuOAc at about 60 ◦ C, ZFS (all compositions in mole%) No. 1 2 3 4 (IR) 5 6 (IR) 7∗ 8∗ 9∗ (IR) 10∗ (IR) 11 12 13∗ 14 15 16 17∗ 18 19 20 21∗ 22 23∗ 24 25 26 27 28∗ 29 30∗ 31 32 33∗ RMSE

p (mbar)

y EtOH (%)

y EtOAc (%)

y BuOH (%)

y BuOAc(%)

−2.03 −1.34 2.93 – – – – – – – – – – −4.01 −3.23 −4.27 −3.84 10.31 5.04 3.33 2.17 – – – – – – – −0.83 −1.17 −2.36 −0.80 −9.52

−0.59 −0.63 −1.04 −1.61 0.64 1.65 −0.19 −1.46 −0.79 −1.45 0.78 1.24 −0.82 0.64 0.50 −0.42 0.26 1.21 0.61 1.90 −0.83 1.41 −1.81 1.02 0.48 1.11 0.85 1.18 1.40 1.85 1.61 1.34 0.64

−0.18 1.19 1.62 0.65 −0.54 −2.19 −0.36 2.04 −0.32 1.67 −0.83 −1.07 0.10 −1.13 −0.81 0.09 −1.08 −0.34 −0.23 −1.76 −0.33 −0.55 1.66 0.64 1.13 0.59 1.28 0.81 −1.37 −1.51 −1.85 −0.98 −1.66

−0.61 −0.25 −1.16 0.38 −0.83 −0.01 −0.33 −0.73 0.08 −0.67 0.37 −0.79 0.03 0.08 −0.01 0.05 −0.01 −0.20 −0.09 −1.30 0.17 −1.20 −0.10 −1.27 −1.30 −1.39 −2.54 −3.46 −0.22 −0.21 −0.38 −0.10 0.09

1.38 −0.32 0.59 0.58 0.73 0.57 0.88 0.15 1.02 0.45 −0.31 0.61 0.69 0.41 0.32 0.28 0.82 −0.68 −0.29 1.16 0.99 0.34 0.27 −0.40 −0.31 −0.31 0.41 1.47 0.18 −0.14 0.62 −0.27 0.93

4.47

1.13

1.15

0.98

0.67

Fig. 9 shows the composition space covered by our experiments. The pseudo-ternary representation in this diagram is possible because product mole fractions in the liquid are equal in all our experiments. Hence, EtOH and BuOAc can be treated as if they were just one product. Almost the entire composition space can be accessed for the system at hand, from close to the unreacted binary system BuOH/EtOAc to the chemical equilibrium line which in this case, corresponds to a chemical equilibrium constant of K = 1. Of course, one can also access liquid compositions beyond the equilibrium line by feeding the opposite binary system into the apparatus. Unequal product mole fractions can be obtained by addition

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Fig. 9. Pseudo-ternary representation of all measured liquid compositions and chemical equilibrium line defined by the equilibrium constant K = 1.

of one of the products to the feed. In this way, the composition space covered by the experiments can be designed to meet the needs of any given application.

9. Conclusions The application of a strict steady state method with zero flux over the phase boundary is a promising tool for phase equilibrium measurements in reacting systems. In our new still for reactive VLE based on this principle, steady states can be obtained reproducibly for a wide range of mean residence times from 30 s to several hours, allowing for liquid compositions from close to the unreacted binary subsystems to chemical equilibrium. The data obtained from such measurements can be used to model phase equilibria as well as chemical kinetics. For the latter, the liquid volume in the still needs to be recorded at the steady states as additional pieces of information. In situ IR analysis proved to be reliable in the vapor phase. It is also useful in the liquid phase but so far does not yield accurate analytical results, because it is impossible to use established calibration methods like PLS for a spontaneously reacting system. One solution might be to evaluate the spectra on the basis of physical knowledge rather than calibration data. This would render GC sampling unnecessary. The experimental technique allows VLE measurements for promising but demanding applications like reactive distillation, especially for autocatalytic or non-catalytic reactions. The general method can potentially be applied for other phase combinations than vapor–liquid if homogeneous mixing is possible and if there is no significant reaction in one phase. List of symbols a, b, c Antoine parameters A, B, C, D chemical components aij binary parameter in the Wilson model

F. Alsmeyer et al. / Fluid Phase Equilibria 203 (2002) 31–51

bij Da f m ˙ k K n n˙ p pi0 t T x x˜ y

binary parameter in the Wilson model (K) Damköhler number degrees of freedom in a model flow (g/s) (pseudo-) first order reaction rate constant (s −1 ) reaction equilibrium constant number of calibration spectra molar flow (mole/s) pressure (1 × 105 Pa) vapor pressure of pure component i (1 × 105 Pa) time (h) temperature (◦ C) liquid mole fraction (mole/mole) or (mole%) estimated liquid mole fraction (mole/mole) or (mole%) vapor mole fraction (mole/mole) or (mole%)

Greek letters  Λij ξ ξw,max τ τVLE

difference between measured and calculated property binary parameters in the Wilson model purity (wt.%) water content (wt.%) mean residence time (s) physical equilibration time (s)

49

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