Ind. Eng. Chem. Res. 2005, 44, 7567-7574
7567
Experimental Measurement and Phase Behavior Modeling of Hydrogen Sulfide-Water Binary System Antonin Chapoy,† Amir H. Mohammadi, and Bahman Tohidi Centre for Gas Hydrate Research, Institute of Petroleum Engineering, Heriot-Watt University, Edinburgh EH14 4AS, Scotland, U.K.
Alain Valtz and Dominique Richon* Centre Energe´ tique et Proce´ de´ s, Ecole Nationale Supe´ rieure des Mines de Paris CEP/TEP, 35 Rue Saint Honore´ , 77305 Fontainebleau, France
Here, new vapor-liquid equilibrium data of H2S-H2O binary system are reported over the 298.16-338.34 K temperature range for pressures up to 3.962 MPa. The experimental method is based on a static analytic apparatus, taking advantage of two ROLSI pneumatic capillary samplers. An extensive literature review has been conducted on the mutual solubilities of H2SH2O systems and H2S hydrate formation conditions. A critical evaluation of the literature data has been performed to identify any inconsistencies in the reported data. A thermodynamic model has been used to represent the experimental data. The Valderrama modification of the PatelTeja equation of state combined with nondensity dependent mixing rules is selected to model the fluid phases. The hydrate phase is modeled by the solid solution theory of van der Waals and Platteeuw with previously reported Kihara potential parameters. The fugacity of ice is calculated by correcting the saturation fugacity of H2O at the same temperature using the Poynting correction. The new H2S solubility data generated in this work are used for tuning the binary interaction parameters between H2S and H2O. The new measured and predicted vaporliquid equilibrium data, as well as model predictions for the hydrate dissociation conditions of H2S, are compared with the experimental data in the literature. The results are in good agreement, demonstrating the reliability of the technique and model presented in this work. 1. Introduction Accurate knowledge of phase behavior in a waterhydrogen sulfide system is crucial to the design and operation of pipelines and production/processing facilities as many sour reservoir fluids contain hydrogen sulfide and water. In general, it is desirable to avoid the formation of condensed water to reduce the risk of gas hydrate formation, ice formation, corrosion, and twophase flow problems. On the other hand, oil and gas producers have been faced with a growing challenge to reduce atmospheric emissions of acid gases, including hydrogen sulfide, produced from sour hydrocarbon reservoirs, because of environmental regulations. When acid gases are extracted, one option for their disposal is by injection into an underground zone. As acid gases are normally saturated with water in gas treatment units, a comprehensive coverage of the many design considerations for acid gas disposal requires knowledge of the phase equilibrium in a water-hydrogen sulfide system. In the present work, experimental data on the solubility of hydrogen sulfide in water and the water content of gaseous hydrogen sulfide, as well as hydrate dissociation conditions, have been gathered from a bibliographic study. The main objective is to identify inconsistencies and gaps in the available data to build a reliable database. As a result of this bibliographic review, it has been concluded that it is necessary to determine complemen* To whom correspondence should be addressed. E-mail:
[email protected]. Tel.: +(33) 1 64 69 49 65. Fax: +(33) 1 64 69 49 68. † On leave from Centre Energe´tique et Proce´de´s, Ecole Nationale Supe´rieure des Mines de Paris, France.
