Experimental Measurements and Predictions of GasHydrate Dissociation Conditions in the Presence ofMethanol and Ethane-1,2-diol Aqueous SolutionsJafar Javanmardi,*,† Saeedeh Babaee,† Ali Eslamimanesh,‡ and Amir H. Mohammadi‡,§
†Department of Chemical Engineering, Shiraz University of Technology, 71555-313, Shiraz, Iran‡MINES ParisTech, CEP/TEPCentre Energetique et Procedes, 35 Rue Saint Honore, 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
ABSTRACT: In this work, experimental hydrate dissociation conditions of methanein the presence of 0.06, 0.10, and 0.20 mass fractions of methanol and 0.10 and 0.25 massfractions of ethane-1,2-diol in aqueous solutions are reported. In addition, phase equilibria ofa ternary mixture of methane (0.9319 mole fraction) + ethane (0.0481 mole fraction) +propane (0.02 mole fraction) in the presence of 0.25 mass fraction of ethane-1,2-diolaqueous solution is investigated. A high-pressure equilibrium cell is used for measurement ofhydrate dissociation conditions in the temperature range of (265.4 to 282.0) K and pressurerange of (1.97 to 6.96) MPa. The experimental gas hydrate dissociation conditions aremodeled using the van der Waals and Platteeuw (vdW-P) solid solution theory for dealingwith the hydrate phase and the Valderrama−Patel−Teja equation of state (VPT-EoS) alongwith the nondensity dependent (NDD) mixing rules to account for the fluid phases. Theobtained experimental data are finally compared with selected experimental data from theliterature as well as the model predictions, and acceptable agreements are observed.
I. INTRODUCTIONGas hydrates (or clathrate hydrates) are crystalline solid compoundscomposed of water and small molecules of a suitable size atappropriate conditions of temperature and pressure. The smallmolecules are trapped in the cavities of hydrogen-bonded watermolecules.1 These crystalline compounds may be formed in oil andgas production, transportation, and processing facilities and canconsequently cause serious economic, operational, and safetyproblems. Thermodynamic inhibitors such as methanol andethane-1,2-diol (ethylene glycol) are generally used to inhibitthe formation of gas hydrates in the petroleum industry.1 Theseinhibitors shift the boundaries of equilibrium of hydrate−liquidwater−liquid hydrocarbon/vapor to higher pressures and lowertemperatures.1 Accurate knowledge of gas hydrate phase equili-brium in the presence of alcohols and glycols is of great interest todetermine the operational conditions of interest, at which theprobability of gas hydrates formation is low. There is still a need togenerate more experimental data for methane (and methane-richhydrocarbon gases) hydrate in the presence of specific massfractions of methanol and ethane-1,2-diol aqueous solutions to tunespecially adapted thermodynamic models for predictions ofdissociation conditions of hydrate systems. In addition, due tolimited corresponding experimental data for the systems containinggas mixtures in the presence of aqueous solutions of inhibitors,generating such data would be fruitful for the petroleum industry.The objective of this study is to measure methane gas
hydrate dissociation conditions in the presence of 0.06, 0.10,and 0.20 mass fractions of methanol and 0.10 and 0.25 mass
fractions of ethane-1,2-diol aqueous solutions. In addition, thephase equilibrium of a ternary mixture of methane (0.9319 molefraction), ethane (0.0481 mole fraction), and propane (0.02 molefraction) gas hydrate in the presence of 0.25 mass fraction ofethane-1,2-diol aqueous solution is reported. Finally, the obtainedexperimental data are compared with thermodynamic modelpredictions and selected experimental data from the literature.
II. EXPERIMENTAL SECTIONA. Materials. The purities and suppliers of the materials are
reported in Table 1. Aqueous solutions were prepared followingthe gravimetric method, using an accurate analytical balance(mass uncertainty ± 0.0001 g). Consequently, uncertainties onthe basis of mole fraction are estimated to be less than 0.01.
