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MEG mixtures flowing through wellhead chokes
Journal of Natural Gas Science and Engineering 74 (2020) 103108
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Predictions on temperatures of high-pressure gas/water/MEG mixtures flowing through wellhead chokes Wenlong Jia a, b, *, Fan Yang a, Xia Wu a, b, Changjun Li a, b, Yubin Wang b a b
School of Petroleum Engineering, Southwest Petroleum University, Chengdu, 610500, China CNPC Key Laboratory of Oil & Gas Storage and Transportation, Southwest Petroleum University, Chengdu, 610500, China
A R T I C L E I N F O
A B S T R A C T
Keywords: Choke Temperature High-pressure gas Cubic-plus-association equation of state Isenthalpic flash
The co-existence of gas, water, and monoethylene glycol (MEG) is common in produced fluids of high-pressure gas wells. Accurate predictions on the temperature changes during the choking process are essential for the design and operation of the choke valve. This paper presents an efficient multiphase isenthalpic flash method based on the cubic-plus-association equation of state (CPA EOS) to calculate the choke temperatures. In com parison with the traditional isenthalpic flash algorithm, this new method accounts for the self- and crossassociation between polar water and MEG molecules, yielding more accurate enthalpy calculation results and multiphase component distributions for fluids containing water and MEG. The proposed model is validated by field test data with pressures from 8.68 MPa to 119.3 MPa. The average absolute deviations between the calculated choke temperatures and measured values are less than 1.6 � C even for vapor-liquid-aqueous threephase mixtures at various pressures. Moreover, case studies show that accounting for the association between polar water/MEG molecules contributes to accurate predictions on choke temperatures. At high pressures, the CPA EOS tends to give higher choke temperatures in comparison with those calculated based on the traditional SRK-Peneloux EOS. In contrast, the CPA EOS tends to yield lower temperatures at low pressures.
Author contribution statement Wenlong Jia: Conceptualization, Methodology, Resources, Soft ware.Fan Yang: Writing- Original draft preparation, Validation, Data curation.Xia Wu: Data curation, Investigation.Changjun Li: Supervi sion, Software.Yubin Wang: Writing- Reviewing and Editing. 1. Introduction The choke valve is often installed near the wellheads to control gas production rates and/or downstream pressures in gas field surface production systems (Naseri et al., 2016; Ghorbani et al., 2017). During the choking process, the fluid temperature varies with the pressure drop across the valve due to the fluid’s Joule-Thomson effect. Accurately predicting the choke temperature is essential for the selection of chokes, for the prevention of gas hydrates, and for the design of gas processing plants. In recent years, many ultra-high pressure gas reservoirs that pressure beyond over 100 MPa at wellheads (Xia et al., 2016; Yao et al., 2018) have been found in Sichuan Basin and Tarim Basin, China. Within the
multi-stage choking process, the gas hydrate is easy to form because of the fluid temperature decreases with the pressure drop. Methanol, ethanol, MEG, and many other glycols can be used as gas hydrate in hibitors. MEG is the most widely used one due to its advantages of economical and low toxic. Hence, the co-existence of gas, water, and MEG is commonly found in produced fluids due to formation water production and hydrate inhibitor injection at wellheads. The interaction between the polar water and MEG molecules can affect the phase behavior and subsequent temperature changes during gas/water/MEG mixtures flowing through chokes at wellheads, resulting in complicated multiphase transitions and temperature variations across the choke. Many methods can be applied to predict the choke temperatures, such as the artificial neural network (ANN) method (Yarveicy, 2018), the empirical correlation method (Attar, 2008; Rostamian and Lotfol lahi, 2020), the statistical method (Rostamian and Lotfollahi, 2019), and thermodynamic models (Nasrifar and Bolland, 2006; Yingchuan et al., 2003). The development of the ANN model and the statistical model needs a large amount of historical production data. However, the pro duction of high-pressure gas wells is not common around the world, which limits the development of such methods. Hence, the empirical
* Corresponding author. School of Petroleum Engineering, Southwest Petroleum University, Chengdu, 610500, China. E-mail address: [email protected] (W. Jia). https://doi.org/10.1016/j.jngse.2019.103108 Received 15 September 2019; Received in revised form 11 December 2019; Accepted 11 December 2019 Available online 14 December 2019 1875-5100/© 2019 Elsevier B.V. All rights reserved.
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Journal of Natural Gas Science and Engineering 74 (2020) 103108
Fig. 1. The schematic diagram of a choke valve. P, T, H, C refer to the fluid pressure, temperature, enthalpy, and velocity, respectively. Subscripts 1 and 2 indicate the upstream and downstream of the choke valve, respectively.
correlation and the thermodynamic model based on EOS are most widely used in predicting choke temperatures. The empirical correlations are often developed from limited experi mental data, such as the Gilbert (1954), Elgibaly and Nashawi (1996), and Attar (2008) correlations. These correlations usually have consid erable accuracy when the target choke parameters fall into the data that used to develop the correlations. Otherwise, these correlations often yield poor results (Yao et al., 2018; Shao et al., 2018). Theoretical models are generally built based on mass, momentum, and energy conservation laws, such as the Perkins model (Prekins et al., 1993) and the Hydro model (Selmer-Olsen and Holm, 1995). However, most of the theoretical models focus on sizing the choke valve according to the choke pressure difference and the required flow rate of the fluid across the valve instead of calculating the choke temperatures. The isenthalpic principle has been widely used to calculate the choke temperatures, which assumes that fluid total enthalpy at the upstream of the choke is equal to that at the downstream of the choke (Li et al., 2012a,b). That means, if the choke inlet pressure, inlet temperature, and outlet pressure are specified, the outlet temperature can be directly calculated from the isenthalpic flash algorithm (Zhu and Okuno, 2014). The accuracy of this method relies on the enthalpy calculation method and the multiphase equilibrium algorithm based on the equation of state. Using the cubic equations of state (EOSs) is a well-known way to calculate the density, enthalpy and many other physical properties of hydrocarbon mixtures because of their simplicity, computational effi ciency, and acceptable accuracy (Wei and Sadus, 2000; Li et al., 2015, 2016; Valiollahi et al., 2016). Many scholars (Riaz et al., 2011; Sarafraz and Peyghambarzadeh, 2012; Sarafraz and Hormozi, 2014a,b; Saberi et al., 2018) discussed the effect of the density, heat capacity and other thermophysical properties of a binary mixture containing alcohols on the prediction of pool boiling heat transfer coefficient. Li et al. (2012a) built a choke temperature model for dry natural gas based on the Peng-Robinson EOS, the van der Waals mixing rule and the energy conservation law. Li et al. (2012b) developed a choke temperature prediction model for high-pressure and high-temperature condensate gas based on the SRK EOS, Lee-Kesler EOS and a modified mixing rule. Teng et al. (2016) proposed a multiphase choked flow model for hy drocarbon mixtures containing high CO2 contents based on the BWRS EOS. The calculation results are in good agreement with the field test data of Daqing Sartu Oilfield. Cubic EOSs are not originally designed to model thermophysical properties of polar components, such as water and MEG. The effect of strong interactions between polar molecules on the enthalpy cannot be desrcibed by the traditional isenthalpic flash algorithm based on the cubic EOSs (Kontogeorgis and Folas, 2009). Hence, the choke temperatures of gas/water/MEG mixtures are difficult to be accurately calculated based on the cubic EOSs. In contrast, Kon togeorgis et al. (2009) proposed a cubic-plus-association (CPA) EOS that provides an efficient method to model fluids containing polar compo nents, including water and glycol. The CPA EOS typically has two parts, namely the physical part and the association part. Without polar com ponents, the CPA EOS reduces to the traditional cubic EOS, such as the SRK EOS. The CPA EOS has been successfully applied to model complex multiphase equilibrium and physical properties of mixtures containing associated fluids. It has been used to predict the vapor-liquid
equilibrium (VLE) and liquid-liquid equilibrium (LLE) of alcoholhydrocarbons (Yakoumis et al., 1997; Voutsas et al., 1997), water-hydrocarbons (Yakoumis et al., 1998; Oliveira et al., 2007; Liang et al., 2014), alcohol-water (Voutsas et al., 1999; Kontogeorgis et al., 2006; Lundstrøm et al., 2006), multi-component water- alcohol-hydrocarbons (Kontogeorgis et al., 1999; Kruger et al., 2018), ethylene glycol-hydrocarbons (Derawi & Michelsen et al., 2003), ethylene glycol-water systems (Derawi & Kontogeorgis et al., 2003). Besides, the CPA EOS also shows good performance when describing the physical properties of mixtures containing water and alcohol. Lundstrøm et al. (2006) stated that the CPA EOS shows better results in calculating the enthalpy, heat capacity, and Joule-Thomson coefficient of water and methanol at high pressures, in comparison with the SRK or SRK-Peneloux EOSs. Previous publications indicate that the CPA EOS has been success fully applied to reproduce the physical properties, VLE and LLE phase equilibrium of hydrocarbon, water and glycol mixtures (Hajiw et al., 2015a,b; Kruger et al., 2018). Hence, we assume that, in comparison with the algorithms based on traditional cubic EOSs, the isenthalpic flash algorithm based on the CPA EOS can accurately calculate the choke temperatures of gas/water/MEG mixtures. The main objective of this research is to study the accuracy of using the isenthalpic flash algorithm combining with the CPA EOS to calculate the choke temperatures of gas/water/glycol mixtures at high pressures. In what follows, a brief introduction of the choking process is fol lowed by the isenthalpic principle. Then the CPA EOS and the isen thalpic flash algorithm applied in this research are described. After that, the accuracy of this method, and the effect of water and MEG contents in fluids on the choke temperature are discussed in case studies. 2. Isenthalpic choking process Surface chokes are often installed near to wellhead to control the production rates and/or downstream pressures. In order to clarify the choking process, the control volume composed of the choke valve, and two short symmetrical pipe sections at upstream and downstream of the choke valve is taken as the research object in this paper. Fig. 1 shows the schematic of this control volume. The main parameters involved in the choking process include the fluid’s temperature, pressure, velocity, enthalpy, etc. For the compressible flow, the fluid velocity across the choke may reach the local sonic velocity. With the fluid velocity increases, the temperature through the choke varies with the pressure drop due to the Joule-Thomson effect. Such a choking process follows the basic energyconservation principle (Li et al., 2012b). Accordingly, the one-dimensional energy-conservation equation can be written as: 1 p1 v1 þ e1 þ C21 þ Z1 þ Q 2
1 W ¼ p2 v2 þ e2 þ C22 þ Z2 2
(1)
where p is the pressure; v is the specific volume; e is the internal energy; Z is the elevation; C is the fluid velocity; Q is the heat transferred from the environment to the fluid; W is the work done by the fluid. The subscripts 1 and 2 represent the upstream and downstream of the choke, respectively. Eq. (1) can be simplified based on the following assumptions (Li 2
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Journal of Natural Gas Science and Engineering 74 (2020) 103108
Table 1 Properties of water, MEG, and some common hydrocarbon components. Component
Tc, K
Pc, kPa
ω
a0,Pa⋅m6⋅mol
H2O MEG N2 H2S CO2 CH4 C2H6 C3H8 i-C4H10
647.3 720.0 126.2 373.2 304.2 190.6 305.4 369.8 408.1
22088.9 9000.0 3394.4 8936.9 7376.5 4600.2 4883.9 4245.5 3647.7
0.344 0.535 0.040 0.100 0.225 0.008 0.098 0.152 0.176
0.123 1.082 0.139 0.386 0.351 0.232 0.551 0.915 1.295
2
b,10
5
m3⋅mol
0.674 0.674 0.543 0.502 0.760 0.447 0.585 0.667 0.713
(2)
g¼
0.0692 0.0141
5.440
0.0583
Kontogeorgis et al. (1999) (Derawi et al., 2003a,b) Kontogeorgis and Folas (2009) Tsivintzelis et al. (2010) Tsivintzelis et al. (2011) Tsivintzelis et al. (2010) Tsivintzelis et al. (2010) Tsivintzelis et al. (2010) Tsivintzelis et al. (2011)
Ai
1 b ; η¼ 1:9η 4v
1
(7)
Calculating Х Ai is related to the association strength ΔAi Bj between association sites belonging to different molecules, given by XA i ¼
Eq. (3) indicates that the total enthalpy at the downstream of the choke is equal to that at the upstream of the choke, which shows that the choking process follows an isenthalpic principle. For multiphase mix tures, the total enthalpy of the fluid should be calculated from the weighted average of each phase enthalpy, as follows:
1þρ
1 P P ; i; j ¼ 1; 2; ⋯; NCA xj XBj ΔAi Bj j
(4)
bij ¼
where mi is the mass fraction of the ith phase; Hi is the specific enthalpy of the ith phase; n is the number of phases. For a given fluid, the enthalpy is determined by the temperature, pressure, and composition, that is:
(8)
Bj
where ρ is the molar density. ΔAi Bj is given by � � Ai Bj � � ε ΔAi Bj ¼ g exp 1 bij βAi Bj RT
i¼1
H ¼ f ðp; T; ComÞ
16.655 19.752
i
(3)
mi Hi
reference
refers to the summation over all sites (Ai, Bi, Ci) on component i; g is the hard-sphere radial distribution function (RDF), determined from Eq. (7):
By introducing the definition of enthalpy H ¼ e þ pv, Eq. (2) is finally given by:
H¼
βAB
where P is the pressure; T is the temperature; v is the molar volume; x is the mole fraction; R is the gas constant; nassoc is the total number of association components; Ai is the active association site A on molecule i; Х Ai is the fraction of sites A on component i that do not form bonds with P P other active sites; refers to the summation over all components;
Using these assumptions, Eq. (1) is simplified as:
n X
1
CPA EOS is written as Eq. (6) when the physical part is taken from the conventional SRK EOS: � � RT a 1 RT ∂ln g X X 1 v xi ð1 XAi Þ (6) P¼ v b vðv þ bÞ 2 v ∂v i Ai
(1) The kinetic energy of the mixture is usually negligible in com parison with its total energy. (2) The elevation change of the fluid across the choke is negligible. (3) The flow process is frictionless. The energy change caused by friction heat is much smaller than that caused by the Joule Thomson effect. (4) The external work done is zero. (5) The flow process is adiabatic. The length of the choke is short, and the fluid velocity is relatively high, resulting in a very limited time for heat transfer.
