Phase Equilibria of H2S-Hydrocarbons (Propane, n-Butane, and n

Article pubs.acs.org/jced

Phase Equilibria of H2S-Hydrocarbons (Propane, n-Butane, and n-Pentane) Binary Systems at Low Temperatures Moussa Dicko,† Christophe Coquelet,*,‡,§ Pascal Theveneau,‡ and Pascal Mougin∥ †

Laboratoire des Sciences des Procédés et des Matériaux, Université Paris 13, CNRS Institut Galilée 99 avenue Jean-Baptiste Clément, 93430 Villetaneuse, France ‡ MINES ParisTech, CEP/TEP-Centre Energétique et Procédés, 35 Rue Saint Honoré, 77305 Fontainebleau, France § Thermodynamics Research Unit, School of Chemical Engineering, University of KwaZulu-Natal, Howard College Campus, Durban, South Africa ∥ IFP Energies Nouvelles, 1 & 4 avenue de Bois-Préau, 92852 Rueil-Malmaison Cedex, France ABSTRACT: Isothermal vapor−liquid equilibrium measurements of three binary systems, H2S + propane, H2S + n-butane, and H2S + n-pentane, have been performed with a static synthetic apparatus at low temperatures. The method of Barker has been implemented to determine the corresponding nonrandom two-liquid (NRTL) parameters and to calculate the liquid mole fractions. The results have been further used along with literature data to adjust binary interaction parameters of the Peng−Robinson equation of state. Good agreement with Dechema values has been found.

1. INTRODUCTION The share of natural gas in the world energy panorama has been appreciably growing for the last 30 years. This trend is expected to increase in the next decades with the progressive diversification of energy sources and the replacement of fuel oil and coal by this relatively environment-friendly source. However, this development will depend on the progress made in technologies allowing access to reserves not exploitable so far. Approximately 30 % of the natural gases produced are actually assumed to be acid gases. In others terms, these gases contain, along with hydrocarbons, acid compounds such as carbon dioxide, hydrogen sulfide, and other sulfur species (mercaptan, CS2, COS). Natural gas should be clear of these compounds before its transport. The quantity of acid gases should classically represent up to 30 % of the total composition. The technologies generally employed to remove these impurities are very often based on their absorption in chemical or/and physical solvents.1 Chemical solvents are mainly composed by aqueous solution of alkanolamine such as diethanolamine or methyl-diethanolamine. They rely on chemical reactions to remove acid gases from sour gas streams. In the case of physical solvents (mixtures of polar compounds like alcohols, ethers, amide in water), the high affinity of acid compounds for polar mixtures is used to remove them from gas streams. The regeneration of a chemical solvent requires heat to inverse the chemical reactions while a physical solvent can be regenerated by a pressure drop without heat. For high amounts of acid compounds, physical solvents tend to be favored over chemical ones.2 © 2012 American Chemical Society

To perform the design of a process with a physical solvent, phase equilibria between acid gases and hydrocarbons are needed. Although the open literature is rich about the carbon dioxide + hydrocarbons mixtures, the data in the presence of hydrogen sulfide are rarer due to the toxic nature of it. As mentioned by Lobo et al.,3 most of the experimental results available about H2S and lighter alkanes come from the years 1940 to 1960. Table 1 shows the available studies about hydrogen sulfur and lighter alkanes. Table 1. Literature Data of Systems Hydrogen Sulfur with Propane, n-Butane, and n-Pentane hydrocarbon propane

n-butane

n-pentane

T/K 243.15 272.04 182.33 324.26 217.04 366.45 182.33 310 to 277.59 207.59

to 288.15 to 366.48 to 367.04 to 344.26 to 418.15 340 to 444.26 to 420.37

reference Steckel20 (1945) Kay and Rambosek21 (1953) Lobo et al.3 (2006) Gilland and Scheeline22 (1940) Brewer and Rodewald23 (1961) Leu and Robinson24 (1989) Lobo et al.3 (2006) Robinson et al.25 (1964) Reamer et al.26 (1953) Cunningham27 (1986)

Received: January 24, 2012 Accepted: March 29, 2012 Published: April 19, 2012 1534

dx.doi.org/10.1021/je300111m | J. Chem. Eng. Data 2012, 57, 1534−1543

Journal of Chemical & Engineering Data

Article

3. METHOD OF DATA TREATMENT If the global composition in the equilibrium cell is known and an appropriate model is selected at equilibrium, the vapor and liquid compositions can be obtained using a mass balance. The method of data reduction assumes that, using two models (one for the liquid and another for the vapor phase, i.e., considering a gamma-phi approach), the bubble-point pressure can be predicted with higher accuracy than the experimental error of the measured total pressure. Abbot and van Ness consider that the method is more accurate considering the bubble pressure. Consequently, during the experiment, it is very important to minimize the vapor phase volume to be close to the bubble-point condition. So, the global composition in the cell, zi, is calculated with the mole number introduced into the cell.

