Hydrate phase equilibrium measurements for (THF + SDS + CO2 + N2) aqueous solution systems in porous media

Fluid Phase Equilibria 370 (2014) 12–18

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Hydrate phase equilibrium measurements for (THF + SDS + CO2 + N2 ) aqueous solution systems in porous media Yi Zhang, Mingjun Yang, Yongchen Song ∗ , Lanlan Jiang, Yanghui Li, Chuanxiao Cheng Key Laboratory of Ocean Energy Utilization and Energy Conservation of Ministry of Education, Dalian University of Technology, Dalian 116024, China

a r t i c l e

i n f o

Article history: Received 12 November 2013 Received in revised form 20 February 2014 Accepted 25 February 2014 Available online 3 March 2014 Keywords: Hydrate phase equilibrium CO2 capture Thermodynamic model Flue gas Porous media

a b s t r a c t Hydrate-based gas separation is a promising technology for CO2 capture and storage. Hydrate phase equilibrium data are the most basic information for hydrate formation and dissociation. The effects and mechanism of the additive mixture (mole fraction 1%, 2%, 3%, 4% and 5% tetrahydrofuran, THF, with 1000 mg/L sodium dodecyl sulphate, SDS) on the hydrate phase equilibrium (THF + SDS + CO2 + N2 + H2 O system) were investigated using an isochoric method. The experimental results showed that the presence of THF resulted in a substantial decrease of the hydrate phase equilibrium pressure. The rate of decrease of the hydrate phase equilibrium pressure with THF concentrations slowed down as the THF concentration exceeded a mole fraction of 3%. An improved model with the PR equation of state associated with a modified Huron–Vidal second-order model mixing rule and non-random two liquid model was proposed further to predict hydrate phase equilibrium. The predictions showed an acceptable agreement with the experimental data. When the hydrate phase equilibrium pressure was higher than 2.00 MPa, the absolute average deviations of the predicted results were obviously smaller. © 2014 Elsevier B.V. All rights reserved.

1. Introduction With the background of the growing crisis of the green house gas effect, carbon dioxide (CO2 ) capture, utilisation and storage (CCUS), an advanced technology that can mitigate CO2 emissions into the atmosphere, is attracting worldwide concern [1–3]. The first step of CCUS is CO2 capture, and there are numerous technologies that can be used for CO2 capture such as post-combustion capture, oxygen-fired combustion, and pre-combustion capture [4,5]. Postcombustion capture, a common method for traditional fossil fuel power plants, offers a significant design challenge due to the relatively low partial pressure of CO2 in flue gas (CO2 /N2 ). Several technologies such as chemical absorption and gas separation membranes can be employed [6,7]. Hydrate-based gas separation is a promising option for capturing CO2 from streaming flue gas [8–10]. The principle of hydrate-based CO2 capture is that CO2 molecules are enclathrated into hydrate cages at a high pressure and low temperature [11,12]. The potential cost reduction of CO2 production for a hydrate-based option is very noticeable [13]. To make hydrate-based gas separation technology available commercially, extensive investigations were carried out to

∗ Corresponding author. Tel.: +86 411 84709093; fax: +86 411 84708015. E-mail addresses: [email protected], [email protected] (Y. Song). http://dx.doi.org/10.1016/j.fluid.2014.02.033 0378-3812/© 2014 Elsevier B.V. All rights reserved.

determine how to mitigate hydrate formation conditions and how to increase hydrate formation rate and gas capacity [4,10,14–25]. Some additives such as tetrahydrofuran (THF) [26–28], tetrabutyl ammonium bromide (TBAB) [29,30], cyclopentane (CP) [31–33], cyclobutanone [34] and dodecyl trimethyl ammonium chloride (DTAC) [35] have been reported to reduce hydrate phase equilibrium pressure. For CO2 /N2 gas separation, Linga et al. investigated CO2 hydrate formation in a semi-batch stirred vessel at a constant pressure and temperature [36], then they reported that the gas uptake and CO2 recovery for flue gas (CO2 /N2 ) with the presence of THF obtained in their work was higher than the values reported in the literature with TBAB and TBAF [37]. Li et al. investigated the effects of DTAC, TBAB, and the initial pressures on hydrate induction time and CO2 separation efficiency and found that a mole fraction of 2.80% DTAC was the most favourable condition for CO2 separation [35]. Li et al. found that the hydrate stability zone increased with the increase in tetra-n-butyl ammonium halide concentration. The phase equilibrium pressure of the CO2 –TBAF–water system is lower than others at the same temperature [38]. The gas uptake and CO2 recovery for CO2 /N2 in the presence of THF have been reported to be greater than the values for TBAB and tetra-n-butyl ammonium fluoride (TBAF) [37]. Generally, surfactant, stirring, and porous media can be used to accelerate the hydrate formation rate and enlarge gas capacity. Addition of surfactants has been demonstrated to provide a safe,