B. Experimental Apparatus. The main part of the experi-mental setup is a high-pressure equilibrium cell with a 75 cm3
internal volume. This cell is made of 316 stainless steelequipped with double sight glasses. Figure 1 shows a schematicpicture of the designed and built-up high-pressure equilibriumcell used in this work. The cell temperature is controlled using athermostatic bath. The pressure of the cell is measured by apressure transducer (ABD), previously calibrated against adead weight balance, within an estimated accuracy of about0.01 MPa. A Pt100 platinum temperature probe inserted in the
Received: December 29, 2011Accepted: March 5, 2012Published: April 10, 2012
cell interior is used to measure the temperature of the system.The uncertainty of the temperature measurements are about ±0.1 K. A data acquisition system is used for recording the systempressure and temperature throughout the experiments. The VarianCP-3800 gas chromatograph is used for compositional analysis ofthe gas mixture of methane, ethane, and propane before startinghydrate dissociation measurements. A schematic diagram of theapparatus used in this work has been sketched in Figure 2.C. Experimental Procedure. After the equilibrium cell was
well-cleaned and then evacuated with vacuum pump, prepared aque-ous solutions containing the known concentrations of inhibitorwere introduced into the cell. Later, the pressure of the cell was
increased to the desired pressure by introducing the hydrateformer into the cell. Following the isochoric pressure-searchmethod,2−4 the temperature was slowly decreased until hydrateformation in the vessel was detected by pressure drop and confirm-ed by visual observation. The temperature was later increased insteps at slow rate of 0.1 K·h−1. After complete decomposition ofexisting gas hydrate in the cell, the point at which the slope ofpressure−temperature plot changes sharply is normally consideredas the hydrate dissociation point. The temperature and pressure ofthe equilibrium cell were recorded using the data acquisition unitevery 108 s. Figure 3 shows a typical heating curve used for thedetermination of the hydrate dissociation point.
III. THERMODYNAMIC MODELING
A general phase equilibrium criterion (equality of fugacities ofeach component throughout all present phases) has been usedto develop a thermodynamic model5 for predicting the gashydrate dissociation conditions in the presence of investigatedaqueous solutions. For this purpose, the thermodynamic modelpresented by Mohammadi and and co-workers5 has been applied,in which the Valderrama modification of the Patel and Teja
Table 1. Purities and Suppliers of the Materials Used in ThisStudy
chemical supplier purity/(mole fraction)
methane Air Product 0.9995ethane Air Product 0.9995propane Air Product 0.9995methanol Merck 0.999ethane-1,2-diol Merck 0.99water deionized water
Figure 1. Schematic of high-pressure equilibrium cell. DCM, DCmotor; GO, gas out; GI, gas in; GP, gas phase; LP, liquid phase; S,stirrer; SG, sight glasses.
Figure 2. Schematic diagram of the apparatus used for measuring hydrate dissociation conditions. V, valve; R, regulator; Ch, check valve; T, thermometer;P, pressure transducer; DAS, data acquisition system; M, methane; E, ethane; P, propane; TB, thermostatted bath; GI, gas in; GO, gas out; C, cell.
Figure 3. General determination of the hydrate dissociation pointfrom the heating curve. DP, dissociation point; NHR, no hydrateregion; DGH, decomposition of gas hydrate.
