Prediction of Gas Hydrate Formation Conditions in Aqueous Solutions

High-Pressure Fluid Phase Behavior and Property Research Laboratory, ... it to the prediction of hydrate formation for systems containing both methano...
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Ind. Eng. Chem. Res. 1999, 38, 1700-1705

Prediction of Gas Hydrate Formation Conditions in Aqueous Solutions Containing Electrolytes and (Electrolytes + Methanol) Jian Liao, Dong-Hai Mei, Ji-Tao Yang,* and Tian-Min Guo High-Pressure Fluid Phase Behavior and Property Research Laboratory, University of Petroleum, Beijing 102200, People’s Republic of China

The prediction of gas hydrate formation conditions in solutions containing single electrolyte and mixed electrolytes and solutions containing both electrolytes and methanol has been performed using the modified Zuo-Gommesen-Guo hydrate model proposed by the authors. The results show that agreement between experimental and calculated values is satisfactory. In the ZGG hydrate model, ∆µH and ∆µW are calculated as follows:

Introduction In recent years, much experimental data and the corresponding methods for predicting gas hydrate formation conditions for systems containing methanol or electrolytes have been reported.1-15 Zuo et al.14 proposed a hydrate model (Zuo-Gommesen-Guo model, ZGG) for natural gas systems containing single electrolytes or polar inhibitors which combines the modified PatelTeja equation of state (MPT EOS)16 developed for systems containing electrolyte or polar components with the simplified multishell hydrate model proposed by Du and Guo.10 It was later extended to solutions containing mixed electrolytes by Tse and Bishnoi.17 Data for carbon dioxide hydrate formation conditions in aqueous solutions containing both electrolytes and methanol were reported by Dholabhai et al.18 Recently, Mei et al.19 measured the hydrate formation conditions of a synthetic natural gas in systems containing both electrolytes and methanol. Although some advances in the theoretical prediction of gas hydrate formation conditions for systems containing methanol or single electrolyte have been achieved, the hydrate formation predicting method for systems containing both methanol and electrolytes has been scarcely reported in the literature. The purpose of this paper is to modify the ZGG hydrate model and extend it to the prediction of hydrate formation for systems containing both methanol and electrolytes.

Modification of ZGG Hydrate Model In hydrate equilibrium calculations, the following condition must be satisfied

∆µH ) ∆µW

(1)

where ∆µH stands for the chemical potential difference of water between the occupied and the completely empty lattice, and ∆µW denotes the chemical potential difference of water between the aqueous phase and the empty lattice. * To whom correspondence should be addressed. E-mail: [email protected].

2

∑ νm ln(1 + ∑j CmjφjyjP)

(2)

Cmj(T) ) (Amj/T)exp(Bmj/T + Dmj/T2)

(3)

∆µH ) RT

m)1

where Amj, Bmj, and Dmj are constants specific to a gas component j in the m-type cavity, which are taken from Du and Guo.10

∆µW(T,P) ∆µ0W(T0,0) ) + RT RT

∆ν

∫0P RTW dP ∆h

∫TT RTW2 dT - ln aW 0

(4)

where ∆µW is sensitive to the activity of water (aW ) γWxW). The MPT EOS developed by Zuo and Guo16 is applied to calculate aw. The gas solubility and the change in gas solubility due to the presence of electrolyte solution have been included in the evaluation of aw by MPT model. To apply the ZGG model for predicting hydrate formation conditions in systems containing both methanol and electrolytes, the following modifications have been made by the authors: 1. The calculation of aw in MPT EOS is simplified by using the classical quadratic mixing rules instead of the sophisticated Kurihara mixing rules used in the ZGG model. 2. The electrolyte-water interaction parameters used in ZGG hydrate model are replaced by ion-water interaction parameters (kij), the fitted kij values are listed in Table 1. 3. The variation of methanol-water interaction parameter (kMeOH,W) with methanol concentration is established as follows:

kMeOH,W ) 4.02x2 - 1.969x + 0.1155

(5)

where x (x g 0.05) is the mass fraction of methanol in aqueous solution. 4. On the basis of the experimental data recently measured by Mei et al.,19 a new correlation of ion-

10.1021/ie9803523 CCC: $18.00 © 1999 American Chemical Society Published on Web 02/11/1999

Ind. Eng. Chem. Res., Vol. 38, No. 4, 1999 1701 Table 1. Fitted Ion-Water Interaction Parametersa system ionic species

Np

kij

AADP (%)

Na+

25

-0.1095

3.79

K+ Ca2+ Mg2+

6 7 20

0.0269 -0.1966 -0.2050

3.73 4.07 7.00

181 27

-0.1715 -0.3512

8.27 8.42

ClHCO3-

gas phase

aqueous phase (mass %)

temperature range (K)

data source (ref no.)

