1 Ecuacion Cocentracion DewP Pcont

Fluid Phase Equilibria 228–229 (2005) 213–221
Advanced equation of state method for modeling TEG–water
for glycol gas dehydration
Chorng H. Twua∗ , Vince Tassoneb , Wayne D. Simb , Suphat Watanasiric
b
a Aspen Technology, Inc., 2811 Loganberry Court, Fullerton, CA 92835, USA
Aspen Technology, Inc., Suite 900, 125 9th Avenue SE, Calgary, Alta., Canada T2G 0P6
c Aspen Technology, Inc., Ten Canal Park, Cambridge, MA 02141, USA
Abstract
An advanced equation of state has been developed for modeling triethylene glycol (TEG)–water system for glycol gas dehydration process.
The dehydration of natural gas is very important in the gas processing industry. It is necessary to remove water vapor present in a gas stream
that may cause hydrate formation at low-temperature conditions that may plug the valves and fittings in gas pipelines. In addition, water
vapor may cause corrosion difficulties when it reacts with hydrogen sulfide or carbon dioxide commonly present in gas streams. The most
effective practice to remove water from natural gas streams is to use TEG in the gas dehydration process. In modeling such a process, it is
crucial that the phase behavior of the TEG–water–natural gas system is correctly modeled, with methane being the predominant component
in natural gas. Of the three binaries, methane–water, methane–TEG and TEG–water, the methane binaries can be adequately modeled by
an equation of state, e.g. [J.R. Cunningham, J.E. Coon, C.H. Twu, Estimation of aromatic hydrocarbon emissions from glycol dehydration
units using process simulation, in: Proceedings of the 72nd Annual Gas Processors Association Convention, San Antonio, TX, March 15–17,
1993]. For the TEG–water binary, the Parrish’s empirical hyperbolic correlation [W.R. Parrish, K.W. Won, M.E. Baltatu, Phase behavior of the
triethylene glycol–water system and dehydration/regeneration design for extremely low dew point requirements, in: Proceedings of the 65th
Annual GPA Convention, San Antonio, TX, March 10–12, 1986] is recommended by GPSA [GPSA Engineering Data Book, 10th ed., First
Revision, Gas Processors Suppliers Association, Tulsa, OK, 1994] and is currently widely used in the industry. In this work, we applied the
TST (Twu–Sim–Tassone) equation of state to model this binary system. A methodology was also developed to determine the water dew point
and calculate water content for this system. The TST equation of state is shown to accurately represent the activity coefficients of TEG–water
solutions as well as water dew point temperatures and water content of gas over the entire application range of temperature, pressure and
concentration encountered in a typical TEG dehydration unit.
© 2004 Elsevier B.V. All rights reserved.
Keywords: Triethylene glycol; Water; Water dew point; Water content; CEoS; TST; Cubic equation of state; Excess energy mixing rule; Activity coefficient;
Gas dehydration
1. Introduction
The dehydration of natural gas is an important operation
in the gas processing industry. The standard method for nat-
∗
Corresponding author. Tel.: +1 403 303 1000; fax: +1 403 303 0914.
E-mail addresses: [email protected] (C.H. Twu),
[email protected] (V. Tassone), [email protected]
(W.D. Sim), [email protected] (S. Watanasiri).
0378-3812/$ – see front matter © 2004 Elsevier B.V. All rights reserved.
doi:10.1016/j.fluid.2004.09.031
ural gas dehydration is by absorption of water using TEG.
Glycol dehydration units typically consist of a contactor, a
flash tank, heat exchangers and a regenerator. The lean TEG
liquid stream enters at the top of the absorber or the contactor
while the natural gas stream containing water to be removed
(wet gas) enters at the bottom of the absorber. The lean TEG
liquid absorbs water as it progresses toward the bottom of the
column. A dry gas exits at the top of the absorber. The rich
TEG stream is sent to the regenerator where water is removed
and the lean TEG liquid is returned to the absorber.
214
C.H. Twu et al. / Fluid Phase Equilibria 228–229 (2005) 213–221
The most important aspect of modeling any dehydration
unit is to correctly model the methane–glycol–water ternary
[1]. This ternary controls the predicted glycol circulation
rates, purities of the lean glycol and the water content of the
dry gas. Of the three binaries, methane–water, methane–TEG
and TEG–water, the methane binaries can be adequately modeled by an equation of state (e.g. [1]). At one time, only
graphical data from vendors were available in the literature
to model the TEG–water binary. These data often were in
disagreement at low water concentration portion resulting in
confusion.
Since the concentration of water in the natural gas is typically low, less than 0.2 mol%, and the concentration of TEG in
the lean TEG solution is high, normally higher than 98 wt.%,
highly concentrated TEG solutions higher than 99.50 wt.%
are usually required if the water concentration in the effluent
gas stream is specified to be very low. Therefore, in order to
have an accurate design of a dehydration unit, vapor–liquid
equilibrium data for TEG–water need to be accurate, especially in the dilute region of water. Parrish et al. [2] gave
an extensive review of the available equilibrium data. Based
on the data reviewed, they found the data of Herskowitz and
Gottlieb [4] to be the most reliable.
