- Email: [email protected]
Prediction of phase equilibrium of clathrate hydrates of multicomponent natural gases containing CO2 and H2S
Journal of Petroleum Science and Engineering ∎ (∎∎∎∎) ∎∎∎–∎∎∎
Contents lists available at ScienceDirect
Journal of Petroleum Science and Engineering journal homepage: www.elsevier.com/locate/petrol
Prediction of phase equilibrium of clathrate hydrates of multicomponent natural gases containing CO2 and H2S Prathyusha Mekala, Jitendra S. Sangwai n Petroleum Engineering Program, Department of Ocean Engineering, Indian Institute of Technology Madras, Chennai 600036, India
art ic l e i nf o
a b s t r a c t
Article history: Received 14 May 2013 Accepted 23 February 2014
The sour natural gas readily forms hydrates and stays stable at higher temperatures and lower pressures and hence is responsible for plugging, corroding the pipelines and causing other flow assurance-related issues. Predictions of formation and dissociation conditions of these hydrates are necessary in applications for preventing such hazards primarily due to the blockages of pipelines. However, natural gases from the gas reservoirs can have combinations of different concentrations of each of the following constituents, CH4, C2H6, C3H8, C4H10, N2, CO2 and H2S. Presence of high concentrations of CO2 and/or H2S along with other components is often found in natural gas, thereby limiting the accurate functioning of several of the available phase behavior models. The major limitation for their inaccuracy can be attributed to the complexity involving CO2 and H2S in hydrate systems. In this work, a new thermodynamic computing approach is developed for predicting the phase equilibria for hydrates of multicomponent sour natural gases (with CO2 and H2S) from different natural gas systems. The model of Chen and Guo (1998) (Chem. Eng. J., 71, 145, 1998) is extended for the multicomponent sour natural gas hydrate system using the Kihara potential functions to model the guest–host interaction energies. In addition, a semi-empirical form is proposed to calculate the equilibrium hydrate temperature for hydrates of natural gas with and without CO2 and H2S. The developed model is fitted with 12 sets of experimental data on the phase equilibria of sour natural gas hydrate system and found to be satisfactory. The average absolute deviation pressure percentage (AADP%) for most of the cases studied is observed to be well within 10%, thus proving its efficacy. The present model can, therefore, find potential applications for developing mitigation techniques for flow assurance issues and for robust natural gas and hydrate reservoir models containing sour gases. & 2014 Elsevier B.V. All rights reserved.
Keywords: carbon dioxide hydrogen sulfide natural gas hydrate phase equilibria sour gas
1. Introduction Gas hydrates are formed due to the combination of sufficient amounts of water and gas at favorably high pressure and low temperature conditions. Gas hydrates, generally referred to as clathrate hydrates, are of snowy ice-like structures formed by ‘guest’ molecules of gases such as methane (CH4), ethane (C2H6), propane (C3H8), butane (C4H10), carbon dioxide (CO2), hydrogen sulfide (H2S), hydrogen (H2), nitrogen (N2), etc., when entrapped in a three-dimensional lattice formed by the ‘host’ water molecules due to H–H bonding (Sloan and Koh, 2008). The difference between ice and hydrate is best elucidated by examining the mechanical, electrical and transport properties (Sloan and Koh, 2008). The formation of gas hydrate is a non-stoichiometric chemical process expected under high pressure and low temperature conditions. In the 1930s, Hammerschmidt (1934) first
n
Corresponding author. Tel.: þ 91 44 22574825 (office); fax: þ 91 44 22574802. E-mail address: [email protected] (J.S. Sangwai).
discovered that natural gas forms hydrates in oil and gas pipelines, thus blocking the flow. In 1966, Makogon (1966) first discovered the presence of gas hydrate in ocean floor during experimentation with core samples and observed that the deep sea sediments and permafrost are the harbingers of stable natural gas hydrates. Makogon (1982) was the first to estimate the hydrate reserves followed by Kvenvolden (1988) who predicted the estimated hydrates reserves to be more than 1015 g, which indeed is a source of a huge amount of natural gas to meet the energy need for decades. The naturally occurring natural gas hydrates mainly consists of methane along with several other guest gas molecules such as CO2, H2S, and N2. Presence of high concentrations of carbon dioxide and hydrogen sulfides in natural gas is, in general, very common, and referred to as a sour gas. Carbon dioxide and hydrogen sulfide are very soluble in water and thermodynamically form clathrates individually or in combination with natural gas at relatively higher temperatures and lower pressures when compared to sweet gas. Therefore, the sour gas readily forms hydrates and stays stable at such higher temperatures and lower pressures (ZareNezhad and
http://dx.doi.org/10.1016/j.petrol.2014.02.018 0920-4105 & 2014 Elsevier B.V. All rights reserved.
Please cite this article as: Mekala, P., Sangwai, J.S., Prediction of phase equilibrium of clathrate hydrates of multicomponent natural gases containing CO2 and H2S. J. Petrol. Sci. Eng. (2014), http://dx.doi.org/10.1016/j.petrol.2014.02.018i
P. Mekala, J.S. Sangwai / Journal of Petroleum Science and Engineering ∎ (∎∎∎∎) ∎∎∎–∎∎∎
2
Nomenclature (aα)m, bmmixture parameters of PR EoS in Eqs. (18) and (19) a, b, m, A, B parameters in PR EoS A', B', C' Antoine constants in Eq. (10) Aij interaction parameter between gas molecule and cavities as in Eq. (10) aw activity of water C Langmuir adsorption constant d collision diameter, f fugacity of gas phase, MPa f0 fugacity of hydrate phase, MPa i gas component kij interaction parameter between guest and host gas molecules as in Eq. (18) l gas component m cavity type n hydration number P equilibrium pressure of natural gas p, q constants in Eq. (14) Pc critical pressure, MPa Pr reduced pressure, P/Pc R universal gas constant, J K 1 mol 1 r cavity radius,
Aminian, 2012; ZareNezhad, 2013; Sun et al., 2003; etc.). These conditions are mostly prevalent in most important commercial oil and gas transmission lines from production facilities, and hence responsible for plugging, corroding the pipelines and causing other flow assurance related issues. Predictions of formation and dissociation conditions of these hydrates are necessary in applications for preventing such hazards, primarily due to the blockages of pipelines. Phase equilibria of hydrates are, therefore, necessary for developing mitigation techniques to resolve the hydrate blockades formed in the offshore pipelines for uninterrupted transport of reservoir fluids and also for robust hydrate reservoir models, which may find due application for production of natural gas from hydrates using CO2 sequestrations, etc. (Goel, 2006; Song et al., 2010). In addition, developing a reliable model assists in extending and extrapolating the equilibrium conditions when performing experiments is expensive, time consuming, cumbersome and often requires repetition.
2. Summary of the review Models for phase equilibria for the hydrate system are developed in the literature following the classical work of van der Waals and Platteeuw (vdW–P) based on the statistical thermodynamic model approach (van der Waals and Platteeuw, 1959). A wellknown hydrate model includes a model developed by Parrish and Prausnitz (1972) that extended vdW–P model prediction for hydrate formation conditions of single and multicomponent gas in water. Lundgaard and Mollerup (1992) used the vdW-P model with Kihara spherical core potential interaction parameters between water and guest gas molecules. Chen and Guo (1996) proposed the kinetic mechanism of the formation of gas hydrate explaining the possible mode of lattice occupancy by guest molecules to account for the local stability of the hydrate structure. Klauda and Sandler (2000) developed the vdW–P model for single component hydrate systems using the concept of fugacities rather than reference energy parameters, thereby decreasing the adjustable guest interaction parameters to three. Kaluda and Sandler
s, t T T0 Tc Tr V x y Z
α β ΔH ϵ θ λ1 λ2 s φa, φb ω ω(r)
constants in Eq. (15) equilibrium temperature of hydrate equilibrium temperature of hydrate with no CO2 and H2S critical temperature, K reduced temperature molar volume of gas, m3 mole fraction of gas component in hydrate phase mole fraction of gas component in gas phase compressibility factor fractional coefficient structural parameter enthalpy of dissociation of hydrate phase depth of intermolecular potential well, erg fraction of linked cavities occupied by gas number of linked cavities per water molecule in the basic hydrate number of gas molecules per water molecule in the basic hydrate structure core distance at zero potential constants for PR EoS in Eq. (24) and Eq. (25) acentric factor interaction between a guest and host summed up over the cage
(2003) extended their earlier work (Klauda and Sandler, 2000) to address the phase equilibrium of multicomponent gas hydrate system. Ballard and Sloan (2002) developed a fugacity based model for hydrate phase equilibria, which accounts for the nonidealities in the hydrate system. The model reduces to the vdW–P model when the non-idealities are ignored. Lee and Holder (2002) developed a hydrate phase behavior model accounting for the host–guest interaction through the chemical potential principal and using the Kihara potential functions. Bahadori's (2007) numerical model approach is based on calculating the vapor–solid equilibrium constant. The above-mentioned models are modified to incorporate certain mathematical equations which explain the solid state phase behavior of hydrate systems. All the above models were published to predict the phase equilibria conditions of single and multicomponent gases forming hydrate, whereas model predictions for natural gases and sour natural gases are found to be scarce. Very few models, for example, Sun et al. (2003) applied Chen and Guo's (1998) model for hydrates of gas mixture with high concentrations of CO2 and H2S and found to be deviating largely from the experimental phase equilibrium observations. Sun and Chen (2005) extended the Chen and Guo model (1998) to the hydrate system containing CO2 and H2S. However, the application of their model was limited to the three component gas hydrate system. Karakatsani and Kontogeorgis (2013), in their recent study of validating cubic plus association (CPA) based model, reported the drawbacks of the model, particularly for the gas hydrate systems containing high concentrations of CO2. ZareNezhad and Aminian (2012) came up with the adaptive neuro fuzzy inference system (ANFIS) model, a multilayer neural network-based approach for modeling the phase behaviors of a sour natural gas hydrate system. They observed that the model deviates from the experimental values as the concentration of H2S increases. ZareNezhad (2013) developed a hydrate phase behavior model for predicting sour gas hydrate dissociation pressures, which are prevalent in sour natural gas reservoirs. They proposed a mixing rule to take into account the affinity between H2S and H2O. ZareNezhad and Ziaee (2013) predicted phase equilibria of sour gases using the CPA equation of state and
Please cite this article as: Mekala, P., Sangwai, J.S., Prediction of phase equilibrium of clathrate hydrates of multicomponent natural gases containing CO2 and H2S. J. Petrol. Sci. Eng. (2014), http://dx.doi.org/10.1016/j.petrol.2014.02.018i
P. Mekala, J.S. Sangwai / Journal of Petroleum Science and Engineering ∎ (∎∎∎∎) ∎∎∎–∎∎∎
electrostatic effects of hydrolytic dissociation of H2S and CO2 gases according to the modified Pitzer–Debye–Hückle model in combination with the Chen and Guo model. However, natural gases from the gas reservoirs can have combinations of different concentrations of each of the following constituents, CH4, C2H6, C3H8, C4H10, N2, CO2 and H2S. Presence of high concentrations of CO2 and/or H2S along with other components is often found in natural gas, thereby limiting accurate functioning of several of these models (Sun et al., 2003; Sun and Chen, 2005; ZareNezhad and Aminian, 2012). The major limitation for the inaccuracy in phase equilibria predictions can be attributed to their complexity involving CO2 and H2S in the hydrate system. In the present study, a phase behavior model is developed to address the hydrate phase behavior of multicomponent natural gases containing CO2 and H2S. The model of Chen and Guo (1998) is extended to the phase behaviors of sour natural gas hydrates due to its simplicity and good elucidation of hydrate formation mechanism in two steps (Sun et al., 2003; Sun and Chen, 2005; Joshi et al., 2012). It is well-known fact that the presence of CO2 and H2S in natural gases attracts complexities in hydrate dissociation prediction. In the absence of sufficient hydrate dissociation data on the multi-component sour natural gas system, we employed a semi-empirical approach along with the PR-EoS and the Chen and Guo model to predict the hydrate dissociation conditions. It was assumed that as the number of guest molecules in the hydrate forming phase increases, the interactions between different gas molecules cannot be ignored, as may be the case with natural gas hydrates containing CO2 and H2S. These interactions can be between ions, molecules and their environment. In order to account for the presence of CO2 and H2S in natural gas systems, we used the Kihara potentials function over Lennard–Jones along with the said hydrate model (which was used otherwise). This approach helped us improve model predictions for multi-component sour natural gases. We believe that the present work provides a simple model and approach of computing hydrate dissociation conditions for multicomponent sour natural gas hydrate systems containing both CO2 and H2S.
