2992
Ind. Eng. Chem. Res. 2010, 49, 2992–3000
Experimental Measurements and Thermodynamic Modeling of CO2 Solubility at High Pressure in Model Apple Juices Giovanna Ferrentino,† Diego Barletta,† Francesco Donsı`,† Giovanna Ferrari,†,‡ and Massimo Poletto*,† Dipartimento di Ingegneria Chimica e Alimentare, UniVersita` degli Studi di Salerno, Via Ponte Don Melillo, I-84084 Fisciano (SA) Italy, and ProdAl S.c.a.r.l.-Centro Regionale di Competenza sulle Produzioni Agroalimentari Via Ponte Don Melillo, I-84084 Fisciano (SA), Italy
High pressure carbon dioxide (HPCD) treatment can be used for the pasteurization of liquid foods. Solubility of CO2 in the liquid affects microbial inactivation. Measurement and prediction of CO2 solubility in a real or model system are of industrial relevance since the knowledge of the solubility limits will avoid the use of excess CO2. An experimental apparatus was set up to measure CO2 solubility in ternary mixtures of water-CO2-glucose and water-CO2-malic acid and in a quaternary mixture of water-CO2-malic acid-glucose at different concentrations of malic acid (0.01 and 2.68 g in 100 g of solution, corresponding to 7.5 × 10-5 and 0.02 mols in 100 mols of solution) and of glucose (4 and 12 g in 100 g of solution, corresponding to 0.02 and 0.07 mols in 100 mols of solution). CO2 solubility was also measured in a more complex solution of water-malic acid-ascorbic acid-pectin-glucose-sucrose, based on apple juice composition and in a commercial apple juice. The range of pressure tested was between 7.5 and 15.0 MPa while the temperature was between 308 and 333 K. CO2 solubility was inversely proportional to the glucose and sucrose concentration. Malic and citric acids only slightly affected CO2 solubility. Slight differences in the value of CO2 solubility were detected between the model solution and the real juice. The experimental results were compared with the equilibrium conditions evaluated using the process simulation software Aspen Plus. The vapor-liquid equilibrium was solved with the Peng-Robinson EOS, where the parameters were evaluated using Wong and Sandler mixing rules (PRWS), and the activity coefficients were defined using the functional groups with the modified UNIFAC method. The CO2 solubility values predicted by the model agreed well with the experimental data in the pressure and temperature range tested. Introduction Accurate description of CO2 solubility in liquid foods and aqueous solutions is of particular interest to better understand the antimicrobial activity of carbon dioxide. In fact, high pressure carbon dioxide (HPCD) treatment has been proposed as an alternative cold pasteurization method for liquid foods.1–3 This method provides some advantages due to the mild conditions employed, particularly because it allows processing at lower temperatures than those used in thermal pasteurization. HPCD can reduce the microbial count of foods while preserving heat sensitive nutrients and the product quality, including flavor, color, and texture. In the HPCD technique, food is in contact with pressurized sub- or supercritical CO2 for a certain time period in batch, semibatch, or continuous manner. Carbon dioxide has low critical temperature and pressure which allow supercritical operations at conditions which minimize damage to biological compounds. Additional advantages are related to the low cost and the availability of CO2 in purified form. Other reasons which make CO2 suitable in food treatments are its chemical inertness, its nontoxicity and the fact that it is a natural component of many foods. The exact microbial inactivation mechanism of HPCD treatments is not yet completely understood though some hypotheses have been proposed.4 In particular, Ferrentino and co-workers5 have demonstrated that HPCD microbial inactivation kinetics can be applied to different buffer solutions provided that the same temperature and CO2 concentration are used. Therefore, the knowledge of CO2 * To whom correspondence should be addressed. E-mail address:
[email protected]. Tel.: +39 089964132. Fax: +39 089964057. † Università degli Studi di Salerno. ‡ ProdAl S.c.a.r.l.
concentration in the liquid foods is of major importance. The correct scale up of laboratory experiments in the design of industrial equipment for the commercial application of HPCD is critical. Solubility of gases in liquids has been studied since the early 19th century.6,7 A large number of experimental studies have been conducted with different techniques to measure CO2 solubility. Dohrn and co-workers8 designed a high pressure apparatus to obtain reliable phase equilibrium data in the glucose-water-CO2 and glucose-water-ethanol-CO2 system at temperatures up to 343 K and pressures up to 30 MPa. They showed that CO2 solubility decreased due to the presence of the glucose while adding ethanol as a polar cosolvent resulted in a substantial increase of the solubility of glucose in the vapor phase at high pressure. Bamberger and co-workers9 designed an apparatus based on the flow technique to obtain binary phase equilibrium data for CO2-water and CO2-acetic acid systems. The experimental results were correlated with the modification of the Peng-Robinson (PR) equation of state10 giving good results for the CO2-water system and for the CO2-acetic acid system when the dimerization of acetic acid in both phases was considered. CO2 solubility in aqueous solutions of NaCl was also measured by Bando and co-workers.11 The experimental apparatus was designed to dissolve CO2 in NaCl aqueous solutions in a pressurized vessel. From the evaluation of the mass of the sample and the pressure of the dissolved gas of the saturated solution removed from the vessel it was possible to calculate CO2 solubility. The experiments were performed using NaCl solutions with mass fractions of 0.01 to 0.03 at 303 to 333 K and 10 to 20 MPa. More recently, Calix and co-workers12 designed an experimental system to measure CO2 solubility in ascorbic acid-sugars-water, citric acid-sugars-water solu-
10.1021/ie9009974 2010 American Chemical Society Published on Web 02/22/2010
Ind. Eng. Chem. Res., Vol. 49, No. 6, 2010
