New VaporâLiquidâLiquid Equilibrium Data for Ethane and Propane

Article pubs.acs.org/jced

New Vapor−Liquid−Liquid Equilibrium Data for Ethane and Propane in Alkanolamine Aqueous Solutions Salim Mokraoui,*,† Mohamed Kamel Hadj-Kali,‡ Alain Valtz,§ and Dominique Richon∥,⊥ †

Sustainable Energy Technologies Center, King Saud University, P.O Box 800, 11421 Riyadh, KSA, Saudi Arabia Chemical Engineering Department, King Saud University, P.O Box 800, 11421 Riyadh, KSA, Saudi Arabia § Mines ParisParis Tech, CEP/TEP, 35, Rue Saint Honoré, 77305 Fontainebleau, France ∥ Thermodynamics Research Unit, School of Chemical Engineering, University of KwaZulu-Natal, Howard College Campus, King George V Avenue, Durban 4041, South Africa ⊥ Department of Biotechnology and Chemical Technology, Aalto University, School of Science and Technology, P.O. Box 16100, 00076 Aalto, Finland ‡

ABSTRACT: New solubility data of ethane and propane in aqueous methyl diethanolamine (MDEA) and diethanolamine (DEA) solutions were measured at different temperatures and pressures. The data concern vapor−liquid−liquid equilibrium (VLLE) conditions. In this work, two weight-based concentrations of aqueous MDEA (w = 0.25 and w = 0.50) and one aqueous solution of DEA (w = 0.35) were considered. These concentration types are commonly used in the gas processing industry. The Henry’s constant is calculated for each system. In addition, useful correlations are proposed for the solubility, salting-in, three-phase vapor pressure, and activity coefficient at infinite dilution.

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INTRODUCTION Aqueous alkanolamines solutions are used in the petroleum industry to remove acid gases from natural gases and liquefied petroleum gases (LPGs) for refining and purification processes. Sweetening LPGs with amines has experienced an increasing interest for a number of years. The main advantage of using alkanolamines solutions is their high selective absorption of acid gases with respect to hydrocarbons. However, the solubility of hydrocarbons in aqueous alkanolamine solutions is not zero and should be taken into account; but still limited data and design information are available in the literature. The importance of knowing the solubility of gaseous or liquid hydrocarbons in aqueous solutions of alkanolamines lies in the problem of quantifying hydrocarbon losses in treating processes. Hence, accurate solubility data of hydrocarbons in amine solutions will lead to efficient optimization of these processes. Data needed for LPGs purification process often involve three-phase equilibrium systems consisting of an aqueous alkanolamine liquid phase, hydrocarbon-rich liquid phase, and hydrocarbon-rich vapor phase. In this paper, focus is made on the solubility measurement of light hydrocarbons ethane and propane in aqueous diethanolamine (DEA) and methyldiethanolamine (MDEA) solutions in three phases coexisting conditions. The concentrations of alkanolamine in the aqueous solutions, used for this study, are wDEA = 0.35, wMDEA = 0.25, and wMDEA = 0.50. Although the process of hydrocarbon sweetening with amine solutions is well-established, there is still a limited amount of © XXXX American Chemical Society

experimental data regarding the solubility of hydrocarbons in aqueous solutions of alkanolamines. Mostly, the solubility of hydrocarbons in aqueous alkanolamines solutions reveals similar behavior as in pure water regarding its dependence on temperature. However, hydrocarbon solubility increases by the presence of amine in water.1 The solubility of ethane in aqueous diethanolamine solutions have been studied by Lawson and Garst2 and Jou and Mather.3 Lawson and Garst2 have presented few data about the solubility of ethane at 310.9 K in (5 and 25) wt % aqueous DEA solutions in VLE conditions. Jou and Mather3 offered more extensive collection of data, ranging from (298 to 398) K for the system 3 M DEA (molarity based concentration) + ethane. The data are mostly provided in vapor−liquid equilibrium (VLE) conditions but also in liquid− liquid equilibrium (LLE) and vapor−liquid−liquid equilibrium (VLLE) conditions. The only data available for the solubility of ethane in MDEA aqueous solutions are provided by Jou et al.4 They studied the system 3 M MDEA + ethane and provided solubility data of ethane for a (298 to 403) K temperature range, mostly in VLE conditions. Carroll et al.5 have extensively investigated the phase equilibrium of the 3 M MDEA (aqueous solution) + propane system. They have reported experimental results involving the VLE, LLE, and VLLE from (298 to 423) K. Received: April 10, 2013 Accepted: June 4, 2013

A

dx.doi.org/10.1021/je400340s | J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Furthermore, Jou et al.6 have presented solubility data of propane in DEA [(1.55 to 6.44) M] and MDEA [(3 to 4.5) M] aqueous solutions all in liquid−liquid equilibrium conditions. However, when compared to the data of Carroll et al.,5 the solubility data of Jou et al.6 regarding propane in MDEA solutions are found to be slightly higher. For the same conditions of temperature, pressure and amine concentration in the aqueous phase, all experimental data from the literature showed that the solubility in aqueous MDEA solutions is higher than that in aqueous DEA solutions for both ethane and propane.

