Hydrate Decomposition Conditions for Liquid ... - ACS Publications

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Hydrate Decomposition Conditions for Liquid Water and Propane Kayode I. Adeniyi, Connor E. Deering, and Robert A. Marriott* Department of Chemistry, University of Calgary, 2500 Research Road NW, Calgary, AB T2L 2K8, Canada ABSTRACT: Because of the industrial importance of C3H8 and because C3H8 hydrate is a reference material for other sII hydrates, the C3H8 hydrate dissociation conditions were independently measured using the phase boundary dissociation and isochoric methods for T = 273.63−278.75 K and p = 0.1887−18.2622 MPa. Along the liquid water Lw−H−C3H8(g) phase boundary, two different purities of 99.5 and 99.999 mol % C3H8 were studied. Data have been used to optimize two semiempirical correlations for rapid calculation of the phase dissociation conditions for p < 20 MPa. For a more rigorous model, the highest purity data have been fit using the van der Waals and Platteuw model and reference quality reduced Helmholtz equations-of-state (EOSs) for the hydrate phase and fluid phases, respectively. The optimized thermodynamic-based model agrees with the experimental data to within the estimated uncertainty of δT = ±0.1 K. The results were also compared to the highly variant literature data for the Lw−H−C3H8(l) phase boundary, where the deviations can be attributed to measurement difficulties when a hydrate is less dense than the liquid hydrate former in the liquid region.

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INTRODUCTION

Because of a lower occupancy of C3H8 in the sII hydrate, the pure C3H8 hydrate (H) in equilibrium with C3H8(l) has received less attention in the literature, where the buoyancy of hydrate causes experimental issues with mixing, transducer isolation, and an inverted solidus. To expand the available data for this hydrate system, this study reports new C3H8 hydrate dissociation pressures and temperatures from T = 273.63− 278.75 K and p = 0.1887−18.2622 MPa, including both the liquid water-hydrate-C3H8(l) (Lw−H−C3H8(l)) and Lw−H− C3H8(g) phase boundaries. The results were modeled using reference quality reduced Helmholtz energy equations of state in combination with the van der Waals and Platteuw (vdWP) hydrate model.10−12 Experimental results and the reference model were compared to previously available literature data,2,13−28 where our Lw−H−C3H8(l) locus data were particularly important for resolving some variance in the literature data.

Gas clathrate hydrates are nonstoichiometric inclusion compounds in which suitably small-sized guest molecules are encaged within the cavities formed by host water molecules.1,2 These compounds have potential applications in hydrogen (H2) storage and gas separation processes (including separation of flue gases)1,3−6 but are often undesirable because they can plug pipelines and block process facilities during oil or natural gas production and transportation.1,6,7 Structures I and II (sI and sII) are the most common structures of gas hydrates encountered in nature and the natural gas industry, respectively.8 The unit cell of a sII gas hydrate consists of 16 small dodecahedral (512 ) and 8 large hexakaidecahedral (5 12 64 ) cages formed by 136 water molecules.1 sII gas hydrates may contain larger gas formers with molecular dimensions in the range of 5.9−7.0 Å, such as propane (C3H8) and isobutane.1,8 In addition to C3H8 being the major component of liquefied petroleum gas (LPG), the C3H8 hydrate is considered the reference material for sII clathrate hydrates. With a diameter of 6.3 Å, C3H8 is too large to occupy the 512 cages; therefore, it can only occupy the large cages of 51264 (6.66 Å) leaving the 512 cages empty.1,2,4,8 As discussed with previous work, the 512 cages in a sII hydrate can potentially accommodate other molecules with smaller diameters such as H2S, CO2 and CH4 at appropriate temperature and pressure conditions. In fact, some smaller formers like H2S often provide a secondary stabilization of the sII hydrate to higher temperatures than the pure C3H8 hydrate;9 therefore, the mixed sII hydrates could be considered for future separation processes. For reference purposes, flow assurance and consideration for future gas separation processes, an accurate description of the pure C3H8 hydrate is necessary. © XXXX American Chemical Society

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EXPERIMENTAL SECTION

Materials. C3H8 with listed purities of 99.999% and 99.5% were supplied by Linde Canada Ltd. and Praxair Inc., respectively. The purity and compositions of C3H8 gases were analyzed with a Bruker 450-gas chromatograph (GC) equipped with a thermal conductivity detector (TCD) and a flame ionization detector (FID). The measured impurities for each fluid are reported in Table 1. Double distilled water was purified using an EMD Millipore model Milli-Q Type 1 water purification system, which produced polished water to a Received: April 11, 2017 Accepted: May 24, 2017