Herskowitz and Gottlieb [4] measured the activity coefficients of water in TEG at two temperatures, 297.60 and
332.60 K. The lowest mole fraction of water for which activities were measured was 0.1938 and 0.2961 at 297.60 and
332.60 K, respectively. They fit their measured activity coefficients to the van Laar equation. They did not measure data
in the infinite dilution region. In order to predict the equilibrium behavior in the infinite dilution region, most researchers
simply extrapolated the measured data at low water concentrations to infinite dilution using an activity coefficient model
such as van Laar. However, extrapolating the van Laar, or any
other activity coefficient model will yield erroneous results
for the infinite dilution activity coefficients.
To help better define the TEG–water system, Parrish et
al. [2] measured activity coefficients at infinite dilution as a
function of temperature. These data, shown in Fig. 1, were
used to evaluate the existing data. The data of Herskowitz
and Gottlieb [4] were found to be in good agreement with the
measured infinite dilution activity coefficient data.
Bestani and Shing [5] subsequently measured activity coefficients of water in TEG at infinite dilution, but their data
are 13–17% higher than those of Parrish as shown in Fig. 1.
Based on the Bestani extrapolation method to 477.15 K, the
predicted water activity coefficient is above 1.0. A value of
water activity coefficient that is greater than unity at 477.15 K
implies that TEG would be a poor dehydrating agent at around
this temperature, which is contrary to plant experience [6].
Therefore, Bestani data are not used in this work.
Parrish et al. [2] combined their infinite dilution activity
coefficients data with the finite-concentration activity coefficients of Herskowitz and Gottlieb and then fit them to the
activity coefficient model of a four-suffix Margules equation
over the entire range of composition at each temperature for
Fig. 1. Infinite dilution activity coefficient of water in water–TEG system:
() Exp., Parrish et al. [2]; () Exp., Bestani and Shing [5]; (—) this work;
(- - -) Parrish et al. [2].
the TEG–water system. However, since the Margules activity
coefficient model is unable to fit the activity coefficients over
an extended temperature range for process design calculations, Parrish et al. proposed an empirical hyperbolic equation to predict the activity coefficients of TEG (1) and water
(2) over the entire range of temperatures and compositions:
ln γ1 =
B2 ln[cosh(τ)] x2 B tanh(τ)
− Cx22
−
A
x1
ln γ2 = B[tanh(τ) − 1] − Cx12
(1)
(2)
where
τ=
Ax2
Bx1
(3)
and tanh and cosh are hyperbolic tangent and cosine functions. The subscript number represents component: 1 for TEG
and 2 for water. A, B, and C are temperature-dependent parameters:
A = exp(−12.792 + 0.03293T )
(4)
B = exp(0.77377 − 0.00695T )
(5)
C = 0.88874 − 0.001915T
(6)
where T is the temperature in Kelvin.
Both Herskowitz and Gottlieb, and Parrish used activity
coefficient models to fit the activity coefficient data as a function of mole fraction and temperature. However, using an
activity coefficient model to describe the liquid phase still
requires the use of an equation of state to handle the nonideality of the gas phase and a Poynting correction factor to
account for the effect of pressure. In addition, the standard
state fugacity as a function of temperature ranging from the
temperatures below 273.15 K to critical temperature need to
be correlated for water for the TEG gas dehydration. Since
different models are used for vapor and liquid, the approach
has limitations. For example, no critical conditions can be
calculated, the K-values near critical region is not reliable,
C.H. Twu et al. / Fluid Phase Equilibria 228–229 (2005) 213–221
other thermodynamic properties such as density cannot be
calculated, modeling light gases requires the use of Henry’s
law constants, etc. Besides, the results of extrapolation to
high temperatures and high pressures may not be reliable.
For example, using the van Laar equation with the given binary interaction parameters from Herskowitz and Gottlieb for
extrapolation to 477.15 K, the van Laar predicts a water activity coefficient of 1.1. As mentioned earlier in the analysis of
Bestani and Shing data, a value of water activity coefficient
that is greater than unity is not realistic. Using the empirical
hyperbolic function of Parrish, a water activity coefficient of
0.9477 is obtained at 477.15 K, which is below unity, but is
still too high. The activity coefficient of water at this temperature is expected to be below 0.80 [6]. Furthermore, Eqs.
(1) and (3) contain mole fraction of component 1, x1 , in the
denominator. These equations will break down when x1 approaches zero. Although the TEG mole fraction is unlikely
to be zero in practical natural gas dehydration process, it is
a notable deficiency that engineers should be aware of. The
Parrish’s correlation is recommended by the GPSA [3] and
is currently widely used in the industry.