Although data involving propane are relatively welldocumented, this is not the case for n-butane and n-pentane: the lower temperature range is still scarce. In this communication, new data are presented for such systems. The range of temperature is from (222.83 to 293.36) K. In the first part, the experimental equipment and the data treatment are described. In the second part of this work, the data are given.

2. EXPERIMENTAL SECTION The phase equilibria measurements have been accomplished with an apparatus which technique is based on synthetic isothermal method4−6 knowing the total pressure. The same technique was used by Haimi et al.7 for butanes and butenes with dimethylsulfide. The equilibrium cell, of which the volume is well-known, is loaded with a controlled amount of a first component and thermostated to a given temperature. Then, a precise amount of a second component is added leading to a rise of the total pressure. The global concentration in the equilibrium cell is known, and an appropriate flexible thermodynamic model is chosen to describe the mixture (vapor and liquid phases). Barker8 and Abbott and van Ness9 have demonstrated that the system is sufficiently defined at equilibrium conditions to obtain the coexisting fluid phases. 2.1. Chemical Products. Hydrogen sulfide (purity 99.5 vol %, checked by gas chromatography), propane (purity 99.95 vol %, checked by gas chromatography), and n-butane (purity 99.95 vol %, checked by gas chromatography) were purchased from Air Liquide. n-Pentane (purity 99 GC %) was purchased from Aldrich. 2.2. Description of the Equipment, Procedure, and Uncertainties. The equilibrium cell is made of a sapphire tube pressed between two pieces. The temperature is determined by two platinum probes inserted in both flanges. Platinum probes were calibrated against a reference resistance (Lyon Aleman Louyot STHP-B 25 Ohms) with an estimated accuracy of ± 0.02 K. The pressure is determined by two pressure transducers (PTX 611 from Druck 0.4 and 1.6 MPa). The two sensors are calibrated against a dead weight balance (Desgranges et Huot 5202 S CP). The estimated absolute errors concerning the two sensors are (0.05 and 0.3) kPa, respectively. The volume of the cell is estimated to be 32.377 ± 0.001 cm3 using one pressure transducer and 33.199 ± 0.001 cm3 using two pressure transducers. Similar equipment is described by Guilbot et al.10 The compressed liquid compounds are stored in volumetric pumps, which allow controlled injections of the compounds into the equilibrium cell. Each pump consists of one variable volume cylinder (internal diameter of 20.190 ± 0.020 mm) connected to one optico-electronic displacement transducer (model LS 406 C, digital display ND 221 from Heidenhain) with a precision of ± 0.003 mm and a pressurizing circuit (nitrogen). The overall accuracy of the charging unit is estimated lower than 0.005 in mole fraction. Prior to each experiment, the vacuum is obtained inside the equilibrium cell. It is thermostated at the desired temperature in the liquid bath (model HS 60 from Huber). A known amount of the first component is introduced into the equilibrium cell, and the vapor pressure of the pure component is recorded. Then, the second component is introduced into the cell through successive loadings. Equilibrium is obtained after an efficient stirring. For each injection of second component, the displacement of the piston is recorded, and from the quantity injected, the total composition is determined. Temperature and pressure are also recorded.

zi =

nitot NC

∑i = 1 nitot

(1)

This global composition is initially assumed to be equal to the liquid composition xi. Using a gamma-phi approach, the bubble pressure can be determined. ⎛ ∫ p v Ldp ⎞ ⎜ P sat i ⎟ v /Φ ) pcal = ∑ (xi γipisat Φisat ·exp⎜ i ⎜ RT ⎟⎟ i i=1 ⎝ ⎠ NC

(2)

where γi is the activity coefficient in the liquid phase, is the vapor pressure of the pure compound, Φsat is the fugacity i coefficient at the saturated conditions, and the exponential term is the Poynting correction which takes into account the pressure effect. Initially, the fugacity coefficients in the vapor phase are assumed to be equal to unity. In the iterative process, an equation of state is used to calculate the vapor molar volume and the fugacity coefficients. In this work, the classical cubic equation of state of Soave−Redlich−Kwong11,12 with the original alpha function is used to determine the fugacity coefficients and the vapor density. The calculation is repeated for all of the data points (Ndata). An activity coefficient model (nonrandom two-liquid, NRTL13) is selected with interaction parameters to represent the liquid Psat i

Table 2. Liquid Densities Pure Component Parameters14 (eq 9) component

hydrogen sulfide

propane

n-butane

n-pentane

A B C D

2.7672 0.27369 373.53 0.29015

1.3757 0.27453 369.83 0.29359

1.0677 0.27188 425.12 0.28688

0.84947 0.26726 469.7 0.27789

Table 3. Obtained NRTL Parameters

1535

system

T/K

τ1,2/cal·mol−1

τ2,1/cal·mol−1

H2S−propane H2S−propane H2S−n-butane H2S−n-butane H2S−n-butane H2S−n-butane H2S−n-butane H2S−n-pentane H2S−n-pentane H2S−n-pentane

