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Measurement and correlation of solubility of carbon dioxide in triglycerides
J. Chem. Thermodynamics 104 (2017) 252–260
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Measurement and correlation of solubility of carbon dioxide in triglycerides Md Shamim Howlader a, William Todd French a,⇑, Hossein Toghiani a, Ben Hartenbower a, Larry Pearson a, Janice DuBien c, Neeraj Rai a,b,⇑ a b c
Dave C. Swalm School of Chemical Engineering, Mississippi State University, Mississippi State, MS 39762, USA Center for Advanced Vehicular Systems, Mississippi State University, Mississippi State, MS 39762, USA Department of Mathematics and Statistics, Mississippi State University, Mississippi State, MS 39762, USA
a r t i c l e
i n f o
Article history: Received 31 March 2016 Received in revised form 25 September 2016 Accepted 26 September 2016 Available online 30 September 2016 Keywords: Solubility Henry’s law constant Biofuels Cell disruption Thermodynamic modeling
a b s t r a c t A new pressure drop solubility gas apparatus was developed to determine the solubility of carbon dioxide in canola oil, a triglyceride consisting primarily of oleic, linoleic, and alpha linoleic acid radicals. Solubility of CO2 in triglycerides was determined at different temperatures (283.2–303.2 K) and pressures (600–2450 kPa). It was found that the solubility of CO2 in triglycerides is higher than that of pure water because triglycerides lack strong hydrogen bond networks that exist in liquid water at the ambient conditions. The experimental solubility was correlated using Krichevsky–Kasarnovsky (KK), Mather-Jou (MJ), and Carvalho-Coutinho (CC) correlations. We find that KK and MJ equations can predict the solubility with higher accuracy. The enthalpy and entropy of absorption of CO2 were calculated using the van’t Hoff plot and were found to be 7.165 kJ.mol1, and 28.791 J.mol1.K1, respectively. Ó 2016 Elsevier Ltd.
1. Introduction In the recent years, there has been intense research focused on developing efficient and cost effective technologies for transportation biofuels for securing energy, reducing environmental concerns and lessening foreign oil dependency [1–3]. One of the key components in a renewable energy portfolio is biodiesel, which is biodegradable, less toxic and has energy density similar to conventional petroleum diesel [4–6]. Oleaginous microorganisms are considered as one of the possible alternative feedstocks for biodiesel as they can accumulate more than 20% lipid on a dry weight basis [7]. To use these lipids as biodiesel feedstock, they must be first extracted from the microorganisms. The traditional Bligh and Dyer [8] method used to extract the lipid from the oleaginous yeast in the laboratory setting would be uneconomical on a commercial scale because of high extraction cost. The conventional oil extraction method [9] for oleaginous algae requires lipid source to be nearly free of water with solid content more than 90%. Since biomass drying accounts for more than 75% total energy consumption, the process becomes economically unfeasible [10]. However, the ⇑ Corresponding authors at: Dave C. Swalm School of Chemical Engineering, Mississippi State University, Mississippi State, MS 39762, USA (N. Rai). E-mail addresses: [email protected] (W.T. French), [email protected]. edu (N. Rai). http://dx.doi.org/10.1016/j.jct.2016.09.035 0021-9614/Ó 2016 Elsevier Ltd.
lipid recovery can be increased if the cell is disrupted prior to extraction, potentially decreasing the need to dry to (P90%) solids [11], and thus reducing the energy requirement for the process [12]. Efficient and economical cell lysing results in enhanced lipid extraction due to the increased mass transfer rates [13]. Some of the commonly available methods for microbial cell disruption are mechanical, physical, chemical, and enzymatic cell disruptions [14]. Cell lysing using chemical solvent is a useful technique that is able to disrupt the microbial cell wall by reacting with lipophilic tail, but seems to be unfeasible due to the cost of solvent recovery. Different solvents were tested to evaluate the feasibility of cell inactivation, and it was found that carbon dioxide is superior to other chemicals such as nitrogen, argon, tetrafluoroethane, etc. [15]. Lin et al. reviewed the microbial cell disruption using supercritical and subcritical CO2 [16]. The lipid extraction cost using supercritical CO2 (pressure and temperature above 7380 kPa and 304.5 K) is significantly higher; thus, a process utilizing subcritical CO2 can potentially reduce the extraction cost. If the cell is disrupted using pressurized CO2 prior to lipid extraction, the extraction kinetics enhances due to the reduced mass transfer limitation since carbon dioxide can penetrate through the phospholipid membrane of the cell [15]. CO2 facilitates the disruption due to the high solubility of carbon dioxide in lipid. Furthermore, CO2 is cheap, nontoxic, nonflammable, and naturally abundant [17].
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A thorough understanding of solubility of carbon dioxide in triglycerides is essential for designing efficient cell disruption processes. Although there is a large number of studies [18–22] conducted on solubility of triglycerides in super critical carbon dioxide for oil extraction, there is a lack of data on low pressure CO2 solubility in triglycerides. This paper presents an experimental design based on pressure drop gas apparatus that not only allows for the measurement of gas solubility but also cell disruption by applying pressure and vacuum in a cyclic manner. The solubility of CO2 in canola oil, a triglyceride consisting primarily of oleic, linoleic, and alpha linoleic acid was measured at different temperatures and pressures. We selected canola oil because its fatty acid profile is very similar to the triglycerides produced by the microbes [7]. The experimental solubility was correlated with three thermodynamic models. Thermodynamic properties such as enthalpy of dissolution, entropy of dissolution and Gibbs energy of dissolution were determined using van’t Hoff’s plot. 2. Experimental 2.1. Materials Refined canola oil was purchased from Fisher Scientific, USA. The iodine value, saponification value, acid value, and peroxide value of canola oil were 111, 190.3, 0.01, and 1.67 as described by the supplier. For the characterization of canola oil, its fatty acid compositions were determined, and compared with the available literature [23]. For fatty acid methyl ester (FAME) analysis, the refined canola oil was transesterified, and analyzed using Agilent 6890N gas chromatograph equipped with a flame-ionization detector (GC-FID; Agilent Technologies Inc., Wilmington, Delaware, USA) with a Zebron ZBFFAP column of 30 m with 0.25 mm inner diameter and film thickness of 0.25 lm, respectively. Each sample was injected three times in the GC. Helium was used as the carrier gas with a rate of 20 mm3.s1 and the detector temperature was 533.2 K. Temperature was increased from 323 to 523 K with a rate of 16.67 102 K s1 [24]. The instrument was calibrated using a standard solution containing known concentration of C9–C24 FAMEs (Sigma Aldrich, USA) [24]. The results of fatty acid obtained from GC analysis are shown in Table 1 along with literature values. Most common fatty acids found in the canola oil were oleic acid (C18:1), linoleic acid (C18:2), linolenic acid (C18:3), and palmitic acid (C16:0) (Supplementary Material, Fig. S1). The fatty acid compositions of canola oil were found to be nearly identical to the available literature [23]. The fatty acid compositions of canola oil were also compared with OM, and found to be similar for oleaginous yeast [7]. The molecular weight of canola oil was determined from its fatty acid composition. The procedure for finding the molecular weight from the fatty acid profile can be found in the literature [25]. The obtained molecular weight
of canola oil is provided in Table 2, which was found to be the same as reported by Leung et al. and Singh et al. [26,27]. A little deviation from the previous work was found due to the variation in fatty acid profile of the present canola oil sample. The water content in the canola oil was determined using volumetric Karl-Fischer titration by the authors and reported as g water/g canola oil, which is provided in Table 2. Carbon dioxide was purchased from Nexair, Columbus, Mississippi. The deionized water from the laboratory was used to determine the solubility of CO2 in water. Table 2 provides the summary of chemicals used for this research along with their purity, source, and purification method. The purity of both CO2 and tetradecane was provided by the supplier and used for the experiment without further purification. 2.2. Apparatus and experimental procedure The experimental set-up is shown in Fig. 1. A dual reactor system was used for measuring the solubility of CO2 in liquids. Two pressure vessels of capacity of 650 and 450 mL, respectively, were purchased from Parr Instrument, USA. Pressure vessel 1 was used for measuring the amount of gas injected initially in the system, and pressure vessel 2 was used for measuring the solubility where a known amount of solvent was placed initially. Pressure vessel 2 was equipped with a stirrer to maximize the contact between the gas and the liquid; hence, equilibrium was obtained in a reasonable time. A type J thermocouple (T) with an uncertainty of ±0.1 K inserted into pressure vessel 2 was used to measure the temperature in the system. A Neslab RTE10 recirculating water bath chiller purchased from Thermo Scientific, USA was used to maintain a uniform temperature in both vessels. Ethylene glycol was the circulating fluid in the chiller that maintains the uniformity of temperature in both vessels. A single-phase high vacuum pump, purchased from Edwards, was used for degassing the solvent. A pressure transducer purchased from Ashcroft, was used to measure the pressure in the system. The accuracy of the pressure transducer is 0.05% with the minimum and maximum reading of 0 and 13,789 kPa, respectively. The resolution of the pressure transducer is 0.1 psi. Before each run, the degassing was conducted three times (each at least 20 min) for the complete removal of any impurities present in the solvent. For degassing, valves V3 and V4 were kept open and all other valves remain closed. After degassing, valves V3 and V4 were closed, and CO2 was injected into pressure vessel 1 by opening valves V2 and V5. When the pressure was stabilized in vessel 1, the initial gauge pressure from the pressure transducer, atmospheric pressure from the barometer, and the temperature from the thermometer were recorded and the amount of total gas charged into vessel 1 and the tubing was determined. After pressure stabilization in vessel 1, valve V6 was opened and the gas came into contact with the liquid present in vessel 2. A constant stirring was applied in vessel 2 throughout the experiment for gas-liquid mixing. After reaching the equilibrium (when there
Table 1 Comparison of fatty acid composition of refined canola oil with literature [23].a
a b c d
Fatty acidd
Mb/(g/mol)
Cx:yc
100 w (This Work)
100 w (Literature)
Palmitic Palmitoleic Stearic Oleic Linoleic Linolenic Arachidic
256.42 254.41 284.47 282.46 280.44 278.43 304.46
C16:0 C16:1 C18:0 C18:1 C18:2 C18:3 C20:4
4.77 ± 0.05 0.40 ± 0.01 1.73 ± 0.03 63.03 ± 0.40 21.45 ± 0.20 7.57 ± 0.07 0.80 ± 0.20
3.6 0.2 1.5 61.6 21.7 9.6 –
Experimental results for fatty acid composition is reported together with its standard uncertainty. Molar mass. Cx:y; x: number of carbons, y: number of double bonds. Behemic and Erucic acids are present in trace amounts.