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(VPT)6 equation of state (EoS) accompanied with nondensity-dependent (NDD)7 mixing rules has been applied to evaluate thefugacities of components in fluid phases (this set of EoS6 andmixing rules7 have been already demonstrated to have highcapabilities in phase equilibrium representations/predictionsespecially for the systems containing polar components likewater, alcohol, or glycol)5 while the hydrate phase is modeled usingthe van der Waals and Platteeuw (vdW-P) solid theory.8 Thefugacity of water in the hydrate phase is calculated as follows:
= −Δμβ
β−⎛⎝⎜⎜
⎞⎠⎟⎟f f
RTexpw
Hw
wH
(1)
where:
=Δμβ
β−⎛⎝⎜⎜
⎞⎠⎟⎟f f
RTexpw w
l wL
(2)
In the preceding equations, R is the universal gas constant,T stands for temperature, fw
H, fwβ , and fw
1 are the fugacities ofwater in hydrate phase, empty hydrate lattice, and pure state,respectively, and Δμwβ−H is chemical potential difference ofwater between the empty hydrate lattice and hydrate phase,which is evaluated as follows:8
∑ ∑Δμ = μ − μ = +β− β RT v C fln(1 )wH
w wH
mm
jjm j
(3)
where vm stands for the number of cavities of type m per watermolecule in the unit hydrate cell, f j denotes the fugacity of thegas component j, and Cjm is the Langmuir constant. Numerical
Table 2. Optimum Values of the Binary InteractionParameters between Ethane-1,2-diol (1)−Ethane (2) andEthane-1,2-diol (1)−Propane (2) Obtained in This Work
aStandard (classical) binary interaction parameter. bBinary interactionparameters for the asymmetric term of the VPT EoS6 and NDDmixing rule.7
Table 3. Hydrate Dissociation Temperature and PressureRanges for Methane and a Mixture of Methane, Ethane, andPropane in the Presence of Different Aqueous Solutions ofInhibitors
hydrateformer aqueous solution TRa/K PRb/MPa
methane pure water (274.7 to 282.0) (3.04 to 6.29)d
methane 0.06 mass fractionmethanolc
(273.9 to 279.5) (3.48 to 5.94)
methane 0.10 mass fractionmethanol
(265.4 to 278.1) (1.97 to 6.54)
methane 0.20 mass fractionmethanol
(265.4 to 273.3) (3.06 to 6.88)
methane 0.10 mass fractionethane-1,2-diol
(272.6 to 279.9) (3.05 to 6.46)
methane 0.25 mass fractionethane-1,2-diol
(268.0 to 275.2) (2.98 to 6.40)
methane +ethane +propane
0.25 mass fractionethane-1,2-diol
(276.9 to 281.7) (3.60 to 6.96)
aRange of gas hydrate dissociation temperatures. bRange of gashydrate dissociation pressures. cThe interval of the confidence forestimating the uncertainties is considered to be 0.95. Therefore, theexpanded uncertainties (Uc) in the reported mass fractions are about ±0.01. dThe interval of the confidence for estimating the uncertainties isconsidered to be 0.95. Therefore, the expanded uncertainties (Uc) inthe reported pressures are about ± 0.01 MPa.
Table 4. Experimental Hydrate Dissociation Conditions ofMethane in the Presence of Pure Water
aPressure. bTemperature. The interval of the confidence for estimatingthe uncertainties is considered to be 0.95. Therefore, the expandeduncertainties (Uc) in the reported temperatures are ± 0.1 K.
Table 5. Experimental Hydrate Dissociation Conditions ofMethane in the Presence of Methanol Aqueous Solutions
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values for the Langmuir constant can be calculated by choosinga model for the guest−host interaction:1,8,9
∫= π −∞ ⎛
⎝⎜⎞⎠⎟C T
kTw rkT
r r( )4
exp( )
djm 02
(4)
where k is the Boltzmann constant. The function w(r) is thespherically symmetric cell potential in the cavity, with r fromthe center, and depends on the intermolecular potential
function chosen for describing the encaged gas−water inter-action. In this work, the Kihara10 potential function is appliedto evaluate the Langmuir constant as follows:1,5,8
= ε σ*
δ + αδ − σ*
δ + α
δ
⎡⎣⎢⎢
⎛⎝⎜⎜
⎞⎠⎟⎟
⎛⎝⎜⎜
⎞⎠⎟⎟⎤⎦⎥⎥w r z
R r R R r R( ) 2
( ) ( )12
1110 11
6
54 5
(5)
where
δ =
−
− α
− +
− α
− −
⎜ ⎟ ⎜ ⎟⎡⎣⎢⎢⎛⎝
⎞⎠
⎛⎝
⎞⎠
⎤⎦⎥⎥N
rR R
rR R
11 1N
N N
(6)
In the two preceding equations, z is the coordination number ofthe cavity (the number of oxygen molecules at the periphery ofeach cavity), ε represents the characteristic energy, α is the radius