3
are filled in these sites through adsorption to form gas hydrates. Gas hydrate generally forms either structure I or II (or else, Sloan and Koh, 2008) each with small and large interstices called as cavities inside the solid lattice structure. The type of structures formed depends on the sizes of guest gas molecules making the hydrate (Sloan and Koh, 2008). In general smaller gas molecules form structure I and larger gas molecules form structure II. Natural gas is a mixture of gases generally forming a structure II type of hydrate. The natural gases having C3 to iC4 components form a structure II type hydrate with diamond lattice made by small 512 and large 51262 cages. Larger hydrocarbon molecules like neopentane, isohexane or methylcyclohexane can form structure H type of hydrate (Mehta et al., 1996). 512 cage is formed by 12 pentagonal rings and 51262 cage by 12 pentagonal and two hexagonal rings. The model development in this work considers a structure II due to the multicomponent ‘guest’ gas molecules containing CO2 and H2S (Holder and Hand, 1982; Adisasmito and Sloan, 1992; Sloan and Koh, 2008). The number of gas molecules encapsulated in the water cage (hydration number) depends on the pressure and temperature of the environment at which these hydrates are formed (Holder and Hand, 1982). 3.2. Hydrate phase model The formation mechanism of gas hydrate is represented by (Chen and Guo, 1998) H2 O þ λ2 G-Gλ2 H2 O
ð1Þ
here, G and λ2 are the gas species and the number of gas molecules per water molecule in the basic hydrate structure, respectively. The overall properties of a mixture hydrate also depend on the filling of gas molecules in the linked cavities. Eqs. (1)–(3) can be established for a mixture of gas hydrate systems. To obtain the equilibrium phase conditions, the fugacity of gas phase, f, and fugacity of hydrate structure, f0, are equated, using the following final form: α 0 f i ¼ xi f i 1 ∑ θi ð2Þ i
3. Model development In this section, firstly, the general hydrate formation mechanism is discussed, followed by the hydrate phase behavior model for the natural gas hydrates containing CO2 and H2S.
∑xi ¼ 1 when
ð3Þ
θ ¼ 0, Eq. (2) becomes 0
∑f i ¼ ∑xi f i
ð4Þ
Hydrates can be formed by either of the chemical reactions between (i) gas and water or (ii) gas and ice, at high pressure and low temperature conditions.
here xi denotes the mole fraction of gas, i, in basic hydrate and fi denotes the fugacity of a gas component i. α ¼ λ1/λ2, where, λ1 and λ2 are the number of linked cavities per water molecule in the basic hydrate and the number of gas molecules per water molecule in the basic hydrate, respectively. θ is the fraction of linked cavities occupied by the gas molecules and defined as
CH4 þnH2O 3 CH4 nH2O þ54.2 kJ/mol (with water)
θ¼
3.1. Hydrate formation mechanism
CH4 þnH2O 3 CH4 nH2O þ18.6 kJ/mol (with ice) n is the hydration number depending on the type of gas and the pressure at which the hydrate is formed (Makogon, 1997). Hydrate formation mechanism followed for the present study has the following two steps. (i) Guest gas molecules surrounded by water molecules forming a basic hydrate (i.e., basic cavities being completely occupied) and (ii) linking of these basic hydrates forming empty linked cavities (Chen and Guo, 1998). Hydrate mixture is more like a real solution since the thermodynamic entropy of mixing for gas encapsulated hydrate structure is equal to the entropy of the basic hydrate structure and the value is not equal to zero as is the case for ideal mixtures. Guest gas molecules, such as H2, CO2, N2, H2S, CH4, etc., with a specific molecular size
Cf 1 þCf
∑ θi ¼ i
ð5Þ
∑ Cif i i
1 þ ∑ Cif i
ð6Þ
i
here C is the Langmuir adsorption constant and is a function of temperature and gas components. In a real solution intermolecular interactions in terms of energy potentials were empirically determined by integrating either Lennard–Jones (Chen and Guo, 1996, 1998; etc.) or Kihara cell potentials functions (Parrish and Prausnitz, 1972; Lundgaard and Mollerup, 1992; Klauda and Sandler, 2000; Lee and Holder, 2002; etc.). The advantages of choosing Kihara potentials over Lennard–Jones potentials are that Kihara core potential function takes care of the impenetrable
Please cite this article as: Mekala, P., Sangwai, J.S., Prediction of phase equilibrium of clathrate hydrates of multicomponent natural gases containing CO2 and H2S. J. Petrol. Sci. Eng. (2014), http://dx.doi.org/10.1016/j.petrol.2014.02.018i
P. Mekala, J.S. Sangwai / Journal of Petroleum Science and Engineering ∎ (∎∎∎∎) ∎∎∎–∎∎∎
4
hard core of the hydrate by subtracting it from the hard sphere diameter shown in the following equation and that Kihara potentials could be applied for non-spherical gas molecules, as well as may be the case in multicomponent systems containing higher hydrocarbon and non-hydrocarbons such as CO2 and H2S. 8 9 < 1 r rd = h i ð7Þ ωðrÞ ¼ 4ε s d12 s d6 r 4 d : ; rd rd where ω(r) is said to be the interaction between a guest and host summed up over the cage, r the radius and d is the collision diameter. Chen and Guo (1998) used Lennard–Jones potential function to obtain the values of the Langmuir adsorption constant, Ci. In this work, in order to compute the amount of gas being adsorbed on the solid surfaces of the hydrate, Ci, are obtained by integrating the Kihara potential (Parrish and Prausnitz, 1972) functions to model the guest–host interaction energies as follows: Am;l Bm;l exp ð8Þ Ci ¼ T T Am,l and Bm,l (m is the cavity type and l the gas component) are constants for structure II cavities for each of the guest gas molecules and reported elsewhere (Parrish and Prausnitz, 1972). The constant C is the reverse function of temperature, which is in accordance with the expectation that the binding energy will increase with decrease in the temperature and vice versa. The hydrate phase fugacity, f 0, is calculated using the following form (Chen and Guo, 1998): 0
0
0
0
f ¼ f ðTÞf ðPÞf ðaw Þ
ð9Þ
previous studies (Mekala and Sangwai, 2012) on pure methane gas hydrate. T is the equilibrium temperature for hydrates of methane with CO2 and H2S. n is the hydration number (Sloan and Koh, 2008). ΔH is the enthalpy of dissociation of hydrates phase. As in Eq. (13), the activity is the function of temperature than pressure, since sub-cooling temperature is a better driving force than pressure for the formation of gas hydrate in a closed system (Sloan and Koh, 2008). Carbon dioxide and hydrogen sulfide hydrates form at lower equilibrium pressure and temperature conditions than methane hydrate (Caroll, 2009); therefore, the presence of CO2 and H2S in the natural gas mixture aids to suppress the hydrate formation temperature. This effect is accomplished by computing the activity of formation of water through Eq. (13). ΔH is computed based on dissociation pressures by Eq. (14), which is a function of dissociation temperature, which is defined as the difference between the equilibrium temperature and the base temperature of 273 K (Holder et al., 1988; Mork, 2002).
ΔHdiss ¼ p ½q 4ðΔTÞ
ð14Þ
Determination of approximate ΔH for each natural gas system is an important step in predicting phase equilibria. The constants p and q in Eq. (14) are fitting parameters and being tuned with the experimental data on phase equilibrium of hydrates of natural gas mixtures. We propose using the following form of equation to calculate, T0, the equilibrium hydrate temperature for hydrates of methane without CO2 and H2S: T 0 ¼ s log ðPÞ þ t
ð15Þ
The Antoine constants A', B', C' and interaction parameter, Aij, depend on the guest occupying the cavities and are obtained from Chen and Guo (1998). The effect of Pressure on f 0 is given as (Chen and Guo, 1998) βP 0 ð11Þ f ðPÞ ¼ exp T
where P is the equilibrium pressure for hydrates of methane without CO2 and H2S. s and t are the best-fit parameters for the hydrates of natural gas mixtures without CO2 or (and) H2S content. The calculated equilibrium pressure and temperature data of Mekala and Sangwai (2012) reported for pure methane gas hydrate are fitted to Eq. (15) to obtain the values of constants s and t. To calculate the gas phase fugacity (as in Eq. (2)) Peng– Robinson (P–R) Equation of state (EoS) is found to be good enough for predicting the fluid phase at high pressures and lower temperatures for this study. The P–R EoS used is as follows:
where P is the system pressure, and β ¼10.224 for structure II. The effect of activity, aw on f0 is given as (Chen and Guo, 1998)
P¼
where 0
f i ðTÞ ¼ exp
∑j Aij θi B' A' exp T C' T
f ðaw Þ ¼ aw 1=λ2 0
ð10Þ
ð12Þ
aw ¼1 for pure water. To propose a model which predicts hydrate phase stability of a multicomponent natural gas containing CO2 and H2S, consideration of hydrate structural changes and activities is necessary. Therefore, selection of activity of water for a respective equilibrium pressure, P, and temperature, T, condition is an important step while computing the phase equilibrium conditions of hydrates of natural gas with CO2 and H2S formed in bulk phase. However, since activity is a property which is termed as the resultant real solution behavior due to the effect of interactions, at certain high pressure and low temperature conditions the activity of water having dissolved natural gases needs to be accounted while accounting for the hydrate formation mechanism. Activity is mostly computed taking reference to ideal gas. In this work aw is determined by Eq. (13) as follows (Nasrifar and Moshfeghian, 2001): ΔH 1 1 lnðaw Þ ¼ ð13Þ nR T T 0 T0 is the reference equilibrium hydrate temperature for hydrates of methane without CO2 and H2S, and is taken from
RT aα V b V ðV þ bÞ
ln
fi yi P
¼
bi ðZ 1Þ lnðZ BÞ bm 2∑j ¼ 1 yi aij bi A ðZ þ2:414BÞ pffiffiffi ln Z 0:414B ðaαÞm bm 2 2B
ð16Þ
ð17Þ
h i pffiffiffiffiffiffiffiffiffiffiffiffi ðaαÞm ¼ ∑ ∑ yi yj ai aj αi αj ð1 kij Þ
ð18Þ
bm ¼ ∑½yi bi
ð19Þ
i
j
i
A¼
B¼
ðaαÞm P
ð20Þ
ðRTÞ2 bm P RT
ð21Þ pffiffiffiffiffi
α ¼ ½1 þ mð1 T r Þ2
ð22Þ
m ¼ 0:480 þ 1:574ω 0:176ω2
ð23Þ
a ¼ φa
R2 T c 2 Pc
ð24Þ
Please cite this article as: Mekala, P., Sangwai, J.S., Prediction of phase equilibrium of clathrate hydrates of multicomponent natural gases containing CO2 and H2S. J. Petrol. Sci. Eng. (2014), http://dx.doi.org/10.1016/j.petrol.2014.02.018i
P. Mekala, J.S. Sangwai / Journal of Petroleum Science and Engineering ∎ (∎∎∎∎) ∎∎∎–∎∎∎
b ¼ φb
RT c Pc
ð25Þ
Tr is the reduced temperature, Pc and Tc are the critical pressure and temperature, ω is the acentric factor, V is the molar volume of gas; and the constants φa and φb have the values 0.45724 and 0.07780, respectively, for all pure gases.