Y. Zhang et al. / Fluid Phase Equilibria 370 (2014) 12–18

low-cost alternative method for storage of natural gas at remote locations [39]. Relative to other surfactants, sodium dodecyl sulphate (SDS) is usually used as a promoter of hydrate formation [40–42]. The optimal SDS concentration for increasing both the hydrate formation rate and the final water-to-hydrate conversion ratio is 1000 mg/L [43]. Because SDS is kinetically additive and has no effects on hydrate equilibrium conditions, some other additives should be used with SDS to improve hydrate formation rate, capacity and stability [41,42]. The recent investigations have added additive mixtures to promote hydrate formation [44,45]. Mechanical stirring is also a potential method to promote hydrate formation [13]. The energy consumption of mechanical agitation is tremendous. The industrial use of hydrate-based gas separation demands that hydrate crystallisation be carried out without mechanical agitation [37]. Micro-scale investigation shows that porous media may be a favourable carrier for hydrate formation. The dispersed water in the porous silica gel system reacts readily with the gas and improves the gas/liquid contact to increase the growth rate of the hydrate [21], thus obviating the need for a stirred reactor and excess water. A nearly fourfold increase in the number of moles of the gas incorporated into the hydrate per mole of water is observed [46], and the CO2 recovery improves from 42% for stirred-tank studies to 51% for the optimum silica. The gas obtained from the hydrate dissociation contained more than a mole fraction of 95% CO2 (70% in the bulk water hydrate) [47], which further validates the feasibility of the CO2 separation process by hydrate formation in a porous silica gel. The latest investigations indicate that the gas uptake is significantly higher in a fixed bed column than in a stirred tank reactor [48]. Furthermore, silica gel with a larger surface area leads to higher gas consumption and reduces the induction time [49], and silica sand can be an effective porous medium for the separation of CO2 from a fuel gas mixture in a fixed bed setup [50]. Although extensive hydrate phase equilibrium data have been obtained for hydrate-based CO2 capture, there is only very limited information for a hydrate system containing additive mixtures. With the background of CCUS, this study focuses on CO2 capture from flue gas. To obtain the mechanism data for the THF–SDS–CO2 –N2 system, the effects of additive mixtures on its thermodynamics were investigated. The information of hydrate phase equilibrium is used to provide fundamental data for the conceptual design of hydrate-based CO2 capture technology. The knowledge obtained from this work is sufficiently general and is expected to be useful in the other applications.

2. Experimental investigation 2.1. Experimental apparatus The experimental apparatus consisted of four subsystems (shown in Fig. 1): (A) a high-pressure vessel to form the hydrate; (B) water and gas high-pressure pumps to provide pore pressure; (C) a temperature control system to cool and heat the vessel; and (D) a data acquisition system to measure pressure and temperature. Further details of the experimental apparatus can be found in the report of our previous investigations [45,51]. The high-pressure resistant vessel is made of 316 stainless steel with a volume of 476 millilitres. Five thermocouples (Yamari Industries, Japan) and two pressure transducers (Nagano Keiki, Japan) were connected to the vessel to measure temperature (T) and pressure (p). The estimated errors of T and p measurements are ±0.1 K and ±0.1 MPa, respectively. A high pressure pump (D-250L, HaianOil Scientific Research Apparatus Co., Ltd., China) was used to increase pore pressure by injecting a solution or a gas mixture. A thermostat bath (F-25 me, JULABO Labortechnik GmbH) filled with a glycol–water solution

13

Fig. 1. Schematic diagram of the gas hydrate experimental apparatus.

