teg water equilibrium

8/10/2019 TEG Water Equilibrium

1/9

Fluid Phase Equilibria 228229 (2005) 213221

Advanced equation of state method for modeling TEGwaterfor glycol gas dehydration

Chorng H. Twua, Vince Tassoneb, Wayne D. Simb, Suphat Watanasirica Aspen Technology, Inc., 2811 Loganberry Court, Fullerton, CA 92835, USA

b Aspen Technology, Inc., Suite 900, 125 9th Avenue SE, Calgary, Alta., Canada T2G 0P6c 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 TEGwaternatural gas system is correctly modeled, with methane being the predominant component

in natural gas. Of the three binaries, methanewater, methaneTEG and TEGwater, 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 1517,

1993]. For the TEGwater binary, the Parrishs empirical hyperbolic correlation [W.R. Parrish, K.W. Won, M.E. Baltatu, Phase behavior of the

triethylene glycolwater system and dehydration/regeneration design for extremely low dew point requirements, in: Proceedings of the 65th

Annual GPA Convention, San Antonio, TX, March 1012, 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 theTST (TwuSimTassone) 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 TEGwater

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).

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.

0378-3812/$ see front matter 2004 Elsevier B.V. All rights reserved.

doi:10.1016/j.fluid.2004.09.031


2/9

214 C.H. Twu et al. / Fluid Phase Equilibria 228229 (2005) 213221

The most important aspect of modeling any dehydration

unit is to correctly model the methaneglycolwater 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, methanewater, methaneTEG

andTEGwater,the methane binaries can be adequately mod-

eled by an equation of state (e.g. [1]). At one time, onlygraphical data from vendors were available in the literature

to model the TEGwater 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 typi-

cally low, less than 0.2 mol%, andthe concentration of TEGin

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, vaporliquid

equilibrium data for TEGwater need to be accurate, espe-

cially in the dilute region of water. Parrish et al. [2] gavean 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 coef-

ficients of water in TEG at two temperatures, 297.60 and

332.60 K. The lowest mole fraction of water for which ac-

tivities were measured was 0.1938 and 0.2961 at 297.60 and

332.60 K, respectively. They fit their measured activity coef-

ficients to the van Laar equation. They did not measure data

in the infinite dilution region. In order to predict the equilib-

rium behavior in the infinite dilution region, most researchers

simply extrapolated the measured data at low water concen-trations 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 TEGwater system, Parrish et

al.[2] measured activity coefficients at infinite dilution as a

function of temperature. These data, shown inFig. 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 co-

efficients of water in TEG at infinite dilution, but their data

are 1317% higher than those of Parrish as shown inFig. 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 TEGwould 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 coef-

ficients 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 waterTEG system:

() Exp., Parrish et al.[2];() Exp., Bestani and Shing[5]; () this work;

(- - -) Parrish et al.[2].

the TEGwater system. However, since the Margules activity

coefficient model is unable to fit the activity coefficients overan extended temperature range for process design calcula-

tions, Parrish et al. proposed an empirical hyperbolic equa-

tion to predict the activity coefficients of TEG (1) and water

(2) over the entire range of temperatures and compositions:

ln 1=B2 ln[cosh()]

A x2B tanh()

x1 Cx22 (1)

ln 2= B[tanh() 1] Cx21 (2)where

=Ax2

Bx1(3)

and tanh and cosh are hyperbolic tangent and cosine func-

tions.The subscriptnumber represents component: 1 for TEG

and 2 for water. A, B, andCare temperature-dependent pa-

rameters:

A = exp(12.792+ 0.03293T) (4)B = exp(0.77377 0.00695T) (5)C = 0.88874 0.001915T (6)whereTis the temperature in Kelvin.

Both Herskowitz and Gottlieb, and Parrish used activity

coefficient models to fit the activity coefficient data as a func-

tion 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 non-

ideality 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,


3/9

C.H. Twu et al. / Fluid Phase Equilibria 228229 (2005) 213221 215

other thermodynamic properties such as density cannot be

calculated, modeling light gases requires the use of Henrys

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 bi-

nary interaction parameters from Herskowitz and Gottlieb for

extrapolation to 477.15 K, the van Laar predicts a water activ-ity 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 tem-

perature 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 whenx1 ap-

proaches 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

Parrishs correlation is recommended by the GPSA [3] andis currently widely used in the industry.

In this work, we applied the TST (TwuSimTassone)

equation of state model[7,8]to describe the phase behavior

of the TEGwater 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.