5
an input, equilibrium pressures were generated through the proposed model. The model prediction for the phase equilibrium of the hydrate system containing CO2 and H2S is shown in Figs. 2–13 for various gas compositions (Table 1) along with the corresponding experimental
4. Results and discussion Accuracy of a model depends on the accuracy of experimental data available, mechanism of hydrate formation, and theories and correlations involved (Bahadori, 2007). The experimental investigations on the phase behavior of hydrate are being studied extensively; however, the data on the phase equilibria of natural gas hydrates containing H2S and CO2 are very limited, may be due to their corrosive and toxic behavior (Sun et al., 2003; Sun and Chen, 2005; ZareNezhad and Aminian, 2012; ZareNezhad, 2013). For this work, 12 sets of experimental data on the phase equilibrium of natural gas hydrate system containing CO2 and H2S for the model validation are considered from various sources and are shown in Table 1. These data sets typically contain the natural gas composition from methane (C1) to hexane (C6 þ) with the presence of non-hydrocarbon gases, such as N2, CO2 and H2S. The phase equilibrium data sets for the multicomponent natural gas mixture (having 6–10 guest gases) are chosen such that these contained sufficient high concentrations of CO2, which are in the range of 0.52–89.62 mol% and/or H2S in the range of 0.25– 16 mol%. The selected data range on CO2 and H2S are believed to be comfortable to check the efficacy of the developed model. The model equations from Eqs. (2)–(25) are solved using a code generated in MatLabs. A step by step flow diagram for calculating the equilibrium pressure and temperature for multicomponent sour natural gas hydrate system is shown in Fig. 1. Computations are initially started by calculation of T0, the equilibrium temperature for natural gas composition, without CO2 and H2S followed by calculation of equilibrium temperature and pressure conditions. T is said to be the equilibrium temperature of the natural gas containing CO2 and H2S as mentioned earlier. The binary interaction parameters, kij, used in PR EoS (Eq. (18)) are given in Table 2 for reference. The parameters, namely, p, q, and s, t in Eq. (14) and Eq. (15), are tuned with the experimental data available (Table 1) to minimize the error between the model perditions and the experimental data and also simultaneously to decrease the error between the fugacity of gas phase and hydrate phase to less than 0.1%. The final tuned values are listed in Table 3 and Table 4, respectively. For the experimental equilibrium temperatures as
Fig. 1. Flow chart for computing equilibrium P and T of multi-component natural gas hydrate.
Table 2 Binary Interaction Parameters (kij in Eq. (18)) taken for the multicomponent system of gases containing CO2 and H2S for model validation (Ahmed, 2006). CO2 N2 H2S CO2 0 N2 H2S C1 C2 C3 i-C4 n-C4 i-C5 n-C5 C6
0 0
C1
C2
C3
0.135 0.105 0.130 0.125 0.130 0.025 0.010 0.090 0 0.070 0.085 0.080 0 0.005 0.010 0 0.005 0
i-C4
n-C4
i-C5
n-C5
C6
0.120 0.095 0.075 0.035 0.005 0.000 0
0.115 0.095 0.075 0.025 0.010 0.000 0.005 0
0.115 0.100 0.070 0.030 0.020 0.015 0.005 0.005 0
0.115 0.100 0.110 0.070 0.030 0.020 0.015 0.005 0.005 0
0.115 0.110 0.070 0.030 0.020 0.010 0.005 0.005 0.000 0.000 0
Table 1 Compositions of different natural gas hydrates referred for validation. Gas
1 2 3 4 5 6 7 8 9 10 11 12
Composition (mol%)
Reference
N2
CO2
H2S
C1
C2
C3
i-C4
n-C4
i-C5
n-C5
C6 þ
1.1 – – – – 0.84 9.59 0.43
3.25 31.40 66.85 83.15 89.62 1.74 3.19 0.51 12.6 12 12 22.3
0.25 – – – – – – – 5.4 8 16 5.7
87.8 52.5 24.42 12.38 7.86 84.19 86.32 93.2 82 80 72 22.3
4.0 8.12 3.99 1.96 1.13 8.76 0.78 4.25 – – – –
2.1 4.74 3.07 1.66 0.86 3.35 0.03 1.61 – – – –
1.5 1.31 0.75 0.37 0.20 0.32 0.01 – – – – –
– 1.88 0.92 0.48 0.33 0.60 0.01 – – – – –
– – – – – 0.08 0.01 – – – – –
– – – – – 0.08 0.01 – – – – –
– – – – – 0.02 0.07 – – – – –
Deaton and Frost (1946) Adisasmito and Sloan (1992)
Ollerich and Nixdorf (1997) Wilcox et al. (1941) Robinson and Hutton (1967)
Please cite this article as: Mekala, P., Sangwai, J.S., Prediction of phase equilibrium of clathrate hydrates of multicomponent natural gases containing CO2 and H2S. J. Petrol. Sci. Eng. (2014), http://dx.doi.org/10.1016/j.petrol.2014.02.018i
P. Mekala, J.S. Sangwai / Journal of Petroleum Science and Engineering ∎ (∎∎∎∎) ∎∎∎–∎∎∎
6
2
Table 3 Tuned parameters p and q (Eq. (14)) for predicting energies of dissociation (Refer to Table 1 for gas details). p
q
1 2 3 4 5 6 7 8 9 10 11 12
4.18 6.10 4.18 4.18 4.18 4.18 6.12 6.12 6.12 6.00 9.55 9.95
13,500 2356 1350 1350 1350 5231 13,500 3610 13,500 13,500 13,950 13,900
1.6 Prassure (MPa)
Gas
1.8
t
1 2 3 4 5 6 7 8 9 10 11 12
8.59 8.13 8.61 8.61 8.61 4.10 9.34 8.60 1.75 2.95 4.85 6.15
266.15 266.10 270.70 263.50 264.00 269.22 276.90 265.70 265.22 266.22 270.90 263.22
1 0.8 0.6 0.2 0 272
274
276
278
280
282
284
Temperature (K) Fig. 3. Model prediction for phase equilibrium of sour natural gas hydrate (with 31.4% CO2 composition) by the improved Chen and Guo model. ____: Model prediction (this work); □: Experimental data (Gas no. 2; Table 1). 2.5
2 Pressure (MPa)
s
1.2
0.4
Table 4 Values of s and t (Eq.(15)) computed for different natural gases (Refer to Table 1 for gas details). Gas
1.4
1.5
1
0.5
0 272
274
276
278
280
282
284
Temperature (K)
Fig. 4. Model prediction for phase equilibrium of sour natural gas hydrate (with 66.85% CO2 composition) by the improved Chen and Guo model. ____: Model prediction (this work); ◇: Experimental data (Gas no. 3; Table 1).
7
5
4
4
3.5
3
3
2 1 0 270
275
280
285
290
295
Temperature (C) Fig. 2. Model prediction for phase equilibrium of sour natural gas hydrate (with 3.25% CO2 and 0.25% H2S composition) by the improved Chen and Guo model. _____: Model prediction (this work); ◇: Experimental data (Gas no.1; Table 1).
Pressure (MPa)
Pressure (MPa)
6
2.5 2 1.5 1 0.5 0 272
274
276
278
280
282
284
Temperature (K)
phase equilibrium data on the hydrate system. The results show that the developed model predicts the phase behavior of the sour gas hydrate satisfactorily for most of the experimental data set considered for this work, except for Gas no. 2 (Fig. 3). The deviations are calculated using the percentage of absolute average deviation pressure (AADP%) at each equilibrium temperature for each gas composition and are tabulated in Table 5. The AADP values are observed to be less than 10% for most of the experimental data sets. The AADP values, in general, show that the proposed model is successful in the prediction of the phase equilibrium data for the various sets of sour natural gas hydrate system. It is observed from the results that for the range of CO2 concentration studied in this work, 0.51–89.62 mol%, the AADP
Fig. 5. Model prediction for phase equilibrium of sour natural gas hydrate (with 83.15% CO2 composition) by the improved model. ____: Model prediction (this work); ◇: Experimental data (Gas no. 4; Table 1).
is observed to be from 0.98% to 19.7%. However, interestingly, for the range of H2S concentration studied, 0.25–16 mol%, the AADP is observed to be from 1.08% to 7.38%. Figs. 10–13 show the model prediction for the experimental data of Robinson and Hutton (1967) (Gases 9–12 from Table 1). This sour gas mixture consists of both CO2 and H2S gases along with CH4. The model predictions are observed to be in good agreement with the experimental data. Figs. 10–13 also show the comparison of the
Please cite this article as: Mekala, P., Sangwai, J.S., Prediction of phase equilibrium of clathrate hydrates of multicomponent natural gases containing CO2 and H2S. J. Petrol. Sci. Eng. (2014), http://dx.doi.org/10.1016/j.petrol.2014.02.018i
4.5
16
4
14
3.5
12
3
Pressure (MPa)
Pressure (MPa)
P. Mekala, J.S. Sangwai / Journal of Petroleum Science and Engineering ∎ (∎∎∎∎) ∎∎∎–∎∎∎
2.5 2 1.5
10 8 6 4
1
2
0.5 0 272
274
276
278
280
282
0 275
284
280
285
290
295
300
Temperature (K)
Temperature (K) Fig. 6. Model prediction for phase equilibrium of sour natural gas hydrate (with 89.62% CO2 composition) by the improved Chen and Guo model.____: Model prediction (this work); △: Experimental data (Gas no. 5; Table 1).
Fig. 9. Model prediction for phase equilibrium of sour natural gas hydrate (with 0.51% CO2 composition) by the improved Chen and Guo model. ____: Model prediction (this work); ◇: Experimental data by Wilcox (Gas no. 8; Table 1). 12
10 9
10
8 7
Pressure (MPa)
Pressure (MPa)
7
6 5 4 3 2
8 6 4 2
1 0 270
275
280
285
290
295
0 287
300
288
Temperature (K)
289
290
291
292
293
Temperature (K)
Fig. 7. Model prediction for phase equilibrium of sour natural gas hydrate (with 1.74% CO2 composition) by the improved Chen and Guo model. ____: Model prediction (this work); ◇: Experimental data (Gas no. 6; Table 1).
Fig. 10. Model prediction for phase equilibrium of sour natural gas hydrate (with 12.6% CO2 and 5.4% H2S composition). ____: Model prediction (this work); —————: Chen and Guo model (Chen and Guo, 1998); △: Experimental data (Gas no. 9; Table 1).
30 9 8 7
20 Pressure (MPa)
Pressure (MPa)
25
15 10 5 0 275
6 5 4 3 2
280
285 Temperature (K)
290
295
Fig. 8. Model prediction for phase equilibrium of sour natural gas hydrate (with 3.19% CO2 composition) by the improved Chen and Guo model. ____: Model prediction (this work); ○: Experimental data (Gas no. 7; Table 1).