was used to control temperature precisely. The temperature stability of the bath was ±0.01 K. The additives were weighed using a balance with a minimum reading up to 0.0001 g (Shanghai Minqiao Precise Science Instrument Co., Ltd., China). The experimental materials are shown in Table 1. All the chemicals were not purified, and deionised water was used in all experiments. The space between the glass beads particles is the position for gas, solution and hydrate formation. There is no pore in the particle itself. The details of the porous media formed with glass beads are shown as follows, the porosity (36.4%), permeability (7.8 ␮m2 ), density (2.6 g/mL). 2.2. Experimental procedures The isochoric method was used to measure the hydrate phase equilibrium by keeping volume constant. The vessel temperature was decreased and increased to make the hydrate form and decompose. Neither gas mixture nor solution was added to the system during the cooling and heating processes. The pressure (p) and temperature (T) are important control and indication parameters for hydrate formation and dissociation. Once hydrate began to form abundantly, T increased rapidly. The following experimental procedures were used. Dry glass beads were packed tightly into the vessel with the configured solution by sedimentation method. The vessel was reconnected to the experimental system, and the gas mixture was used to drive out some of the solution. The thermostat bath temperature was set to a value and kept constant, which is higher than the estimated hydrate equilibrium T to prevent hydrate formation in the vessel. Gas mixture was then injected slowly into the vessel (about 0.1 MPa/min) to the target p (shown in Table 2), and the p and T was kept constant for 2 h to make gas dissolved and to verify the tightness. Subsequently, the thermostat bath T was decreased to the target value, which was usually lower than the predicted equilibrium T for the initial p. The cooling rate is about 0.25 K/min. During the cooling process, the pressure Table 1 Properties and suppliers of materials. Material

Purity/composition

Particle size

Supplier

CO2 /N2

19.8/80.2% (mole fraction)

–

BZ-01

Soda glass

0.105–0.125 mm

THF

≥99.0%

–

SDS

≥91.0%

–

Dalian Guangming Special Gas Co., Ltd., China As-One Co., Ltd., Japan Sinopharm Chemical Reagent Co., Ltd., China Tianjing Bodi Chemical Holding Co., Ltd., China

14

Y. Zhang et al. / Fluid Phase Equilibria 370 (2014) 12–18

Table 2 Hydrate phase equilibrium for CO2 –N2 –THF–SDS–H2 O system in glass beads. THF mole fraction

T (K)

p (MPa)

THF mole fraction

T (K)

p (MPa)

1% THF

287.65 286.85 285.95 284.65 283.95 283.15 282.65 281.15 278.15 290.75 289.45 288.25 287.85 286.35 284.65 283.85 282.85 291.55 291.65 290.15 289.35 288.45 287.05 286.25 284.95 282.05 281.15 279.85 278.45

6.30 5.00 4.30 3.70 3.27 2.61 2.20 1.30 0.80 7.00 5.90 5.00 4.50 3.70 2.40 2.00 1.50 7.10 7.10 5.40 4.80 4.00 3.20 2.60 2.00 1.00 0.80 0.60 0.40

4% THF

292.95 293.05 291.65 291.55 291.15 290.65 289.55 288.85 287.75 286.65 285.65 284.15 282.55 279.95 277.45 292.25 291.45 290.75 290.35 289.75 288.95 287.75 286.65 285.65 283.85 282.95 280.35

8.30 8.30 7.20 6.40 6.20 5.60 4.70 4.10 3.50 2.70 2.15 1.60 0.91 0.58 0.14 7.50 6.51 6.00 5.41 4.80 4.10 3.50 2.80 2.30 1.60 1.10 0.60

3% THF

decreased slightly due to the temperature decrease, which obeys the equation of state. When hydrates began to form in the vessel, a rapid pressure drop was observed due to encapsulation of CO2 in the hydrate, or an abrupt T increase was observed due to the exothermic hydrate crystallisation process. The formation of hydrates was considered to be finished when there was no pressure change in the system. After the hydrate formation, the bath was warmed slowly (about 0.1 K/h) to dissociate the hydrates 5 h later. The p and T conditions at the end of the hydrate decomposition were considered to be hydrate phase equilibrium conditions. 3. Results and discussion

value (approximately 282.15 K), hydrate starts to form. The abrupt decrease of p and increase of T at approximately 80 min indicate the beginning of hydrate formation. Then, the T remains at 282.15 K for approximately 1000 min (from point C to E). There is a fluctuation in the p and T curves at 720 min (point D). Considering that there is no operation and the simultaneous increase of p and T, we believe that this fluctuation is a system error. The vessel is then heated to initiate hydrate dissociation (point E). We propose that the hydrate dissociation is finished at 4276 min (point G). The partially enlarged drawing for the cooling and hydrate formation process is shown in Fig. 3. The inflexions of T curves occur at different times in Fig. 3, indicating that the hydrate formation is inhomogeneous in this experimental case. The sequence for hydrate formation sites is T1 , T2 , T5 , T3 and T4 for this case. The maximum T increase is approximately 2.00 K. The first hydrate formation site is random for all cases in this investigation. The time

