Excess molar enthalpies of the binary system carbon dioxide + butyl levulinate at 298.15 and 303.15 K and 5.0–7.0 MPa

Fluid Phase Equilibria 502 (2019) 112288

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Excess molar enthalpies of the binary system carbon dioxide þ butyl levulinate at 298.15 and 303.15 K and 5.0e7.0 MPa Hiroyuki Matsuda*, Takafumi Okamoto, Yuki Nishino, Kiyofumi Kurihara, Katsumi Tochigi, Kenji Ochi Department of Materials and Applied Chemistry, Nihon University, 1-8-14 Kanda Surugadai, Chiyoda-ku, Tokyo, 101-8308, Japan

a r t i c l e i n f o

a b s t r a c t

Article history: Received 5 July 2019 Received in revised form 17 August 2019 Accepted 20 August 2019 Available online 21 August 2019

The excess molar enthalpies (HE) of the binary system carbon dioxide (CO2) þ butyl levulinate (a solvent obtainable from biomass) were determined near the critical point of CO2, using a flow-type isothermal microcalorimeter. Values are reported for temperatures of 298.15 and 303.15 K and pressures in the range of 5.0e7.0 MPa. A maximum exothermic value of approximately 8.1 kJ mol1 was determined, similar to the significant exotherms observed in our previous work for other binary systems. The experimental HE data were well correlated with a composition-dependent equation and the Peng-Robinson equation of state in conjunction with the conventional mixing rule. © 2019 Elsevier B.V. All rights reserved.

Keywords: Excess molar enthalpy Carbon dioxide Biomass-based solvent

1. Introduction Biomass resources are receiving increasing attention as potential fuels or raw materials for chemical products, due to concerns regarding limited fossil fuel resources, global warming and rising crude oil prices. In particular, the sustainable synthesis of solvents is of interest because these compounds can be easily obtained from biomass. Among these solvents, the various esters of levulinic acid obtained from reactions with alcohols are important because the raw materials can be obtained from cellulose, which is the most abundant nonedible biomass resource [1], as well as from algal residues [2]. A number of useful chemicals can be synthesized from levulinic acid and its esters, such as fuel additives, polyacrylates, polycarbonates, bio-degradable herbicides and photo-synthesis promotors [1]. For these reasons, levulinic acid was selected as one of the top 12 building blocks obtainable from biomass resources in a report by the United States National Renewable Energy Laboratory [1]. Thus, these compounds have significant potential in the field of biomass refining. Levulinic acid esters have also been used to replace toxic organic solvents and volatile organic compounds (VOCs), because they are non-toxic and exhibit good lubrication properties, suitable flashpoints and acceptable low temperature flow characteristics [3,4]. As

* Corresponding author. E-mail address: [email protected] (H. Matsuda). https://doi.org/10.1016/j.fluid.2019.112288 0378-3812/© 2019 Elsevier B.V. All rights reserved.

such, these esters are widely used in many applications, including as additives for gasoline and diesel [5e8], in the fragrance, food and pharmaceutical industries [3,4], as plasticizers, and as solvents in the production of polymers, textiles and coatings [3,5,8]. Deng et al. demonstrated that these compounds could also act to physically absorb carbon dioxide (CO2) as a means of CO2 capture and sequestration [9]. It has also been reported that levulinic acid esters are better replacements for conventional organic solvents compared to other so-called green solvents, such as ionic liquids, fluorinated compounds and supercritical fluids [10], because the technologies required for their use are similar to those currently in place. That is, these esters could be used without any modification of present-day equipment or procedures, thus reducing costs [11]. However, at present, there is insufficient information available in the literature regarding the physical properties of these esters [3,4,12,13], which limits their applications. Accurate physical property data for both pure levulinic acid esters and their mixtures are very important during the design of processes involving these compounds. For these reasons, the present work determined the excess molar enthalpies (HE) of a binary system CO2 þ butyl levulinate. Our group has recently reported the HE values for binary systems composed of CO2 with dialkyl carbonates [14,15], ethers [16,17], and esters [18] near the critical point of CO2 (Tc ¼ 304.12 K and Pc ¼ 7.374 MPa [19]). Our experimental data indicated exothermic behavior with a maximum absolute HE value of approximately