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Table 2 Specifications and sources of chemicals used in this work. Chemicals Canola oil Tetradecaned Carbon dioxidef Water a b c d e f g
Supplier Fischer Scientific Sigma Aldrich NexAir Deionized in Laboratoryg
Ma/(g.mol1) 879.34 198.39 44.01 18.01
Mass fraction purity
102 g water/g sample (Karl Fischer) 0.062 ± 0.005
b
Analysis method c
GC-FID GC
e
0.999 0.999
Molar mass. Water content was measured in our laboratory. Gas chromatography-flame ionization detector. Refractive index of tetradecane is 1.429 (at T = 293.2 K) and the purity was provided by the supplier. Gas chromatography. Purity of CO2 was provided by the supplier. Resistivity of water was 18.2 Xm.cm.
Fig. 1. Experimental set up for solubility measurement.v1, v2, v3, v4, v5, v5, v6, v7 are the valves used in the experiment. P1 is the vacuum pressure gauge and P2 is the pressure transducer. The vacuum pump was used to degas the solvent. The cooling coil was coupled with the vessel 1 and 2, through which the circulating fluid flowed from the chiller to pressure vessel 1 and 2. The stirrer was used to enhance the mixing of gas and liquid. The thermocouple was used to measure the temperature in the system.
was no pressure change), the final gauge pressure, the atmospheric pressure, and the temperature were recorded again. The amount of gas in the headspace of vessel 2, in the tubing, and in vessel 1 (i.e. in the free space) was calculated. The amount of dissolved CO2 in triglycerides was estimated by subtracting the amount of gas in the free space from the total amount of gas charged initially. 2.3. Solubility measurement With known initial pressure (P1) and temperature (T1), molar volume of CO2 in pressure vessel 1 and tubing was calculated using the Span and Wagner [28] EoS provided in the NIST data base. Span and Wagner EoS can predict the PVT properties of CO2 in a region of triple point temperature to 1100 K at a pressure up to 800 MPa. Once the molar volume in the initial state is known, the total number of moles of CO2 injected initially in the system was determined. After releasing the gas into pressure vessel 2 with known equilibrium pressure and temperature, the number of moles of CO2 in the free space was calculated from the molar volume in the final state. By subtracting the number of moles of CO2 in the free space from the total number of moles of CO2, the amount of CO2 dissolved in the liquid was obtained. As the total moles of liquid placed into
pressure vessel 2 prior to experiment is known, the mole fraction solubility of CO2 in liquid can be calculated. The step-by-step procedure for finding the mole fraction solubility of carbon dioxide in liquid is described below. Step 1: Initial pressure P1, initial temperature T1 were known, molar volume of CO2 in the initial state, V m1 =ðcm3 =molÞ was estimated using Span and Wagner EoS. Step 2: Total number of moles of CO2, nT was calculated from V m1 using
nT =mol ¼ V 1 =V m1
ð1Þ
where V 1 =cm3 is the volume of vessel 1 and tubing determined manually. Step 3: Equilibrium pressure P2, equilibrium temperature T2 were known, molar volume of CO2 in the final state,V m2 =ðcm3 =molÞ was calculated by Span and Wagner EoS. Step 4: The amount of CO2 in the headspace of vessel 2, in the tubing and in vessel 1 (free space) n2 was measured from V m2 using
n2 =mol ¼ ðV 2 V solv ent Þ=V m2
ð2Þ
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where V 2 =cm3 is the volume of free space (vessel 1 volume + tubing volume + free space volume of vessel 2) determined manually and V solv ent =cm3 is the volume of the solvent. Step 5: The amount of CO2 dissolved in the liquid was estimated by
ndissolv ed =mol ¼ n2 nT :
ð3Þ
Step 6: The solubility (molality) of carbon dioxide in the liquid was calculated by
S=ðmol=kgÞ ¼ ndissolv ed =msolv ent
ð4Þ
where msolv ent =kg is the amount of solvent. Step 7: The mole fraction solubility of CO2 was calculated using the following relation
xCO2 ¼ ndissolv ed =ðndissolv ed þ nsolv ent Þ
ð5Þ
where nsolv ent =mol was the moles of solvent obtained using solvent molecular weight and mass. The Poynting correction factor [29] of water and triglycerides were found to be insignificant since the experimental pressure considered in this study were not very high, thus not considered in this work. The Poynting correction factor for water and triglycerides at different pressures and temperatures are provided in the Supplementary Material. 3. Results and discussion 3.1. Data validation To validate the experimental set-up, the solubility of CO2 in water was determined at three different temperatures of 288.2, 293.2 and 298.2 K, respectively at different pressures and compared with the data available in the literature [30–33]. The
experiments were conducted in triplicate to ensure the accuracy of the data obtained from this work. From Table 3, it is evident that there is a good agreement with the previous experimental data as the deviation was small, which indicates the suitability of our methodology for gas solubility measurement. The comparison of CO2 solubility in water is also depicted in Fig. 3, where the mole fraction solubility is plotted against the pressure at different temperatures of 288.2, 293.2 and 298.2 K. From the figure, the CO2water of the present data followed the similar trend as was reported in the literature [30–33]. Since carbon dioxide is reactive to water and it is possible for some of the CO2 to react with water to form carbonic acid during the pressurization, the apparatus was further validated using the solubility of CO2 in tetradecane, a long chain alkane. The experiments were conducted at different pressures from (980–2000 kPa) at 323.2 K. The mole fraction solubility (xCO2 ) of CO2 in tetradecane at these conditions is also presented in Table 3 and Fig. 2. Since tetradecane has very low vapor pressure (0.002 kPa at T = 298.2 K) [34], the total pressure and partial pressure is the same, which is reported in the table. The solubility of CO2 is compared the work of Kariznovi et al. [35], and it was found that at low pressure our apparatus can determine the mole fraction solubility of CO2 in tetradecane similar to Kariznovi et al., but at higher pressure the solubility obtained from this work deviates from the data of Kariznovi et al. The difference in solubility at high pressure might arise due to the way of determining the solubility by two different methods. For us, we followed a straightforward solubility determination using the pressure drop method, while Kariznovi et al. determined the solubility using a method different from us where they have kept the pressure and temperature constant throughout the experiment. Later, we have compared our triglycerides solubility data with available literature [36] and found that the mass fraction solubility of CO2 in canola oil and high oleic sunflower oil are nearly same, which gives the further evidence of suitability of our apparatus.
Table 3 Comparison of solubility of CO2 in water and tetradecane with literature [30–33,35].a Compounds
T/K
This work Ptotal/kPa
Water
Tetradecane
a b c d e f g
b
288.2 288.2b 288.2b 293.2b 288.2b 288.2b 298.2b 298.2b 298.2b 288.2b 288.2b 288.2b 293.2b 293.2b 293.2b 298.2b 323.2b 323.2b 323.2b 323.2b
371 ± 4 409 ± 6 469 ± 1 336 ± 2 493 ± 1 1108 ± 2 383 ± 1 506 ± 1 616 ± 5 697 ± 1 1056 ± 2 1251 ± 6 502 ± 1 749 ± 4 1002 ± 1 755 ± 6 986 ± 1 2061 ± 14 1304 ± 2 1565 ± 2
Literature P CO2 /kPa 369 ± 4 407 ± 6 467 ± 4 334 ± 2 491 ± 1 1106 ± 2 380 ± 1 503 ± 1 613 ± 5 695 ± 1 1054 ± 2 1249 ± 6 500 ± 1 747 ± 4 1000 ± 1 752 ± 6 986 ± 1 2061 ± 14 1304 ± 2 1565 ± 2
103 xCO2 3.00 ± 0.20 3.28 ± 0.20 3.76 ± 0.20 2.38 ± 0.04 3.99 ± 0.02 8.52 ± 0.04 2.49 ± 0.01 3.30 ± 0.01 3.61 ± 0.11 5.41 ± 0.04 7.99 ± 0.03 9.53 ± 0.20 3.49 ± 0.04 5.10 ± 0.02 6.75 ± 0.03 4.43 ± 0.08 95.7 ± 0.6 181.2 ± 6.3 120.1 ± 0.6 139.6 ± 0.9
Experimental results for pressure and solubility are reported together with their standard uncertainties. Standard uncertainty of temperature is u(T) = ±0.1 K. Dalmolin et al. [30]. Chapoy et al. [31]. Campos et al. [32]. Lucile at al [33]. Kariznovi et al. [35].
P/kPa
103 xCO2 c
Source
365 409 466 353 496 1103 380 501 610
2.97 3.25c 3.65c 2.42c 4.01d 8.67d 2.50e 3.32e 3.62f
Dalmolin et al.
980 2060
97g 196g
Kariznovi et al.
Chapoy et al. Campos et al. Lucile et al.