Chen and Guo model (Sun et al., 2003) with the present model. It is evident from these figures that the present model shows better match and hence is more reliable. One of the recent publications (ZareNezhad and Ziaee, 2013) also attempt to predict the dissociation conditions of hydrates of three component sour natural gas systems using an improved Chen and Guo model along with CPA EoS. Their work was primarily applied for three component natural gas hydrate systems containing H 2S and CO2. The AADP values are observed to lie in the range of 2.15–8.67% for the three component sour natural gas system as against our model, AADP values being in the range of 1.08–7.38
1 0 288
289
290
291
292
293
Temperature (K)
Fig. 11. Model prediction for phase equilibrium of sour natural gas hydrate (with 12% CO2 and 8% H2S composition). ____: Model prediction (this work); —————: the Chen and Guo model (Chen and Guo, 1998); □: Experimental data (Gas no. 10; Table 1).
for a similar system (Gas nos. 9–12) showing better prediction. The developed model in general can predict phase equilibrium of the sour natural gas hydrate system satisfactorily. It is important to generate more experimental data on the phase equilibrist of sour natural gas hydrate system for the development and testing of the robust model which are vital for effective flow assurance issue to hydrate plugging or for robust reservoir models for natural gas production from the hydrate reservoirs.
Please cite this article as: Mekala, P., Sangwai, J.S., Prediction of phase equilibrium of clathrate hydrates of multicomponent natural gases containing CO2 and H2S. J. Petrol. Sci. Eng. (2014), http://dx.doi.org/10.1016/j.petrol.2014.02.018i
P. Mekala, J.S. Sangwai / Journal of Petroleum Science and Engineering ∎ (∎∎∎∎) ∎∎∎–∎∎∎
8 7
293.69 K temperature ranges on the phase equilibria of sour natural has hydrate system and found to be satisfactory. The average absolute deviation pressure percentage (AADP%) for most of the cases studied is observed to be well within 10%, thus proving its efficacy. The present model can, therefore, find potential applications for developing mitigation techniques for flow assurance issues and for robust natural gas and hydrate reservoir models containing sour gases.
6
Pressure (MPa)
5 4 3 2 1 0 291
Declaration 292
293
294
295
The authors declare no competing financial interest.
296
Temperature (K)
Fig. 12. Model prediction for phase equilibrium of sour natural gas hydrate (with 12% CO2 and 16% H2S composition). ____: Model prediction (this work); —————: the Chen and Guo model (Chen and Guo, 1998); ○: Experimental data (Gas no.11; Table 1). 12
Pressure (MPa)
10 8
4 2
280
285
290
295
Temperature (K)
Fig. 13. Model prediction for phase equilibrium of sour natural gas hydrate (with 22.3% CO2 and 5.7% H2S composition). ____: Model prediction (this work); □: Experimental data (Gas no. 12; Table 1).
Table 5 Percentage of Average Absolute Deviation Pressure (AADP) computed for the gases studied for corresponding equilibrium temperature and pressure ranges (Refer to Table 1 for gas details). Gas
T (K)
P (MPa)
Np
AADPa (%)
1 2 3 4 5 6 7 8 9 10 11 12
275.4–289.3 273.7–282 273.7–282 273.7–282 273.7–282 273.65–293.11 276.63–292.59 277.7–293.3 287.5–292.3 289.1–292.1 291.5–295.3 284.22–293.55
0.95–5.25 0.6–1.7 0.758–2.22 1.36–3.51 1.33–3.47 8.3–9.02 3.8–24.3 1.6–14.1 4.4–8.8 4.1–6.0 3.3–5.2 2.65–11.1
4 4 4 4 4 15 9 5 4 3 3 7
3.2 19.7 6.3 0.98 1.19 12.6 10.3 5.2 3.52 1.31 1.08 7.38
a
AADP is defined as
AADPð%Þ ¼
Financial support from Earth System Science Organization, Ministry of Earth Sciences, Government of India, through NIOT, Chennai, India (Grant: OEC/10-11/105/NIOT/JITE) and IIT Madras (Grant: OEC/10-11/530/NFSC/JITE) are gratefully acknowledged. References
6
0
Acknowledgments
1 Np P cal P exp 100 ∑ N p j ¼ 1 P exp
5. Conclusion In this work, the classical Chen and Guo model (Chem. Eng. J., 71, 145, 1998) for hydrates is extended for hydrates of sour natural gases with high concentrations of CO2 and H2S using the Kihara potential functions to model the guest–host interaction energies. The developed model is fitted with 12 sets of experimental data ranging from 0.6 MPa to 24.3 MPa pressure and 273.7 K to
Adisasmito, S., Sloan, E.D., 1992. Hydrates of carbon dioxide and methane mixtures. J. Chem. Eng. Data 343, 343–349. Ahmed, T., 2006. Reservoir Engineering Handbook. Gulf Professional Publishing, Burlington, MA, USA Bahadori, A., 2007. A new approach for multicomponent vapor solid equilibrium calculations in gas hydrate formation. In: Paper 2007-047 Presented at Canadian International Petroleum Conference, 1–13 June, Alberta. Ballard, A.L., Sloan Jr, E.D., 2002. The next generation of hydrate prediction I. Hydrate standard states and incorporation of spectroscopy. Fluid Ph. Equilib. 197, 371–383. Caroll, J., 2009. Natural Gas Hydrates: A Guide for Engineers, 2nd ed. USA: Gulf Professional Publishing, Burlington, MA, USA Chen, G., Guo, T., 1996. Thermodynamic modeling of hydrate formation based on new concepts. Fluid Ph. Equilib. 122, 43–65. Chen, G., Guo, T., 1998. A new approach to gas hydrate modeling. Chem. Eng. J. 71, 145–151. Deaton, W.M., Frost Jr., E.M., 1946. Gas Hydrates and their Relation to the Operation of Natural Gas Pipelines, U.S. Bureau of Mines Monograph 8. Goel, N., 2006. In situ methane hydrate dissociation with carbon dioxide sequestration: current knowledge and issues. J. Pet. Sci. Eng. 51, 169–184. Hammerschmidt, E.G., 1934. Formation of gas hydrates in natural gas transmission lines. Ind. Eng. Chem. 26, 851–855. Holder, G., Hand, J., 1982. Multiple phase equilibria in hydrates from methane, ethane, propane and water mixtures. AIChE J. 28 (12), 440–447. Holder, G.D., Zetts, S., Pradhan, N., 1988. Phase behavior in systems containing clathrate hydrates: a review. Rev. Chem. Eng. 5 (1–4), 1–70. Joshi, A., Mekala, P., Sangwai, J.S., 2012. Modeling phase equilibria of semiclathrate hydrates of CH4, CO2 and N2 in aqueous solution of tetra-n-butyl ammonium bromide (TBAB). J. Nat. Chem. 21 (4), 459–465. Karakatsani, E.K., Kontogeorgis, G.M., 2013. Thermodynamic modeling of natural gas systems containing water. Ind. Eng. Chem. Res. 52 (9), 3499–3513. Klauda, J.B., Sandler, S.I., 2000. A fugacity model for gas hydrate phase equilibria. Ind. Eng. Chem. Res. 39, 3377–3386. Klauda, J.B., Sanlder, S.I., 2003. Phase behavior of clathrate hydrates: a model for single and multiple gas component hydrates. Chem. Eng. Sci. 58, 27–41. Kvenvolden, K.A., 1988. Methane hydrate – a major reservoir of carbon in the shallow geosphere. Chem. Geol. 71, 41–51. Lee, S.Y., Holder, G.D., 2002. Model for gas hydrate equilibria using a variable reference chemical potential: part 1. AIChE J. 48 (1), 161–167. Lundgaard, L., Mollerup, J., 1992. Calculation of phase diagrams of gas–hydrates. Fluid Ph. Equilib. 76, 141–149. Makogon, Y., 1966. Features of natural gas fields exploitation in permafrost zone. Gazov. Prom. 9, 1–17. Makogon, Y.F., 1982. Perspectives for the development of gas–hydrate deposits. In: Proceedings of the 4th Canadian Permafrost Conference, pp. 299–304. Makogon, Y.F., 1997. Hydrates of Hydrocarbons. Penn Well, Tulsa, USA Mehta, A.P., Makogon, T.Y., Burruss, R.C., Wendlandt, R.F., Sloan, E.D., 1996. A composite phase diagram of structure H hydrates using Schreinemakers' geometric approach. Fluid Ph. Equilib. 121 (1–2), 141–165. Mekala, P., Sangwai, J.S., 2012. Predictability of equation of state (EoS)-based gas hydrate models for single and binary gas mixtures. J. Pet. Eng. Technol. 2 (3), 9–17. Mork, M., 2002. Formation Rate of Reactor Experiments and Models (Ph.D. thesis). Norwegian University of Science and Technology, Norway.
Please cite this article as: Mekala, P., Sangwai, J.S., Prediction of phase equilibrium of clathrate hydrates of multicomponent natural gases containing CO2 and H2S. J. Petrol. Sci. Eng. (2014), http://dx.doi.org/10.1016/j.petrol.2014.02.018i
P. Mekala, J.S. Sangwai / Journal of Petroleum Science and Engineering ∎ (∎∎∎∎) ∎∎∎–∎∎∎ Nasrifar, K., Moshfeghian, M., 2001. A model for prediction of gas hydrates formation conditions in aqueous solutions containing electrolytes and/or alcohol. J. Chem. Thermodyn. 33 (9), 999–1014. Ollerich, L.R., Nixdorf, J., 1997. Experimental determination of hydrate equilibrium conditions for pure gases, binary and ternary mixtures and natural gases. Fluid Ph. Equilib. 139, 325–333. Parrish, W.R., Prausnitz, J.M., 1972. Dissociation pressures of gas hydrates formed by gas mixtures. Ind. Eng. Chem. Proc. Des. Dev. 11 (1), 26–35. Robinson, D.B., Hutton, J.M., 1967. Hydrate formation in systems containing methane, hydrogen sulphide and carbon dioxide. J. Can. Pet. Technol. 6, 6–9. Sloan, E.D., Koh, C.A., 2008. Clathrate Hydrates of Natural Gas, 3rd ed. CRC Press, New York Song, Y., Yang, M., Chen, Y., Li, Q., 2010. An improved model for predicting hydrate phase equilibrium in marine sediment environment. J. Nat. Gas Chem. 19 (3), 241–245. Sun, C.Y., Chen, G.J., 2005. Modeling the hydrate formation condition for sour gas and mixtures. Chem. Eng. Sci. 60 (17), 4879–4885.
9
Sun, C.Y., Chen, G.J., Lin, W., Guo, T.M., 2003. Hydrate formation conditions of sour natural gases. J. Chem. Eng. Data 48 (3), 600–602. van der Waals, J.H., Platteeuw, J.C., 1959. Clathrate solutions. Adv. Chem. Phys. 2, 1–57. Wilcox, W., Carson, D., Katz, L., 1941. Natural gas hydrates. Ind. Eng. Chem. 33 (8), 662–665. ZareNezhad, B., 2013. Predicting the sour gas hydrate dissociation pressures regarding sour natural gas production from gas–condensate reservoirs. J. Chem. Technol. Metall. 1, 92–98. ZareNezhad, B., Aminian, A., 2012. Accurate prediction of sour gas hydrate equilibrium dissociation conditions by using an adaptive neuro fuzzy inference system. Energy Convers. Manag. 57, 143–147. ZareNezhad, B., Ziaee, M., 2013. Accurate prediction of H2S and CO2 containing sour gas hydrates formation conditions considering hydrolytic and hydrogen bonding association effects. Fluid Ph. Equilib. 356 (25), 321–328.
