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Experimental measurement and thermodynamic modelling of clathrate hydrate equilibria and salt solubility in aqueous ethylene glycol and electrolyte solutions
Fluid Phase Equilibria 219 (2004) 157–163
Experimental measurement and thermodynamic modelling of clathrate hydrate equilibria and salt solubility in aqueous ethylene glycol and electrolyte solutions Rahim Masoudi, Bahman Tohidi∗ , Ross Anderson, Rod W. Burgass, Jinhai Yang Institute of Petroleum Engineering, Centre for Gas Hydrate Research, Heriot-Watt University, Edinburgh EH14 4AS, UK Received 17 October 2003; accepted 30 January 2004
Abstract We present the extension of a recently developed method for modelling saline water to the thermodynamic prediction of phase behaviour for mixed salt–organic clathrate hydrate inhibitor aqueous solutions. Novel freezing point, boiling point and salt solubility data have been generated for NaCl–ethylene glycol (EG) and KCl–EG aqueous solutions. These data have been used in the optimisation of binary interaction parameters between salts and ethylene glycol. The extended thermodynamic model is capable of predicting complex vapour–liquid–solid (VLSE) equilibria for aqueous electrolytes and/or organic inhibitor solutions over a wide range of pressures, temperatures and inhibitor concentrations. Reliable hydrate dissociation data for two mixed salt–organic inhibitor quaternary systems (CH4 –H2 O–NaCl–EG and CH4 –H2 O–KCl–EG) have been measured at pressures up to 50 MPa. These data are used to validate the predictive capabilities of the model for hydrate equilibria. Good agreement between experimental data and predictions is observed, demonstrating the reliability of the developed model. © 2004 Elsevier B.V. All rights reserved. Keywords: Electrolyte solutions; Phase equilibria; Salt solubility; Gas hydrates; Ethylene glycol; Experimental data
1. Introduction Gas hydrates, or clathrate hydrates, are ice-like crystalline compounds formed by the inclusion of low molecular diameter organic molecules (usually gases) inside cavities formed by water molecules. Although clathrates have similar properties to ice, they differ in that they may form at temperatures well above the freezing point of water at elevated pressure conditions. Gas hydrates are reviewed in depth by Sloan [1]. In petroleum exploration and production operations, gas hydrates pose a serious economic and safety concern. Hydrates can block pipelines, subsea transfer lines, and, in the event of a gas kick during drilling, can form in the well, in risers, blow-out preventers (BOPs) and chokelines [2]. Where the salinity of produced water alone is inadequate for hydrate prevention, the risk of clathrate problems during drilling and production can be reduced by a number ∗ Corresponding author. Tel.: +44-131-451-3672; fax: +44-131-451-3127. E-mail address: [email protected] (B. Tohidi).
0378-3812/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.fluid.2004.01.031
of methods, including keeping operating conditions outside the hydrate stability region (e.g. by heating/insulating or reducing pressure in specific areas), removing/reducing free water, adding thermodynamic inhibitors (e.g. electrolytes and/or organic inhibitors) to drilling/reservoir fluids, or by a combination of these methods. The use of organic hydrate inhibitors such as methanol and ethylene glycol (MEG/EG) for hydrate prevention is common practice, particularly in deepwater operations, however, this can increase the potential for a further flow assurance problem—salt precipitation, commonly termed ‘salting out’ [3,4]. Petroleum production is commonly associated with the production of saline formation water. NaCl and KCl are the principal electrolyte components of almost all produced water. The salinity of produced water varies in different reservoirs, but high water salinities, in some cases very close to saturation, are not uncommon. During production, pressure/temperature changes may result in salt super-saturation in the produced water, inducing in salt precipitation [5]. Excluding chemical reactions that can result in scale deposition (e.g. seawater injection into the formation for pressure maintenance resulting in interaction between sulphate
158
R. Masoudi et al. / Fluid Phase Equilibria 219 (2004) 157–163
ions in the sea water with barium ions in the formation water producing barium sulphate), processes leading to salt precipitation generally follow one of the following four scenarios: 1. Temperature reductions as fluids are transported from the reservoir to the surface, resulting in a reduction in salt solubility. 2. Salt concentration of brines increase as produced gas strips water, leaving the salt behind (assisted by a reduction in the system pressure, resulting in an increase in water partial pressure). 3. The addition of organic hydrate inhibitors (e.g. methanol, glycol) generally reduces salt solubility in the aqueous phase. 4. A reduction in CO2 concentration in the aqueous phase can result in the deposition of bicarbonates as carbonates. Salt precipitation can pose a serious flow assurance problem due to potential salt plug formation in the well-bore, tubing and pipelines. Furthermore, the loss of salt from the aqueous phase may also reduce the hydrate preventative characteristics of the system, increasing the likelihood of clathrate formation. Therefore, reliable determination of the phase behaviour of systems containing salts and/or organic inhibitors is crucial to the success of any flow assurance strategy. Several thermodynamic hydrate prediction models have been described in the literature [6–8], and experimental dissociation data for mixed methanol and electrolyte solutions have been reported [9,10]. However, predictions of existing models for salt–methanol solutions can be in error by up to 4.5–5.6 K [4]. To our knowledge, no previous work available in the literature covers the simultaneous representation of vapour–liquid–solid salt equilibria (VLSE) and gas hydrate stability in aqueous solutions of ethylene glycol and electrolytes. In a recent communication [11], we presented a rigorous thermodynamic model developed for predicting phase equilibria in aqueous electrolyte solutions. The model is based on the equality of fugacities for salt in the salt phase and in the aqueous phase, which are calculated from an EoS, and
this was successfully applied to the prediction of hydrate stability for such systems. Here, this model is extended to the phase behaviour of aqueous solutions containing both salts and ethylene glycol. Newly generated experimental data for freezing point depression, boiling point elevation, and salt solubility—required for tuning binary interaction parameters (BIPs) of thermodynamic model—are reported. In addition, we present novel experimental methane hydrate dissociation data for mixed sodium chloride− and potassium chloride−ethylene glycol aqueous solutions. Experimental data are used to investigate the hydrate inhibition characteristics of these systems, and to validate the developed thermodynamic model.