LAUDA) in which the desired temperature is controlled and maintained within ± 0.01 K. The temperature measurements are performed using two 100 Ω platinum resistance thermometer devices (Pt 100) after careful periodic calibrations against a 25 Ω reference platinum resistance thermometer (TINSLEY precision instruments). Following those calibrations, the uncertainty on temperature measurements is estimated to be within ± 0.02 K. Pressure measurements are achieved by means of a Druck pressure transducer at (0 to 6) MPa, which is maintained at constant temperature (higher than the maximum temperature of the study) and calibrated against a dead-weight pressure balance [Desgranges & Huot 5202S, CP (0.3 to 40) MPa, Aubervilliers, France]. The resulting uncertainties on pressure measurement are estimated to be within ± 0.3 kPa. The analytical work was carried out using a gas chromatograph (Varian model CP-3800) having two detectors in series: a thermal conductivity detector (TCD) and a flame ionization detector (FID). The TCD was used to quantify water and amine contents in the samples, whereas ethane and propane were detected with FID. Both detectors are calibrated by injecting and analyzing known masses of each compound. For each compound, the uncertainties on mole numbers are estimated to be within ± 2 % for water, ± 2.5 % for DEA and MDEA, ± 2 % for ethane, and ± 2.5 % for propane. The mole fraction uncertainties were calculated based on the mole number uncertainty and accounting for the repeatability test on the sequential analysis of the aqueous phase. The results are presented in the Results/Discussion section. The separation of hydrocarbons, water and amine compounds is achieved thanks to the gas chromatograph circuit presented in Figure 1. Hydrocarbon and water are separated by column A2 (Hayesep T 100/120 mesh column; silcosteel tube, length: 1.5 m, diameter: 1/8 in.), while amine is retained by column A1 (Porapak Q 100/120 mesh column; silcosteel tube, length: 0.06 m, diameter: 1/8 in.) and directly sent to TCD 2 after rotating the commuting valve.

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EXPERIMENTAL SECTION Materials. Ethane and propane with a certified purity greater than 99.995 vol % were purchased from Messer-Griesheim, while MDEA and DEA were provided by Aldrich (Germany) with purity greater than 99 vol %. Deionized water was used to prepare amine aqueous solutions after careful degassing of components. The water−amine solutions were prepared gravimetrically using an analytical balance (0.1 mg precision). The carrier gas (helium) for GC analyses is supplied by L’Air Liquide (France) and is pure grade with only traces of water (3 ppm) and of hydrocarbons (0.5 ppm). All the chemicals were used as received without any purification, except for careful degassing of liquid components. Apparatus and Experimental Procedure. The apparatus and experimental procedure used in this work concern a “staticanalytic” method with vapor and/or liquid-phase samplings. They are similar to what was described by Laugier and Richon7 and have already been presented in a previous work.8 Samplings are achieved through rapid online sampler−injector (ROLSI) samplers. ROLSI is a trademark of ARMINES; it is protected by several patents (PCT patent 2004/090508, PCT patent 2000/ 011462, EPO patent EP 1105722). The phase equilibrium is achieved inside a cylindrical cell which involves a sapphire tube; the cell volume is about 28 cm3. The cell is dropped inside a constant−temperature liquid bath (ULTRA-KRYOMAT

Figure 1. Analytical circuit. A1, A2: analytical columns; AG: auxiliary gas; C: commuting valve; FID: flame ionization detector; I: injectors; O: oven; TCD1, TCD2: thermal conductivity detectors; VS, LS: vapor and liquid samplers. B



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THERMODYNAMIC TREATMENT Phase Equilibrium Equations. The critical temperature (Tc), critical pressure (Pc), and acentric factor (ω) of each component are provided9 in Table 1. The vapor pressure of each

Equilibrium between the aqueous and the hydrocarbon-rich liquid phases: A A A L L xhc γhc(x ̅ , T ) = xhc γhc(x ̅ L , T ) ≅ 1

(5)

Equilibrium between the aqueous and the vapor phases: Table 1. Critical Temperature, Critical Pressure, and Acentric Factor of Compounds9 CAS number

Tc/K

Pc/MPa

ω

74-84-0 74-98-6 7732-18-5 111-42-2 105-59-9

305.32 369.83 647.13 736.6 675

4.872 4.247 22.050 4.27 3.829

0.099 0.152 0.345 0.953 1.165

ethane propane water DEA MDEA

A xhc /(T , P) = yhc PφhcV (y ̅ , T , P)

Hence, eqs 5 and 6 have been used, respectively, to calculate the activity coefficient and the Henry’s law constant of the hydrocarbon in aqueous alkanolamine solution. The fugacity coefficient in the vapor phase, φVhc, is estimated through the Peng−Robinson equation of state by neglecting the binary interaction parameters. The mole fraction of the hydrocarbon in vapor phase is calculated as follows:

compound is calculated according to the following formula proposed by Reid et al.10 ln(P sat /Pa) = A + B /T + C ln(T ) + DT ET /K

yhc = (P − Psolv)/P

Psolv = x wAPwsat + xaAPasat

9

Table 2. Parameters of Equation 1 A

B

C

D

E

51.857 59.078 73.649 106.38 253.07

−2598.7 −3492.6 −7258.2 −13714 −18378

−5.1283 −6.0669 −7.3037 −11.06 −33.972

1.49·10−5 1.09·10−5 4.17·10−6 3.26·10−18 2.33·10−5

2 2 2 6 2

(2)

L L L sat sat f hc = xhc γhc(x ̅ L , T )φhcsatPhc ≅ φhcsatPhc

(3)

f hcV

(4)

=

yhc PφhcV (y ̅ ,

T , P)

(8)

where the mole fractions of water (xAw) and alkanolamine (xAa ) in the aqueous phase are approached by the initial molar concentrations of the aqueous solution. Salting-In Effect. As an alternative for the calculation of the solubility, some authors introduce a parameter called the “saltingin ratio”. In fact, it has been stated earlier by many authors,11,12 and this will be discussed later in this work, that the solubility of light hydrocarbons is increased by the presence of the amine in water. This solubility increase is called “salting-in”, usually used to describe the solubility of gases in electrolyte solutions. The salting-in effect is also established to describe the solubility of hydrocarbons in amine solutions.12 The solubility of a given hydrocarbon in amine solution can be determined using the salting-in ratio, Shc‑a, expressed as follows:

The systems studied in this work involve three phases: aqueous amine phase (A), liquid (L), and vapor (V) hydrocarbon rich phases. Due to the nature of these systems, the following assumptions are considered: The solvent is assumed to escape into the vapor phase according to the Raoult’s law. Therefore, the amount of water or alkanolamine in the condensed organic phase is ignored. The effect of the total pressure on the molar volume of each component is negligible. Consequently, the Poynting correction factor is approximated to unity. The first assumption is supported by previous experimental work,5 while the second is imposed by the difficulty of getting the molar volume variation with pressure. With respect to the above assumptions, the fugacities of the hydrocarbon compound in each of the three phases are given by the following equations: A A A sat A f hcA = xhc γhc(x ̅ , T )φhcsatPhc = xhc /(T , P)

(7)

where Psolv is the partial pressure of the solvent constituted of water and alkanolamine; it is approximated by Raoult’s law by applying the following equation:

(1)

The values of the parameters A, B, C, D, and E are taken from Daubert et al.9 and presented in Table 2.

ethane propane water DEA MDEA

(6)

A w w A S hc − a = xhc /xhc ≅ / hc // hc

(9)

where subscript hc-a stands for hydrocarbon-amine pair, and superscripts A and w stand, respectively, for aqueous solution and pure water. It has been found that the salting-in ratio is a function of both temperature and amine concentration in the aqueous solution. The concentration effect can be adequately modeled using the Setchenow coefficients, khc‑a,11,13 via the following equation:

ln(S hc − a) = k hc − a·Ca

(10)

where Ca is the amine concentration in the aqueous solution expressed as molarity (mol·L−1).

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RESULTS AND DISCUSSION Three-Phase Vapor Pressure. The three-phase vapor pressure P3 is the pressure at which aqueous phase and hydrocarbon liquid and vapor phases coexist. This pressure is slightly above the vapor pressure of the pure hydrocarbons. For each system, the three phase vapor pressures were determined simultaneously with the solubility measurements. According to the Gibbs phase rule, the degree of freedom for a three phase−three component system is equal to two. This means that the pressure P3 depends on both composition and temperature. However, for nonvolatile aqueous solvents, the P3 pressure and the vapor pressure of low soluble gases are too close.

where xA̅ , xL̅ , and y,̅ are, respectively, the compositions of the aqueous, liquid hydrocarbon, and vapor phases. In eq 2, the Henry’s law constant “/ ” has been used to correlate the solubility data. As the hydrocarbon rich phase is mainly composed of hydrocarbon, the composition and activity coefficient, in eq 3, are both set to unity. The equality condition of the fugacities, settled by the equilibrium between the three phases, leads to the following two equations: C



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Table 5. Values of Parameters for Calculating Three-Phase Vapor Pressure

This is what we have observed for light hydrocarbons in aqueous alkanolamine solutions as shown in Figure 2. This is due to the small effect of hydrocarbons solubility on the overall composition of the system. As a consequence, the composition remains constant, and the P3 pressure is only temperaturedependent. Tables 3 and 4 report the measured and calculated P3 data. The calculated data were correlated using eq 11: APi

T /K

APi

BPi

ARD (%)

MRD (%)

T range/K

ethane propane

21.67 21.42

−1912.64 −2281.03

0.57 0.20

2.84 0.61

283−305 298−333

respectively at (283.15 and 298.15) K. The pressure varies up to the three phase vapor pressure. Those experiments were conducted as leading experiments prior to the VLLE measurements. The results are displayed in Figures 3 and 4 where it is shown that solubility is increasing function of both pressure and amine concentration. On the other hand, Tables 8 and 9 report the experimental VLLE solubility data for ethane and propane in aqueous amine solutions. The experimental uncertainties estimated through repeatability tests of the sequential analyses are included to assert for the variability of the measurements. The VLLE data are also plotted in Figures 5 and 6 as −ln(xAhc) versus 1/T. In these figures, the solubility of ethane and propane in water, obtained in our previous work,14 are included both with the data of Jou et al.4 and Carroll et al.5 Clearly, hydrocarbon solubility is increasing function of the MDEA concentration. Furthermore, by comparing our data with the published ones (for the same amine’s mass fraction), it can be deduced that the hydrocarbons are more soluble in MDEA than in DEA, particularly for propane. The same remark has been done by Critchfield et al.15 This is due to the larger number of aliphatic groups in MDEA compared to DEA. Temperature Dependence of the Solubility. The new temperature-dependent experimental solubilities are correlated using the following equation:

Figure 2. Variation of the three-phase pressure with temperature. The symbols represent the experimental points. ○, ethane−aqueous amine; ◇, propane−aqueous amine. The solid lines represent the calculations according to eq 11 and dashed lines the pure component vapor pressure.

ln(P3/MPa) = AiP + BiP /T

i

(11)

BPi ,

where parameters and given in Table 5, were obtained by minimizing the sum of the quadratic difference between the calculated and experimental pressures. For each hydrocarbon, these parameters have been obtained by putting together all of the P3 experimental data of all aqueous amine solutions. The deviation between experimental and calculated data does not exceed 1 % for both hydrocarbons, except one value for ethane, while the maximum deviation for propane is 0.61 %. Solubility. In addition to the VLLE data, some VLE solubility measurements are presented. Tables 6 and 7 report these data for ethane and propane in different aqueous amine solutions

A ln(xhc ) = Aix + Bix /T

T /K

(12)

Table 10 reports the fitted and parameters obtained by minimizing the sum of the quadratic difference between the calculated and experimental solubilities. The mean relative deviation between experimental and calculated data is less than 0.5 % and 2 %, respectively, for ethane and propane in aqueous Axi

Bxi

Table 3. Experimental and Calculated Three-Phase Vapor Pressure for Ethane−Aqueous Amine Systemsa aqueous MDEA (w = 0.25)

a

aqueous MDEA (w = 0.5)

aqueous DEA (w = 0.35)

T/K

Pcal/MPa

Pexp/MPa

RD/%

Pexp/MPa

RD/%

Pexp/MPa

RD/%

283.15 288.15 293.15 298.15 303.15 305.15

3.007 3.380 3.786 4.223 4.695 4.893

3.021 3.377 3.767 4.191 4.712 5.036

0.48 −0.10 −0.49 −0.77 0.37 2.8

3.017 3.377 3.766 4.191

0.35 −0.10 −0.52 −0.77

3.023 3.381 3.770 4.195 4.662 4.891

0.54 0.02 −0.41 −0.67 −0.70 −0.04

Standard uncertainties u are u(T) = 0.02 K and u(P) = 0.3 kPa.