Please cite this article as: Mekala, P., Sangwai, J.S., Prediction of phase equilibrium of clathrate hydrates of multicomponent natural gases containing CO2 and H2S. J. Petrol. Sci. Eng. (2014), http://dx.doi.org/10.1016/j.petrol.2014.02.018i
Contents lists available at ScienceDirect
Journal of Petroleum Science and Engineering journal homepage: www.elsevier.com/locate/petrol
Prediction of phase equilibrium of clathrate hydrates of multicomponent natural gases containing CO2 and H2S Prathyusha Mekala, Jitendra S. Sangwai n Petroleum Engineering Program, Department of Ocean Engineering, Indian Institute of Technology Madras, Chennai 600036, India
art ic l e i nf o
a b s t r a c t
Article history: Received 14 May 2013 Accepted 23 February 2014
The sour natural gas readily forms hydrates and stays stable at higher temperatures and lower pressures and hence is responsible for plugging, corroding the pipelines and causing other flow assurance-related issues. Predictions of formation and dissociation conditions of these hydrates are necessary in applications for preventing such hazards primarily due to the blockages of pipelines. However, natural gases from the gas reservoirs can have combinations of different concentrations of each of the following constituents, CH4, C2H6, C3H8, C4H10, N2, CO2 and H2S. Presence of high concentrations of CO2 and/or H2S along with other components is often found in natural gas, thereby limiting the accurate functioning of several of the available phase behavior models. The major limitation for their inaccuracy can be attributed to the complexity involving CO2 and H2S in hydrate systems. In this work, a new thermodynamic computing approach is developed for predicting the phase equilibria for hydrates of multicomponent sour natural gases (with CO2 and H2S) from different natural gas systems. The model of Chen and Guo (1998) (Chem. Eng. J., 71, 145, 1998) is extended for the multicomponent sour natural gas hydrate system using the Kihara potential functions to model the guest–host interaction energies. In addition, a semi-empirical form is proposed to calculate the equilibrium hydrate temperature for hydrates of natural gas with and without CO2 and H2S. The developed model is fitted with 12 sets of experimental data on the phase equilibria of sour natural gas hydrate system and found to be satisfactory. The average absolute deviation pressure percentage (AADP%) for most of the cases studied is observed to be well within 10%, thus proving its efficacy. The present model can, therefore, find potential applications for developing mitigation techniques for flow assurance issues and for robust natural gas and hydrate reservoir models containing sour gases. & 2014 Elsevier B.V. All rights reserved.
Keywords: carbon dioxide hydrogen sulfide natural gas hydrate phase equilibria sour gas
1. Introduction Gas hydrates are formed due to the combination of sufficient amounts of water and gas at favorably high pressure and low temperature conditions. Gas hydrates, generally referred to as clathrate hydrates, are of snowy ice-like structures formed by ‘guest’ molecules of gases such as methane (CH4), ethane (C2H6), propane (C3H8), butane (C4H10), carbon dioxide (CO2), hydrogen sulfide (H2S), hydrogen (H2), nitrogen (N2), etc., when entrapped in a three-dimensional lattice formed by the ‘host’ water molecules due to H–H bonding (Sloan and Koh, 2008). The difference between ice and hydrate is best elucidated by examining the mechanical, electrical and transport properties (Sloan and Koh, 2008). The formation of gas hydrate is a non-stoichiometric chemical process expected under high pressure and low temperature conditions. In the 1930s, Hammerschmidt (1934) first
n
Corresponding author. Tel.: þ 91 44 22574825 (office); fax: þ 91 44 22574802. E-mail address: [email protected] (J.S. Sangwai).
discovered that natural gas forms hydrates in oil and gas pipelines, thus blocking the flow. In 1966, Makogon (1966) first discovered the presence of gas hydrate in ocean floor during experimentation with core samples and observed that the deep sea sediments and permafrost are the harbingers of stable natural gas hydrates. Makogon (1982) was the first to estimate the hydrate reserves followed by Kvenvolden (1988) who predicted the estimated hydrates reserves to be more than 1015 g, which indeed is a source of a huge amount of natural gas to meet the energy need for decades. The naturally occurring natural gas hydrates mainly consists of methane along with several other guest gas molecules such as CO2, H2S, and N2. Presence of high concentrations of carbon dioxide and hydrogen sulfides in natural gas is, in general, very common, and referred to as a sour gas. Carbon dioxide and hydrogen sulfide are very soluble in water and thermodynamically form clathrates individually or in combination with natural gas at relatively higher temperatures and lower pressures when compared to sweet gas. Therefore, the sour gas readily forms hydrates and stays stable at such higher temperatures and lower pressures (ZareNezhad and
http://dx.doi.org/10.1016/j.petrol.2014.02.018 0920-4105 & 2014 Elsevier B.V. All rights reserved.
Please cite this article as: Mekala, P., Sangwai, J.S., Prediction of phase equilibrium of clathrate hydrates of multicomponent natural gases containing CO2 and H2S. J. Petrol. Sci. Eng. (2014), http://dx.doi.org/10.1016/j.petrol.2014.02.018i
P. Mekala, J.S. Sangwai / Journal of Petroleum Science and Engineering ∎ (∎∎∎∎) ∎∎∎–∎∎∎
2
Nomenclature (aα)m, bmmixture parameters of PR EoS in Eqs. (18) and (19) a, b, m, A, B parameters in PR EoS A', B', C' Antoine constants in Eq. (10) Aij interaction parameter between gas molecule and cavities as in Eq. (10) aw activity of water C Langmuir adsorption constant d collision diameter, f fugacity of gas phase, MPa f0 fugacity of hydrate phase, MPa i gas component kij interaction parameter between guest and host gas molecules as in Eq. (18) l gas component m cavity type n hydration number P equilibrium pressure of natural gas p, q constants in Eq. (14) Pc critical pressure, MPa Pr reduced pressure, P/Pc R universal gas constant, J K 1 mol 1 r cavity radius,
Aminian, 2012; ZareNezhad, 2013; Sun et al., 2003; etc.). These conditions are mostly prevalent in most important commercial oil and gas transmission lines from production facilities, and hence responsible for plugging, corroding the pipelines and causing other flow assurance related issues. Predictions of formation and dissociation conditions of these hydrates are necessary in applications for preventing such hazards, primarily due to the blockages of pipelines. Phase equilibria of hydrates are, therefore, necessary for developing mitigation techniques to resolve the hydrate blockades formed in the offshore pipelines for uninterrupted transport of reservoir fluids and also for robust hydrate reservoir models, which may find due application for production of natural gas from hydrates using CO2 sequestrations, etc. (Goel, 2006; Song et al., 2010). In addition, developing a reliable model assists in extending and extrapolating the equilibrium conditions when performing experiments is expensive, time consuming, cumbersome and often requires repetition.
2. Summary of the review Models for phase equilibria for the hydrate system are developed in the literature following the classical work of van der Waals and Platteeuw (vdW–P) based on the statistical thermodynamic model approach (van der Waals and Platteeuw, 1959). A wellknown hydrate model includes a model developed by Parrish and Prausnitz (1972) that extended vdW–P model prediction for hydrate formation conditions of single and multicomponent gas in water. Lundgaard and Mollerup (1992) used the vdW-P model with Kihara spherical core potential interaction parameters between water and guest gas molecules. Chen and Guo (1996) proposed the kinetic mechanism of the formation of gas hydrate explaining the possible mode of lattice occupancy by guest molecules to account for the local stability of the hydrate structure. Klauda and Sandler (2000) developed the vdW–P model for single component hydrate systems using the concept of fugacities rather than reference energy parameters, thereby decreasing the adjustable guest interaction parameters to three. Kaluda and Sandler
s, t T T0 Tc Tr V x y Z
α β ΔH ϵ θ λ1 λ2 s φa, φb ω ω(r)
constants in Eq. (15) equilibrium temperature of hydrate equilibrium temperature of hydrate with no CO2 and H2S critical temperature, K reduced temperature molar volume of gas, m3 mole fraction of gas component in hydrate phase mole fraction of gas component in gas phase compressibility factor fractional coefficient structural parameter enthalpy of dissociation of hydrate phase depth of intermolecular potential well, erg fraction of linked cavities occupied by gas number of linked cavities per water molecule in the basic hydrate number of gas molecules per water molecule in the basic hydrate structure core distance at zero potential constants for PR EoS in Eq. (24) and Eq. (25) acentric factor interaction between a guest and host summed up over the cage
(2003) extended their earlier work (Klauda and Sandler, 2000) to address the phase equilibrium of multicomponent gas hydrate system. Ballard and Sloan (2002) developed a fugacity based model for hydrate phase equilibria, which accounts for the nonidealities in the hydrate system. The model reduces to the vdW–P model when the non-idealities are ignored. Lee and Holder (2002) developed a hydrate phase behavior model accounting for the host–guest interaction through the chemical potential principal and using the Kihara potential functions. Bahadori's (2007) numerical model approach is based on calculating the vapor–solid equilibrium constant. The above-mentioned models are modified to incorporate certain mathematical equations which explain the solid state phase behavior of hydrate systems. All the above models were published to predict the phase equilibria conditions of single and multicomponent gases forming hydrate, whereas model predictions for natural gases and sour natural gases are found to be scarce. Very few models, for example, Sun et al. (2003) applied Chen and Guo's (1998) model for hydrates of gas mixture with high concentrations of CO2 and H2S and found to be deviating largely from the experimental phase equilibrium observations. Sun and Chen (2005) extended the Chen and Guo model (1998) to the hydrate system containing CO2 and H2S. However, the application of their model was limited to the three component gas hydrate system. Karakatsani and Kontogeorgis (2013), in their recent study of validating cubic plus association (CPA) based model, reported the drawbacks of the model, particularly for the gas hydrate systems containing high concentrations of CO2. ZareNezhad and Aminian (2012) came up with the adaptive neuro fuzzy inference system (ANFIS) model, a multilayer neural network-based approach for modeling the phase behaviors of a sour natural gas hydrate system. They observed that the model deviates from the experimental values as the concentration of H2S increases. ZareNezhad (2013) developed a hydrate phase behavior model for predicting sour gas hydrate dissociation pressures, which are prevalent in sour natural gas reservoirs. They proposed a mixing rule to take into account the affinity between H2S and H2O. ZareNezhad and Ziaee (2013) predicted phase equilibria of sour gases using the CPA equation of state and
Please cite this article as: Mekala, P., Sangwai, J.S., Prediction of phase equilibrium of clathrate hydrates of multicomponent natural gases containing CO2 and H2S. J. Petrol. Sci. Eng. (2014), http://dx.doi.org/10.1016/j.petrol.2014.02.018i
P. Mekala, J.S. Sangwai / Journal of Petroleum Science and Engineering ∎ (∎∎∎∎) ∎∎∎–∎∎∎
electrostatic effects of hydrolytic dissociation of H2S and CO2 gases according to the modified Pitzer–Debye–Hückle model in combination with the Chen and Guo model. However, natural gases from the gas reservoirs can have combinations of different concentrations of each of the following constituents, CH4, C2H6, C3H8, C4H10, N2, CO2 and H2S. Presence of high concentrations of CO2 and/or H2S along with other components is often found in natural gas, thereby limiting accurate functioning of several of these models (Sun et al., 2003; Sun and Chen, 2005; ZareNezhad and Aminian, 2012). The major limitation for the inaccuracy in phase equilibria predictions can be attributed to their complexity involving CO2 and H2S in the hydrate system. In the present study, a phase behavior model is developed to address the hydrate phase behavior of multicomponent natural gases containing CO2 and H2S. The model of Chen and Guo (1998) is extended to the phase behaviors of sour natural gas hydrates due to its simplicity and good elucidation of hydrate formation mechanism in two steps (Sun et al., 2003; Sun and Chen, 2005; Joshi et al., 2012). It is well-known fact that the presence of CO2 and H2S in natural gases attracts complexities in hydrate dissociation prediction. In the absence of sufficient hydrate dissociation data on the multi-component sour natural gas system, we employed a semi-empirical approach along with the PR-EoS and the Chen and Guo model to predict the hydrate dissociation conditions. It was assumed that as the number of guest molecules in the hydrate forming phase increases, the interactions between different gas molecules cannot be ignored, as may be the case with natural gas hydrates containing CO2 and H2S. These interactions can be between ions, molecules and their environment. In order to account for the presence of CO2 and H2S in natural gas systems, we used the Kihara potentials function over Lennard–Jones along with the said hydrate model (which was used otherwise). This approach helped us improve model predictions for multi-component sour natural gases. We believe that the present work provides a simple model and approach of computing hydrate dissociation conditions for multicomponent sour natural gas hydrate systems containing both CO2 and H2S.