tions, and in commercial orange and apple juice as a function of pressure (7-16 MPa) at 313 K showing that CO2 solubility in these solutions and in the real juices was always lower than that in pure water, due to the presence of solutes. A complete survey of the experimental data available in the literature can be found in recent reviews.13–15 The high pressure (vapor-liquid and vapor-liquid-liquid) equilibria are commonly correlated and predicted with an equation of state (φ-φ models) or with an equation of state combined with an excess Gibbs free energy model (γ-φ models). The use of an appropriate equation of state requires binary interaction parameters which cannot be predicted but have to be determined from accurate experimental high pressure (vapor-liquid) equilibrium data of the binary (or multicomponent) mixtures. The vapor-liquid phase equilibrium of the CO2-H2O system has been studied extensively with both the φ-φ and γ-φ thermodynamic approaches. In the former approach, an equation of state is used to describe the nonideal behavior of both the vapor and the liquid phases. In the γ-φ approach, an equation of state is used to describe the nonideality of the vapor CO2-rich phase, and Henry’s law or an excess molar Gibbs free energy model is used to describe the nonideality of the liquid H2O-rich phase. Carroll and Mather16 studied phase equilibria of the CO2-H2O system using the KrichevskyKasarnovsky equation of state which resulted reliable at temperatures lower than 373 K. Kiepe and co-workers17 calculated gas solubilities for the CO2-H2O system at temperatures and pressures in the range of 313-393 K and 0-10 MPa, respectively, by coupling the predictive Soave-Redlich-Kwong (PSRK) equation of state with the LIFAC group contribution method. Their prediction was in agreement with the experimental data. The φ-φ approach was also applied by Shyu and co-workers18 who correlated the phase equilibria for the CO2-H2O system based on the Peng-Robinson (PR) equation of state with the Wong-Sandler (WS) mixing rule. The van Laar model was used to calculate the excess Gibbs energy with three parameters, two energy parameters for the liquid phase, and one interaction parameter for the gas phase. The calculated solubility of CO2 in water was accurate over a wide range of temperatures (298-623 K) and pressures (1-100 MPa). Valtz and co-workers19 combined the Peng-Robinson (PR) equation of state with the Wong-Sandler (WS) mixture combining rule to calculate the VLE for the CO2-H2O system at a temperature and pressure of 278-318 K and 0.4-8.0 MPa with the NRTL (nonrandom two liquid) local composition model used to obtain the excess molar Gibbs free energy. The calculated results for the vapor composition were accurate, especially at low temperatures. While there are many vapor-liquid equilibrium data available for the binary system CO2-water, less attention has been focused on ternary or more complex systems with the exception of water solutions with salts (mainly NaCl) of interest for CO2 sequestration issues.15 For aqueous solutions addressing the composition of liquid foods, some studies are available in the literature on the CO2-ethanol-water system20,21 and on the CO2water-carbohydrates systems.8,12 Dohrn and co-workers8 measured the solubility of CO2 in solutions containing glucose, water, and ethanol. More recently Calix and co-workers12 evaluated the CO2 solubility in water-glucose-malic acid and water-glucose-citric acid solutions showing that the amount of CO2 dissolved is a function of the composition of the solution. This paper is part of a wider project aiming at explaining the microbial inactivation mechanisms of the HPCD process. Considering that the amount of CO2 dissolved in the liquid foods is the driving force inducing microbial death,22 the overall
2993
Figure 1. Schematics of the high pressure batch CO2 solubility apparatus:22 (HPP) high pressure pump; (V1, V2, V3, V4) manual valves; (PG2) pressure gauge; (T) thermocouple.
project aims at expressing the inactivation kinetics of microorganisms with a unified model based on CO2 solubility and temperature, instead of pressure, temperature, and composition of the suspending medium. In particular, the objective of this work is to obtain reliable phase equilibrium data in ternary systems (glucose-water-CO2 and malic acid-water-CO2), a quaternary system (glucose-water-malic acid-CO2), and in more complex aqueous solutions emulating apple juice composition. The process simulation software Aspen Plus (Aspen Technology, Inc., Burlington, MA) is used to assess the ability of three different thermodynamic models to describe the vapor-liquid equilibrium of the above mentioned solutions. This paper focuses the attention on the experimental technique presenting the results and discussing the ability of the thermodynamic models to predict the experimental data for aqueous solutions addressing the composition of liquid foods. Material and Methods Experimental Setup. The equipment used was originally built for the treatment of liquid and solid foods with CO2 under pressure at the Department of Chemical and Food Engineering of the University of Salerno (Figure 1). The vessel (100 mL) was a modified version of a Parr Stirred Reactor (FKV srl, Bergamo, Italy) with a maximum operative pressure of 20.0 MPa. The reactor was equipped with a four-bladed impeller magnetically coupled to a DC motor (model No. A1120HC6) allowing adjustable mixing speeds. A fixed thermocouple (type J) was used to measure the temperature inside the vessel. The removable vessel head was fitted with the stirrer, all inlet and outlet lines, a calibrated rupture disk for emergency pressure relief, a thermocouple, and a pressure gauge for gross reading of the internal temperature and pressure. The CO2 pump was a Jasco model PU-1580 for chromatography with flow control based on volume displacement or on the output pressure. It withdrew liquid CO2 (99.99% purity, SOL SpA, Italy) from a cylinder and pumped it into the reactor through an on-off valve that was kept closed after pumping. The time required for the reactor pressurization and heating was about 5 min. The CO2 pump had an internal pressure transducer with an accuracy declared by the manufacture of 0.1 MPa. During the test, this transducer was used to read the system pressure visualized on the pump display. The vessel had a jacket in which thermostatted water was circulated from an external high precision water bath
2994
Ind. Eng. Chem. Res., Vol. 49, No. 6, 2010
Table 1. Composition of the Solutions Used for the Solubility Experiments solutiona
glucose
water-glucose water-malic acid water-citric acid water-sucrose water-pectin water-glucose-malic acid water-glucose-sucrosemalic acid-citric acid-pectin
4-12 (0.02-0.07)
a
citric acid
sucrose
malic acid
pectin
0.01-2.68 (7.5 × 10-5-0.02)
0.01 (5.2 × 10-5) 7.8 (0.02) 12 (0.07) 2.16 (0.01)
0.01 (5.2 × 10-5)
7.8 (0.02)
0.01 (7.5 × 10-5) 0.85 (0.006)
0.14 0.14 (7 × 10-6)
Data are reported in grams per 100 g of solution; data in parentheses are reported in moles per 100 mol of solution.