tary vapor-liquid equilibrium (VLE) data for the H2SH2O binary mixture because measurements at low temperatures (T < 298.15) and intermediate pressures are scarce and some of the data reported at higher temperature are scattered. Corresponding new data are reported herein in the 298.16-338.34 K temperature range for pressures up to 3.962 MPa. The compositions of the coexisting phases were measured using gas chromatography (GC). The isotherms presented in this paper were determined on the basis of a static analytic method using an apparatus taking advantage of two ROLSI (Rapid On-line Sampler Injector) capillary samplers.1 The Valderrama modification of the Patel-Teja equation of state (VPT-EoS)2 with nondensity dependent mixing rules (NDD)3 is used to model the fluid phases. The hydrate phase was modeled using the solid solution theory of van der Waals and Platteeuw.4 The fugacity of ice was calculated by correcting the saturation fugacity of water at the same temperature using the Poynting correction. The binary interaction parameters (BIP) between hydrogen sulfide and water were tuned using the new experimental results on hydrogen sulfide solubility in water. The new experimental water content data are then compared with the model predictions. The predictions are in good agreement, demonstrating the reliability of the experimental technique and the modeling work used in this study. The developed model is finally used to estimate the deviations between the literature data and predictions. 2. Review of Experimental Data 2.1. Hydrogen Sulfide Solubility in Water. Two reviews on this topic have been published.5,6 The
10.1021/ie050201h CCC: $30.25 © 2005 American Chemical Society Published on Web 08/18/2005
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Ind. Eng. Chem. Res., Vol. 44, No. 19, 2005
Table 1. List of Experimental Gas Solubility Data (Vapor-Liquid Equilibrium) and Henry’s Constants for the Hydrogen Sulfide-Water System ref
T (K)
7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23a 24 25
273.15-363.15 298.15 278.15-333.15 273.2-298.1 310.93-444.26 303.15-316.15 353.15 502.15 - 603.15 303.15 323.15-443.15 273.15-323.15 273.15-293.15 283.15-453.15 275.25-303.07 310.93-588.70.3-13.8 297.15-367.15 313.15-378.15 293.95-594.15 313.15
7 9 11 14 26 17 19 27 22 28 24 29 30
273.15-363.15 278.15-333.15 310.93-444.26 433.15-603.15 273.15-458.15 273.15-323.15 283.15-453.15 313.15-623.15 298.15-358.5
P (MPa) solubility data atmospheric atmospheric 0.04-0.5 atmospheric 0.7-20.7 1.7 2.8-12.6 atmospheric 1.7-2.3 0.05-0.1 atmospheric ≈0.3-6.5 atmospheric 15 atmospheric 2.8-9.24 0.2-13.9 0.5-2.5
no. of exptl points 14 1 52 3 63 15 12 1 35 35 3 >270 5 6.7(6.6) 39 5 49 9
AADb (%) 5.6(5.6) 15.4(11.5) 8.5(8.5) 10.1(8.7) 4.1(4.1) 5.9(3.4) 6.7(6.7) 4.1(3.7) 5.7(6.3) 7.0(3.7) 2.7(2.7)
Henry’s constants
293.15-593.15 298-333.15 298.15-313.15
n/ac
14 9 5 10 9 9 10 >98 4 74 3 2
a Solubility on the vapor-liquid water-liquid hydrogen sulfide (VLL) locus. b Average absolute deviations (AAD) in blankets are in the N 273.15-338.4 K temperature range; AAD ) (1/N) ∑i)1 |(xi,exp - xi,cal)/xi,exp|. c n/a ) not available.
Figure 1. Location of the H2S solubility data below 373.15 K in the P vs T plot. The dashed line is the hydrogen sulfide-water vapor-liquid hydrogen sulfide-liquid water/hydrate locus (model predictions), the solid line is the hydrate dissociation line (model predictions), and the gray line is the water vapor pressure. (], literature data; [, this work).
authors have gathered a large number of available experimental data. Carroll and Mather5 have also developed a Henry’s law correlation. Table 1 presents the literature data with temperature and pressure ranges, number of data points, statistical analysis, and the source of data. Figure 1 shows the temperatures and pressures of all the data investigated in this work. 2.2. Water Content in the Vapor Phase of the Hydrogen Sulfide-Water System. The list of experi-
mental data reported in the literature on the water content of the vapor phase appears in Table 2 (data are plotted in Figure 2). Table 2 displays the temperature and pressure ranges, number of data points, statistical analysis, and the source of the data. As can be seen, there are limited data on the water content of the H2Srich phase, indicating a need for new data. As shown in Figure 2, the water content in the vapor phase of the H2S-H2O system is pressure and temperature dependent. At sub-critical conditions and constant temperature, the water content in the vapor phase is normally a decreasing function of total pressure. However, in supercritical conditions, this is verified only in a limited pressure range (e.g., around 8-10 MPa) (see Figure 2). 2.3. Phase Equilibria for Hydrogen Sulfide Hydrates. Hydrogen sulfide is known to form structure I gas hydrates under the appropriate temperature and pressure conditions. As hydrogen sulfide is sub-critical at hydrate forming conditions and has a relatively low vapor pressure, different phases can be found in the hydrogen sulfide-water system: a hydrate phase, a water-rich liquid phase, an ice phase, a hydrogen sulfide-rich vapor phase, and a hydrogen sulfide-rich liquid phase, as well as two quadruple points (e.g., Q1 at 272.8 K and 0.093 MPa and Q2 at 302.7 K and 2.239 MPa).11 Experimental data for hydrogen sulfide hydrates have been measured and reported by various authors in different hydrate regions. Table 3 gives a list of these data, reporting the temperature range, the number of data points, and the source of the experi-
Ind. Eng. Chem. Res., Vol. 44, No. 19, 2005 7569 Table 2. List of Experimental Water Content Data for the Hydrogen Sulfide-Water System ref
T (K)
P (MPa)
no. of exptl points
AAD (%)
9 11 12 16 19 21 23
278.15-333.15 310.93-444.3 303.15-316.15 323.15-443.15 363.15-443.15 310.93-583.15 313.15-378.15
0.04-0.5 0.6-20.7 1.7 1.7-2.3 1.5-3.5 up to VLL Locus 2.8-9.24
52 63 15 35 15 17 5
12.6a 11.0b 11.5 3.9 20.4 4.1 56.2
a Without taking into consideration points measured in equilibrium with metastable water. b Without taking into consideration the set of data at T)377.59 K.