(CH4 + N2) (CH4 + N2) SNG SNG SNG (CH4 + N2) (CH4 + N2) SNG

NaCl (5%) NaCl (10%) NaCl (10%) KCl (10%) CaCl2 (10%) MgCl2 (5%) MgCl2 (10%) MgCl2 (5%)

271.2-284.5 272.7-281.6 267.1-279.8 269.1-279.8 266.7-279.7 271.3-285.2 270.3-285.2 269.0-279.6

NaHCO3 (5%) NaHCO3 (3%) NaHCO3 (5%)

274.3-284.3 269.8-285.8 271.0-285.4

20 20 19 19 19 20 20 21 19-22 21 20 20

CH4 (CH4 + N2) (CH4 + N2)

a Composition of gas mixtures (mole %) (CH + N ), CH ) 89.24%, N ) 10.76%; SNG, CH ) 97.25%, C H ) 1.42%, C H ) 1.08%, 4 2 4 2 4 2 6 3 8 i-C4H10 ) 0.25%.

Table 2. Fitted Ion-Methanol Interaction Parametersa system ionic species

Np

a0

Na+

13

-0.53

K+

13

Ca2+ Cla

a1

AADP (%)

gas phase

aqueous phase (mass %)

temperature range (K)

7.4

1.87

0.44

0.9

6.83

13

-0.95

3.0

6.03

0.56

NaCl (10%) + CH3OH (10%) NaCl (10%) + CH3OH (20%) KCl (10%) + CH3OH (10%) KCl (10%) + CH3OH (20%) CaCl2 (10%) + CH3OH (10%) CaCl2 (10%) + CH3OH (20%)

264.7-277.5 260.8-269.0 266.5-279.5 264.6-275.5 267.0-279.4 264.5-272.4

39

-3.4

SNG SNG SNG SNG SNG SNG

Data source: ref 19. Composition of gas mixture SNG (mole %): CH4 ) 97.25%, C2H6 ) 1.42%, C3H8 ) 1.08%, i-C4H10 ) 0.25%.

Table 3. Average Deviations of the Predicted Hydrate Formation Conditions for Systems Containing Single Electrolytesa gas phase CH4 C2H6 C3H8

CO2

(CH4 + CO2)

overall a

electrolyte species

electrolyte concn (mass %)

temperature range (K)

Np

AADP (%)

AADT (%)

data source (ref no.)

3.00 20.00 12.30 15.00 5.02 10.03 14.99 5.00 10.01 5.00 9.99 15.00 10.00 15.20 10.57 3.00 5.00 10.00 15.00 3.00 5.01 10.02 14.97 3.03 5.02 9.99 14.97 5.02 9.99 15.00 20.00 5.00 10.00 15.01 9.91 15.00 20.00

272.7-279.4 265.4-271.9 269.5-278.4 267.2-275.2 270.5-275.2 267.6-270.7 263.4-265.6 270.9-275.1 269.1-273.4 271.3-275.6 268.1-272.0 263.0-267.4 268.8-277.4 267.4-274.4 267.4-278.0 272.2-279.0 271.2-280.0 268.0-276.1 265.4-273.0 272.7-281.1 272.1-280.5 269.0-277.9 269.0-276.0 272.6-280.9 271.1-280.1 268.0-277.9 263.4-273.2 271.6-282.0 268.5-279.0 264.8-277.2 262.0-274.3 271.4-282.0 269.2-279.0 267.0-277.1 268.6-279.1 266.6-276.9 263.8-273.7 262.0-282.0

6 5 5 5 4 4 3 3 3 3 3 3 8 5 7 4 5 5 4 6 7 4 4 4 4 5 4 4 4 5 4 4 4 4 4 4 4 164

1.27 1.81 0.77 0.70 2.21 3.60 10.69 2.97 6.49 4.46 9.15 7.60 3.35 6.69 2.94 6.00 7.25 5.59 7.54 6.39 7.38 8.17 9.62 5.38 5.31 6.41 9.66 5.17 1.94 7.60 3.56 2.40 3.14 0.57 0.96 6.57 7.40 4.94