Table 4. Experimental and Calculated Three-Phase Vapor Pressure for Propane−Aqueous Amine Systemsa aqueous MDEA (w = 0.25)

a



T/K

Pcal/MPa

Pexp/MPa

RD/%

Pexp/MPa

RD/%

Pexp/MPa

RD/%

298.15 303.15 308.15 313.15 323.15 333.15

0.955 1.084 1.224 1.378 1.727 2.134

0.955 1.082 1.223 1.377 1.725 2.137

−0.02 −0.15 −0.12 −0.08 −0.09 0.13

0.952 1.080

−0.33 −0.34

0.961 1.087

0.61 0.31

1.376 1.722 2.133

−0.15 −0.27 −0.06

1.381 1.728 2.140

0.21 0.08 0.27

Standard uncertainties u are u(T) = 0.02 K and u(P) = 0.3 kPa. D



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Table 6. Solubility of Ethane in Different Aqueous Solutions at 283.15 K (VLE)a aqueous MDEA (w = 0.25)



P/MPa

x·103

δx·105

P/MPa

x·103

δx·105

P/MPa

x·103

δx·105

1.243 1.325 1.539 1.994 2.503 2.945

0.759 0.779 0.876 1.073 1.269 1.397

1 2 7 2 3 4

1.429 1.992 2.504

1.157 1.505 1.823

4 4 6

0.508 0.997 1.498 1.998 2.508 2.957

0.407 0.693 1.099 1.346 1.458 1.586

2 5 2 2 5 4

Standard (combined) uncertainties are u(P) = 0.3 kPa and uc(x) = 6·10−5. δx: deviation observed through repeatability tests of the sequential analyses of the aqueous phase. a

Table 7. Solubility of Propane in Different Aqueous Solutions at 298.15 K (VLE)a aqueous MDEA (w = 0.25)



P/MPa

x·103

δx·106

P/MPa

x·103

δx·106

P/MPa

x·103

δx·106

0.355 0.545 0.742 0.875

0.159 0.227 0.302 0.345

2 4 2 2

0.368 0.554 0.699 0.851

0.362 0.524 0.645 0.759

8 3 11 20

0.515 0.660 0.803

0.250 0.315 0.367

5 7 8

a Standard (combined) uncertainties are u(P) = 0.3 kPa and uc(x) = 2·10−5. δx: deviation observed through repeatability tests of the sequential analyses of the aqueous phase.

of temperatures of each system. Moreover, Figures 5 and 6 show the solubility curves presenting linear behavior over the whole temperature range considered in this study. As the measurements were carried out in the liquid−liquid− vapor three-phase region, the analysis of the solubility’s dependence with temperature should account for the pressure effect simultaneously. As shown in Tables 8 and 9 and in Figures 5 and 6, solubility of ethane is a decreasing function of temperature in pure water, aqueous MDEA (w = 0.25), and DEA (w = 0.35) but increases in aqueous MDEA solutions (w = 0.35 and w = 0.5). On the other hand, the solubility of propane increases with the temperature in all aqueous alkanoamine systems and exhibits a minimum in pure water. These observations may indicate the existence of a minimum solubility for the hydrocarbon−aqueous amine solutions. This minimum moves to low temperatures with the increase of amine concentration and with the decrease of carbon atom number. Indeed, it is well-established for light hydrocarbon−water systems that the solubility undergoes a minimum throughout the temperature change at constant pressure.16 The same behavior is also observed for light hydrocarbon−aqueous solutions of alkanolamine systems11 even if this minimum cannot be highlighted with eq 12 formulation. This phenomenon could be explained by analyzing the relationship between the temperature derivative of the solubility and the partial molar enthalpy of the solute in the solvent (heat of solution):

Figure 3. Variation of VLE experimental solubilities of ethane with pressure for different aqueous alkanolamine solutions at 283.15 K. The symbols represent the experimental points whereas the dashed lines represent linear trend lines. △, w = 0.25 of MDEA; ○, w = 0.35 of DEA; □, w = 0.50 of MDEA.

A (∂ ln(xhc )/∂(1/T ))P ≅ −Δhhc ̅ /R

(13)

According to Prausnitz et al.,13 the heat of solution Δh̅hc includes two parts (terms in parentheses in eq 14: L

L

G L L G Δhhc = (hhc ) + (hhc − hhc ) ̅ = hhc ̅ − hhc ̅ − hhc

Figure 4. Variation of VLE experimental solubilities of propane with pressure for different aqueous alkanolamine solutions at 298.15 K. The symbols represent the experimental points, whereas the dashed lines represent linear trend lines. △, w = 0.25 of MDEA; ○, w = 0.35 of DEA; □, w = 0.50 of MDEA.