H1 ¼ H2
εAB, kPa⋅m3⋅mol
κ
1.452 5.140 2.678 2.920 2.720 2.910 4.290 5.870 7.510
et al., 2012b; Nejatian et al., 2014; Teng et al., 2016):
p1 v1 þ e1 ¼ p2 v2 þ e2 :
1
bi þ bj 2
(9) (10)
where εAi Bj is the association energy for the association between Ai and Bj; βAi Bj is the association volume that represents the finite distance at which the inter-particle potential between Ai and Bj is zero; b is the covolume. The energy parameter a in Eq. (6)is given by
(5)
where T is the temperature; Com is the fluid composition. If the upstream pressure and upstream temperatures are specified, the total enthalpy at the upstream of the choke can be calculated. With the specification of the downstream pressure, the downstream temper ature can be solved to match the downstream total enthalpy and the upstream total enthalpy. So, the enthalpy calculation method is essential for the accurate calculation of downstream temperature. Traditionally, we use cubic EOSs, such as the PR and SRK EOSs, to calculate the enthalpy, which cannot account for the effect of interactions between polar components on the enthalpy (Twu et al., 2005). In this research, we use the CPA EOS to model the isenthalpic choking process for the first time with accounting for the interaction between polar components, including the water and MEG.
� a ¼ a0 1 þ κ 1
pffiffiffiffi ��2 Tr
(11)
For the pure associating component, five parameters a0, b, κ, εAi Bj , β in CPA EOS should be determined to represent its thermophysical properties. They are typically fitted from the vapor pressures and liquid densities of a pure component. For inert (not self-associating) compo nents, only three parameters a0, b, κ are required, which are usually calculated from the critical pressure (Pc), critical temperature (Tc), and acentric factor (ω). When the CPA EOS is applied to mixtures, the van der Waals mixing rule is employed for a and b in the physical part, as expressed by Eqs. (12)–(14). XX a¼ xi xj aij (12) Ai Bj
3. Mathematical method
i
3.1. CPA EOS
j
pffiffiffiffiffiffiffi aij ¼ ai aj 1
The CPA EOS is firstly developed by Kontogeorgis et al. (1999). The 3
kij
�
(13)
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Journal of Natural Gas Science and Engineering 74 (2020) 103108
Fig. 2. Comparisons of derivative properties of water and MEG calculated from the CPA EOS against those calculated from the SRK EOS. The calculated fluid is single-component H2O or MEG. The calculated pressures cover the range from 9.07 MPa to 119.3 MPa, and the temperatures range from 18.97 � C to 50.9 � C.
b¼
X xi bi
3.2. Solution method of the CPA EOS
(14)
i
To solve the CPA EOS, it is here rewritten in terms of the compressibility factor Z. According to the definition Z ¼ Pv/(RT), Eq. (6) is written as:
where kij is the binary interaction parameters, and it is the only binary adjustable parameters of the CPA EOS. The εAi Bj , βAi Bj for mixtures are calculated from the CR-1 combining rule as follows: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi βAi Bj ¼ βAi Bi βAj Bj (15)
ε
Ai Bj
¼
εAi Bi þ εAj Bj 2
Z¼
Z Z
XA i ¼ :
(16)
A ZþB
B
Zþ
X X 0:5Z xi ð1 Z 0:475B i Ai
Z P P xj XBj γAi Bj j
XA i Þ
(17) (18)
Bj
where, A ¼ aP/(RT)2, B ¼ bP/(RT), and γAi Bj ¼ PΔAi Bj =ðRTÞ. Eq. (17) has no analytical solutions due to the nonlinear and implicit form in terms of Z and Х Ai . It is recommended to be solved by using the bisection method and the Newton iteration method. Eq. (17) typically has one to three real roots. In the case of more than one real root, the compressibility factor that gives the lowest Gibbs free energy is selected (Nasrabadi et al., 2016).
The parameters used to reproduce the properties of water, MEG, and some common hydrocarbon components are listed in Table 1. Besides, this method also can be applied to other glycols once association pa rameters for these glycol molecules are specified, such as ethanol and methanol. The methods used to determine these association parameters can refer to Kontogeorgis and Folas (2009).
4
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Journal of Natural Gas Science and Engineering 74 (2020) 103108
Besides, the fugacity coefficient equation is derived as follows (Jia and Okuno, 2018): 0 P 1 2 xj aij � � � � bi B A A@ j bi A ZþB þ ln lnφi ¼ lnðZ BÞ þ B Z b Z B ZþB a b
Table 2 Fluid compositions collected from the PY gas field. Component
Mole, %
Component
Mole %
H2O MEG N2 CO2 CH4 C2H6 C3H8
12.74 3.85 0.24 11.14 66.81 3.19 0.95
i-C4H10 n-C4H10 i-C5H12 n-C5H12 n-C6H14 n-C7H16 n-C8H18
0.21 0.24 0.12 0.08 0.18 0.09 0.11
Ai
H ¼ H0 þ
ρ
2
�
∂P ∂T
Z P� v
�2 � �
∂P ∂ρ
ρ
� T
0
∂v ∂T
XAi Þ
∂ln g ∂xi
∂ln g 0:475B bi ¼ : ∂xi Z 0:475B b
Many derivative properties of the fluid can be calculated from the basic thermodynamic relations by using the CPA EOS (Haghbakhsh et al., 2014), including the specific heat capacity, enthalpy, and fugacity. The specific heat capacity and enthalpy formula are as follows: Z ρ� � 2 � � T ∂P Cv ¼ C0v (19) dρ ρ2 ∂ T 2 ρ 0 T
1X X xi ð1 2 i Ai
(22)
3.3. Derivative properties of the CPA EOS
CP ¼ Cv
X lnXAi
where φi is the fugacity of the ith component. The CPA EOS is specially designed for fluids containing polar com ponents. The additional association term in the CPA EOS changes the calculation methods of derivate properties, which will further affect the isenthalpic-flash results. For pure water and MEG, comparisons of Cv, Cp, H, and φi values calculated from the CPA EOS with those calculated from the SRK EOS are shown in Fig. 2. These figures cover the pressures from 9.07 MPa to 119.3 MPa, and temperatures from 18.97 � C to 50.9 � C. It shows that Cv and Cp of water calculated by CPA EOS are lower than those of SRK EOS, whereas H and φi of water calculated by CPA EOS are higher than those calculated by the SRK EOS. For MEG, Cp, H and φi calculated by CPA EOS are lower than those calculated by the SRK EOS, but Cv is higher than SRK EOS.
� (20) T
� � dP
(23)
(21)
P
where Cv is the specific heat capacity at constant volume; Cp is the specific heat capacity at constant pressure; the superscript 0 refers to the ideal gas state.
3.4. Isenthalpic flash algorithm The P–H flash model is composed of the fugacity equations, material
Table 3 Measured production data collected from the PY gas field.a No.
Pin (MPa)
Tin (� C)
Pout (MPa)
Tout (� C)
Qg (m3/h)
Qo (m3/h)
Qw (m3/h)
QMEG (L/h)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
20.23 21.70 20.47 20.70 21.78 20.68 22.60 21.85 20.17 20.39 20.77 19.94 21.51 20.04 21.24 19.88 20.12 20.47 20.28 20.32
45.59 43.35 42.25 41.45 42.51 39.66 42.21 39.86 35.25 34.27 33.68 30.49 32.8 29.54 29.92 28.69 28.39 27.69 27.22 26.73
8.68 9.07 8.84 9.00 9.20 8.84 8.78 8.94 9.37 9.45 9.46 9.79 9.44 9.84 9.53 9.93 9.61 9.35 9.17 8.91
21.20 18.50 18.10 17.10 16.60 15.00 14.70 13.70 12.60 11.40 10.30 9.90 8.90 8.00 7.40 6.70 6.00 4.50 3.50 2.70
11000.17 9631.21 9577.57 10545.76 9554.98 10312.51 8853.90 9335.69 9976.68 9718.22 9346.81 8577.09 8605.35 9642.39 7760.48 9445.96 9369.40 8750.71 8959.20 9354.06
0.19 0.17 0.17 0.19 0.18 0.18 0.16 0.16 0.17 0.17 0.17 0.15 0.15 0.17 0.14 0.17 0.17 0.16 0.16 0.16
3.21 4.00 1.99 3.26 3.21 3.43 2.84 3.09 1.87 1.84 1.58 1.45 1.47 0.75 1.37 1.50 1.70 1.67 1.67 0.95
1201.02 1198.03 1059.94 1178.62 1016.33 1192.83 1212.24 1200.64 811.44 794.04 793.46 1002.63 778.70 987.65 1017.05 997.24 991.02 1012.98 1292.31 1392.87
a
P indicates the pressure; T indicates the temperature; Q indicates the production rate; the subscripts in, out refer to the upstream and downstream of the choke, respectively; the subscripts g, o, w, MEG refers to the gas, oil, water, and monoethylene glycol, respectively. Table 4 Physical properties of each phase calculated from the isenthalpic flash algorithm based on the CPA EOS. Location
Choke valve upstream
Choke valve downstream
P (MPa) T (� C) phase Mole (%) Weight (%) Volume (%) ρ (g/cm3) H (kJ/kg)
21.70 43.35 Total 100.00 100.00 100.00 0.26 413.30
9.07 18.97 Total 100.00 100.00 100.00 0.13 413.30
V 83.21 78.90 94.72 0.21 96.76
W 16.79 21.10 5.28 1.02 1596.84
5
V 83.14 78.66 97.39 0.10 71.75
L 0.10 0.28 0.05 0.63 343.83
W 16.76 21.07 2.55 1.03 1689.53
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Journal of Natural Gas Science and Engineering 74 (2020) 103108
Table 5 Comparisons of the calculated composition of each phase according to the isenthalpic-flash algorithm based on the CPA EOS and SRK-Peneloux EOS. The compositions are in terms of weight, %. location
Choke upstream
Model
SRK Peneloux
Phase
Total
H2O 15.99 MEG 4.84 N2 0.22 CO2 10.58 63.45 CH4 C2H6 3.03 0.91 C3H8 i-C4H10 0.20 n-C4H10 0.23 0.11 i-C5H12 n-C5H12 0.08 0.17 n-C6H14 n-C7H16 0.09 0.10 n-C8H18 Mass fraction (%)
Choke downstream CPA
SRK Peneloux
CPA
V
W
V
W
V
L
W
V
L
W
0.06 0.00 0.22 10.56 63.45 3.03 0.91 0.20 0.23 0.11 0.08 0.17 0.09 0.10 79.21
15.94 4.84 0.00 0.02 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 20.79
0.06 0.00 0.22 10.45 63.27 3.02 0.90 0.20 0.23 0.11 0.08 0.17 0.09 0.10 78.90
15.95 4.85 0.00 0.15 0.15 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 21.10
0.02 0.00 0.22 10.54 63.29 3.02 0.90 0.20 0.23 0.11 0.07 0.16 0.08 0.08 78.91
0.00 0.00 0.00 0.03 0.08 0.01 0.01 0.00 0.01 0.01 0.00 0.02 0.03 0.06 0.27
15.97 4.84 0.00 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 20.82
0.02 0.00 0.22 10.50 63.08 3.01 0.90 0.20 0.23 0.11 0.07 0.16 0.08 0.08 78.66
0.00 0.00 0.00 0.03 0.08 0.01 0.01 0.00 0.01 0.01 0.00 0.02 0.03 0.06 0.28
16.16 4.90 0.00 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 21.07
Although the adaptive iteration method is employed, the conver gence of the P–H flash algorithm is still limited by the solution method of the multiphase Rachford-Rice (RR) equation that is also well-known as the material balance equation for multiphase flash (Michelsen, 1987, Paterson et al., 2019). The convergence of the conventional RR equation solution method relies on the initial guess K values, which are mostly calculated from some empirical correlations developed for hydrocar bons. These correlations designed for hydrocarbon components possible give poor initial K values for non-hydrocarbon components, such as water and glycol, resulting in the failure of the P–H flash. Okuno et al. (2010) developed an efficient algorithm for solving the RR equation, which guarantees the correct convergence of RR equation for any number of phases, and also suitable for the negative flash calculations. When the robust solution method for the RR equation and initial K-values obtained from multiple ways are applied, the P–H flash algo rithm can be successfully performed by the use of the adaptive Newton and bisection methods. In this paper, the P–H flash model is solved based on the DS method and the bisection method (Zhu and Okuno, 2015). The material balance equation is solved by the method proposed by Okuno et al. (2010). All the fluid properties (density, compressibility factor, specific heat ca pacity, fugacity et al.) are calculated from the CPA EOS. The P–H flash model can be efficiently solved by the use of the combination of the above methods. However, the solution process takes more time than solving the P–H model based on the SRK EOS because solving CPA EOS is much more difficult.
