Determination and Calculation of Phase Equilibrium for

Article pubs.acs.org/jced

Determination and Calculation of Phase Equilibrium for Tetrahydrofuran + Sodium Sulfate + Magnesium Sulfate + Water System at 5 °C Guo-En Li, Ji-Lin Cao,* Pan-Pan Chen, and Bin Zhao* Hebei Provincial Key Lab of Green Chemical Technology and High Efficient Energy Saving, College of Chemical Engineering, Hebei University of Technology, Tianjin 300130, China ABSTRACT: In order to develop a new process for concentrating and separating sodium sulfate (Na2SO4) and magnesium sulfate (MgSO4) of the bloedite based on tetrahydrofuran (THF) hydrate method, the equilibrium of the ternary systems THF−Na2SO4−H2O and THF−MgSO4−H2O and the quaternary system THF−Na2SO4−MgSO4−H2O were measured at 5 °C, and the phase digrams of these three systems were investigated. It showed that the mass percentage of Na2SO4 (MgSO4) in equilibrium liquid was higher than in feed and we could obtain Na2SO4·10H2O and MgSO4·7H2O in turn. It proved that THF hydrate could be used to the concentration and separation of Na2SO4 and MgSO4. The extended Pitzer model of the electrolyte−electrolyte−nonelectrolyte−water system was derived and applied into THF−Na2SO4−MgSO4−H2O system and its subsystems. The necessary thermodynamic parameters had been derived from a least-squares optimization program. The model calculation value was in good agreement with experimental solubility for ternary and quaternary mixtures, which indicated that the Pitzer model could be successfully used to predict the phase equilibrium of the electrolyte−electrolyte−nonelectrolyte−water systems containning THF hydrate.

1. INTRODUCTION Bloedite (Na2SO4·MgSO4·4H2O) is a double salt of Na2SO4 and MgSO4 which has huge reserves in nature. The resources only located in A-La-Shan league, Inner Mongolia of China, reach billions of tons.1 For mining and processing these resources, the solid−liquid equilibrium data and the phase diagram for the ternary system Na2SO4−MgSO4−H2O have been studied.2 The phase diagram analysis indicated that the proper method to separate Na2SO4 and MgSO4 was to produce Na2SO4 first by the cooling−crystallization process, and then MgSO4 was produced by evaporating and concentrating the solutions after Na2SO4 separation. Obviously, the traditional process was not economical in energy consumption. Based on the assumption of concentrating magnesium sulfate mother liquor by propane gas hydrate at low temperatures, the authors studied the equilibrium of the system H2O−Na2SO4−MgSO4− C3H8 under different conditions3 and the decomposition kinetics of C3H8 gas hydrate. It was found that the propane gas hydrate contained a great quantity of mother liquid and the reaction cycle was long, which limited the concentration effectiveness of MgSO4 solutions. Tetrahydrofuran (THF) is a kind of substance that could form hydrate more easily than propane. THF could form hydrate under mild conditions, and THF could be able to generate nuclei rapidly, lower the amount of the mother liquid entrainment, and improve the separation efficiency of hydrate method.4 In view of this, a study on the phase equilibrium of the system THF−Na2SO4−MgSO4−H2O at 5 °C was carried out, and the phase diagrams of this system and its subsystems were investigated in this paper. In addition, the solubilities of the above system and its subsystems were © 2013 American Chemical Society

calculated based on the Pitzer electrolyte solution theory model.

2. EXPERIMENTAL SECTION 2.1. Materials. The chemicals of Na2SO4, MgSO4·7H2O, and tetrahydrofuran (THF) supplied by Tianjin First Reagent Corporation were pure grade with a minimum purity of ω = 0.99. The water used to prepare solutions in this work was twice-distilled water (conductivity < 5 μS·cm−1). 2.2. Apparatus. The experimental apparatus of the phase equilibrium, as shown in Figure 1, mainly includes a transparent