302.5

3.1. Hydrate formation and dissociation processes The hydrate formation process is driven by temperature (T) decrease for isochoric method, where the pressure (p) decrease is caused by cooling or hydrate formation. The changes of p and T are important for the discussion of hydrate formation and dissociation. Typical p and T curves during hydrate formation and dissociation are shown in Fig. 2. T1 , T2 , T3 , T4 and T5 represent the T for five different positions in the vessel. The total time for this measurement is 5412 min. The vessel is cooled from 302.00 K to 282.00 K in 80 min (0.25 K/min). When the vessel T decreases to the target

6.4

A T1 T2 T3 T4 T5 p

300 297.5 295

T/k

Hydrate was formed and dissociated in a porous medium in the presence of additive mixture solutions. The presence of glass beads makes hydrate formation rapidly by promoting the contact of gas and water. Once there is no porous media, the hydrate are usually formed by mechanical stirring in the vessel. The experiments were carried out in the T range of 277.45–292.95 K and p range of 0.14–8.30 MPa. Five THF mole fraction (1%, 2%, 3%, 4% and 5%) coupled with 1000 mg/L SDS were studied experimentally. The experimental data were compared with the phase equilibrium conditions of CO2 /N2 hydrate in glass beads. A modified hydrate thermodynamic model was proposed to predict the hydrate phase equilibrium conditions.

5% THF

G

6 5.6 5.2

292.5

4.8

290

4.4

287.5

p/MPa

2% THF

4

285

3.6 C

D

282.5

E

3.2

B 280

0

500

2.8 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500

t/min

Fig. 2. Typical p and T changes with time for CO2 /N2 gas hydrate formation and dissociation in additive mixture (THF and SDS) solution (five-point temperatures).

Y. Zhang et al. / Fluid Phase Equilibria 370 (2014) 12–18 10

6

295 T1 T2 T3 T4 T5 p

292.5

290

15

5.5

0 mol% THF 1 mol% THF 2 mol% THF 3 mol% THF 4 mol% THF 5 mol% THF

8

5

4.5

p/MPa

287.5

p/MPa

T/k

6

4 285

4

C

282.5

2

3.5 B

280

0

20

40

60

80

100

t/min

120

140

160

3 180

0 274

276

278

280

282

284

286

288

290

292

294

T/K

Fig. 3. Typical p and T changes during CO2 /N2 gas hydrate formation (a partial enlarged drawing of Fig. 2).

Fig. 5. Experimental data of hydrate phase equilibrium conditions for CO2 /N2 gas hydrate with different THF concentrations and 1000 mg/L SDS.

interval is very small for each T increase due mainly to the small size of the vessel, in which hydrate formation spreads rapidly from one thermocouple site to another. Because the THF hydrate crystallisation process exhibits exothermic and volume-increasing behaviour, p and T increase simultaneously as the THF hydrate forms in the closed vessel. The decrease of p and increase of T in Fig. 3 indicate the hydrate formation, which has conflict with the p and T changes when THF hydrate forms. That is to say the gas phase has been enclathrated into hydrate cavities as the THF hydrate forms, which causes the p decrease. Fig. 4 shows the p–T curve of the experimental case (the case shown in Fig. 2), which is used to obtain the hydrate-phased equilibrium point. The symbols of points correspond with each other in Figs. 2 and 4. The vessel is cooled from point A to point B by the thermostat bath. When the hydrate begins to form at point B (approximately 282.50 K and 5.50 MPa), p decreases sharply and T remains nearly constant in Fig. 4. Is it a “conflict” that the hydrate formation causes T to increase and p to decrease in Fig. 2? The answer is “No”. The T increase and the p decrease are caused by the selection of T. Because p represents as a macroscopic parameter of the vessel and the T value is a local parameter, the profile of the B–C–E curve is controlled by the selection of T in Fig. 4. Five different profiles of the B–C–E section can be obtained by selecting different thermocouples. The T value then increases dramatically with a