Figure 2. Experimental data on the water content of vapor phase. The dashed line is the hydrogen sulfide-water vapor-liquidliquid locus (model predictions), the gray solid line is the hydrate dissociation line (model predictions), and the solid lines are the predicted water content from left to right at 278.15-338.15 (every 5 K), 344.26, 363.15, 377.59, 383.15, 403.15, 410.93, 423.15, and 444.26 K (O, this work; b, data from Wright and Mass;9 ×, data from Clarke and Glew;17 [, data from Burgess and Germann;16 2, data from Selleck et al.;11 0, data from Gillespie and Wilson;21 4, data from Carroll and Mather23). Table 3. List of Experimental Data for Dissociation Conditions of Hydrogen Sulfide Hydrates ref
T (K)
no. of exptl points
31 11
ice-hydrate-vapor 247.15-272.15 250.5-272.8
16 10
32a 33a 34 35 31 9 36 11 5
liquid water-hydrate-vapor 273.65-301.65 274.15-298.15 273.15-278.35 289.65-302.65 274.15-280.15 275.35-283.65 283.2-302.7 272.8-302.7 298.6-300.8
11 10 16 11 4 5 4 14 13
11 5
liquid hydrogen sulfide-hydrate-vapor 259.2-302.7 15 298.6-302.6 19
32 11
liquid hydrogen sulfide-hydrate-liquid water 302.65 (Q2) 1 302.7-305.4 17
a
Hydrate formation measurements.
mental data. These data are plotted in Figure 3a and b. Results from de Forcrand32 and Cailletet and Bordet33 are also plotted in Figure 3a and b, although they reported the pressure of hydrate formation. 3. Experimental Section 3.1. Materials. Hydrogen sulfide was purchased from Air Liquide with a certified purity greater than 99.995
Figure 3. (a) Comparison of the experimental and predicted dissociation conditions for H2S hydrates (2, data from Selleck et al.;11 4, data from Scheffer and Meyer;31 0, data from Scheffer;35 *, data from de Forcrand and Villard;34 9, data from Cailletet and Bordet;$, 33 O, data from de Forcrand;$, 32 ], data from de Forcrand(Q2);32 gray filled circles, data from Wright and Mass;9 gray filled triangles, data from Bond and Russell;36 [, data from Burgess and Germann;16 +, data from Carroll and Mather23). V, I, LH2O, LH2S, and H stand for the vapor, ice, liquid water, liquid hydrogen sulfide, and hydrate states, respectively. (b) Comparison of the experimental and predicted dissociation conditions for H2S hydrates (2, data from Selleck et al.;11 4, data from Scheffer and Meyer;31 0, data from Scheffer;35 *, data from de Forcrand and Villard;34 9, data from Cailletet and Bordet;33 O, data from de Forcrand;32 ], data from de Forcrand(Q2);32 gray filled circles, data from Wright and Mass;9 gray filled traingles, data from Bond and Russell;36 [, data from Burgess and Germann;16 +, data from Carroll and Mather23).