Figure 1. Schematic diagram of experimental apparatus: 1, cryostat device; 2, motor; 3, stirrer; 4, transparent reactor; 5, liquid sampling. Received: January 24, 2013 Accepted: April 10, 2013 Published: April 18, 2013 1301

dx.doi.org/10.1021/je400081x | J. Chem. Eng. Data 2013, 58, 1301−1307

Journal of Chemical & Engineering Data

Article

Table 1. Phase Equilibrium Data of the THF−Na2SO4−H2O System at 5 °C

reactor, cryostat, temperature measurement instruments, and sampling system. The transparent batch reactor with a double jacket is connected to an external cooler (DFY-10/20) maintaining the temperature range from −15 °C to 100 °C with a precision of 0.05 °C. The pressure of the reactor can be raised up to 1.6 MPa. There is a clover stirrer in the transparent reactor. There are two temperature sensor ports, a feeding port at the upper portion of the reactor, a liquid sampling port, and two jacket cooling medium entrances at the bottom of the reactor. In order to guarantee the low temperature required for the reaction environment, dilute glycol solution is used as a circulating refrigerant. The temperature is monitored by two Pt100 probes, one in the reaction solution and the other one in the jacket (Prosensor instrument, precision of 0.05 °C). 2.3. Experimental Procedure. First, a solution with a certain mass percentage of Na2SO4, MgSO4, and THF was prepared and added into the clean reactor. The experimental temperature of the system was controlled and maintained by the circulating refrigerant of the cryostat. When the system temperature dropped to the experimental temperature, the stirrer was started. We sampled once every 1 h until the liquid composition was unchanged which indicated that the system reached equilibrium. After 30 h, the liquid−solid phase composition were no longer changed, then the composition of the system was the composition of phase equilibrium system at this temperature. When the system reached equilibrium, there were three phases which were in turn the THF hydrate, the equilibrium solution, and the precipitated salt from top to bottom of the reactor. In this work, since this reaction occurred at atmospheric pressure, the THF hydrate did not decompose rapidly at the atmospheric pressure. So the following methods could be used to sample: when the sample liquid valve was opened, the equilibrium solution and the precipitated salt could be respectively extracted until no liquid flew from the reactor. The THF hydrate phase was pulled out, and then the composition of Na2SO4, MgSO4 and THF were subject to chemical analysis. Changing the mass percentage of Na2SO4, MgSO4, and THF and repeating the steps above, the composition of the equilibrium could also be measured. 2.4. Analytical Methods. The magnesium ion concentration was determined by the titration of ethylenediaminetetraacetic acid (EDTA) standard solution. The sulfate ion concentration was determined by the weight method of barium sulfate. The sodium sulfate concentration was determined by the subtraction method from sulfate ion concentration to magnesium ion concentration. The analytical work of tetrahydrofuran was carried out using a gas chromatograph (SP-3420, from BFRL, China) equipped with a flame ionization detector (FID) and an analytical column (SE-54).

composition of feed (wt %)

composition of equilibrium liquid phase (wt %)

composition of hydrate phase (wt %)

Na2SO4

THF

Na2SO4

THF

Na2SO4

THF

equilibrium precipitated solid phase

0 1.24 1.50 1.95 2.83 6.09

11.05 10.10 9.56 10.57 10.11 7.43

0 1.59 2.71 3.81 4.44 4.48

8.44 8.34 5.61 5.23 3.61 3.55

0 0.71 1.18 1.68 2.25 3.53

14.43 10.56 10.21 11.01 11.98 8.71

S10a S10

a

S10: Na2SO4·10H2O.

Figure 2. Phase diagram of the THF−Na2SO4−H2O system at 5 °C.

Table 2. Phase Equilibrium Data of the THF−MgSO4−H2O System at 5 °C composition of feed (wt %)

3. RESULTS AND DISCUSSION 3.1. Phase Equilibrium of the Ternary System THF− Na2SO4−H2O at 5 °C. Data in Table 1 are the experimental results of the system THF−Na2SO4−H2O at 5 °C. Compared with the results in literature,3 it can be found that the time of THF hydrate formation is short and concentration efficiency is improved in this system. The induction time of the reaction in THF system is shorter than in the C3H8 system, which is due to the great solubility of THF in water. THF hydrate nuclei can be generated in any place of the solution. As THF hydrate is more sensitive to temperature and the kettle wall is the relatively lowest temperature location, THF hydrate starts generating from the kettle wall accordingly. When the mass percentage of



MgSO4

THF

MgSO4

THF

MgSO4

THF


0 1.16 1.50 3.32 4.07 5.39 7.64 10.69 13.09 15.43

11.05 9.93 9.56 9.06 8.34 8.49 10.15 9.06 6.73 8.73

0 2.06 2.71 4.82 5.82 7.59 11.91 15.89 20.97 16.62

8.44 7.88 5.61 5.46 6.63 7.12 3.44 5.46 3.06 4.52

0 1.01 1.18 2.01 2.51 3.32 5.57 8.04 10.25 15.25

14.43 10.53 10.21 9.82 10.37 10.85 10.51 10.93 9.81 9.75

M7a

a

M7: MgSO4·7H2O.