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M.S. Howlader et al. / J. Chem. Thermodynamics 104 (2017) 252–260 Table 4 Experimental solubility of CO2 in triglycerides at different temperatures and pressures.a T/K
Ptotal/kPa
xCO2
283.2b
607 ± 11 895 ± 2 1245 ± 10 1596 ± 4 2040 ± 6 612 ± 4 922 ± 4 1258 ± 3 1615 ± 2 2040 ± 8 2394 ± 19 622 ± 3 932 ± 1 1269 ± 3 1633 ± 2 2040 ± 5 2406 ± 10 632 ± 6 947 ± 3 1285 ± 3 1651 ± 1 2065 ± 7 2413 ± 8 652 ± 7 963 ± 3 1306 ± 1 1675 ± 2 2079 ± 4 2426 ± 7
0.303 ± 0.007 0.417 ± 0.001 0.495 ± 0.005 0.582 ± 0.002 0.654 ± 0.002 0.291 ± 0.006 0.392 ± 0.003 0.476 ± 0.002 0.554 ± 0.001 0.625 ± 0.003 0.674 ± 0.005 0.278 ± 0.003 0.375 ± 0.001 0.457 ± 0.002 0.530 ± 0.001 0.595 ± 0.001 0.639 ± 0.003 0.265 ± 0.005 0.359 ± 0.002 0.437 ± 0.002 0.506 ± 0.001 0.563 ± 0.002 0.604 ± 0.003 0.243 ± 0.007 0.341 ± 0.003 0.415 ± 0.001 0.480 ± 0.003 0.536 ± 0.001 0.572 ± 0.001
288.2b
293.2b Fig. 2. Depiction of mole fraction solubility of CO2 in water and tetradecane as a function of pressure. For CO2 in water: circles, stars, and squares represent the present work, Dalmolin et al. [30], and Chapoy et al. [31], respectively at 288.2 K; diamonds and filled diamond represent the present work and Dalmolin et al. [30], respectively at 293.2 K; triangles left, triangles right, and filled triangle left represent the present work, Campos et al. [32], and Lucile et al. [33], respectively at 298.2 K. For CO2 in tetradecane: triangles up and triangles down represent the present work and Kariznovi et al. [35], respectively at 323.2 K. Dashed dotted lines are guide to the eye for the data generated in the current work.
298.2b
303.2b
a Experimental results for pressure and solubility are reported together with their standard uncertainties. b Standard uncertainty of temperature is u(T) = ±0.1 K.
Fig. 3. Solubility of CO2 in triglycerides as function of pressure at different temperatures: Circles, squares, diamonds, triangles up, and triangles down represent solubility at 283.2, 288.2, 293.2, 298, and 303.2 K respectively.
polar solvents at comparable temperature and pressure [39–41]. Not surprising, as can be seen in Table 4 and Fig. 3, the solubility of CO2 in triglycerides was found to be also significantly higher than that of in the pure water. This is because both CO2 and triglycerides are nonpolar in nature and triglycerides lack strong hydrogen bond networks that exist in liquid water at the ambient conditions. Furthermore, it is anticipated that available free volume is significantly larger in triglycerides than in water and other solvents capable of hydrogen bonding. Scovazzo et al. [42] have shown that solubility parameters of solute and solvent can be used to correlate
3.2. Solubility of carbon dioxide in triglycerides Solubility of carbon dioxide in triglycerides was determined at five different temperatures of 283.2, 288.2, 293.2, 298.2, and 303.2 K, respectively as a function of pressure. The result is presented in Table 4, where the mole fraction solubility of CO2 is tabulated along with uncertainties at each run. The partial pressure of CO2 and total experimental pressure is the same due to negligible vapor pressure of vegetable oil [37], which is reported in Table 4. The experiment was conducted in triplicate to observe the variability and statistical consistency at each run. Fig. 3 shows the solubility change as a function of pressure from temperatures 283.2–303.15 K. From the figure, it is evident that solubility of carbon dioxide in triglycerides increases with increasing pressure and decreases with increasing temperature, which suggests that CO2trilgycerides interactions as primarily physical in nature [38]. The temperature dependence of CO2 solubility in triglycerides is similar to that in other polar solvents such as methanol, ethanol [39], cyclohexanol [40], and ethylene glycol [41]. However, mole fraction solubility is significantly higher in triglyceride than in these
Fig. 4. Plot of CO2 fugacity vs. mole fraction solubility in triglycerides at 303.2 K. Circles show the present work and the solid line represents the Raoult’s law.
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gas solubility. They find that solute solubility is higher if the solubility parameters of both solvent and solute are alike. The plot of fugacity of carbon dioxide against its mole fraction shown in Fig. 4 and shows negative deviation from the Raoult’s law. From Fig. 4, the deviation from the ideality is not too high and the CO2 solubility is governed by nonspecific interactions; hence, the regular solution theory (RST), developed by Scott and Hildebrand [43] for nonelectrolyte solutions, can be applied to predict the solubility of CO2 in triglycerides [44,45]. Scovazzo et al. [42] have used solubility parameter to correlated the solubility of CO2 in room temperature ionic liquids (RTILs) using RST. In an extensive review [46] of CO2 solubility in different ionic liquids where they have also used RST for correlating the gas solubility and reported that the solubility of CO2 is higher when the solubility parameter of CO2 and ionic liquids were identical. It is also reported by Arul et al. that the maximum solubility is occurred when the solute and solvent solubility parameters are the same [47]. Since it is known from the literature that the solubility parameter for CO2 (17.85 MPa1/2) and vegetable oils (triglycerides) (16.0 MPa1/2) are similar, which is different from pure water (47.81 MPa1/2) [48,49]; hence, the solubility of CO2 in triglycerides is higher than that of in the water. The solubility of CO2 in triglycerides was compared with the available literature [36,50] of similar solvents. The comparison of CO2 solubility in canola oil with the solubility of CO2 in high oleic sunflower oil (HOSO) is shown Fig. 5, where the mass fraction CO2 in two different solvents is plotted as a function of pressure at 298.2 K. From the figure it can be seen that this work’s solubility report follows the similar trend obtained from the work by Regueira et al. [36]. They have also reported the solubility of CO2 in rapeseed oil and castor oil. It can be seen from that the CO2 solubility in canola oil (this work) have nearly similar results for rapeseed oil and HOSO whereas the solubility of CO2 in castor oil is different from this work. From the fatty acid composition of rapeseed and HOSO, both have higher oleic acid content, which is same for canola oil of this work followed similar results. It was also found that the solubility of CO2 in pentaerythritol ester oils reported by Fandino et al. [50] is similar to our work. 3.3. Correlation of CO2 solubility using thermodynamic models The experimental solubility was correlated using three thermodynamic modeling. The reason for using these three correlations was that these models are relatively simple and they are previously applied for CO2 solubility in different solvents [51–53]. The first
Fig. 5. Comparison of mass fraction solubility of CO2 in canola oil with the solubility of CO2 in high oleic sunflower oil (HOSO) at 298.2 K. Circles and squares represent the present work and results reported by Regueira et al. [36], respectively.
approach was to use the Krichevsky–Kasarnovsky (KK) equation, commonly used to correlated CO2 solubility in ionic liquids [51,54–56]. The KK equation is defined as follows [57]: Ps
S lnfðf CO2 =kPaÞ=xCO2 g ¼ lnðkH;CO2 Þ þ V 1 CO2 ðP P Þ=RT
ð6Þ PS
where f CO2 =kPa the fugacity of CO2 in the gas phase, kH;CO2 =kPa the 3 Henry’s constant at solvent vapor pressure, V 1 CO2 =ðcm =molÞ the partial molar volume of CO2 at infinite dilution, xCO2 the mole fraction of CO2 in triglycerides, and Ps/kPa the vapor pressure of pure triglycerides. Since vegetable oil has negligible vapor pressure [37], after some modification, Eq. (6) becomes,
0
lnfðf CO2 =kPaÞ=xCO2 g ¼ lnðkH;CO2 Þ þ V 1 CO2 P=RT
ð7Þ
0
where kH;CO2 =kPa represents the Henry’s constant at zero pressure. The intercept and the slope of plotlnfðf CO2 =kPaÞ=xCO2 g vs. P/kPa gives 0
3 kH;CO2 =kPa and V 1 CO2 =ðcm =molÞ,respectively of CO2. The fugacity of CO2 was calculated from the following correlation,
f CO2 =kPa ¼ uCO2 P
ð8Þ
where, uCO2 the fugacity coefficient of pure CO2 and P/kPa the total pressure. The fugacity coefficient of pure CO2 was evaluated from PR EoS [58]. The plot of lnfðf CO2 =kPaÞ=xCO2 g vs. P/kPa at different temperatures is shown in Fig. 6, where the extrapolations of data were conducted using linear regression to obtain the intercept and slope. The second approach of correlating the solubility was an empirical equation developed by Mather and Jou [52] defined as,
lnðP=kPaÞ ¼ A þ BðlnSÞ
ð9Þ
where S/(mol CO2/mol triglycerides) the solubility, P/kPa the experimental pressure, and A and B are temperature dependent empirical constants correlated as follows,
A ¼ 10:9499 0:0454T þ 11:228 105 T 2 ;
ð10Þ
B ¼ 1:1395 6:941 103 T
ð11Þ
The MJ correlation was used to correlate the experimental solubility data as well as to compare the predicted solubility obtained from the KK correlation. MJ correlation was primarily used for the measurement of CO2 solubility in a mixture of methyldiethanolamine, N methyldiethanolamine and water [52].
Fig. 6. lnfðf CO2 =kPaÞ=xCO2 g as a function of pressure using KK correlation for CO2 solubility in triglycerides. The circles, squares, triangles up, triangles down, and diamonds represent experimental data at temperature of 283.2, 288.2, 293.2, 298.2 and 303.2 K, respectively. Solid lines represent the linear fitting.
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The third approach to correlate the solubility was to use a modeling proposed by Carvalho and Coutinho [53], which was mainly developed for correlating CO2 solubility in nonvolatile solvents at low to moderate pressure, temperature, and solubility. The Carvalho and Countinho (CC) correlation can be expressed as the following equation,
P=kPa ¼ mCO2 eðAB=TÞ
P=kPa ¼ mCO2 eð12:6741605:795=TÞ
ð13Þ
The deviation of the predicted solubility from the experimental solubility for different models were reported as the percentage average absolute deviation (AAD), which is defined according to the following equation, N 1X ABS N i¼1
xexp CO2
xcal CO2 xexp CO2
283.2a 288.2a 293.2a 298.2a 303.2a a
and N the number of data points. The comparison of different correlations with experimental solubility is shown in Fig. 7. The percentage AAD for each model is shown in Table 5. From Table 5 and Fig. 7, the percentage AAD for KK correlation varied from 0.63 to 1.16 whereas for MJ correlation, the percentage AAD varied from 0.17 to 1.04 and the percentage AAD for CC correlation varied from 1.73 to 3.57. Hence, KK and MJ correlation can predict the CO2 solubility with higher accuracy due to its smaller deviation from experiential data. From the solubility data (both Fig. 3 and Table 4), the solubility behavior is linear at low temperature when the pressure is low to moderate. Hence, CC correlation poorly predicted the solubility at low temperature. As the temperature rises, the CC correlation predicts the solubility with smaller deviation from the experimental data. Both the ln (kH/kPa) and partial molar volume (cm3/mol) at infinite dilution of CO2 obtained from the slope and intercept of lnfðf CO2 =kPaÞ=xCO2 g vs. P/kPa plot is shown in Table 6 along with the standard uncertainties at each
MJ correlation
CC correlation
1.125 1.162 0.871 0.745 0.628
0.925 0.849 0.372 0.174 1.044
3.492 3.571 2.674 1.734 1.781
Standard uncertainty of temperature is u(T) = ±0.1 K.