Fig. 3. Comparisons of measured choke temperatures and calculated choke temperatures based on the SRK-Peneloux EOS, SRK-HV EOS, and the CPA EOS. MT refers to the measured temperature.
balance equations, and the enthalpy constraint equation. According to Eqs. (5), (21) and (22), the fugacity and enthalpy are dependent on the pressure, temperature, and fluid composition. In addition, for the multiphase fluid, calculating the fluid composition of each phase is dependent on the equilibrium constant in the material balance equation. Hence, the independent variables in the P–H flash model are the phase equilibrium constant K-values and the temperature. These variables can be solved by the use of the above equations and suitable methods. If the total enthalpy at the choke inlet and the outlet pressure is given, the outlet temperature can be directly solved based on the P–H flash model. The direct substitution (DS) algorithm originally proposed by Michelsen (1987) is the most widely used method to solve the P–H flash model. However, Zhu and Okuno (2015) found that the DS algorithm becomes degenerate for narrow-boiling fluids, such as multiphase water-containing hydrocarbon mixtures. To solve this problem, a new solution method that adaptively switches between Newton’s method and the bisection method is proposed to solve the P–H flash model. They presented that this algorithm is robust for narrow-boiling mixtures even for the fluid with one degree of freedom (Zhu and Okuno, 2015).
4. Case studies In this section, the P–H flash algorithm based on the CPA EOS is applied to various gas/water/MEG mixtures. Results show the accuracy of this method as well as the effect of water and MEG contents on choke temperatures. Case 1: Gas/water/MEG mixtures in the PY gas field in the South China Sea. The PY gas field locates in the South China Sea. The subsea chokes are installed at wellheads to control the production rates and pressures. The monoethylene glycol (MEG) is injected into the upstream of the choke to prevent the gas hydrate formation. The fluid composition is listed in Table 2. Twenty groups of measured production data are given in Table 3, including the upstream and downstream pressures and temperatures. The field measured data cover the upstream pressures from 19.88 MPa to 22.60 MPa, upstream temperatures from 26.73 � C to 45.59 � C, downstream pressures from 8.68 MPa to 9.93 MPa, and downstream temperatures from 2.70 � C to 21.20 � C. 6
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Table 6 Fluid Compositions collected from three wells in the JL gas field. The compo sitions are expressed in terms of mole, %. Component
JL04
JL16
JL23
CH4 C2H6 C3H8 i-C4H10 n-C4H10 i-C5H12 n-C5H12 n-C6H14 n-C7H16 H2O H2S CO2 N2 H2 He
97.365 0.130 0.000 0.005 0.008 0.001 0.006 0.001 0.148 1.295 1.006 0.005 0.006 0.002 0.022
95.383 0.394 0.039 0.006 0.010 0.010 0.012 0.045 0.000 1.295 0.000 0.325 2.155 0.001 0.325
96.122 1.007 0.089 0.011 0.016 0.008 0.010 0.000 0.000 1.855 0.000 0.642 0.197 0.000 0.043
related compositions are essential for the choke temperature prediction. Table 5 lists the composition of each phase at the upstream and downstream of the choke. It presents that the new liquid phase at the downstream of the choke mainly contains CH4, n-C7H16, and n-C8H18, which is also called the condensate-oil phase. At the downstream and upstream of the choke, the aqueous phase is mainly composed of water and MEG. Results demonstrate that the W-phase calculated from the CPA EOS contains more water and MEG but fewer hydrocarbon com ponents. That is because the CPA EOS considers the hydrogen-bond association between polar water and MEG molecules, which makes the polar components more likely to form liquid phase together. Also, different components of each phase further cause the different mass fraction of each phase that represents an important parameter for computing isenthalpic choke temperatures according to Eq. (4). In addition to the results given in Tables 4 and 5, all measured choke temperatures are applied to validate the proposed P–H flash method based on the CPA EOS, as shown in Fig. 3. Also, results calculated based on the SRK EOS with the Peneloux volume shift method (SRK-Peneloux EOS), and on the SRK EOS with Huron-Vidal mixing rule (SRK-HV EOS) (Michelsen, 1990) are depicted in Fig. 3. The Peneloux volume shift is used to correct the liquid volume in the EOS, and the Huron-Vidal mixing rule enables the SRK EOS to model the hydrogen-bond interac tion between water molecules. The maximum deviations between the calculated choke tempera tures based on the CPA, SRK-Peneloux, and SRK-HV EOSs are equal to 1.76 � C, 2.74 � C, and 2.82 � C, respectively. The corresponding average absolute deviations (AAD) between calculated values and measured data defined by Eq. (24) are equal to 0.68 � C, 1.48 � C, and 1.58 � C, respectively.
Fig. 4. The Five-stage choking process used in the JL gas field. The fifth choke valve is far away from the wellhead, so it is cannot be displayed here.
AAD ¼
Take the case with Pin ¼ 21.70 MPa, Tin ¼ 43.35 � C, Pout ¼ 9.07 MPa as an example to show the isenthalpic multiphase flash results for this choking process, as given in Table 4. It is presented that the calculated downstream temperature is 18.97 � C, which is only 0.47 � C higher than the measured value. The vapor (V) and aqueous (W) two-phase co-ex istence fluid at the upstream of the choke splits to three phases fluids, including the vapor (V), liquid (L), and aqueous phases (W) at the downstream the choke. However, the total enthalpy during the choking process keeps a constant because the P–H flash model is constrained by the constant enthalpy equation (Michelsen, 1987; Zhu and Okuno, 2015). These results present that the enthalpy of the polar aqueous phase (W-phase) at the choke upstream is 336.93 kJ/kg that takes the 81.1% of the fluid total enthalpy, whereas the enthalpy of the W-phase takes the 85.85% of the fluid total enthalpy at the downstream of the choke. Hence, accurate calculations of the polar liquid enthalpy and
N � 1 X �Tcali N i¼1
� Texp i �
(24)
where N is the total number of data points; Tcal i is the calculated tem perature; Texp i is the measured temperature. Case 2: Choke temperature calculations at the JL gas field, China. The pressure at wellheads in the JL gas field, China, often beyond 100 MPa. The five-stage choke valves shown in Fig. 4 are widely used at wellheads to release the pressures and to control the production rates. As shown in Fig. 4, the flow direction of natural gas is from the Christmas tree to the 1st, 2nd, 3rd, 4th, and 5th choke valves. The fifth choke valve is far away from the wellhead, so it is difficult to be displayed in Fig.4 (a) and Fig.4 (b). The wellhead pressures and temperatures are taken as the inlet pressures and temperatures of the first-stage choke valve. The resulting downstream pressures and temperatures are used as the inlet parameters of the choke valve at the next stage. So, the choke parame ters, including the pressures, temperatures at wellheads and 7
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Table 7 Calculated choke temperatures in the JL gas field based on the isenthalpic flash algorithm combining with the CPA EOS. Location JL04
JL16
JL23
Pexp (MPa) Texp (� C) Tcal (� C) Deviation (� C) Pexp (MPa) Texp (� C) Tcal (� C) Deviation (� C) Pexp (MPa) Texp (� C) Tcal (� C) Deviation (� C)
Wellhead
Downstream of the 1st choke
Downstream of the 2nd choke
Downstream of the 3rd choke
Downstream of the 4th choke
88.50 32.60 – – 77.49 48.91 – – 119.30 35 – –
75.70 37.30 36.72 0.58 72.13 49.39 50.30 0.91 90.00 44.9 46.77 1.87
49.50 39.83 41.73 1.90 34.00 46.80 49.29 2.49 65.00 50.9 51.68 0.78
22.30 25.83 27.85 2.02 12.80 23.60 20.87 2.73 45.00 50.5 51.87 1.37
20.70 23.52 23.76 0.24 10.15 15.29 15.47 0.18 20.00 33.2 35.47 2.27
Case 3: Effect of water and MEG contents on the choke temperatures. This subsection designed a three-stage choking process to research the effect of water and MEG contents on the choke temperatures. The overall gas composition is in accordance with that of JL04 well given in Table 6. The upstream pressures and temperatures are set to specified values as listed in Table 8, and the downstream pressures are also specified so that the P–H flash algorithm can be performed. The pressure difference across the choke is designed by the critical-flow choking method proposed by Wu et al. (2017). The water contents and MEG contents are set as specified values from 0 to 50% in terms of the mole fraction. The SRK-Peneloux EOS, SRK-HV EOS, and the CPA EOS are used here to calculate the temperatures at the downstream of chokes when the gas contains different amounts of water and MEG. The calculated temper atures at the downstream of each-choke are depicted in Fig.s 5 to 7. Figs. 5–7 show that these three EOSs give exactly the same results when the water content is zero because the CPA EOS reduces to the traditional SRK EOS under this condition. However, results demonstrate that the deviations between the CPA EOS and SRK-based EOSs increases with increasing water and MEG contents. That is because the SRK-Peneloux EOS, SRK-HV EOS do not account for the association between polar water/MEG molecules, which might cause deviations on estimating the water enthalpy. As a result, calculated temperatures deviate from actual values. Taking the high-pressure first-stage choking process as an example,
Table 8 The upstream pressures, upstream temperatures, and downstream pressures designed for a three-stage choking process. Location
Upstream pressure (MPa)
Upstream temperature (� C)
Downstream pressure (MPa)
The 1st-stage choke The 2nd-stage choke The 3rd-stage choke
110.0
40.00
34.0
34.0
55.70
12.0
12.0
24.65
4.1
downstream of each choke valve, are measured to validate the proposed method. Table 6 lists the fluid compositions collected from three wells, namely JL04, JL16, and JL23. Table 7 presents the measured tempera tures and calculated temperatures at the downstream of each choke valve of the above three wells. In particular, the pressure at the JL23 wellhead is 119.30 MPa, which represents almost the highest pressure at gas wellheads around the world as far as we know. Results demonstrate that the average deviations between the measured and calculated tem peratures for these three gas wells are equal to 1.19 � C, 1.57 � C, and 1.57 � C, respectively. These results show that the method proposed in this paper can be extended to pressures up to 100 MPa.