(DC-10 thermostatic bath, Enco s.r.l., VE, Italy). It was verified at ambient pressure that this system allowed to keep the temperature inside the vessel within a range (0.1 K around the set temperature of the thermostatic bath. The accuracy of the bath thermometer and of the pump pressure transducer was periodically checked with higher class instruments available in the laboratory. During the solubility experiments, a valve at the bottom of the vessel was used to withdraw small samples of the internal liquid phase. At the end of the experiments, the system could be easily depressurized by opening the on-off valve on the vessel outlet line. Sample Preparation. Pure Water and NaCl Solutions. Experiments were performed on pure water and NaCl solutions, and the results were compared with data in the literature. Pure deionized water was used with a volume of 100 mL per run. Solutions were prepared by weighting NaCl (certified ACS reagents, Fischer Scientific, Fair Lawn, NJ) on an analytic balance (maximum uncertainty of about (0.1 mg) and dissolving it in water to obtain 100 g of solution. The resulting solutions had a mass fraction of 0.01 (corresponding to a molar fraction of 3.1 × 10-3). Ternary, Quaternary Solutions, and Apple Juice. Solubility experiments were performed for the CO2-glucose-water system at two different concentrations of glucose (certified ACS reagents, Fischer Scientific, Fair Lawn, NJ) and on CO2-malic acid-water system at two different concentrations of malic acid (certified ACS reagent, Presque Isle Wine Cellars Philadelphia, PA). All the solutions were prepared weighting the reagents with an analytic balance (maximum uncertainty of about (0.1 mg). Further solubility experiments were carried out on a quaternary solution of CO2-malic acid-glucose-water and on a more complex solution emulating the apple juice composition. The amounts and the components of the solution were chosen on the basis of the composition of different varieties of apple juices reported by Eisele and co-workers.23 The solution had a final pH of 2.18 and a final °Brix value of 10 (Table 1) where °Brix is defined as the weight mass fraction of the dissolved sugar in a liquid solution and, for this model solution, corresponds to the total content of soluble solids. The solubility experiments performed on the model solutions were compared to the one performed on a commercial apple juice purchased from a local market. This juice had a pH of 3.40 and a °Brix value of 12. Experimental Procedure. The vessel was operated in batch mode. It was loaded with the liquid mixture and then carefully closed. The external jacket was connected to the water bath and the system was heated to the experimental temperature. Next, CO2 was pumped until the desired experimental pressure was reached. After the pressure reached the desired level, the system was stirred for almost one more hour to ensure the attainment of the thermodynamic equilibrium. In all the tests, the same stirring speed (approximately 850 rpm) was used to promote the dissolution of CO2 in the liquid phase.
At the end of the equalization period, a plastic syringe (60 mL syringe catheter) with scale divisions of 1 mL and previously calibrated with distilled water was connected to the bottom valve of the vessel through an on-off valve. Before sampling, the piston of the syringe had been pushed all the way to the front in order to remove the air from it. A small amount of liquid phase was drawn into the syringe by opening the bottom valve. The operation time was short and the small amount of liquid drawn did not significantly change the pressure and temperature of the pressurized reactor. The syringe expansion took into account the volume of CO2 and that of the liquid solution. The syringe was then disconnected from the vessel and weighted on a high precision balance (Laboratory electronic balance, Gibertini Elettronica s.r.l., MI, Italy) with a maximum uncertainty of about (0.1 mg to obtain the mass of the sampled liquid. The total volume expansion in the syringe was read. The total weight took into account the mass of the liquid. From the density of the liquid mixture, the volume of the liquid was calculated and subtracted from the total volume to find the CO2 volume. Multiplying the CO2 density and the CO2 volume, the grams of CO2 were obtained. The ratio between the grams of CO2 and the grams of liquid gave the solubility value,22 expressed in grams of CO2 per 100 g of noncarbonated solution. The set of experimental conditions to validate the setup and the procedure was repeated in triplicate, and the mean value was compared to the literature results. The experiments to evaluate CO2 solubility for the ternary, the quaternary solutions, and the apple juice were run in triplicate, and the mean value and the standard deviation were reported. A calculation taking into account all uncertainties in the measured variables showed that the maximum relative uncertainty in CO2 solubility is about (0.1 g CO2/ 100 g solution. Vapor-Liquid Equilibrium Simulation. The process simulation software Aspen Plus version 2004.1 (Aspen Technology, Inc., Burlington, MA) was used to study the vapor-liquid equilibrium of the system. In particular, the RGibbs simulation block of Aspen Plus was used to solve the equations for the vapor-liquid