In this work, we applied the TST (Twu–Sim–Tassone)
equation of state model [7,8] to describe the phase behavior
of the TEG–water system. We also presented a methodology
to determine water dew point and calculate water content for
this system. The TST equation of state represents accurately
the activity coefficients for water and TEG, the water dew
point temperatures and water content over the entire range
of temperature, pressure and composition encountered in a
typical TEG dehydration unit.
215
The TST cubic equation of state is represented by the
following equation:
P=
a
RT
−
v − b v2 + 2.5bv − 1.5b2
(7)
Eq. (7) can be rewritten in another form as
P=
RT
a
−
v − b (v + 3b)(v − 0.5b)
(8)
The values of a and b at the critical temperature are found
by setting the first and second derivatives of pressure with
respect to volume to zero at the critical point resulting in
ac = 0.470507
R2 Tc2
Pc
(9)
RTc
Pc
(10)
bc = 0.0740740
Zc = 0.296296
(11)
where subscript c denotes the critical point. It is noted
that the values of Zc from the Soave–Redlich–Kwong [9]
and Peng–Robinson [10] models are both larger than 0.3
(0.333333 and 0.307401, respectively), but that for TST is
slightly below 0.3, which is closer to the typical value of Zc
for most compounds.
The parameter a is a function of temperature. The value
of a at any temperature a(T) can be calculated from
a(T ) = α(T )ac
(12)
where the alpha function, α(T), is a function only of reduced
temperature, Tr = T/Tc . We use the Twu alpha function [11]:
2. Advanced TST (Twu–Sim–Tassone) equation of
state model
Twu, Sim and Tassone (TST) recently developed CEoS/AE
mixing rules [7,8] that permit a smooth transition of the mixing rules to the conventional van der Waal’s one-fluid mixing
rules. They also proposed a cubic equation of state for better handling of polar and heavy components and a GE model,
which when combined with the CEoS/AE mixing rules allows
both a van der Waal’s fluid and highly non-ideal mixtures to
be described over a broad range of temperatures and pressures in a consistent and unified framework. It is extremely
desirable to have the CEoS/AE mixing rules reduce to the
classical quadratic mixing rules because the classical mixing
rules work very well for nonpolar and slightly polar systems.
Introducing this capability into an excess energy model ensures that the binary interaction parameters for the classical
mixing rules available in many existing databanks for systems involving hydrocarbons and gases can be used directly
in the new excess energy mixing rules. In other words, it
allows the equation of state to describe some binaries in a
multi-component mixture using the van der Waal’s one-fluid
mixing rules, while other pairs with more non-ideal interactions are described by the excess energy mixing rules.
NM )
α = TrN(M−1) eL(1−Tr
(13)
Eq. (13) has three parameters, L, M and N. These parameters
are unique to each component and are determined from the
regression of pure component vapor pressure data. Table 1
lists the L, M and N parameters for TEG and water for use
with the TST equation of state in this paper. The values of L,
M and N for N2 , CO2 , H2 S and light hydrocarbons in natural
gas from methane to n-decane are also included in the table
for future applications.
The TST zero-pressure mixing rules for the mixture a and
b parameters are
∗
E
E
A
a
A
1
0
a∗ = b∗ vdw
+
− 0vdw
(14)
∗
bvdw
Cr RT
RT
b = bvdw
(15)
The parameters a* and b* in Eq. (14) are defined as
a∗ =
Pa
R2 T 2
(16)
b∗ =
Pb
RT
(17)
216
C.H. Twu et al. / Fluid Phase Equilibria 228–229 (2005) 213–221
Table 1
L, M and N parameters of Twu α function with the TST CEoS
ID
Component
Tc (K)
Pc (kPa)
L
M
N
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
TEG
H2 O
N2
CO2
H2 S
CH4
C2
C3
NC4
NC5
NC6
NC7
NC8
NC9
NC10
769.50
647.13
126.20
304.21
373.53
190.564
305.32
369.83
425.12
469.70
507.60
540.20
568.70
594.60
617.70
3320.00
22055.00
3400.00
7383.00
8962.90
4599.00
4872.00
4248.00
3796.00
3370.00
3025.00
2740.00
2490.00
2290.00
2110.00
0.196667
0.430058
0.0649944
0.945951
0.231877
0.0813821
0.147335
0.172517
0.515633
0.385772
0.119904
0.658164
0.486147
0.477371
0.436564
0.863521
0.870932
0.892385
0.888652
0.784346
0.905296
0.879706
0.879570
0.846523
0.817594
0.858552
0.829578
0.809629
0.796573
0.800707
5.10947
1.67211
2.34000
0.65000
1.12000
2.13000
1.98500
2.20000
1.02632
1.35710
3.17252
1.11729
1.49823
1.58848
1.82508
Note that the temperature-independent van der Waal’s mixing
rule bvdw is used for the b parameter in Eq. (15). The expression of bvdw is given below in Eq. (22). The TST zero-pressure
mixing rules assume that AE0vdw , the excess Helmholtz energy
of van der Waal’s fluid at zero pressure, can be approximated
by AE∞vdw , the excess Helmholtz energy of van der Waal’s
fluid at infinite pressure:
∗
a∗
AE∞vdw
avdw
AE0vdw
i
=
(18)
xi ∗
= C1 ∗ −
RT
RT
bvdw
bi
i
With this assumption, the zero-pressure mixing rule transitions smoothly to the conventional van der Waal’s one-fluid
mixing rule. The C1 in Eq. (18) is a constant and is defined
as
1
1+w
C1 = −
ln
(19)
(w − u)
1+u
where u and w are equation-of-state-dependent constants
used to represent a general two-parameter cubic equation of
state. For the TST equation of state, u is 3 and w is −0.5 as
shown in Eq. (8).