Fig. 5. Comparisons of temperatures at downstream of the first-stage choke calculated from the SRK-Peneloux, SRK-HV, and CPA EOSs. The upstream pressure is 110 MPa, and the upstream temperature is 40 � C. The downstream pressure is set to 34 MPa. 8
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Fig. 6. Comparisons of temperatures at downstream of the second-stage choke calculated from the SRK-Peneloux, SRK-HV, and CPA EOSs. The upstream pressure is 34 MPa, and the upstream temperature is 55.7 � C. The downstream pressure is set to 12.0 MPa.
Fig. 7. Comparisons of temperatures at downstream of the third-stage choke calculated from the SRK-Peneloux, SRK-HV, and CPA EOSs. The upstream pressure is 12 MPa, and the upstream temperature is 24.65 � C. The downstream pressure is set to 4.1 MPa. Table 9 Comparisons of calculated mass fractions and enthalpies of each phase according to the isenthalpic-flash algorithm based on the CPA EOS and on the SRK-Peneloux EOS. Location
Model
The 1st-stage choke
CPA EOS
The 3rd-stage choke
SRK Peneloux EOS CPA EOS SRK Peneloux EOS
Total Weight (%) Enthalpy (J/kg) Weight (%) Enthalpy (J/kg) Weight (%) Enthalpy (J/kg) Weight (%) Enthalpy (J/kg)
Upstream 100.00 542260.01 100.00 583095.86 100.00 566487.98 100.00 609916.56
9
Downstream
V
L
V
L
78.20 60889.75 78.33 60994.20 78.27 55948.05 78.33 55999.57
21.80 481370.26 21.67 522101.65 21.73 510539.93 21.67 553916.98
78.29 59500.89 78.38 62234.07 78.28 36654.55 78.32 32737.60
21.71 482759.12 21.62 520861.79 21.72 529833.43 21.68 577178.96
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20 mol% water and 80 mol% natural gas are selected as a typical case to analyze further the reasons for causing the temperature differences be tween the CPA EOS and SRK-Peneloux EOS at high pressures and low pressures. The enthalpies and mass fractions of each phase calculated based on the CPA EOS and on the SRK-Peneloux EOS are given in Table 9. The main compositions of the aqueous phase are shown in Table 10. Tables 9 and 10 present that the CPA EOS and SRK-Peneloux EOS give different compositions and mass fractions of the aqueous phase, resulting in the different enthalpy difference across the choke. For example, the aqueous phase calculated from the CPA EOS contains more H2S due to the association between the water and H2S molecule is more likely to dissolve H2S in water (Tsivintzelis et al., 2010). Also, previous literature shows that the CPA EOS can accurately predict the CH4 sol ubility in water (Jia and Okuno, 2018). So, we can conclude that the CPA EOS predicts the composition of the aqueous phase better, which will contribute to accurate enthalpy values since the enthalpy is dependent on the pressure, temperature, and composition. Fig. 8 shows the enthalpy curves of the fluid at a specified pressure and different temperatures, the isenthalpic choking routes of the firstand third-stage choking processes. During the first-stage choking pro cess, the CPA EOS gives higher downstream temperatures in comparison with the SRK-Peneloux EOS when the pressure reduces from 110 MPa to 34 MPa. However, the CPA EOS yields lower downstream temperatures during the third-stage choking process. That is because the different EOSs give different component distributions and related total en thalpies. It should note that the upstream pressures and temperatures are specified in Table 8, so the total enthalpies of the first- and thirdstage choking processes are different. Previous cases show the effect of water or MEG on the choke tem perature. The co-existence of water and MEG in gas mixtures is common when the MEG is injected into the upstream of the choke valve to pre vent the gas hydrate formation. The effect of the co-existence of water and MEG on choke temperatures are shown in Fig. 9 to Fig. 11. The
Table 10 Comparisons of the calculated main composition of the aqueous-phase accord ing to the isenthalpic-flash algorithm based on the CPA EOS and on the SRKPeneloux EOS. The compositions are in terms of mole, %. Location
Component
The 1ststage choke The 3rdstage choke
H2O H2S CH4 H2O H2S CH4
CPA EOS
SRK Peneloux EOS
Upstream
Downstream
Upstream
Downstream
99.360 0.087 0.552 99.721 0.078 0.201
99.585 0.079 0.336 99.826 0.064 0.109
99.964 0.035 0.000 99.977 0.023 0.000
99.962 0.037 0.001 99.988 0.012 0.000
the choke temperature calculated from the CPA EOS is 54.18 � C when the water content is 50%, whereas the SRK-Peneloux and SRK-HV EOSs yields 51.88 � C and 51.79 � C, respectively. Similarly, the temperature calculated from the CPA EOS is 2.5 � C higher than those calculated from the SRK-Peneloux and SRK-HV EOSs when the MEG content is 50%. Previous research shows that traditional EOSs tend to give lower choke temperatures at high pressures (Li et al., 2012b). Hence, the CPA EOS is more likely to yield accurate results at high pressures. During the second- and the third-stage choking process, the down stream temperatures calculated from the CPA EOS are slightly lower than those calculated from the SRK-Peneloux and SRK-HV EOSs when natural gas contains different amounts of water. In contrast, when nat ural gas contains MEG, the CPA EOS yields slightly higher temperatures in comparison with SRK-Peneloux and SRK-HV EOSs at the second-stage choke, but yields lower results at the third-stage choke. These interesting results indicate that the association between polar components and related phase change does not always increase the choke temperatures. The temperature change across the choke is dependent on the specified choke parameters, such as the upstream pressure, temperatures, and downstream pressure. The first- and third-stage choking process of the mixture consisted of
Fig. 8. Curves of temperature and enthalpy change under different choke pressures using the isenthalpic-flash algorithm based on the CPA EOS and SRK-Peneloux EOS. kCPA, kSRK denotes the slope of a straight line,� C/(J/kg). 10
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Fig. 9. Comparisons of temperatures at downstream of the first-stage choke calculated from the SRK-Peneloux, SRK-HV, and CPA EOSs. The mixtures are composed of 10 mol% H2O and 0–20 mol% MEG.
Fig. 11. Comparisons of temperatures at downstream of the third-stage choke calculated from the SRK-Peneloux, SRK-HV, and CPA EOSs. The mixtures are composed of 10 mol% H2O and 0–20 mol% MEG.
water/MEG mixtures flowing through choke valves. However, the pro posed method can further be extended to model mixtures containing many other polar hydrogen-bond components (methanol, ethanol, diethylene glycol and triethylene glycol) if the association parameters for these components in the CPA EOS can be specified. Some of these parameters have already been reported in the literature (Tsivintzelis et al., 2010; Arya et al., 2014; Sarafraz and Hormozi, 2014a,b; Hajiw et al., 2015a,b), which provides good references for further research on the choke temperatures of other gas/water/glycols mixtures. 5. Conclusions A multiphase isenthalpic flash algorithm based on the CPA EOS is proposed to calculate the downstream temperatures of chokes. The derivation of the isenthalpic choking process, the CPA EOS, and the related isenthalpic flash algorithm are introduced. This method can directly calculate the downstream temperature according to the speci fied upstream pressure, upstream temperature, downstream pressure and the fluid composition, instead of using the complicated temperature iteration method. The conclusions are as follows: 1. In comparison with the traditional isenthalpic flash algorithm based on the cubic EOSs, this new method accounts for the self- and crossassociation between water, MEG molecules, and other polar mole cules yielding more accurate methods for the enthalpy calculation of gas/water/MEG mixtures as well as choke temperatures. 2. A total of thirty-two groups measured data are applied to validate the proposed method, which covers temperatures from 2.70 � C to 50.9 � C, and pressures from 8.68 MPa to 119.3 MPa. Results demonstrate that the average absolute deviation between the measured and calculated temperatures at downstream of chokes based on the proposed method is less than 1.6 � C even for vapor-liquid-aqueous three-phase mixtures at pressures up to 100 MPa. In contrast, the isenthalpic flash methods based on the traditional SRK-HV and SRK Peneoux EOSs tend to give much lower choke temperatures at high pressures. 3. The co-existence of water and MEG affects the phase transition and related choke temperatures. The gas/water/MEG mixture is in the vapor-liquid two phases at the choke inlet. However, it splits to vapor-liquid-aqueous three-phases at downstream of the choke. With
Fig. 10. Comparisons of temperatures at downstream of the second-stage choke calculated from the SRK-Peneloux, SRK-HV, and CPA EOSs. The mix tures are composed of 10 mol% H2O and 0–20 mol% MEG.
specified choke parameters keep the same as those listed in Table 8. Fig. 9 shows that the deviations between the results calculated from the CPA EOS and those calculated from the SRK-based EOSs increase with increasing MEG contents when the gas contains 10 mol% H2O and 0–20 mol% MEG. The CPA EOS yields overall higher downstream tem peratures than the SRK-Peneloux and SRK-HV EOSs. These results demonstrate that the association between water and MEG molecules increases the choke temperatures at the first-stage choke. However, as depicted in Fig. 10 and Fig. 11, the CPA EOS gives lower temperatures at the second- and third-stage chokes. The reasons for causing these special results have been previously illustrated in Fig. 8. These results show the superiority of using the CPA EOS and isenthalpic flash algorithm to predict choke temperatures. This paper focuses on predicting the choke temperatures of gas/ 11
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consideration of the interaction between water, MEG, and other polar molecules, the aqueous phase can dissolve more MEG and other polar components, which contributes to accurate predictions of choke temperatures. Moreover, the effects of association between polar water/MEG molecules on choke temperatures are dependent on the specified inlet pressures, temperatures, and fluid components.
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Declaration of competing interest The authors declare that there is no conflict of interest. Acknowledgments This study was financially supported by the National Natural Science Foundation of China (No., 51604233, 51674213), a sub-project of the National Science and Technology Major Project of China (No. 2016ZX05028-001-006). Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi. org/10.1016/j.jngse.2019.103108. References Arya, A., Maribo-Mogensen, B., Tsivintzelis, I., Kontogeorgis, G.M., 2014. Process design of industrial triethylene glycol processes using the cubic-plus-association (CPA) equation of state. Ind. Eng. Chem. Res. 53 (29), 11766–11778. Attar, H.A., 2008. Performance of wellhead chokes during sub-critical flow of gas condensates. J. Pet. Sci. Eng. 60, 205–212. Derawi, S., Michelsen, M.L., Kontogeorgis, G., et al., 2003. Application of the CPA equation of state to glycol/hydrocarbons liquid-liquid equilibria. Fluid Phase Equilib. 209 (2), 163–184. Derawi, S.O., Kontogeorgis, G.M., Michelsen, M.L., Stenby, E.H., 2003. Extension of the cubic-plus-association equation of state to glycol water cross-associating systems. Ind. Eng. Chem. Res. 42 (7), 1470–1477. Elgibaly, A.A.M., Nashawi, I.S., 1996. Prediction of two-phase flow through chokes for Middle East oil wells. In: Proceeding of the International Petroleum Exhibition and Conference, Abu Dhabi, UAE, 13–16 October 1996, vol. 1996. Society of Petroleum Engineers, Richardson, TX, USA. SPE36274-MS. Ghorbani, H., Moghadasi, J., Wood, D.A., 2017. Prediction of gas flow rates from gas condensate reservoirs through wellhead chokes using a firefly optimization algorithm. J. Nat. Gas Sci. Eng. 45, 256–271. Gilbert, W.E., 1954. Flowing and gas-lift well performance. In: Drilling and Production Practice. American Petroleum Institute. Drilling and Production Practice, vol. 20, pp. 126–157. Haghbakhsh, R., Konttorp, M., Raeissi, S., Peters, C.J., O’Connell, J.P., 2014. Derivative properties from high-precision equations of state. J. Phys. Chem. B 118, 14397–14409. Hajiw, M., Chapoy, A., Coquelet, C., 2015. Hydrocarbons–water phase equilibria using the CPA equation of state with a group contribution method. Can. J. Chem. Eng. 93, 432–442. Hajiw, M., Chapoy, A., Coquelet, C., Lauermann, G., 2015. Prediction of methanol content in natural gas with the GC-PR-CPA model. J. Nat. Gas Sci. Eng. 27, 745–750. Jia, W.L., Okuno, R., 2018. Modeling of asphaltene and water associations in petroleum reservoir fluids using cubic-plus-association EOS. AIChE J. 63, 3429–3442. Kontogeorgis, G.M., Yakoumis, I.V., Meijer, H., Hendriks, E., Moorwood, T., 1999. Multicomponent phase equilibrium calculations for water–methanol–alkane mixtures. Fluid Phase Equilib. 158, 201–209. Kontogeorgis, G.M., Michelsen, M.L., Folas, G.K., Derawi, S., von Solms, N., Stenby, E.H., 2006. Ten years with the CPA (Cubic-Plus-Association) equation of state. Part 1. Pure compounds and self-associating systems. Ind. Eng. Chem. Res. 45, 4855–4868. Kontogeorgis, G.M., Folas, G.K., 2009. Thermodynamic Models for Industrial Applications: from Classical and Advanced Mixing Rules to Association Theories. John Wiley & Sons. Kruger, F.J., Danielsen, M.V., Kontogeorgis, G.M., Solbraa, E., von Solms, N., 2018. Ternary vapor–liquid equilibrium measurements and modeling of ethylene glycol (1) þ water (2)þ methane (3) systems at 6 and 12.5 MPa. J. Chem. Eng. Data 63, 1789–1796. Li, C., Jia, W., Liu, E., Wu, X., 2012. A Temperature prediction model for high pressure natural gas through chokes. Energy Education Science And Technology Part AEnergy Science And Research 30 (1), 113–122. Li, C., Jia, W., Wu, X., 2012. Temperature prediction for high pressure high temperature condensate gas flow through chokes. Energies 5, 670–682. Li, C., Peng, Y., Dong, J., Chen, L., 2015. Prediction of the dew point pressure for gas condensate using a modified Peng–Robinson equation of state and a four-coefficient molar distribution function. J. Nat. Gas Sci. Eng. 27, 967–978.