equilibrium, once the user had chosen the system pressure and temperature and the preferred thermodynamic model. By minimizing the Gibbs free energy,24,25 the software calculated the molar and mass fractions of the two phases at equilibrium. Each used thermodynamic model required a calculation procedure. One thermodynamic model used was the Peng-Robinson-Wong-Sandler (PRWS) model. This is based on the Peng-Robinson equation of state (PR-EOS) with the Wong and Sandler26 mixing rule. According to the model classification described in the Introduction, it is a φ-φ thermodynamic model used to describe the nonideality of both the CO2-rich phase and H2O-rich phase with an equation of state. In particular, the Wong Sandler mixing rule combines the Peng-Robinson equation of state with a free-energy model to
Ind. Eng. Chem. Res., Vol. 49, No. 6, 2010
2995
Table 2. Thermodynamic Models model PRWS
equation of state PR EOS
P)
RT a(T) - 2 V-b V + 2bV - b2
[
mixing rules
GγE(T, zi) a ) + bRT C*RT RT
[∑
(b - RTa )
) ij
P)
a(T) RT V-b V(V + b)
a ) bRT b)
i
zi
∑
zi
i
1 2
]
ij
j
i
SRK EOS
i
i j
RT -
PSRK
i
a ∑ ∑ z z (b - bRT ) i
b)
ai
∑ z b RT
ai + bi
[(
bi -
component activity
GγE(T, zi) C*
GγE(T, zi) from the UNIFAC method27
]
) (
ai aj + bj RT RT
(
E ai 1 Gγ + + biRT A0 RT
∑
zi ln
i
)]
(1 - kij)
( ))
GγE(T, zi)
b bi
from the UNIFAC method27
∑zb
i i
i
ELECNRTL
RK EOS
P)
RT a V-b √T · V(V + b)
gas phase √a )
∑ y √a b ) ∑ y b i
i
obtain the a and b parameters of the PR-EOS for a mixture. The PR-EOS and the corresponding mixing rule are reported in Table 2. The excess Gibbs free energy, GγE, can be calculated with any excess Gibbs free-energy model. In the present work, the group contribution method UNIFAC27 was used. As a result, the binary interaction parameters kij (see Table 2) are adjustable parameters which make the model not fully predictive. Wong and Sandler26 proposed finding out the proper kij values by searching the best fit at low pressure between the excess Gibbs free-energy predicted by the combined EOS-free-energy method E , and the one evaluated according to (in this case PRWS), GEOS the excess Gibbs free-energy GγE calculated with the UNIFAC method. In this study, the kij values were evaluated by the best fit of experimental VLE values at a single reference condition. The activity coefficients were calculated with the functional groups expressed by the UNIFAC system. In particular, the search for the kij values was carried out step by step in systems with increasing complexity. First, the best fitting procedure was applied to the binary system water-CO2 at a reference temperature. Then, keeping the obtained binary interaction parameters constant, the procedure was applied to the ternary systems at reference condition of temperature and of solute concentration to evaluate the two additional kij values between each species (glucose, sucrose, malic acid, citric acid, pectin) and water and CO2, respectively. The obtained values were used to test the ability of the PRWS model to predict the CO2 solubility in binary, ternary, and quaternary systems at different temperatures and concentrations of the carbohydrates and acids. Two other thermodynamic models summarized in Table 2 were also tested to simulate the vapor liquid equilibrium for the binary system CO2-water: the electrolytic nonrandom two liquids (ELECNRTL) model28 and the completely predictive Soave-Redlich-Kwong (PSRK) thermodynamic
i i
i
liquid phase fiL(T, P, xi)
i
[
VL(P - P0) ) xiγ* i (T, P0, xi)Hi(T, P0) exp RT
]
γ* i (T, P, xi) refers to infinite dilution33 and is calculated with the electrolyte NRTL model28
model.29 The ELECNRTL thermodynamic model is a γ-φ model where the Redlich-Kwong EOS (RK EOS)30 is used to calculate the fugacity of vapor CO2-rich phase, while the fugacity of the liquid H2O-rich phase is based on the Henry’s law corrected on the pressure with the use of activity coefficients referred to the infinite dilution of the solutes calculated according to the electrolyte NRTL model,28 an excess molar Gibbs free energy model. In the PSRK thermodynamic model, the equilibrium calculations are solved with the Soave-Redlich-Kwong EOS (SRK EOS)31 and the modified UNIFAC method27 describing the activity coefficients through the Holderbaum and Gmehling29 predictive mixing rules. Complete details on these models and the results were reported by Ferrentino and co-workers.32 Results and Discussion Validation of the Experimental Setup. To verify and demonstrate the accuracy and precision of the high-pressure CO2 solubility apparatus and the measurement procedure, the experimental results of CO2 solubility in pure water and in pure water-NaCl solutions were compared with the values presented in the literature. The CO2 solubility chart developed by Wiebe and Gaddy6 was used as a reference for pure water, and the results reported by Bando and co-workers11 were used as a reference for water-NaCl solutions. The comparison was performed at 313 K for different values of pressure and is reported in Tables 3 and 4 for pure water and the water-NaCl solution, respectively. These tables report solubility values obtained in single tests, the corresponding mean value, and the standard deviation value. Results suggest that the high pressure apparatus can reproduce accurate solubility values which are very close to those reported in previously published works. Figure 2 reports the experimental solubility data obtained in this work for pure water at 313 K in the range of pressures