sustained p decrease due to the hydrate formation near the selected thermocouple. Because the hydrate phase equilibrium condition is obtained during the hydrate dissociation process, the B–C–E curve profile does not affect the measured hydrate phase equilibrium conditions, and the B–C–E curve profile is not discussed further. When the exothermal energy of hydrate formation can no longer counterbalance the cool transfer from the bath, T decreases again to 282.15 K. After the hydrate formation is complete, the vessel is heated and the hydrates begin to dissociate. The dissociation process finishes at point E, after which the p–T curve returns to point A along the BA curve with T increase.

7 6.5 6

G

p/MPa

5.5

A

B

5 4.5 4 3.5 3 281

C D E 282

283

284

285

286

287

288

289

290

291

T/K Fig. 4. Typical p–T curve for CO2 /N2 gas hydrate formation and dissociation in additive mixtures (THF and SDS) solution.

3.2. Measurement of the hydrate phase equilibrium conditions Seen from Fig. 5, the effects of THF concentration on hydrate phase equilibrium for the CO2 –N2 –THF–H2 O system can be divided into two stages by the pressure value. A boundary is found at 2.00 MPa. The THF concentration has obvious effect on hydrate phase equilibrium above 2.00 MPa, while the difference in hydrate phase equilibrium is little for different THF concentrations below 2.00 MPa. The presence of THF causes a significant decrease in the hydrate phase equilibrium p coupled with an increase in the T above 2.00 MPa. The presence of THF obviously expands the hydrate stability region of the CO2 –N2 –THF–H2 O-hydrate system. The experimental data for hydrate phase equilibrium conditions are also shown in Table 2. Compared with hydrate phase equilibrium conditions of pure water at 3.30 MPa, the hydrate phase equilibrium T increases by approximately 4.50 K due to the presence of a mole fraction of 1% THF and increases further with the increase in THF concentration. The hydrate phase equilibrium T is approximately 286.85 K at 5.00 MPa in the presence of a mole fraction of 1% THF, and the hydrate equilibrium T is as high as 288.25 K in aqueous solution in the presence of a mole fraction of 2% THF. When the THF concentration increases to a mole fraction of 3%, the hydrate equilibrium T reaches approximately to 289.45 K. There is no further hydrate equilibrium T increase when the THF concentration increases from 3% to 5% mole fraction. When the hydrate phase equilibrium pressure is lower than 2.00 MPa, the hydrate phase equilibrium curves approach each other with the pressure decrease, indicating that the effects of THF concentration on hydrate phase equilibrium are slight at lower pressure. We can propose that THF has a great influence on the hydrate phase equilibrium of the CO2 –N2 –THF–H2 O-hydrate system. The fundamental theory is that the addition of a small amount of hydrocarbon with a higher molecular weight (e.g., propane) in

Y. Zhang et al. / Fluid Phase Equilibria 370 (2014) 12–18

some hydrate former gas (which forms structure I hydrate, s-I) causes the transition from s-I to s-II. This transition indicates a dramatic decrease in the hydrate equilibrium p [52]. The presence of 1% C3 H8 causes the hydrate phase equilibrium pressure to decrease from 5.35 MPa to 3.12 MPa at 280.4 K [52]. In previous work, we found that a “pseudo retrograde” phenomenon appears in the CO2 –H2 –THF–H2 O system [53]. There is no “pseudo retrograde” behaviour in this investigation. A “pseudoretrograde” behaviour usually occurs in a pseudo binary system containing two types (s-I and s-II) of hydrate formers with fairly low vapour pressures. The essential requirement of “pseudoretrograde” behaviour for CO2 –N2 –THF–H2 O system is that the fugacity of CO2 must be high enough to compete with THF to occupy large cavities of s-II hydrates. Because of the lower CO2 concentration in experimental gas, the fugacity of CO2 is below 3.00 MPa in this experiment. That is to say, there is no sufficient CO2 to compete with THF for the large cages of s-II. There is no “pseudo-retrograde” behaviour. We have also stated that the induction time decreases with the increase of THF concentration, and the hydrate induction times approach each other for 3 and 4 mol% THF concentrations at the same pressure [53]. THF (3% mol fraction) is the optimal choice for a shorter hydrate induction time and phase equilibrium conditions for the CO2 –N2 –THF–H2 O system. 3.3. Thermodynamic model for hydrate An improved hydrate thermodynamic model is proposed to predict the hydrate equilibrium conditions for the CO2 –N2 –THF–H2 O system in glass beads. The improved hydrate thermodynamic model is based on the traditional model of van der Waals and Platteeuw [54]. The chemical potentials of water in the hydrate phase and in the coexisting liquid phase are equal to each other when the system reaches phase equilibrium. The chemical potential of water in the hydrate phase is calculated using statistical thermodynamic models. The present model is also based on the contribution of Song et al. [55], who introduced Li’s method to solve the mechanical equilibrium of force (interfacial energy) between the interfaces in a hydrate–liquid–vapour system [56]. The basic equation of the model is shown as follows [55]:

Tf

0W

−

RT0

T0

+

 i

HW dT + RT 2

Pf

VW dP − ln (W XW ) RTf

0

i ln (1 − Yi ) − lnasw +

2hw v1 cos  = 0 rRT

(1)

Eq. (1) is the phase equilibrium model for hydrates in porous media with the presence of electrolyte. The capillary effect in porous sediments is solved using a modified equation from Henry et al. [57], which has been used to calculate hydrate phase equilibrium in porous media. The Peng–Robinson equation of state (P–R Eos) with the modification by Stryjek and Vera (PRSV) is chosen to calculate the fugacity of the hydrate former [58], which is associated with the modified Huron–Vidal second-order model (MHV2) mixing rule [59]. The non-random two liquid (NTRL) model is used to obtain the excess free energy and the activity coefficient [60]. The expression for calculating Langmuir constants was given by Munck et al. [61], and the A and B parameters of N2 were cited from it. The reference values for the “empty” hydrate are taken from Martínez et al. [62], and the A and B parameters for Langmuir constants of THF and CO2 can also be found in Martínez et al. [62]. The parameters used to calculate Langmuir constants for CO2 , N2 and THF are shown in Table 3. SDS is a kinetic promoter, and it has little effect on the hydrate thermodynamic character.

10 1 mol% THF 2 mol% THF 3 mol% THF 4 mol% THF 5 mol% THF Cal. for 1 mol% THF Cal. for 2 mol% THF Cal. for 3 mol% THF Cal. for 4 mol% THF Cal. for 5 mol% THF

8

6

p/MPa

16

4

2

0 276

278

280

282

284

286

288

290

292

294

296

T/K Fig. 6. Comparison of experimental data and calculated results for CO2 /N2 gas hydrate phase equilibrium conditions with different THF concentration.

The prediction results are shown in Fig. 6, and these results are compared with the experimental data for the hydrate phase equilibrium conditions in this study. The predictions overall show a good agreement with the experimental data, especially when the hydrate phase equilibrium pressure is higher than 2.00 MPa. The agreement changes a little with THF concentration. When the mole fraction of THF is 1%, the overall agreement is the best. The predicted hydrate phase equilibrium pressure is slightly lower than experimental data. For example, the predicted results are 288.15 K and 4.72 MPa, while the experimental data are 288.25 K and 5.00 MPa. The predicted hydrate phase equilibrium pressure is slightly higher than the experimental data when the mole fraction of THF are 3%, 4% and 5%. The predicted results show that the effects of THF concentration on the hydrate phase equilibrium pressure are minimal when the temperature is lower than 282.15 K. For example, the hydrate phase equilibrium pressure is 0.73, 0.52, 0.47 and 0.44 MPa for 2%, 3%, 4%, and 5% (mole fraction) THF at 282.15 K, while the hydrate phase equilibrium pressure is 1.87 MPa (282.15 K) for a mole fraction of 1% THF. The predicted hydrate phase equilibrium pressure difference is 0.34 MPa for mole fraction of 1% and 2% THF at 279.15 K, indicating that the effect of THF concentration on hydrate phase equilibrium is small at low pressures. Most of the predicted pressure is lower than the experimental data when the pressure is lower than 2.00 MPa. To obtain the quantitative definition of the improved model, the absolute average deviations of pressure and temperature was calculated. The absolute average deviations of the predicted T (AADT ) and p (AADP ) are defined as follows:

 AADT =

 AADP =

1 Np

  Np   Tcal − Texp     Texp  × 100 j=1

j

  Np   pcal − pexp  1    pexp  × 100 Np j=1

(2)

(3)

j

where Np denotes the number of data points. Error analysis of the predicted hydrate equilibrium conditions in a porous medium is shown in Table 4. The overall AADT values for the improved model are within 0.46%, and all the AADP values are from 7.86% to 21.50%. The absolute average deviations are large for the results at a mole fraction of 3% THF mainly because of the deviation at lower pressures. When the hydrate phase equilibrium pressure is higher than 2.00 MPa, the absolute average deviation is obviously smaller than the value shown in Table 4. The AADT values are 0.06%, 0.09%, 0.27%, 0.13% and 0.09% for the five THF

Y. Zhang et al. / Fluid Phase Equilibria 370 (2014) 12–18

17

Table 3 The calculation parameters for Langmuir constants of N2 , CO2 and THF [61,62]. Large cavities

Structure II

A (K/Pa) B (K−1 )

Small cavities

N2

CO2

THF

N2

CO2

THF

1.8 × 10−7 1.728

8.40 × 10−6 2.025

6.5972 1003.22

1.742 × 10−9 3.082

8.34 × 10−10 3.615

– –

Table 4 Absolute average deviations of predicted hydrate equilibrium conditions. THF mole fraction (%)

T range (K)

p Range (MPa)

Np

AADT (%)

AADP (%)

1 2 3 4 5

278.15–287.65 282.85–290.75 278.45–291.55 277.45–292.95 280.35–292.25

0.80–6.29 1.50–7.00 0.40–7.10 0.14–8.30 0.60–7.50

9 8 12 15 12

0.12 0.12 0.46 0.24 0.24

7.86 13.35 21.50 12.82 16.62

concentrations (mole fraction from 1% to 5%), while the AADP values are 2.96%, 9.54%, 5.39%, 4.56% and 4.44%. The deviation of the predicted results is caused mainly by the presence of THF, which makes the hydrate formation mechanism more complicated. The deviations between the measurements and the modelling results are not surprising due to the complexity of the system. The results show that the improved model provides acceptable predictions for the equilibrium conditions of the hydrate mixture. 4. Conclusions The effects of additive mixtures (THF/SDS) on the thermodynamics of the CO2 /N2 gas hydrates were investigated using an isochoric method. The pressure and temperature changes during hydrate formation indicated that the gas phase had been enclathrated into hydrate cavities. The presence of THF in the system resulted in a drastic decrease in the hydrate phase equilibrium pressure, and higher THF concentrations led to more decreases in the equilibrium pressure. The effect of THF concentration on the hydrate phase equilibrium was slight when the pressure was lower than 2.00 MPa. There was no “pseudo-retrograde” behaviour in this investigation. Furthermore, 3 mol% THF is optimal. An improved model was proposed to calculate hydrate phase equilibrium conditions. The improved model was based on the traditional model of van der Waals and Platteeuw, and the improved model was verified using the experimental data. The predictions overall show a good agreement with experimental data, especially for equilibrium pressures higher than 2.00 MPa. The lowest AADT and AADP values were 0.12% and 7.86% for the prediction results overall. The lowest AADT and AADP values were 0.06% and 2.96% when the pressure was higher than 2.00 MPa. The deviations between the measurements and the modelling results are not surprising due to the complexity of the system. Acknowledgements

[2] [3] [4] [5] [6] [7] [8] [9] [10] [11]

[12] [13] [14] [15] [16] [17] [18] [19] [20]

[21] [22]

[23] [24] [25] [26] [27] [28]

This project is financially supported by the National Natural Science Foundation of China (51106018, 50736001 and 51227005), the Major National Science and Technology Programs of China (2011ZX05026-004), the High-tech Research and Development Program of China (2006AA09A209-5, 2013AA09250302), the Major State Basic Research Development Program of China (2011CB707304) and the Fundamental Research Funds for the Central Universities of China (DUT13LAB19). References [1] A. Raoof, H.M. Nick, T.K.T. Wolterbeek, C.J. Spiers, Int. J. Greenhouse Gas Control 11 (2012) S67–S77.

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