Cr in Eq. (14) is a function of a parameter r, which is the
reduced liquid volume at zero pressure:
r+w
1
Cr = −
ln
(20)
w−u
r+u
The value of r = 1.18 is recommended by Twu et al. [12].
Using r = 1.18, Cr = −0.518850 is used in this work.
AE∞ and AE0 in above equations are the excess Helmholtz
free energies at infinite pressure and zero pressure, respectively. The subscript vdw in AE∞vdw and AE0vdw denotes that
the properties are evaluated from the cubic equation of state
using the van der Waal’s mixing rule for its a and b parameters, avdw and bvdw :
√
avdw =
xi xj ai aj (1 − kij )
(21)
i
j
bvdw =
i
xi xj
j
1
(bi + bj )
2
(22)
Since AE0 in these equations is at zero pressure, its value is
identical to the excess Gibbs free energy GE at zero pressure.
Therefore, any activity model such as the NRTL equation
can be used directly for the excess Helmholtz free energy
expression AE0 in Eq. (14).
The TST zero-pressure mixing rule assumes that the excess Helmholtz free energy of the van der Waal’s fluid (AE0vdw ,
Eq. (18)) is independent of pressure. This approximation is
required to allow a smooth transition to the conventional van
der Waal’s one-fluid mixing rule. Therefore, a binary interaction parameter kij is introduced in Eq. (21) to correct for this
approximation. In this work, kij is not needed to adequately
fit the TEG–water VLE data and is set equal to zero.
Twu et al. [7,8] proposed a multi-component equation for a
liquid activity model for use in the TST excess energy mixing
rules:
n
n
GE
j xj τji Gji
=
xi n
(23)
RT
k xk Gki
i
Eq. (23) has the same functional form as the NRTL equation, but there is a fundamental difference between them.
NRTL assumes that Aij , Aji and αij are the parameters of the
model, but the excess Gibbs energy model proposed by Twu
et al. [7,8] assumes that τ ij and Gij are the binary interaction
parameters. More importantly, any appropriate temperaturedependent function can be applied to τ ij and Gij . For example,
to obtain the NRTL model, τ ji and Gji are calculated as usual
from the NRTL parameters Aji , Aij and αji :
τji =
Aji
T
Gji = exp(−αji τji )
(24)
(25)
In this way, the NRTL parameters reported in the DECHEMA
Chemistry Data Series can be used directly in our mixing
C.H. Twu et al. / Fluid Phase Equilibria 228–229 (2005) 213–221
Table 2
Binary interaction parameters for use in TST zero-pressure mixing rule
Binary
TEG(1)/H2 O(2)
A12
A21
B12
B21
α12
−141.490
158.166
0.254489
5.83380
0.278879
rule and there is no difference between NRTL model and our
model in the prediction of phase equilibrium calculations.
We also note that Eq. (23) can recover the conventional
van der Waal’s mixing rules when the following expressions
are used for τ ji and Gji :
τji =
Gji =
1
2 δij bi
C1
δij = −
RT
(27)
√
√ √ √ 2
aj
ai
ai aj
−
+ 2kij
bi
bj
bi bj
(28)
Eqs. (26) and (27) are expressed in terms of cubic equation
of state parameters ai and bi , and the binary interaction parameter kij . The above discussion demonstrates that Eq. (23)
is more generic in its form than the NRTL model. Both the
NRTL and van der Waal’s one-fluid mixing rule are special
cases of our excess Gibbs free energy function.
3. Correlation of activity coefficients
The TST equation of state and mixing rules described in
the previous section are used to correlate the infinite dilution
activity coefficient data of Parrish et al. [2] and the finiteconcentration activity coefficients of Herskowitz and Gottlieb
[4]. To cover the entire application range of temperature, Eq.