2996
Ind. Eng. Chem. Res., Vol. 49, No. 6, 2010
Table 3. Solubility of CO2 in Pure Water at 313 K pressure MPa 7.50 10.0 12.5 15.0
solubilitya 5.02 (2.05) 4.99 (2.04) 5.10 (2.09) 5.45 (2.23) 5.18 (2.12) 5.19 (2.13) 5.40 (2.21) 5.48 (2.24) 5.84 (2.39) 5.80 (2.37) 5.79 (2.37) 5.60 (2.29)
meana
literature dataa,b
st deva -2
-2
5.04 (2.06)
6 × 10
(2 × 10 )
5.04 (2.06)
5.27 (2.16)
2 × 10-1 (6 × 10-2)
5.43 (2.22)
5.57 (2.28)
2 × 10-1 (1 × 10-1)
5.60 (2.29)
5.73 (2.34)
1 × 10-1 (4 × 10-2)
5.74 (2.35)
a Data are reported in grams per 100 g of solution; data in parentheses are reported in moles per 100 mol of solution. b Data reported by Wiebe and Gaddy.6
Table 4. Solubility of CO2 in Water-NaCl Solution at 313 K pressure MPa 10.0 15.0
solubilitya
meana
st deva
literature dataa,b
5.10 (2.09) 5.01 (2.05) 5.18 (2.12) 5.39 (2.20) 5.23 (2.14) 5.22 (2.13)
5.09 (2.08)
8 × 10-2 (3 × 10-2)
4.96 (2.03)
5.28 (2.16)
9 × 10-2 (4 × 10-2)
5.28 (2.16)
a
Data are reported in grams per 100 g of noncarbonated solution; data in parentheses are reported in moles per 100 mol of noncarbonated solution. b Data reported by Bando and co-workers.11
Table 5. Coefficients of Binary Interaction Evaluated for the PRWS Thermodynamic Model Coefficient of Binary Interaction kij component
water glucose citric acid malic acid sucrose pectin
carbon dioxide 0.240 water glucose citric acid malic acid sucrose pectin
1.905 1.5
0.815 1.25 0
1.05 1.2 0 0
0.305 0.045 0 0 0
0.455 -0.35 0 0 0 0
solubility under different temperatures (308 and 323 K) was tested by keeping constant the kij value found at 313 K. Corresponding results are reported in Figure 3 together with the experimental results by Wiebe and Gaddy.6 The comparison suggests good agreement in the range of temperatures tested. Further inspection of Figure 3 regarding the effect of pressure reveals that the model fits very well in the range of pressure 10.0-13.0 MPa. At lower pressure values and in particular at 7.5 MPa, near the critical point, there is some deviation (lower than 25%) between the experimental data and the thermodynamic model. Good results were also obtained with the PRWS thermodynamic model reported by Shyu and co-workers18and Valtz and co-workers.19 In particular, Shyu and co-workers18 modeled the phase behavior for the CO2-H2O system over a wide range of temperatures (298-623 K) and pressures (1-100 MPa) using the van Laar model to calculate GγE. The calculated CO2 solubility in water was accurate but required two additional parameters derived from the application of the van Laar model. Valtz and co-workers,19 instead, used the NRTL local composition model to calculate GγE by adjusting the values of three parameters (kij and two NRTL parameters) for each temperature value (in the range 278 -318 K) to obtain results in very good agreement with the experimental CO2 solubilities in the pressure range between 0.4 and 16 MPa. The PRWS thermodynamic model tested in the present work with the UNIFAC group contribution method to evaluate the excess Gibbs free energy does not introduce further adjustable parameters than the kij values in the mixing rules which are kept constant in range of temperature tested (308-323 K). In spite of this reduced number of parameters, the model provides results in good agreement with the experiments. CO2 Solubility in Ternary Solutions. Solutions were prepared to determine the CO2 solubility in water-glucose and
Figure 2. CO2 solubility in pure water at 313 K: b, experiments, O, Wiebe and Gaddy6 experiments; - - -, PSRK model; · · · , ELECNRTL model; ;, PRWS model.
between 7.5 and 15.0 MPa, together with the results reported by Wiebe and Gaddy.6 In the same figure, the values obtained by vapor-liquid equilibrium simulation of PRWS, ELECNRTL, and PSRK thermodynamic models are also reported for comparison with the experimental results. Results obtained with the ELECNRTL and the PSRK thermodynamic models do not show a good agreement with the experimental CO2 solubility values having a deviation that is more evident at high pressures. Similar discrepancies between the results of these models and the experimental results were observed at different temperatures.32 Much better agreement was obtained with the PRWS model, as shown in Figure 2. Data for this model were obtained by fitting to the experimental data and by adjusting the coefficient of binary interaction kij between water and CO2 (reported in Table 5) which, for this system, is the only model parameter. Subsequently, the PRWS model’s ability to predict CO2
Figure 3. CO2 solubility in pure water at different temperatures: 2, 323; b, 313; 9, 308 K. Symbols are literature data;6 short dashed lines are the PRWS thermodynamic model results at different temperatures.
Ind. Eng. Chem. Res., Vol. 49, No. 6, 2010
Figure 4. CO2 solubility for a water-glucose system. T ) 313 K, solute concentrations (100 g solution basis): b, 4 g glucose; 9, 12 g glucose. Solubility is expressed as g of CO2 per 100 g of noncarbonated solution. Symbols are experimental values; short dashed lines are the PRWS thermodynamic model results. For the sake of comparison, CO2 solubility values in water (4) are also reported.