T/K 283.2 288.2a 293.2a 298.2a 303.2a a
lnðkH;CO2 =kPaÞ
3 V1 CO2 =ðcm =molÞ
7.408 ± 0.023 7.533 ± 0.014 7.544 ± 0.014 7.603 ± 0.011 7.708 ± 0.012
670 ± 40 573 ± 21 636 ± 21 645 ± 17 596 ± 18
0
a
ð14Þ
cal where xexp CO2 the experimental solubility, xCO2 the calculated solubility
KK correlation
Table 6 Henry’s constant and partial molar volume at infinite dilution of CO2 at different temperatures.
! 100
102 Average absolute deviation (AAD)
T/K
ð12Þ
where P/kPa the pressure, mCO2 =ðmol=kgÞ the solubility, T/K the temperature, A and B are correlation constants. After fitting with the experimental data, Eq. (13) was obtained from Eq. (12) defined as
AAD ¼
Table 5 Comparison of deviation among Krichevsky–Kasarnovsky [57], Mather and Jou [52], and Carvalho-Coutinho correlations from the experimental data.
Standard uncertainty of temperature is u(T) = ±0.1 K.
temperature. Following empirical correlation was obtained by fit0
ting the Henry’s constant that relates kH;CO2 =kPa and temperature, 0
kH;CO2 =kPa ¼ 23:5962 8:26 103 =T þ 1:0403 106 =T 2
ð15Þ
0
From the plot of kH;CO2 =kPa vs. T/K shown in Fig. 8, it was observed that the solubility of CO2 in triglycerides increases as the temperature decreases, which follows the typical gas solubility behavior [59]. Since it is evident from both Table 6 and Fig. 8 that the Henry’s constant increase with the increasing temperature, and the relation of Henry’s constant with partial pressure of the gas is defined according to Eq. (16), the mole fraction solubility decreases as the Henry’s constant increase at a fixed pressure [60]. 0
xCO2 ¼ P CO2 =kCO2
ð16Þ
The value of partial molar volume at infinite dilution for different temperatures is presented in Table 6 and the plot of partial molar volume of CO2 as a function of temperature is shown in
Fig. 7. Comparison of solubility data with different correlations at two temperatures: Open and solid circles represent experimental solubility at 293.2 and 303.2 K, respectively; Solid and long dashed lines represent KK correlations at 293.2 and 303.2 K, respectively; Dotted and dash-dotted lines represent MJ correlations at 293.2 and 303.2 K, respectively; dashed and dash-double dotted lines represent CC correlation at 293.2 and 303.2 K, respectively.
Fig. 8. Henry’s constant of CO2 in triglycerides as a function of temperature. The circles show the present work and solid line represents the fitting of Eq. (15), respectively.
M.S. Howlader et al. / J. Chem. Thermodynamics 104 (2017) 252–260
Fig. 9. Partial molar volume of CO2 at infinite dilution as a function of temperature. The circles represent the present work and the solid line represents the quadratic fitting, respectively.
3 Fig. 9. It is observed from the V 1 CO2 =ðcm =molÞ data for different temperatures that partial molar volume of CO2 in triglycerides decreases from 670 cm3.mol1 at 283.2 K to 596 cm3.mol1 at 303.2 K. It is interesting to note that Rahmati-Rostami et al. [55] observed a similar trend for partial molar volume of H2S in ionic liquids i.e. partial molar volume of H2S decreases with increasing temperature. The partial molar volume can be an indirect indicator of strength of the interaction between the solvent and solute molecules [61]. Although molecular interactions present in ionic liquid are very different when compared to triglycerides, it is possible that the solubility of CO2 is governed primarily by weaker dispersion (physical interactions) due to the quadruple nature of CO2 molecule.
3.4. Enthalpy and entropy of dissolution Thermodynamic properties of solution such as enthalpy of dissolution, entropy of dissolution, and Gibbs energy change for the dissolution can be estimated from the experimental solubility data using the van’t Hoff equation [62–66]. The enthalpy of dissolution can be correlated with the following equation according to Liu et al. [64]
DHS =ðkJ=molÞ ¼ R
dlnxCO2 dð1=T 1=T ref Þ
ð17Þ
where xCO2 the CO2 solubility, Tref/K the reference temperature (298.2 K). From Eq. (17), the DHs/(kJ/mol) can be obtained from the slope of lnxCO2 vs. (1/T 1/Tref)/K1. The plot of lnxCO2 vs. (1/T 1/Tref)/K1 at 2040 kPa is shown in Fig. 10, where the slope is 861.859. Hence, the enthalpy of dissolution for CO2 in triglycerides was 7.165 kJ.mol1. It is known that the enthalpy of dissolution is responsible for the molecular interaction between the solute and solvent, and entropy of dissolution is responsible for the degree of ordering of solute/solvent mixture [67,68]. The enthalpy of solution of CO2 in triglyceride was found to be significantly lower than that of found in water (19.57 kJ/mol) [69]. Although CO2 can preferentially bind to the polar groups in triglycerides, interaction is not as strong as between CO2 and water molecules. The lower value of enthalpy also suggests that lower energy is required to overcome the cohesive force between the solute and the solvent, which also indicates a weak temperature dependence of solubility [70,71]. The Gibbs energy (DGs) of the dissolution can be obtained using the following equation according to Krug et al. [72]
259
Fig. 10. Mole fraction solubility (lnxCO2 ) as a function of inverse temperature (1/T 1/Tref) for carbon dioxide in triglycerides; the solid line represents the linear fitting.
DGS =ðkJ=molÞ ¼ RT ref intercept ¼ DHS T ref DSS
ð18Þ
The intercept of Fig. 10 is 0.5726 and the Gibbs energy for the dissolution was 1.419 kJ.mol1. The entropy of dissolution can be obtained as Eq. (19) from Eq. (18). 1
DSs =ðJ:mol K 1 Þ ¼
DHS DGS T ref
ð19Þ
The dissolution of entropy for carbon dioxide in triglycerides was 28.79 J.mol1.K1. The negative value of entropy dissolution indicates higher degree of CO2 solvation in triglycerides. As a result the solubility of CO2 in triglycerides increases with decreasing temperature. It also indicates reduced translational freedom of carbon dioxide molecule in solution as compared to the gas phase. 4. Conclusions A new pressure drop gas apparatus was developed to measure the solubility of gases in liquids. The apparatus was validated using both solubility of carbon dioxide in water as well as CO2 solubility in tetradecane. The solubility of carbon dioxide in triglycerides was measured at different temperatures and pressures, and it was found that solubility of CO2 in triglycerides is significantly higher than that of pure water. The solubility was correlated using Krichevsky–Kasarnovsky (KK), Mather-Jou (MJ), and CarvalhoCoutinho (CC) correlations. It was found the MJ predicted the CO2 solubility with highest accuracy where the percentage average absolute deviation varied from 0.17 to 1.04 at different temperatures. The solubility data was used to determine Henry’s constant and partial molar volume of CO2 at infinite dilution at different temperatures, and it was found that Henry’s constant followed a increasing trend with increasing temperature showing that the solubility of CO2 decreases as the temperatures increases. From the van’t Hoff equation, the thermodynamic properties were estimated and it was found that the solubility is a weak function of temperature. Acknowledgements Md Howlader is thankful to the Dave C. Swalm School of Chemical Engineering, Mississippi State University for the financial support. He is grateful to Mrs. Sara Shields-Menard for helping in GC analysis, Mr. Peter Alzobaidi for his help setting up the experiment,
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Mrs. Magan Green for her help in FAME analysis and Dr. Bill Elmore for his general help during the research. The author is cordially acknowledges the help of Dr. Keisha B. Waters for providing the Karl-Fischer instrument and Mrs. Anandi Varadarajan for helping to determine water content in canola oil using KF titration. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.jct.2016.09.035. References [1] A. Demirbas, Appl. Energy 86 (2009) 108–117. [2] A. Demirbas, Energy Convers. Manage. 50 (2009) 2239–2249. [3] J. Sheehan, V. Camobreco, J. Duffield, M. Graboski, H. Shapouri, U.S.Department Agric. U.S Dep. Energy (1998) 1–60. [4] A.B.M. Sharif Hossain, S. Aishah, Am. J. Biochem. Biotechnol. 4 (2008) 250–254. [5] A. Demirbas, Prog. Energy Combust. Sci. 31 (2005) 466–487. [6] V. Hofman, North Dakota State Univ. AE-1240 (2003) 4. [7] X. Meng, J. Yang, X. Xu, L. Zhang, Q. Nie, M. Xian, Renewable Energy 34 (2009) 1–5. [8] E.G. Bligh, W.J. Dyer, Can. J. Biochem. Physiol. 37 (1959) 911–917. [9] O. Bernard, Environ. Sci. Technol. 43 (2009) 6475–6481. [10] K.Y. Show, D.J. Lee, J.H. Tay, T.M. Lee, J.S. Chang, Bioresour. Technol. 184 (2015) 258–266. [11] R. Halim, R. Harun, M.K. Danquah, P.A. Webley, Appl. Energy 91 (2012) 116– 121. [12] D. Wang, Y. Li, X. Hu, W. Su, M. Zhong, Int. J. Mol. Sci. 16 (2015) 7707–7722. [13] H.M. Amaro, A.C. Guedes, F.X. Malcata, Appl. Energy 88 (2011) 3402–3410. [14] Y. Chisti, M. Moo-Young, Enzyme Microb. Technol. 8 (1986) 194–204. [15] L. Garcia-Gonzalez, A.H. Geeraerd, S. Spilimbergo, K. Elst, L. Van Ginneken, J. Debevere, J.F. Van Impe, F. Devlieghere, Int. J. Food Microbiol. 117 (2007) 1–28. [16] H.M. Lin, E.C. Chan, C. Chen, L.F. Chen, Biotechnol. Prog. 7 (1991) 201–204. [17] J. Zhang, T.A. Davis, M.A. Matthews, M.J. Drews, M. LaBerge, Y.H. An, J. Supercrit. Fluids 38 (2006) 354–372. [18] Z. Yu, B. Singh, S. Rizvi, J. Zollweg, J. Supercrit. Fluids 7 (1994) 51–59. [19] D.L. Pearce, Solubility of Trigl Ycerides in Supercritical Carbon Dioxide, University of Canterbury, 1990. [20] O. Guclu-Ustundag, F. Temelli, Ind. Eng. Chem. Res. 39 (2000) 4756–4766. [21] B.M.C. Soares, F.M.C. Gamarra, L.C. Paviani, L.A.G. Gonçalves, F.A. Cabral, J. Supercrit. Fluids 43 (2007) 25–31. [22] P. Maheshwari, Z.L. Nikolov, T.M. White, R. Hartel, J. Am. Oil Chem. Soc. 69 (1992) 1069–1076. [23] N.A.M. Eskin, B.E. McDONALD, Dept. Foods Nutr. 63 (1990) 138–146. [24] S.A. Shields-Menard, M. Amirsadeghi, B. Sukhbaatar, E. Revellame, R. Hernandez, J.R. Donaldson, W.T. French, J. Ind. Microbiol. Biotechnol. 42 (2015) 693–699. [25] Vegetable Oil Molecular Weight Calculator.