Na2SO4 in the feed is less than 2.83 %, in the equilibrium system, there are only two phases which are in turn the THF hydrate and the equilibrium solution from top to bottom of the reactor. When the mass percentage of Na2SO4 in the feed is 1302



Article

Figure 3. Phase diagram of the THF−MgSO4−H2O system at 5 °C.

Figure 4. Dry salt phase diagram of the THF−Na2SO4−MgSO4−H2O system at 5 °C.

more than 2.83 %, there are three phases which are in turn the THF hydrate, the equilibrium solution and the precipitated salt (Na2SO4·10H2O) from top to bottom of the reactor. Because Na2SO4·10H2O precipitates a lot at the bottom, both the mass percentage of Na2SO4 in the THF hydrate and the equilibrium solution are less than in the feed. In addition, the pure THF hydrate (THF·17H2O) should contain about 19 wt % of THF,5,6 but the experimental data value is 14.43 wt %. It is worth mentioning that the difference between experimental values and the literature values is caused by the presence of water entrainment during the THF hydrate formation process. Based on the data in Table 1, the phase diagram of the system THF−Na2SO4−H2O at 5 °C is plotted in Figure 2. There is an isothermal invariant point A which corresponds to the coexistence of solids Na2SO4·10H2O and THF·17H2O with the saturated solution as shown in Figure 2. Points E and D correspond to the composition of Na2SO4·10H2O and THF·17H2O. Points B and C correspond to the solubilities of Na2SO4 and THF in water solution. There are three crystallization fields: field ABE corresponding to the salt Na2SO4·10H2O with saturated solution; field ACD correspond-

ing to the coexistence of THF·17H2O with saturated solution; field ADE corresponding to Na2SO4·10H2O and THF·17H2O with saturated solution; field DEGF corresponding to the pure solid phases of Na2SO4·10H2O and THF·17H2O which we did not study. 3.2. Phase Equilibrium of the Ternary System THF− MgSO4−H2O at 5 °C. Data in Table 2 are the experimental results of the system THF−MgSO4−H2O at 5 °C. The experimental results show that, in this system, the solubility of MgSO4 is larger than Na2SO4. When the mass percentage of MgSO4 in feed is more than 15 %, the MgSO4·7H2O begins to precipitate. From the data in Table 2, it is found that, when the mass percentage of MgSO4 is lower, the relative concentration difference between the feed and the equilibrium liquid phase is larger, and the separation effect is better. Compared with the results in literature,3 the concentration efficiency in this system is more satisfactory. It indicates that MgSO4 can slightly inhibit the THF hydrate formation. When the MgSO4·7H2O is not precipitated, the mass percentage of MgSO4 in equilibrium solution phase is higher than in feed. It proves that the THF

Table 3. Phase Equilibrium Data of the THF−Na2SO4−MgSO4−H2O System at 5 °C composition of feed (wt %)



MgSO4

Na2SO4

THF

MgSO4

Na2SO4

THF

MgSO4

Na2SO4

THF


1.03 2.40 4.43 6.61 8.15 10.52 12.40 3.69 3.94 5.43 7.00 11.58 12.90 25.12 25.84

5.27 3.36 3.65 1.85 2.15 2.19 2.68 5.76 6.03 6.39 5.00 8.19 4.02 5.96 6.06

10.39 8.90 8.10 9.20 9.59 10.24 12.48 8.13 12.32 9.36 12.84 8.93 9.14 0.82 0

2.06 3.81 5.76 9.92 10.56 19.07 19.40 7.24 6.34 8.68 10.40 16.70 19.65 20.00 20.00

4.12 4.47 5.24 4.28 3.50 6.09 3.66 4.07 4.17 4.58 4.46 4.14 4.19 4.43 4.63

4.79 6.33 6.47 7.19 3.20 6.54 1.18 3.72 5.61 2.63 2.43 2.02 2.17 1.07 0

0.99 1.62 3.06 4.37 5.81 9.21 8.40 3.36 3.13 5.60 5.50 9.28 9.42 0 0

3.00 1.88 1.98 1.46 1.52 2.38 1.85 2.19 2.58 3.26 3.57 3.29 3.74 0 0

14.76 10.55 9.57 10.48 10.51 11.80 13.25 13.55 12.96 9.63 12.97 9.80 15.05 0 0

M7 S10 S10 S10 S10 S10 S10+M7 S10+M7 S10+M7

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Table 4. Particle Interaction Parameters of the System at 5 °C λTHF,THF