243.19 273.11 222.83 243.03 262.99 283.23 293.36 223.19 243.01 263.03

709.0 687.0 1023.2 827.7 718.6 776.3 731.9 1038.2 1023.8 1019.5

35.1 −58.3 −89.6 −26.6 −43.9 −157.0 −166.0 −72.3 −152.8 −231.0



Article

Table 4. Experimental Resultsa and Calculated Mole Fractions in the Liquid Phase for the H2S−Propane System at 243.19 K

a

Texp/K

Pexp/MPa

zexp

xcalc

Texp/K

Pexp/MPa

zexp

xcalc

243.22 243.23 243.24 243.23 243.22 243.23 243.22 243.23 243.23 243.23 243.23 243.22 243.22 243.22 243.22 243.22 243.22 243.22 243.22 243.22 243.22 243.22 243.21 243.22 243.23 243.23 243.23 243.23 243.23 243.23 243.23 243.23 243.22 243.22 243.22 243.22 243.23 243.22 243.22 243.22 243.22 243.22 243.22

0.1758 0.1870 0.2078 0.2271 0.2467 0.2646 0.2807 0.2938 0.3055 0.3165 0.3231 0.3299 0.3369 0.3439 0.3509 0.3589 0.3671 0.3748 0.3832 0.3957 0.4052 0.4121 0.4134 0.4147 0.1680 0.1813 0.1962 0.2243 0.2498 0.2696 0.2898 0.3084 0.3237 0.3388 0.3520 0.3643 0.3896 0.4024 0.4052 0.4090 0.4111 0.4120 0.4124

0.010 0.024 0.050 0.076 0.105 0.134 0.162 0.187 0.211 0.235 0.251 0.268 0.287 0.307 0.329 0.356 0.388 0.422 0.465 0.549 0.639 0.740 0.767 0.788 0.000 0.016 0.034 0.070 0.107 0.139 0.175 0.212 0.248 0.287 0.327 0.372 0.500 0.605 0.634 0.680 0.713 0.724 0.730

0.010 0.023 0.047 0.072 0.100 0.129 0.156 0.181 0.205 0.229 0.245 0.262 0.281 0.302 0.324 0.351 0.384 0.418 0.462 0.547 0.638 0.739 0.767 0.788 0.000 0.015 0.032 0.067 0.103 0.135 0.171 0.207 0.243 0.283 0.323 0.369 0.499 0.605 0.634 0.680 0.713 0.724 0.730

243.23 243.23 243.18 243.18 243.19 243.19 243.19 243.18 243.18 243.19 243.19 243.19 243.19 243.19 243.19 243.19 243.19 243.19 243.19 243.18 243.21 243.20 243.21 243.20 243.21 243.21 243.21 243.21 243.21 243.21 243.21 243.21 243.20 243.20 243.20 243.21 243.21 243.21 243.21 243.21 243.21 243.20

0.4127 0.1682 0.3823 0.3840 0.3879 0.3922 0.3973 0.4013 0.4051 0.4078 0.4100 0.4121 0.4128 0.4130 0.4127 0.4121 0.4115 0.4106 0.4101 0.3802 0.3828 0.3860 0.3885 0.3911 0.3929 0.3940 0.3959 0.3978 0.4002 0.4023 0.4044 0.4068 0.4087 0.4100 0.4113 0.4118 0.4118 0.4115 0.4112 0.4103 0.4097 0.3794

0.732 0.000 0.996 0.993 0.985 0.974 0.959 0.943 0.924 0.904 0.884 0.851 0.819 0.787 0.757 0.733 0.709 0.684 0.669 1.000 0.994 0.987 0.981 0.974 0.970 0.966 0.961 0.954 0.944 0.934 0.922 0.906 0.889 0.870 0.847 0.822 0.796 0.774 0.751 0.729 0.708 1.000

0.732 0.000 0.996 0.993 0.985 0.974 0.959 0.943 0.924 0.904 0.884 0.851 0.819 0.787 0.757 0.733 0.709 0.684 0.669 1.000 0.994 0.987 0.981 0.975 0.970 0.967 0.961 0.955 0.944 0.934 0.922 0.906 0.889 0.870 0.847 0.822 0.796 0.774 0.751 0.729 0.707 1.000

Uncertainty u(T,k = 2) = ± 0.02 K; u(P,k = 2) = ± 0.05 kPa; u(z) = ± 0.005.