A

DOI: 10.1021/acs.jced.7b00343 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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evacuated autoclave by suction. This amount of water corresponds to an approximate mole ratio of 80:1 water/ C3H8 (after final charge) so that liquid water is always present throughout the experiments, that is, the maximum ratio for the sII hydrate would be 17:1. C3H8 was then added directly to the vessel from the liquid−gas supply cylinder. For measurements in the Lw−H−C3H8(l) region, varying quantity of water was delivered to the autoclave through a syringe pump after first loading the autoclave with liquid C3H8. After loading, the C3H8−H2O mixtures were mixed for 8 h until pressure was stable to within ±0.005 MPa. Once the system had reached equilibrium, it was cooled and held at 273.35 K for 18 h to form hydrates. Figure 2a,b shows example

Table 1. Measured Gas Impurities (mol %) for C3H8 Fluids Used in This Work supplier

N2

Praxiar Inc. Linde Ltd.

0.409 0.000025

CO2 0.002 not detected

CH4

C3H8

i-C4H10

0.00682 0.00138

99.425 99.999

0.1573 not detected

resistivity of 18 MΩ·cm−1. Water was further degassed under vacuum for at least 12 h before any experiments. Measurement Apparatus. The small stirred Hastelloy C276 autoclave used for this work is shown Figure 1, where a

Figure 1. Schematic diagram of the setup used for the measurement of C3H8 hydrate dissociation points. VA1, VA2, and PT represent the inlet feed valve, outlet valve, and pressure transducer, respectively.

more detailed description can be found elsewhere.29,30 The apparatus was originally commissioned with a Paroscientific Inc. Digiquartz 410 KR-HT-101 pressure transducer and an internal four-wire 100 Ω platinum resistance thermometer with a PT-104 temperature data logger (Pico Technologies). The transducer and thermometer were calibrated in-house and found to have a precision of δp = ±3.45 × 10−4 MPa and δT = ±0.001 K, respectively. The Paroscientific Inc. pressure transducer was later replaced with a Keller Druckmesstechnik PA-33X transducer with a precision of δp = ±0.001 MPa for measurements along the Lw−H−C3H8(l) locus. The total internal autoclave volume with the Keller transducer was measured using pure water and found to be 46.21 cm3. Both the vessel and bottom portion of the transducer were placed inside a PolyScience PP07R-40 refrigerated circulating bath controlling the temperature to within ±0.004 K. The stirring assembly was controlled by an in-house assembled voltage regulation controller and a Hall effect rotational speed sensor. For data acquisition, the setup was interfaced with Laboratory Virtual Instrument Engineering Workbench (LabVIEW), which records the pressure and temperature of the system continuously and averages every 30 s. Experimental Procedures. Before each measurement, the autoclave was placed under a vacuum of 2.5 × 10−7 MPa for a period of 24 h. C3H8 gas was then flowed through the feed valve, VA1, up to 5 times to purge any impurities before loading. For the study in the Lw−H−C3H8(g) phase boundary, 10 cm3 of polished and degassed water was injected into the

Figure 2. A typical p−T curve of a cooling, heating, and hydrate dissociation for (a) C3H8(g) + H2O(l) and (b) C3H8(l) + H2O(l).

data sets for cooling and heating binary systems in the C3H8(g) and C3H8(l) regions, respectively. During the heating stage, only stable pressures were used after holding the temperature isothermal for 4 to 6 h to allow for equilibration. Phase Boundary Dissociation (PBD) Method. The PBD method is a modification of the isochoric method in which the hydrates are formed by reducing the temperature of gas−water system inside a constant volume followed by a controlled dissociation of the formed hydrates along a phase boundary (e.g. Lw−H−V).30,31 The temperature and pressure of the system will remain on the triple loci for as long as the three phases coexist (according to the Gibbs phase rule). This method was used for the measurements along the Lw−H− C3H8(g) phase boundary and is shown along the hydrate dissociation in Figure 2a. Isochoric Pressure Search Method. The isochoric pressure search method is a more common data analysis method for phase boundaries that cannot be well traversed over a larger B

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of the hydrate crystal structure (lower dissociation pressure), impurities in the fluid phase can also lead to hydrate destabilization (through entropic stabilization of the fluid phase).1,2,8 In this case, the freezing-point depression effect is small but apparent; whereas if the impurities were species such as H2S, one would expect the opposite effect. The experimental dissociation conditions for 99.999 mol % C3H8 on the Lw−H−C3H8(l) phase boundary are reported in Table 3. The experimental dissociation results for the highest

temperature range or if the inflection for the lower portion of the boundary is less obvious. With this method, the point of intersection between the cooling and heating data is taken as the equilibrium hydrate condition at which all hydrate has been dissociated upon heating. Both methods utilize the same experimental procedure; however, the PBD method has the advantage of more dissociation data points in less time. In this work, only the isochoric pressure search method could be used for the Lw−H−C3H8(l) phase boundary measurements (see Figure 2b for an example).