μTHF,THF,THF

θTHF,Na,SO4

ψ(0) THF,Na,SO4

ψ(1) THF,Na,SO4

0 aTHF·17H 2O

θTHF,Mg,SO4

ψ(0) THF,Mg,SO4

ψ(1) THF,Mg,SO4

−0.8784

0.1748

5.5190

−5.7798

−8.0503

−1.3253

−90.3676

−508.3945

−15.64182

THF·17H2O. Points J and I correspond to the solubilities of Na2SO4 and THF in water solution. There are three crystallization fields: field HLJ corresponding to the salt MgSO4·7H2O with saturated solution; field HIK corresponding to the coexistence of THF·17H2O with saturated solution; field HKL corresponding to the solids MgSO 4 ·7H 2 O and THF·17H2O with saturated solution; field LKMN corresponding to the pure solid phases of MgSO4·7H2O and THF·17H2O which we did not study. 3.3. Phase Equilibrium of the Quaternary System THF−Na2SO4−MgSO4−H2O at 5 °C. Data in Table 3 show the equilibrium composition in the system THF−Na2SO4− MgSO4−H2O at 5 °C. When the mass percentage of Na2SO4 in feed is less than 2.68 % and the mass percentage of MgSO4 is less than 12.40 %, the equilibrium solution is concentrated, and no salt precipitates. When the mass percentage of feed Na2SO4 is over 4 % and the mass percentage of feed MgSO4 is less than 12.90 %, Na2SO4·10H2O starts to precipitate and the mass percentage of MgSO4 increases in equilibrium solution. When the mass percentage of MgSO4 in feed is more than 12.90 %, MgSO4·7H2O begins to precipitate. Compared with data of C3H8 system in literature,3 the results of separating Na2SO4 and MgSO4 in this work are more efficient and satisfactory. In addition, the ratio of the mass percentage of Na2SO4 to the mass percentage of MgSO4 in the balanced liquid phase and the hydrate phase are different. Some of the reasons for this phenomenon can be briefly stated as follows. Due to THF hydrate formation consumes water of the surrounding environment, thereby the total dissolved salt concentration around the THF hydrate increases, that is, the salt-removing effect;7 The THF hydrate adsorption effects on different anions and cations are different. The salt-removing effect makes the dissolved salt concentration around the THF hydrate increased and promotes THF hydrate adsorption effect.8 Thus the above causes the change trend of the ion mass concentration in the two phases are different, and the ratios of the mass percentage of Na2SO4 to the mass percentage of MgSO4 in the balanced liquid phase and the hydrate phase are different.

Table 5. Calculated and Measured Values of the System THF−Na2SO4−H2Oa w(THF) wt % 8.34 5.61 5.23 3.61 3.55 a

m(THF) mol·kg

−1

H2O

m(Na2SO4)exp mol·kg

1.2618 0.8242 0.7653 0.5194 0.5104

−1

H2O

m(Na2SO4)cal mol·kg−1 H2O

AD/%

0.1246 0.1889 0.2694 0.3101 0.3673

0.24 9.23 4.81 4.38 7.12

0.1243 0.2081 0.2830 0.3243 0.3429

AD: Absolute deviation AD = |(mexp − mcal)/mexp|.

Table 6. Calculated and Measured Values of the System THF−MgSO4−H2O w(THF)

m(THF)

m(MgSO4)exp

m(MgSO4)cal

wt %

mol·kg−1 H2O

mol·kg−1 H2O

mol·kg−1 H2O

AD/%

0.88 5.61 5.46 6.63 7.12 3.44 5.46 3.06 4.52

1.2134 0.8488 0.8439 1.0502 1.1577 0.5636 0.9627 0.5586 0.7949

0.1900 0.2456 0.4463 0.5523 0.7393 1.1689 1.6785 2.2932 1.7509

0.1721 0.2600 0.4064 0.5079 0.6393 1.0496 1.5173 2.1001 1.5769

9.42 5.86 8.94 8.04 13.53 10.21 9.60 8.42 9.94

hydrate can be used to the concentration of MgSO4. When the mass percentage of MgSO4 in the feed is 15.43 %, the mass percentage of MgSO4 in equilibrium solution phase is less than that in feed as the precipitation of MgSO4·7H2O at the bottom of the reactor. Based on the data in Table 2, the phase diagram of the system THF−Na2SO4−H2O at 5 °C are plotted in Figure 3. As shown in Figure 3, there is an isothermal invariant point H which corresponds to the coexistence of solids MgSO4·7H2O and THF·17H2O with the saturated solution. Points L and K correspond to the composition of MgSO 4 ·7H 2 O and