(24) is modified to include a temperature-dependent binary
interaction parameter Bji as follows:
τji =
Table 3
Comparison of Parrish et al. [2] measured infinite dilution activity coefficients of water (2) in TEG (1) solution with those calculated using TST
CEoS and Parrish’s hyperbolic equation
T (K)
γ2∞ (measured)
This work
γ2∞
300.43
311.71
323.26
333.76
343.43
355.93
364.93
378.32
AAD%
0.5510
0.575
0.5900
0.6170
0.6240
0.6360
0.6690
0.6920
(calc.)
0.5565
0.5773
0.5979
0.6159
0.6318
0.6515
0.6651
0.6845
Parrish et al. [2]
Devi%
γ2∞ (calc.)
Devi%
0.99
0.41
1.34
−0.19
1.25
2.44
−0.58
−1.08
0.5587
0.5826
0.6072
0.6296
0.6503
0.6772
0.6966
0.7257
1.40
1.32
2.91
2.04
4.21
6.47
4.13
4.87
1.03
3.42
(26)
bj
bi
where
217
Aji + Bji T
T
error of ±1.03%. Parrish’s model systematically overpredicts
the data with a positive average error of +3.42%. Fig. 1 also
indicates that Eq. (2) represents data at low temperatures better than those at higher temperatures. The TST EoS, on the
other hand, more accurately fits the data over the entire temperature range.
Table 4 shows the finite-concentration activity coefficients
of water in TEG measured by Herskowitz and Gottlieb as
functions of temperature and composition. For comparison,
the table again includes results from this work and those using
Eq. (2). Data in Table 4 are also shown graphically in Fig. 2.
Reviewing Fig. 2, it is observed that the data of Herskowitz
and Gottlieb are not quite consistent with the data of Parrish.
Due to the curvature of Herskowitz data, the extrapolation to
water mole fraction of zero (i.e., TEG mole fraction of 1.0)
will give infinite dilution activity coefficients of water in TEG
of about 0.65 at 297 K. This is much larger than the infinite
dilution activity coefficient data of Parrish at the same temperature (<0.55). Since both the TST EoS and Eq. (2) fit the
infinite dilution activity coefficient data well, the fit to Herskowitz and Gottlieb data at high TEG concentration is quite
(29)
where T is the temperature in K. The unit of Aji is in K and
Bji is dimensionless.
Table 2 lists the values of the binary interaction parameters
Aij , Aji , Bij , Bji and αij obtained for the TEG–water system.
Table 3 compares measured and calculated infinite dilution
activity coefficients of water in TEG as a function of temperature. Also shown in the table are the infinite dilution activity
coefficients calculated from Parrish’s empirical hyperbolic
equation (Eq. (2)) for comparison. Data in Table 3 are also
shown graphically in Fig. 1. Results shown in Table 3 and
Fig. 1 indicate that the TST equation of state can accurately
correlate the infinite dilution activity coefficients of water in
TEG covering a wide range of temperature with an average
Fig. 2. Activity coefficient of water vs. liquid mole fraction TEG. Exp.,
Herskowitz and Gottlieb [4]: () T = 297.6 K, () T = 332.6 K; (—) this
work; (- - -) Parrish et al. [2].
218
C.H. Twu et al. / Fluid Phase Equilibria 228–229 (2005) 213–221
Table 4
Comparison of Herskowitz and Gottlieb [4] measured activity coefficients of water (2) in TEG (1) solution with those calculated using TST CEoS and Parrish’s
hyperbolic equation
T (K)
X (1)
γ 2 (measured)
This work
γ 2 (calc.)
Devi%
γ 2 (calc.)