The mole number in the vapor phase is calculated from mass balance in the equilibrium cell.

phase. These parameters are determined by minimizing the objective function on the pressure. F=

1 Ndata

NP

⎛ |p − p | ⎞ cal exp ⎟ ⎟ p ⎠ ⎝ exp

∑ ⎜⎜ 1

0 = Vcell − [v L(n tot − n V ) + v V n V ] (3)

The molar volume of the vapor phase is directly obtained from the equation of state. The vapor composition is determined from:

The next step is the determination of the number of moles in the vapor phase. The total volume of the cell is well-known a priori. Concerning the liquid molar volume, since the excess volume is unknown, we used:

∑ xiviL i=1

⎛ p v L dp ⎞ ⎜ P sat i ⎟ v sat sat xi γipi Φi ·exp⎜ i ⎟⎟ /Φi pcal ⎜

∫

yi =

NC

vL =

(5)

(4)

⎝

RT

⎠

(6)

Finally, the mole number of each component in the vapor phase is then calculated.

The molar volume of each pure compound is calculated from specific correlations as explained in the next paragraph. 1536



Article

Table 5. Experimental Resultsa and Calculated Mole Fractions in the Liquid Phase for the H2S−Propane System at 273.11 K

Table 6. Experimental Resultsa and Calculated Mole Fractions in the Liquid Phase for the H2S−n-Butane System at 222.83 K

Texp/K

Pexp/MPa

zexp

xcalc

Texp/K

Pexp/MPa

zexp

xcalc

273.12 273.12 273.12 273.12 273.12 273.12 273.11 273.11 273.12 273.12 273.11 273.12 273.12 273.12 273.11 273.12 273.12 273.12 273.12 273.12 273.11 273.12 273.12 273.12 273.12 273.13 273.11 273.1 273.11 273.1 273.1 273.1 273.11 273.1 273.11 273.1 273.11 273.12 273.12

1.0334 1.0406 1.0496 1.0723 1.0802 1.0801 1.0746 1.0548 1.0329 1.0302 1.0327 1.0382 1.0477 1.0583 1.0708 1.0772 1.0788 1.0795 1.0798 1.0795 1.0790 1.0775 1.0755 1.0709 1.0610 1.0293 0.5038 0.5456 0.5877 0.6342 0.6820 0.7416 0.8041 0.8581 0.9077 0.9476 0.9865 1.0271 0.4735

0.996 0.987 0.973 0.919 0.865 0.816 0.763 0.661 0.585 1.000 0.996 0.989 0.976 0.956 0.921 0.888 0.870 0.855 0.840 0.823 0.808 0.791 0.769 0.740 0.688 1.000 0.019 0.044 0.072 0.104 0.139 0.187 0.244 0.300 0.361 0.419 0.487 0.578 0.000

0.996 0.987 0.974 0.919 0.866 0.816 0.762 0.660 0.585 1.000 0.996 0.989 0.976 0.957 0.921 0.888 0.871 0.855 0.840 0.823 0.808 0.790 0.769 0.740 0.688 1.000 0.017 0.042 0.068 0.099 0.133 0.181 0.237 0.294 0.355 0.415 0.484 0.577 0.000

222.83 222.83 222.84 222.82 222.83 222.82 222.83 222.83 222.82 222.84 222.83 222.83

0.1655 0.1632 0.1605 0.1579 0.1555 0.1530 0.1500 0.1464 0.1424 0.1371 0.1307 0.1673

0.983 0.958 0.926 0.889 0.850 0.802 0.742 0.673 0.603 0.522 0.442 1.000

0.983 0.958 0.925 0.888 0.849 0.801 0.740 0.671 0.601 0.521 0.442 1.000


a


a Uncertainty u(T,k = 2) = ± 0.02 K; u(P,k = 2) = ± 0.05 kPa; u(z) = ± 0.005.

V niV = yn i

(7)

nLi

For the liquid phase, = then determined from: xi =

niL NC ∑i = 1 niL

ntot i

−

nVi

a new liquid composition is

Texp/K

Pexp/MPa

zexp

xcalc

243.03 243.01 243.02 243.04 243.03 243.03 243.03 243.03 243.03 243.02 243.03 243.03 243.03 243.03 243.02 243.04 243.03 243.03 243.03 243.02 243.03 243.02 243.03 243.03 243.03 243.02

0.0291 0.3800 0.3760 0.3724 0.3677 0.3620 0.3564 0.3503 0.3440 0.3377 0.3306 0.3209 0.3119 0.2995 0.2859 0.0488 0.0669 0.0914 0.1093 0.1322 0.1532 0.1832 0.2097 0.2365 0.2583 0.3840

0.000 0.982 0.964 0.947 0.923 0.893 0.860 0.822 0.781 0.740 0.695 0.636 0.584 0.520 0.455 0.022 0.044 0.075 0.099 0.132 0.164 0.214 0.266 0.326 0.383 1.000

0.000 0.981 0.964 0.946 0.922 0.892 0.858 0.819 0.778 0.737 0.691 0.633 0.581 0.519 0.454 0.021 0.042 0.072 0.096 0.128 0.160 0.210 0.261 0.322 0.379 1.000


a

(8)

volume of the equilibrium cell. The operator must take care about the molar quantity and purity of each component introduced into the cell and control the stability of the temperature and so the pressure. The main advantage is that we do not need an appropriate analytical device, consequently to calibrate it and to take care of the sampling of each phase. The duration of the experiment is then reduced. However this method can only be applied for low pressure measurements: this technique needs the selection of an appropriate model with

The procedure is repeated until the change in both vapor and liquid phases' mole numbers (or compositions) are below the tolerance. In this work, a deviation lower than 10−8 is applied.