Table 7. Calculated and Measured Values of the System THF−Na2SO4−MgSO4−H2O w(THF)

m(THF)

m(Na2SO4)exp

m(Na2SO4)cal

m(MgSO4)exp

m(MgSO4)cal

wt %

mol·kg−1 H2O

mol·kg−1 H2O

mol·kg−1 H2O

AD/%

mol·kg−1 H2O

mol·kg−1 H2O

AD/%

4.79 6.33 6.47 7.19 3.20 6.54 1.18 3.72 5.61 2.63 2.43 2.02 2.17 1.07

0.7461 1.0280 1.0872 1.2684 0.5363 1.3279 0.2160 0.6071 0.9275 0.4336 0.4074 0.3631 0.4067 0.1992

0.3258 0.3685 0.4470 0.3833 0.2978 0.6277 0.3401 0.3372 0.3500 0.3834 0.3796 0.3778 0.3987 0.4186

0.3119 0.4001 0.4854 0.3517 0.2743 0.6205 0.3300 0.3013 0.3664 0.4077 0.4192 0.4201 0.4478 0.4509

4.27 8.58 8.59 8.24 7.89 1.15 2.97 10.65 4.86 6.34 10.43 11.20 12.32 7.72

0.1922 0.3707 0.5798 1.0484 1.0603 2.3196 2.1274 0.7079 0.6279 0.8574 1.0446 1.7986 2.2064 2.2303

0.2047 0.3572 0.5560 1.1442 0.9827 1.9926 2.0006 0.6393 0.6392 0.9337 1.1441 1.5553 2.1649 2.1922

6.50 1.35 4.10 9.14 7.32 14.10 5.96 9.69 1.80 8.90 9.53 13.53 1.88 1.71

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Using νM, νX and νN, νX’ as the number of cations and anions of per molecule, respectively, the weight mole concentration of MX and NX are mMX and mNX then

The solubilities of the quaternary system THF−Na2SO4− MgSO4−H2O at 5 °C are given in Table 3. Figure 4 is the corresponding dry salt phase diagram which is plotted according to the each composition mass fractions per 100 g of salt. As shown in Figure 3, there is an isothermal invariant points O which corresponds to the coexistence of solids Na2SO4·10H2O, MgSO4·7H2O, and THF·17H2O with the saturated solution. There are three crystallization fields: field OPRQ corresponding to the salt MgSO4·7H2O with saturated solution; field OQST corresponding to the salt Na2SO4·10H2O with saturated solution; and field OPUT corresponding to THF·17H2O with saturated solution. Obviously, the compound Na2SO4·10H2O can be directly prepared in this system as the larger crystallization field of Na2SO4·10H2O in the figure. 3.4. Calculation of Phase Equilibrium. So far, there are two types of gas hydrate phase equilibrium models used frequently. First, based on the characteristics of the hydrate crystal structure and the approach of classical statistical thermodynamics, van der Waals and Platteeuw proposed the van der Waals−Platteeuw model,9,10 which was combined with Langmuir gas adsorption isotherm theory in 1959. Second, Chen and Guo put forward the Chen−Guo model11−14 on the basis of the gas hydrate formation mechanism, which was completely different from the van der Waals−Platteeuw model. In this paper, the phase equilibrium of this system is seen as the liquid−solid phase equilibrium of the THF hydrate with the electrolyte solution. The research system contains a total of H2O, Na2SO4, MgSO4, and THF four substances. Therefore, the system is equivalent to the MX−NX−A−H2O system. MX and NX represent electrolyte with the same anion, and A represents a neutral nonelectrolyte. Currently, the Pitzer electrolyte solution theory model is often used to calculate the solubility of the salt−water system.15−17 The extended Pitzer model is able to apply to both the electrolyte solution and electrolyte−nonelectrolyte solution. In this paper, the calculations of phase equilibrium for the THF−Na2SO4− MgSO4−H2O system are carried out based on the Pitzer model. We set up a solution containing nw kg of water, ni moles of i solute ions, nj moles of j solute ions, and nA moles of nonelectrolyte A; then eq 1 calculates the total excess Gibbs free energy GE for nw kg of water.18

⎧ mX = νXmMX + νX′mNX ⎪ ⎨ mM = νMmMX ⎪ ⎩ mN = νNmNX

From the partial derivative of eq 2 to nM and nX, respectively, and eq 2 substituting eq 1, and: (0) BMX = βMX +

′ = BMX

CMX =

I=

+

1 n w2

1 + 2 nw

i

j

k

1 nw

[1 − (1 + αI1/2)exp( −αI1/2)]

(3)