2. Experimental work Experimental work reported in this paper covers two main areas, physical property measurements, and hydrate dissociation point determinations. 2.1. Freezing point, boiling point and salt solubility The term ‘physical property data’ here refers to freezing point, boiling point and salt solubility data for aqueous solutions of salts and organic inhibitors. These data are required for the development of the thermodynamic model, and have been generated experimentally for systems where no literature data are available, or available data are considered unreliable. A simple and reliable method for freezing point measurement of liquids has been developed at Heriot-Watt University. The method is differential temperature based, relying on detection of the latent heat required to melt ice within a sample, and has demonstrated good reliability, when the results are compared with the available experimental data from International Critical Tables [12]. Required boiling point data were determined using an approach developed from that of Cottrell [13]. In this method, using a Cottrell Pump, the boiling point is measured at a location where the boiling liquid and its vapour are in equilibrium, giving reliable results. For accurate and reliable measurement of
Table 1 Experimental (this work) and predicted water freezing point temperatures for aqueous NaCl–EG and KCl–EG solutions Salt
Salt concentration (mass%)
EG concentration (mass%)
Freezing point temperature Experimental (±0.1 K)
Predicted (K)
Error (%)
NaCl
2.6 5.3 8.1 11.1 15.1
5.8 5.1 8.7 11.3 14.9
269.50 268.30 264.80 261.30 252.26
269.70 268.09 264.28 260.04 252.98
−0.08 0.08 0.20 0.48 −0.28
KCl
2.9 10.0 14.1 10.3
2.5 9.8 15.3 27.5
270.70 263.30 257.10 251.80
270.99 263.69 257.10 251.04
−0.11 −0.15 0.00 0.30
R. Masoudi et al. / Fluid Phase Equilibria 219 (2004) 157–163
159
Table 2 Experimental (this work) and predicted water boiling point temperatures for aqueous NaCl–EG and KCl–EG solutions Salt
Salt concentration (mass%)
EG concentration (mass%)
Boiling point temperature Experimental (±0.1 K)
Predicted (K)
Error (%)
NaCl
5.2 9.3 15.2 13.4
5.8 12.7 24.2 35.8
374.65 376.65 381.15 383.75
374.53 376.42 381.18 383.75
0.03 0.06 −0.01 0.00
KCl
4.9 8.9 15.5 17.2 5.8 5.9
4.7 9.4 15.9 16.8 33.6 55.2
374.25 375.65 378.25 378.95 378.75 384.95
374.13 375.29 377.60 378.20 378.61 385.38
0.03 0.10 0.17 0.20 0.04 −0.11
Table 3 Experimental (this work) and predicted maximum soluble mass of NaCl in aqueous ethylene glycol solutions at various temperatures Temperature (±0.1 K)
EG concentration (mass%)
NaCl concentration Experimental (mass%)
Predicted (mass%)
Error (%)
273.15
0.000
21.920
21.909
−0.05
298.15
0.000 22.052 44.317
26.300 20.436 14.753
26.449 19.982 14.753
0.57 −2.22 0.00
323.15
0.000 22.052 44.317
30.000 23.928 17.614
30.000 23.713 17.606
0.00 −0.90 −0.05
348.15
0.000 22.052 44.317
33.100 26.872 20.300
32.974 26.927 20.300
−0.38 0.20 0.00
salt solubility, the technique selected was that utilised by Chiavone-Filho and Rasmussen [14]. In this procedure, the solute concentration is accurately determined by gravimetric means following evaporation of a known mass of the saturated solution in question.
Measured freezing point and boiling point data for aqueous NaCl–EG and KCl–EG solutions are presented in Tables 1 and 2, respectively. Experimental NaCl solubility data for EG aqueous solutions are reported in Table 3 and presented in Fig. 1.
30
NaCl / mass%
25
20
15
0 mass% EG [21] 10 mass% EG [This work] 25 mass% EG [This work]
10
40 mass% EG [This work] Predictions 5 270
290
310
330
350
T/K Fig. 1. Experimental (this work) and predicted maximum soluble mass of NaCl in aqueous ethylene glycol solutions at various temperatures. EG concentrations are shown on a salt-free basis.
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R. Masoudi et al. / Fluid Phase Equilibria 219 (2004) 157–163
Table 4 Experimental (this work) methane hydrate dissociation conditions for NaCl–EG and KCl–EG aqueous solutions Salt
NaCl
KCl
Salt concentration (mass%)
EG concentration (mass%)
Dissociation point Temperature (±0.1 K)
Pressure (±0.008 MPa)
15.0
21.3
262.3 268.4 274.3 277.9
5.068 11.431 27.758 46.698
12.0
30.8
262.4 267.3 270.5 275.2
6.957 13.610 22.946 46.691
10.0
23.0
265.5 273.4 279.1 283.9
4.164 10.356 22.760 44.513
8.0
35.0
259.3 267.0 273.0 277.6
3.930 9.935 23.442 45.050
2.2. Hydrate equilibria For many electrolytes and organic inhibitors (and their combinations), hydrate dissociation data are insufficient, unavailable, or unreliable. Therefore, it is vital to generate high-quality experimental data for such compounds, allowing the investigation of inhibitor characteristics, and the validation of predictive models. In this work, hydrate dissociation point measurements were made by a method known as step-heating. In step-heating, the system temperature is raised in steps, with sufficient time being given following each step time for equilibrium to be achieved. Only equilibrium (stable pressure) data are used to determine dissociation conditions.
This method has been previously demonstrated as being considerably more reliable and repeatable than conventional continuous-heating and/or visual techniques [15]. Methane hydrate dissociation conditions have been measured for aqueous solutions of NaCl–EG and KCl–EG of different concentrations at pressures up to 50 MPa. Data are presented in Table 4.