0.05 0.05 0.02 0.02 0.04 0.06 0.17 0.05 0.10 0.07 0.14 0.12 0.10 0.17 0.09 0.19 0.22 0.17 0.23 0.19 0.21 0.25 0.29 0.16 0.16 0.19 0.31 0.18 0.07 0.24 0.11 0.08 0.11 0.02 0.03 0.22 0.23 0.14

4 3 3 3 6 6 6 6 6 6 6 6 9 9 9 5 5 5 5 5 5 5 5 5 5 5 5 7 7 7 7 7 7 7 7 7 7

NaCl NaCl KCl CaCl2 NaCl NaCl NaCl KCl KCl CaCl2 CaCl2 CaCl2 NaCl NaCl CaCl2 NaCl NaCl NaCl NaCl KCl KCl KCl KCl CaCl2 CaCl2 CaCl2 CaCl2 NaCl NaCl NaCl NaCl KCl KCl KCl CaCl2 CaCl2 CaCl2 37

Composition of gas mixture (CH4 + CO2) (mole %): CH4 ) 80%, CO2 ) 20%.

methanol interaction parameter (kion,MeOH) is established:

kion,MeOH ) a0 + a1x

(6)

where a0 and a1 are constants; typical values for some ion species are listed in Table 2. 5. For improving the prediction of hydrate formation conditions in mixed electrolyte solutions, the following

1702 Ind. Eng. Chem. Res., Vol. 38, No. 4, 1999 Table 4. Average Deviations of the Predicted Hydrate Formation Conditions for Systems Containing Mixed Electrolytesa aqueous phase (mass %)

temperature range (K)

Np

AADP (%)

AADT (%)

data source (ref no.)

5% NaCl + 3% NaHCO3 10% NaCl + 10% CaCl2 10% CaCl2 + 5% MgCl2 5% NaCl + 5% MgCl2 5% NaCl + 5% MgCl2 + 5% CaCl2 5% NaCl + 5% KCl + 3% MgCl2 + 3% CaCl2 2% NaCl + 0.5% CaCl2 + 0.5% KCl 5% NaCl + 10% KCl 10% KCl + 5% CaCl2 5% NaCl + 10% CaCl2 10% NaCl + 5% CaCl2 6% NaCl + 5% KCl + 4% CaCl2 10% NaCl + 10% CaCl2 10% NaCl + 5% KCl 6% NaCl + 5% KCl + 4% CaCl2 3% NaCl + 3% KCl 5% NaCl + 5% KCl 5% NaCl + 10% KCl 5% NaCl + 15% KCl 10% NaCl + 12% KCl 15% NaCl + 8% KCl 3% NaCl + 3% CaCl2 6% NaCl + 3% CaCl2 10% NaCl + 3% CaCl2 10% NaCl + 6% CaCl2 3% NaCl + 10% CaCl2 6% NaCl + 10% CaCl2 10% NaCl + 10% KCl 10% NaCl + 5% CaCl2 5% CaCl2 + 10% KCl 10% NaCl + 5% KCl 6% NaCl + 3% CaCl2 + 5% KCl 5% NaCl + 3% CaCl2 + 5% KCl + 5% KBr 3% NaCl + 3% KCl 7% NaCl + 10% KCl 15% NaCl + 5% KCl 5% NaCl + 5% KCl 2% NaCl + 8% CaCl2 5% NaCl + 15% CaCl2 3% NaCl + 3% CaCl2 8% NaCl + 2% CaCl2 15% NaCl + 5% CaCl2 6% CaCl2 + 7.5% NaCl 7.5% KCl + 7.5% NaCl 7.5% CaCl2 + 7.5% KCl 5% CaCl2 + 7.5% NaCl + 7.5% KCl 3% NaCl + 3% CaCl2 2% NaCl + 8% CaCl2 8% NaCl + 2% CaCl2 2% NaCl + 2% KCl + 2% CaCl2 50