4. RESULTS AND DISCUSSION Before the presentation of the results, the authors would like to discuss the advantages and limitations of this principle. This method needs only calibrations on temperature, pressure, and 1537



Article

Table 8. Experimental Resultsa and Calculated Mole Fractions in the Liquid Phase for the H2S−n-Butane System at 262.99 K Texp/K

Pexp/MPa

zexp

xcalc

263.00 262.99 263.00 262.99 262.99 262.99 263.00 262.97 263.00 262.99 263.01 263.00 263.02 262.99 262.99 263.01 262.99 263.00 263.00 263.01 262.99 262.99 263.01 263.00

0.7582 0.7549 0.7508 0.7437 0.7364 0.7271 0.7163 0.7031 0.6894 0.6752 0.6629 0.1303 0.1723 0.2111 0.2453 0.2792 0.3378 0.3713 0.4069 0.4377 0.4710 0.5042 0.5365 0.5743

0.994 0.987 0.977 0.962 0.944 0.922 0.894 0.858 0.817 0.772 0.731 0.042 0.074 0.105 0.133 0.163 0.219 0.253 0.293 0.330 0.373 0.422 0.474 0.543

0.994 0.987 0.977 0.961 0.944 0.921 0.893 0.857 0.816 0.771 0.731 0.039 0.070 0.099 0.127 0.156 0.211 0.245 0.285 0.323 0.367 0.416 0.469 0.540


Uncertainty u(T,k = 2) = ± 0.02 K; u(P,k = 2) = ± 0.05 kPa; u(z) = ± 0.005. a

Table 9. Experimental Resultsa and Calculated Mole Fractions in the Liquid Phase for the H2S−n-Butane System at 283.23 K Texp/K

Pexp/MPa

zexp

xcalc

283.21 283.21 283.20 283.22 283.18 283.20 283.21 283.21 283.21 283.21 283.21 283.20 283.21 283.21 283.21 283.21 283.21 283.21 283.21 283.30 283.30 283.29 283.30 283.30 283.30 283.31 283.28 283.28 283.31

0.2047 0.2559 0.3056 0.4100 0.4608 0.4990 0.5515 0.5976 0.6591 0.6978 0.7484 0.7910 0.8473 0.8968 0.9455 0.9966 1.0479 1.1000 1.1476 1.3745 1.3646 1.3526 1.3388 1.3216 1.2983 1.2705 1.2394 1.1982 1.1402

0.027 0.054 0.080 0.137 0.166 0.188 0.219 0.247 0.286 0.312 0.346 0.377 0.419 0.460 0.502 0.550 0.601 0.657 0.712 0.991 0.980 0.967 0.951 0.931 0.903 0.867 0.827 0.773 0.698

0.024 0.048 0.072 0.125 0.153 0.175 0.205 0.232 0.271 0.297 0.332 0.363 0.407 0.449 0.493 0.543 0.596 0.654 0.711 0.991 0.980 0.966 0.950 0.930 0.901 0.865 0.824 0.770 0.696

Texp/K

Pexp/MPa

zexp

xcalc

293.38 293.38 293.38 293.37 293.38 293.38 293.36 293.37 293.40 293.38 293.35 293.39 293.39 293.36 293.38 293.36 293.36 293.40 293.36 293.32 293.35 293.39 293.36 293.36 293.26 293.37 293.33 293.34 293.34 293.37 293.31 293.43

0.2108 0.2548 0.3117 0.3770 0.4413 0.4950 0.5809 0.6647 0.7293 0.7903 0.8521 0.9120 0.9675 1.0197 1.0778 1.1547 1.2285 1.5091 1.5347 1.5601 1.5868 1.6181 1.6577 1.6720 1.7051 1.7311 1.7455 1.7653 1.7740 1.7832 1.7865 1.7937

0.000 0.019 0.043 0.071 0.099 0.123 0.162 0.200 0.231 0.262 0.293 0.325 0.356 0.385 0.420 0.467 0.517 0.740 0.764 0.788 0.813 0.843 0.880 0.893 0.923 0.946 0.959 0.976 0.984 0.992 0.996 1.000