(14)

where: In the absence of solvation, the first term is positive due to the hydrophobic interactions between hydrocarbon and water molecules, while the second term due to the heat of condensation is negative. At low temperatures, the condensation effect is predominating, and the heat of solution is exothermic. As the

amine solutions. Therefore, eq 12 is the most useful representation of the solubility over the corresponding ranges E



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Table 8. VLLE Experimental and Calculated Solubilities of Ethane in MDEA and DEA Aqueous Solutionsa aqueous MDEA (w = 0.25)



T/K

Pexp/MPa

xexp·103

xcal·103

RD %

δx·105

Pexp/MPa

xexp·103

xcal·103

RD %

δx·105

Pexp/MPa

xexp·103

xcal·103

RD %

δx·105

283.15 288.15 293.15 298.15 303.15 305.15

3.021 3.377 3.767 4.191 4.712 5.036

1.42 1.38 1.34 1.31 1.29 1.28

1.41 1.38 1.35 1.32 1.29 1.28

0.38 0.01 −0.53 −0.46 0.25 0.35

6 5 3 3 1 2

3.017 3.377 3.766 4.191

1.99 2.09 2.23 2.33

1.99 2.10 2.22 2.34

0.15 −0.52 0.59 −0.22

4 5 6 6

3.023 3.381 3.770 4.195 4.662 4.891

1.60 1.57 1.53 1.50 1.54 1.44

1.61 1.57 1.53 1.49 1.46 1.45

−0.38 0.25 0.10 0.47 5.2 −0.45

3 3 2 2 3 2


Table 9. VLLE Experimental and Calculated Solubilities of Propane in MDEA and DEA Aqueous Solutionsa aqueous MDEA (w = 0.25)



T/K

Pexp/MPa

xexp·103

xcal·103

RD %

δx·106

Pexp/MPa

xexp·103

xcal·103

RD %

δx·106

Pexp/MPa

xexp·103

xcal·103

RD %

δx·106

298.15 303.15 308.15 313.15 323.15 333.15

0.955 1.082 1.223 1.377 1.725 2.137

3.86 3.92 3.94 4.06 4.27 4.72

3.78 3.89 4.01 4.13 4.36 4.60

2.2 0.77 −1.8 −1.7 −2.2 2.6

1 3 2 3 2 6

0.952 1.080

8.27 8.88

8.17 8.91

1.2 −0.38

6 4

0.961 1.087

4.14 4.51

4.25 4.40

−2.6 2.5

5 12

1.376 1.722 2.133

10.48 11.98 14.52

10.52 12.30 14.24

−0.23 −2.5 1.8

11 8 10

1.381 1.728 2.140

4.73 4.97 5.25

4.69 4.98 5.28

0.83 −0.31 −0.53

7 4 8


temperature increases, the hydrophobic effect increases, and the cavitation effect decreases which leads to a solubility decrease. The hydrocarbon solubility goes through a minimum at a given temperature (Tmin) when the two effects are equal. The above statement remains also true if pressure is increasing with temperature. However, the solubility minimum occurs before that we can observe if the pressure is constant. In fact, the pressure increase compensates the effect of temperature on the solubility and assists it to increase. Based on eq 13, and taking into account the temperature dependence of the heat17 of solution Δh̅hc, the following equation can be used to correlate the hydrocarbon solubility in amine aqueous solutions: A ln(xhc ) = Aix + Bix /T + Cix ln(T )

Figure 5. VLLE experimental solubility of ethane in water and aqueous amine solutions. ◆, Pure water (Mokraoui et al.14); ○, w = 0.35 of MDEA (Jou et al.4); ■, w = 0.25 of MDEA (*); ▲, w = 0.50 of MDEA (*); ●, w = 0.35 of DEA (*). * denotes this work.

T /K

(15)

Equation 15 could enable us to calculate the temperature at which the solubility goes through a minimum for each studied system (Tmin). However this step was not performed due to the too small experimental temperature range. Henry’s Constant. The Henry’s law constant / depends on temperature, pressure, and solvent. Even though it has the same unit as the vapor pressure, the fact that it depends on solvent makes it very different from the vapor pressure which is independent of solvent. The Henry’s law constant is introduced to express the linear proportionality between the fugacity of a very dilute solute in a solvent to its molar fraction. In this work, the Henry’s constants / expressed in MPa were calculated using eq 6 for each system. Table 11 shows the calculated data for ethane with the three different solvents, and Table 12 reports the calculated ones for propane. The absolute and relative uncertainties on the calculated values are given in the same tables. As expected, the Henry’s constant increases with the temperature and decreases with the amine concentration. Based on eq 6, the variation of Henry’s constant is affected by the change in pressure and solubility. As the experiments are carried out at the three-phase locus of each system, an increase in

Figure 6. VLLE experimental solubility of propane in water and aqueous amine solutions. ◆, Pure water (Mokraoui et al.14); ○, w = 0.35 of MDEA (Carroll et al.5); ■, w = 0.25 of MDEA (*); ▲, w = 0.50 of MDEA (*); ●, w = 0.35 of DEA (*). * denotes this work. F



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Table 10. Values of Parameters for Calculating Solubility VLLE (eq 12) i

ethane

propane

solvent

Axi

Bxi

ARD/%

T range/K

Axi

Bxi

ARD/%

T range/K

aqueous MDEA (w = 0.25) aqueous MDEA (w = 0.5) aqueous DEA (w = 0.35)