Figure 5. CO2 solubility for water-malic acid system. T ) 313 K, solute concentrations (100 g solution basis): b, 0.01 g malic acid; 9, 2.68 g malic acid. Solubility is expressed as g of CO2 per 100 g of noncarbonated solution. Symbols are experimental values; short dashed lines are the PRWS thermodynamic model results. For comparison, CO2 solubility values in water 4 are also reported.
water-malic acid solutions. The experiments were carried out at 313 K and with solutions at different concentrations of glucose and malic acid, respectively. Figures 4 and 5 show that CO2 solubility decreases significantly for the water-glucose system with respect to the pure water system at the same conditions of pressure and temperature. Moreover, an increase in the glucose concentration from 4 to 12 g in 100 g of solution causes a marked drop in CO2 solubility. These results confirm the experimental findings reported by Dohrn and co-workers8 according to which CO2 solubility decreases with increasing glucose concentration. For the malic acid-water system (Figure 5), the results do not show a significant dependence of the CO2 solubility value on the malic acid concentration in the solutions within the tested concentration range. Also comparing the CO2 solubility values with those in pure water, significant differences are not detected in the range of pressures tested. The vapor-liquid equilibrium of the two ternary systems was also modeled with the PRWS thermodynamic model already used for the water-CO2 system. In particular, the value of the
2997
coefficient of binary interaction between water and CO2 found from the study of the binary system was not changed. The kij values accounting for the interaction between H2O and each of the two solutes and between CO2 and each of the two solutes were determined by searching the best fit of experimental equilibrium data of the ternary systems at fixed concentrations of glucose (12 g/100 g solution) or malic acid (2.68 g/100 g solution), respectively, at a reference temperature (313 K). The kij values found are reported in Table 5. The model with these values for kij was used to predict the other experimental equilibrium points yielding results in very good agreement (as shown in Figures 4 and 5). Similar experiments and modeling analysis were performed on other ternary systems formed by water, CO2, and a third component chosen among those usually present in fruit juices (sucrose, citric acid, pectin). In particular, the chosen concentration of the third component is in the order of magnitude typical for apple juices. Experimental results reported in Figure 6 show that sucrose causes the most significant decrease of CO2 solubility. The relevant coefficients of binary interaction between H2O or CO2 and each of these species for the PRWS thermodynamic model were obtained by the best fitting procedure and are reported in Table 5. CO2 Solubility in Quaternary Solutions. The next step was to study CO2 solubility in more complex aqueous solutions of four components approaching in compositional complexity the fruit juices. In particular, CO2 solubility was measured in a water-malic acid-glucose system with a composition of 12 g of glucose and 0.01 g of malic acid in 100 g of solution. Experiments were performed at two temperatures (313 and 323 K) in the range 7.5-15 MPa. The results reported in Figure 7 show that an increase of temperature causes a decrease of the CO2 solubility. Also for this quaternary system, the solubility data were simulated with the PRWS thermodynamic model, by using the values of the binary interaction coefficients obtained from the fitting of previously investigated binary and ternary systems and reported in Table 5. Inspection of Figure 7 reveals that the model predicts well the experimental data at both temperatures. The binary interaction coefficients for the couple malic acid-glucose were put to zero. It was verified that other values provided worse agreement between model and experiments. CO2 Solubility in Real and Model Fruit Juices. Further investigations were carried out on a model apple juice with a composition similar to that of a real apple juice (water, citric acid, malic acid, sucrose, glucose, pectin). The complete composition is reported in Table 1. Figure 8 reports the experimental solubility results at 313 K and PRWS model predictions obtained using all the kij values reported in Table 5. The fitting parameters found for the ternary systems were used without change. Also considering the results found for the quaternary system, the binary interaction coefficients for all the couples of solid solutes included in this model solution were assumed to be zero. Figure 8 suggests good agreement between experimental and model results. The CO2 solubility in a similar multicomponent aqueous solution of glucose, sucrose, fructose, malic acid, and citric acid was measured and modeled by Calix and co-workers12 by the electrolyte nonrandom two liquid (NRTL) model with the Redlich-Kwong (RK) equation of state for aqueous and mixed solvent applications. These model predictions were not as successful as those obtained with the PRWS model used in this work.
2998
Ind. Eng. Chem. Res., Vol. 49, No. 6, 2010
Figure 6. CO2 solubility in water solution of solid solutes at 313 K. Solutes and weight fraction are reported in the figures. Solubility is expressed as grams of CO2 per 100 g of noncarbonated solution. Symbols are experimental values; continuous lines correspond to the PRWS thermodynamic model results.
Figure 7. CO2 solubility for water-malic acid (0.01 g/100 g of solution)-glucose (12 g/100 g of solution) system at different temperatures: b, 313; 9, 323 K. For comparison, CO2 solubility values in water are reported: O, 313; 0, 323 K. Solubility is expressed as grams of CO2 per 100 g of noncarbonated solution. Symbols are experimental values; solid lines and short dashed lines correspond to the PRWS thermodynamic model results.
Figure 8. CO2 solubility for water-citric acid (0.01 g/100 g of solution)malic acid (0.85 g/100 g of solution)-sucrose (7.8 g/100 g of solution)glucose (2.16 g/100 g of solution)-pectin (0.14 g/100 g of solution) system (b), for a commercial apple juice (9), and water (4) for comparison at 313 K. Solubility is expressed as grams of CO2 per 100 g of non carbonated solution. The continuous line corresponds to the PRWS thermodynamic model results for the water-citric acid-malic acid-sucrose-glucosepectin solution.
