Liquid-liquid equilibria of quaternary system with two partially miscible solvent pairs: water + methanol + 1,1-dimethylethyl methyl ether + benzene

Chen Yao, Cao Chenyu, Fu Min, Chen Enping, Zhang Yansong
(Department of Chemistry, Jinan University, Guangzhou, 510632)

Abstract The experimental liquid-liquid equilibria data of quaternary mixtures of (water + methanol + 1,1-dimethylethyl methyl ether + benzene) were measured at 298.15 K and ambient pressure. The extended UNIQUAC model including binary and multibody interaction parameters is used to correlate the quaternary experimental results. The calculated results are further compared with those correlated by modified UNIQUAC model.

INTRODUCTION
1,1-Dimethylethyl methyl ether(MTBE), 1,1-dimethylpropyl methyl ether(TAME), and diisopropyl ether(DIPE) are commonly added into gasoline to improve the octane rating and reduce the air-pollution. In the recent years, studies of phase equilibria of multicomponent systems consisting of oxygenated compounds, such as MTBE, TAME and DIPE, have gained interest as can be seen in literatures ^[1-5]. The thermodynamic behavior of these components in liquid mixtures is also of interest not only in its application for reformulated gasoline but also in extraction or separation operations with other components.
In this work, we report experimental liquid-liquid equilibrium(LLE) data for quaternary mixtures of (water + methanol + MTBE + benzene), and relevant ternary mixtures of (water + MTBE + benzene) at 25°C. The experimental results were correlated by means of the extended and modified UNIQUAC models ^[6,7] including both ternary and quaternary parameters coming from multicomponent intermolecular interactions, in addition to binary parameters. The binary vapour-liquid equilibria(VLE), mutual solubility and ternary LLE relevant to the quaternaries have been available from the literatures: (methanol + benzene) ^[8], (methanol + MTBE) ^[9], (methanol + water) ^[10], (MTBE + benzene) ^[11], (water + benzene) ^[12], (water + MTBE) ^[13], (water + methanol + benzene) ^[14], (water + methanol + MTBE) ^[15], and (water + MTBE + benzene) measured in this work.
EXPERIMENTS
2.1 Materials
MTBE was supplied by Tedia Company, Inc. with minimum mass fraction purity of 0.998. Methanol and benzene were provided from Guangzhou Chemical Reagent Factory, with mass fraction purities of 0.995 and 0.997, respectively. Water provided from Jinan University was distilled twice and had a mass fraction purity of 0.999. The g.c. analysis gave mass fractions purities of 0.997 for MTBE, 0.995 for benzene, and 0.998 for methanol. All chemicals were used directly in this work.
2.2 Apparatus and Procedures
Ternary and quaternary LLE measurements were carried out at the temperature (298.15 ± 0.01) K. The experimental apparatus was the same that reported in detail previously^[4]. The quaternary mixtures whose volume is about 80 cm³were loaded in the equilibrium glass cell placed in a thermostated water bath. The mixture was then stirred vigorously by magnetic stirrer for 3 h and allowed to settle 3 h, which was sufficient for separation into two phases. Dry nitrogen gas was used to prevent contamination with moisture in the headspace of the equilibrium cell. The liquid samples about 5 cm³, withdrawn from both upper and lower phases in the cell by using a milliliter syringe without changing the phase equilibria between two layers, were analyzed by a gas chromatograph (Shimadzu, GC-14C) equipped with a thermal conductivity detector. Each component of the ternary and quaternary mixtures was separated clearly using a stainless steel column (2 m long, 3 mm i.d.) packed with Porapak SQ. The temperatures of the injection and detector were set at 483.15 K. The initial temperature and final temperature of the oven were kept at 453.15 K. The hydrogen flow rates for both the separation and reference columns were set at 1.0 cm³· s^D1. The peak areas of the components, detected with a chromatopac (Zhejiang, N2000), were calibrated by gravimetrically weighted mixtures. The mass of each component of the mixture was determined from the calibration and converted to mole fraction. Three analyses at least for each sample were made to obtain a mean value. The accuracy of the experimental measurements was estimated to be within ±0.001.
The quaternary mixtures for (water + methanol + MTBE + benzene) were prepared by mixing binary mixtures of (MTBE + benzene) whose compositions are M1, M2, and M3 with water then methanol stepwise to cover the two-phase region shown in Figure 1. Figure 1 shows schematically a tetrahedron to depict three planes of the quaternary mixtures of (water + methanol + MTBE + benzene). The values of M1, M2, and M3 are approximate 0.25, 0.50, and 0.75, respectively, indicating the mole fraction of MTBE in (MTBE + benzene).
2.3 Experimental results
Tables 1 and 2 show experimental LLE data for the (water + MTBE + benzene) and (water + methanol + MTBE + benzene) mixtures.