Table 7. Experimental Hydrate Dissociation Conditions for aTernary Mixture of 0.9319 mole fraction of Methane, 0.0481mole fraction of Ethane, and 0.02 mole fraction of Propanein the Presence of 0.25 mass fraction of Ethane-1,2-diol
P/MPa T/K
3.62 276.94.52 278.55.63 280.36.96 281.7
Figure 4. Experimental and predicted methane hydrate dissociationconditions in the presence of pure water. Symbols representexperimental dissociation conditions. ●, this work; ×, ref 14; ◊, ref 15.Solid curve, predictions of the thermodynamic model.5
Figure 5. Experimental and predicted methane hydrate dissociationconditions in the presence of methanol aqueous solutions. Symbolsrepresent experimental dissociation conditions. Pure water: *, this work. A0.06 mass fraction methanol aqueous solution: ▲, this work. A 0.10 massfraction methanol aqueous solution: ■, this work; +, ref 16; ○, ref 17. A0.20 mass fraction methanol aqueous solution: ●, this work; ×, ref 16; □,ref 17. Solid curve, predictions of thermodynamic model.5
Figure 6. Experimental and predicted methane hydrate dissociationconditions in the presence of ethane-1,2-diol aqueous solutions. Symbolsrepresent experimental dissociation conditions. Pure water: ●, this work.A 0.10 mass fraction ethane-1,2-diol aqueous solution: ■, this work; ○,ref 17; △, ref 18. A 0.25 mass fraction ethane-1,2-diol aqueous solution:▲, this work. Solid curve, predictions of the thermodynamic model.5
Figure 7. Experimental and predicted hydrate dissociation conditionsfor a ternary mixture of 0.9319 mole fraction of methane, 0.0481 molefraction of ethane, and 0.02 mole fraction of propane in the presenceof 0.25 mass fraction ethane-1,2-diol aqueous solution: ▲, this work.Solid curve, predictions of the thermodynamic model in the presenceof 0.25 mass fraction ethane-1,2-diol aqueous solution. Dashed curve,predictions of thermodynamic model in pure water.5
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of spherical molecular core, R stands for the cavity radius, andN is an integer equals to 4, 5, 10, or 11. In addition, σ* =σ − 2α, where σ is the collision diameter.1
Holder et al.9 showed that the chemical potential differenceof water between the empty hydrate lattice and the liquid phase(Δμwβ−L) is defined as:
∫ ∫
Δμ=
μ−
μ
=Δμ
−Δ
+Δ
β− β
β− β−RT
T P
RT
T P
RT
RTh
RTdT
vRT
P
( , ) ( , )
d
L
T
T
P
P
wL
w w
w0
0
wL
2w
L
0 0
(7)
where superscripts 0 refers to reference property and β−Lstands for the difference property between empty hydratelattice and water in liquid state. Δμw0 is the reference chemicalpotential difference between water in empty hydrate lattice andpure water in the ice phase at standard condition (here it is273.15 K), Δv is the molar volume difference, and Δh standsfor the enthalpy difference. The subscript w stands for water. Asmentioned earlier, the VPT EoS6 along with NDD7 has beenemployed to determine the fugacities of hydrate former(s),water, and inhibitor in aqueous and vapor phases throughperforming the flash calculations. Details of the applied EoS canbe found elsewhere.5 The optimum values of binary interactionparameters of the NDD mixing rule7 (l0pi, l
1pi and kij) between
ethane-1,2-diol-ethane and ethane-1,2-diol-propane have beenalready obtained using the experimental data of ethane andpropane solubilities in ethane-1,2-diol, reported by Jou et al.11 and
Wang et al.,12 by the minimization of the follow-ing objective function (Fobj):
∑=| − |⎛
⎝⎜⎜
⎞⎠⎟⎟F
x x
x1
NDPobj1
NDPexp cal
exp (8)
where NDP is the number of experimental data points, x is molefraction of ethane/propane in ethane-1,2-diol liquid phase, andsubscripts exp and cal refer to experimental and calculated valuesof the solubilities, respectively. Table 2 shows the optimum valuesof the binary interaction parameters. The binary interactionparameters between other investigated components have beentaken from literature.7,13