2

H. Matsuda et al. / Fluid Phase Equilibria 502 (2019) 112288

9.0 kJ mol1. This exotherm is extremely high compared with the values typically observed when mixing liquids at low pressures. As reported in our previous papers, the large exotherm obtained by mixing CO2 with those solvents could be used in a heat supply system [16]. If this unusual behavior is also observed in the binary system CO2 þ butyl levulinate, it could be possible to develop a new environmentally-friendly heat supply system using the naturally occurring compound CO2 together with butyl levulinate obtained from biomass. Furthermore, the synthesis of esters from levulinic acid in supercritical CO2 as a greener reaction medium has been proposed by Badgujar et al. [20]. Mixtures of various bio-based solvents with supercritical CO2 also have potential applications [21e25] in chemical synthesis [22], supercritical fluid extraction [23] and particle formation [24,25]. Considering these applications, knowledge of the thermophysical properties of the binary system CO2 þ butyl levulinate will be essential to the design and development of new processes using supercritical CO2 and levulinic acid esters. In this work, we obtained HE values for the system CO2 þ butyl levulinate near the critical point of CO2 (i.e., at temperatures of 298.15 and 303.15 K and pressures of 5.0, 6.0 and 7.0 MPa), using a flow isothermal microcalorimeter. The experimental HE data were correlated by the modified Redlich-Kister (mRK) model proposed by Myers and Scott [26], and those calculated employing the PengRobinson (PR) equation of state (EOS) [27] coupled with the van der Waals one fluid mixing rule.

2. Experimental section 2.1. Materials and density The chemicals used in this work are summarized in Table 1. The CO2 was passed through a 0.5 mm inline filter (Nupro Company, Japan) before use and the purity of the butyl levulinate was ascertained by gas chromatography (GC-1700, Shimadzu Co. Ltd., Kyoto, Japan) with a flame ionization detector. The water content of butyl levulinate was determined using a Karl Fischer moisture meter (CA-200, Mitsubishi Chemical Co., Ltd., Tokyo, Japan). The density (r) of the ester at 298.15 K was measured using a precision digital oscillating U-tube densimeter (DMA 4500, Anton Paar GmbH, Graz, Austria) with a reproducibility of 102 kg m3. The experimental r at 298.15 K for butyl levulinate are listed in Table 1 together with the literature value [12]. During the experimental trials, flow rates originally measured in cm3 min1 at 283.15 K were converted to mole min1 and then to mole fractions using the r values for the pure components. The r values for CO2 at 283.15 K and 5.0, 6.0 and 7.0 MPa were calculated using the EOS for CO2 proposed by Span and Wagner [28,29], while those for butyl levulinate under the same conditions were obtained by interpolating data published by Guerrero et al. [12]. The estimated r values are provided in Table 2.

Table 2 Densities (r) of the pure components at 283.15 K

r (kg m3)

P (MPa)

5.00 6.00 7.00 a b

CO2a

Butyl levulinateb

868.63 881.78 893.11

986.45 987.06 987.67

Span and Wagner [28,29]. Guerrero et al. [12].