Devi%
297.60
297.60
297.60
297.60
297.60
297.60
297.60
297.60
297.60
297.60
297.60
297.60
297.60
297.60
297.60
297.60
297.60
297.60
297.60
297.60
297.60
297.60
297.60
297.60
332.60
332.60
332.60
332.60
332.60
332.60
332.60
332.60
332.60
332.60
332.60
332.60
332.60
332.60
332.60
332.60
0.8062
0.7838
0.6731
0.6731
0.5809
0.5449
0.5001
0.4967
0.3996
0.3898
0.3057
0.2505
0.2187
0.1894
0.1657
0.1575
0.1157
0.1077
0.1051
0.1026
0.0657
0.0641
0.0549
0.0541
0.7039
0.5107
0.4970
0.4562
0.3759
0.3614
0.2886
0.2853
0.2429
0.1993
0.1562
0.1212
0.1170
0.0808
0.0796
0.0454
0.6604
0.6640
0.6760
0.6871
0.7062
0.7201
0.7407
0.7371
0.7823
0.7876
0.8264
0.8608
0.8784
0.8994
0.9177
0.9225
0.9507
0.9526
0.9542
0.9563
0.9802
0.9811
0.9836
0.9866
0.8022
0.8215
0.8504
0.8571
0.8839
0.8901
0.9088
0.9133
0.9276
0.9451
0.9641
0.9767
0.9768
0.9893
0.9897
0.9980
0.6299
0.6394
0.6875
0.6875
0.7290
0.7456
0.7664
0.7680
0.8138
0.8184
0.8585
0.8849
0.9000
0.9139
0.9252
0.9292
0.9494
0.9534
0.9547
0.9559
0.9745
0.9753
0.9799
0.9803
0.7254
0.8029
0.8085
0.8252
0.8581
0.8640
0.8934
0.8947
0.9115
0.9283
0.9447
0.9580
0.9596
0.9737
0.9741
0.9877
−4.62
−3.71
1.71
0.06
3.23
3.54
3.47
4.19
4.02
3.91
3.89
2.80
2.46
1.62
0.82
0.72
−0.13
0.08
0.05
−0.04
−0.58
−0.59
−0.37
−0.63
−9.58
−2.26
−4.93
−3.72
−2.92
−2.93
−1.69
−2.03
−1.74
−1.77
−2.01
−1.91
−1.76
−1.58
−1.57
−1.04
0.6255
0.6338
0.6742
0.6742
0.7078
0.7210
0.7378
0.7390
0.7777
0.7819
0.8220
0.8545
0.8765
0.8994
0.9198
0.9272
0.9649
0.9716
0.9736
0.9756
0.9957
0.9961
0.9980
0.9982
0.7597
0.8611
0.8687
0.8911
0.9328
0.9397
0.9686
0.9697
0.9811
0.9889
0.9937
0.9963
0.9966
0.9984
0.9984
0.9995
−5.28
−4.55
−0.26
−1.87
0.22
0.13
−0.40
0.26
−0.58
−0.72
−0.53
−0.74
−0.22
0.00
0.23
0.51
1.50
1.99
2.04
2.01
1.58
1.53
1.47
1.17
−5.30
4.82
2.15
3.97
5.54
5.57
6.58
6.17
5.77
4.64
3.07
2.01
2.02
0.92
0.88
0.15
AAD%
poor. The predicted trend from the two correlations as the
mole fraction of TEG approaches unity will be very different
from what this set of experimental data would suggest. Fig. 2
also indicates that Eq. (2) was fitted preferentially to the data
at 297.6 K while the fit to the data at 332.6 K is significantly
poorer. The TST EoS is less accurate at 297.6 K, but is more
accurate at the higher temperature of 332.6 K.
Another important observation can be made from Fig. 2.
The TST EoS predicts slightly lower activity coefficients
than the experimental data at higher temperature. On the
other hand, Parrish’s model predicts higher activity coefficients at higher temperature. This difference in the predicted
trend can have significant consequences in the extrapolation
of activity coefficients to high temperatures. To test the ex-
Parrish et al. [2]
2.27
2.23
trapolation capability, both the TST equation of state and
the Parrish model are extrapolated to 204 ◦ C (477.15 K). The
ability to extrapolate the model to high temperatures to predict accurate activity coefficients is quite important for stripping processes. Ref. [6] reports that at 204 ◦ C (477.15 K)
and 1.2 atm (121.59 kPa), experience shows approximately
1.2 wt.% water in the lean glycol. The TST equation of state
predicts 1.2 wt.% of water in the lean glycol at 477.15 K under pressure of 123.91 kPa, which is very close to the observed 121.59 kPa, a deviation of only 1.91%. This result
corresponds to a water activity coefficient of approximately
0.7960 at 204 ◦ C. At the same temperature of 204 ◦ C, the
Parrish model gives a value of 0.9477 for the water activity
coefficient. This activity coefficient value will predict a pres-
C.H. Twu et al. / Fluid Phase Equilibria 228–229 (2005) 213–221
sure well over the expected value of 121.59 kPa. The TST
EoS provides a clear advantage to the use of Eq. (2) because
it can (1) accurately correlate the infinite dilution activity coefficients data over a wide temperature range, (2) correlate
finite concentration activity coefficients data with reasonable
accuracy and (3) extrapolate well to higher temperatures.
4. Prediction of water dew point and water content
VLE data for TEG–water system commonly are represented as charts of water dew point lines as a function of contactor temperature and liquid TEG concentrations [3]. The
water dew point is the dew point of the gas, Td , which would
be obtained if the gas were brought to equilibrium with the
TEG solution at the contactor temperature, T. In this work,
the TST equation of state is used to predict the water dew
point and the water content of the TEG–water system as an
alternative to using the water dew point charts [3].
At phase equilibrium, the fugacities of TEG and water in
the liquid and vapor phases are the same:
L
V
fTEG
= fTEG
(30)
fwL = fwV
(31)
where fi is the fugacity of component i in the solution. The
fugacity of component i is calculated from the TST equation of state presented in this work. Assuming that the liquid
compositions and the system temperature, T, are known, Eqs.