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Xia, J., Yang, C., Wang, X., 2016. Key technologies for well drilling and completion in ultra-deep sour gas reservoirs, Yuanba Gasfield, Sichuan Basin. Nat. Gas. Ind. B 3 (6), 607–613. Yakoumis, I.V., Kontogeorgis, G.M., Voutsas, E.C., Tassios, D.P., 1997. Vapor-liquid equilibria for alcohol hydrocarbon systems using the CPA equation of state. Fluid Phase Equilib. 130 (1–2), 31–47. Yakoumis, I.V., Kontogeorgis, G.M., Voutsas, E.C., Hendriks, E.M., Tassios, D.P., 1998. Prediction of phase equilibria in binary aqueous systems containing alkanes, cycloalkanes, and alkenes with the cubic-plus-association equation of state. Ind. Eng. Chem. Res. 37 (10), 4175–4182.
Yarveicy, H., Ghiasi, M.M., Mohammadi, A.H., 2018. Determination of the gas hydrate formation limits to isenthalpic Joule–Thomson expansions. Chem. Eng. Res. Des. 132, 208–214. Yao, G., Wu, X., Sun, Z., Yu, C., Ge, Y., Yang, X., Zhang, J., 2018. Status and prospects of exploration and exploitation key technologies of the deep petroleum resources in onshore China. J. Nat. Gas GEOSci. 3 (1), 25–35. Yingchuan, L., Shunqu, H., Chunqiu, G., 2003. Model of temperature drop mechanism when gas flowing through chokes. Nat. Gas. Ind. 23 (3), 70–72. Zhu, D., Okuno, R., 2014. A robust algorithm for isenthalpic flash of narrow-boiling fluids. Fluid Phase Equilib. 379, 26–51. Zhu, D., Okuno, R., 2015. Robust isenthalpic flash for multiphase water/hydrocarbon mixtures. SPE J. 20, 1–350.
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Journal of Natural Gas Science and Engineering journal homepage: http://www.elsevier.com/locate/jngse
Predictions on temperatures of high-pressure gas/water/MEG mixtures flowing through wellhead chokes Wenlong Jia a, b, *, Fan Yang a, Xia Wu a, b, Changjun Li a, b, Yubin Wang b a b
School of Petroleum Engineering, Southwest Petroleum University, Chengdu, 610500, China CNPC Key Laboratory of Oil & Gas Storage and Transportation, Southwest Petroleum University, Chengdu, 610500, China
A R T I C L E I N F O
A B S T R A C T
Keywords: Choke Temperature High-pressure gas Cubic-plus-association equation of state Isenthalpic flash
The co-existence of gas, water, and monoethylene glycol (MEG) is common in produced fluids of high-pressure gas wells. Accurate predictions on the temperature changes during the choking process are essential for the design and operation of the choke valve. This paper presents an efficient multiphase isenthalpic flash method based on the cubic-plus-association equation of state (CPA EOS) to calculate the choke temperatures. In com parison with the traditional isenthalpic flash algorithm, this new method accounts for the self- and crossassociation between polar water and MEG molecules, yielding more accurate enthalpy calculation results and multiphase component distributions for fluids containing water and MEG. The proposed model is validated by field test data with pressures from 8.68 MPa to 119.3 MPa. The average absolute deviations between the calculated choke temperatures and measured values are less than 1.6 � C even for vapor-liquid-aqueous threephase mixtures at various pressures. Moreover, case studies show that accounting for the association between polar water/MEG molecules contributes to accurate predictions on choke temperatures. At high pressures, the CPA EOS tends to give higher choke temperatures in comparison with those calculated based on the traditional SRK-Peneloux EOS. In contrast, the CPA EOS tends to yield lower temperatures at low pressures.
Author contribution statement Wenlong Jia: Conceptualization, Methodology, Resources, Soft ware.Fan Yang: Writing- Original draft preparation, Validation, Data curation.Xia Wu: Data curation, Investigation.Changjun Li: Supervi sion, Software.Yubin Wang: Writing- Reviewing and Editing. 1. Introduction The choke valve is often installed near the wellheads to control gas production rates and/or downstream pressures in gas field surface production systems (Naseri et al., 2016; Ghorbani et al., 2017). During the choking process, the fluid temperature varies with the pressure drop across the valve due to the fluid’s Joule-Thomson effect. Accurately predicting the choke temperature is essential for the selection of chokes, for the prevention of gas hydrates, and for the design of gas processing plants. In recent years, many ultra-high pressure gas reservoirs that pressure beyond over 100 MPa at wellheads (Xia et al., 2016; Yao et al., 2018) have been found in Sichuan Basin and Tarim Basin, China. Within the
multi-stage choking process, the gas hydrate is easy to form because of the fluid temperature decreases with the pressure drop. Methanol, ethanol, MEG, and many other glycols can be used as gas hydrate in hibitors. MEG is the most widely used one due to its advantages of economical and low toxic. Hence, the co-existence of gas, water, and MEG is commonly found in produced fluids due to formation water production and hydrate inhibitor injection at wellheads. The interaction between the polar water and MEG molecules can affect the phase behavior and subsequent temperature changes during gas/water/MEG mixtures flowing through chokes at wellheads, resulting in complicated multiphase transitions and temperature variations across the choke. Many methods can be applied to predict the choke temperatures, such as the artificial neural network (ANN) method (Yarveicy, 2018), the empirical correlation method (Attar, 2008; Rostamian and Lotfol lahi, 2020), the statistical method (Rostamian and Lotfollahi, 2019), and thermodynamic models (Nasrifar and Bolland, 2006; Yingchuan et al., 2003). The development of the ANN model and the statistical model needs a large amount of historical production data. However, the pro duction of high-pressure gas wells is not common around the world, which limits the development of such methods. Hence, the empirical
* Corresponding author. School of Petroleum Engineering, Southwest Petroleum University, Chengdu, 610500, China. E-mail address: [email protected] (W. Jia). https://doi.org/10.1016/j.jngse.2019.103108 Received 15 September 2019; Received in revised form 11 December 2019; Accepted 11 December 2019 Available online 14 December 2019 1875-5100/© 2019 Elsevier B.V. All rights reserved.
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Journal of Natural Gas Science and Engineering 74 (2020) 103108
Fig. 1. The schematic diagram of a choke valve. P, T, H, C refer to the fluid pressure, temperature, enthalpy, and velocity, respectively. Subscripts 1 and 2 indicate the upstream and downstream of the choke valve, respectively.
correlation and the thermodynamic model based on EOS are most widely used in predicting choke temperatures. The empirical correlations are often developed from limited experi mental data, such as the Gilbert (1954), Elgibaly and Nashawi (1996), and Attar (2008) correlations. These correlations usually have consid erable accuracy when the target choke parameters fall into the data that used to develop the correlations. Otherwise, these correlations often yield poor results (Yao et al., 2018; Shao et al., 2018). Theoretical models are generally built based on mass, momentum, and energy conservation laws, such as the Perkins model (Prekins et al., 1993) and the Hydro model (Selmer-Olsen and Holm, 1995). However, most of the theoretical models focus on sizing the choke valve according to the choke pressure difference and the required flow rate of the fluid across the valve instead of calculating the choke temperatures. The isenthalpic principle has been widely used to calculate the choke temperatures, which assumes that fluid total enthalpy at the upstream of the choke is equal to that at the downstream of the choke (Li et al., 2012a,b). That means, if the choke inlet pressure, inlet temperature, and outlet pressure are specified, the outlet temperature can be directly calculated from the isenthalpic flash algorithm (Zhu and Okuno, 2014). The accuracy of this method relies on the enthalpy calculation method and the multiphase equilibrium algorithm based on the equation of state. Using the cubic equations of state (EOSs) is a well-known way to calculate the density, enthalpy and many other physical properties of hydrocarbon mixtures because of their simplicity, computational effi ciency, and acceptable accuracy (Wei and Sadus, 2000; Li et al., 2015, 2016; Valiollahi et al., 2016). Many scholars (Riaz et al., 2011; Sarafraz and Peyghambarzadeh, 2012; Sarafraz and Hormozi, 2014a,b; Saberi et al., 2018) discussed the effect of the density, heat capacity and other thermophysical properties of a binary mixture containing alcohols on the prediction of pool boiling heat transfer coefficient. Li et al. (2012a) built a choke temperature model for dry natural gas based on the Peng-Robinson EOS, the van der Waals mixing rule and the energy conservation law. Li et al. (2012b) developed a choke temperature prediction model for high-pressure and high-temperature condensate gas based on the SRK EOS, Lee-Kesler EOS and a modified mixing rule. Teng et al. (2016) proposed a multiphase choked flow model for hy drocarbon mixtures containing high CO2 contents based on the BWRS EOS. The calculation results are in good agreement with the field test data of Daqing Sartu Oilfield. Cubic EOSs are not originally designed to model thermophysical properties of polar components, such as water and MEG. The effect of strong interactions between polar molecules on the enthalpy cannot be desrcibed by the traditional isenthalpic flash algorithm based on the cubic EOSs (Kontogeorgis and Folas, 2009). Hence, the choke temperatures of gas/water/MEG mixtures are difficult to be accurately calculated based on the cubic EOSs. In contrast, Kon togeorgis et al. (2009) proposed a cubic-plus-association (CPA) EOS that provides an efficient method to model fluids containing polar compo nents, including water and glycol. The CPA EOS typically has two parts, namely the physical part and the association part. Without polar com ponents, the CPA EOS reduces to the traditional cubic EOS, such as the SRK EOS. The CPA EOS has been successfully applied to model complex multiphase equilibrium and physical properties of mixtures containing associated fluids. It has been used to predict the vapor-liquid