Table 1 Equilibrium phase compositions in mole fraction (x) for the ternary of (water + MTBE + benzene) at 25ºC

organic phase			aqueous phase
x₁	x₂	1-x₁–x₂	x₁	x₂	1-x₁–x₂
0.0379	0.6955	0.2666	0.9944	0.0056	0.0000
0.0298	0.5712	0.3990	0.9955	0.0045	0.0000
0.0250	0.4834	0.4916	0.9959	0.0039	0.0002
0.0215	0.4228	0.5557	0.9965	0.0032	0.0003
0.0213	0.3675	0.6112	0.9966	0.0030	0.0004
0.0176	0.3333	0.6491	0.9971	0.0026	0.0003
0.0152	0.2919	0.6929	0.9975	0.0022	0.0003
0.0202	0.2359	0.7439	0.9979	0.0021	0.0000
0.0412	0.7819	0.1769	0.9936	0.0064	0.0000
0.0410	0.6248	0.3342	0.9953	0.0047	0.0000
0.0267	0.5198	0.4535	0.9963	0.0037	0.0000

Table 2 Equilibrium phase compositions in mole fraction x for the quaternary mixtures of (water + methanol + MTBE + benzene) at 25ºC

organic phase			aqueous phase
x₁	x₂	x₃	x₁		x₂	x₃
{ x₁water +x₂methanol + x₃MTBE+(1-x₁–x₂-x₃)benzene}
M1= 0.25
0.0213	0.0222	0.2932	0.9042		0.0924	0.0034
0.0271	0.0476	0.2686	0.8267		0.1694	0.0039
0.0400	0.0777	0.2490	0.7508		0.2434	0.0058
0.0418	0.0835	0.2024	0.7105		0.2808	0.0067
0.0463	0.1012	0.1939	0.6717		0.3173	0.0081
0.0471	0.1301	0.1881	0.6109		0.3735	0.0111
0.0500	0.1420	0.1554	0.5552		0.4210	0.0132
0.0456	0.1516	0.1453	0.5429		0.4326	0.0131
0.0457	0.1674	0.1331	0.4837		0.4770	0.0172
0.0503	0.1826	0.1225	0.4489		0.5037	0.0197
0.0297	0.0600	0.1992	0.7623		0.2330	0.0047
0.0408	0.1045	0.1739	0.6411		0.3453	0.0090
M2= 0.50
0.0600	0.1067	0.3906		0.7631	0.2275	0.0094
0.0959	0.1788	0.3570		0.6799	0.2996	0.0177
0.1117	0.2295	0.3147		0.6126	0.3561	0.0257
0.1249	0.2561	0.2946		0.5814	0.3793	0.0311
0.1179	0.2451	0.2904		0.5882	0.3764	0.0281
0.0561	0.0925	0.4655		0.8046	0.1864	0.0090
0.0321	0.0184	0.4929		0.9388	0.0563	0.0049
0.0464	0.0590	0.4535		0.8620	0.1315	0.0065
0.0884	0.1548	0.3633		0.6997	0.2831	0.0152
0.1005	0.2001	0.3270		0.6399	0.3334	0.0219
M3= 0.75
0.0768	0.0516	0.6489		0.8898	0.1017	0.0085
0.0982	0.1013	0.5893		0.8232	0.1655	0.0113
0.1424	0.1781	0.4972		0.7360	0.2439	0.0201
0.1605	0.2131	0.4549		0.7074	0.2680	0.0231
0.1820	0.2488	0.4090		0.6699	0.2949	0.0323
0.2387	0.3046	0.3210		0.5996	0.3421	0.0507
0.2126	0.2884	0.3436		0.6056	0.3396	0.0473
0.2126	0.2995	0.3254		0.5975	0.3449	0.0485
0.0730	0.0421	0.6569		0.9036	0.0887	0.0077
0.0931	0.0866	0.6051		0.8384	0.1515	0.0101
0.1129	0.1434	0.5468		0.7798	0.2053	0.0149
0.1909	0.2586	0.3911		0.6487	0.3101	0.0372