2.2. Apparatus and procedure A high-pressure, flow-type isothermal microcalorimeter (CSC 4400, Calorimetry Sciences Corporation, USA) was used to determine HE values. The apparatus consisted of sample and reference cells, a highly stable thermostatic water bath (7238, Hart Scientific, USA), two high-pressure syringe pumps (100DX, Teledyne ISCO, USA) to supply the liquids, a pressure adjustment device, a refrigerating/heating circulator (TRL 108HII, THOMAS KAGAKU Co. Ltd., Japan) for the syringe, a degassing unit and a computer for signal collection and data processing. Pressure of the system was monitored with a pressure transducer (PDCR 330, Druck, UK) which is connected to a digital indicator (DPI 145, Druck, UK). Further details regarding the experimental apparatus and procedure have been described in our previous papers [14e18,30]. The uncertainties in temperature and pressure are 0.01 K and 0.01 MPa, respectively. The uncertainty associated with our experimental HE data was estimated to be 3.0% and resulted primarily from the high sensitivity of HE to small changes in temperature and pressure. During the trials, the total flow rate varied from 0.05 to 0.20 cm3 min1 and the effect of the total flow rate on the measurement of HE was taken into consideration. The optimal total flow rate was 0.10 cm3 min1 in all cases. To acquire HE data, each pure component was loaded into an ISCO syringe after degassing. The temperatures of the syringes and their contents were kept constant (using the refrigerating/heating circulator) at 283.15 K, which is approximately 20 K below the critical temperature of CO2, to prevent variations in density resulting from slight changes in temperature and pressure. The uncertainty associated with the mole fractions of the experimental mixtures was 0.001. 3. Results and discussion 3.1. Experimental HE data The experimental HE data obtained for the binary system CO2 þ butyl levulinate at temperatures of 298.15 and 303.15 K and pressures of 5.00, 6.00 and 7.00 MPa over the entire composition range are summarized in Table 3. Plots of HE as functions of the liquid mole fraction of CO2 (x1) at 298.15 and 303.15 K are presented in Figs. 1 and 2, respectively. The data at all mole fractions,

Table 1 Chemicals used in this work. Component

CO2 Butyl levulinatea a b c d e

Source

Showa Denko Gas Products Co. Ltd. Wako Pure Chemical Industries Ltd.

Grade

First grade

Molecular sieve

13X

IUPAC name: 4-oxovaleric acid butyl ester. Volume fraction. Mass fraction. At P ¼ 101 kPa. Standard uncertainties are u(r) ¼ 0.01 kg m3, u(T) ¼ 0.01 K, and u(P) ¼ 1 kPa. Reference [12].

Purity

Water content (ppm)

b

0.9999 0.993c

29

r (298.15 K) (kg m3)d Experimental

Literaturee

969.79

969.88

H. Matsuda et al. / Fluid Phase Equilibria 502 (2019) 112288

3

Table 3 Experimental excess molar enthalpies (HE) for the system CO2 (1) þ butyl levulinate (2) at temperatures (T) 298.15 and 303.15 K.a x1 T ¼ 298.15 K, 0.301 0.400 0.500 0.600 0.700 T ¼ 298.15 K, 0.101 0.201 0.300 0.400 0.499 0.600 T ¼ 298.15 K, 0.099 0.200 0.300 0.401 0.500 T ¼ 303.15 K, 0.200 0.300 0.400 0.500 0.600 T ¼ 303.15 K, 0.101 0.300 0.400 0.499 0.600 0.700 T ¼ 303.15 K, 0.300 0.500 0.700 0.800

HE (kJ mol1) P ¼ 5.00 MPa 3.38 4.50 5.69 6.89 7.96 P ¼ 6.00 MPa 1.05 2.16 3.18 4.50 5.15 6.11 P ¼ 7.00 MPa 0.32 0.67 0.99 1.25 1.54 P ¼ 5.00 MPa 2.30 3.60 4.72 5.78 6.98 P ¼ 6.00 MPa 1.09 3.25 4.36 5.35 6.44 7.24 P ¼ 7.00 MPa 2.68 4.32 5.70 6.44

x1

HE (kJ mol1)

0.800b 0.900b 0.920b 0.950b 0.980b

8.07 3.96 3.29 1.95 0.79

0.700 0.800 0.900 0.920 0.950b 0.980b

6.98 7.72 8.26 8.18 5.72 2.16

0.600 0.700 0.800 0.900

1.72 1.86 1.86 1.62

0.700 0.800b 0.900b 0.920b 0.940b

7.94 6.09 3.07 2.41 1.50

0.800 0.900b 0.920b 0.950b 0.980b

8.04 5.10 3.95 2.52 0.98

0.900 0.920 0.950 0.980

6.72 6.73 6.43 5.94

a Standard uncertainties, u, are u(T) ¼ 0.01 K, u(P) ¼ 0.01 MPa and u(x1) ¼ 0.001. The combined expanded uncertainty, Uc, is Uc(HE) ¼ 3.0%. b Two-phase region.