2. Advanced TST (TwuSimTassone) equation of

state model

Twu, Sim and Tassone (TST)recently developed CEoS/AE

mixing rules[7,8]that permit a smooth transition of the mix-

ing rules to the conventional van der Waals one-fluid mixing

rules. They also proposed a cubic equation of state for bet-

ter handling of polar and heavy components and aGE model,

which when combined with the CEoS/AE mixing rules allows

both a van der Waals fluid and highly non-ideal mixtures to

be described over a broad range of temperatures and pres-

sures 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 en-

sures that the binary interaction parameters for the classical

mixing rules available in many existing databanks for sys-

tems 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 Waals one-fluid

mixing rules, while other pairs with more non-ideal interac-

tions are described by the excess energy mixing rules.

The TST cubic equation of state is represented by the

following equation:

P= RTv b

a

v2 + 2.5bv 1.5b2 (7)

Eq.(7)can be rewritten in another form as

P= RTv b

a

(v+ 3b)(v 0.5b) (8)

The values ofa 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= 0.470507R2T2c

Pc(9)

bc= 0.0740740RTc

Pc(10)

Zc=

0.296296 (11)

where subscript c denotes the critical point. It is noted

that the values of Zc from the SoaveRedlichKwong [9]

and PengRobinson [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 ofZcfor most compounds.

The parameter a is a function of temperature. The value

ofaat any temperature a(T) can be calculated from

a(T) = (T)ac (12)where the alpha function,(T), is a function only of reduced

temperature,Tr= T/Tc. We use the Twu alpha function[11]:

= TN(M1)r eL(1TNMr ) (13)

Eq.(13)has three parameters,L,MandN. These parameters

are unique to each component and are determined from the

regression of pure component vapor pressure data. Table 1

lists the L, Mand Nparameters for TEG and water for use

with the TST equation of state in this paper. The values ofL,

MandNfor N2, CO2, H2S and light hydrocarbons in natural

gas from methane ton-decane are also included in the table

for future applications.

The TST zero-pressure mixing rules for the mixtureaand

bparameters are

a= bavdwbvdw

+ 1Cr

AE0

RT A

E0vdw

RT

(14)

b = bvdw (15)The parametersa* andb* in Eq.(14)are defined as

a= PaR2T2

(16)

b= PbRT

(17)


4/9


Table 1

L,MandNparameters of Twufunction with the TST CEoS

ID Component Tc(K) Pc (kPa) L M N

1 TEG 769.50 3320.00 0.196667 0.863521 5.10947

2 H2O 647.13 22055.00 0.430058 0.870932 1.67211

3 N2 126.20 3400.00 0.0649944 0.892385 2.34000

4 CO2 304.21 7383.00 0.945951 0.888652 0.65000

5 H2S 373.53 8962.90 0.231877 0.784346 1.120006 CH4 190.564 4599.00 0.0813821 0.905296 2.13000

7 C2 305.32 4872.00 0.147335 0.879706 1.98500

8 C3 369.83 4248.00 0.172517 0.879570 2.20000

9 NC4 425.12 3796.00 0.515633 0.846523 1.02632

10 NC5 469.70 3370.00 0.385772 0.817594 1.35710

11 NC6 507.60 3025.00 0.119904 0.858552 3.17252

12 NC7 540.20 2740.00 0.658164 0.829578 1.11729

13 NC8 568.70 2490.00 0.486147 0.809629 1.49823

14 NC9 594.60 2290.00 0.477371 0.796573 1.58848

15 NC10 617.70 2110.00 0.436564 0.800707 1.82508

Note that the temperature-independent vander Waals mixing

rulebvdwis used for thebparameter in Eq.(15).The expres-

sionofbvdw isgivenbelowinEq. (22). The TST zero-pressure

mixing rules assume thatAE0vdw, theexcess Helmholtz energy

of van der Waals fluid at zero pressure, can be approximated

by AEvdw, the excess Helmholtz energy of van der Waalsfluid at infinite pressure:

AE0vdw

RT= A

EvdwRT

= C1avdwbvdw

i

xiaibi

(18)

With this assumption, the zero-pressure mixing rule transi-

tions smoothly to the conventional van der Waals one-fluid

mixing rule. TheC1 in Eq.(18)is a constant and is defined

as

C1= 1

(w u) ln

1+ w1+ u

(19)

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 andw is 0.5 asshown in Eq.(8).

Crin Eq.(14)is a function of a parameter r, which is the

reduced liquid volume at zero pressure:

Cr

=

1

w uln r + w

r + u (20)The value of r= 1.18 is recommended by Twu et al. [12].