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Table 3. Experimental Dissociation Conditions for 99.999 mol % C3H8 Hydrates along the Lw−H−C3H8(l) Phase Boundary

RESULTS AND DISCUSSION Previous studies conducted using this experimental setup have demonstrated the accurate determination of equilibrium conditions of CH4 and H2S gas hydrates.30 New experimental dissociation conditions of C3H8 hydrates using two fluid purities (99.5 and 99.999 mol %) along the Lw−H−C3H8(g) phase boundary measurements are reported in Table 2. The Table 2. Experimental Dissociation Conditions for C3H8 Hydrates along the Lw−H−C3H8(g) Phase Boundary 99.999 mol % C3H8

99.5 mol % C3H8

a

p/MPa

273.63 273.83 274.03 274.23 274.42 274.62 274.83 275.02 275.22 275.43 275.63 275.83 276.03 276.22 276.42 276.62 276.82 277.03 277.22 277.42 277.63 277.83 278.03 278.23 278.43 278.62

0.1887 0.1957 0.2038 0.2131 0.2223 0.2318 0.2420 0.2524 0.2637 0.2758 0.2882 0.3005 0.3135 0.3280 0.3434 0.3594 0.3754 0.3927 0.4109 0.4302 0.4501 0.4709 0.4939 0.5167 0.5408 0.5654

T/K

b

T/Ka

p/MPab

273.63 273.83 274.03 274.23 274.43 274.63 274.83 275.03 275.23 275.43 275.63 275.83 276.03 276.23 276.43 276.63 276.84 277.04 277.23 277.44 277.63 277.83 278.03 278.23 278.43 278.63

0.2052 0.2130 0.2212 0.2298 0.2398 0.2489 0.2589 0.2698 0.2799 0.2929 0.3048 0.3175 0.3305 0.3441 0.3582 0.3731 0.3887 0.4062 0.4226 0.4404 0.4637 0.4840 0.5045 0.5262 0.5501 0.5774

T/Ka

p/MPab

278.64 278.65 278.65 278.64 278.68 278.67 278.68 278.69 278.69 278.68 278.73 278.74 278.75 278.75 278.75 278.75 278.76

18.2622 15.9072 13.3852 13.3478 12.4553 11.9547 11.6402 10.5883 9.4884 7.2316 4.2907 2.2420 2.0535 1.0952 0.8096 0.7855 0.5717

a

Uncertainty for hydrate temperature measurements using the calibrated PRT was estimated to be ±0.1 K. bUncertainty for the hydrate pressure measurements was estimated to ±0.001 MPa.

purity C3H8 (both phases) were used to fit a simple semiempirical correlation and calibrate parameters within a more rigorous thermodynamic reference model. A Simple Semiempirical Model for Hydrate Dissociation Pressure. The experimental data for the three phase boundaries were used to fit a semiempirical correlation based on the Clausius−Clapeyron relation for the rapid calculation of the hydrate formation conditions. The Lw−H−C3H8(g) locus can be calculated using 27150.7 ln p = 0.5778 T + − 259.0014 (1) T Similarly, the Lw−H−C3H8(l) phase boundary also can be calculated from the relationship

a

Uncertainty for hydrate temperature measurements using the calibrated PRT was estimated to be ±0.1 K. bUncertainty for the hydrate pressure measurements was estimated to be ±0.0069 MPa.

p = 36704 − 131.668 T

(2)

where p and T are pressure and temperature in MPa and K, respectively. Equation 2 should not be used to extrapolate beyond the pressures of our experimental data and should only be used for p < 20 MPa. Deviations from these two equations are shown in subsequent discussion. Thermodynamic Modeling. In order to rigorously define the equilibrium between coexisting species, the partial molar free energy (chemical potential or fugacity) of each individual species in each phase needs to be well-defined at relevant temperatures, pressures, and molar compositions. By definition,

dissociation pressures for 99.5 mol % C3H8 are about 0.015 MPa larger than that of the 99.999 mol % C3H8 for T = 273.63−278.63 K. In this case, the small increase in pressure can be attributed to the presence of the impurities N2, CO2, and CH4 (assessed by GC TCD/FID as shown in Table 1). These molecules can occupy both the small (512) and large (51264) cages of a sII hydrate but have a higher propensity for occupying the small cages. While a larger fraction of cage occupancy by some impurities can result in further stabilization C