(1) 2βMX ⎤ ⎡ ⎛ 1 ⎞ −1 + ⎜1 + αI1/2 + α 2I ⎟exp( −αI1/2)⎥ 2 2 ⎢ ⎝ ⎦ 2 ⎠ αI ⎣

1 2

ϕ CMX

2 |Z MZ X|1/2

(5)

∑ mizi 2

(6)

i

ln γ±MX =

⎛ 2ν ⎞ 1 |Z MZ X|f ′(I ) + ⎜ M ⎟ ⎝ ν ⎠ 2 ⎛ 2νX ⎞ ⎟ ν ⎠

∑ ma[BMa + (∑ mz)CMa] + ⎜⎝ a

∑ mc[Bc X + (∑ mz)Cc X] c

+

⎡

∑ ∑ mcma⎢⎣|Z MZ X|B′ca + c

a

⎛ 2ν ⎞ + ⎜ X ⎟∑ maθXa(I ) + ⎝ ν ⎠ a

(νMψMca + νX ψca X) +

2νMZ M ⎤ Cca⎥ ⎦ ν

∑ ∑ mcma · 1 c

a

ν

1 ∑ ∑ mama ′ 2 a a′

⎤ ⎡⎛ νM ⎞ ⎢⎜⎝ ⎟⎠ψMaa ′ + |ZMZ X|θ′aa ′(I )⎥ ⎦ ⎣ ν mA 1 (νMθAM + νXθAX) + [2νM ∑ ψAMj(I ) + ν ν j

j

∑ ∑ ∑ μijk ninjnk +

α 2I

(1) ϕ β(0) MX, βMX, and CMX are the virial coefficients of electrolyte MX, and then,

∑ ∑ λij(I )ninj i

(1) 2βMX

(4)

⎛ GE ⎞ ⎛ GE ⎞ ⎛ GE ⎞ GE =⎜ +⎜ ⎟ ⎟ ⎟ +⎜ RT ⎝ RT ⎠i − i ⎝ RT ⎠ A − i ⎝ RT ⎠ A − A 1 = n w f (I ) + nw

(2)

∑ θAinA ni

+ 2νX ∑ ψAXj(I )]mA mj

i

∑ ∑ ψAij(I )nA ninj + 1 λAA nA2 + 12 μAAA nA3 nw nw i j

j

+

(1)

Here, i and j represent any ionic species except water, while nw is the number of kilograms of water, ni and nj are the numbers of moles, θ and λ are considered binary ionic−ionic interaction parameters, λAA and μAAA are considered binary and ternary molecule−molecule interaction parameters, respectively. (GE/ RT), (GE/RT)i−i, (GE/RT)i−A, and (GE/RT)A−A, represent the total excess Gibbs free energy, the ionic−ionic interaction contribution, the ionic−molecule interaction contribution, and the molecule−molecule interaction contribution, respectively.

2 ZM νM

2ν

∑ ∑ ψ ′Akj mA mjmk j

k

Z 2ν + X X ∑ ∑ ψ ′Akj mA mjmk 2ν j k

(7)

ψAij(I) dependends on ionic strength. On the contrary, λAA, μAAA, θAi, and μijk would be assumed to be independent of ionic strength. ψAij(I) can be given by ψAij(I ) = ψA(0) + F(I )ψA(1) ij ij 1305

(8)



Article

2 [1 − (1 + αI 0.5)exp(−αI 0.5)] α 2I

F (I ) =

(α = 2)

(1) ψ(1)THF,Na,SO4, a0THF·17H2O, θTHF,Mg,SO4, ψ(0) THF,Mg,SO4, and ψTHF,Mg,SO4 e correlated and regressed from the solubility data of ternary system. Although the model calculation does not consider ψTHF,Na,Mg, the calculating data are in good agreement with experimental data. The activity of water is related to the osmotic coefficient, ϕ, by the equation

(9)

From the partial derivative of eq 1 to ni and nA, respectively, we can calculate the activity coefficients of ions and nonelectrolyte in the electrolyte−electrolyte−nonelectrolyte− water system.16 Then the expression of the activity coefficient of γNa2SO4, γMgSO4, and γTHF can be obtained by the usual derivations: ln γNa SO 2

4

ln a H2O = −

2 = f ′(I ) + (2mSO4 + mNa ) 3 2 mMg [BMgSO4 + (∑ mz)CMgSO4] 3 ⎤ ⎡ 4 ′ 2SO4 + C Na 2SO4 ⎥ + mNa mSO4 ⎢2B Na ⎦ ⎣ 3 +