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JCT 16-247
Contents lists available at ScienceDirect
J. Chem. Thermodynamics journal homepage: www.elsevier.com/locate/jct
Measurement and correlation of solubility of carbon dioxide in triglycerides Md Shamim Howlader a, William Todd French a,⇑, Hossein Toghiani a, Ben Hartenbower a, Larry Pearson a, Janice DuBien c, Neeraj Rai a,b,⇑ a b c
Dave C. Swalm School of Chemical Engineering, Mississippi State University, Mississippi State, MS 39762, USA Center for Advanced Vehicular Systems, Mississippi State University, Mississippi State, MS 39762, USA Department of Mathematics and Statistics, Mississippi State University, Mississippi State, MS 39762, USA
a r t i c l e
i n f o
Article history: Received 31 March 2016 Received in revised form 25 September 2016 Accepted 26 September 2016 Available online 30 September 2016 Keywords: Solubility Henry’s law constant Biofuels Cell disruption Thermodynamic modeling
a b s t r a c t A new pressure drop solubility gas apparatus was developed to determine the solubility of carbon dioxide in canola oil, a triglyceride consisting primarily of oleic, linoleic, and alpha linoleic acid radicals. Solubility of CO2 in triglycerides was determined at different temperatures (283.2–303.2 K) and pressures (600–2450 kPa). It was found that the solubility of CO2 in triglycerides is higher than that of pure water because triglycerides lack strong hydrogen bond networks that exist in liquid water at the ambient conditions. The experimental solubility was correlated using Krichevsky–Kasarnovsky (KK), Mather-Jou (MJ), and Carvalho-Coutinho (CC) correlations. We find that KK and MJ equations can predict the solubility with higher accuracy. The enthalpy and entropy of absorption of CO2 were calculated using the van’t Hoff plot and were found to be 7.165 kJ.mol1, and 28.791 J.mol1.K1, respectively. Ó 2016 Elsevier Ltd.
1. Introduction In the recent years, there has been intense research focused on developing efficient and cost effective technologies for transportation biofuels for securing energy, reducing environmental concerns and lessening foreign oil dependency [1–3]. One of the key components in a renewable energy portfolio is biodiesel, which is biodegradable, less toxic and has energy density similar to conventional petroleum diesel [4–6]. Oleaginous microorganisms are considered as one of the possible alternative feedstocks for biodiesel as they can accumulate more than 20% lipid on a dry weight basis [7]. To use these lipids as biodiesel feedstock, they must be first extracted from the microorganisms. The traditional Bligh and Dyer [8] method used to extract the lipid from the oleaginous yeast in the laboratory setting would be uneconomical on a commercial scale because of high extraction cost. The conventional oil extraction method [9] for oleaginous algae requires lipid source to be nearly free of water with solid content more than 90%. Since biomass drying accounts for more than 75% total energy consumption, the process becomes economically unfeasible [10]. However, the ⇑ Corresponding authors at: Dave C. Swalm School of Chemical Engineering, Mississippi State University, Mississippi State, MS 39762, USA (N. Rai). E-mail addresses: [email protected] (W.T. French), [email protected]. edu (N. Rai). http://dx.doi.org/10.1016/j.jct.2016.09.035 0021-9614/Ó 2016 Elsevier Ltd.
lipid recovery can be increased if the cell is disrupted prior to extraction, potentially decreasing the need to dry to (P90%) solids [11], and thus reducing the energy requirement for the process [12]. Efficient and economical cell lysing results in enhanced lipid extraction due to the increased mass transfer rates [13]. Some of the commonly available methods for microbial cell disruption are mechanical, physical, chemical, and enzymatic cell disruptions [14]. Cell lysing using chemical solvent is a useful technique that is able to disrupt the microbial cell wall by reacting with lipophilic tail, but seems to be unfeasible due to the cost of solvent recovery. Different solvents were tested to evaluate the feasibility of cell inactivation, and it was found that carbon dioxide is superior to other chemicals such as nitrogen, argon, tetrafluoroethane, etc. [15]. Lin et al. reviewed the microbial cell disruption using supercritical and subcritical CO2 [16]. The lipid extraction cost using supercritical CO2 (pressure and temperature above 7380 kPa and 304.5 K) is significantly higher; thus, a process utilizing subcritical CO2 can potentially reduce the extraction cost. If the cell is disrupted using pressurized CO2 prior to lipid extraction, the extraction kinetics enhances due to the reduced mass transfer limitation since carbon dioxide can penetrate through the phospholipid membrane of the cell [15]. CO2 facilitates the disruption due to the high solubility of carbon dioxide in lipid. Furthermore, CO2 is cheap, nontoxic, nonflammable, and naturally abundant [17].
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A thorough understanding of solubility of carbon dioxide in triglycerides is essential for designing efficient cell disruption processes. Although there is a large number of studies [18–22] conducted on solubility of triglycerides in super critical carbon dioxide for oil extraction, there is a lack of data on low pressure CO2 solubility in triglycerides. This paper presents an experimental design based on pressure drop gas apparatus that not only allows for the measurement of gas solubility but also cell disruption by applying pressure and vacuum in a cyclic manner. The solubility of CO2 in canola oil, a triglyceride consisting primarily of oleic, linoleic, and alpha linoleic acid was measured at different temperatures and pressures. We selected canola oil because its fatty acid profile is very similar to the triglycerides produced by the microbes [7]. The experimental solubility was correlated with three thermodynamic models. Thermodynamic properties such as enthalpy of dissolution, entropy of dissolution and Gibbs energy of dissolution were determined using van’t Hoff’s plot. 2. Experimental 2.1. Materials Refined canola oil was purchased from Fisher Scientific, USA. The iodine value, saponification value, acid value, and peroxide value of canola oil were 111, 190.3, 0.01, and 1.67 as described by the supplier. For the characterization of canola oil, its fatty acid compositions were determined, and compared with the available literature [23]. For fatty acid methyl ester (FAME) analysis, the refined canola oil was transesterified, and analyzed using Agilent 6890N gas chromatograph equipped with a flame-ionization detector (GC-FID; Agilent Technologies Inc., Wilmington, Delaware, USA) with a Zebron ZBFFAP column of 30 m with 0.25 mm inner diameter and film thickness of 0.25 lm, respectively. Each sample was injected three times in the GC. Helium was used as the carrier gas with a rate of 20 mm3.s1 and the detector temperature was 533.2 K. Temperature was increased from 323 to 523 K with a rate of 16.67 102 K s1 [24]. The instrument was calibrated using a standard solution containing known concentration of C9–C24 FAMEs (Sigma Aldrich, USA) [24]. The results of fatty acid obtained from GC analysis are shown in Table 1 along with literature values. Most common fatty acids found in the canola oil were oleic acid (C18:1), linoleic acid (C18:2), linolenic acid (C18:3), and palmitic acid (C16:0) (Supplementary Material, Fig. S1). The fatty acid compositions of canola oil were found to be nearly identical to the available literature [23]. The fatty acid compositions of canola oil were also compared with OM, and found to be similar for oleaginous yeast [7]. The molecular weight of canola oil was determined from its fatty acid composition. The procedure for finding the molecular weight from the fatty acid profile can be found in the literature [25]. The obtained molecular weight
of canola oil is provided in Table 2, which was found to be the same as reported by Leung et al. and Singh et al. [26,27]. A little deviation from the previous work was found due to the variation in fatty acid profile of the present canola oil sample. The water content in the canola oil was determined using volumetric Karl-Fischer titration by the authors and reported as g water/g canola oil, which is provided in Table 2. Carbon dioxide was purchased from Nexair, Columbus, Mississippi. The deionized water from the laboratory was used to determine the solubility of CO2 in water. Table 2 provides the summary of chemicals used for this research along with their purity, source, and purification method. The purity of both CO2 and tetradecane was provided by the supplier and used for the experiment without further purification. 2.2. Apparatus and experimental procedure The experimental set-up is shown in Fig. 1. A dual reactor system was used for measuring the solubility of CO2 in liquids. Two pressure vessels of capacity of 650 and 450 mL, respectively, were purchased from Parr Instrument, USA. Pressure vessel 1 was used for measuring the amount of gas injected initially in the system, and pressure vessel 2 was used for measuring the solubility where a known amount of solvent was placed initially. Pressure vessel 2 was equipped with a stirrer to maximize the contact between the gas and the liquid; hence, equilibrium was obtained in a reasonable time. A type J thermocouple (T) with an uncertainty of ±0.1 K inserted into pressure vessel 2 was used to measure the temperature in the system. A Neslab RTE10 recirculating water bath chiller purchased from Thermo Scientific, USA was used to maintain a uniform temperature in both vessels. Ethylene glycol was the circulating fluid in the chiller that maintains the uniformity of temperature in both vessels. A single-phase high vacuum pump, purchased from Edwards, was used for degassing the solvent. A pressure transducer purchased from Ashcroft, was used to measure the pressure in the system. The accuracy of the pressure transducer is 0.05% with the minimum and maximum reading of 0 and 13,789 kPa, respectively. The resolution of the pressure transducer is 0.1 psi. Before each run, the degassing was conducted three times (each at least 20 min) for the complete removal of any impurities present in the solvent. For degassing, valves V3 and V4 were kept open and all other valves remain closed. After degassing, valves V3 and V4 were closed, and CO2 was injected into pressure vessel 1 by opening valves V2 and V5. When the pressure was stabilized in vessel 1, the initial gauge pressure from the pressure transducer, atmospheric pressure from the barometer, and the temperature from the thermometer were recorded and the amount of total gas charged into vessel 1 and the tubing was determined. After pressure stabilization in vessel 1, valve V6 was opened and the gas came into contact with the liquid present in vessel 2. A constant stirring was applied in vessel 2 throughout the experiment for gas-liquid mixing. After reaching the equilibrium (when there
Table 1 Comparison of fatty acid composition of refined canola oil with literature [23].a
a b c d
Fatty acidd
Mb/(g/mol)
Cx:yc
100 w (This Work)
100 w (Literature)
Palmitic Palmitoleic Stearic Oleic Linoleic Linolenic Arachidic
256.42 254.41 284.47 282.46 280.44 278.43 304.46
C16:0 C16:1 C18:0 C18:1 C18:2 C18:3 C20:4
4.77 ± 0.05 0.40 ± 0.01 1.73 ± 0.03 63.03 ± 0.40 21.45 ± 0.20 7.57 ± 0.07 0.80 ± 0.20
3.6 0.2 1.5 61.6 21.7 9.6 –
Experimental results for fatty acid composition is reported together with its standard uncertainty. Molar mass. Cx:y; x: number of carbons, y: number of double bonds. Behemic and Erucic acids are present in trace amounts.