Fig. 1. Experimental excess molar enthalpies for the system CO2 (1) þ butyl levulinate (2) at 298.15 K. Legend: Experimental data at C 5.00 MPa; : 6.00 MPa; - 7.00 MPa. Results obtained from d mRK model; — PR EOS; d$d, Eq. (16). Calculated solubility limits of CO2 in butyl levulinate at B 5.00 MPa; D 6.00 MPa.

Fig. 2. Experimental excess molar enthalpies for the system CO2 (1) þ butyl levulinate (2) at 303.15 K. Legend: Experimental data at C 5.00 MPa; : 6.00 MPa; - 7.00 MPa. Results obtained from d mRK model; — PR EOS; d$d, Eq. (16). Calculated solubility limits of CO2 in butyl levulinate at B 5.00 MPa; D 6.00 MPa.

temperatures and pressures show exothermic behavior. In particular, an extremely large exothermic behavior was observed in the CO2-rich region at 5.00 and 6.00 MPa and both 298.15 and 303.15 K, with large negative HE values. These characteristics agree with our previous experimental HE values obtained for the systems CO2 þ dialkyl carbonate, þ ester and þ ether [14e18]. The maximum absolute values, jHEjmax, were approximately 8.1 and 8.0 kJ mol1 at 298.15 and 303.15 K, respectively. At each temperature and pressure, the mole fraction of CO2 at which jHEjmax. appeared was shifted to the CO2-rich side with increasing pressure. In addition, at 298.15 K, the exotherm decreased sharply as the pressure increased from 6.00 to 7.00 MPa, as was also the case for our previous experimental HE data for the system CO2 þ ethyl acetate [18]. Interestingly, this trend was not observed at 303.15 K. The jHEjmax values obtained in this work were similar to those obtained in our prior studies using the CO2 þ dialkyl carbonate and þ ethyl acetate systems [14,15,18]. Similar trends of the HE data were also observed for the mixtures CO2 þ organic solvent by the group of Pando et al. [31e35]. The solvents studied by them were ethyl acetate [31], N-methyl-2-pyrrolidone [32], N,N-dimethylformamide [33], acetone [34], and dimethylsulfoxide [35]. At all temperatures and pressures (except for 7.00 MPa at both 298.15 and 303.15 K), HE varied linearly with composition in the CO2-rich region, which corresponded to a two-phase (vapor and liquid) region. In our previous papers, the large exothermic behavior of HE was discussed on the basis of the change-of-state contribution, i.e., the changes in the state and densities of the pure components and their mixtures [16e18]. Zahran et al. have also used this approach for the HE behavior of the system CO2 þ ethyl acetate [31]. Furthermore, Aida et al. have performed a molecular dynamics simulation for the CO2 þ ester mixtures, and found that the carbonyl atom in the ester attracts very strongly CO2 molecules [36]. This strong CO2 e ester interactions leads to the endothermic contribution to HE. Here we discuss the present experimental HE data using these two approaches. Densities of CO2 and butyl levulinate at the investigated temperatures and pressures calculated by the same methods with Table 2 are summarized in Table 4. CO2 was a liquid at 298.15 K and

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H. Matsuda et al. / Fluid Phase Equilibria 502 (2019) 112288

Table 4 Densities (r) and phases of the pure components at the temperatures and pressures studied in the HE measurements. T (K)

298.15

303.15

a b

r (kg m3)

P (MPa)

5.00 6.00 7.00 5.00 6.00 7.00

calculated using the equations:

aii ðTÞ ¼ ac;i

(3)