Usingr= 1.18,Cr=0.518850 is used in this work.AEand A

E0 in above equations are the excess Helmholtz

free energies at infinite pressure and zero pressure, respec-

tively. The subscript vdw inAEvdw and AE0vdwdenotes that

the properties are evaluated from the cubic equation of state

using the van der Waals mixing rule for its aand bparame-

ters,avdwand bvdw:

avdw=i

j

xixjaiaj(1 kij) (21)

bvdw

=i j xixj1

2

(bi

+bj) (22)

Since AE0 in these equations is at zero pressure, its value is

identical to the excess Gibbs free energyGE at zero pressure.

Therefore, any activity model such as the NRTL equation

can be used directly for the excess Helmholtz free energy

expressionAE0 in Eq.(14).

The TST zero-pressure mixing rule assumes that the ex-

cess Helmholtzfree energyof thevan derWaals fluid (AE0vdw,

Eq.(18))is independent of pressure. This approximation is

required to allow a smooth transition to the conventional van

der Waals one-fluid mixing rule. Therefore, a binary interac-

tion parameterkijis introduced in Eq.(21)to correct for this

approximation. In this work, kij is not needed to adequately

fit the TEGwater VLE data and is set equal to zero.

Twu et al.[7,8] proposed a multi-componentequationfor a

liquid activity model for use in the TSTexcess energy mixing

rules:

GE

RT=

ni

xi

njxjjiGjinkxkGki

(23)

Eq.(23) has the same functional form as the NRTL equa-

tion, but there is a fundamental difference between them.

NRTL assumes thatAij,Aji and ijare the parameters of the

model, but the excess Gibbs energy model proposed by Twuet al.[7,8]assumes thatijand Gijare the binary interaction

parameters. More importantly, any appropriate temperature-

dependent function canbe applied to ijand Gij. For example,

to obtain the NRTL model,jiandGjiare calculated as usual

from the NRTL parametersAji,Aijand ji:

ji=Aji

T(24)

Gji= exp(jiji) (25)In this way, theNRTL parameters reported in theDECHEMA

Chemistry Data Series can be used directly in our mixing


5/9


Table 2

Binary interaction parameters for use in TST zero-pressure mixing rule

Binary TEG(1)/H2O(2)

A12 141.490A21 158.166

B12 0.254489

B21 5.83380

12 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 Waals mixing rules when the following expressions

are used forji and Gji:

ji= 12ijbi (26)

Gji=bj

bi(27)

where

ij= C1

RT

ai

biaj

bj

2+ 2kij

ai

bi

aj

bj

(28)

Eqs.(26) and (27)are expressed in terms of cubic equation

of state parameters ai andbi, and the binary interaction pa-

rameterkij. The above discussion demonstrates that Eq.(23)

is more generic in its form than the NRTL model. Both the

NRTL and van der Waals 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 finite-

concentration 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 parameterBjias follows:

ji=Aji + BjiT

T(29)

whereTis the temperature in K. The unit ofAji is in K and

Bjiis dimensionless.

Table 2 lists thevalues of the binary interaction parameters

Aij,Aji,Bij,Bji andij obtained for the TEGwater system.

Table 3compares measured and calculated infinite dilution

activity coefficients of water in TEG as a function of temper-

ature. Also shown in the table are the infinite dilution activity

coefficients calculated from Parrishs empirical hyperbolic

equation (Eq.(2))for comparison. Data inTable 3are also

shown graphically inFig. 1. Results shown inTable 3and

Fig. 1indicate 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

Table 3

Comparison of Parrish et al. [2] measured infinite dilution activity coeffi-

cients of water (2) in TEG (1) solution with those calculated using TST

CEoS and Parrishs hyperbolic equation

T(K) 2 (measured) This work Parrish et al.[2]

2 (calc.) Devi% 2 (calc.) Devi%

300.43 0.5510 0.5565 0.99 0.5587 1.40311.71 0.575 0.5773 0.41 0.5826 1.32

323.26 0.5900 0.5979 1.34 0.6072 2.91

333.76 0.6170 0.6159 0.19 0.6296 2.04343.43 0.6240 0.6318 1.25 0.6503 4.21

355.93 0.6360 0.6515 2.44 0.6772 6.47

364.93 0.6690 0.6651 0.58 0.6966 4.13378.32 0.6920 0.6845 1.08 0.7257 4.87AAD% 1.03 3.42

error of1.03%. Parrishs modelsystematically overpredictsthe data with a positive average error of +3.42%.Fig. 1also

indicates that Eq. (2) represents data at low temperatures bet-

ter than those at higher temperatures. The TST EoS, on theother hand, more accurately fits the data over the entire tem-

perature 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,

thetableagain includes results from this work andthoseusing

Eq.(2). Data inTable 4are also shown graphically inFig. 2.