0.000 0.017 0.039 0.064 0.091 0.114 0.151 0.188 0.219 0.249 0.281 0.313 0.344 0.374 0.410 0.459 0.510 0.739 0.762 0.786 0.811 0.841 0.878 0.891 0.922 0.945 0.958 0.976 0.984 0.992 0.996 1.000


a

several parameters. One important thing concerns the determination of the molar volume for both phases especially for the liquid phase. The quality of the results depends on the accuracy of the selected thermodynamic model. The results are more accurate when the excess volume of the liquid phase is known (at low pressure). Concerning our study, the liquid molar density of each compound was calculated using the DIPPR correlation14 (see eq 9). This equation is used to estimate the liquid molar volume mentioned in the mass balance (eq 5). Table 2 gives the parameter values. A ρ/kmol ·m−3 = D (1 + (1 − TC ) ) (9) B The excess Helmholtz free energy is calculated through the NRTL (Renon and Prausnitz13) local composition model. G (T , P )E = RT

∑ xi ∑ i

j

τj , i

(

xj exp −αj , i RT

(

) τk , i

∑k xk exp −αk , i RT

)

τj , i (10)

τi,i = 0 and αi,i = 0. αj,i, τj,i, and τi,j are adjustable parameters. For our system which belongs to a given polar mixture type, it is recommended10 to


1538



Article

Table 11. Experimental Resultsa and Calculated Mole Fractions in the Liquid Phase for the H2S−n-Pentane System at 223.19 K

Table 13. Experimental Resultsa and Calculated Mole Fractions in the Liquid Phase for the H2S−n-Pentane System at 263.03 K

Texp/K

Pexp/MPa

zexp

xcalc

Texp/K

Pexp/MPa

zexp

xcalc

223.11 223.11 223.13 223.13 223.13 223.15 223.15 223.15 223.15 223.18 223.18 223.18 223.19 223.22 223.22 223.23 223.23 223.24 223.27 223.28 223.28

0.1040 0.1502 0.0423 0.1458 0.1478 0.0881 0.1179 0.1268 0.0672 0.0173 0.1388 0.1425 0.1483 0.1501 0.1469 0.1532 0.1519 0.1598 0.1556 0.1635 0.1576

0.301 0.764 0.106 0.682 0.726 0.232 0.375 0.443 0.171 0.056 0.573 0.631 0.739 0.774 0.703 0.845 0.810 0.935 0.879 0.974 0.913

0.296 0.764 0.102 0.681 0.725 0.227 0.371 0.439 0.167 0.054 0.571 0.629 0.739 0.774 0.702 0.845 0.809 0.935 0.879 0.974 0.912

262.85 262.85 262.85 262.85 262.92 262.92 262.93 262.93 262.93 262.93 262.93 262.93 262.93 263.18 263.18 263.19 263.20 263.21 263.22 263.22 263.24 263.27

0.0577 0.2887 0.5186 0.5833 0.6073 0.6269 0.1305 0.2123 0.3577 0.4263 0.4755 0.5555 0.6433 0.6940 0.6492 0.6200 0.7106 0.7453 0.6797 0.6349 0.6645 0.7231

0.056 0.232 0.510 0.631 0.682 0.726 0.106 0.171 0.301 0.375 0.443 0.573 0.764 0.879 0.774 0.703 0.913 0.974 0.845 0.739 0.810 0.935

0.051 0.219 0.501 0.626 0.679 0.724 0.097 0.160 0.288 0.362 0.432 0.566 0.763 0.878 0.772 0.701 0.911 0.973 0.843 0.737 0.808 0.934



a

Table 12. Experimental Resultsa and Calculated Mole Fractions in the Liquid Phase for the H2S−n-Pentane System at 243.01 K Texp/K

Pexp/MPa

zexp

xcalc

242.89 242.89 242.89 242.89 242.89 242.89 242.89 242.89 242.89 242.89 242.89 242.91 242.93 243.12 243.14 243.17 243.18 243.19 243.20 243.20 243.22 243.22

0.0325 0.0774 0.1258 0.2378 0.2610 0.2803 0.2952 0.3072 0.3164 0.3239 0.3308 0.1688 0.2047 0.3624 0.3451 0.3394 0.3339 0.3585 0.3291 0.3230 0.3740 0.3524

0.056 0.106 0.171 0.375 0.443 0.510 0.573 0.631 0.682 0.726 0.764 0.232 0.301 0.935 0.845 0.810 0.774 0.913 0.739 0.703 0.974 0.879

0.053 0.100 0.164 0.367 0.436 0.505 0.569 0.628 0.680 0.725 0.763 0.223 0.293 0.935 0.844 0.808 0.773 0.912 0.738 0.702 0.974 0.878