⎤ ⎡ 4 ′ 4 + CMgSO4 ⎥ + mMg mSO4 ⎢2BMgSO ⎦ ⎣ 3 2 1 + mMg mSO4 ψNa,Mg,SO + m THFθTHF,SO4 ,Na 4 3 3 4 (0) (1) ] + m THFmSO4 [ψTHF,Na,SO + F(I )ψTHF,Na,SO 4 4 3 2 (0) (1) ] + m THFmNa [ψTHF,Na,SO + F(I )ψTHF,Na,SO 4 4 3 2 (0) (1) ] + m THFmMg [ψTHF,Mg,SO + F(I )ψTHF,Mg,SO 4 4 3 (1) + 2m THFmSO4 mNa F ′(I )ψTHF,Na,SO

4

+

(10)

4

+ (∑ mz)CMgSO4] + mNa [B Na 2SO4 + (∑ mz)C Na 2SO4] + mMg ′ 4 + 2C MgSO4] + mNa mSO4 mSO4 [4BMgSO 1 mNa mSO4 ψNa,Mg,SO 4 2

(0) (1) ] + m THFmSO4 [ψTHF,Mg,SO + F(I )ψTHF,Mg,SO 4

+

(0) m THFmMg [ψTHF,Mg,SO 4

4

+

(1) ] F(I )ψTHF,Mg,SO 4

(0) (1) ] + m THFmNa [ψTHF,Na,SO + F(I )ψTHF,Na,SO 4

+

4

(1) 4m THFmMg mSO4 F ′(I )ψTHF,Mg,SO 4

(1) + 4m THFmNa mSO4 F ′(I )ψTHF,Na,SO

(11)

4

ln γTHF = mNa θTHF,Na,SO4 + mMg θC3H8,Mg,SO4 + 2mNa (0) (1) + F(I )ψTHF,Na,SO ] mSO4 [ψTHF,Na,SO 4

+

4

(0) 2mMg mSO4 [ψTHF,Mg,SO 4

+ 2m THFλ THF,THF +

■

(1) + F(I )ψTHF,Mg,SO ]

2 μTHF,THF,THF 3m THF

ϕ

(13)

4. CONCLUSION (1) The liquid and solid equilibrium composition of the ternary system THF−Na2SO4(MgSO4)−H2O and the quaternary system THF−Na2SO4−MgSO4−H2O at 5 °C are measured. The phase diagrams of these three systems were constructed, and the invariant points and crystalline zones have been analyzed. The results indicate that THF could form stable THF hydrate at 5 °C and atmospheric pressure. The mass percentage of Na2SO4(MgSO4) in equilibrium liquid is higher than in feed. It shows that, when the mass percentage of Na2SO4 in the feed is more than 2.83 % and the mass percentage of MgSO4 in the feed is more than 12.90 %, Na2SO4·10H2O and MgSO4·7H2O can be easily directly separated from bloedite one after the other at 5 °C. (2) The extended Pitzer model of electrolyte−electrolyte− nonelectrolyte−water system is derived and applied into the THF−Na2SO4−MgSO4−H2O system. The applicability of the extended Pitzer model can be used to obtain a sufficiently precise description of the particle interaction parameters of ternary and quaternary solutions with the participation of Na2SO4·10H2O, MgSO4·7H2O, and THF·17H2O. The solubilities of the above quaternary system and its subsystems are calculated, and the calculated results are in good agreement with the experimental data.

ln γMgSO = 2f ′(I ) + (mSO4 + mMg )[BMgSO4

′ 2SO4 + 2C Na 2SO4] + [4B Na

55.51

where mi represents the concentration expressed as molality of the ions, ∑ mi represents summing all ions besides the nonelectrolyte, and 55.51 is the molar amount of 1000 g of water. According to the structure of THF hydrate, the molecular formula of THF hydrate is regarded as THF·17H2O. The values of the activity of THF·17H2O in the system have not been determined by any authors, so we calculate it as an unknown quantity with other interaction parameter in this paper. Using the experimental data in Tables 1 and 2, the Pitzer parameter,16 the interaction parameters, and the activity of THF·17H2O are calculated and given in Table 4. On the basis of the phase equilibrium principle, the activity of a same solid phase crystallized in the quaternary system or its subsystems is the same. Using the activity eq 9−12, the solubilities of quaternary system and its subsystems can be calculated from the interaction parameters in Table 4 and the virial coefficients of Na2SO4 and MgSO4.16 The calculated results are given in Tables 5 to 7 and in good agreement with the experimental data, and the absolute deviation is less than 10 %.