3. Thermodynamic modelling We detail here the extension of a recently developed thermodynamic model for electrolyte solutions to the prediction of equilibria involving salts and/or organic hydrate inhibitors. A comprehensive description of the model is given elsewhere [11]. In summary, the statistical thermodynamics model uses the Valderrama modification of the Patel and Teja equation of state (VPT EoS) for fugacity calculations in all fluid phases [16]. Non-density dependent (NDD) mixing rules are applied to model polar–nonpolar and polar–polar interaction [17]. Salts are considered as entity pseudo-components in a modified VPT EoS by defining their critical properties and acentric factors [11]. The hydrate phase is modelled by using the solid solution theory of van der Waals and Platteeuw [18], as implemented by Parrish and Prausnitz [19]. The Kihara model for spherical molecules is applied to calculate the potential functions for compounds forming the hydrate phase [20]. 3.1. Modelling freezing point, boiling point and salt solubility Experimental data for physical properties (freezing point, boiling point and salt solubility) of aqueous EG–salt solutions, as detailed, have been used to optimise salt–EG binary interaction parameters. Since ethylene glycol and salts are both polar molecules, asymmetric mixing is applied
Table 5 Binary interaction parameters for the VPT EoS and the NDD mixing rules kij
H2 O
CH4
EG
NaCl
KCl
H2 O CH4 EG NaCl KCl
0 0.5058 −0.0981 −0.1793 −0.1856
0.5058 0 0.3762 1.13 0.9835
−0.0972 0.3762 0 −0.243 −0.0466
−0.2049 1.13 −0.325 0 −0.3872
−0.2139 0.9835 −0.0275 −0.3416 0
lij0 H2 O NaCl KCl EG
0 0.4425 0.3694 −0.009
1.818 52.88 −24.131 0.6614
−0.0023 −0.1528 −0.179 0
−0.0484 0 −2.3508 −0.432
−0.1044 −1.9144 0 0.2006
lij1 × 1E+4 H2 O NaCl KCl EG
0 46.47 17.156 3.4127
49 7638.77 2347.553 22.147
3.0459 73.266 −4.984 0
−2.5 0 8.2241 −20.774
3.08 173.703 0 24.148
R. Masoudi et al. / Fluid Phase Equilibria 219 (2004) 157–163
161
35 273.15 K, [14] 298.15 K, [14] 323.15 K, [14] 348.15 K, [14] Predictions
KCl / mass%
30
25
20
15
10 0
5
10
15
20
25
30
35
40
45
EG / mass% Fig. 2. Experimental and calculated the dependency of KCl solubility on EG concentration in aqueous solutions. EG concentrations are shown on a salt-free basis. 100
P / MPa
10 mass% EG [22] 30 mass% EG [22] 50 mass% EG [22] CH4-distilled water [23,24,25] Predictions
10
1 260
265
270
275
280
285
290
295
T/K Fig. 3. Experimental and predicted methane hydrate dissociation conditions in the presence of different concentrations of EG.
P / MPa
100
10
21.3% EG / 15% NaCl 30.8% EG / 12% NaCl CH4-distilled water [23,24,25] Predictions 1 255
265
275
285
295
305
T/K Fig. 4. Experimental and predicted methane hydrate dissociation conditions in the presence of NaCl and EG (concentrations in mass%).
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R. Masoudi et al. / Fluid Phase Equilibria 219 (2004) 157–163
P / MPa
100
10
23.0% EG / 10.0 %KCl 35% EG / 8.0 % KCl CH4-distilled water [23,24,25] Predictions 1 255
265
275
285
295
305
T/K Fig. 5. Experimental (points) and predicted (solid lines) methane hydrate dissociation conditions in the presence of KCl and EG (concentrations in mass%).
for non-density dependent mixing rules when modelling these systems. As detailed in our previous publication [11], for non-density dependent mixing rules (NDD), three parameters require optimisation: one classical (kij ), and two asymmetric binary interaction parameters (lij0 , lij1 ). These parameters are presented in Table 5. Model calculations for freezing points of aqueous EG–NaCl and EG–KCl solutions are compared with experimental data in Table 1. Table 2 presents experimental data and model calculations for the boiling point of EG–NaCl and EG–KCl aqueous solutions. Fig. 1 shows experimental ([21] and newly generated data) and calculated NaCl solubility in aqueous EG as a
function of temperature and EG concentration. As can be seen, NaCl solubility is reduced considerably as EG concentration increases, although there is a slight increase in solubility at higher temperatures. Fig. 2 presents experimental [14] and calculated dependency of KCl solubility on ethylene glycol concentration in aqueous solutions at various temperatures. As with sodium chloride, data show that the solubility of potassium chloride in aqueous ethylene glycol solutions decreases significantly with increasing ethylene glycol concentration, although increases with temperature. Figs. 1 and 2 essentially show the maximum concentrations of NaCl and KCl that can exist with EG in aqueous
Table 6 Comparison of the model predictions (this work and the models reported in the literature) with experimental data for methane hydrate dissociation conditions in the presence of mixed salt–EG aqueous solutions Salt
Salt (mass%)
EG (mass%)
P (MPa)
T (K)
T (K)
Difference (K)
T (K)
T (K)
Difference (K)
NaCl
15.0
21.3
5.068 11.431 27.758 46.698
262.3 268.4 274.3 277.9
261.8 268.5 275.0 279.0
−0.5 0.1 0.7 1.1
264.7 271.8 278.3 282.2
2.4 3.4 4.0 4.3
266.0 272.6 278.4 281.7
3.7 4.2 4.1 3.8
12.0
30.8
6.957 13.610 22.946 46.691
262.4 267.3 270.5 275.2
260.7 266.2 269.5 274.8
−1.7 −1.1 −1.0 −0.4
267.4 273.0 276.9 282.3
5.0 5.7 6.4 7.1
267.2 272.0 275.3 279.6
4.8 4.7 4.8 4.4
10.0
23.0
4.164 10.356 22.760 44.513
265.5 273.4 279.1 283.9
265.4 273.7 279.9 285.0
−0.1 0.3 0.8 1.1
269.4 277.9 284.1 289.3
3.9 4.5 5.0 5.4
267.2 274.9 280.3 284.7
1.7 1.5 1.2 0.8
8.0
35.0
3.930 9.935 23.442 45.050
259.3 267.0 273.0 277.6
259.3 267.7 274.1 279.1
0.0 0.7 1.1 1.5
266.7 275.5 282.4 287.6
7.4 8.5 9.4 10.0
264.1 271.5 277.0 281.0
4.8 4.5 4.0 3.4
KCl
AAD AAD: average absolute deviation.