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and pure liquid water phase, at reference conditions of To = 273.15 K and po = 0.1 MPa. Δvm represents the reference molar volume change for the formation of empty hydrate cage from the pure liquid water phase. Δhw represents the molar enthalpy change for the formation of the empty hydrate lattice from the liquid water phase. Δhw is expressed as37

equilibrium is obtained when the free energy of each species in each phase is equal μi L = μi V = μi H

fiL = fiV = fiH

or

(3)

where μ and f are the chemical potential and fugacity of component i, respectively. By solving eq 3 iteratively, one can mathematically find the equilibrium conditions, that is, pressure and temperature, between H2O in a C3H8 gas and H2O that has been incorporated into a C3H8 gas hydrate. The hydrocarbon fluid (vapor and/or liquid C3H8) and hydrate phase fugacities for this study were calculated by using reduced Helmholtz energy EOSs and the modified vdWP model proposed by Chen and Guo (1996) because of the sound physical background and high accuracy of these equations in the dense phase region.10−12,32,33 The fluid phases. Accurate modeling of the hydrate phase conditions depend on the correct fugacities of the fluid phases34 fi (T , p , n) = xipϕi(T , p , n)

Δhw = Δhwο +

where is the reference standard difference in heat capacity between ice and liquid water and b represent the coefficient of temperature correction. Table 4 shows the values of constants in eq 7, 8, and 9 used in this study. Table 4. Thermodynamic Reference Properties for Structure II Used in This Studya

RT

RTο

−

∫T

T

ο

source

1025 J mol−1 937 J mol−1 −37.32 J mol−1 K−1 3.4 cm3 mol−1 0.179 J mol−1 K−2

Dharmawardhana et al.38 Dharmawardhana et al.38 Holder et al.37 Parrish and Prausnitz39 Holder et al.37

Van der waals and Platteeuw derived the change in chemical potential of water in a hydrate phase and the hypothetical empty hydrate cage as12 Δμwβ− H = RT ∑ vm̅ ln(1 − m

(5)

Δhw 2

dT +

∫p

ο

p

Δvw dp RT

∑ θjm) j

(10)

where vm̅ represents the number of cavities of type m per water molecule and θjm is the fractional occupancy of the guest molecules j within the hydrate cavities m. The fractional occupancy of the gas molecule within the cavities is calculated by using the Langmuir adsorption equation which is expressed as12,37 θjm =

Cjmf j 1 + ∑j Cjmf j

(11)

where f j is the fugacity of hydrate former j in cavity m, which was calculated from the saturation calculations given with the fluid phase calculations. The Langmuir constant (Cjm) is used to measure the attraction between the enclathrated gas and water molecules in the cavity and is calculated for this study using the Kihara potential via the correlation provided by Parrish and Prausnitz39 Ajm Bjm exp Cjm(T ) = (12) T T The Kihara correlation parameters for the C3H8 hydrate have been previously reported by Parrish and Prausnitz (Ajm = 0.12353 K MPa−1 and Bjm = 4406.1 K).39 We have further optimized these parameters by minimizing the squared difference between the calculated fugacities of H2O in the C3H8 phase and hydrate phase at the conditions measured in

(6)

RT

structure II

Δhow Δμow Δcopw Δvm b

A value of −6009.5 J mol−1 and 1.6 cm3 mol−1 is added to Δhow and Δvm, respectively, to account for conversion of ice to liquid water.

was calculated from the Wagner and Pruß (2002) reduced Helmholtz energy EOS.11 Classical thermodynamics can be used to derive the expression for Δμβ−L w , where the simplified method of Holder et al. (1980) was used for calculating Δμβ−L w by directly integrating over pressure and temperature while using hexagonal ice (ice Ih) water as a reference point from the relationship37 Δμwο

reference parameter

a

f Lw

=

(9)

Δcopw

where is the reference fugacity of the empty hydrate cavity that is expressed as

Δμw β − L

(8)

ο Δc pw = Δc pw + b(T − Tο)

f βw

f wβ

Δc pw dT

The change in heat capacity (Δcpw) between the empty hydrate and pure water phase is also dependent on temperature