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Table 2 Specifications and sources of chemicals used in this work. Chemicals Canola oil Tetradecaned Carbon dioxidef Water a b c d e f g
Supplier Fischer Scientific Sigma Aldrich NexAir Deionized in Laboratoryg
Ma/(g.mol1) 879.34 198.39 44.01 18.01
Mass fraction purity
102 g water/g sample (Karl Fischer) 0.062 ± 0.005
b
Analysis method c
GC-FID GC
e
0.999 0.999
Molar mass. Water content was measured in our laboratory. Gas chromatography-flame ionization detector. Refractive index of tetradecane is 1.429 (at T = 293.2 K) and the purity was provided by the supplier. Gas chromatography. Purity of CO2 was provided by the supplier. Resistivity of water was 18.2 Xm.cm.
Fig. 1. Experimental set up for solubility measurement.v1, v2, v3, v4, v5, v5, v6, v7 are the valves used in the experiment. P1 is the vacuum pressure gauge and P2 is the pressure transducer. The vacuum pump was used to degas the solvent. The cooling coil was coupled with the vessel 1 and 2, through which the circulating fluid flowed from the chiller to pressure vessel 1 and 2. The stirrer was used to enhance the mixing of gas and liquid. The thermocouple was used to measure the temperature in the system.
was no pressure change), the final gauge pressure, the atmospheric pressure, and the temperature were recorded again. The amount of gas in the headspace of vessel 2, in the tubing, and in vessel 1 (i.e. in the free space) was calculated. The amount of dissolved CO2 in triglycerides was estimated by subtracting the amount of gas in the free space from the total amount of gas charged initially. 2.3. Solubility measurement With known initial pressure (P1) and temperature (T1), molar volume of CO2 in pressure vessel 1 and tubing was calculated using the Span and Wagner [28] EoS provided in the NIST data base. Span and Wagner EoS can predict the PVT properties of CO2 in a region of triple point temperature to 1100 K at a pressure up to 800 MPa. Once the molar volume in the initial state is known, the total number of moles of CO2 injected initially in the system was determined. After releasing the gas into pressure vessel 2 with known equilibrium pressure and temperature, the number of moles of CO2 in the free space was calculated from the molar volume in the final state. By subtracting the number of moles of CO2 in the free space from the total number of moles of CO2, the amount of CO2 dissolved in the liquid was obtained. As the total moles of liquid placed into
pressure vessel 2 prior to experiment is known, the mole fraction solubility of CO2 in liquid can be calculated. The step-by-step procedure for finding the mole fraction solubility of carbon dioxide in liquid is described below. Step 1: Initial pressure P1, initial temperature T1 were known, molar volume of CO2 in the initial state, V m1 =ðcm3 =molÞ was estimated using Span and Wagner EoS. Step 2: Total number of moles of CO2, nT was calculated from V m1 using
nT =mol ¼ V 1 =V m1
ð1Þ
where V 1 =cm3 is the volume of vessel 1 and tubing determined manually. Step 3: Equilibrium pressure P2, equilibrium temperature T2 were known, molar volume of CO2 in the final state,V m2 =ðcm3 =molÞ was calculated by Span and Wagner EoS. Step 4: The amount of CO2 in the headspace of vessel 2, in the tubing and in vessel 1 (free space) n2 was measured from V m2 using
n2 =mol ¼ ðV 2 V solv ent Þ=V m2
ð2Þ
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where V 2 =cm3 is the volume of free space (vessel 1 volume + tubing volume + free space volume of vessel 2) determined manually and V solv ent =cm3 is the volume of the solvent. Step 5: The amount of CO2 dissolved in the liquid was estimated by
ndissolv ed =mol ¼ n2 nT :
ð3Þ
Step 6: The solubility (molality) of carbon dioxide in the liquid was calculated by
S=ðmol=kgÞ ¼ ndissolv ed =msolv ent
ð4Þ
where msolv ent =kg is the amount of solvent. Step 7: The mole fraction solubility of CO2 was calculated using the following relation
xCO2 ¼ ndissolv ed =ðndissolv ed þ nsolv ent Þ
ð5Þ
where nsolv ent =mol was the moles of solvent obtained using solvent molecular weight and mass. The Poynting correction factor [29] of water and triglycerides were found to be insignificant since the experimental pressure considered in this study were not very high, thus not considered in this work. The Poynting correction factor for water and triglycerides at different pressures and temperatures are provided in the Supplementary Material. 3. Results and discussion 3.1. Data validation To validate the experimental set-up, the solubility of CO2 in water was determined at three different temperatures of 288.2, 293.2 and 298.2 K, respectively at different pressures and compared with the data available in the literature [30–33]. The
experiments were conducted in triplicate to ensure the accuracy of the data obtained from this work. From Table 3, it is evident that there is a good agreement with the previous experimental data as the deviation was small, which indicates the suitability of our methodology for gas solubility measurement. The comparison of CO2 solubility in water is also depicted in Fig. 3, where the mole fraction solubility is plotted against the pressure at different temperatures of 288.2, 293.2 and 298.2 K. From the figure, the CO2water of the present data followed the similar trend as was reported in the literature [30–33]. Since carbon dioxide is reactive to water and it is possible for some of the CO2 to react with water to form carbonic acid during the pressurization, the apparatus was further validated using the solubility of CO2 in tetradecane, a long chain alkane. The experiments were conducted at different pressures from (980–2000 kPa) at 323.2 K. The mole fraction solubility (xCO2 ) of CO2 in tetradecane at these conditions is also presented in Table 3 and Fig. 2. Since tetradecane has very low vapor pressure (0.002 kPa at T = 298.2 K) [34], the total pressure and partial pressure is the same, which is reported in the table. The solubility of CO2 is compared the work of Kariznovi et al. [35], and it was found that at low pressure our apparatus can determine the mole fraction solubility of CO2 in tetradecane similar to Kariznovi et al., but at higher pressure the solubility obtained from this work deviates from the data of Kariznovi et al. The difference in solubility at high pressure might arise due to the way of determining the solubility by two different methods. For us, we followed a straightforward solubility determination using the pressure drop method, while Kariznovi et al. determined the solubility using a method different from us where they have kept the pressure and temperature constant throughout the experiment. Later, we have compared our triglycerides solubility data with available literature [36] and found that the mass fraction solubility of CO2 in canola oil and high oleic sunflower oil are nearly same, which gives the further evidence of suitability of our apparatus.
Table 3 Comparison of solubility of CO2 in water and tetradecane with literature [30–33,35].a Compounds
T/K
This work Ptotal/kPa
Water
Tetradecane
a b c d e f g
b
288.2 288.2b 288.2b 293.2b 288.2b 288.2b 298.2b 298.2b 298.2b 288.2b 288.2b 288.2b 293.2b 293.2b 293.2b 298.2b 323.2b 323.2b 323.2b 323.2b
371 ± 4 409 ± 6 469 ± 1 336 ± 2 493 ± 1 1108 ± 2 383 ± 1 506 ± 1 616 ± 5 697 ± 1 1056 ± 2 1251 ± 6 502 ± 1 749 ± 4 1002 ± 1 755 ± 6 986 ± 1 2061 ± 14 1304 ± 2 1565 ± 2
Literature P CO2 /kPa 369 ± 4 407 ± 6 467 ± 4 334 ± 2 491 ± 1 1106 ± 2 380 ± 1 503 ± 1 613 ± 5 695 ± 1 1054 ± 2 1249 ± 6 500 ± 1 747 ± 4 1000 ± 1 752 ± 6 986 ± 1 2061 ± 14 1304 ± 2 1565 ± 2
103 xCO2 3.00 ± 0.20 3.28 ± 0.20 3.76 ± 0.20 2.38 ± 0.04 3.99 ± 0.02 8.52 ± 0.04 2.49 ± 0.01 3.30 ± 0.01 3.61 ± 0.11 5.41 ± 0.04 7.99 ± 0.03 9.53 ± 0.20 3.49 ± 0.04 5.10 ± 0.02 6.75 ± 0.03 4.43 ± 0.08 95.7 ± 0.6 181.2 ± 6.3 120.1 ± 0.6 139.6 ± 0.9
Experimental results for pressure and solubility are reported together with their standard uncertainties. Standard uncertainty of temperature is u(T) = ±0.1 K. Dalmolin et al. [30]. Chapoy et al. [31]. Campos et al. [32]. Lucile at al [33]. Kariznovi et al. [35].