(30) and (31) can be used to determine the equilibrium pressure P and vapor-phase compositions. In the context of gas
dehydration, the equilibrium temperature T is referred to as
the contact temperature (temperature of the top tray of the
contactor). The vapor mixture at the contact temperature is at
its dew point. However, the specification for the equilibrium
vapor in gas dehydration is normally in term of its water dew
point (Td ), i.e. the temperature at which pure liquid water
may condense out of the gas phase. One can view this temperature as a hypothetical temperature. In order to compute
Td , TEG is excluded from the gas phase during the dew point
temperature calculation. Since it is assumed that the first drop
of liquid condensed from the vapor at the water dew point is
pure water, we have
fw0L (Td ) = fwV (Td )
(32)
where fw0L (Td ) is the liquid fugacity of pure water at the
water dew point temperature Td and equilibrium pressure P
and fwV (Td ) the vapor fugacity of water in the mixture without
TEG at the dew point temperature Td , equilibrium pressure
P and equilibrium vapor-phase compositions yi . Note that
when the dew point temperature is below the triple point of
water, 273.16 K, the condensed phase is either solid ice or
subcooled water. Following the work of Parrish et al. [2],
subcooled water was used as the standard state fugacity in
this work. The equilibrium P and yi are solved from Eqs.
219
(30) and (31) as discussed above. Rewrite Eq. (32) as
0L
V
(Td ) = fwV (Td ) = yw Pφw
(Td )
fw0L (Td ) = Pφw
(33)
or
yw =
0L (T )
φw
d
V (T )
φw
d
(34)
where yw is the vapor mole fraction of water (without TEG)
in equilibrium with the TEG solution at equilibrium temperature (contact temperature) T. The vapor and liquid fugacity
coefficients of water are calculated using the TST equation
of state at Td and at the equilibrium pressure P. Since TEG
is removed from the gas mixture when the water dew point
is performed, the vapor mole fraction of water is normalized
to give yw = 1.0 in this case. Eq. (34) is used to solve for the
water dew point temperature Td . After that, the liquid fugacity of pure water at Td , fw0L (Td ), can then be calculated from
the equation of state.
When the value of fw0L (Td ) at the water dew point temperature Td is obtained, the water content in lbH2 O /MMSCF at
standard condition of T0 = 60 ◦ F (288.71 K) and the equilibrium pressure P can be calculated from the following equation:
P
n
(35)
=
V
Z0 RT0
where Z0 is the gas compressibility factor at T0 and P, and
n the number of moles in vapor volume V. The number of
moles of water, nw , in the vapor then becomes
P
nw
= yw
V
Z0 RT0
(36)
where yw is the mole fraction of water in the gas phase without
TEG. Rewrite Eq. (36) using Eq. (33) and assuming that the
vapor fugacity coefficient of water is 1.0,
nw
yw P
fwV
=
≈
V
Z0 RT0
Z0 RT0
(37)
Substituting Eq. (32) into Eq. (37), we obtain
nw
fw0L
=
V
Z0 RT0
(38)
Given T0 = 60 ◦ F (288.71 K), the gas constant R and assuming
Z0 = 1.0, we obtain the water content in lbH2 O /MMSCF in
terms of fw0L (Td ) at the water dew point temperature Td ,
Water content in lbH2 O /MMSCF = 222 72.23fw0L (Td ) (39)
The water content in SI units is expressed in kg/106 scm:
Water content in kg/106 scm = 356 765.00fw0L (Td )
(40)
where fw0L (Td ) is in the pressure unit of kPa. Since the water
content of lbH2 O /MMSCF is commonly used in the US and
in the field, this unit is used in Table 6.
The typical application range is shown in Tables 5 and 6.
Table 5 shows the prediction of the water dew point temperatures of vapor in equilibrium with TEG solutions from the
220
C.H. Twu et al. / Fluid Phase Equilibria 228–229 (2005) 213–221
Table 5
Prediction of the water dew point temperature of vapor containing TEG and water in equilibrium with TEG solutions from TST equation of state and prediction
from GPSA recommended model
99.97 wt.% TEG
Contact temperature (K)
Water dew points of vapor (K)
GPSA
TST
277.59
288.71
299.82
310.93
322.04
333.15
344.26
208.15
208.86
214.26
214.99
220.37
221.00
225.93
226.91
232.04
232.74
237.59
238.52
243.15
244.30
277.59
288.71
299.82
310.93
322.04
333.15
344.26
232.04
232.66
239.82
240.47
247.59
248.16
255.93
255.75
263.15
263.22
270.93
270.58
278.71
277.84
99.50 wt.% TEG
Contact temperature (K)
Water dew points of vapor (K)
GPSA
TST
tact temperature at various TEG concentrations ranging from
95.00 to 99.99 wt.% TEG. The result from the TST equation
is quite interesting because it illustrates that the water dew
point is a linear function of the contact temperature at a constant wt.% of TEG. This plot is similar to those presented
in Refs. [2,3] and is useful for practical use in estimating
the water dew point without actually solving the equation of
state.