Using the mixing parameters of Kunz and Wagner (2012),35 the C3H8 equation of state of Lemmon et al. (2009),10 and the water equation of state of Wagner and Pruβ (2002),11 one can calculate the fugacity coefficients, ϕi(T,p,n). Saturation compositions and fugacities for the C3H8 + H2O system for this work were iteratively solved using REFPROP.36 For verification, calculated and experimentally determined aqueous C3H8 solubilities for T = 235.55−399.89 K and pressure p = 0.7720−67.3962 MPa were compared for this work and are shown in more detail elsewhere.29 The results showed an agreement to literature data to within an average deviation of less than 0.2%. These equations generally perform better in the high-density regions (liquid−liquid) when compared to standard cubic equations-of-state. The Hydrate Phase. The modified vdWP model outlined by Chen and Guo (1996) was used for modeling the hydrate phase in this study.33 The model is based on the equality of fugacities for water in all phases present at equilibrium, that is, the equality of eq 3 for i = H2O or w. f Hw can be expressed by the change in chemical potential for water in a hydrate phase 1,33 and the hypothetical empty hydrate cage, Δμβ−H w , from eq 5

⎛ −Δμ β− L ⎞ w ⎟⎟ = f wL exp⎜⎜ RT ⎝ ⎠

T

ο

(4)

⎛ −Δμ β− H ⎞ w ⎟⎟ f wH = f wβ exp⎜⎜ ⎝ RT ⎠

∫T

(7)

Δμow

where is the experimentally determined reference chemical potential difference between water in the empty hydrate lattice D

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this work. Our optimized parameters are Ajm = 0.1459 K MPa−1 and Bjm = 3833.66 K (SSE = 0.00017 Pa2). The optimized Ajm parameter is in good agreement with the value reported by Parrish and Prausnitz39 but less than those reported by Kontogeorgis group (0.799 K MPa −1 ; 0.999992 K MPa−1).40,41 In contrast, the new Bjm parameter is in much better agreement with those reported by the Kontogeorgis group (3886 K; 3794.48 K).40,41 These optimized values for Ajm and Bjm can be used to iteratively solve for the hydrate formation temperature at any pressure and have been used in our subsequent comparison of experimental data. A summary of all measured conditions for this study, literature data, and calculated values predicted by the model along the Lw−H−C3H8(g) and Lw−H−C3H8(l) phase boundaries are shown in Figure 3. For the discussion of the

Figure 4. Temperature difference between the model and experimental data, literature data and correlations along the Lw−H− C3H8(g) locus. , reference model described in this work. Experimental data: blue circle, this study (99.5% C3H8); navy circle, this study (99.999% C3H8); □, Reamer et al. (1952);13 ×, Tumba et al. (2014);14 +, Patil (1987);15 ●, Robinson and Mehta (1976);16 ⧫, Englezos and Ngan (1993);17 *, Verma (1974);18 gray solid square, Kubota et al. (2003);19 gray solid diamond, Deaton and Frost (1946);20 ■, Thakore and Holder (1987);21 ◊, Mooijer-van den Heuvel et al. (2001);22 ▲, Nixdorff (1997);23 maroon solid circle, Maekawa (2008);24 gray solid line, Miller and Strong (1946);25 ......., Kamath correlation (2008);26 -------, Carroll correlation (2003);2 blue dashed line, this study Clausius−Clapeyron equation; •−•−, Maekawa correlation (2008).24

through various alternate objective functions (relative squared differences, weighting, and so forth); however, removing the bias in the gas phase resulted in a slight bias in the liquid phase. Regardless of altering the bias, the dissociation of propane hydrate in the liquid always showed a lower temperature with increasing pressure, that is, propane hydrate is less dense than propane or water liquids. While one could optimize each region separately, the model would not be physically correct at the propane vapor pressure, that is, the nature of the solid should not change when going from a liquid hydrocarbon to a gaseous hydrocarbon phase. We also explored the relationship between the purities and average deviation (AD) of the literature data to the optimized model, see Figure 5. Generally, the higher the purity of C3H8 reported in the literature for measurements along the Lw−H− C3H8(g) region, the lower the deviation in temperature from this study’s model. The only exception to this trend was observed for the data reported by Tumba et al. (2014) for the two experimental points.14 The temperature difference between their two values and the model presented in this study was unusually small (AD = −0.05 K) and lower than the deviations observed for other literature data with similar purities, that is, 99.5 mol % C3H8 and some higher purities. Englezos and Ngan (1993), Robinson and Mehta (1976), Patil (1987) and this study reported dissociation data using 99.5 mol % C3H8; however, the other authors did not report any analysis of impurities. The data all show a similar AD of ∼0.2 K for pressures, p = 0.26−0.5774 MPa when compared to the model in this study except those of Patil, which show a higher AD =