vol %. Helium (carrier gas), from Air Liquide, is pure grade with only traces of water (3 ppm) and hydrocarbons (0.5 ppm). Deionized water was used after careful degassing. 3.2. Apparatus. The apparatus used in this work is based on a static-analytic method with fluid phase sampling. This apparatus is similar to that described originally by Chapoy et al.37 and Mohammadi et al.38 The phase equilibrium is achieved in a cylindrical cell
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made of sapphire, the cell volume is about 28 cm3 (internal diameter ) 25 mm) and it can be operated at up to 8 MPa of pressure between 223.15 and 473.15 K. The cell is immersed in an ULTRA-KRYOMAT LAUDA constant-temperature liquid bath that controls and maintains the desired temperature within ( 0.01 K. To perform accurate temperature measurements in the equilibrium cell and to check for thermal gradients, the temperature is measured at two locations corresponding to the vapor and liquid phases through two 100 Ω platinum resistance thermometer devices (Pt100) connected to an HP data acquisition unit (HP34970A). The two Pt100 devices are carefully and periodically calibrated against a 25 Ω reference platinum resistance thermometer (TINSLEY Precision Instruments). The resulting uncertainty is not higher than (0.02 K. The 25 Ω reference platinum resistance thermometer was calibrated by the Laboratoire National d'Essais (Paris) based on the 1990 International Temperature Scale (ITS 90). Pressure is measured by means of a Druck pressure transducer connected to the HP data acquisition unit (HP34970A); the pressure transducer is maintained at a constant temperature (temperature higher than the highest temperature of the study) by means of a specially made air-thermostat, which is controlled using a PID regulator (WEST, model 6100). The pressure transducer is calibrated against a dead weight pressure balance (Desgranges & Huot 5202S, CP 0.3 to 40 MPa, Aubervilliers, France). Pressure measurement uncertainties are estimated to be within (1 kPa in the 0.2 to 5 MPa range. The analytical work was carried out using a GC (VARIAN model CP-3800) equipped with a thermal conductivity detector (TCD) connected to a data acquisition system fitted with BORWIN software (version 1.5, from JMBS, Le Fontanil, France). The analytical column is a Hayesep R 100/120 mesh column (silcosteel tube; length, 1.5 m; diameter, 1/8 in.). The TCD was used to detect both compounds; it was repeatedly calibrated by injecting known amounts of each compound through “liquid-type” syringes for water and through “gas-type” syringes for hydrogen sulfide. The uncertainties on the calculated moles of water are estimated to be within (2% in the 1.6 × 10-5-2 × 10-4 mol range (calibration for the liquid phase) and to be within (5% in the 2 × 10-8-2 × 10-7 mol range (calibration for the vapor phase). The relative uncertainties on the hydrogen sulfide mole numbers are about (2% (in the whole calibration range). The sampling is carried out using capillary samplers, ROLSITM1, for each phase. Two capillary sampler injectors, for each phase, are connected to the cell through two 0.1 mm internal diameter capillary tube. The withdrawn samples are swept to the Varian 3800 gas chromatograph for analysis. 3.3. Experimental Procedure. The equilibrium cell and its loading lines were evacuated down to 0.1 Pa prior to the introduction of about 5 cm3 of degassed water. Then, hydrogen sulfide is introduced into the cell directly from the commercial cylinder (through preliminary evacuated transfer lines) to a pressure level corresponding to the pressure of the first measurement. More hydrogen sulfide is introduced after each sampling and analysis steps up to the highest pressure of the studied solubility curve. After each introduction of gas into the cell, efficient stirring is started and the pressure is stabilized within a few minutes; solubility measurements are performed only when the pressure is constant within the experimental uncertainty (pressure is veri-