Experimental
This work
NM [26]
0.8
JMM [8] Difference (K)
5.8
3.5
R. Masoudi et al. / Fluid Phase Equilibria 219 (2004) 157–163
solution without any salt precipitation. In all cases, the agreement between experimental data and model calculations is very good, demonstrating the accuracy of the extended model. 3.2. Modelling hydrate equilibria In this section, the extended model is validated against the independent newly generated experimental data for the gas hydrate inhibition effect of aqueous solutions containing salts and ethylene glycol. Fig. 3 shows experimental [22–25] and predicted methane hydrate dissociation conditions for aqueous solutions of ethylene glycol. Very good agreement between model predictions and experimental data is observed. Methane hydrate dissociation data for aqueous solutions of NaCl–EG and KCl–EG, measured as part of this work, are compared with model predictions in Figs. 4 and 5, respectively. In addition, a quantitative comparison between the predictions of our model and two existing literature models [8,26] is presented in Table 6. It should be emphasised that the hydrate dissociation point data have not been used to optimise binary interaction parameters, and are therefore, entirely independent data. Predictions show a good match with experimental data, demonstrating the reliability of the developed model.
4. Conclusions Novel freezing point, boiling point and salt solubility data have been measured for NaCl–EG and KCl–EG aqueous solutions. These data have been used in the optimisation of binary interaction parameters between salts and ethylene glycol in order to extend a recently developed thermodynamic model to include the prediction of phase equilibria involving combinations of salts and organic inhibitors. The extended thermodynamic model is capable of predicting complex vapour–liquid–solid equilibria for aqueous electrolytes and/or organic inhibitor solutions over a wide range of pressures, temperatures and inhibitor concentrations. Reliable hydrate dissociation data for two quaternary systems—CH4 –H2 O–NaCl–EG and CH4 –H2 O–NaCl– EG—have been measured at pressures up to 50 MPa. These data have been used to validate the predictive capabilities of the model for hydrate equilibria. Good agreement between independent experimental data and predictions is observed, demonstrating the reliability of the developed model. List of symbols kij classical binary interaction parameter asymmetric binary interaction parameter lij0 , lij1 between the polar and the other components
163
Acknowledgements This work was part of a joint industrial project supported by ABB Offshore Systems, Petrobras, Shell UK Exploration and Production, and Total in conjunction with the UK Department of Trade and Industry (DTI). Mr. Rahim Masoudi wishes to thank the National Iranian Oil Company (NIOC) for financial support. The authors thank Jim Pantling and Colin Flockhart for manufacture and maintenance of the experimental equipment. References [1] E.D. Sloan, Clathrate Hydrates of Natural Gases, Marcel Dekker, New York, 1998. [2] J.W. Barker, R.K. Gomez, JPT 41 (3) (1989) 297–301. [3] T.K. Amy, F. Gongmin, A.W. Malene, B.T. Mason, SPE 74657 (2002). [4] P.N. Matthews, S. Subramanian, J. Creek, in: Proceedings of the 4th International Conference on Gas Hydrates, May 19–23 2002, Yokohama, pp. 899–905. [5] W.K. Joseph, B.D. James, SPE 74662 (2002). [6] M.A. Clarke, P.R. Bishnoi, in: Proceedings of the 4th International Conference on Gas Hydrates, May 19–23 2002, Yokohama, pp. 406–411. [7] V.Q. Vu, P.D. Suchaux, W. Fürst, Fluid Phase Equilib. 194–197 (2002) 361–370. [8] J. Javanmardi, M. Moshfeghian, R.N. Maddox, Can. J. Chem. Eng. 79 (2001) 367–373. [9] M.D. Jager, C.J. Peters, E.D. Sloan, Fluid Phase Equilib. 193 (2002) 17–28. [10] P.R. Bishnoi, P.D. Dholabhai, Fluid Phase Equilib. 158–160 (1999) 821–827. [11] R. Masoudi, B. Tohidi, A. Danesh, A.C. Todd, Fluid Phase Equilib. 215 (2004) 163–174. [12] Washburn, International Critical Tables (ICT) of Numerical Data, Physics, Chemistry and Technology, National Research Council, 1926–1930. [13] F.G. Cottrell, J. Am. Chem. Soc. 41 (1919) 721–729. [14] O. Chiavone-Filho, P. Rasmussen, J. Chem. Eng. Data 38 (3) (1993) 367–369. [15] B. Tohidi, R.W. Burgass, A. Danesh, K.K. Østergaard, A.C. Todd, Ann. NY Acad. Sci. 912 (2000) 924–931. [16] J.O. Valderrama, J. Chem. Eng. Jpn. 23 (1) (1990) 87–91. [17] D. Avlonitis, A. Danesh, A.C. Todd, Fluid Phase Equilib. 94 (1994) 181–216. [18] J.H. Van der Waals, J.C. Platteeuw, Adv. Chem. Phys. 2 (1959) 1–57. [19] W.R. Parrish, J.M. Prausnitz, Ind. Eng. Chem. Proc. Des. Dev. 11 (1972) 26–35. [20] T. Kihara, Rev. Mod. Phys. 25 (4) (1953) 831–843. [21] CRC Hand Book of Chemistry and Physics, CRC Press, Boca Raton, FL, USA, 1989. [22] D.B. Robinson, H.-J. Ng, J. Can. Petrol Tech. 25 (4) (1986) 26– 30. [23] W.M. Deaton, E.M. Frost, US Bur. Mines Monogr. 8 (1946) 101. [24] H.O. McLoed, J.M. Campbell, J. Pet. Technol. 222 (1961) 590. [25] J. Jhaveri, D.B. Robinson, Can. J. Chem. Eng. 43 (1965) 75– 78. [26] K. Nasrifar, M. Moshfeghian, J. Chem. Thermodyn. 33 (2001) 999– 1014.