IV. RESULTS AND DISCUSSIONThe investigated dissociation pressure ranges for methane andmixture of methane, ethane, and propane hydrates in thepresence of different aqueous solutions of methanol or ethane-1,2-diol are reported in Table 3. Tables 4 to 7 report themeasured gas hydrate dissociation conditions in the presence ofdifferent aqueous solutions. Furthermore, the hydrate dissoci-ation pressures versus temperature diagrams are shown inFigures 4 to 7. Selected experimental data from literature alongwith the applied model predictions have also been indicated inthese figures. As can be seen, acceptable agreement between themeasured data and the ones reported in the literature as well asthe model5 predictions is observed. The applied parameters ofthe thermodynamic model are reported in Tables 8 and 9.The results show that thermodynamic inhibitors such as
methanol and ethane-1,2-diol shift the hydrate dissociation con-ditions to high pressures and low temperatures, as expected.Table 10 reports the results of comparison between the obtain-ed experimental methane hydrate dissociation temperatureswith the thermodynamic model5 predictions, which indicate theaverage absolute deviation (AAD) of the model results fromexperimental ones to be around 0.2 K. The measured gashydrate dissociation conditions of ternary mixture containing0.9319 mole fraction of methane, 0.0481 mole fraction ofethane, and 0.02 mole fraction of propane in the presence of0.25 mass fraction of ethane-1,2-diol are shown in Figure 7.The optimum values of the binary interaction parameters(reported in Table 2) have been used to predict the hydratedissociation conditions of this mixture in the presence ofethane-1,2-diol with AAD of around 0.2 K of the predictionsfrom the measured experimental data.
V. CONCLUSIONSIn this communication, gas hydrate dissociation conditions ofmethane and a ternary system of methane (0.9319 mole fraction) +
Table 8. Phase Transition Parameters from Water toStructure I (sI) and Structure II (sII) Hydrate19
aThe reference chemical potential difference between water in emptyhydrate lattice and pure water in the ice phase at standard condition(here it is 273.15 K). bEnthalpy difference. cMolar volume difference.
aThe radius of the spherical molecular core. bσ* = σ − 2α, where σ isthe collision diameter. cε is the characteristic energy, and k is theBoltzmann constant.
Table 10. Average Absolute Deviation (AAD) of Predicted Methane Hydrate Dissociation Temperatures in the Presence ofMethanol or Ethane-1,2-diol Aqueous Solution Evaluated Using the Thermodynamic Model5 from Experimental Values
aqueous phase no. data points TRa/K PRb/MPa AADc/K
pure water 7 (274.7 to 282.0) (3.04 to 6.29) 0.10.06 mass fraction methanol 5 (273.9 to 279.5) (3.48 to 5.94) 0.10.10 mass fraction methanol 8 (265.4 to 278.1) (1.97 to 6.54) 0.20.20 mass fraction methanol 5 (265.4 to 273.3) (3.06 to 6.88) 0.20.10 mass fraction ethane-1,2-diol 5 (272.6 to 279.9) (3.05 to 6.46) 0.10.25 mass fraction ethane-1,2-diol 7 (268.0 to 275.2) (2.98 to 6.40) 0.2total 37 (265.4 to 282.0) (1.97 to 6.88) 0.2
aTemperature range. bPressure range. cAAD = (1/NP)∑i=1NP|Texp − Tcal|i, where NP is the number of the experimental data.
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ethane (0.0481 mole fraction) + propane (0.02 mole fraction)in the presence of pure water and aqueous solutions of methanolor ethane-1,2-diol were measured (reported in Tables 4 to 7)using an isochoric pressure-search method2−4 in a high-pressure equilibrium cell. The hydrate dissociation conditionsin the presence of investigated inhibitors were predicted using adeveloped thermodynamic model5 based on the equality offugacities of all components in present phases. The obtainedexperimental data were compared with the model5 predictionsand selected experimental data reported in the literature, andacceptable agreements were observed. The generated data inthis work can be applied to tune thermodynamic models for anaccurate prediction of the operational conditions of natural gasprocesses for avoiding hydrate formations.
■ AUTHOR INFORMATIONCorresponding Author*Phone: +98-711-7354520. E-mail: [email protected] authors appreciate the financial support of the Researchand Development branch of Parsian Gas Company.NotesThe authors declare no competing financial interest.
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