Table 4. Critical Properties and Acentric Factors39 compound
Pc (MPa)
Tc (K)
vc (m3 kmol-1)
ω
water hydrogen sulfide
22.048 8.940
647.30 373.20
0.0560 0.0986
0.3442 0.0810
fied to be constant throughout the sample analyses). For each equilibrium condition, at least 10 samples of both liquid and vapor phases are withdrawn using the ROLSITM 1 pneumatic samplers and are analyzed to check for measurement repeatability. 4. Thermodynamic Model 4.1. Pure Compound Properties. The critical temperature (Tc), critical pressure (Pc), critical volume (vc), and acentric factor (ω) for each pure compound are provided in Table 4. 4.2. Description of the Model. A general phase equilibrium model based on the equality of fugacity of each component throughout all the phases39,40 is used to model the equilibrium conditions. The VPT-EoS2 with NDD mixing rules3 was used to determine component fugacities in the fluid phases. This combination has proved to be a strong tool in modeling systems with polar as well as nonpolar compounds.3 The VPT-EoS2 is given by
P)
RT a v - b v(v + b) + c(v - b)
(1)
with
a)a j R(Tr) 2
(2) 2
ΩaR Tc Pc
(3)
b)
ΩbRTc Pc
(4)
c)
Ωc*RTc Pc
(5)
a j)
R(Tr) ) [1 + F(1 - TrΨ)]2
(6)
where P, R, and T refer to pressure, the gas constant, and temperature, respectively. The variables v, a, a j , b, c, and R(Tr) stand for the molar volume, the attractive parameter, the parameter of the equation of state, the repulsive parameter, the parameter of the equation of state, and the temperature dependent function, respectively, and ψ ) 0.5. The subscripts c and r denote critical and reduced properties, respectively. The coefficients Ωa, Ωb, Ωc*, and F are given by
Ωa ) 0.66121 - 0.76105Zc
(7)
Ωb ) 0.02207 + 0.20868Zc
(8)
Ωc* ) 0.57765 - 1.87080Zc
(9)
F ) 0.46283 + 3.58230(ωZc) + 8.19417(ωZc)2
(10)
where Zc is the critical compressibility factor and ω is the acentric factor. Tohidi-Kalorazi41 relaxed the alpha function for water, Rw(Tr), using experimental water vapor pressure data in the range of 258.15 to 374.15 K to improve the predicted water fugacity
Ind. Eng. Chem. Res., Vol. 44, No. 19, 2005 7571
Rw(Tr) ) 2
3
2.4968 - 3.0661Tr + 2.7048Tr - 1.2219Tr (11) This relationship is used in the present work. In this work, the NDD mixing rules developed by Avlonitis et al.3 are applied to describe mixing in the a parameter
a ) aC + aA
(12)
where aC is given by the classical quadratic mixing rules as follows
aC )
∑i ∑j xixjaij
(13)
c)
hydrogen sulfide a
∑i xibi
(14)
∑i xici
(15)
aij ) (1 - kij)xaiaj
(16)
∑p xp2∑i xiapilpi
(17)
api ) xapai
(18)
l1pi
(19)
lpi )
-
l2pi(T
- T0)
where p is the index of polar components and l represents the binary interaction parameter for the asymmetric term. Superscripts 1 and 2 refer to the nontemperature-dependent and temperature-dependent terms in the NDD mixing rules,3 respectively, and T0 stands for the reference temperature, 273.15 K. Using the VPT-EoS2 and NDD mixing rules,3 the fugacity of each component in all fluid phases is calculated from
ln φi )
1 RT
[( )
∫Vh∞
∂P ∂ni
]
- RT/V h dV h - ln Z
T,V h ,nj*i
(20)
for i ) 1, 2, ..., nc
fi ) xiφiP
(21)
where φ, n, Z, and f refer to fugacity coefficient, number of moles, compressibility factor, and fugacity, respectively. V h and nc are the total volume and number of components, respectively. The fugacity of ice is rigorously calculated by correcting the saturation fugacity of water at the same temperature by using the Poynting correction
fIw
)
sat φsat w PI
(
σ*a (Å)
/k′ (Κ)
0.7178
2.877
210.6
σ* ) σ - 2R.