Figure 8 also reports for comparison CO2 solubility measured in a commercial apple juice. In the same graph, CO2 solubility in pure water is also reported as a reference. For both systems, CO2 solubility is lower than that in pure water. The curves of the model solution and the commercial juice are very close, and the small difference between them could be attributed to other minor components present in the real juice. The results obtained confirm those reported by Calix and co-workers12 who
measured CO2 solubility in a commercial apple and orange juice and in aqueous solutions emulating the composition of both juices. Conclusions The experimental results show that the composition of the investigated aqueous solutions affects the amount of CO2 that
Ind. Eng. Chem. Res., Vol. 49, No. 6, 2010
2999
List of Symbols a ) attraction factor in the equation of state [-] ai ) attraction factor of the i species in the mixture [-] aj ) attraction factor of the j species in the mixture [-] A0 ) empirical constant in the PSRK model equal to -0.647 b ) covolume in the equation of state [-] bi ) covolume of the i species in the equation of state [-] bj ) covolume of the j species in the equation of state [-] C* ) empirical constant in the PR EOS () [ln(2 - 1)]/2) fiL ) fugacity of the i species in the liquid mixture [MPa] GγE ) excess Gibbs free energy [J kmol-1] Hi ) Henry’s law constant [MPa] kij ) coefficient of binary interaction [-] P ) pressure [MPa] P0 ) reference pressure [MPa] R ) ideal gas constant [J K-1 kmol-1] T ) temperature [K] VL) molar volume [m3 kmol-1] xi ) mole fraction of the i species in the liquid phase [-] yi ) mole fraction of the i species in the vapor phase [-] zi ) mole fraction of the i species [-] zj ) mole fraction of the j species [-] γ*i ) activity coefficient of the i species at infinite dilution [-] Figure 9. Comparison between CO2 solubility experimental results and PRWS model prediction results in all the investigated solutions: +, water T ) 313 K; 0, water-glucose (4 g/100 g of solution) T ) 313 K; 0, water-glucose (12 g/100 g of solution) T ) 313 K; 4, water-malic acid (0.01 g/100 g of solution) T ) 313 K; 3, water-malic acid (2.68 g/100 g of solution) T ) 313 K; ], water-malic acid (0.01 g/100 g of solution)-glucose (12 g/100 g of solution) T ) 313 K; b, water-malic acid (0.01 g/100 g of solution)-glucose (12 g/100 g of solution) T ) 323 K; 9, water-pectin (0.14 g/100 g of solution) T ) 313 K; 2, water-citric acid (0.01 g/100 g of solution) T ) 313 K; 1, water-sucrose (7.8 g/100 g of solution) T ) 313 K; [, water-glucose (2.16 g/100 g of solution)-sucrose (7.8 g/100 g of solution)-citric acid (0.01 g/100 g of solution)-malic acid (0.85 g/100 g of solution)-pectin (0.14 g/100 g of solution) T ) 313 K. Solubility is expressed as g of CO2 per 100 g of noncarbonated solution.
can be dissolved. In particular, CO2 solubility strongly depends on glucose and sucrose concentration, while it is only slightly affected by malic acid and citric acid concentration. In water-glucose and water-sucrose systems, CO2 solubility is lower than in pure water at the same conditions of pressure and temperature and decreases when the carbohydrate concentration increases. General conclusions on the predictive ability of the PRWS thermodynamic model can be drawn by observing the parity plot reported in Figure 9 comparing the CO2 solubility mean values experimentally measured with those resulting from model predictions for all the aqueous solutions investigated. The experimental solubility results are accurately predicted by the PRWS thermodynamic model. In particular, once the main coefficients of binary interaction (between water and the other species and between CO2 and the other species) are obtained by a best fit procedure for a single reference condition in binary and ternary systems, the model has a good predictive capability in the full range of pressure, temperature, and composition tested for ternary, quaternary, and more complex systems. The number of adjustable parameters used in the modeling procedure is, therefore, limited. The paper demonstrates that the combined use of simple solubility experiments and model equilibrium calculations is promising in the experimental interpretation and design of applications involving high pressure carbon dioxide.
Literature Cited (1) Arreola, A. G.; Balaban, M. O.; Marshall, M. R.; Peplow, A. J.; Wei, C. I.; Cornell, J. A. Supercritical carbon dioxide effects on some quality attributes of single strength orange juice. J. Food Sci. 1991, 56, 1030. (2) Balaban, M. O.; Kincal, D.; Hill, S.; Marshall, M. R.; Wildasin, R. The synergistic use of carbon dioxide and pressure in non thermal processing of juices; IFT Annual Meeting Book of Abstracts: New Orleans, LA; Chicago, IL, 2001. (3) Yagiz, Y.; Lim, S. L.; Balaban, M. O. Continuous high pressure CO2 processing of mandarin juice; IFT Annual Meeting Book of Abstracts: New Orleans, LA; Chicago, IL, 2005. (4) Garcia-Gonzalez, L.; Geeraerd, A. H.; Spilimbergo, S.; Elst, K.; Van Ginneken, L.; Debevere, J.; Van Impe, J. F.; Devlieghere, F. High pressure carbon dioxide inactivation of microorganisms in foods: The past, the present and the future. Int. J. Food Microbiol. 2007, 117, 1. (5) Ferrentino, G.; Balaban, M. O.; Ferrari, G.; Poletto, M. Food treatment with high pressure carbon dioxide. S. cereVisiae inactivation kinetics expressed as a function of CO2 solubility. J. Supercrit. Fluids 2010, 52, 151. (6) Wiebe, R.; Gaddy, V. L. The solubility in water of carbon dioxide at various temperatures and at pressures to 500 atm. J. Am. Chem. Soc. 1940, 61, 315. (7) Battino, R.; Clever, H. L. The solubility of gases in liquids. Chem. ReV. 1965, 66, 395. (8) Dohrn, R.; Bunz, A. P.; Devlieghere, F.; Thelen, D. Experimental measurements of phase equilibria for ternary and quaternary systems of glucose, water, CO2 and ethanol with a novel apparatus. Fluid Phase Equilib. 1993, 83, 149. (9) Bamberger, A.; Sieder, G.; Maurer, G. High - pressure (vapor + liquid) equilibrium in binary mixtures of (carbon dioxide + water or acetic acid) at temperatures from 313 to 353 K. J. Supercrit. Fluids 2000, 17, 97. (10) Melhem, G. A.; Saini, R.; Goodwin, B. M. A modified PengRobinson equation of state. Fluid Phase Equilib. 1989, 47, 189. (11) Bando, S.; Takemura, F.; Nishio, M.; Hihara, E.; Akai, M. Solubility of CO2 in aqueous solutions of NaCl at (30 to 60) °C and (10 to 20) MPa. J. Chem. Eng. Data 2003, 48, 576. (12) Calix, T. F.; Ferrentino, G.; Balaban, M. O. Measurement of high pressure carbon dioxide solubility in orange juice, apple juice and model liquid solutions. J. Food Sci. 2008, 73, E439. (13) Diamond, L. W.; Afinkiev, N. N. Solubility of CO2 in water from1.5 to 100 °C and from 0.1 to 100 MPa: evaluation of literature data and thermodynamic modeling. Fluid Phase Equilib. 2003, 208, 265. (14) Chapoy, A.; Mohammadi, A. H.; Chareton, A.; Tohidi, B.; Richon, D. Measurement and modeling of gas solubility and literature review of the properties for the carbon dioxide-water system. Ind. Eng. Chem. Res. 2004, 43, 1794.