The experimental results along with the molar fraction calculated with the procedure described in section 3 are presented in Tables 4 to 13. Figures 1 to 4 present the results obtained for the propane + H2S binary system at (243.19 and 273.11) K, for the n-butane + H2S binary system at (222.83, 243.03, 262.99, 283.23, and 293.26) K, and for the n-pentane + H2S binary system at (223.19, 243.01, and 263.03) K. To compare the new data with the existing literature data, a simple model is used. Caroll and Mather15 and Valderrama et al.16 have considered that, for such systems, the utilization of the classical mixing rules with one interaction parameters is enough to represent the phase diagram. A phi-phi approach based on the original Peng−Robinson equation of state (EoS)17 is selected to perform bubble-point pressure calculations. A classical mixing-rule and Mathias−Copeman (MC) alpha function18 have been used. The objective function considered only the equilibrium pressure. The necessary parameters including MC parameters (c1, c2, and c3) are indicated in Table 14. Figures 5, 6, and 7 present the relative deviations on calculated vapor pressures. Globally, the average relative deviation is less than 15 %. For the system H2S−n-butane, some calculation points lead to LLE. It is not surprising as for these temperatures the pressure is quasiconstant for an important range of composition. If these points are removed along with the data set of Lobo et al.,3 the relative deviation is reduced to a similar order of magnitude than the two other systems (Figure 8).

a Uncertainty u(T,k = 2) = ± 0.02 K; u(P,k = 2) = ± 0.05 kPa; u(z) = ± 0.005.

5. CONCLUSION A static total pressure apparatus has been used to obtain new experimental data on H2S−propane, H2S−n-butane, and H2S− n-pentane systems. The importance of these data is due to their rarity especially in the treated temperature range.

use αj,i = 0.3. τj,i and τi,j are adjusted directly on vapor−liquid equilibrium (VLE) data. Table 3 presents the obtained parameters for the studied systems at different temperatures. 1539



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Figure 1. Vapor−liquid equilibria for the system hydrogen sulfide (1) + propane (2) at (243.19 and 273.11) K. ×, experimental values; from Steckel20 at (243.15 and 273.15) K; □, values from Kay and Rambosek21 at 272.04 K; solid line, calculated values.

△,

values

Figure 2. Vapor−liquid equilibria for the system hydrogen sulfide (1) + n-butane (2) at (222.83, 243.03, and 262.99) K. ×, experimental values; solid line, calculated values. 1540



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Figure 3. Vapor−liquid equilibria for the system hydrogen sulfide (1) + n-butane (2) at (283.23 and 293.26) K. ×, experimental values; solid line, calculated values.

Figure 4. Vapor−liquid equilibria for the system hydrogen sulfide (1) + n-pentane (2) at (223.19, 243.01, and 263.03) K. ×, experimental values; solid line, calculated values. 1541



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Table 14. Parameters for Data Correlation Using the PR EoS critical properties14

Mathias−Copeman parameters18

kij

system

TC/K

PC/MPa

acentric factor ω

c1

c2

c3

this work

Dechema19

H2S−propane H2S−n-butane H2S−n-pentane

369.83 425.12 469.7

4.248 3.796 3.37

0.152291 0.200164 0.251506

0.600066 0.677341 0.762864

−0.00630377 −0.0810913 −0.224305

0.173899 0.298538 0.669507

0.07963 0.08107 0.05365

0.08 0.07 0.063

Figure 7. Relative deviations for the system H2S−n-pentane. Experimental data are taken from △, Kay and Rambosek;21 and ×, this work.

Figure 5. Relative deviations for the system H2S−propane. Experimental data are taken from △, Steckel;20 □, Kay and Rambosek;21 and ×, this work.

Figure 8. Relative deviation for the system H2S−n-butane on the entire range of experimental pressure. Experimental data are taken from △, Leu and Robinson;24 and ×, this work.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Telephone: +33 1 64694962. Fax: +33 1 64694968. Notes

The authors declare no competing financial interest.

■

Figure 6. Relative deviations for the system H2S−n-butane (enlargement between (0 and 2) MPa). Experimental data are taken from □, Lobo et al.;3 △, Leu and Robinson;24, and ×, this work.

REFERENCES

(1) Kohl, A.; Nielsen, R. Gas purification, 5th ed.; Gulf Publishing Compagny: Houston, TX, 1997. (2) Burr, B.; Lyddon, L. A comparison of physical solvents for acid gas removal, 87th Annual GPA convention, Grapevine, TX, March 2−5, 2008. (3) Lobo, L. Q.; Ferreira, A. G. M.; Fonseca, I. A.; Senra, A. M. P. Vapour pressure and excess Gibbs free energy of binary mixtures of hydrogen sulphide with ethane, propane and n-butane at temperature of 182.33 K. J. Chem. Thermodyn. 2006, 38, 1651−1654. (4) Fonseca, J. M. S.; Dohrn, R.; Peper, S. High-pressure fluid-phase equilibria investigated (2005−2008). Fluid Phase Equilib. 2011, 300, 1−69. (5) Raal, J. D.; Mühlbauer, A. L. Phase Equilibria: Measurement and Computation; Taylor and Francis: Bristol, PA, 1998.