Experimental measurement and thermodynamic modelling of clathrate hydrate equilibria and salt solubility in aqueous ethylene glycol and electrolyte solutions Rahim Masoudi, Bahman Tohidi∗ , Ross Anderson, Rod W. Burgass, Jinhai Yang Institute of Petroleum Engineering, Centre for Gas Hydrate Research, Heriot-Watt University, Edinburgh EH14 4AS, UK Received 17 October 2003; accepted 30 January 2004
Abstract We present the extension of a recently developed method for modelling saline water to the thermodynamic prediction of phase behaviour for mixed salt–organic clathrate hydrate inhibitor aqueous solutions. Novel freezing point, boiling point and salt solubility data have been generated for NaCl–ethylene glycol (EG) and KCl–EG aqueous solutions. These data have been used in the optimisation of binary interaction parameters between salts and ethylene glycol. The extended thermodynamic model is capable of predicting complex vapour–liquid–solid (VLSE) equilibria for aqueous electrolytes and/or organic inhibitor solutions over a wide range of pressures, temperatures and inhibitor concentrations. Reliable hydrate dissociation data for two mixed salt–organic inhibitor quaternary systems (CH4 –H2 O–NaCl–EG and CH4 –H2 O–KCl–EG) have been measured at pressures up to 50 MPa. These data are used to validate the predictive capabilities of the model for hydrate equilibria. Good agreement between experimental data and predictions is observed, demonstrating the reliability of the developed model. © 2004 Elsevier B.V. All rights reserved. Keywords: Electrolyte solutions; Phase equilibria; Salt solubility; Gas hydrates; Ethylene glycol; Experimental data
1. Introduction Gas hydrates, or clathrate hydrates, are ice-like crystalline compounds formed by the inclusion of low molecular diameter organic molecules (usually gases) inside cavities formed by water molecules. Although clathrates have similar properties to ice, they differ in that they may form at temperatures well above the freezing point of water at elevated pressure conditions. Gas hydrates are reviewed in depth by Sloan [1]. In petroleum exploration and production operations, gas hydrates pose a serious economic and safety concern. Hydrates can block pipelines, subsea transfer lines, and, in the event of a gas kick during drilling, can form in the well, in risers, blow-out preventers (BOPs) and chokelines [2]. Where the salinity of produced water alone is inadequate for hydrate prevention, the risk of clathrate problems during drilling and production can be reduced by a number ∗ Corresponding author. Tel.: +44-131-451-3672; fax: +44-131-451-3127. E-mail address: [email protected] (B. Tohidi).
0378-3812/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.fluid.2004.01.031
of methods, including keeping operating conditions outside the hydrate stability region (e.g. by heating/insulating or reducing pressure in specific areas), removing/reducing free water, adding thermodynamic inhibitors (e.g. electrolytes and/or organic inhibitors) to drilling/reservoir fluids, or by a combination of these methods. The use of organic hydrate inhibitors such as methanol and ethylene glycol (MEG/EG) for hydrate prevention is common practice, particularly in deepwater operations, however, this can increase the potential for a further flow assurance problem—salt precipitation, commonly termed ‘salting out’ [3,4]. Petroleum production is commonly associated with the production of saline formation water. NaCl and KCl are the principal electrolyte components of almost all produced water. The salinity of produced water varies in different reservoirs, but high water salinities, in some cases very close to saturation, are not uncommon. During production, pressure/temperature changes may result in salt super-saturation in the produced water, inducing in salt precipitation [5]. Excluding chemical reactions that can result in scale deposition (e.g. seawater injection into the formation for pressure maintenance resulting in interaction between sulphate
158
R. Masoudi et al. / Fluid Phase Equilibria 219 (2004) 157–163
ions in the sea water with barium ions in the formation water producing barium sulphate), processes leading to salt precipitation generally follow one of the following four scenarios: 1. Temperature reductions as fluids are transported from the reservoir to the surface, resulting in a reduction in salt solubility. 2. Salt concentration of brines increase as produced gas strips water, leaving the salt behind (assisted by a reduction in the system pressure, resulting in an increase in water partial pressure). 3. The addition of organic hydrate inhibitors (e.g. methanol, glycol) generally reduces salt solubility in the aqueous phase. 4. A reduction in CO2 concentration in the aqueous phase can result in the deposition of bicarbonates as carbonates. Salt precipitation can pose a serious flow assurance problem due to potential salt plug formation in the well-bore, tubing and pipelines. Furthermore, the loss of salt from the aqueous phase may also reduce the hydrate preventative characteristics of the system, increasing the likelihood of clathrate formation. Therefore, reliable determination of the phase behaviour of systems containing salts and/or organic inhibitors is crucial to the success of any flow assurance strategy. Several thermodynamic hydrate prediction models have been described in the literature [6–8], and experimental dissociation data for mixed methanol and electrolyte solutions have been reported [9,10]. However, predictions of existing models for salt–methanol solutions can be in error by up to 4.5–5.6 K [4]. To our knowledge, no previous work available in the literature covers the simultaneous representation of vapour–liquid–solid salt equilibria (VLSE) and gas hydrate stability in aqueous solutions of ethylene glycol and electrolytes. In a recent communication [11], we presented a rigorous thermodynamic model developed for predicting phase equilibria in aqueous electrolyte solutions. The model is based on the equality of fugacities for salt in the salt phase and in the aqueous phase, which are calculated from an EoS, and
this was successfully applied to the prediction of hydrate stability for such systems. Here, this model is extended to the phase behaviour of aqueous solutions containing both salts and ethylene glycol. Newly generated experimental data for freezing point depression, boiling point elevation, and salt solubility—required for tuning binary interaction parameters (BIPs) of thermodynamic model—are reported. In addition, we present novel experimental methane hydrate dissociation data for mixed sodium chloride− and potassium chloride−ethylene glycol aqueous solutions. Experimental data are used to investigate the hydrate inhibition characteristics of these systems, and to validate the developed thermodynamic model.