Phase

CO2a

Butyl levulinateb

CO2

Butyl levulinate

131.27 190.61 743.03 124.02 171.44 266.56

973.20 973.86 974.52 968.84 969.53 970.20

Vapor Vapor Liquid Vapor Vapor Vapor

Liquid Liquid Liquid Liquid Liquid Liquid

ac;i ¼

0:45724R2 T 2c;i

(4)

Pc;i sffiffiffiffiffiffiffi !#2 T 1 Tc;i

"

ai ðTÞ ¼ 1 þ mi

(5)

Span and Wagner [28,29]. Guerrero et al. [12].

mi ¼ 0:37464 þ 1:5422ui  0:26992u2i 7.00 MPa and a vapor at all other temperatures and pressures applied. In contrast, butyl levulinate (Tc ¼ 692 K and Pc ¼ 2.41 MPa [5]) was a liquid at all temperatures and pressures. When the CO2 vapor was mixed with the liquid butyl levulinate, the CO2 dissolved in butyl levulinate, and thus transitioned from a vapor to a component of a liquid mixture. As a consequence, the enthalpy of condensation of the CO2 from a vapor to a liquid contributed to the large exothermic effects observed in this work. At temperature 298.15 K, this change-of-state contribution to HE leads to the large exothermic behavior, because CO2 was a vapor before mixing with butyl levulinate at pressures 5.00 and 6.00 MPa. Also, the contribution due to the strong CO2 e butyl levulinate interactions may be limited when the change-of-state contribution occurs. These factors lead to above-mentioned extremely large exothermic behavior. In contrast, at pressure 7.00 MPa, CO2 was a liquid, and the resulting mixtures are also liquid. Besides, the molecular interaction contribution to HE may be expected to change only slightly with temperature and pressure in the intervals studied in this work [31]. Therefore, the change-of-state contribution is small, and the strong molecular CO2 e butyl levulinate interaction may result in the moderate behavior of jHEjmax. (about 1.9 kJ mol1) measured in this condition. At temperature 303.15 K, CO2 was a liquid at all pressures studied. Thus, the change-of-state contribution occurs. jHEjmax. at 7.00 MPa was about 6.7 kJ mol1, while that at 6.00 MPa was about 8.0 kJ mol1. This difference of jHEjmax. can be explained in terms of changes in the CO2 density [31]. It increases with an increase of the pressure from Table 4. Therefore, the mixing of CO2 with butyl levulinate at 7.00 MPa becomes less exothermic than that at 6.00 MPa.

(6)

and

bi ¼

0:07780RTc;i Pc;i

(7)

where Tc,i and Pc,i are the critical temperature and critical pressure for pure component i, respectively, and ui is the acentric factor. The van der Waals one fluid mixing rules were used to find the mixture energy parameter, a, and the size parameter, b, based on the equations:

aðTÞ ¼ 

NC X NC X

 0:5   xi xj aii ajj 1  kij

i¼1 j¼1

kij ¼ kji ; kii ¼ kjj ¼ 0

(8)



and

b¼

NC X

(9)

xi bi

i¼1

where kij is a binary interaction parameter. The pure component parameters Tc,i, Pc,i and ui [5,19,37] used to calculate the a and b values for the pure components CO2 and butyl levulinate are provided in Table 5. The acentric factor, ui, for butyl levulinate was estimated based on the Edmister method, using the Tc,i and Pc,i values reported by Nikitin et al. [5] and the normal boiling point given by Schuette and Cowley (510.97 K) [38]. The HE is thermodynamically given by Eqs. (10) e (12) from the P-v-T relationship of the mixture and pure components [39]:

3.2. Data reduction The experimental HE data in the one-phase region were fitted using a polynomial expression based on the composition and EOS. The mRK model was employed to derive the polynomial, written as: E

H ¼ x1 ð1  x1 Þ

NP1 X i¼0

ai ð2x1  1Þi 1  kð2x1  1Þ

RT aðTÞ  v  b vðv þ bÞ þ bðv  bÞ

NC X

(2)

where P is the pressure, R is the gas constant, T is the temperature, v is the molar volume, a is the energy parameter and b is the size parameter. These parameters for pure components i, aii and bi, were

xi H Ri

(10)

i¼1

# ðv "   vP H ¼ Pv  RT þ  P dv T vT v;xi R

(11)