5.819 10.803 5.93

406.608 −908.454 411.049

0.33 0.37 0.33

283−305 283−298 283−305

7.804 11.996 8.115

−557.48 −1577.3 −615.08

1.36 1.22 1.87

298−333 298−333 298−333

Table 11. Henry’s Constant of Ethane in Various Amine Aqueous Solutions

Table 14. Values of Parameters for Calculating the Setchenow Coefficient

/ /MPa T/K



283.15 288.15 293.15 298.15 303.15 305.15 u(T) = 0.02 K

1531 1727 1929 2132 2351 2464 u(/ ) = 77 MPa

1096 1162 1189 1233 u(/ ) = 47 MPa

MDEA aqueous DEA (w = 0.35)

ethane propane

1364 1511 1688 1864 1930 2174 u(/ ) = 61 MPa

a

b·10

−1.01 −0.813

4.00 3.71


298.15 303.15 308.15 313.15 323.15 333.15 u(T) = 0.02 K

2088 2295 2537 2727 3130 3375 u(/ ) = 72 MPa

973 1012

1959 2003

1056 1115 1096 u(/ ) = 22 MPa

2344 2695 3037 u(/ ) = 51 MPa

AHi

T /K

−0.569 −0.441

2.31 2.16

T/K


2.12


4.27

aqueous MDEA (w = 0.35) data from Jou et al.4

2.95


3.44

aqueous DEA (w = 0.05) date from Carroll and Mather18 aqueous DEA (w = 0.25) data from Carroll and Mather18 aqueous DEA (w = 0.3) data from Jou and Mather3

0.48

283.15 288.15 293.15 298.15 303.15 305.15 283.15 288.15 293.15 298.15 298.15 313.15 343.15 348.15 373.15 283.15 288.15 293.15 298.15 303.15 305.15 310.95 338.75

1.19 1.23 1.28 1.32 1.37 1.39 1.67 1.87 2.10 2.35 1.87 2.46 2.89 3.07 3.62 1.35 1.40 1.45 1.50 1.56 1.59 1.17 1.18

0.02 0.03 0.02 0.04 0.06 0.06 0.04 0.07 0.09 0.11 0.05 0.13 0.12 0.09 0.15 0.04 0.04 0.04 0.04 0.05 0.05 0.03 0.01

1.29 1.34 1.40 1.46 1.53 1.55 1.67 1.82 1.98 2.16 1.70 2.03 2.89 3.06 4.11 1.34 1.39 1.45 1.51 1.57 1.59 1.07 1.11

−8 −9 −10 −11 −11 −11 0 3 6 8 9 18 0 0 −14 1 0 0 0 −1 −1 8 6

2.43

310.95 338.75

1.52 1.68

0.04 0.05

1.44 1.68

5 0

3

298.15 323.15

1.67 1.87

0.09 0.05

1.43 1.70

14 8

(16)

BHi

The coefficients and for each system are reported in Table 13. They were obtained by minimizing the sum of the quadratic difference between the calculated and the derived Henry’s constant. The average relative deviation between Henry’s constant calculated with eq 16 and those derived from eq 6 is about 0.5 % for ethane and 2 % for propane. Nevertheless, one must notice that eq 16 is only valid in the temperature range of this study, that is, (283.15 to 305.15) K for ethane and (298.15 to 333.15) K for propane. Salting-in Ratio. In this work, we have used eq 9 to estimate the salting-in ratio from the values of the Henry’s constants in

Shc‑a

exp cal (eq 9) u(S) (eq 17) RD/%

Ca/mol·L−1


temperature leads systematically to increasing the pressure; this will raise the Henry’s constant and counterbalance the effect of solubility increase. To provide a useful temperature-dependent correlation for the Henry’s constant, the calculated data reported in Tables 11 and 12 were regressed with the following equation: ln(/i/MPa) = AiH + BiH /T

b·103

Shc‑a

/ /MPa aqueous MDEA (w = 0.25)

a

Table 15. Comparison of Experimental Reduced and Calculated Salting-in Ratio of Ethane in Amine Aqueous Solutionsa

Table 12. Henry’s Constant of Propane in Various Amine Aqueous Solutions

T/K

DEA 3

a

Standard uncertainty is u(T) = 0.02 K.

aqueous amine solution and in pure water. The Henry’s constant in the aqueous solution is given by eq 16, while that in pure water

Table 13. Values of Parameters for Calculating Henry’s Law Constant, VLLE i

ethane

solvent

AHi

BHi


14.0389 8.94373 13.867

−1890.78 −543.369 −1877.74

propane

G

ARD/%

AHi

BHi

ARD/%

0.3 0.3 0.5

12.3562 8.21708 12.0374

−1394.03 −391.206 −1333.31

2.1 1.5 1.3



Article

Table 16. Comparison between Experimental Reduced and Calculated Salting-in Ratio of Propane in Aqueous Amine Solutionsa Shc‑a Ca/mol·L−1

T/K

exp (eq 9)


2.12


4.27

aqueous MDEA (w = 0.35) data from Carroll et al.5

2.95

aqueous MDEA data from Jou et al.6

3.00 4.50 4.37 4.42 2.93 3.29 4.42 3.44

298.15 303.15 308.15 313.15 323.15 333.15 298.15 303.15 313.15 323.15 333.15 298.15 313.15 323.15 348.15 313.15 313.15 333.15 333.15 348.15 348.15 348.15 298.15 303.15 313.15 323.15 333.15 313.15 313.15 313.15 313.15 313.15 333.15 333.15 333.15 348.15 348.15

1.73 1.82 1.91 1.98 2.08 2.14 3.75 4.18 5.05 5.87 6.60 2.30 2.74 3.02 3.63 2.72 5.40 6.64 7.05 4.14 4.47 8.29 1.94 2.05 2.24 2.38 2.45 1.63 1.99 2.15 2.24 3.19 2.29 2.43 3.58 2.54 3.97


aqueous DEA data from Jou et al.6

a

1.57 2.97 3.07 3.22 4.60 3.00 3.00 4.47 3.00 4.50

Shc‑a u(S) 0.03 0.04 0.04 0.05 0.04 0.07 0.06 0.07 0.09 0.10 0.12 0.09 0.06 0.11 0.16

0.03 0.04 0.04 0.04 0.05

cal (eq 17)

RD/%

1.86 1.93 2.01 2.09 2.26 2.45 3.50 3.79 4.44 5.20 6.10 2.37 2.79 3.12 4.10 2.85 4.80 6.35 6.48 4.06 4.83 8.29 2.01 2.08 2.24 2.41 2.60 1.45 2.01 2.06 2.13 2.95 2.30 2.30 3.47 2.54 4.05

−8 −6 −6 −6 −9 −15 7 9 12 11 8 −3 −2 −3 −13 −5 11 4 −8 2 8 0 −4 −1 0 −2 6 11 −1 4 5 8 −1 5 3 0 −2

Figure 7. Logarithm of the salting-in ratio as a function of amine concentration: ethane−aqueous MDEA. ×, Jou et al.4 (298 to 403) K; ○, 283 K (*); □, 288 K (*); △, 293 K (*); ◇, 298 K (*); ∗, 303 K (*); +, 305 K (*). * denotes this work.