equilibrium (VLE) and liquid-liquid equilibrium (LLE) of alcoholhydrocarbons (Yakoumis et al., 1997; Voutsas et al., 1997), water-hydrocarbons (Yakoumis et al., 1998; Oliveira et al., 2007; Liang et al., 2014), alcohol-water (Voutsas et al., 1999; Kontogeorgis et al., 2006; Lundstrøm et al., 2006), multi-component water- alcohol-hydrocarbons (Kontogeorgis et al., 1999; Kruger et al., 2018), ethylene glycol-hydrocarbons (Derawi & Michelsen et al., 2003), ethylene glycol-water systems (Derawi & Kontogeorgis et al., 2003). Besides, the CPA EOS also shows good performance when describing the physical properties of mixtures containing water and alcohol. Lundstrøm et al. (2006) stated that the CPA EOS shows better results in calculating the enthalpy, heat capacity, and Joule-Thomson coefficient of water and methanol at high pressures, in comparison with the SRK or SRK-Peneloux EOSs. Previous publications indicate that the CPA EOS has been success fully applied to reproduce the physical properties, VLE and LLE phase equilibrium of hydrocarbon, water and glycol mixtures (Hajiw et al., 2015a,b; Kruger et al., 2018). Hence, we assume that, in comparison with the algorithms based on traditional cubic EOSs, the isenthalpic flash algorithm based on the CPA EOS can accurately calculate the choke temperatures of gas/water/MEG mixtures. The main objective of this research is to study the accuracy of using the isenthalpic flash algorithm combining with the CPA EOS to calculate the choke temperatures of gas/water/glycol mixtures at high pressures. In what follows, a brief introduction of the choking process is fol lowed by the isenthalpic principle. Then the CPA EOS and the isen thalpic flash algorithm applied in this research are described. After that, the accuracy of this method, and the effect of water and MEG contents in fluids on the choke temperature are discussed in case studies. 2. Isenthalpic choking process Surface chokes are often installed near to wellhead to control the production rates and/or downstream pressures. In order to clarify the choking process, the control volume composed of the choke valve, and two short symmetrical pipe sections at upstream and downstream of the choke valve is taken as the research object in this paper. Fig. 1 shows the schematic of this control volume. The main parameters involved in the choking process include the fluid’s temperature, pressure, velocity, enthalpy, etc. For the compressible flow, the fluid velocity across the choke may reach the local sonic velocity. With the fluid velocity increases, the temperature through the choke varies with the pressure drop due to the Joule-Thomson effect. Such a choking process follows the basic energyconservation principle (Li et al., 2012b). Accordingly, the one-dimensional energy-conservation equation can be written as: 1 p1 v1 þ e1 þ C21 þ Z1 þ Q 2
1 W ¼ p2 v2 þ e2 þ C22 þ Z2 2
(1)
where p is the pressure; v is the specific volume; e is the internal energy; Z is the elevation; C is the fluid velocity; Q is the heat transferred from the environment to the fluid; W is the work done by the fluid. The subscripts 1 and 2 represent the upstream and downstream of the choke, respectively. Eq. (1) can be simplified based on the following assumptions (Li 2
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Journal of Natural Gas Science and Engineering 74 (2020) 103108
Table 1 Properties of water, MEG, and some common hydrocarbon components. Component
Tc, K
Pc, kPa
ω
a0,Pa⋅m6⋅mol
H2O MEG N2 H2S CO2 CH4 C2H6 C3H8 i-C4H10
647.3 720.0 126.2 373.2 304.2 190.6 305.4 369.8 408.1
22088.9 9000.0 3394.4 8936.9 7376.5 4600.2 4883.9 4245.5 3647.7
0.344 0.535 0.040 0.100 0.225 0.008 0.098 0.152 0.176
0.123 1.082 0.139 0.386 0.351 0.232 0.551 0.915 1.295
2
b,10
5
m3⋅mol
0.674 0.674 0.543 0.502 0.760 0.447 0.585 0.667 0.713
(2)
g¼
0.0692 0.0141
5.440
0.0583
Kontogeorgis et al. (1999) (Derawi et al., 2003a,b) Kontogeorgis and Folas (2009) Tsivintzelis et al. (2010) Tsivintzelis et al. (2011) Tsivintzelis et al. (2010) Tsivintzelis et al. (2010) Tsivintzelis et al. (2010) Tsivintzelis et al. (2011)
Ai
1 b ; η¼ 1:9η 4v
1
(7)
Calculating Х Ai is related to the association strength ΔAi Bj between association sites belonging to different molecules, given by XA i ¼
Eq. (3) indicates that the total enthalpy at the downstream of the choke is equal to that at the upstream of the choke, which shows that the choking process follows an isenthalpic principle. For multiphase mix tures, the total enthalpy of the fluid should be calculated from the weighted average of each phase enthalpy, as follows:
1þρ
1 P P ; i; j ¼ 1; 2; ⋯; NCA xj XBj ΔAi Bj j
(4)
bij ¼
where mi is the mass fraction of the ith phase; Hi is the specific enthalpy of the ith phase; n is the number of phases. For a given fluid, the enthalpy is determined by the temperature, pressure, and composition, that is:
(8)
Bj
where ρ is the molar density. ΔAi Bj is given by � � Ai Bj � � ε ΔAi Bj ¼ g exp 1 bij βAi Bj RT
i¼1
H ¼ f ðp; T; ComÞ
16.655 19.752
i
(3)
mi Hi
reference
refers to the summation over all sites (Ai, Bi, Ci) on component i; g is the hard-sphere radial distribution function (RDF), determined from Eq. (7):
By introducing the definition of enthalpy H ¼ e þ pv, Eq. (2) is finally given by:
H¼
βAB
where P is the pressure; T is the temperature; v is the molar volume; x is the mole fraction; R is the gas constant; nassoc is the total number of association components; Ai is the active association site A on molecule i; Х Ai is the fraction of sites A on component i that do not form bonds with P P other active sites; refers to the summation over all components;
Using these assumptions, Eq. (1) is simplified as:
n X
1
CPA EOS is written as Eq. (6) when the physical part is taken from the conventional SRK EOS: � � RT a 1 RT ∂ln g X X 1 v xi ð1 XAi Þ (6) P¼ v b vðv þ bÞ 2 v ∂v i Ai
(1) The kinetic energy of the mixture is usually negligible in com parison with its total energy. (2) The elevation change of the fluid across the choke is negligible. (3) The flow process is frictionless. The energy change caused by friction heat is much smaller than that caused by the Joule Thomson effect. (4) The external work done is zero. (5) The flow process is adiabatic. The length of the choke is short, and the fluid velocity is relatively high, resulting in a very limited time for heat transfer.
H1 ¼ H2
εAB, kPa⋅m3⋅mol
κ
1.452 5.140 2.678 2.920 2.720 2.910 4.290 5.870 7.510
et al., 2012b; Nejatian et al., 2014; Teng et al., 2016):
p1 v1 þ e1 ¼ p2 v2 þ e2 :
1
bi þ bj 2
(9) (10)
where εAi Bj is the association energy for the association between Ai and Bj; βAi Bj is the association volume that represents the finite distance at which the inter-particle potential between Ai and Bj is zero; b is the covolume. The energy parameter a in Eq. (6)is given by
(5)
where T is the temperature; Com is the fluid composition. If the upstream pressure and upstream temperatures are specified, the total enthalpy at the upstream of the choke can be calculated. With the specification of the downstream pressure, the downstream temper ature can be solved to match the downstream total enthalpy and the upstream total enthalpy. So, the enthalpy calculation method is essential for the accurate calculation of downstream temperature. Traditionally, we use cubic EOSs, such as the PR and SRK EOSs, to calculate the enthalpy, which cannot account for the effect of interactions between polar components on the enthalpy (Twu et al., 2005). In this research, we use the CPA EOS to model the isenthalpic choking process for the first time with accounting for the interaction between polar components, including the water and MEG.
� a ¼ a0 1 þ κ 1
pffiffiffiffi ��2 Tr
(11)
For the pure associating component, five parameters a0, b, κ, εAi Bj , β in CPA EOS should be determined to represent its thermophysical properties. They are typically fitted from the vapor pressures and liquid densities of a pure component. For inert (not self-associating) compo nents, only three parameters a0, b, κ are required, which are usually calculated from the critical pressure (Pc), critical temperature (Tc), and acentric factor (ω). When the CPA EOS is applied to mixtures, the van der Waals mixing rule is employed for a and b in the physical part, as expressed by Eqs. (12)–(14). XX a¼ xi xj aij (12) Ai Bj
3. Mathematical method
i
3.1. CPA EOS
j
pffiffiffiffiffiffiffi aij ¼ ai aj 1
The CPA EOS is firstly developed by Kontogeorgis et al. (1999). The 3
kij
�
(13)
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Journal of Natural Gas Science and Engineering 74 (2020) 103108
Fig. 2. Comparisons of derivative properties of water and MEG calculated from the CPA EOS against those calculated from the SRK EOS. The calculated fluid is single-component H2O or MEG. The calculated pressures cover the range from 9.07 MPa to 119.3 MPa, and the temperatures range from 18.97 � C to 50.9 � C.
b¼
X xi bi
3.2. Solution method of the CPA EOS
(14)
i
To solve the CPA EOS, it is here rewritten in terms of the compressibility factor Z. According to the definition Z ¼ Pv/(RT), Eq. (6) is written as:
where kij is the binary interaction parameters, and it is the only binary adjustable parameters of the CPA EOS. The εAi Bj , βAi Bj for mixtures are calculated from the CR-1 combining rule as follows: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi βAi Bj ¼ βAi Bi βAj Bj (15)
ε
Ai Bj
¼
εAi Bi þ εAj Bj 2
Z¼
Z Z
XA i ¼ :
(16)
A ZþB
B
Zþ
X X 0:5Z xi ð1 Z 0:475B i Ai
Z P P xj XBj γAi Bj j
XA i Þ
(17) (18)
Bj
where, A ¼ aP/(RT)2, B ¼ bP/(RT), and γAi Bj ¼ PΔAi Bj =ðRTÞ. Eq. (17) has no analytical solutions due to the nonlinear and implicit form in terms of Z and Х Ai . It is recommended to be solved by using the bisection method and the Newton iteration method. Eq. (17) typically has one to three real roots. In the case of more than one real root, the compressibility factor that gives the lowest Gibbs free energy is selected (Nasrabadi et al., 2016).
The parameters used to reproduce the properties of water, MEG, and some common hydrocarbon components are listed in Table 1. Besides, this method also can be applied to other glycols once association pa rameters for these glycol molecules are specified, such as ethanol and methanol. The methods used to determine these association parameters can refer to Kontogeorgis and Folas (2009).
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Journal of Natural Gas Science and Engineering 74 (2020) 103108
Besides, the fugacity coefficient equation is derived as follows (Jia and Okuno, 2018): 0 P 1 2 xj aij � � � � bi B A A@ j bi A ZþB þ ln lnφi ¼ lnðZ BÞ þ B Z b Z B ZþB a b
Table 2 Fluid compositions collected from the PY gas field. Component
Mole, %
Component
Mole %
H2O MEG N2 CO2 CH4 C2H6 C3H8
12.74 3.85 0.24 11.14 66.81 3.19 0.95
i-C4H10 n-C4H10 i-C5H12 n-C5H12 n-C6H14 n-C7H16 n-C8H18
0.21 0.24 0.12 0.08 0.18 0.09 0.11
Ai
H ¼ H0 þ
ρ
2
�
∂P ∂T
Z P� v
�2 � �
∂P ∂ρ
ρ
� T
0
∂v ∂T
XAi Þ
∂ln g ∂xi
∂ln g 0:475B bi ¼ : ∂xi Z 0:475B b
Many derivative properties of the fluid can be calculated from the basic thermodynamic relations by using the CPA EOS (Haghbakhsh et al., 2014), including the specific heat capacity, enthalpy, and fugacity. The specific heat capacity and enthalpy formula are as follows: Z ρ� � 2 � � T ∂P Cv ¼ C0v (19) dρ ρ2 ∂ T 2 ρ 0 T
1X X xi ð1 2 i Ai
(22)
3.3. Derivative properties of the CPA EOS
CP ¼ Cv
X lnXAi
where φi is the fugacity of the ith component. The CPA EOS is specially designed for fluids containing polar com ponents. The additional association term in the CPA EOS changes the calculation methods of derivate properties, which will further affect the isenthalpic-flash results. For pure water and MEG, comparisons of Cv, Cp, H, and φi values calculated from the CPA EOS with those calculated from the SRK EOS are shown in Fig. 2. These figures cover the pressures from 9.07 MPa to 119.3 MPa, and temperatures from 18.97 � C to 50.9 � C. It shows that Cv and Cp of water calculated by CPA EOS are lower than those of SRK EOS, whereas H and φi of water calculated by CPA EOS are higher than those calculated by the SRK EOS. For MEG, Cp, H and φi calculated by CPA EOS are lower than those calculated by the SRK EOS, but Cv is higher than SRK EOS.
� (20) T
� � dP
(23)
(21)
P
where Cv is the specific heat capacity at constant volume; Cp is the specific heat capacity at constant pressure; the superscript 0 refers to the ideal gas state.
3.4. Isenthalpic flash algorithm The P–H flash model is composed of the fugacity equations, material
Table 3 Measured production data collected from the PY gas field.a No.