∞

(1)

where ai and k are adjustable parameters, x1 is the liquid mole fraction of CO2 and NP is the number of adjustable parameters, ai. We also used the PR EOS for data reduction, written as:

P¼

HE ¼ HR 

Table 5 Critical temperature, Tc, critical pressure, Pc, and acentric factor, u, values for the pure components. Component

Tc (K)

Pc (MPa)

u

CO2 Butyl levulinate

304.12a 692b

7.374a 2.410b

0.225a 0.672c

a b c

Poling et al. [19]. Nikitin et al. [5]. Estimated by the Edmister method [37].

H. Matsuda et al. / Fluid Phase Equilibria 502 (2019) 112288

# ðvi "   vP HRi ¼ Pvi  RT þ  P dvi T vT vi

(12)

where HR is the residual molar enthalpy. By applying the PR EOS to Eqs. (10) e (12), the HE is expressed by Eqs. (13) e (15):

  vaðTÞ  3   aðTÞ 2v þ 1  pffiffiffi 2 b vT v;xi E  pffiffiffi H ¼ ln4 pffiffiffi  5 2 2b vþ 1þ 2 b T

 vaii ðTÞ  3  T  aii ðTÞ 2v þ 1  pffiffiffi NC 2 bi X vT i vi  pffiffiffi þ xi ln4 pffiffiffi  5 2 2bi vi þ 1 þ 2 bi i¼1 NC X

(13)

vaðTÞ vT

"



 ¼

xi vi

v;xi

NC X NC   1X x x 1  kij 2 i¼1 j¼1 i j

 sffiffiffiffiffiffiffiffiffiffiffiffi   sffiffiffiffiffiffiffiffiffiffiffiffi # ajj ðTÞ vajj ðTÞ vaii ðTÞ aii ðTÞ þ vT ajj ðTÞ aii ðTÞ vT vi vj

vaii ðTÞ vT

 vi

sffiffiffiffiffiffiffiffiffiffiffi ai ðTÞ ¼ ac;i mi Tc;i T

D1a (kJ mol1) D2b (%) D1a (kJ mol1) D2b (%)

!

k a0 (kJ mol1) a1 (kJ mol1) a2 (kJ mol1) D1a (kJ mol1) D2b (%)

i¼1



k a0 (kJ mol1) a1 (kJ mol1) a2 (kJ mol1) D1a (kJ mol1) D2b (%) A B



þP v 

Table 6 Determined parameters and deviations between the experimental HE and values calculated using Eqs. (1) and (16) for the system CO2 (1) þ butyl levulinate (2). Parameter

∞

(14)

A B

Da1 (kJ mol1) D2b (%)

(15)

Within the two-phase region, the linear expression for the mole fraction of CO2, x1, was used. This expression is:

5

D1a (kJ mol1) D2b (%) a

5.00 MPa

6.00 MPa

29815 K one-phase region 9.8917  101 9.3381  101 2.2821  101 2.0974  101 2.3309 1.8009 8.0672  101 0.02 0.06 0.3 1.8 29815 K two-phase region 4.0478  101 1.1922  102 4.0517  101 1.1946  102 0.04 0.00 1.5 0.0 298.15 K overall 0.03 0.05 0.9 1.5 30315 K one-phase region 1.0097 9.9322  101 2.3410  101 2.1602  104 1.3551 1.0582  103 1.9058 1.8770  103 0.04 0.03 1.0 0.6 30315 K two-phase region 3.1642  101 5.0864  101 3.1881  101 5.0907  101 0.11 0.04 5.0 1.1 303.15 K overall 0.07 0.03 2.6 0.8

H ¼ A þ Bx1

NDP X k¼1

HEexptl:  HEcalcd:

9.9066  101 1.7366  104 1.2031  103 1.5823  103 0.06 1.1

0.06 1.1

b

k

(16)

where A and B are adjustable parameters. The fitting parameters ai, and k in Eq. (1), k12 in Eq. (8) along with A and B in Eq. (16) were determined through regression by minimizing the objective function (Fobj), determined as:

Fobj ¼

0.01 0.8

k¼1

k¼1

E

9.0827  101 6.1006  101 9.2020  101 6.7996  101 0.01 0.8

NDP P

E ðH exptl:  HEcalcd: Þ =NDP k NDP P E D2 ¼ ð100=NDPÞ ðHexptl:  HEcalcd: Þ=HEexptl:

D1 ¼

7.00 MPa

2 k

(17)

where NDP is the number of experimental data points while H Eexptl: and H Ecalcd: are the experimental and calculated HE, respectively. The parameters employed in the mRK model and in Eq. (16) along with the average absolute and relative deviations of the experimental and calculated HE, D1 and D2, respectively, are provided in Table 6. The value of NP in Eq. (1) was set to 2 or 3 at each temperature and pressure when working with the HE data, based on the correlation accuracy associated with the mRK model. The parameter k12 in the PR EOS was determined at each temperature independent of the pressure, except for the combination of 298.15 K and 7.00 MPa, at which different behavior was observed compared to the other temperatures and pressures. The estimated k12 value and the deviations obtained using the PR EOS are also included in Table 7. The mRK model gave D2 less than 1.8% for each dataset in the one-phase region, while D2 in the PR EOS was less than 3.4%. Thus, both models show reasonable correlation of the results for both models at all temperatures and pressures in the one-phase region, although the mRK model gave better results. Figs. 3 and 4 shows the relative deviations between the experimental and calculated HE, D3 defined as ðH Eexptl:  H Ecalcd: Þ =H Eexptl:  100 ð%Þ, as a function of CO2 mole fraction at 298.15 and 303.15 K, respectively. In the mRK model, the

Table 7 Determined parameters and deviations between the experimental HE and values calculated using the PR EOS combined with the van der Waals one fluid mixing rule for the system CO2 (1) þ butyl levulinate (2). 5.00 MPa

D1a (kJ mol1) D2b (%) D1a (kJ mol1) D2b (%)

6.00 MPa

k12 ¼ 6.3611  102 298.15 K one-phase region 0.12 0.09 2.4 1.8 303.15 K one-phase region 0.09 0.07 1.9 1.3

7.00 MPa

0.18 3.4

 PNDP  E E k¼1 Hexptl:  Hcalcd: =NDP

a

D1 ¼

b

 . P E E E .D2 ¼ ð100=NDPÞ NDP Hexptl: k¼1 Hexptl:  Hcalcd:

k

k

value was almost within the uncertainty of the experimental HE, Uc(HE), although higher values of D3 than Uc(HE) were detected in some data. In contrast, the PR EOS gave the D3 values of over Uc(HE) at the conditions of mainly 298.15 K and 5.00 MPa, and 303.15 K and 7.00 MPa. The results of calculations using the mRK model, PR EOS and linear expression in the two-phase region are summarized graphically in Figs. 1 and 2. Finally, we determined the liquid mole fractions of CO2, xVL 1 , at the vapor-liquid equilibrium (VLE) of each mixture at temperatures and pressures corresponding to the two-phase region. The xVL 1 values were obtained by combining Eqs. (1) and (16), and the reE sults, along with the corresponding H , are summarized in Table 8 and plotted in Figs. 1 and 2. It would have been helpful to compare

6

H. Matsuda et al. / Fluid Phase Equilibria 502 (2019) 112288 Table 8 E Solubility limits (xVL 1 ) obtained from H data for the system CO2 (1) þ butyl levulinate (2).a P (MPa) 298.15 K 5.00 5.50 303.15 K 5.00 5.50

xVL 1

HE (kJ mol1) (calculated)

0.784 0.929

8.71 8.21

0.733 0.837

8.27 8.27

a Standard uncertainties, u, are u(T) ¼ 0.01 K, u(P) ¼ 0.01 MPa and u(x1) ¼ 0.001. The combined expanded uncertainty, Uc, is Uc(HE) ¼ 3.0%.