Figure 3. Lw−H−C3H8(g) and Lw−H−C3H8(l) phase boundaries (experimental and model) for the C3H8 sII hydrate system. , reference model described in this work; ---, vapor pressure of pure C3H8.10 Experimental data: blue solid circle, this study (99.5% C3H8); navy solid circle, this study (99.999% C3H8); □, Reamer et al. (1952);13 ×, Tumba et al. (2014);14 +, Patil (1987);15 ●, Robinson and Mehta (1976);16 ⧫, Englezos and Ngan (1993);17 *, Verma (1974);18 gray solid square, Kubota et al. (2003);19 gray solid diamond, Deaton and Frost (1946);20 ■, Thakore and Holder (1987);21 ◊, Mooijer-van den Heuvel et al. (2001);22 ▲, Nixdorff (1997);23 maroon solid circle, Maekawa (2008);24 gray solid line, Miller and Strong (1946);25 Δ, Makogon (2003);27 ○,Wilcox et al. (1941).28

deviations from the model and a more detailed comparison of literature data, the deviations have been divided into the Lw− H−C3H8(g) and Lw−H−C3H8(l) phase boundary regions. For the Lw−H−C3H8(g) region, the deviations between the calculated and measured dissociation temperatures of this study for (99.999% C3H8; p = 0.26−0.5654 MPa) are within ±0.12 K. The visual representation of the deviation between the model and the other data (literature and correlations) are shown in Figure 4. The deviations from our calculations are slightly biased along the gas phase loci due to the optimization influence of the Lw−H−C3H8(l) data. Here our measured points are 0.15 K larger than the model at the lower temperature and 0.15 K smaller than the model at the quadruple point. We attempted to try to remove this small bias E

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Figure 5. Relationship between C3H8 purities and average deviation (AD) of the literature data along the Lw−H−C3H8(g) locus to the model presented in this study. , reference model described in this work. Experimental data: blue solid circle, this study (99.5% C3H8); navy solid circle, this study (99.999% C3H8); □, Reamer et al. (1952);13 ×, Tumba et al. (2014);14 +, Patil (1987);15 ●, Robinson and Mehta (1976);16 ⧫, Englezos and Ngan (1993);17 *, Verma (1974);18 gray solid square, Kubota et al. (2003);19 gray solid diamond, Deaton and Frost (1946);20 ■, Thakore and Holder (1987);21 ◊, Mooijer-van den Heuvel et al. (2001);22 ▲, Nixdorff (1997);23 maroon solid circle, Maekawa (2008).24

Figure 6. Hydrate dissociation temperature differences between the model in this study and experimental data along the Lw−H−C3H8(l) locus. , reference model described in this work. Experimental data: navy solid circle, this study (99.999% C3H8); □, Reamer et al. (1952);13 *, Verma (1974);18 ◊, Mooijer-van den Heuvel et al. (2001);22 Δ, Makogon (2003);27 ○, Wilcox et al. (1941);28 -----, this study Clausius−Clapeyron equation.

H−C3H8(g) region, temperature deviation from this model does not correlate with the C3H8 purity. For example, the reported data for Makogon (2003) and Mooijer-van den Heuvel et al. (2001) was 99.995 mol % C3H8 purity,22,27 whereas the data fo Mooijer-van den Heuvel et al. show a significantly lower deviation.22 The large difference for the Makogon (2003)27 data can be attributed to the technique used for measuring the dissociation point, which relied on visual determination of phase transition from one phase to another, where propane hydrates may float out of view. The Reamer et al. (1952) data show the lowest deviation to this model for >99 mol % C3H8.13 The purity of C3H8 used by Wilcox et al. (1941) was not reported but the data were still comparable to the model of this study to with AD < 0.25 K.28 The Clausius− Clapeyron equation also compares favorably to the model presented in this study to within an AD = 0.01 K for pressure ranges p = 0.5717−18.2622 MPa. As shown in Figure 3, Lw−H−C3H8(l) locus leans toward lower temperature as pressure increases, as opposed to higher temperatures as is reported with some models.34,40 This behavior is expected when the formed C3H8 hydrates are at a lower density compared to the liquid water and liquid C3H8 phases (increase in volume upon solidification). A similar trend also was observed by Makogon (2003), although at lower temperatures than the temperatures reported for this study.27 Because this propane hydrate floats on both liquids, it tends to form in small spaces above the mixing vessel, such as in the transducer line. This inhibits mass transfer and contributes to