P/kPa
103 xCO2 c
Source
365 409 466 353 496 1103 380 501 610
2.97 3.25c 3.65c 2.42c 4.01d 8.67d 2.50e 3.32e 3.62f
Dalmolin et al.
980 2060
97g 196g
Kariznovi et al.
Chapoy et al. Campos et al. Lucile et al.
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M.S. Howlader et al. / J. Chem. Thermodynamics 104 (2017) 252–260 Table 4 Experimental solubility of CO2 in triglycerides at different temperatures and pressures.a T/K
Ptotal/kPa
xCO2
283.2b
607 ± 11 895 ± 2 1245 ± 10 1596 ± 4 2040 ± 6 612 ± 4 922 ± 4 1258 ± 3 1615 ± 2 2040 ± 8 2394 ± 19 622 ± 3 932 ± 1 1269 ± 3 1633 ± 2 2040 ± 5 2406 ± 10 632 ± 6 947 ± 3 1285 ± 3 1651 ± 1 2065 ± 7 2413 ± 8 652 ± 7 963 ± 3 1306 ± 1 1675 ± 2 2079 ± 4 2426 ± 7
0.303 ± 0.007 0.417 ± 0.001 0.495 ± 0.005 0.582 ± 0.002 0.654 ± 0.002 0.291 ± 0.006 0.392 ± 0.003 0.476 ± 0.002 0.554 ± 0.001 0.625 ± 0.003 0.674 ± 0.005 0.278 ± 0.003 0.375 ± 0.001 0.457 ± 0.002 0.530 ± 0.001 0.595 ± 0.001 0.639 ± 0.003 0.265 ± 0.005 0.359 ± 0.002 0.437 ± 0.002 0.506 ± 0.001 0.563 ± 0.002 0.604 ± 0.003 0.243 ± 0.007 0.341 ± 0.003 0.415 ± 0.001 0.480 ± 0.003 0.536 ± 0.001 0.572 ± 0.001
288.2b
293.2b Fig. 2. Depiction of mole fraction solubility of CO2 in water and tetradecane as a function of pressure. For CO2 in water: circles, stars, and squares represent the present work, Dalmolin et al. [30], and Chapoy et al. [31], respectively at 288.2 K; diamonds and filled diamond represent the present work and Dalmolin et al. [30], respectively at 293.2 K; triangles left, triangles right, and filled triangle left represent the present work, Campos et al. [32], and Lucile et al. [33], respectively at 298.2 K. For CO2 in tetradecane: triangles up and triangles down represent the present work and Kariznovi et al. [35], respectively at 323.2 K. Dashed dotted lines are guide to the eye for the data generated in the current work.
298.2b
303.2b
a Experimental results for pressure and solubility are reported together with their standard uncertainties. b Standard uncertainty of temperature is u(T) = ±0.1 K.
Fig. 3. Solubility of CO2 in triglycerides as function of pressure at different temperatures: Circles, squares, diamonds, triangles up, and triangles down represent solubility at 283.2, 288.2, 293.2, 298, and 303.2 K respectively.
polar solvents at comparable temperature and pressure [39–41]. Not surprising, as can be seen in Table 4 and Fig. 3, the solubility of CO2 in triglycerides was found to be also significantly higher than that of in the pure water. This is because both CO2 and triglycerides are nonpolar in nature and triglycerides lack strong hydrogen bond networks that exist in liquid water at the ambient conditions. Furthermore, it is anticipated that available free volume is significantly larger in triglycerides than in water and other solvents capable of hydrogen bonding. Scovazzo et al. [42] have shown that solubility parameters of solute and solvent can be used to correlate
3.2. Solubility of carbon dioxide in triglycerides Solubility of carbon dioxide in triglycerides was determined at five different temperatures of 283.2, 288.2, 293.2, 298.2, and 303.2 K, respectively as a function of pressure. The result is presented in Table 4, where the mole fraction solubility of CO2 is tabulated along with uncertainties at each run. The partial pressure of CO2 and total experimental pressure is the same due to negligible vapor pressure of vegetable oil [37], which is reported in Table 4. The experiment was conducted in triplicate to observe the variability and statistical consistency at each run. Fig. 3 shows the solubility change as a function of pressure from temperatures 283.2–303.15 K. From the figure, it is evident that solubility of carbon dioxide in triglycerides increases with increasing pressure and decreases with increasing temperature, which suggests that CO2trilgycerides interactions as primarily physical in nature [38]. The temperature dependence of CO2 solubility in triglycerides is similar to that in other polar solvents such as methanol, ethanol [39], cyclohexanol [40], and ethylene glycol [41]. However, mole fraction solubility is significantly higher in triglyceride than in these
Fig. 4. Plot of CO2 fugacity vs. mole fraction solubility in triglycerides at 303.2 K. Circles show the present work and the solid line represents the Raoult’s law.
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gas solubility. They find that solute solubility is higher if the solubility parameters of both solvent and solute are alike. The plot of fugacity of carbon dioxide against its mole fraction shown in Fig. 4 and shows negative deviation from the Raoult’s law. From Fig. 4, the deviation from the ideality is not too high and the CO2 solubility is governed by nonspecific interactions; hence, the regular solution theory (RST), developed by Scott and Hildebrand [43] for nonelectrolyte solutions, can be applied to predict the solubility of CO2 in triglycerides [44,45]. Scovazzo et al. [42] have used solubility parameter to correlated the solubility of CO2 in room temperature ionic liquids (RTILs) using RST. In an extensive review [46] of CO2 solubility in different ionic liquids where they have also used RST for correlating the gas solubility and reported that the solubility of CO2 is higher when the solubility parameter of CO2 and ionic liquids were identical. It is also reported by Arul et al. that the maximum solubility is occurred when the solute and solvent solubility parameters are the same [47]. Since it is known from the literature that the solubility parameter for CO2 (17.85 MPa1/2) and vegetable oils (triglycerides) (16.0 MPa1/2) are similar, which is different from pure water (47.81 MPa1/2) [48,49]; hence, the solubility of CO2 in triglycerides is higher than that of in the water. The solubility of CO2 in triglycerides was compared with the available literature [36,50] of similar solvents. The comparison of CO2 solubility in canola oil with the solubility of CO2 in high oleic sunflower oil (HOSO) is shown Fig. 5, where the mass fraction CO2 in two different solvents is plotted as a function of pressure at 298.2 K. From the figure it can be seen that this work’s solubility report follows the similar trend obtained from the work by Regueira et al. [36]. They have also reported the solubility of CO2 in rapeseed oil and castor oil. It can be seen from that the CO2 solubility in canola oil (this work) have nearly similar results for rapeseed oil and HOSO whereas the solubility of CO2 in castor oil is different from this work. From the fatty acid composition of rapeseed and HOSO, both have higher oleic acid content, which is same for canola oil of this work followed similar results. It was also found that the solubility of CO2 in pentaerythritol ester oils reported by Fandino et al. [50] is similar to our work. 3.3. Correlation of CO2 solubility using thermodynamic models The experimental solubility was correlated using three thermodynamic modeling. The reason for using these three correlations was that these models are relatively simple and they are previously applied for CO2 solubility in different solvents [51–53]. The first
Fig. 5. Comparison of mass fraction solubility of CO2 in canola oil with the solubility of CO2 in high oleic sunflower oil (HOSO) at 298.2 K. Circles and squares represent the present work and results reported by Regueira et al. [36], respectively.
approach was to use the Krichevsky–Kasarnovsky (KK) equation, commonly used to correlated CO2 solubility in ionic liquids [51,54–56]. The KK equation is defined as follows [57]: Ps
S lnfðf CO2 =kPaÞ=xCO2 g ¼ lnðkH;CO2 Þ þ V 1 CO2 ðP P Þ=RT
ð6Þ PS
where f CO2 =kPa the fugacity of CO2 in the gas phase, kH;CO2 =kPa the 3 Henry’s constant at solvent vapor pressure, V 1 CO2 =ðcm =molÞ the partial molar volume of CO2 at infinite dilution, xCO2 the mole fraction of CO2 in triglycerides, and Ps/kPa the vapor pressure of pure triglycerides. Since vegetable oil has negligible vapor pressure [37], after some modification, Eq. (6) becomes,
0
lnfðf CO2 =kPaÞ=xCO2 g ¼ lnðkH;CO2 Þ þ V 1 CO2 P=RT
ð7Þ
0
where kH;CO2 =kPa represents the Henry’s constant at zero pressure. The intercept and the slope of plotlnfðf CO2 =kPaÞ=xCO2 g vs. P/kPa gives 0
3 kH;CO2 =kPa and V 1 CO2 =ðcm =molÞ,respectively of CO2. The fugacity of CO2 was calculated from the following correlation,
f CO2 =kPa ¼ uCO2 P
ð8Þ
where, uCO2 the fugacity coefficient of pure CO2 and P/kPa the total pressure. The fugacity coefficient of pure CO2 was evaluated from PR EoS [58]. The plot of lnfðf CO2 =kPaÞ=xCO2 g vs. P/kPa at different temperatures is shown in Fig. 6, where the extrapolations of data were conducted using linear regression to obtain the intercept and slope. The second approach of correlating the solubility was an empirical equation developed by Mather and Jou [52] defined as,
lnðP=kPaÞ ¼ A þ BðlnSÞ
ð9Þ
where S/(mol CO2/mol triglycerides) the solubility, P/kPa the experimental pressure, and A and B are temperature dependent empirical constants correlated as follows,
A ¼ 10:9499 0:0454T þ 11:228 105 T 2 ;
ð10Þ
B ¼ 1:1395 6:941 103 T
ð11Þ
The MJ correlation was used to correlate the experimental solubility data as well as to compare the predicted solubility obtained from the KK correlation. MJ correlation was primarily used for the measurement of CO2 solubility in a mixture of methyldiethanolamine, N methyldiethanolamine and water [52].