CALCULATION PROCEDURE AND RESULTS
3.1 Calculation procedure
The extended UNIQUAC ^[6] and modified UNIQUAC ^[7] models including binary and multibody interaction parameters were used to correlate the experimental LLE data.
The binary parameter defined by the binary energy parameter a_ji is expressed as
(1)
The binary energy parameters for the miscible mixtures were obtained from the VLE data reduction using the following thermodynamic equations ^[16]:
(2)
(3)
where P, x, y, and g are the total pressure, the liquid-phase mole fraction, the vapor-phase mole fraction, and the activity coefficient, respectively. The pure component vapor pressure, , was calculated by using the Antoine equation with coefficients taken from the literatures ^[17,18]. The liquid molar volume, , was obtained by a modified Rackett equation ^[19]. The fugacity coefficient, F, was calculated by the eqn.(3). The pure and cross second virial coefficients, B, were estimated by the method of Hayden and O’Connell ^[20]. The binary energy parameters for the partially miscible mixtures were obtained by solving the following thermodynamic equations simultaneously.
(4)
and ( I, II = two liquid phases ) (5)
Ternary parameters t₂₃₁, t₃₁₂, and t₁₂₃ were obtained by fitting the two models to the ternary LLE data and then the quaternary parameters t₂₃₄₁, t₁₃₄₂, t₁₂₄₃and t₁₂₃₄ were determined from the quaternary experimental LLE data using a simplex method ^[21] by minimizing the objective function:
F= (6)
where min denotes minimum values, i = 1 to 3 for ternary mixtures or i = 1 to 4 for quaternary mixtures, j = 1, 2 (phases), k = 1, 2, …，M (number of tie lines), M = 2ni, and x is the liquid-phase mole fraction.
3.2 Calculation results
Table 3 shows the molecular-structural volume and area parameters, r and q, for MTBE taken from the reference ^[18], while the others are taken from Prausnitz et al. ^[16], together with the interaction correction factor q‘, for which the value for self-associating components was taken from the literature ^[6,7], while that for nonassociating components was set to q‘ = q^0.20 in the extended UNIQUAC model and q‘ = q^0.75 in the modified UNIQUAC model. Table 4 presents the constituent binary energy parameters of the modified and extended UNIQUAC models. Table 5 shows the ternary parameters obtained in fitting the modified and extended UNIQUAC models to the experimental ternary LLE systems, and root-mean-square deviation of the mole fraction of tie lines between the experimental and calculated results for the systems. Figure 2 compares the experimental and correlated LLE of the ternary mixtures making up the quaternary mixtures of (water + methanol + MTBE + benzene) at 25ºC. The quaternary system exhibits type 2 quaternary LLE behavior, which is composed of two ternary LLE for the (water + methanol + MTBE) and (water + methanol + benzene) are classified as type 1, and one ternary LLE for the (water + MTBE + benzene) as type 2 are illustrated in Figure 2. Table 6 summarizes the correlated results for the quaternary mixtures obtained in fitting the extended and modified UNIQUAC models with binary, ternary, and quaternary parameters to the experimental quaternary LLE data, together with the predicted results by these models with only binary parameters listed in Table 4. It seems that the extended UNIQUAC model correlated the quaternary LLEs more successfully than the modified UNIQUAC model, and both the models can give a much more accurate representation for the quaternary LLEs by including the ternary and quaternary parameters in addition to the binary ones.