3
are filled in these sites through adsorption to form gas hydrates. Gas hydrate generally forms either structure I or II (or else, Sloan and Koh, 2008) each with small and large interstices called as cavities inside the solid lattice structure. The type of structures formed depends on the sizes of guest gas molecules making the hydrate (Sloan and Koh, 2008). In general smaller gas molecules form structure I and larger gas molecules form structure II. Natural gas is a mixture of gases generally forming a structure II type of hydrate. The natural gases having C3 to iC4 components form a structure II type hydrate with diamond lattice made by small 512 and large 51262 cages. Larger hydrocarbon molecules like neopentane, isohexane or methylcyclohexane can form structure H type of hydrate (Mehta et al., 1996). 512 cage is formed by 12 pentagonal rings and 51262 cage by 12 pentagonal and two hexagonal rings. The model development in this work considers a structure II due to the multicomponent ‘guest’ gas molecules containing CO2 and H2S (Holder and Hand, 1982; Adisasmito and Sloan, 1992; Sloan and Koh, 2008). The number of gas molecules encapsulated in the water cage (hydration number) depends on the pressure and temperature of the environment at which these hydrates are formed (Holder and Hand, 1982). 3.2. Hydrate phase model The formation mechanism of gas hydrate is represented by (Chen and Guo, 1998) H2 O þ λ2 G-Gλ2 H2 O
ð1Þ
here, G and λ2 are the gas species and the number of gas molecules per water molecule in the basic hydrate structure, respectively. The overall properties of a mixture hydrate also depend on the filling of gas molecules in the linked cavities. Eqs. (1)–(3) can be established for a mixture of gas hydrate systems. To obtain the equilibrium phase conditions, the fugacity of gas phase, f, and fugacity of hydrate structure, f0, are equated, using the following final form: α 0 f i ¼ xi f i 1 ∑ θi ð2Þ i
3. Model development In this section, firstly, the general hydrate formation mechanism is discussed, followed by the hydrate phase behavior model for the natural gas hydrates containing CO2 and H2S.
∑xi ¼ 1 when
ð3Þ
θ ¼ 0, Eq. (2) becomes 0
∑f i ¼ ∑xi f i
ð4Þ
Hydrates can be formed by either of the chemical reactions between (i) gas and water or (ii) gas and ice, at high pressure and low temperature conditions.
here xi denotes the mole fraction of gas, i, in basic hydrate and fi denotes the fugacity of a gas component i. α ¼ λ1/λ2, where, λ1 and λ2 are the number of linked cavities per water molecule in the basic hydrate and the number of gas molecules per water molecule in the basic hydrate, respectively. θ is the fraction of linked cavities occupied by the gas molecules and defined as
CH4 þnH2O 3 CH4 nH2O þ54.2 kJ/mol (with water)
θ¼
3.1. Hydrate formation mechanism
CH4 þnH2O 3 CH4 nH2O þ18.6 kJ/mol (with ice) n is the hydration number depending on the type of gas and the pressure at which the hydrate is formed (Makogon, 1997). Hydrate formation mechanism followed for the present study has the following two steps. (i) Guest gas molecules surrounded by water molecules forming a basic hydrate (i.e., basic cavities being completely occupied) and (ii) linking of these basic hydrates forming empty linked cavities (Chen and Guo, 1998). Hydrate mixture is more like a real solution since the thermodynamic entropy of mixing for gas encapsulated hydrate structure is equal to the entropy of the basic hydrate structure and the value is not equal to zero as is the case for ideal mixtures. Guest gas molecules, such as H2, CO2, N2, H2S, CH4, etc., with a specific molecular size
Cf 1 þCf
∑ θi ¼ i
ð5Þ
∑ Cif i i
1 þ ∑ Cif i
ð6Þ
i
here C is the Langmuir adsorption constant and is a function of temperature and gas components. In a real solution intermolecular interactions in terms of energy potentials were empirically determined by integrating either Lennard–Jones (Chen and Guo, 1996, 1998; etc.) or Kihara cell potentials functions (Parrish and Prausnitz, 1972; Lundgaard and Mollerup, 1992; Klauda and Sandler, 2000; Lee and Holder, 2002; etc.). The advantages of choosing Kihara potentials over Lennard–Jones potentials are that Kihara core potential function takes care of the impenetrable
Please cite this article as: Mekala, P., Sangwai, J.S., Prediction of phase equilibrium of clathrate hydrates of multicomponent natural gases containing CO2 and H2S. J. Petrol. Sci. Eng. (2014), http://dx.doi.org/10.1016/j.petrol.2014.02.018i
P. Mekala, J.S. Sangwai / Journal of Petroleum Science and Engineering ∎ (∎∎∎∎) ∎∎∎–∎∎∎
4
hard core of the hydrate by subtracting it from the hard sphere diameter shown in the following equation and that Kihara potentials could be applied for non-spherical gas molecules, as well as may be the case in multicomponent systems containing higher hydrocarbon and non-hydrocarbons such as CO2 and H2S. 8 9 < 1 r rd = h i ð7Þ ωðrÞ ¼ 4ε s d12 s d6 r 4 d : ; rd rd where ω(r) is said to be the interaction between a guest and host summed up over the cage, r the radius and d is the collision diameter. Chen and Guo (1998) used Lennard–Jones potential function to obtain the values of the Langmuir adsorption constant, Ci. In this work, in order to compute the amount of gas being adsorbed on the solid surfaces of the hydrate, Ci, are obtained by integrating the Kihara potential (Parrish and Prausnitz, 1972) functions to model the guest–host interaction energies as follows: Am;l Bm;l exp ð8Þ Ci ¼ T T Am,l and Bm,l (m is the cavity type and l the gas component) are constants for structure II cavities for each of the guest gas molecules and reported elsewhere (Parrish and Prausnitz, 1972). The constant C is the reverse function of temperature, which is in accordance with the expectation that the binding energy will increase with decrease in the temperature and vice versa. The hydrate phase fugacity, f 0, is calculated using the following form (Chen and Guo, 1998): 0
0
0
0
f ¼ f ðTÞf ðPÞf ðaw Þ
ð9Þ
previous studies (Mekala and Sangwai, 2012) on pure methane gas hydrate. T is the equilibrium temperature for hydrates of methane with CO2 and H2S. n is the hydration number (Sloan and Koh, 2008). ΔH is the enthalpy of dissociation of hydrates phase. As in Eq. (13), the activity is the function of temperature than pressure, since sub-cooling temperature is a better driving force than pressure for the formation of gas hydrate in a closed system (Sloan and Koh, 2008). Carbon dioxide and hydrogen sulfide hydrates form at lower equilibrium pressure and temperature conditions than methane hydrate (Caroll, 2009); therefore, the presence of CO2 and H2S in the natural gas mixture aids to suppress the hydrate formation temperature. This effect is accomplished by computing the activity of formation of water through Eq. (13). ΔH is computed based on dissociation pressures by Eq. (14), which is a function of dissociation temperature, which is defined as the difference between the equilibrium temperature and the base temperature of 273 K (Holder et al., 1988; Mork, 2002).
ΔHdiss ¼ p ½q 4ðΔTÞ
ð14Þ
Determination of approximate ΔH for each natural gas system is an important step in predicting phase equilibria. The constants p and q in Eq. (14) are fitting parameters and being tuned with the experimental data on phase equilibrium of hydrates of natural gas mixtures. We propose using the following form of equation to calculate, T0, the equilibrium hydrate temperature for hydrates of methane without CO2 and H2S: T 0 ¼ s log ðPÞ þ t
ð15Þ
The Antoine constants A', B', C' and interaction parameter, Aij, depend on the guest occupying the cavities and are obtained from Chen and Guo (1998). The effect of Pressure on f 0 is given as (Chen and Guo, 1998) βP 0 ð11Þ f ðPÞ ¼ exp T
where P is the equilibrium pressure for hydrates of methane without CO2 and H2S. s and t are the best-fit parameters for the hydrates of natural gas mixtures without CO2 or (and) H2S content. The calculated equilibrium pressure and temperature data of Mekala and Sangwai (2012) reported for pure methane gas hydrate are fitted to Eq. (15) to obtain the values of constants s and t. To calculate the gas phase fugacity (as in Eq. (2)) Peng– Robinson (P–R) Equation of state (EoS) is found to be good enough for predicting the fluid phase at high pressures and lower temperatures for this study. The P–R EoS used is as follows:
where P is the system pressure, and β ¼10.224 for structure II. The effect of activity, aw on f0 is given as (Chen and Guo, 1998)
P¼
where 0
f i ðTÞ ¼ exp
∑j Aij θi B' A' exp T C' T
f ðaw Þ ¼ aw 1=λ2 0
ð10Þ
ð12Þ
aw ¼1 for pure water. To propose a model which predicts hydrate phase stability of a multicomponent natural gas containing CO2 and H2S, consideration of hydrate structural changes and activities is necessary. Therefore, selection of activity of water for a respective equilibrium pressure, P, and temperature, T, condition is an important step while computing the phase equilibrium conditions of hydrates of natural gas with CO2 and H2S formed in bulk phase. However, since activity is a property which is termed as the resultant real solution behavior due to the effect of interactions, at certain high pressure and low temperature conditions the activity of water having dissolved natural gases needs to be accounted while accounting for the hydrate formation mechanism. Activity is mostly computed taking reference to ideal gas. In this work aw is determined by Eq. (13) as follows (Nasrifar and Moshfeghian, 2001): ΔH 1 1 lnðaw Þ ¼ ð13Þ nR T T 0 T0 is the reference equilibrium hydrate temperature for hydrates of methane without CO2 and H2S, and is taken from
RT aα V b V ðV þ bÞ
ln
fi yi P
¼
bi ðZ 1Þ lnðZ BÞ bm 2∑j ¼ 1 yi aij bi A ðZ þ2:414BÞ pffiffiffi ln Z 0:414B ðaαÞm bm 2 2B
ð16Þ
ð17Þ
h i pffiffiffiffiffiffiffiffiffiffiffiffi ðaαÞm ¼ ∑ ∑ yi yj ai aj αi αj ð1 kij Þ
ð18Þ
bm ¼ ∑½yi bi
ð19Þ
i
j
i
A¼
B¼
ðaαÞm P
ð20Þ
ðRTÞ2 bm P RT
ð21Þ pffiffiffiffiffi
α ¼ ½1 þ mð1 T r Þ2
ð22Þ
m ¼ 0:480 þ 1:574ω 0:176ω2
ð23Þ
a ¼ φa
R2 T c 2 Pc
ð24Þ
Please cite this article as: Mekala, P., Sangwai, J.S., Prediction of phase equilibrium of clathrate hydrates of multicomponent natural gases containing CO2 and H2S. J. Petrol. Sci. Eng. (2014), http://dx.doi.org/10.1016/j.petrol.2014.02.018i
P. Mekala, J.S. Sangwai / Journal of Petroleum Science and Engineering ∎ (∎∎∎∎) ∎∎∎–∎∎∎
b ¼ φb
RT c Pc
ð25Þ
Tr is the reduced temperature, Pc and Tc are the critical pressure and temperature, ω is the acentric factor, V is the molar volume of gas; and the constants φa and φb have the values 0.45724 and 0.07780, respectively, for all pure gases.