268.1-283.2 269.9-279.8 269.6-281.8 272.1-285.2 270.2-280.4 269.2-279.4 273.2-281.2 265.1-281.3 265.1-281.6 265.5-276.7 265.5-278.7 265.5-278.2 264.1-270.8 265.8-275.5 266.0-275.5 271.4-279.2 270.3-281.5 267.5-279.0 266.3-276.2 264.6-274.2 264.4-272.1 270.4-281.8 271.3-280.1 269.4-277.3 266.0-274.3 268.8-279.7 268.6-277.1 269.2-275.1 266.9-276.1 268.1-276.4 267.1-276.5 269.0-278.4 269.4-278.8 271.5-279.9 267.6-274.1 262.9-269.8 270.0-277.3 267.8-277.5 259.2-267.3 271.0-279.2 267.8-276.0 259.0-267.4 265.9-269.8 265.2-269.0 266.3-270.1 261.9-265.2 271.0-275.1 268.0-272.2 267.7-272.3 271.0-274.5 259.0-285.2

8 7 8 7 8 8 5 4 4 4 4 4 4 4 4 7 7 4 4 5 4 4 4 4 4 4 4 4 5 5 5 5 5 5 4 4 4 4 5 5 4 4 6 5 7 10 3 3 3 3 245

1.53 2.45 11.39 7.26 11.51 11.65 6.33 2.39 4.71 13.12 11.15 4.68 4.52 6.16 4.37 1.59 3.31 14.72 4.91 5.84 19.20 2.93 3.53 6.82 13.08 6.80 14.73 13.40 17.21 1.49 11.01 3.91 1.43 2.61 22.77 8.76 3.94 2.34 20.51 1.90 2.84 10.13 7.78 10.15 24.92 4.20 3.73 1.40 6.71 10.47 8.02

0.06 0.08 0.43 0.24 0.49 0.43 0.19 0.07 0.15 0.47 0.38 0.16 0.15 0.22 0.16 0.06 0.12 0.47 0.18 0.21 0.76 0.11 0.13 0.26 0.52 0.25 0.57 0.38 0.52 0.04 0.32 0.11 0.04 0.07 0.54 0.25 0.12 0.07 0.70 0.05 0.08 0.32 0.13 0.16 0.36 0.07 0.06 0.02 0.11 0.16 0.24

20 20 20 20 20 20 19 7 7 7 7 7 7 7 7 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3 3 3 3 5 5 5 5 5 5 5 5 5 8 8 8 8 6 6 6 6

gas phase (CH4 + N2)

SNG (CH4 + CO2)1

(CH4 + CO2)2 CH4

C2H6

CO2

CO2 C3H8

overall

a Composition of gas mixtures (mole %): (CH + N ), CH ) 89.24%, N ) 10.76%; (CH + CO )1, CH ) 80%, CO ) 20%; (CH + 4 2 4 2 4 2 4 2 4 CO2)2, CH4 ) 50%, CO2 ) 50%; SNG, CH4 ) 97.25%, C2H6 ) 1.42%, C3H8 ) 1.08%, i-C4H10 ) 0.25%.

mixing rule proposed by Patwardhan and Kumar23 is adopted: ns

ln aW,mix )

0 (mk/m0k) ln aW,k ∑ k)1

(7)

where aW,mix denotes the activity of water in an aque0 stands ous solution containing mixed electrolytes; aW,k for the activity of water in a single electrolyte (k) solution having the same ionic strength as that of a mixed electrolyte solution in which electrolyte k is one of the components; mk denotes the molality of electrolyte k in the mixed solution; m0k stands for the molality of k in a solution containing electrolyte k only, which has the same ionic strength as that of the mixed solution; and ns denotes the number of electrolytes. 6. It is assumed that all ion-ion interaction parameters are equal to zero.

Results and Discussion The modified ZGG hydrate model proposed in this work has been tested extensively on data reported for systems containing single electrolyte, mixed electrolytes, and both electrolytes and methanol in the three-phase (aqueous solution, vapor, and incipient hydrate) equilibrium region. The absolute average deviations of the predicted hydrate formation pressure (AADP) and temperature (AADT) reported in this work are defined as

AADP(%) )

AADT(%) )

1 Np 1

Pexp - Pcal

∑ | j)1 Np

∑| Np

Np j)1

Pexp

|

Texp - Tcal Texp

× 100%

(8)

× 100%

(9)

j

|

j

where Np denotes the number of data points. The

Ind. Eng. Chem. Res., Vol. 38, No. 4, 1999 1703 Table 5. Average Deviations of the Predicted Hydrate Formation Conditions for Systems Containing Both Electrolyte and Methanola gas phase SNG CO2

overall a

aqueous phase (mass %)

Np

temperature range (K)

AADP (%)

AADT (%)

data source (ref no.)