NRTL parameters have also been identified by Barker's method. These parameters can further be used to provide an estimation of the compositions. A simple data treatment has been proposed. The Peng−Robinson EoS has been selected to fit the obtained data along with literature data. The obtained interaction parameters seem in good agreement with the ones from Dechema19 obtained with a higher temperature range of the data (Table 14). 1542



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(6) Gibbs, R. E.; van Ness, H. C. Vapour liquid equilibria from total pressure measurements: a new apparatus. Ind. Eng. Chem. Fundam. 1972, 11, 410−413. (7) Haimi, P.; Uusi-Kyyny, P.; Pokki, J. P.; Pakkanen, M.; Aittamaa, J.; Keskinen, K. I. Isothermal binary vapour-liquid equilibrium for butanes and butenes with dimethylsulphide. Fluid Phase Equilib. 2008, 266, 143−153. (8) Barker, J. A. Determination of Activity Coefficient from Total Pressure Measurements. Aust. J. Chem. 1953, 6, 207. (9) Abbott, M. M.; van Ness, H. C. An extension of Barker's method for reduction of VLE data. Fluid Phase Equilib. 1977, 1, 3−11. (10) Guilbot, P.; Theveneau, P.; Baba-Ahmed, A.; Horstmann, S.; Fisher, K.; Richon, D. Vapor Liquid equilibrium data and critical points for the system H2S + COS. Extension of the PSRK group contribution equation of state. Fluid Phase Equilib. 2000, 170, 193−202. (11) Redlich, O.; Kwong, J. N. S. On the Thermodynamics of Solutions. V. An equation of state. Fugacities of Gaseous solutions. Chem. Rev. 1948, 44, 233−244. (12) Soave, G. Equilibrium constants for modified Redlich-Kwong equation of state. Chem. Eng. Sci. 1972, 4, 1197−1203. (13) Renon, H.; Prausnitz, J. M. Local composition in thermodynamic excess function for liquid mixtures. AIChE J. 1968, 14, 135− 144. (14) Daubert, T. E.; Danner, R. P.; Sibel, H. M.; Stebbins, C. C. Physical and thermodynamic properties of pure chemicals. Data Compilation; Taylor & Francis: Washington, DC, 1997. (15) Carroll, J. J.; Mather, A. E. A generalized correlation for the Peng-Robinson interaction coefficients for paraffin hydrogen sulfide binary systems. Fluid Phase Equilib. 1995, 105, 221−228. (16) Valderrama, J. O.; Arce, P. F.; Ibrahim, A. A. Vapour−liquid equilibrium of H2S-Hydrocarbon mixtures using a generalized cubic equation of state. Can. J. Chem. Eng. 1999, 77, 1239−1243. (17) Peng, D. Y.; Robinson, D. B. A new two parameters equation of state. Ind. Eng. Chem. Fundam. 1976, 15, 59−64. (18) Mathias, P. M.; Copeman, T. W. Extension of The Peng Robinson Equation of State to Complex Mixtures: Evaluation of the Various Forms of the Local Composition Concept. Fluid Phase Equilib. 1983, 13, 91−108. (19) Knapp, H.; Döring, R.; Oellrich, L.; Plöcker, U.; Prausnitz, J. M. Vapor-Liquid Equilibria for Mixtures of Low-Boiling Substances; DECHEMA Chemistry Data Series, Vol. VI; DECHEMA: Frankfurt/Main, 1982. (20) Steckel, F. Dampf-Flüssigkeit-Gleichwichte einiger binärer schwefelwasserstoff-haltiger. Systeme unter Druck. Svensk. Kem. Tidst. 1945, 57, 209. (21) Kay, W. B.; Rambosek, G. M. Liquid vapour equilibrium relations in binary systems. Ind. Eng. Chem. 1953, 45, 221−226. (22) Gilliland, E. R.; Scheeline, H. W. High pressure vapor-liquid equilibrium. Ind. Eng. Chem. 1940, 32, 48. (23) Brewer, J.; Rodewald, N.; Kurata, F. Phase equilibria of the propane-hydrogen sulfide from the cricondentherm to the solid liquid vapor region. AIChE J. 1961, 7, 13−16. (24) Leu, A. D.; Robinson, D. B. Equilibrium phase properties of the n-butane-hydrogen sulfide and isobutane-hydrogen sulfide binary system. J. Chem. Eng. Data 1989, 34, 315−319. (25) Robinson, D. B.; Hughes, R. E.; Sandercock, J. A. W. Phase behaviour of the n-butane hydrogen sulphide system. Can. J. Chem. Eng. 1964, 42, 143−146. (26) Reamer, H.; Sage, B.; Lacey, W. Phase equilibria in hydrocarbon systems. Volumetric and phase behavior of the n-pentane−hydrogen sulfide system. Ind. Eng. Chem. 1953, 45, 1805−1809. (27) Cunningham, J. Enthalpies and phase boundary measurements: equal molar mixtures of n-pentane with carbon dioxide and hydrogen sulfide; GPA RR 103; Gas Processors Association: Tulsa, OK, 1986.

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