[B Na 2SO4 + (∑ mz)C Na 2SO4]

(1) 2m THFmSO4 mMg F ′(I )ψTHF,Mg,SO 4

∑i mi

4

(12)

AUTHOR INFORMATION

Corresponding Author

(1) ϕ where β(0) MX, βMX, and CMX are virial coefficient for electrolyte (0) MX, λ THF,THF , μ THF,THF,THF , θ THF,N a,SO 4 , ψ THF,Na,SO , 4

*E-mail: [email protected]; [email protected]. Phone: +86 22 26564731; +86 13702093697. 1306



Article

Funding

The financial support received from the National Natural Science Foundation of China (No. 21076057), Key Laboratory of Renewable Energy and Gas Hydrate of Chinese Academy of Sciences (No. 0907kl), and Program for Changjiang Scholars and Innovative Research Team in University (No. IRT1059) is gratefully acknowledged. Notes

The authors declare no competing financial interest.

■

REFERENCES

(1) Lv, F.; Lv, Y.; Yan, T. The utilization of glauber and bloedite composite mineral. J. Technol. Chem. Ind. Min. 1989, 18, 35−37. (2) Yu, J.; Chen, M. Study on the phase diagram of Na2SO4-MgSO4H2O system. J. Salt Chem. Ind. 1994, 4, 32−36. (3) Chen, P.-p.; Li, G.-e.; Guo, H.-f.; Cao, J.-l. Phase equilibrium study on the quaternary system H2O-Na2SO4-MgSO4-C3H8 at 0 °C and Pressure. Adv. Mater. Res. 2012, 553, 2690−2694. (4) Zhang, Q.; Chen, G.-J.; Huang, Q. Hydrate formation conditions of a hydrogen + methane gas mixture in tetrahydrofuran + water. J. Chem. Eng. Data 2005, 50 (1), 234−236. (5) Yamamuro, O.; Suga, H. Thermodynamic studies of clathrate hydrates. J. Therm. Anal. 1989, 35, 2025−2064. (6) Devarakonda, S.; Groysman, A.; Myerson, A. S. THF−water hydrate crystallization: an experimental investigation. J. Cryst. Growth 1999, 204, 525−538. (7) Liu, C.; Chen, Q.; Ye, Y. Salt-removing effect and affecting factors for forming methane hydrate in porous media. Acta Pet. Sin. 2006, 27 (5), 57−60. (8) Zhang, J. S.; Lo, C.; Somasundaran, P.; Lee, J. W. Competitive adsorption between SDS and carbonate on tetrahydrofuran hydrates. J. Colloid Interface Sci. 2010, 341, 286−288. (9) van der Waals, J. A.; Platteeuw, J C. Clathrate Solution. Adv. Chem. Phys. 1959, 2, 2−57. (10) Parrish, W. R.; Prausnitz, J. M. Dissociation Pressure of Gas Hydrate Formed by Gas Mixtures. Ind. Eng. Chem. Process Des. Dev. 1972, 11, 27−35. (11) Chen, G. J.; Guo, T. M. Thermodynamic Modeling of Hydrate Formation Based on New Concepts. Fluid Phase Equilib. 1996, 122, 43−65. (12) Ma, Q. L.; Chen, G. J.; Guo, T. M. Prediction of Structure-H Gas Hydrate Formation Conditions for Reservoir Fluids. Chin. J. Chem. Eng. 2005, 56 (9), 1599−1605. (13) Chen, G.; Guo, T. Thermodynamic study of the hydrate formation process. J. Univ. Pet. 1995, 1, 19−24. (14) Liu, H.; Cao, J.; Gao, C. Equilibrium studies on the system water + hydrogen peroxide + urea + carbon dioxide. J. Chem. Eng. Data 2010, 55 (12), 5715−5718. (15) Pitzer, K. S. Thermodynamics of Electrolytes. I. Theoretical Basis and General Equations. J. Phys. Chem. 1973, 77 (2), 268−277. (16) Pitzer, K. S.; Kim, J. J. Thermodynamics of electrolytes. IV. Activity and osmotic coefficients for mixed electrolytes. J. Am. Chem. Soc. 1974, 96 (18), 5701−5707. (17) Marshall, S. L.; May, P. M.; Hefter, G. T. Least-squares analysis of osmotic coefficient data at 25 .degree.C according to Pitzer’s equation 1.1:1 electrolytes. J. Chem. Eng. Data 1995, 40 (5), 1041− 1052. (18) Li, Y. G. Metallic Solvent Extraction Thermodynamics, 1st ed.; Tsinghua University: Beijing, 1988; Chapter 3.

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Determination and Calculation of Phase Equilibrium for

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