5
an input, equilibrium pressures were generated through the proposed model. The model prediction for the phase equilibrium of the hydrate system containing CO2 and H2S is shown in Figs. 2–13 for various gas compositions (Table 1) along with the corresponding experimental
4. Results and discussion Accuracy of a model depends on the accuracy of experimental data available, mechanism of hydrate formation, and theories and correlations involved (Bahadori, 2007). The experimental investigations on the phase behavior of hydrate are being studied extensively; however, the data on the phase equilibria of natural gas hydrates containing H2S and CO2 are very limited, may be due to their corrosive and toxic behavior (Sun et al., 2003; Sun and Chen, 2005; ZareNezhad and Aminian, 2012; ZareNezhad, 2013). For this work, 12 sets of experimental data on the phase equilibrium of natural gas hydrate system containing CO2 and H2S for the model validation are considered from various sources and are shown in Table 1. These data sets typically contain the natural gas composition from methane (C1) to hexane (C6 þ) with the presence of non-hydrocarbon gases, such as N2, CO2 and H2S. The phase equilibrium data sets for the multicomponent natural gas mixture (having 6–10 guest gases) are chosen such that these contained sufficient high concentrations of CO2, which are in the range of 0.52–89.62 mol% and/or H2S in the range of 0.25– 16 mol%. The selected data range on CO2 and H2S are believed to be comfortable to check the efficacy of the developed model. The model equations from Eqs. (2)–(25) are solved using a code generated in MatLabs. A step by step flow diagram for calculating the equilibrium pressure and temperature for multicomponent sour natural gas hydrate system is shown in Fig. 1. Computations are initially started by calculation of T0, the equilibrium temperature for natural gas composition, without CO2 and H2S followed by calculation of equilibrium temperature and pressure conditions. T is said to be the equilibrium temperature of the natural gas containing CO2 and H2S as mentioned earlier. The binary interaction parameters, kij, used in PR EoS (Eq. (18)) are given in Table 2 for reference. The parameters, namely, p, q, and s, t in Eq. (14) and Eq. (15), are tuned with the experimental data available (Table 1) to minimize the error between the model perditions and the experimental data and also simultaneously to decrease the error between the fugacity of gas phase and hydrate phase to less than 0.1%. The final tuned values are listed in Table 3 and Table 4, respectively. For the experimental equilibrium temperatures as
Fig. 1. Flow chart for computing equilibrium P and T of multi-component natural gas hydrate.
Table 2 Binary Interaction Parameters (kij in Eq. (18)) taken for the multicomponent system of gases containing CO2 and H2S for model validation (Ahmed, 2006). CO2 N2 H2S CO2 0 N2 H2S C1 C2 C3 i-C4 n-C4 i-C5 n-C5 C6
0 0
C1
C2
C3
0.135 0.105 0.130 0.125 0.130 0.025 0.010 0.090 0 0.070 0.085 0.080 0 0.005 0.010 0 0.005 0
i-C4
n-C4
i-C5
n-C5
C6
0.120 0.095 0.075 0.035 0.005 0.000 0
0.115 0.095 0.075 0.025 0.010 0.000 0.005 0
0.115 0.100 0.070 0.030 0.020 0.015 0.005 0.005 0
0.115 0.100 0.110 0.070 0.030 0.020 0.015 0.005 0.005 0
0.115 0.110 0.070 0.030 0.020 0.010 0.005 0.005 0.000 0.000 0
Table 1 Compositions of different natural gas hydrates referred for validation. Gas
1 2 3 4 5 6 7 8 9 10 11 12
Composition (mol%)
Reference
N2
CO2
H2S
C1
C2
C3
i-C4
n-C4
i-C5
n-C5
C6 þ
1.1 – – – – 0.84 9.59 0.43
3.25 31.40 66.85 83.15 89.62 1.74 3.19 0.51 12.6 12 12 22.3
0.25 – – – – – – – 5.4 8 16 5.7
87.8 52.5 24.42 12.38 7.86 84.19 86.32 93.2 82 80 72 22.3
4.0 8.12 3.99 1.96 1.13 8.76 0.78 4.25 – – – –
2.1 4.74 3.07 1.66 0.86 3.35 0.03 1.61 – – – –
1.5 1.31 0.75 0.37 0.20 0.32 0.01 – – – – –
– 1.88 0.92 0.48 0.33 0.60 0.01 – – – – –
– – – – – 0.08 0.01 – – – – –
– – – – – 0.08 0.01 – – – – –
– – – – – 0.02 0.07 – – – – –
Deaton and Frost (1946) Adisasmito and Sloan (1992)
Ollerich and Nixdorf (1997) Wilcox et al. (1941) Robinson and Hutton (1967)
Please cite this article as: Mekala, P., Sangwai, J.S., Prediction of phase equilibrium of clathrate hydrates of multicomponent natural gases containing CO2 and H2S. J. Petrol. Sci. Eng. (2014), http://dx.doi.org/10.1016/j.petrol.2014.02.018i
P. Mekala, J.S. Sangwai / Journal of Petroleum Science and Engineering ∎ (∎∎∎∎) ∎∎∎–∎∎∎
6
2
Table 3 Tuned parameters p and q (Eq. (14)) for predicting energies of dissociation (Refer to Table 1 for gas details). p
q
1 2 3 4 5 6 7 8 9 10 11 12
4.18 6.10 4.18 4.18 4.18 4.18 6.12 6.12 6.12 6.00 9.55 9.95
13,500 2356 1350 1350 1350 5231 13,500 3610 13,500 13,500 13,950 13,900
1.6 Prassure (MPa)
Gas
1.8
t
1 2 3 4 5 6 7 8 9 10 11 12
8.59 8.13 8.61 8.61 8.61 4.10 9.34 8.60 1.75 2.95 4.85 6.15
266.15 266.10 270.70 263.50 264.00 269.22 276.90 265.70 265.22 266.22 270.90 263.22
1 0.8 0.6 0.2 0 272
274
276
278
280
282
284
Temperature (K) Fig. 3. Model prediction for phase equilibrium of sour natural gas hydrate (with 31.4% CO2 composition) by the improved Chen and Guo model. ____: Model prediction (this work); □: Experimental data (Gas no. 2; Table 1). 2.5
2 Pressure (MPa)
s
1.2
0.4
Table 4 Values of s and t (Eq.(15)) computed for different natural gases (Refer to Table 1 for gas details). Gas
1.4
1.5
1
0.5
0 272
274
276
278
280
282
284
Temperature (K)
Fig. 4. Model prediction for phase equilibrium of sour natural gas hydrate (with 66.85% CO2 composition) by the improved Chen and Guo model. ____: Model prediction (this work); ◇: Experimental data (Gas no. 3; Table 1).
7
5
4
4
3.5
3
3
2 1 0 270
275
280
285
290
295
Temperature (C) Fig. 2. Model prediction for phase equilibrium of sour natural gas hydrate (with 3.25% CO2 and 0.25% H2S composition) by the improved Chen and Guo model. _____: Model prediction (this work); ◇: Experimental data (Gas no.1; Table 1).
Pressure (MPa)
Pressure (MPa)
6
2.5 2 1.5 1 0.5 0 272
274
276
278
280
282
284
Temperature (K)
phase equilibrium data on the hydrate system. The results show that the developed model predicts the phase behavior of the sour gas hydrate satisfactorily for most of the experimental data set considered for this work, except for Gas no. 2 (Fig. 3). The deviations are calculated using the percentage of absolute average deviation pressure (AADP%) at each equilibrium temperature for each gas composition and are tabulated in Table 5. The AADP values are observed to be less than 10% for most of the experimental data sets. The AADP values, in general, show that the proposed model is successful in the prediction of the phase equilibrium data for the various sets of sour natural gas hydrate system. It is observed from the results that for the range of CO2 concentration studied in this work, 0.51–89.62 mol%, the AADP
Fig. 5. Model prediction for phase equilibrium of sour natural gas hydrate (with 83.15% CO2 composition) by the improved model. ____: Model prediction (this work); ◇: Experimental data (Gas no. 4; Table 1).
is observed to be from 0.98% to 19.7%. However, interestingly, for the range of H2S concentration studied, 0.25–16 mol%, the AADP is observed to be from 1.08% to 7.38%. Figs. 10–13 show the model prediction for the experimental data of Robinson and Hutton (1967) (Gases 9–12 from Table 1). This sour gas mixture consists of both CO2 and H2S gases along with CH4. The model predictions are observed to be in good agreement with the experimental data. Figs. 10–13 also show the comparison of the
Please cite this article as: Mekala, P., Sangwai, J.S., Prediction of phase equilibrium of clathrate hydrates of multicomponent natural gases containing CO2 and H2S. J. Petrol. Sci. Eng. (2014), http://dx.doi.org/10.1016/j.petrol.2014.02.018i
4.5
16
4
14
3.5
12
3
Pressure (MPa)
Pressure (MPa)
P. Mekala, J.S. Sangwai / Journal of Petroleum Science and Engineering ∎ (∎∎∎∎) ∎∎∎–∎∎∎
2.5 2 1.5
10 8 6 4
1
2
0.5 0 272
274
276
278
280
282
0 275
284
280
285
290
295
300
Temperature (K)
Temperature (K) Fig. 6. Model prediction for phase equilibrium of sour natural gas hydrate (with 89.62% CO2 composition) by the improved Chen and Guo model.____: Model prediction (this work); △: Experimental data (Gas no. 5; Table 1).
Fig. 9. Model prediction for phase equilibrium of sour natural gas hydrate (with 0.51% CO2 composition) by the improved Chen and Guo model. ____: Model prediction (this work); ◇: Experimental data by Wilcox (Gas no. 8; Table 1). 12
10 9
10
8 7
Pressure (MPa)
Pressure (MPa)
7
6 5 4 3 2
8 6 4 2
1 0 270
275
280
285
290
295
0 287
300
288
Temperature (K)
289
290
291
292
293
Temperature (K)
Fig. 7. Model prediction for phase equilibrium of sour natural gas hydrate (with 1.74% CO2 composition) by the improved Chen and Guo model. ____: Model prediction (this work); ◇: Experimental data (Gas no. 6; Table 1).
Fig. 10. Model prediction for phase equilibrium of sour natural gas hydrate (with 12.6% CO2 and 5.4% H2S composition). ____: Model prediction (this work); —————: Chen and Guo model (Chen and Guo, 1998); △: Experimental data (Gas no. 9; Table 1).
30 9 8 7
20 Pressure (MPa)
Pressure (MPa)
25
15 10 5 0 275
6 5 4 3 2
280
285 Temperature (K)
290
295
Fig. 8. Model prediction for phase equilibrium of sour natural gas hydrate (with 3.19% CO2 composition) by the improved Chen and Guo model. ____: Model prediction (this work); ○: Experimental data (Gas no. 7; Table 1).