Pin (MPa)
Tin (� C)
Pout (MPa)
Tout (� C)
Qg (m3/h)
Qo (m3/h)
Qw (m3/h)
QMEG (L/h)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
20.23 21.70 20.47 20.70 21.78 20.68 22.60 21.85 20.17 20.39 20.77 19.94 21.51 20.04 21.24 19.88 20.12 20.47 20.28 20.32
45.59 43.35 42.25 41.45 42.51 39.66 42.21 39.86 35.25 34.27 33.68 30.49 32.8 29.54 29.92 28.69 28.39 27.69 27.22 26.73
8.68 9.07 8.84 9.00 9.20 8.84 8.78 8.94 9.37 9.45 9.46 9.79 9.44 9.84 9.53 9.93 9.61 9.35 9.17 8.91
21.20 18.50 18.10 17.10 16.60 15.00 14.70 13.70 12.60 11.40 10.30 9.90 8.90 8.00 7.40 6.70 6.00 4.50 3.50 2.70
11000.17 9631.21 9577.57 10545.76 9554.98 10312.51 8853.90 9335.69 9976.68 9718.22 9346.81 8577.09 8605.35 9642.39 7760.48 9445.96 9369.40 8750.71 8959.20 9354.06
0.19 0.17 0.17 0.19 0.18 0.18 0.16 0.16 0.17 0.17 0.17 0.15 0.15 0.17 0.14 0.17 0.17 0.16 0.16 0.16
3.21 4.00 1.99 3.26 3.21 3.43 2.84 3.09 1.87 1.84 1.58 1.45 1.47 0.75 1.37 1.50 1.70 1.67 1.67 0.95
1201.02 1198.03 1059.94 1178.62 1016.33 1192.83 1212.24 1200.64 811.44 794.04 793.46 1002.63 778.70 987.65 1017.05 997.24 991.02 1012.98 1292.31 1392.87
a
P indicates the pressure; T indicates the temperature; Q indicates the production rate; the subscripts in, out refer to the upstream and downstream of the choke, respectively; the subscripts g, o, w, MEG refers to the gas, oil, water, and monoethylene glycol, respectively. Table 4 Physical properties of each phase calculated from the isenthalpic flash algorithm based on the CPA EOS. Location
Choke valve upstream
Choke valve downstream
P (MPa) T (� C) phase Mole (%) Weight (%) Volume (%) ρ (g/cm3) H (kJ/kg)
21.70 43.35 Total 100.00 100.00 100.00 0.26 413.30
9.07 18.97 Total 100.00 100.00 100.00 0.13 413.30
V 83.21 78.90 94.72 0.21 96.76
W 16.79 21.10 5.28 1.02 1596.84
5
V 83.14 78.66 97.39 0.10 71.75
L 0.10 0.28 0.05 0.63 343.83
W 16.76 21.07 2.55 1.03 1689.53
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Table 5 Comparisons of the calculated composition of each phase according to the isenthalpic-flash algorithm based on the CPA EOS and SRK-Peneloux EOS. The compositions are in terms of weight, %. location
Choke upstream
Model
SRK Peneloux
Phase
Total
H2O 15.99 MEG 4.84 N2 0.22 CO2 10.58 63.45 CH4 C2H6 3.03 0.91 C3H8 i-C4H10 0.20 n-C4H10 0.23 0.11 i-C5H12 n-C5H12 0.08 0.17 n-C6H14 n-C7H16 0.09 0.10 n-C8H18 Mass fraction (%)
Choke downstream CPA
SRK Peneloux
CPA
V
W
V
W
V
L
W
V
L
W
0.06 0.00 0.22 10.56 63.45 3.03 0.91 0.20 0.23 0.11 0.08 0.17 0.09 0.10 79.21
15.94 4.84 0.00 0.02 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 20.79
0.06 0.00 0.22 10.45 63.27 3.02 0.90 0.20 0.23 0.11 0.08 0.17 0.09 0.10 78.90
15.95 4.85 0.00 0.15 0.15 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 21.10
0.02 0.00 0.22 10.54 63.29 3.02 0.90 0.20 0.23 0.11 0.07 0.16 0.08 0.08 78.91
0.00 0.00 0.00 0.03 0.08 0.01 0.01 0.00 0.01 0.01 0.00 0.02 0.03 0.06 0.27
15.97 4.84 0.00 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 20.82
0.02 0.00 0.22 10.50 63.08 3.01 0.90 0.20 0.23 0.11 0.07 0.16 0.08 0.08 78.66
0.00 0.00 0.00 0.03 0.08 0.01 0.01 0.00 0.01 0.01 0.00 0.02 0.03 0.06 0.28
16.16 4.90 0.00 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 21.07
Although the adaptive iteration method is employed, the conver gence of the P–H flash algorithm is still limited by the solution method of the multiphase Rachford-Rice (RR) equation that is also well-known as the material balance equation for multiphase flash (Michelsen, 1987, Paterson et al., 2019). The convergence of the conventional RR equation solution method relies on the initial guess K values, which are mostly calculated from some empirical correlations developed for hydrocar bons. These correlations designed for hydrocarbon components possible give poor initial K values for non-hydrocarbon components, such as water and glycol, resulting in the failure of the P–H flash. Okuno et al. (2010) developed an efficient algorithm for solving the RR equation, which guarantees the correct convergence of RR equation for any number of phases, and also suitable for the negative flash calculations. When the robust solution method for the RR equation and initial K-values obtained from multiple ways are applied, the P–H flash algo rithm can be successfully performed by the use of the adaptive Newton and bisection methods. In this paper, the P–H flash model is solved based on the DS method and the bisection method (Zhu and Okuno, 2015). The material balance equation is solved by the method proposed by Okuno et al. (2010). All the fluid properties (density, compressibility factor, specific heat ca pacity, fugacity et al.) are calculated from the CPA EOS. The P–H flash model can be efficiently solved by the use of the combination of the above methods. However, the solution process takes more time than solving the P–H model based on the SRK EOS because solving CPA EOS is much more difficult.
Fig. 3. Comparisons of measured choke temperatures and calculated choke temperatures based on the SRK-Peneloux EOS, SRK-HV EOS, and the CPA EOS. MT refers to the measured temperature.
balance equations, and the enthalpy constraint equation. According to Eqs. (5), (21) and (22), the fugacity and enthalpy are dependent on the pressure, temperature, and fluid composition. In addition, for the multiphase fluid, calculating the fluid composition of each phase is dependent on the equilibrium constant in the material balance equation. Hence, the independent variables in the P–H flash model are the phase equilibrium constant K-values and the temperature. These variables can be solved by the use of the above equations and suitable methods. If the total enthalpy at the choke inlet and the outlet pressure is given, the outlet temperature can be directly solved based on the P–H flash model. The direct substitution (DS) algorithm originally proposed by Michelsen (1987) is the most widely used method to solve the P–H flash model. However, Zhu and Okuno (2015) found that the DS algorithm becomes degenerate for narrow-boiling fluids, such as multiphase water-containing hydrocarbon mixtures. To solve this problem, a new solution method that adaptively switches between Newton’s method and the bisection method is proposed to solve the P–H flash model. They presented that this algorithm is robust for narrow-boiling mixtures even for the fluid with one degree of freedom (Zhu and Okuno, 2015).
4. Case studies In this section, the P–H flash algorithm based on the CPA EOS is applied to various gas/water/MEG mixtures. Results show the accuracy of this method as well as the effect of water and MEG contents on choke temperatures. Case 1: Gas/water/MEG mixtures in the PY gas field in the South China Sea. The PY gas field locates in the South China Sea. The subsea chokes are installed at wellheads to control the production rates and pressures. The monoethylene glycol (MEG) is injected into the upstream of the choke to prevent the gas hydrate formation. The fluid composition is listed in Table 2. Twenty groups of measured production data are given in Table 3, including the upstream and downstream pressures and temperatures. The field measured data cover the upstream pressures from 19.88 MPa to 22.60 MPa, upstream temperatures from 26.73 � C to 45.59 � C, downstream pressures from 8.68 MPa to 9.93 MPa, and downstream temperatures from 2.70 � C to 21.20 � C. 6
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Table 6 Fluid Compositions collected from three wells in the JL gas field. The compo sitions are expressed in terms of mole, %. Component
JL04
JL16
JL23
CH4 C2H6 C3H8 i-C4H10 n-C4H10 i-C5H12 n-C5H12 n-C6H14 n-C7H16 H2O H2S CO2 N2 H2 He
97.365 0.130 0.000 0.005 0.008 0.001 0.006 0.001 0.148 1.295 1.006 0.005 0.006 0.002 0.022
95.383 0.394 0.039 0.006 0.010 0.010 0.012 0.045 0.000 1.295 0.000 0.325 2.155 0.001 0.325
96.122 1.007 0.089 0.011 0.016 0.008 0.010 0.000 0.000 1.855 0.000 0.642 0.197 0.000 0.043
related compositions are essential for the choke temperature prediction. Table 5 lists the composition of each phase at the upstream and downstream of the choke. It presents that the new liquid phase at the downstream of the choke mainly contains CH4, n-C7H16, and n-C8H18, which is also called the condensate-oil phase. At the downstream and upstream of the choke, the aqueous phase is mainly composed of water and MEG. Results demonstrate that the W-phase calculated from the CPA EOS contains more water and MEG but fewer hydrocarbon com ponents. That is because the CPA EOS considers the hydrogen-bond association between polar water and MEG molecules, which makes the polar components more likely to form liquid phase together. Also, different components of each phase further cause the different mass fraction of each phase that represents an important parameter for computing isenthalpic choke temperatures according to Eq. (4). In addition to the results given in Tables 4 and 5, all measured choke temperatures are applied to validate the proposed P–H flash method based on the CPA EOS, as shown in Fig. 3. Also, results calculated based on the SRK EOS with the Peneloux volume shift method (SRK-Peneloux EOS), and on the SRK EOS with Huron-Vidal mixing rule (SRK-HV EOS) (Michelsen, 1990) are depicted in Fig. 3. The Peneloux volume shift is used to correct the liquid volume in the EOS, and the Huron-Vidal mixing rule enables the SRK EOS to model the hydrogen-bond interac tion between water molecules. The maximum deviations between the calculated choke tempera tures based on the CPA, SRK-Peneloux, and SRK-HV EOSs are equal to 1.76 � C, 2.74 � C, and 2.82 � C, respectively. The corresponding average absolute deviations (AAD) between calculated values and measured data defined by Eq. (24) are equal to 0.68 � C, 1.48 � C, and 1.58 � C, respectively.
Fig. 4. The Five-stage choking process used in the JL gas field. The fifth choke valve is far away from the wellhead, so it is cannot be displayed here.