−0.42 K.15−17 The highest purity of C3H8 in Lw−H−C3H8(g) phase boundary reported in literature was 99.999 mol % by Maekawa (2008), which is the same as that used in this study. As expected, the data were comparable to the model presented in this study to within AD = −0.02 K.24 Also, similar deviations were observed for data obtained by Nixdorff and Oellrich (1997) for >99.995 mol % C3H8.23 The temperatures predicted by Carroll’s and Kamath’s empirical correlations deviate from this model as the pressure increases from 0.2650 to 0.5616 MPa; although, the Kamath correlation tends to predict a higher dissociation average temperature T = ∼0.25 K than the Carroll correlation for the same pressure.2,26 The Clausius− Clapeyron equation reported in this study and Maekawa correlation also compared favorably with the model to within an average temperature of −0.05 K.24 The number of data points, purities, AD, and pressure and temperature ranges compared to the model presented in this study along the Lw−H−C3H8(l) locus are presented in Table 5, while the experimentally measured and calculated conditions with their corresponding deviations along the Lw−H−C3H8(l) phase boundary are shown in Figure 6.18,22,27,28 The model calculates the dissociation temperature to an AD = 0.01 K (for this data only). The literature data in the Lw−H−C3H8(l) region were all within an AD = ±0.2 K except for the data reported by Makogon (2003).18,22,27,28 As opposed to the Lw−

Table 5. Summary of Literature Data and Corresponding Purities along the Lw−H−C3H8(l) Phase Boundary T/K

p/MPa

no. of data points

purity/mol %

AD/K

source

278.05−278.28 278.55−278.88 278.2−278.6 278.6−278.8 278.6−279.2

0.555−35.00 0.643−9.893 0.562−11.30 0.684−2.046 0.807−6.115

9 17 4 3 7

99.95 99.95 >99.50 >99.00

−0.43 0.04 −0.20 −0.03 0.10

Makogon27 Mooijer-van den Heuvel et al.22 Verma18 Reamer et al.13 Wilcox et al.28

F

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Notes

the difficulty in measuring points along Lw−H−C3H8(l) locus, that is, in this case the hydrate density is most likely responsible for the variance in the literature data. The upper quadruple point, Q2, for this study and other literature are reported in Table 6.2,16,18,22,27 All pQ2 in the

The authors declare no competing financial interest.

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(1) Sloan, E. D., Koh, C. A. Clathrate Hydrates of Natural Gases, 3rd ed.; CRC Press: Boca Raton, FL, 2007. (2) Carroll, J. Natural Gas Hydrates, A Guide for Engineers, 2nd ed.; Gulf Professional Publishing: Burlington, MA, 2009. (3) Sloan, E. D. Fundamental Principles and Applications of Natural Gas Hydrates. Nature 2003, 426, 353−363. (4) Sun, C.; Li, W.; Yang, X.; Li, F.; Yuan, Q.; Mu, L.; Chen, J.; Liu, B.; Chen, G. Progress in Research of Gas Hydrate. Chin. J. Chem. Eng. 2011, 19, 151−162. (5) Koh, C. A.; Sloan, E. D.; Sum, A. K.; Wu, D. T. Fundamental and Applications of Gas Hydrates. Annu. Rev. Chem. Biomol. Eng. 2011, 2, 237−257. (6) Eslamimanesh, A.; Mohammadi, A.; Richon, D.; Naidoo, P.; Ramjugernath, D. Application of Gas Hydrate Formation in Separation Processes: A Review of Experimental Studies. J. Chem. Thermodyn. 2012, 46, 62−71. (7) Hammerschmidt, E. Formation of Gas Hydrates in Natural Gas Transmission Lines. Ind. Eng. Chem. 1934, 26, 851−855. (8) Koh, C. A.; Sum, A. K.; Sloan, E. D. Natural Gas Hydrates in Flow Assurance; Gulf Professional Publishing: Burlington, MA, 2011. (9) Ward, Z. T.; Marriott, R. A.; Sum, A. K.; Sloan, E. D.; Koh, C. A. Equilibrium Data of Gas Hydrates containing Methane, Propane, and Hydrogen Sulfide. J. Chem. Eng. Data 2015, 60, 424−428. (10) Lemmon, E. W.; McLinden, M. O.; Wagner, W. Thermodynamic Properties of Propane. III. A Reference Equation of State for Temperatures from the Melting line to 650 K and Pressures up to 1000 MPa. J. Chem. Eng. Data 2009, 54, 3141−3180. (11) Wagner, W.; Pruß, A. The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use. J. Phys. Chem. Ref. Data 2002, 31, 387−535. (12) Van der Waals, J. H.; Platteeuw, J. C. Clathrate Solutions. Adv. Chem. Phys. 1958, 2, 1−57. (13) Reamer, H. H.; Selleck, F. T.; Sage, B. H. Some Properties of Mixed Paraffinic and Olefinic Hydrates. JPT, J. Pet. Technol. 1952, 4, 197−202. (14) Tumba, K.; Babaee, S.; Naidoo, P.; Mohammadi, A. H.; Ramjugernath, D. Phase Equilibria of Clathrate Hydrates of Ethyne + Propane. J. Chem. Eng. Data 2014, 59, 2914−2919. (15) Patil, S. L. Measurement of Multiphase Gas Hydrate Phase Equilibria: Effect of Inhibitors and Heavier Hydrocarbon Components. M.S Thesis, University of Alaska, AK, 1987. (16) Robinson, D.; Metha, B. Hydrates in the Propane−Carbon dioxide−Water System. J. Can. Pet. Technol. 1971, 10, 642−644. (17) Englezos, P.; Ngan, Y. T. Incipient Equilibrium Data for Propane Hydrate Formation in Aqueous Solutions of NaCl, KCl, and CaC12. J. Chem. Eng. Data 1993, 38, 250−253. (18) Verma, V. K. Gas Hydrates from Liquid Hydrocarbon-Water Systems. Ph.D. Dissertation, University of Michigan, Ann Arbor, MI, 1974. (19) Kubota, H.; Shimizu, K.; Tanaka, Y.; Makita, T. Thermodynamic Properties of R13 (CClF3), R23 (CHF3), R152a (C2H4F2) and Propane Hydrates for Desalination of Seawater. J. Chem. Eng. Jpn. 1984, 17, 423−429. (20) Deaton, W.; Frost, J. E. Gas Hydrates and Their Relation to the Operation of Natural-Gas Pipe Lines. U.S. Bureau Mines, Monograph 8, 1946. (21) Thakore, J. L.; Holder, G. D. Solid Vapor Azeotropes in Hydrate-Forming Systems. Ind. Eng. Chem. Res. 1987, 26, 462−469. (22) Den Heuvel, M. M. M.; Peters, C. J.; de Swaan Arons, J. Gas Hydrate Phase Equilibria for Propane in the Presence of Additive Components. Fluid Phase Equilib. 2002, 193, 245−259. (23) Nixdorf, J.; Oellrich, L. R. Experimental Determination of Hydrate Equilibrium Conditions for Pure Gases, Binary and Ternary Mixtures and Natural gases. Fluid Phase Equilib. 1997, 139, 325−333.