2. Experimental work Experimental work reported in this paper covers two main areas, physical property measurements, and hydrate dissociation point determinations. 2.1. Freezing point, boiling point and salt solubility The term ‘physical property data’ here refers to freezing point, boiling point and salt solubility data for aqueous solutions of salts and organic inhibitors. These data are required for the development of the thermodynamic model, and have been generated experimentally for systems where no literature data are available, or available data are considered unreliable. A simple and reliable method for freezing point measurement of liquids has been developed at Heriot-Watt University. The method is differential temperature based, relying on detection of the latent heat required to melt ice within a sample, and has demonstrated good reliability, when the results are compared with the available experimental data from International Critical Tables [12]. Required boiling point data were determined using an approach developed from that of Cottrell [13]. In this method, using a Cottrell Pump, the boiling point is measured at a location where the boiling liquid and its vapour are in equilibrium, giving reliable results. For accurate and reliable measurement of
Table 1 Experimental (this work) and predicted water freezing point temperatures for aqueous NaCl–EG and KCl–EG solutions Salt
Salt concentration (mass%)
EG concentration (mass%)
Freezing point temperature Experimental (±0.1 K)
Predicted (K)
Error (%)
NaCl
2.6 5.3 8.1 11.1 15.1
5.8 5.1 8.7 11.3 14.9
269.50 268.30 264.80 261.30 252.26
269.70 268.09 264.28 260.04 252.98
−0.08 0.08 0.20 0.48 −0.28
KCl
2.9 10.0 14.1 10.3
2.5 9.8 15.3 27.5
270.70 263.30 257.10 251.80
270.99 263.69 257.10 251.04
−0.11 −0.15 0.00 0.30
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Table 2 Experimental (this work) and predicted water boiling point temperatures for aqueous NaCl–EG and KCl–EG solutions Salt
Salt concentration (mass%)
EG concentration (mass%)
Boiling point temperature Experimental (±0.1 K)
Predicted (K)
Error (%)
NaCl
5.2 9.3 15.2 13.4
5.8 12.7 24.2 35.8
374.65 376.65 381.15 383.75
374.53 376.42 381.18 383.75
0.03 0.06 −0.01 0.00
KCl
4.9 8.9 15.5 17.2 5.8 5.9
4.7 9.4 15.9 16.8 33.6 55.2
374.25 375.65 378.25 378.95 378.75 384.95
374.13 375.29 377.60 378.20 378.61 385.38
0.03 0.10 0.17 0.20 0.04 −0.11
Table 3 Experimental (this work) and predicted maximum soluble mass of NaCl in aqueous ethylene glycol solutions at various temperatures Temperature (±0.1 K)
EG concentration (mass%)
NaCl concentration Experimental (mass%)
Predicted (mass%)
Error (%)
273.15
0.000
21.920
21.909
−0.05
298.15
0.000 22.052 44.317
26.300 20.436 14.753
26.449 19.982 14.753
0.57 −2.22 0.00
323.15
0.000 22.052 44.317
30.000 23.928 17.614
30.000 23.713 17.606
0.00 −0.90 −0.05
348.15
0.000 22.052 44.317
33.100 26.872 20.300
32.974 26.927 20.300
−0.38 0.20 0.00
salt solubility, the technique selected was that utilised by Chiavone-Filho and Rasmussen [14]. In this procedure, the solute concentration is accurately determined by gravimetric means following evaporation of a known mass of the saturated solution in question.
Measured freezing point and boiling point data for aqueous NaCl–EG and KCl–EG solutions are presented in Tables 1 and 2, respectively. Experimental NaCl solubility data for EG aqueous solutions are reported in Table 3 and presented in Fig. 1.
30
NaCl / mass%
25
20
15
0 mass% EG [21] 10 mass% EG [This work] 25 mass% EG [This work]
10
40 mass% EG [This work] Predictions 5 270
290
310
330
350
T/K Fig. 1. Experimental (this work) and predicted maximum soluble mass of NaCl in aqueous ethylene glycol solutions at various temperatures. EG concentrations are shown on a salt-free basis.
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Table 4 Experimental (this work) methane hydrate dissociation conditions for NaCl–EG and KCl–EG aqueous solutions Salt
NaCl
KCl
Salt concentration (mass%)
EG concentration (mass%)
Dissociation point Temperature (±0.1 K)
Pressure (±0.008 MPa)
15.0
21.3
262.3 268.4 274.3 277.9
5.068 11.431 27.758 46.698
12.0
30.8
262.4 267.3 270.5 275.2
6.957 13.610 22.946 46.691
10.0
23.0
265.5 273.4 279.1 283.9
4.164 10.356 22.760 44.513
8.0
35.0
259.3 267.0 273.0 277.6
3.930 9.935 23.442 45.050
2.2. Hydrate equilibria For many electrolytes and organic inhibitors (and their combinations), hydrate dissociation data are insufficient, unavailable, or unreliable. Therefore, it is vital to generate high-quality experimental data for such compounds, allowing the investigation of inhibitor characteristics, and the validation of predictive models. In this work, hydrate dissociation point measurements were made by a method known as step-heating. In step-heating, the system temperature is raised in steps, with sufficient time being given following each step time for equilibrium to be achieved. Only equilibrium (stable pressure) data are used to determine dissociation conditions.
This method has been previously demonstrated as being considerably more reliable and repeatable than conventional continuous-heating and/or visual techniques [15]. Methane hydrate dissociation conditions have been measured for aqueous solutions of NaCl–EG and KCl–EG of different concentrations at pressures up to 50 MPa. Data are presented in Table 4.