to water and ice, respectively. The term fIw is the fugacity of water in the ice phase, φsat w is the water fugacity coefficient in the vapor phase at pressure equal to the ice vapor pressure, Psat I is the ice vapor pressure, and vI is the ice molar volume. The ice molar volume, vI, is calculated using the following expression41
where vI and T are in m3 gmol-1 and K, respectively. 41 The ice vapor pressure, Psat I , is calculated using
log(Psat I ) ) -1033/T + 51.06 log(T) - 0.09771T + 7.036 × 10-5 × T2 - 98.51 (24) where T and Psat I are in K and mm Hg, respectively. The fugacity of water in the hydrate phase, fH w , is given by42
where k is the BIP. The term aA corrects for asymmetric interaction, which cannot be efficiently accounted for by classical mixing rules
aA )
R (Å)
vI ) [19.655 + 0.0022364(T - 273.15)] × 10-6 (23)
where x stands for the mole fraction and subscripts i and j denote components i and j, respectively. Variables b, c, and aij are expressed by
b)
Table 5. Kihara Potential Parameters for Hydrogen Sulfide-Water Interactions41
)
vI(P - Psat I ) exp RT
(22)
where superscripts I and sat stand for ice and saturation conditions, respectively, and subscripts w and I refer
fH w
)
fβw
(
)
∆µβ-H w exp RT
(25)
where superscripts H and β refer to hydrate and empty hydrate lattice, respectively, and µ stands for the chemical potential. The term fβw is the fugacity of water is the chemin the empty hydrate lattice, while ∆µβ-H w ical potential difference of water between the empty hydrate lattice, µβw, and the hydrate phase, µH w , which is given by the following equation:4,42,43
) µβw - µH ∆µβ-H w w ) RT
vj m ln(1 + ∑Cmjfj) ∑ m j
(26)
where vj m is the number of cavities of type m per water molecule in the unit cell, fj is the fugacity of the gas component j, and Cmj is the Langmuir constant, which is a function of temperature according to the relationship 4,42,43
Cmj(T) )
4π k′T
∫0∞ exp(- k′T )r2dr w(r)
(27)
where k′ is the Boltzmann’s constant and w(r) is the spherically symmetric cell potential in the cavity, with r measured from center, and it depends on the intermolecular potential function chosen for describing the encaged guest-water interaction. In the present work, the Kihara potential function with a spherical core is used43
Γ(r) ) ∞ Γ(r) ) 4
12
r e 2R 6
[(r -σ*2R) - (r -σ*2R) ]
(28) r > 2R
where Γ(r) is the potential energy of interaction between two molecules when the distance between their centers is equal to r. The term is the characteristic energy, R is the radius of the spherical molecular core, and σ* ) σ - 2R where σ is the collision diameter (i.e., the
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distance where Γ ) 0). The Kihara potential parameters, R, σ, and , are taken from Tohidi-Kalorazi41 (Table 5). On the basis of the chosen potential energy function, the spherically symmetric cell potential in the cavities (eq 27) needs to be derived. McKoy and Sinanogˇlu44 summed up all of these guest-water binary interactions inside the cell to yield an overall cell potential43,44
[
w(r) ) 2z
(σ*)12 R h 11r
(δ
10
)]
(σ*)6 R R + δ11 - 5 δ4 + δ5 R h R h R h r
)
(
(29)
where δ is calculated using the following equation:
δNh )
1 r r R -Nh R -Nh 1- - 1+ N h R h R h R h R h
[(
)
) ]
(
(30)
where z is the coordination number of the cavity (i.e., the number of oxygen molecules at the periphery of each cavity), R h is the cavity radius, r is the distance of the guest molecule from the cavity center, and N h is an integer equal to 4, 5, 10, or 11. The fugacity of water in the empty hydrate lattice, fβw in eq 25, is given by42
fβw
)
fI/L w
(
)
∆µβ-I/L w exp RT
(31)
where superscript L stands for liquid and fI/L w is the fugacity of pure ice or liquid water, and the quantity inside the parentheses is given by the following equation:42,45
∆µβ-I/L µβw(T, P) µI/L w w (T, P) ) RT RT RT )
∆µ0w RT0
∫TT
0
∆hβ-I/L w RT2
dT +
∫0P
∆vβ-I/L w dP RT
(32)
where superscript 0 stands for reference property and h refers to molar enthalpy. µβw and µI/L w are the chemical potential of the empty hydrate lattice and of pure water in the ice (I) or liquid (L) state, respectively. ∆µ0w is the reference chemical potential difference between the water in the empty hydrate lattice and pure water at and ∆vβ-I/L are the molar enthalpy 273.15 K. ∆hβ-I/L w w and molar volume differences between an empty hyis given by drate lattice and ice or liquid water. ∆hβ-I/L w the following equation:42,45
) ∆h0w + ∆hβ-I/L w
∫TT∆C′Pw dT 0
(33)
where C′ and subscript P refer to molar heat capacity and pressure, respectively. ∆h0w is the enthalpy difference between the empty hydrate lattice and pure water, at the ice point and zero pressure. The heat capacity difference between the empty hydrate lattice and the pure liquid water phase, ∆C′Pw is also temperature dependent and the equation recommended by Holder et al.45 is used
∆C′Pw ) -37.32 + 0.179(T - T0)
T > T0
(34)
where ∆C′Pw is in J mol-1 K-1. Furthermore, the heat capacity difference between the hydrate structures and
Table 6. Thermodynamic Reference Properties for Structure I Hydrates reference property
value
ref
∆µow (J mol-1) ∆how (J mol-1)a ∆vw (cm3 mol-1)b -1 K-1)c ∆C′° Pw (J mol
1297 1389 3.0 -37.32
46 46 43 45
a In the liquid water region subtract 6009.5 J mol-1 from ∆ho . w In the liquid water region add 1.601 cm3 mol-1 to ∆vw. c Values 45 to be used in ∆C′Pw ) ∆C′° Pw + 0.179(T - To).