Table 6. Quadruple Point Conditions from This Study and Literature source

purity/mol %

p/MPa

T/K

Makogon27 Robinson and Mehta16 Mooijer-van den Heuvel et al.22 Carroll2 Verma18 this studya this studyb

99.95 99.5 99.95

0.555 0.5516 0.6 0.556 0.562 0.5591 0.5692

278.3 278.87 278.62 278.75 278.4 278.68 278.71

99.999 99.999

a

Q2 was calculated from the point of intersection of Lw−H−C3H8(g) and Lw−H−C3H8(l) using the semiempirical Clausius−Clapeyron equations. bQ2 was calculated from the point of intersection of the calculated Lw−H−C3H8(g) and Lw−H−C3H8(l) loci by the thermodynamic model reported in this study.

literature fall within the uncertainties of this study (±0.007 MPa). Similarly, most of the quadruple point temperatures, TQ2, reported in the literature fall within 95% confidence interval, TQ2 = 278.68 ± 0.1 K except that of Robinson and Mehta (1974).16

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CONCLUSIONS New measured formation conditions for C3H8 hydrate in equilibrium with gaseous and liquid C3H8 were reported for 99.999% purity, where previously the reported literature for the liquid C3H8 region showed a large variance. Two semiempirical Clausius−Clapeyron equations have been reported for rapid calculation of the Lw−H−C3H8(g) and Lw−H−C3H8(l) loci but are limited to p < 20 MPa. For further extrapolation, a reference thermodynamic model was optimized using reduced Helmholtz energy EOSs and the modified vdWP model proposed by Chen and Guo (1996).33 Measurements with 99.5% purity and review of literature data show that small amount of impurity was found to be important when studying C3H8 hydrate dissociation conditions, where larger deviations from the model were observed for the studies that used lower purity C3H8 for measurements along the Lw−H−C3H8(g) locus. The Lw−H−C3H8(l) locus showed a trend toward lower temperatures with increasing pressures. This inclination is expected because the density of C3H8 hydrate is less than the densities of the other two coexisting liquid phases.

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Robert A. Marriott: 0000-0002-1837-8605 Funding

This research has been funded through the Natural Science and Engineering Research Council of Canada (NSERC) and Alberta Sulphur Research Ltd. (ASRL) Industrial Research Chair program in Applied Sulfur Chemistry. The authors are grateful to NSERC and supporting member companies of ASRL. G

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H

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