5. Conclusions
The TST cubic equation of state has been developed successfully to represent the TEG–water binary, which is an industrial important system for modeling TEG gas dehydration.
This work is an improvement over the empirical hyperbolic
equation of Parrish et al. We also present a methodology for
using the TST equation of state to calculate water dew point
and water content in natural gas systems. The infinite-dilution
and finite-concentration activity coefficients of water in TEG,
water dew point temperatures and water content over the entire application range of temperature, pressure and composition encountered in a typical TEG dehydration unit predicted
from the TST equation of state match the reported data very
closely.
Fig. 3. Equilibrium water dew point vs. contact temperature at various TEG
concentrations in wt.%.
TST equation of state. The water dew points from GPSA are
also included for comparison. Both GPSA and TST equation
of state predict very similar water dew point temperatures,
generally within 1 K.
Table 6 shows the equilibrium water content in
lbH2 O /MMSCF gas in equilibrium with 99.50 wt.% TEG.
The results predicted from the TST equation of state are compared with the reported data [13,14], which cover the range
of temperature from 222 to 277 K. The predicted water content from the equation of state model agrees with the reported
data very closely over the entire range of temperature. The
calculated equilibrium pressure is also included in Table 6.
Fig. 3 presents the water dew point predicted from the TST
equation of state developed in this work as a function of con-
List of symbols
a,
b cubic equation of state parameters
A
Helmholtz energy
Aij , Aji , Bij , Bji NRTL binary interaction parameters
Table 6
Prediction of the equilibrium water content in lbH2 O /MMSCF from TST equation of state in equilibrium with 99.50 wt.% TEG
T dew (K)
Reported by
Predicted from TST equation of state
McKetta and Wehe [13]
Bukacek [14]
Water content
Pressure (Pa)
277.59
266.48
255.37
244.26
233.15
222.04
390
170
70
28
9.2
2.4
396
176
72
27
9.1
2.8
393
174
71
26
9
2.6
838.0
370.0
151.0
56.1
18.7
6.0
C.H. Twu et al. / Fluid Phase Equilibria 228–229 (2005) 213–221
Cr
C1
G
kij
L, M, N
P
r
R
T
xi
yi
defined in Eq. (20)
defined in Eq. (19)
Gibbs energy
binary interaction parameter
parameters in the Twu’s α function
pressure
reduced liquid volume
gas constant
temperature
liquid mole fraction of component i
vapor mole fraction of component i
Greek letters
α
cubic equation of state alpha function
αij
NRTL binary interaction parameters
γi
activity coefficient of component i
characteristic of the interaction between molecules
δij
i and j
φi
the fugacity coefficient of component i in the mixture
∞
infinite pressure
Subscripts
c
critical property
i, j
property of component i, j
ij
interaction property between components i and j
vdw
van der Waals
0
zero pressure
Superscripts
*
reduced property
E
excess property
L
V
221
liquid phase
vapor phase
References
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simulation, in: Proceedings of the 72nd Annual Gas Processors Association Convention, San Antonio, TX, March 15–17, 1993.
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extremely low dew point requirements, in: Proceedings of the 65th
Annual GPA Convention, San Antonio, TX, March 10–12, 1986.
[3] GPSA Engineering Data Book, Tenth Edition, First Revision, Gas
Processors Suppliers Association, Tulsa, OK, 1994.
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[5] B. Bestani, K.S. Shing, Fluid Phase Equilib. 50 (1989) 209–221.
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Conference, Norman, Oklahoma, 1994.
[7] C.H. Twu, W.D. Sim, V. Tassone, Fluid Phase Equilib. 65–74 (2001)
183–184.
[8] C.H. Twu, W.D. Sim, V. Tassone, Fluid Phase Equilib. 194–197
(2002) 385–399.
[9] G. Soave, Chem. Eng. Sci. 27 (1972) 1197–1203.
[10] D.Y. Peng, D.B. Robinson, Ind. Eng. Chem. Fundam. 15 (1976)
58–64.
[11] C.H. Twu, D. Bluck, J.R. Cunningham, J.E. Coon, Fluid Phase Equilib. 69 (1991) 33–50.
[12] C.H. Twu, J.E. Coon, D. Bluck, B. Tilton, M. Rowland, Fluid Phase
Equilib. 153 (1998) 39–44.
[13] J.J. McKetta, A.H. Wehe, GPA Engineering Data Book Fig. 15-10,
Ninth Edition, Fourth Revision, Gas Processors Suppliers Associations, Tulsa, OK, 1979.
[14] R.F. Bukacekm, Equilibrium moisture content of natural gases, Research Bulletin 8, Institute of Gas Technology, Chicago, IL, 1955.