Chen and Guo model (Sun et al., 2003) with the present model. It is evident from these figures that the present model shows better match and hence is more reliable. One of the recent publications (ZareNezhad and Ziaee, 2013) also attempt to predict the dissociation conditions of hydrates of three component sour natural gas systems using an improved Chen and Guo model along with CPA EoS. Their work was primarily applied for three component natural gas hydrate systems containing H 2S and CO2. The AADP values are observed to lie in the range of 2.15–8.67% for the three component sour natural gas system as against our model, AADP values being in the range of 1.08–7.38
1 0 288
289
290
291
292
293
Temperature (K)
Fig. 11. Model prediction for phase equilibrium of sour natural gas hydrate (with 12% CO2 and 8% H2S composition). ____: Model prediction (this work); —————: the Chen and Guo model (Chen and Guo, 1998); □: Experimental data (Gas no. 10; Table 1).
for a similar system (Gas nos. 9–12) showing better prediction. The developed model in general can predict phase equilibrium of the sour natural gas hydrate system satisfactorily. It is important to generate more experimental data on the phase equilibrist of sour natural gas hydrate system for the development and testing of the robust model which are vital for effective flow assurance issue to hydrate plugging or for robust reservoir models for natural gas production from the hydrate reservoirs.
Please cite this article as: Mekala, P., Sangwai, J.S., Prediction of phase equilibrium of clathrate hydrates of multicomponent natural gases containing CO2 and H2S. J. Petrol. Sci. Eng. (2014), http://dx.doi.org/10.1016/j.petrol.2014.02.018i
P. Mekala, J.S. Sangwai / Journal of Petroleum Science and Engineering ∎ (∎∎∎∎) ∎∎∎–∎∎∎
8 7
293.69 K temperature ranges on the phase equilibria of sour natural has hydrate system and found to be satisfactory. The average absolute deviation pressure percentage (AADP%) for most of the cases studied is observed to be well within 10%, thus proving its efficacy. The present model can, therefore, find potential applications for developing mitigation techniques for flow assurance issues and for robust natural gas and hydrate reservoir models containing sour gases.
6
Pressure (MPa)
5 4 3 2 1 0 291
Declaration 292
293
294
295
The authors declare no competing financial interest.
296
Temperature (K)
Fig. 12. Model prediction for phase equilibrium of sour natural gas hydrate (with 12% CO2 and 16% H2S composition). ____: Model prediction (this work); —————: the Chen and Guo model (Chen and Guo, 1998); ○: Experimental data (Gas no.11; Table 1). 12
Pressure (MPa)
10 8
4 2
280
285
290
295
Temperature (K)
Fig. 13. Model prediction for phase equilibrium of sour natural gas hydrate (with 22.3% CO2 and 5.7% H2S composition). ____: Model prediction (this work); □: Experimental data (Gas no. 12; Table 1).
Table 5 Percentage of Average Absolute Deviation Pressure (AADP) computed for the gases studied for corresponding equilibrium temperature and pressure ranges (Refer to Table 1 for gas details). Gas
T (K)
P (MPa)
Np
AADPa (%)
1 2 3 4 5 6 7 8 9 10 11 12
275.4–289.3 273.7–282 273.7–282 273.7–282 273.7–282 273.65–293.11 276.63–292.59 277.7–293.3 287.5–292.3 289.1–292.1 291.5–295.3 284.22–293.55
0.95–5.25 0.6–1.7 0.758–2.22 1.36–3.51 1.33–3.47 8.3–9.02 3.8–24.3 1.6–14.1 4.4–8.8 4.1–6.0 3.3–5.2 2.65–11.1
4 4 4 4 4 15 9 5 4 3 3 7
3.2 19.7 6.3 0.98 1.19 12.6 10.3 5.2 3.52 1.31 1.08 7.38
a
AADP is defined as
AADPð%Þ ¼
Financial support from Earth System Science Organization, Ministry of Earth Sciences, Government of India, through NIOT, Chennai, India (Grant: OEC/10-11/105/NIOT/JITE) and IIT Madras (Grant: OEC/10-11/530/NFSC/JITE) are gratefully acknowledged. References
6
0
Acknowledgments
1 Np P cal P exp 100 ∑ N p j ¼ 1 P exp
5. Conclusion In this work, the classical Chen and Guo model (Chem. Eng. J., 71, 145, 1998) for hydrates is extended for hydrates of sour natural gases with high concentrations of CO2 and H2S using the Kihara potential functions to model the guest–host interaction energies. The developed model is fitted with 12 sets of experimental data ranging from 0.6 MPa to 24.3 MPa pressure and 273.7 K to
Adisasmito, S., Sloan, E.D., 1992. Hydrates of carbon dioxide and methane mixtures. J. Chem. Eng. Data 343, 343–349. Ahmed, T., 2006. Reservoir Engineering Handbook. Gulf Professional Publishing, Burlington, MA, USA Bahadori, A., 2007. A new approach for multicomponent vapor solid equilibrium calculations in gas hydrate formation. In: Paper 2007-047 Presented at Canadian International Petroleum Conference, 1–13 June, Alberta. Ballard, A.L., Sloan Jr, E.D., 2002. The next generation of hydrate prediction I. Hydrate standard states and incorporation of spectroscopy. Fluid Ph. Equilib. 197, 371–383. Caroll, J., 2009. Natural Gas Hydrates: A Guide for Engineers, 2nd ed. USA: Gulf Professional Publishing, Burlington, MA, USA Chen, G., Guo, T., 1996. Thermodynamic modeling of hydrate formation based on new concepts. Fluid Ph. Equilib. 122, 43–65. Chen, G., Guo, T., 1998. A new approach to gas hydrate modeling. Chem. Eng. J. 71, 145–151. Deaton, W.M., Frost Jr., E.M., 1946. Gas Hydrates and their Relation to the Operation of Natural Gas Pipelines, U.S. Bureau of Mines Monograph 8. Goel, N., 2006. In situ methane hydrate dissociation with carbon dioxide sequestration: current knowledge and issues. J. Pet. Sci. Eng. 51, 169–184. Hammerschmidt, E.G., 1934. Formation of gas hydrates in natural gas transmission lines. Ind. Eng. Chem. 26, 851–855. Holder, G., Hand, J., 1982. Multiple phase equilibria in hydrates from methane, ethane, propane and water mixtures. AIChE J. 28 (12), 440–447. Holder, G.D., Zetts, S., Pradhan, N., 1988. Phase behavior in systems containing clathrate hydrates: a review. Rev. Chem. Eng. 5 (1–4), 1–70. Joshi, A., Mekala, P., Sangwai, J.S., 2012. Modeling phase equilibria of semiclathrate hydrates of CH4, CO2 and N2 in aqueous solution of tetra-n-butyl ammonium bromide (TBAB). J. Nat. Chem. 21 (4), 459–465. Karakatsani, E.K., Kontogeorgis, G.M., 2013. Thermodynamic modeling of natural gas systems containing water. Ind. Eng. Chem. Res. 52 (9), 3499–3513. Klauda, J.B., Sandler, S.I., 2000. A fugacity model for gas hydrate phase equilibria. Ind. Eng. Chem. Res. 39, 3377–3386. Klauda, J.B., Sanlder, S.I., 2003. Phase behavior of clathrate hydrates: a model for single and multiple gas component hydrates. Chem. Eng. Sci. 58, 27–41. Kvenvolden, K.A., 1988. Methane hydrate – a major reservoir of carbon in the shallow geosphere. Chem. Geol. 71, 41–51. Lee, S.Y., Holder, G.D., 2002. Model for gas hydrate equilibria using a variable reference chemical potential: part 1. AIChE J. 48 (1), 161–167. Lundgaard, L., Mollerup, J., 1992. Calculation of phase diagrams of gas–hydrates. Fluid Ph. Equilib. 76, 141–149. Makogon, Y., 1966. Features of natural gas fields exploitation in permafrost zone. Gazov. Prom. 9, 1–17. Makogon, Y.F., 1982. Perspectives for the development of gas–hydrate deposits. In: Proceedings of the 4th Canadian Permafrost Conference, pp. 299–304. Makogon, Y.F., 1997. Hydrates of Hydrocarbons. Penn Well, Tulsa, USA Mehta, A.P., Makogon, T.Y., Burruss, R.C., Wendlandt, R.F., Sloan, E.D., 1996. A composite phase diagram of structure H hydrates using Schreinemakers' geometric approach. Fluid Ph. Equilib. 121 (1–2), 141–165. Mekala, P., Sangwai, J.S., 2012. Predictability of equation of state (EoS)-based gas hydrate models for single and binary gas mixtures. J. Pet. Eng. Technol. 2 (3), 9–17. Mork, M., 2002. Formation Rate of Reactor Experiments and Models (Ph.D. thesis). Norwegian University of Science and Technology, Norway.
Please cite this article as: Mekala, P., Sangwai, J.S., Prediction of phase equilibrium of clathrate hydrates of multicomponent natural gases containing CO2 and H2S. J. Petrol. Sci. Eng. (2014), http://dx.doi.org/10.1016/j.petrol.2014.02.018i
P. Mekala, J.S. Sangwai / Journal of Petroleum Science and Engineering ∎ (∎∎∎∎) ∎∎∎–∎∎∎ Nasrifar, K., Moshfeghian, M., 2001. A model for prediction of gas hydrates formation conditions in aqueous solutions containing electrolytes and/or alcohol. J. Chem. Thermodyn. 33 (9), 999–1014. Ollerich, L.R., Nixdorf, J., 1997. Experimental determination of hydrate equilibrium conditions for pure gases, binary and ternary mixtures and natural gases. Fluid Ph. Equilib. 139, 325–333. Parrish, W.R., Prausnitz, J.M., 1972. Dissociation pressures of gas hydrates formed by gas mixtures. Ind. Eng. Chem. Proc. Des. Dev. 11 (1), 26–35. Robinson, D.B., Hutton, J.M., 1967. Hydrate formation in systems containing methane, hydrogen sulphide and carbon dioxide. J. Can. Pet. Technol. 6, 6–9. Sloan, E.D., Koh, C.A., 2008. Clathrate Hydrates of Natural Gas, 3rd ed. CRC Press, New York Song, Y., Yang, M., Chen, Y., Li, Q., 2010. An improved model for predicting hydrate phase equilibrium in marine sediment environment. J. Nat. Gas Chem. 19 (3), 241–245. Sun, C.Y., Chen, G.J., 2005. Modeling the hydrate formation condition for sour gas and mixtures. Chem. Eng. Sci. 60 (17), 4879–4885.
9
Sun, C.Y., Chen, G.J., Lin, W., Guo, T.M., 2003. Hydrate formation conditions of sour natural gases. J. Chem. Eng. Data 48 (3), 600–602. van der Waals, J.H., Platteeuw, J.C., 1959. Clathrate solutions. Adv. Chem. Phys. 2, 1–57. Wilcox, W., Carson, D., Katz, L., 1941. Natural gas hydrates. Ind. Eng. Chem. 33 (8), 662–665. ZareNezhad, B., 2013. Predicting the sour gas hydrate dissociation pressures regarding sour natural gas production from gas–condensate reservoirs. J. Chem. Technol. Metall. 1, 92–98. ZareNezhad, B., Aminian, A., 2012. Accurate prediction of sour gas hydrate equilibrium dissociation conditions by using an adaptive neuro fuzzy inference system. Energy Convers. Manag. 57, 143–147. ZareNezhad, B., Ziaee, M., 2013. Accurate prediction of H2S and CO2 containing sour gas hydrates formation conditions considering hydrolytic and hydrogen bonding association effects. Fluid Ph. Equilib. 356 (25), 321–328.
Please cite this article as: Mekala, P., Sangwai, J.S., Prediction of phase equilibrium of clathrate hydrates of multicomponent natural gases containing CO2 and H2S. J. Petrol. Sci. Eng. (2014), http://dx.doi.org/10.1016/j.petrol.2014.02.018i