b
Table 7. Experimental (xH2S,exp) and Calculated(xH2S,cal) H2S Mol Fractions in the Aqueous Phase of H2S-H2O Systems T (K)
P (MPa)
xH2S,exp × 103
xH2S,cal × 103
ADa (%)
298.16 298.16 298.16 308.2 308.2 308.2 308.2 308.2 308.2 318.21 318.21 318.21 318.21 318.21 318.21 318.21 328.28 328.28 328.28 328.28 328.28 328.28 328.28 338.34 338.34 338.34 338.34 338.34 338.34 338.34 338.34
0.503 0.690 0.797 0.483 0.763 1.193 1.748 2.175 2.483 0.507 1.053 1.507 2.024 2.139 2.570 3.094 0.497 1.008 1.498 1.978 2.468 3.034 3.475 0.509 0.536 1.053 1.688 2.215 2.796 3.370 3.962
9.12 12.78 14.69 6.69 10.69 17.09 24.73 30.36 34.01 5.81 12.50 17.87 23.90 24.72 29.59 35.07 4.96 10.05 14.89 19.50 24.41 29.50 33.56 4.35 4.59 9.23 14.71 19.15 24.20 28.82 31.83
9.32 12.69 14.59 7.14 11.20 17.26 24.74 30.21 34.00 6.15 12.67 17.88 23.60 24.84 29.35 34.57 5.05 10.26 15.12 19.70 24.22 29.21 32.85 4.41 4.65 9.24 14.71 19.09 23.74 28.18 31.70
2.2 0.7 0.7 6.7 4.8 1.0 0.0 0.5 0.0 5.9 1.4 0.1 1.3 0.5 0.8 1.4 1.8 2.1 1.5 1.0 0.8 1.0 2.1 1.4 1.3 0.1 0.0 0.3 1.9 2.2 0.4
a
AD ) |(xH2S,exp - xH2S,cal)/xH2S,exp|.
Table 8. BIPs between H2S and H2O for the VPT-EoS2 and NDD Mixing Rules3 system
kH2O-H2S
lH2O-H2S0
lH2O-H2S1 × 104
H2S - H2O
0.1231
0.3785
16.9462
ice is set equal to zero. The reference properties used are summarized in Table 6. 5. Results and Discussions To develop the thermodynamic model, the BIPs between hydrogen sulfide-water were adjusted directly to the new gas solubility data reported in Table 7 using a Simplex algorithm and the objective function, FOB, displayed in eq 35
FOB )
1
N
xi,exp - xi,cal | xi,exp
∑| Ni)1
(35)
where N is the number of data points, xi,exp is the measured solubility, and xi,cal is the calculated solubility. These BIPs are reported in Table 8. The newly generated solubility data sets are well represented with the VPT-EoS2 and NDD mixing rules3
Ind. Eng. Chem. Res., Vol. 44, No. 19, 2005 7573 Table 9. Experimental (yH2O,exp) and Predicted (yH2O,prd) Water Mole Fractions in the Vapor Phase of H2S-H2O Systems
Figure 4. H2S solubility in water from this work. The dashed line is the hydrogen sulfide-water liquid-liquid locus, and the gray solid line is the hydrate dissociation line (points for the new solubility data: b, 298.16 K; ], 308.2 K; [, 318.21 K; O, 328.28 K; 2, 338.34 K).