Figure 8. Logarithm of the salting-in ratio as a function of amine concentration: ethane−aqueous DEA. ○, Carroll et al.18 (310 K, 339 K); △, Jou et al.3 (298 K); ●, 283 K (*); ■, 288 K (*); ▲, 293 K (*); ◆, 298 K (*); ∗, 303 K (*); +, 305 K (*). * denotes this work.

Standard uncertainty is u(T) = 0.02 K.

is taken from our previous work.14 The estimated values of the salting-in ratio are fitted to the following correlation, resulting from eq 10 in which the Setchenow coefficient is considered as a linear function of temperature: S hc − a = (a + bT )Ca

T /K

(17)

Figure 9. Logarithm of the salting-in ratio as a function of amine concentration: propane−aqueous MDEA. ○, 298 K (Carroll et al.5); +, 305 K (Carroll et al.5); △, 313 K (Jou et al.6); ◇, 323 K (Carroll et al.5); ×, 333 K (Jou et al.6); □, 348 K (Jou et al.6); ●, 298 K (*); ■, 303 K (*); ▲, 313 K (*); ◆, 323 K (*); ∗, 333 K (*). * denotes this work.

The adjusted a and b parameters are given in Table 14. They were obtained by minimizing the sum of the relative difference between calculated and experimental derived salting-in ratio. Tables 15 and 16 report the results of the salting-in ratio obtained from eq 9 for the different studied systems. Additional data, from the literature, have been included in order to achieve a better and comprehensive correlation for the Setchenow coefficient with temperature and amine concentration. The relative uncertainty on the calculated salting-in ratio values does not exceed 5 % for all systems. Similarly, Figures 7 to 10 present the estimated salting-in ratio as ln(S) versus concentration and

temperature for the different hydrocarbon−amine systems. The first glance to the previous tables and figures allows the general deduction that the salting-in ratio increases with temperature and obviously with the concentration. A more thorough comparison shows that at the same temperature and concentration (either masse fraction or molarity), the salting-in ratio of the H



■

CONCLUSION New data were obtained for the solubility of ethane and propane in alkanolamine aqueous solutions (VLLE conditions). These data are important to design the LPGs sweetening processes encountered in the petroleum industry. Useful correlations for solubility, Henry’s constant, salting-in ratio, and activity coefficients have been derived from experimental data. The relative deviations between the derived experimental data and the calculated ones are satisfactory. Furthermore, a good agreement was found between our data and those of the literature, especially for the salting-in ratio. The presence of a minimum solubility has been underlined and supported by the analysis of our results. However, further experimental work in a larger range of temperature need to be accomplished in order to highlight this minimum and its relation with amine concentration and carbon atom number.

Figure 10. Logarithm of the salting-in ratio as a function of amine concentration: propane−aqueous DEA. ○, 298 K (Jou et al.6); △, 313 K (Jou et al.6); +, 333 (Jou et al.6); ●, 298 K (*); ■, 303 K (*); ▲, 313 K (*); ◆, 323 K (*); ∗, 333 K (*). * denotes this work.

■

T /K

AUTHOR INFORMATION

Corresponding Author

hydrocarbon-MDEA pair is greater than that of the hydrocarbonDEA pair. In addition, as can be seen from Tables 15 and 16, the ARD between the salting-in ratio derived from the experimental data and the salting-in ratio calculated from eq 17 is acceptable. The average deviations for ethane-MDEA and ethane-DEA systems are, respectively, 6.2 % and 1.6 %; while for propaneMDEA and propane-DEA systems, the average deviations are respectively 5.5 % and 2.5 %. These results lead to the conclusion that the linear temperature dependence (eq 17) used to correlate the Setchenow coefficient is relatively satisfactory for the representation of the salting-in effect of the studied hydrocarbon−aqueous amine solutions. Activity Coefficient. The activity coefficient of a solute in a solvent is nearly independent of the solute’s mole fraction provided the latter is sufficiently small. Our data are used to produce new correlations for the activity coefficients as a function of temperature only. The activity coefficient is estimated through eq 5, and the correlation is expressed by the following equation: ln(γhcA ) = Aiγ + Biγ /T

Article

*Tel.: +966-1-4676832. Fax: +966-1-4697122. E-mail: [email protected]. Funding

The authors wish to convey their gratitude to the Gas Processors Association (GPA, USA) for the financial support of this research. Notes

The authors declare no competing financial interest.