3. Thermodynamic modelling We detail here the extension of a recently developed thermodynamic model for electrolyte solutions to the prediction of equilibria involving salts and/or organic hydrate inhibitors. A comprehensive description of the model is given elsewhere [11]. In summary, the statistical thermodynamics model uses the Valderrama modification of the Patel and Teja equation of state (VPT EoS) for fugacity calculations in all fluid phases [16]. Non-density dependent (NDD) mixing rules are applied to model polar–nonpolar and polar–polar interaction [17]. Salts are considered as entity pseudo-components in a modified VPT EoS by defining their critical properties and acentric factors [11]. The hydrate phase is modelled by using the solid solution theory of van der Waals and Platteeuw [18], as implemented by Parrish and Prausnitz [19]. The Kihara model for spherical molecules is applied to calculate the potential functions for compounds forming the hydrate phase [20]. 3.1. Modelling freezing point, boiling point and salt solubility Experimental data for physical properties (freezing point, boiling point and salt solubility) of aqueous EG–salt solutions, as detailed, have been used to optimise salt–EG binary interaction parameters. Since ethylene glycol and salts are both polar molecules, asymmetric mixing is applied
Table 5 Binary interaction parameters for the VPT EoS and the NDD mixing rules kij
H2 O
CH4
EG
NaCl
KCl
H2 O CH4 EG NaCl KCl
0 0.5058 −0.0981 −0.1793 −0.1856
0.5058 0 0.3762 1.13 0.9835
−0.0972 0.3762 0 −0.243 −0.0466
−0.2049 1.13 −0.325 0 −0.3872
−0.2139 0.9835 −0.0275 −0.3416 0
lij0 H2 O NaCl KCl EG
0 0.4425 0.3694 −0.009
1.818 52.88 −24.131 0.6614
−0.0023 −0.1528 −0.179 0
−0.0484 0 −2.3508 −0.432
−0.1044 −1.9144 0 0.2006
lij1 × 1E+4 H2 O NaCl KCl EG
0 46.47 17.156 3.4127
49 7638.77 2347.553 22.147
3.0459 73.266 −4.984 0
−2.5 0 8.2241 −20.774
3.08 173.703 0 24.148
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161
35 273.15 K, [14] 298.15 K, [14] 323.15 K, [14] 348.15 K, [14] Predictions
KCl / mass%
30
25
20
15
10 0
5
10
15
20
25
30
35
40
45
EG / mass% Fig. 2. Experimental and calculated the dependency of KCl solubility on EG concentration in aqueous solutions. EG concentrations are shown on a salt-free basis. 100
P / MPa
10 mass% EG [22] 30 mass% EG [22] 50 mass% EG [22] CH4-distilled water [23,24,25] Predictions
10
1 260
265
270
275
280
285
290
295
T/K Fig. 3. Experimental and predicted methane hydrate dissociation conditions in the presence of different concentrations of EG.
P / MPa
100
10
21.3% EG / 15% NaCl 30.8% EG / 12% NaCl CH4-distilled water [23,24,25] Predictions 1 255
265
275
285
295
305
T/K Fig. 4. Experimental and predicted methane hydrate dissociation conditions in the presence of NaCl and EG (concentrations in mass%).
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P / MPa
100
10
23.0% EG / 10.0 %KCl 35% EG / 8.0 % KCl CH4-distilled water [23,24,25] Predictions 1 255
265
275
285
295
305
T/K Fig. 5. Experimental (points) and predicted (solid lines) methane hydrate dissociation conditions in the presence of KCl and EG (concentrations in mass%).
for non-density dependent mixing rules when modelling these systems. As detailed in our previous publication [11], for non-density dependent mixing rules (NDD), three parameters require optimisation: one classical (kij ), and two asymmetric binary interaction parameters (lij0 , lij1 ). These parameters are presented in Table 5. Model calculations for freezing points of aqueous EG–NaCl and EG–KCl solutions are compared with experimental data in Table 1. Table 2 presents experimental data and model calculations for the boiling point of EG–NaCl and EG–KCl aqueous solutions. Fig. 1 shows experimental ([21] and newly generated data) and calculated NaCl solubility in aqueous EG as a
function of temperature and EG concentration. As can be seen, NaCl solubility is reduced considerably as EG concentration increases, although there is a slight increase in solubility at higher temperatures. Fig. 2 presents experimental [14] and calculated dependency of KCl solubility on ethylene glycol concentration in aqueous solutions at various temperatures. As with sodium chloride, data show that the solubility of potassium chloride in aqueous ethylene glycol solutions decreases significantly with increasing ethylene glycol concentration, although increases with temperature. Figs. 1 and 2 essentially show the maximum concentrations of NaCl and KCl that can exist with EG in aqueous
Table 6 Comparison of the model predictions (this work and the models reported in the literature) with experimental data for methane hydrate dissociation conditions in the presence of mixed salt–EG aqueous solutions Salt
Salt (mass%)
EG (mass%)
P (MPa)
T (K)
T (K)
Difference (K)
T (K)
T (K)
Difference (K)
NaCl
15.0
21.3
5.068 11.431 27.758 46.698
262.3 268.4 274.3 277.9
261.8 268.5 275.0 279.0
−0.5 0.1 0.7 1.1
264.7 271.8 278.3 282.2
2.4 3.4 4.0 4.3
266.0 272.6 278.4 281.7
3.7 4.2 4.1 3.8
12.0
30.8
6.957 13.610 22.946 46.691
262.4 267.3 270.5 275.2
260.7 266.2 269.5 274.8
−1.7 −1.1 −1.0 −0.4
267.4 273.0 276.9 282.3
5.0 5.7 6.4 7.1
267.2 272.0 275.3 279.6
4.8 4.7 4.8 4.4
10.0
23.0
4.164 10.356 22.760 44.513
265.5 273.4 279.1 283.9
265.4 273.7 279.9 285.0
−0.1 0.3 0.8 1.1
269.4 277.9 284.1 289.3
3.9 4.5 5.0 5.4
267.2 274.9 280.3 284.7
1.7 1.5 1.2 0.8
8.0
35.0
3.930 9.935 23.442 45.050
259.3 267.0 273.0 277.6
259.3 267.7 274.1 279.1
0.0 0.7 1.1 1.5
266.7 275.5 282.4 287.6
7.4 8.5 9.4 10.0
264.1 271.5 277.0 281.0
4.8 4.5 4.0 3.4
KCl
AAD AAD: average absolute deviation.