Fig. 6. lnfðf CO2 =kPaÞ=xCO2 g as a function of pressure using KK correlation for CO2 solubility in triglycerides. The circles, squares, triangles up, triangles down, and diamonds represent experimental data at temperature of 283.2, 288.2, 293.2, 298.2 and 303.2 K, respectively. Solid lines represent the linear fitting.
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The third approach to correlate the solubility was to use a modeling proposed by Carvalho and Coutinho [53], which was mainly developed for correlating CO2 solubility in nonvolatile solvents at low to moderate pressure, temperature, and solubility. The Carvalho and Countinho (CC) correlation can be expressed as the following equation,
P=kPa ¼ mCO2 eðAB=TÞ
P=kPa ¼ mCO2 eð12:6741605:795=TÞ
ð13Þ
The deviation of the predicted solubility from the experimental solubility for different models were reported as the percentage average absolute deviation (AAD), which is defined according to the following equation, N 1X ABS N i¼1
xexp CO2
xcal CO2 xexp CO2
283.2a 288.2a 293.2a 298.2a 303.2a a
and N the number of data points. The comparison of different correlations with experimental solubility is shown in Fig. 7. The percentage AAD for each model is shown in Table 5. From Table 5 and Fig. 7, the percentage AAD for KK correlation varied from 0.63 to 1.16 whereas for MJ correlation, the percentage AAD varied from 0.17 to 1.04 and the percentage AAD for CC correlation varied from 1.73 to 3.57. Hence, KK and MJ correlation can predict the CO2 solubility with higher accuracy due to its smaller deviation from experiential data. From the solubility data (both Fig. 3 and Table 4), the solubility behavior is linear at low temperature when the pressure is low to moderate. Hence, CC correlation poorly predicted the solubility at low temperature. As the temperature rises, the CC correlation predicts the solubility with smaller deviation from the experimental data. Both the ln (kH/kPa) and partial molar volume (cm3/mol) at infinite dilution of CO2 obtained from the slope and intercept of lnfðf CO2 =kPaÞ=xCO2 g vs. P/kPa plot is shown in Table 6 along with the standard uncertainties at each
MJ correlation
CC correlation
1.125 1.162 0.871 0.745 0.628
0.925 0.849 0.372 0.174 1.044
3.492 3.571 2.674 1.734 1.781
Standard uncertainty of temperature is u(T) = ±0.1 K.
T/K 283.2 288.2a 293.2a 298.2a 303.2a a
lnðkH;CO2 =kPaÞ
3 V1 CO2 =ðcm =molÞ
7.408 ± 0.023 7.533 ± 0.014 7.544 ± 0.014 7.603 ± 0.011 7.708 ± 0.012
670 ± 40 573 ± 21 636 ± 21 645 ± 17 596 ± 18
0
a
ð14Þ
cal where xexp CO2 the experimental solubility, xCO2 the calculated solubility
KK correlation
Table 6 Henry’s constant and partial molar volume at infinite dilution of CO2 at different temperatures.
! 100
102 Average absolute deviation (AAD)
T/K
ð12Þ
where P/kPa the pressure, mCO2 =ðmol=kgÞ the solubility, T/K the temperature, A and B are correlation constants. After fitting with the experimental data, Eq. (13) was obtained from Eq. (12) defined as
AAD ¼
Table 5 Comparison of deviation among Krichevsky–Kasarnovsky [57], Mather and Jou [52], and Carvalho-Coutinho correlations from the experimental data.
Standard uncertainty of temperature is u(T) = ±0.1 K.
temperature. Following empirical correlation was obtained by fit0
ting the Henry’s constant that relates kH;CO2 =kPa and temperature, 0
kH;CO2 =kPa ¼ 23:5962 8:26 103 =T þ 1:0403 106 =T 2
ð15Þ
0
From the plot of kH;CO2 =kPa vs. T/K shown in Fig. 8, it was observed that the solubility of CO2 in triglycerides increases as the temperature decreases, which follows the typical gas solubility behavior [59]. Since it is evident from both Table 6 and Fig. 8 that the Henry’s constant increase with the increasing temperature, and the relation of Henry’s constant with partial pressure of the gas is defined according to Eq. (16), the mole fraction solubility decreases as the Henry’s constant increase at a fixed pressure [60]. 0
xCO2 ¼ P CO2 =kCO2
ð16Þ
The value of partial molar volume at infinite dilution for different temperatures is presented in Table 6 and the plot of partial molar volume of CO2 as a function of temperature is shown in
Fig. 7. Comparison of solubility data with different correlations at two temperatures: Open and solid circles represent experimental solubility at 293.2 and 303.2 K, respectively; Solid and long dashed lines represent KK correlations at 293.2 and 303.2 K, respectively; Dotted and dash-dotted lines represent MJ correlations at 293.2 and 303.2 K, respectively; dashed and dash-double dotted lines represent CC correlation at 293.2 and 303.2 K, respectively.
Fig. 8. Henry’s constant of CO2 in triglycerides as a function of temperature. The circles show the present work and solid line represents the fitting of Eq. (15), respectively.
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Fig. 9. Partial molar volume of CO2 at infinite dilution as a function of temperature. The circles represent the present work and the solid line represents the quadratic fitting, respectively.
3 Fig. 9. It is observed from the V 1 CO2 =ðcm =molÞ data for different temperatures that partial molar volume of CO2 in triglycerides decreases from 670 cm3.mol1 at 283.2 K to 596 cm3.mol1 at 303.2 K. It is interesting to note that Rahmati-Rostami et al. [55] observed a similar trend for partial molar volume of H2S in ionic liquids i.e. partial molar volume of H2S decreases with increasing temperature. The partial molar volume can be an indirect indicator of strength of the interaction between the solvent and solute molecules [61]. Although molecular interactions present in ionic liquid are very different when compared to triglycerides, it is possible that the solubility of CO2 is governed primarily by weaker dispersion (physical interactions) due to the quadruple nature of CO2 molecule.
3.4. Enthalpy and entropy of dissolution Thermodynamic properties of solution such as enthalpy of dissolution, entropy of dissolution, and Gibbs energy change for the dissolution can be estimated from the experimental solubility data using the van’t Hoff equation [62–66]. The enthalpy of dissolution can be correlated with the following equation according to Liu et al. [64]
DHS =ðkJ=molÞ ¼ R
dlnxCO2 dð1=T 1=T ref Þ
ð17Þ
where xCO2 the CO2 solubility, Tref/K the reference temperature (298.2 K). From Eq. (17), the DHs/(kJ/mol) can be obtained from the slope of lnxCO2 vs. (1/T 1/Tref)/K1. The plot of lnxCO2 vs. (1/T 1/Tref)/K1 at 2040 kPa is shown in Fig. 10, where the slope is 861.859. Hence, the enthalpy of dissolution for CO2 in triglycerides was 7.165 kJ.mol1. It is known that the enthalpy of dissolution is responsible for the molecular interaction between the solute and solvent, and entropy of dissolution is responsible for the degree of ordering of solute/solvent mixture [67,68]. The enthalpy of solution of CO2 in triglyceride was found to be significantly lower than that of found in water (19.57 kJ/mol) [69]. Although CO2 can preferentially bind to the polar groups in triglycerides, interaction is not as strong as between CO2 and water molecules. The lower value of enthalpy also suggests that lower energy is required to overcome the cohesive force between the solute and the solvent, which also indicates a weak temperature dependence of solubility [70,71]. The Gibbs energy (DGs) of the dissolution can be obtained using the following equation according to Krug et al. [72]
259
Fig. 10. Mole fraction solubility (lnxCO2 ) as a function of inverse temperature (1/T 1/Tref) for carbon dioxide in triglycerides; the solid line represents the linear fitting.
DGS =ðkJ=molÞ ¼ RT ref intercept ¼ DHS T ref DSS
ð18Þ
The intercept of Fig. 10 is 0.5726 and the Gibbs energy for the dissolution was 1.419 kJ.mol1. The entropy of dissolution can be obtained as Eq. (19) from Eq. (18). 1
DSs =ðJ:mol K 1 Þ ¼
DHS DGS T ref
ð19Þ
The dissolution of entropy for carbon dioxide in triglycerides was 28.79 J.mol1.K1. The negative value of entropy dissolution indicates higher degree of CO2 solvation in triglycerides. As a result the solubility of CO2 in triglycerides increases with decreasing temperature. It also indicates reduced translational freedom of carbon dioxide molecule in solution as compared to the gas phase. 4. Conclusions A new pressure drop gas apparatus was developed to measure the solubility of gases in liquids. The apparatus was validated using both solubility of carbon dioxide in water as well as CO2 solubility in tetradecane. The solubility of carbon dioxide in triglycerides was measured at different temperatures and pressures, and it was found that solubility of CO2 in triglycerides is significantly higher than that of pure water. The solubility was correlated using Krichevsky–Kasarnovsky (KK), Mather-Jou (MJ), and CarvalhoCoutinho (CC) correlations. It was found the MJ predicted the CO2 solubility with highest accuracy where the percentage average absolute deviation varied from 0.17 to 1.04 at different temperatures. The solubility data was used to determine Henry’s constant and partial molar volume of CO2 at infinite dilution at different temperatures, and it was found that Henry’s constant followed a increasing trend with increasing temperature showing that the solubility of CO2 decreases as the temperatures increases. From the van’t Hoff equation, the thermodynamic properties were estimated and it was found that the solubility is a weak function of temperature. Acknowledgements Md Howlader is thankful to the Dave C. Swalm School of Chemical Engineering, Mississippi State University for the financial support. He is grateful to Mrs. Sara Shields-Menard for helping in GC analysis, Mr. Peter Alzobaidi for his help setting up the experiment,
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JCT 16-247