■

NOMENCLATURE ARD Average relative deviation APi , BPi Parameters of each hydrocarbon i in the three-phase pressure correlation Axi , Bxi , Cxi Parameters of each hydrocarbon i in the solubility correlation AHi , BHi Parameters of each hydrocarbon i in the Henry’s constant correlation Aγi , Bγi Parameters of each hydrocarbon i in the activity coefficient correlation C Concentration (mol·L−1) ΔC̅ pi Heat capacity of solution (J·K−1·mol−1) fi Fugacity of species (MPa) Henry’s law constant (MPa) / h Molar enthalpy (J·mol−1) Δh̅i Heat of solution (J·mol−1) k Setchenow coefficient MRD Maximum relative deviation P Pressure (MPa) R Gas constant (J·mol−1·K−1) RD Relative deviation S Salting-in ratio T Temperature (K) x Liquid mole fraction y Vapor mole fraction w The mass fraction

(18)

The fitted parameters Aγi and Bγi are reported in Table 17. They were obtained by minimizing the sum of the quadratic difference between the calculated and derived activity coefficients. The average relative deviation generated with this correlation is about 0.5 % for ethane−aqueous amine and 2 % for propane−aqueous amine solutions. This correlation is valid in the temperature range of this study, that is, (283.15 to 305.15) K for ethane and (298.15 to 333.15) K for propane. Finally, it should be mentioned that the fitted parameters of the last equation both with those of correlations 11, 12, and 16 were determined using the regression tool available within Simulis Thermodynamics environment, a thermophysical properties calculation server provided by ProSim.19 The same software was used to estimate the fugacity coefficients.

Table 17. Values of Parameters for Calculating Activity Coefficients i

ethane

propane

solvent

Aγi

Bγi

ARD/%

Aγi

Bγi

ARD/%


7.99826 2.97034 7.8914

−407.211 920.896 −413.005

0.34 0.27 0.53

6.04717 1.85276 5.67451

546.603 1567.16 623.395

1.8 1.5 1.4

I


Journal of Chemical & Engineering Data u uc φi γi

Article

(15) Critchfield, J.; Holub, P.; Ng, H.-J.; Mather, A. E.; Bacon, T. Solubility of hydrocarbons in aqueous solutions of gas treating amines. Proceedings of the Laurence Reid Gas Conditioning Conference, Norman, OK, Feb 25−28, 2001; pp 199−227. (16) Tsonopoulos, C. Thermodynamic analysis of the mutual solubilities of normal alkanes and water. Fluid Phase Equilib. 1999, 156, 21−33. (17) Perry, R. H.; Chilton, C. H.; Green, D. W. Perry’s Chemical Engineers Handbook, 7th rev ed.; McGraw-Hill Publishing Co.: New York, 1997. (18) Carroll, J. J.; Mather, A. E. A Model for the Solubility of Light Hydrocarbons in Water and Aqueous Solutions of Alkanolamines. Chem. Eng. Sci. 1997, 52, 545−552. (19) http://www.prosim.net (accessed June 4, 2013).

Standard uncertainty Standard combined uncertainty Fugacity coefficient of species i Activity coefficient of species i

Superscripts

A G L sat V W

Related to aqueous phase Gas phase Related to the hydrocarbon-rich liquid phase At saturation Related to hydrocarbon-rich vapor phase Related to pure water phase

Subscripts

3 a c cal exp hc hc-a P solv w

■

Related to the three-phase point Amine Critical properties Calculated Experimental Hydrocarbon species hydrocarbon-amine pair Pressure Solvent Water

REFERENCES

(1) Sada, E.; Kumazawa, H.; Butt, M. A. Solubilities of Gases in Aqueous Solutions of Amine. J. Chem. Eng. Data 1977, 22 (2), 272−273. (2) Lawson, J. D.; Garst, A. W. Hydrocarbon gas solubility in sweetening solutions: methane and ethane in aqueous monoethanolamine and diethanolamine. J. Chem. Eng. Data 1976, 21, 30−32. (3) Jou, F.-Y.; Mather, A. E. Solubility of ethane in aqueous solutions of monoethanolamine and diethanolamine. J. Chem. Eng. Data 2006, 51, 1141−1143. (4) Jou, F.-Y.; Carroll, J. J.; Mather, A. E.; Otto, F. D. The solubility of methane and ethane in aqueous solutions of methyldiethanolamine. J. Chem. Eng. Data 1998, 43, 781−784. (5) Carroll, J. J.; Jou, F.-Y.; Mather, A. E.; Otto, F. D. Phase equilibria in the system water-methyldiethanolamine-propane. AIChE J. 1992, 38, 511−520. (6) Jou, F.-Y.; Ng, H.-J.; Mather, A. E. Solubility of propane in aqueous alkanolamine solutions. Fluid Phase Equilib. 2002, 194, 825−830. (7) Laugier, S.; Richon, D. New Apparatus to perform fast Determinations of Mixture Vapor−Liquid Equilibria up to 10 MPa and 423 K. Rev. Sci. Instrum. 1986, 57, 469−472. (8) Chapoy, A.; Mokraoui, S.; Valtz, A.; Richon, D.; Mohammadi, A. H.; Tohidi, B. Solubility measurement and modeling for the system Propane-Water from 277.62 to 368.16 K. Fluid Phase Equilib. 2004, 226, 213−220. (9) 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. (10) Reid, R. C.; Prausnitz, J. M.; Poling, B. E. The properties of gases and liquids, 4th ed.; McGraw-Hill Book Company: New York, 1987. (11) Carroll, J. J.; Maddocks, J.; Mather, A. E. The solubility of hydrocarbons in amine solutions. Laurence Reid Gas Conditioning Conference, University of Oklahoma, Norman, OK, Mar 1−4, 1998. (12) Hatcher, N. A.; Jones, C. E.; Weiland, R. H. Hydrocarbon and fixed gas solubility in amine treating solvent. Laurence Reid Gas Conditioning Conference, University of Oklahoma, Norman, OK, Feb 24−27, 2013. (13) Prausnitz, J. M.; Lichtenthaler, R. N.; Azevedo, E. G. Molecular thermodynamics of fluid-phase equilibria, 3rd ed.; Prentice Hall: Upper Saddle River, NJ, 1999. (14) Mokraoui, S.; Coquelet, C.; Valtz, A.; Hegel, P. E.; Richon, D. New Solubility Data of Hydrocarbons in Water and Modelling concerning Vapor−liquid−liquid Binary Systems. Ind. Eng. Chem. Res. 2007, 46, 9257−9262. J


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