Fig. 3. Relative deviations between the experimental and calculated HE D3 vs. CO2 mole fraction for the system CO2 (1) þ butyl levulinate (2) at 298.15 K. Legend: mRK model at C 5.00 MPa; : 6.00 MPa; - 7.00 MPa. PR EOS at B 5.00 MPa; D 6.00 MPa. Eq. (16) at ◊ 5.00 MPa; *, 6.00 MPa.

and pressures from 5.0 to 7.0 MPa. The experimental HE data indicate exothermic behaviors for all compositions at all the temperatures and pressures studied. The maximum exotherm was determined to be approximately 8.1 kJ mol1 at 298.15 K and 5.0 MPa. At all temperatures and pressures except 7.0 MPa at both 298.15 and 303.15 K a two-phase region was observed in the CO2 rich region, within which HE varied linearly with composition. The experimental HE data were discussed in terms of the change-ofstate contribution of the pure components and their mixtures to HE and strong interactions between CO2 molecules and carbonyl atom in butyl levulinate. The experimental results were found to correlate well with values obtained using the mRK model based on a polynomial expression of the composition and using the PR EOS with a linear expression for the mole fraction of CO2 in the twophase region. The CO2 liquid composition at vapor-liquid equilibrium was also determined from the HE data. These experimental HE values demonstrate significant heat release from this system. The results of this work should be useful not only because they provide new thermophysical data for mixtures containing levulinic acid esters, but also because they may assist in designing new processes using supercritical CO2 combined with such esters.

Acknowledgements We thank Mr. Yusuke Hotta and Sodai Ebina of the Department of Materials and Applied Chemistry, Nihon University, for assistance with HE measurements. We thank Edanz Group (www. edanzediting.com/ac) for editing a draft of this manuscript.

List of symbols

Fig. 4. Relative deviations between the experimental and calculated HE D3 vs. CO2 mole fraction for the system CO2 (1) þ butyl levulinate (2) at 303.15 K. Legend: mRK model at C 5.00 MPa; : 6.00 MPa; - 7.00 MPa. PR EOS at B 5.00 MPa; D 6.00 MPa; , 7.00 MPa. Eq. (16) at ◊ 5.00 MPa; *, 6.00 MPa.

the xVL 1 values determined in this work with the literature VLE data for this system. However, to the best of our knowledge, solubility data for CO2 in butyl levulinate are only available for the temperature range of 283.15e323.15 K and pressures up to approximately 560 kPa [9], meaning that VLE data that correspond to the temperature and pressure ranges of the present HE data are unavailable. 4. Conclusions The HE values were obtained for the binary system CO2 þ butyl levulinate over a wide composition range at 298.15 and 303.15 K

a ai A b B Fobj HE k k12 mi NDP NP P R T v x

energy parameter in the PR EOS (Pa m6 mol2) parameter in Eq. (1) (kJ mol1) parameter in Eq. (15) (kJ mol1) size parameter in the PR EOS (m3 mol1) parameter in Eq. (15) (kJ mol1) objective function excess enthalpy (kJ mol1) parameter in Eq. (1) binary interaction parameter in the PR EOS parameter in the PR EOS number of data points per system number of ai parameters in Eq. (1) pressure gas constant (8.314 J mol1 K1) absolute temperature (K) liquid molar volume (m3 mol1) liquid phase mole fraction

H. Matsuda et al. / Fluid Phase Equilibria 502 (2019) 112288

Greek letters ai parameter in the PR EOS D1 average absolute deviation between experimental and calculated HE values (kJ mol1) D2 average absolute relative percent deviation between experimental and calculated HE values (%) D3 relative percent deviation between experimental and calculated HE values (%) u acentric factor r density (kg m3) Superscript L liquid phase R residual VL vapor-liquid equilibrium Subscripts 1, 2, i, j c calcd. exptl.

components 1, 2, i, and j critical calculated experimental

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