Experimental
This work
NM [26]
0.8
JMM [8] Difference (K)
5.8
3.5
R. Masoudi et al. / Fluid Phase Equilibria 219 (2004) 157–163
solution without any salt precipitation. In all cases, the agreement between experimental data and model calculations is very good, demonstrating the accuracy of the extended model. 3.2. Modelling hydrate equilibria In this section, the extended model is validated against the independent newly generated experimental data for the gas hydrate inhibition effect of aqueous solutions containing salts and ethylene glycol. Fig. 3 shows experimental [22–25] and predicted methane hydrate dissociation conditions for aqueous solutions of ethylene glycol. Very good agreement between model predictions and experimental data is observed. Methane hydrate dissociation data for aqueous solutions of NaCl–EG and KCl–EG, measured as part of this work, are compared with model predictions in Figs. 4 and 5, respectively. In addition, a quantitative comparison between the predictions of our model and two existing literature models [8,26] is presented in Table 6. It should be emphasised that the hydrate dissociation point data have not been used to optimise binary interaction parameters, and are therefore, entirely independent data. Predictions show a good match with experimental data, demonstrating the reliability of the developed model.
4. Conclusions Novel freezing point, boiling point and salt solubility data have been measured for NaCl–EG and KCl–EG aqueous solutions. These data have been used in the optimisation of binary interaction parameters between salts and ethylene glycol in order to extend a recently developed thermodynamic model to include the prediction of phase equilibria involving combinations of salts and organic inhibitors. The extended thermodynamic model is capable of predicting complex vapour–liquid–solid equilibria for aqueous electrolytes and/or organic inhibitor solutions over a wide range of pressures, temperatures and inhibitor concentrations. Reliable hydrate dissociation data for two quaternary systems—CH4 –H2 O–NaCl–EG and CH4 –H2 O–NaCl– EG—have been measured at pressures up to 50 MPa. These data have been used to validate the predictive capabilities of the model for hydrate equilibria. Good agreement between independent experimental data and predictions is observed, demonstrating the reliability of the developed model. List of symbols kij classical binary interaction parameter asymmetric binary interaction parameter lij0 , lij1 between the polar and the other components
163
Acknowledgements This work was part of a joint industrial project supported by ABB Offshore Systems, Petrobras, Shell UK Exploration and Production, and Total in conjunction with the UK Department of Trade and Industry (DTI). Mr. Rahim Masoudi wishes to thank the National Iranian Oil Company (NIOC) for financial support. The authors thank Jim Pantling and Colin Flockhart for manufacture and maintenance of the experimental equipment. References [1] E.D. Sloan, Clathrate Hydrates of Natural Gases, Marcel Dekker, New York, 1998. [2] J.W. Barker, R.K. Gomez, JPT 41 (3) (1989) 297–301. [3] T.K. Amy, F. Gongmin, A.W. Malene, B.T. Mason, SPE 74657 (2002). [4] P.N. Matthews, S. Subramanian, J. Creek, in: Proceedings of the 4th International Conference on Gas Hydrates, May 19–23 2002, Yokohama, pp. 899–905. [5] W.K. Joseph, B.D. James, SPE 74662 (2002). [6] M.A. Clarke, P.R. Bishnoi, in: Proceedings of the 4th International Conference on Gas Hydrates, May 19–23 2002, Yokohama, pp. 406–411. [7] V.Q. Vu, P.D. Suchaux, W. Fürst, Fluid Phase Equilib. 194–197 (2002) 361–370. [8] J. Javanmardi, M. Moshfeghian, R.N. Maddox, Can. J. Chem. Eng. 79 (2001) 367–373. [9] M.D. Jager, C.J. Peters, E.D. Sloan, Fluid Phase Equilib. 193 (2002) 17–28. [10] P.R. Bishnoi, P.D. Dholabhai, Fluid Phase Equilib. 158–160 (1999) 821–827. [11] R. Masoudi, B. Tohidi, A. Danesh, A.C. Todd, Fluid Phase Equilib. 215 (2004) 163–174. [12] Washburn, International Critical Tables (ICT) of Numerical Data, Physics, Chemistry and Technology, National Research Council, 1926–1930. [13] F.G. Cottrell, J. Am. Chem. Soc. 41 (1919) 721–729. [14] O. Chiavone-Filho, P. Rasmussen, J. Chem. Eng. Data 38 (3) (1993) 367–369. [15] B. Tohidi, R.W. Burgass, A. Danesh, K.K. Østergaard, A.C. Todd, Ann. NY Acad. Sci. 912 (2000) 924–931. [16] J.O. Valderrama, J. Chem. Eng. Jpn. 23 (1) (1990) 87–91. [17] D. Avlonitis, A. Danesh, A.C. Todd, Fluid Phase Equilib. 94 (1994) 181–216. [18] J.H. Van der Waals, J.C. Platteeuw, Adv. Chem. Phys. 2 (1959) 1–57. [19] W.R. Parrish, J.M. Prausnitz, Ind. Eng. Chem. Proc. Des. Dev. 11 (1972) 26–35. [20] T. Kihara, Rev. Mod. Phys. 25 (4) (1953) 831–843. [21] CRC Hand Book of Chemistry and Physics, CRC Press, Boca Raton, FL, USA, 1989. [22] D.B. Robinson, H.-J. Ng, J. Can. Petrol Tech. 25 (4) (1986) 26– 30. [23] W.M. Deaton, E.M. Frost, US Bur. Mines Monogr. 8 (1946) 101. [24] H.O. McLoed, J.M. Campbell, J. Pet. Technol. 222 (1961) 590. [25] J. Jhaveri, D.B. Robinson, Can. J. Chem. Eng. 43 (1965) 75– 78. [26] K. Nasrifar, M. Moshfeghian, J. Chem. Thermodyn. 33 (2001) 999– 1014.