AAD ¼
Take the case with Pin ¼ 21.70 MPa, Tin ¼ 43.35 � C, Pout ¼ 9.07 MPa as an example to show the isenthalpic multiphase flash results for this choking process, as given in Table 4. It is presented that the calculated downstream temperature is 18.97 � C, which is only 0.47 � C higher than the measured value. The vapor (V) and aqueous (W) two-phase co-ex istence fluid at the upstream of the choke splits to three phases fluids, including the vapor (V), liquid (L), and aqueous phases (W) at the downstream the choke. However, the total enthalpy during the choking process keeps a constant because the P–H flash model is constrained by the constant enthalpy equation (Michelsen, 1987; Zhu and Okuno, 2015). These results present that the enthalpy of the polar aqueous phase (W-phase) at the choke upstream is 336.93 kJ/kg that takes the 81.1% of the fluid total enthalpy, whereas the enthalpy of the W-phase takes the 85.85% of the fluid total enthalpy at the downstream of the choke. Hence, accurate calculations of the polar liquid enthalpy and
N � 1 X �Tcali N i¼1
� Texp i �
(24)
where N is the total number of data points; Tcal i is the calculated tem perature; Texp i is the measured temperature. Case 2: Choke temperature calculations at the JL gas field, China. The pressure at wellheads in the JL gas field, China, often beyond 100 MPa. The five-stage choke valves shown in Fig. 4 are widely used at wellheads to release the pressures and to control the production rates. As shown in Fig. 4, the flow direction of natural gas is from the Christmas tree to the 1st, 2nd, 3rd, 4th, and 5th choke valves. The fifth choke valve is far away from the wellhead, so it is difficult to be displayed in Fig.4 (a) and Fig.4 (b). The wellhead pressures and temperatures are taken as the inlet pressures and temperatures of the first-stage choke valve. The resulting downstream pressures and temperatures are used as the inlet parameters of the choke valve at the next stage. So, the choke parame ters, including the pressures, temperatures at wellheads and 7
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Table 7 Calculated choke temperatures in the JL gas field based on the isenthalpic flash algorithm combining with the CPA EOS. Location JL04
JL16
JL23
Pexp (MPa) Texp (� C) Tcal (� C) Deviation (� C) Pexp (MPa) Texp (� C) Tcal (� C) Deviation (� C) Pexp (MPa) Texp (� C) Tcal (� C) Deviation (� C)
Wellhead
Downstream of the 1st choke
Downstream of the 2nd choke
Downstream of the 3rd choke
Downstream of the 4th choke
88.50 32.60 – – 77.49 48.91 – – 119.30 35 – –
75.70 37.30 36.72 0.58 72.13 49.39 50.30 0.91 90.00 44.9 46.77 1.87
49.50 39.83 41.73 1.90 34.00 46.80 49.29 2.49 65.00 50.9 51.68 0.78
22.30 25.83 27.85 2.02 12.80 23.60 20.87 2.73 45.00 50.5 51.87 1.37
20.70 23.52 23.76 0.24 10.15 15.29 15.47 0.18 20.00 33.2 35.47 2.27
Case 3: Effect of water and MEG contents on the choke temperatures. This subsection designed a three-stage choking process to research the effect of water and MEG contents on the choke temperatures. The overall gas composition is in accordance with that of JL04 well given in Table 6. The upstream pressures and temperatures are set to specified values as listed in Table 8, and the downstream pressures are also specified so that the P–H flash algorithm can be performed. The pressure difference across the choke is designed by the critical-flow choking method proposed by Wu et al. (2017). The water contents and MEG contents are set as specified values from 0 to 50% in terms of the mole fraction. The SRK-Peneloux EOS, SRK-HV EOS, and the CPA EOS are used here to calculate the temperatures at the downstream of chokes when the gas contains different amounts of water and MEG. The calculated temper atures at the downstream of each-choke are depicted in Fig.s 5 to 7. Figs. 5–7 show that these three EOSs give exactly the same results when the water content is zero because the CPA EOS reduces to the traditional SRK EOS under this condition. However, results demonstrate that the deviations between the CPA EOS and SRK-based EOSs increases with increasing water and MEG contents. That is because the SRK-Peneloux EOS, SRK-HV EOS do not account for the association between polar water/MEG molecules, which might cause deviations on estimating the water enthalpy. As a result, calculated temperatures deviate from actual values. Taking the high-pressure first-stage choking process as an example,
Table 8 The upstream pressures, upstream temperatures, and downstream pressures designed for a three-stage choking process. Location
Upstream pressure (MPa)
Upstream temperature (� C)
Downstream pressure (MPa)
The 1st-stage choke The 2nd-stage choke The 3rd-stage choke
110.0
40.00
34.0
34.0
55.70
12.0
12.0
24.65
4.1
downstream of each choke valve, are measured to validate the proposed method. Table 6 lists the fluid compositions collected from three wells, namely JL04, JL16, and JL23. Table 7 presents the measured tempera tures and calculated temperatures at the downstream of each choke valve of the above three wells. In particular, the pressure at the JL23 wellhead is 119.30 MPa, which represents almost the highest pressure at gas wellheads around the world as far as we know. Results demonstrate that the average deviations between the measured and calculated tem peratures for these three gas wells are equal to 1.19 � C, 1.57 � C, and 1.57 � C, respectively. These results show that the method proposed in this paper can be extended to pressures up to 100 MPa.
Fig. 5. Comparisons of temperatures at downstream of the first-stage choke calculated from the SRK-Peneloux, SRK-HV, and CPA EOSs. The upstream pressure is 110 MPa, and the upstream temperature is 40 � C. The downstream pressure is set to 34 MPa. 8
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Fig. 6. Comparisons of temperatures at downstream of the second-stage choke calculated from the SRK-Peneloux, SRK-HV, and CPA EOSs. The upstream pressure is 34 MPa, and the upstream temperature is 55.7 � C. The downstream pressure is set to 12.0 MPa.
Fig. 7. Comparisons of temperatures at downstream of the third-stage choke calculated from the SRK-Peneloux, SRK-HV, and CPA EOSs. The upstream pressure is 12 MPa, and the upstream temperature is 24.65 � C. The downstream pressure is set to 4.1 MPa. Table 9 Comparisons of calculated mass fractions and enthalpies of each phase according to the isenthalpic-flash algorithm based on the CPA EOS and on the SRK-Peneloux EOS. Location
Model
The 1st-stage choke
CPA EOS
The 3rd-stage choke
SRK Peneloux EOS CPA EOS SRK Peneloux EOS
Total Weight (%) Enthalpy (J/kg) Weight (%) Enthalpy (J/kg) Weight (%) Enthalpy (J/kg) Weight (%) Enthalpy (J/kg)
Upstream 100.00 542260.01 100.00 583095.86 100.00 566487.98 100.00 609916.56
9
Downstream
V
L
V
L
78.20 60889.75 78.33 60994.20 78.27 55948.05 78.33 55999.57
21.80 481370.26 21.67 522101.65 21.73 510539.93 21.67 553916.98
78.29 59500.89 78.38 62234.07 78.28 36654.55 78.32 32737.60
21.71 482759.12 21.62 520861.79 21.72 529833.43 21.68 577178.96
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20 mol% water and 80 mol% natural gas are selected as a typical case to analyze further the reasons for causing the temperature differences be tween the CPA EOS and SRK-Peneloux EOS at high pressures and low pressures. The enthalpies and mass fractions of each phase calculated based on the CPA EOS and on the SRK-Peneloux EOS are given in Table 9. The main compositions of the aqueous phase are shown in Table 10. Tables 9 and 10 present that the CPA EOS and SRK-Peneloux EOS give different compositions and mass fractions of the aqueous phase, resulting in the different enthalpy difference across the choke. For example, the aqueous phase calculated from the CPA EOS contains more H2S due to the association between the water and H2S molecule is more likely to dissolve H2S in water (Tsivintzelis et al., 2010). Also, previous literature shows that the CPA EOS can accurately predict the CH4 sol ubility in water (Jia and Okuno, 2018). So, we can conclude that the CPA EOS predicts the composition of the aqueous phase better, which will contribute to accurate enthalpy values since the enthalpy is dependent on the pressure, temperature, and composition. Fig. 8 shows the enthalpy curves of the fluid at a specified pressure and different temperatures, the isenthalpic choking routes of the firstand third-stage choking processes. During the first-stage choking pro cess, the CPA EOS gives higher downstream temperatures in comparison with the SRK-Peneloux EOS when the pressure reduces from 110 MPa to 34 MPa. However, the CPA EOS yields lower downstream temperatures during the third-stage choking process. That is because the different EOSs give different component distributions and related total en thalpies. It should note that the upstream pressures and temperatures are specified in Table 8, so the total enthalpies of the first- and thirdstage choking processes are different. Previous cases show the effect of water or MEG on the choke tem perature. The co-existence of water and MEG in gas mixtures is common when the MEG is injected into the upstream of the choke valve to pre vent the gas hydrate formation. The effect of the co-existence of water and MEG on choke temperatures are shown in Fig. 9 to Fig. 11. The
Table 10 Comparisons of the calculated main composition of the aqueous-phase accord ing to the isenthalpic-flash algorithm based on the CPA EOS and on the SRKPeneloux EOS. The compositions are in terms of mole, %. Location
Component
The 1ststage choke The 3rdstage choke
H2O H2S CH4 H2O H2S CH4
CPA EOS
SRK Peneloux EOS
Upstream
Downstream
Upstream
Downstream
99.360 0.087 0.552 99.721 0.078 0.201
99.585 0.079 0.336 99.826 0.064 0.109
99.964 0.035 0.000 99.977 0.023 0.000
99.962 0.037 0.001 99.988 0.012 0.000
the choke temperature calculated from the CPA EOS is 54.18 � C when the water content is 50%, whereas the SRK-Peneloux and SRK-HV EOSs yields 51.88 � C and 51.79 � C, respectively. Similarly, the temperature calculated from the CPA EOS is 2.5 � C higher than those calculated from the SRK-Peneloux and SRK-HV EOSs when the MEG content is 50%. Previous research shows that traditional EOSs tend to give lower choke temperatures at high pressures (Li et al., 2012b). Hence, the CPA EOS is more likely to yield accurate results at high pressures. During the second- and the third-stage choking process, the down stream temperatures calculated from the CPA EOS are slightly lower than those calculated from the SRK-Peneloux and SRK-HV EOSs when natural gas contains different amounts of water. In contrast, when nat ural gas contains MEG, the CPA EOS yields slightly higher temperatures in comparison with SRK-Peneloux and SRK-HV EOSs at the second-stage choke, but yields lower results at the third-stage choke. These interesting results indicate that the association between polar components and related phase change does not always increase the choke temperatures. The temperature change across the choke is dependent on the specified choke parameters, such as the upstream pressure, temperatures, and downstream pressure. The first- and third-stage choking process of the mixture consisted of
Fig. 8. Curves of temperature and enthalpy change under different choke pressures using the isenthalpic-flash algorithm based on the CPA EOS and SRK-Peneloux EOS. kCPA, kSRK denotes the slope of a straight line,� C/(J/kg). 10
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Fig. 9. Comparisons of temperatures at downstream of the first-stage choke calculated from the SRK-Peneloux, SRK-HV, and CPA EOSs. The mixtures are composed of 10 mol% H2O and 0–20 mol% MEG.
Fig. 11. Comparisons of temperatures at downstream of the third-stage choke calculated from the SRK-Peneloux, SRK-HV, and CPA EOSs. The mixtures are composed of 10 mol% H2O and 0–20 mol% MEG.
water/MEG mixtures flowing through choke valves. However, the pro posed method can further be extended to model mixtures containing many other polar hydrogen-bond components (methanol, ethanol, diethylene glycol and triethylene glycol) if the association parameters for these components in the CPA EOS can be specified. Some of these parameters have already been reported in the literature (Tsivintzelis et al., 2010; Arya et al., 2014; Sarafraz and Hormozi, 2014a,b; Hajiw et al., 2015a,b), which provides good references for further research on the choke temperatures of other gas/water/glycols mixtures. 5. Conclusions A multiphase isenthalpic flash algorithm based on the CPA EOS is proposed to calculate the downstream temperatures of chokes. The derivation of the isenthalpic choking process, the CPA EOS, and the related isenthalpic flash algorithm are introduced. This method can directly calculate the downstream temperature according to the speci fied upstream pressure, upstream temperature, downstream pressure and the fluid composition, instead of using the complicated temperature iteration method. The conclusions are as follows: 1. In comparison with the traditional isenthalpic flash algorithm based on the cubic EOSs, this new method accounts for the self- and crossassociation between water, MEG molecules, and other polar mole cules yielding more accurate methods for the enthalpy calculation of gas/water/MEG mixtures as well as choke temperatures. 2. A total of thirty-two groups measured data are applied to validate the proposed method, which covers temperatures from 2.70 � C to 50.9 � C, and pressures from 8.68 MPa to 119.3 MPa. Results demonstrate that the average absolute deviation between the measured and calculated temperatures at downstream of chokes based on the proposed method is less than 1.6 � C even for vapor-liquid-aqueous three-phase mixtures at pressures up to 100 MPa. In contrast, the isenthalpic flash methods based on the traditional SRK-HV and SRK Peneoux EOSs tend to give much lower choke temperatures at high pressures. 3. The co-existence of water and MEG affects the phase transition and related choke temperatures. The gas/water/MEG mixture is in the vapor-liquid two phases at the choke inlet. However, it splits to vapor-liquid-aqueous three-phases at downstream of the choke. With
Fig. 10. Comparisons of temperatures at downstream of the second-stage choke calculated from the SRK-Peneloux, SRK-HV, and CPA EOSs. The mix tures are composed of 10 mol% H2O and 0–20 mol% MEG.
specified choke parameters keep the same as those listed in Table 8. Fig. 9 shows that the deviations between the results calculated from the CPA EOS and those calculated from the SRK-based EOSs increase with increasing MEG contents when the gas contains 10 mol% H2O and 0–20 mol% MEG. The CPA EOS yields overall higher downstream tem peratures than the SRK-Peneloux and SRK-HV EOSs. These results demonstrate that the association between water and MEG molecules increases the choke temperatures at the first-stage choke. However, as depicted in Fig. 10 and Fig. 11, the CPA EOS gives lower temperatures at the second- and third-stage chokes. The reasons for causing these special results have been previously illustrated in Fig. 8. These results show the superiority of using the CPA EOS and isenthalpic flash algorithm to predict choke temperatures. This paper focuses on predicting the choke temperatures of gas/ 11
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consideration of the interaction between water, MEG, and other polar molecules, the aqueous phase can dissolve more MEG and other polar components, which contributes to accurate predictions of choke temperatures. Moreover, the effects of association between polar water/MEG molecules on choke temperatures are dependent on the specified inlet pressures, temperatures, and fluid components.
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