Table 3 Structural parameters for pure components

Component	r	q	q‘^a	q‘^b
water	0.92	1.40	1.28	0.96
methanol	1.43	1.43	1.48	1.00
benzene	3.19	2.40	q 0.75	q^0.20
MTBE	4.07	3.63	q 0.75	q^0.20

aModified UNIQUAC model.
^bExtended UNIQUAC model.

Table 4 The results of fitting both models to the binary phase equilibria data and root-mean-square deviations s_P, s_T, s_x and s_y for binary mixtures

Mixture	T/K	Model	a₁₂/K	a₂₁/K	sP/mmHg	sT/K	10³s_x	10³s_y
methanol + benzene	298.15	I II	22.70 7.61	1026.75 958.54	1.0 1.1	0.0 0.0	0.7 0.8	8.0 8.5
methanol + MTBE	313.15	I II	C107.03 C63.71	569.52 540.64	0.1 0.1	0.0 0.0	0.1 0.6	0.5 4.7
methanol + water	298.14	I II	C160.39 C71.81	158.59 70.15	0.1 0.1	0.0 0.0	0.6 0.6	4.0 4.1
MTBE + benzene	313.15	I II	C142.60 C108.86	199.40 179.99	1.9 1.9	0.1 0.1	0.8 0.8	5.0 5.0
water + benzene	298.15	I II	765.18 753.20	1663.40 1365.10
water + MTBE	298.15	I II	173.24 399.09	1196.10 1023.70

I, modified UNIQUAC model.
II, extended UNIQUAC model.

Table 5 The results of fitting both models to the ternary LLE data at 25ºC

Mixture	N^a	Ternary parameters		Deviations^d
Mixture	N^a	I^b	II^c	I^b	II^c
water + methanol + benzene	14	t₂₃₁= C0.2628 t₁₃₂= C0.0785 t₁₂₃= C0.1311	t₂₃₁= 0.0022 t₁₃₂= C0.6935 t₁₂₃= 0.0539	1.61^e 1.18^f	3.05 1.31
water + methanol + MTBE	6	t₂₃₁= C0.0007 t₁₃₂= C0.0427 t₁₂₃= 0.0330	t₂₃₁= 0.1497 t₁₃₂= C0.0411 t₁₂₃= C0.4815	0.64 0.59	0.83 0.37
water + MTBE + benzene	11	t₂₃₁= 0.0190 t₁₃₂= 0.1172 t₁₂₃= 0.1215	t₂₃₁= C0.0140 t₁₃₂= 1.5224 t₁₂₃= C0.0882	0.33 0.16	0.34 0.17

a N, no. of tie-lines. ^b I, modified UNIQUAC model. ^c II, extended UNIQUAC model.
^dRoot-mean-square deviations (mol%). ^ePredicted results using binary parameters alone.
^fCorrelated results using binary and ternary parameters.

Table 6 The results of fitting both models to the quaternary LLE data at 25ºC

Mixture	N^a	Quaternary parameters		Deviations^d
Mixture	N^a	I^b	II^c	I^b	II^c
water + methanol + MTBE + benzene	34	t₂₃₄₁=0.1185 t₁₃₄₂= C1.9860 t₁₂₄₃= 2.7185 t₁₂₃₄= 0.0350	t₂₃₄₁= C0.0542 t₁₃₄₂= C0.2141 t₁₂₄₃=C11.7981 t₁₂₃₄= 5.5108	1.89^e 0.95^f	3.44 1.04

Figure 1 Phase equilibria of (water + methanol + MTBE + benzene). M1, M2 and M3 denote quaternary section planes.

Figure 2 Experimental and calculated LLE of three ternary mixtures making up (water + methanol + MTBE + benzene) at 25ºC. ●- – -●, experimental tie line; ――, correlated by the extended UNIQUAC model with binary and ternary parameters taken from tables 4 and 5.

CONCLUSION
LLE data were measured for the ternary mixtures of (water + MTBE + benzene) and quaternary mixtures of (water + methanol + MTBE + benzene) at 25 ºC. The experimental ternary and quaternary LLE data were better correlated by using both the extended and modified UNIQUAC models including binary, ternary and quaternary parameters. The correlated results obtained by the models are better than the predicted results, and show a good agreement with the experimental quaternary LLE results.