2% NaCl + 0.5% KCl + 0.5% CaCl2 + 10% CH3OH 2% NaCl + 0.5% KCl + 0.5% CaCl2 + 20% CH3OH 5% NaCl + 5% CH3OH 15% NaCl + 5% CH3OH 10% NaCl + 10% CH3OH 5% NaCl + 15% CH3OH 10% CaCl2 + 5% CH3OH 15% CaCl2 + 5% CH3OH 10% CaCl2 + 10% CH3OH 5% CaCl2 + 15% CH3OH 10% KCl + 5% CH3OH 10% KCl + 10% CH3OH 12

6 7 3 3 3 3 3 3 3 3 4 3 44

268.6-281.5 266.5-279.0 270.6-276.2 263.4-269.2 264.0-270.8 264.8-270.8 265.9-274.2 265.2-270.7 264.7-270.9 264.7-270.8 265.5-274.7 265.6-271.8 263.4-281.5

8.62 3.45 7.71 2.86 2.56 9.17 5.86 12.82 3.03 4.14 1.74 1.59 5.27

0.25 0.10 0.24 0.09 0.08 0.26 0.18 0.42 0.09 0.13 0.05 0.05 0.16

19 19 18 18 18 18 18 18 18 18 18 18

Composition of gas mixture SNG (mole %): CH4 ) 97.25%, C2H6 ) 1.42%, C3H8 ) 1.08%, i-C4H10 ) 0.25%.

Figure 1. Comparison of predicted results and experimental data for CO2 hydrate in aqueous NaCl (mass %) solutions (data source: ref 5).

Figure 2. Comparison of predicted results and experimental data for methane hydrate in solutions containing NaCl and KCl (mass %) (data source: ref 4).

hydrate formation systems predicted in the following text are not included in the evaluation of the model parameters. 1. Systems Containing Single Electrolytes. A total of 37 systems for pure gases, binary gas mixtures and a synthetic natural gas in aqueous single electrolyte

Figure 3. Comparison of predicted results and experimental data for a SNG hydrate in aqueous (mixed electrolytes + CH3OH) solutions (data source: ref 19). Solution 1 (mass %): 2% NaCl + 0.5% KCl + 0.5% CaCl2 + 10% CH3OH. Solution 2 (mass %): 2% NaCl + 0.5% KCl + 0.5% CaCl2 + 20% CH3OH.

Figure 4. Comparison of predicted results and experimental data for CO2 hydrate in aqueous (NaCl + CH3OH) (mass %) solutions (data source: ref 18).

solutions were predicted using the new model, and the results are shown in Table 3. The overall AADP and AADT are 4.94% and 0.14%, respectively, so satisfactory agreements with experimental data are observed. The results are a little better than those reported by Mei et

1704 Ind. Eng. Chem. Res., Vol. 38, No. 4, 1999

hydrate model proposed by the authors. Satisfactory results were observed from the systems tested. Acknowledgment The authors gratefully acknowledge the financial support provided by the National Natural Science Foundation and the China National Petroleum Corporation. Literature Cited

Figure 5. Comparison of predicted results and experimental data for CO2 hydrate in aqueous (CaCl2 + CH3OH) (mass %) solutions (data source: ref 18).

Figure 6. Comparison of predicted results and experimental data for CO2 hydrate in aqueous (KCl + CH3OH) (mass %) solutions (data source: ref 18).

al.24 A comparison of the calculated pressure-temperature (P-T) curves based on the new model with the experimental data for CO2 hydrate in aqueous NaCl solutions is shown in Figure 1. 2. Systems Containing Mixed Electrolytes. The new model was applied to predict the hydrate formation conditions for 50 systems containing mixed electrolytes, and the results are shown in Table 4. The overall AADP and AADT are 8.02% and 0.24%, respectively, which are acceptable. A comparison of the predictions and experimental data for methane hydrate in solutions containing both NaCl and KCl is shown in Figure 2. 3. Systems Containing both Electrolytes and Methanol. The new model was also used to predict the hydrate formation conditions for 12 systems containing both electrolytes and methanol, and the results are shown in Table 5 and Figures 3-6. The overall AADP and AADT are 5.27% and 0.16%, respectively. Conclusions The prediction of gas hydrate formation conditions in solutions containing electrolytes and (electrolytes + methanol) was performed using the modified ZGG

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Received for review June 4, 1998 Revised manuscript received December 4, 1998 Accepted December 7, 1998 IE9803523