Figure 5. H2S solubility in water from selected literature data. The dashed line is the hydrogen sulfide-water liquid-liquid locus, and the gray solid line is the hydrate dissociation line (b, data from Wright and Mass;9 ×, data from Clarke and Glew;17 [, data from Burgess and Germann;16 O, data from Lee and Mather;19 2, data from Selleck et al.11).
with an AAD equal to 1.3%. The absolute deviations (AD) are reported in Table 7 and new data are plotted in Figure 4. Figure 5 shows a comparison between some of the selected literature data and model predictions. The agreement is good, indicating the reliability of the gas solubility data generated in the present work. Henry’s constants of H2S in H2O have been derived from our data adjusting parameters of eq 36
log(HH2S-H2O) ) 90.44 + 0.010845T - 3.792 × 103/T - 29.5008 log(T) (36) where H is Henry’s constant in MPa and T is the temperature in K. The developed thermodynamic model was then employed to predict new data on the water content of the H2S vapor phase. These data along with ADs are indicated in Table 9 and are plotted in Figure 2. The agreement is good with a 5.7% AAD, demonstrating the reliability of the data generated in this work. To further evaluate the reliability of the data and the performance of the model, a comparison between some selected literature data and the new water content data, as well as model predictions, is also made in Figure 2. Good agreement was achieved demonstrating the reliability of the data and the modeling work.
T (K)
P (MPa)
yH2O,exp × 102
yH2O,prd × 102
ADa (%)
298.16 298.16 308.20 308.20 308.20 308.20 308.20 308.20 318.21 318.21 318.21 318.21 318.21 318.21 318.21
0.503 0.690 0.503 0.762 0.967 1.401 1.803 2.249 0.518 0.999 1.053 1.519 1.944 2.531 2.778
6.53 4.70 10.46 7.19 5.77 4.38 3.64 3.20 21.28 11.30 11.16 7.44 5.92 4.70 4.61
6.64 4.94 11.78 7.99 6.43 4.65 3.79 3.21 19.47 10.58 10.09 7.34 6.00 4.93 4.63
1.7 5.1 12.6 11.1 11.4 6.2 4.1 0.3 8.5 6.4 9.6 1.3 1.4 4.9 0.4
a
AD ) |(yH2O,exp - yH2O,prd)/yH2O,exp|.
Below the critical temperature of hydrogen sulfide, there is good agreement between the different authors, with the exception of some data reported by Clarke and Glew17 at T < 293.15 K in the metastable region and the set of data reported by Carroll and Mather,23 however the authors state that at the lowest temperature the determination of the water content was inaccurate. At high-temperature conditions (i.e., T > 373.2 K), there is good agreement between the different authors, with the exception of the data reported by Lee and Mather.19 It should be noted that these researchers mentioned difficulties, in their paper, in obtaining satisfactory and reproducible water content measurements. The developed model was also used to evaluate the reliability of solubility data reported in the literature. Tables 1 and 2 show the AADs between the experimental and predicted data. As can be seen, the model predictions are generally in acceptable agreement with the experimental data collected from the open literature. Figure 3a and b shows the experimental and predicted phase boundaries for hydrogen sulfide hydrates. As can be seen, the model predictions are in acceptable agreement with the experimental data collected from the open literature, even with the oldest hydrate dissociation measurements. 6. Conclusions Accurate data on the phase equilibria of H2S-H2O systems are necessary for different purposes. In this work, we completed a comprehensive review of the literature data on H2S-H2O mutual solubilities and reported H2S hydrate dissociation conditions. We also reported new gas solubility and water content data for the H2S -H2O systems from 298.16-338.34 K for pressures up to 3.962 MPa. A technique based on a static analytic method with fluid phase sampling was used to generate the experimental data. The experimental gas solubility data were used to tune the binary interaction parameters between H2S and H2O in the EoS, and the resulting thermodynamic model was used to predict H2S solubility in water and the water content of the H2S vapor phase, as well as the H2S hydrate phase boundary, over wide ranges of temperature and pressure conditions. The predictions, from the model, are in good agreement with the experimental data demonstrating the reliability of the techniques used in this work. Acknowledgment Financial support from the European Infrastructure for Energy Reserve Optimization (EIERO) and the Gas
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Received for review February 19, 2005 Revised manuscript received June 10, 2005 Accepted June 23, 2005 IE050201H