3000
Ind. Eng. Chem. Res., Vol. 49, No. 6, 2010
(15) Ji, Y.; Ji, X.; Feng, X.; Liu, C.; Lu, L. Progress in the Study on the Phase Equilibria of the CO2-H2O and CO2-H2O-NaCl Systems. Chin. J. Chem. Eng 2007, 15, 439. (16) Carroll, J. J.; Mather, A. E. The system carbon dioxide-water and the Krichevsky-Kasamovsky equation. J. Solution Chem. 1992, 21, 607. (17) Kiepe, J.; Horstmann, S.; Fischer, K.; Gmehling, J. Experimental determination and prediction of gas solubility data for CO2 + H2O mixtures containing NaCl or KCI at temperatures between 313 and 393 K and pressures up to 10 MPa. Ind. Eng. Chem. Res. 2002, 41, 4393. (18) Shyu, G. S.; Hanif, N. S.; Hall, K. R.; Eubank, P. T. Carbon dioxidewater phase equilibria results from the Wong-Sandler combining rules. Fluid Phase Equilib. 1997, 130, 73. (19) Valtz, A.; Chapoy, A.; Coquelet, C.; Paricaud, P.; Richon, D. Vapour-liquid equilibria in the carbon dioxide-water system, measurement and modelling from 278.2 to 318.2 K. Fluid Phase Equilib. 2004, 226, 333. (20) Gilbert, M. E.; Paulaitis, M. L. Gas-liquid equilibria for EtOHH2O-CO2 mixtures at elevated pressures. J. Chem. Eng. Data 1986, 31, 296. (21) Takishima, S.; Saiki, K.; Arai, K.; Saito, S. Phase equilibria for CO2-C2H2OH-H2O system. J. Chem. Eng. Jpn. 1986, 19, 48. (22) Ferrentino, G. Microbial stabilization of liquid food with carbon dioxide under pressure. Ph.D. Thesis, University of Salerno, Fisciano (SA), Italy, 2009. (23) Eisele, T. A.; Drake, S. R. The partial compositional characteristics of apple juice from 175 apple varieties. J. Food Comp. Anal. 2005, 18, 213. (24) Aspen Plus Unit Operation Models; Aspen Technology Inc: Cambridge, MA, 2003.
(25) Sandler, S. I. Chemical, biochemical, and engineering thermodynamics; Wiley: Hoboken, NJ, 2006; pp 346-350. (26) Wong, S. H.; Sandler, S. I. A Theoretically Correct Mixing Rule for Cubic Equations of State. AIChE J. 1992, 38, 671. (27) Fredenslund, A. A.; Gmehling, J.; Rasmussen, P. Vapor-Liquid Equilibria Using UNIFAC; Elsevier Press: Amsterdam, 1977. (28) Chen, C. C.; Evans, L. B. A local composition model for the excess Gibbs energy of aqueous electrolyte systems. AIChE J. 1986, 32, 444. (29) Holderbaum, T.; Gmehling, J. PSRK: A Group Contribution Equation of State Based on UNIFAC. Fluid Phase Equilib. 1991, 70, 251. (30) Redlich, O.; Kwong, J. N. S. On the thermodynamics of solutions V. An equation-of-state. Fugacities of Gaseous Solutions. Chem. ReV. 1979, 44, 223. (31) Soave, G. Equilibrium constants for a modified Redlich-Kwong equation-of-state. Chem. Eng. Sci. 1972, 27, 1196. (32) Ferrentino, G.; Barletta, D.; Balaban, M. O.; Ferrari, G.; Poletto, M. Measurement and prediction of CO2 solubility in sodium phosphate monobasic solutions for food treatment with high pressure carbon dioxide. J. Supercrit. Fluids 2010, 52, 142. (33) Sandler, S. I. Chemical, biochemical, and engineering thermodynamics; Wiley: Hoboken NJ, 2006; pp 576-585.
ReceiVed for reView June 19, 2009 ReVised manuscript receiVed January 25, 2010 Accepted February 3, 2010 IE9009974