ReviewingFig. 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 tem-

perature (


6/9


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 Parrishs

hyperbolic equation

T(K) X(1) 2(measured) This work Parrish et al.[2]

2(calc.) Devi% 2(calc.) Devi%

297.60 0.8062 0.6604 0.6299 4.62 0.6255 5.28297.60 0.7838 0.6640 0.6394 3.71 0.6338 4.55297.60 0.6731 0.6760 0.6875 1.71 0.6742 0.26297.60 0.6731 0.6871 0.6875 0.06 0.6742 1.87297.60 0.5809 0.7062 0.7290 3.23 0.7078 0.22

297.60 0.5449 0.7201 0.7456 3.54 0.7210 0.13

297.60 0.5001 0.7407 0.7664 3.47 0.7378 0.40297.60 0.4967 0.7371 0.7680 4.19 0.7390 0.26

297.60 0.3996 0.7823 0.8138 4.02 0.7777 0.58297.60 0.3898 0.7876 0.8184 3.91 0.7819 0.72297.60 0.3057 0.8264 0.8585 3.89 0.8220 0.53297.60 0.2505 0.8608 0.8849 2.80 0.8545 0.74297.60 0.2187 0.8784 0.9000 2.46 0.8765 0.22297.60 0.1894 0.8994 0.9139 1.62 0.8994 0.00

297.60 0.1657 0.9177 0.9252 0.82 0.9198 0.23

297.60 0.1575 0.9225 0.9292 0.72 0.9272 0.51

297.60 0.1157 0.9507 0.9494 0.13 0.9649 1.50297.60 0.1077 0.9526 0.9534 0.08 0.9716 1.99

297.60 0.1051 0.9542 0.9547 0.05 0.9736 2.04

297.60 0.1026 0.9563 0.9559 0.04 0.9756 2.01297.60 0.0657 0.9802 0.9745 0.58 0.9957 1.58297.60 0.0641 0.9811 0.9753 0.59 0.9961 1.53297.60 0.0549 0.9836 0.9799 0.37 0.9980 1.47297.60 0.0541 0.9866 0.9803 0.63 0.9982 1.17332.60 0.7039 0.8022 0.7254 9.58 0.7597 5.30332.60 0.5107 0.8215 0.8029 2.26 0.8611 4.82332.60 0.4970 0.8504 0.8085 4.93 0.8687 2.15332.60 0.4562 0.8571 0.8252 3.72 0.8911 3.97332.60 0.3759 0.8839 0.8581 2.92 0.9328 5.54332.60 0.3614 0.8901 0.8640 2.93 0.9397 5.57332.60 0.2886 0.9088 0.8934 1.69 0.9686 6.58332.60 0.2853 0.9133 0.8947 2.03 0.9697 6.17332.60 0.2429 0.9276 0.9115 1.74 0.9811 5.77332.60 0.1993 0.9451 0.9283 1.77 0.9889 4.64332.60 0.1562 0.9641 0.9447 2.01 0.9937 3.07332.60 0.1212 0.9767 0.9580 1.91 0.9963 2.01332.60 0.1170 0.9768 0.9596 1.76 0.9966 2.02332.60 0.0808 0.9893 0.9737 1.58 0.9984 0.92332.60 0.0796 0.9897 0.9741 1.57 0.9984 0.88332.60 0.0454 0.9980 0.9877 1.04 0.9995 0.15AAD% 2.27 2.23

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 fromFig. 2.

The TST EoS predicts slightly lower activity coefficients

than the experimental data at higher temperature. On the

other hand, Parrishs model predicts higher activity coeffi-

cients 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-

trapolation capability, both the TST equation of state and

the Parrish model are extrapolated to 204 C (477.15 K). Theability to extrapolate the model to high temperatures to pre-

dict accurate activity coefficients is quite important for strip-

ping 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 un-

der pressure of 123.91 kPa, which is very close to the ob-

served 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, theParrish model gives a value of 0.9477 for the water activity

coefficient. This activity coefficient value will predict a pres-


7/9


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 co-

efficients 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 TEGwater system commonly are repre-

sented as charts of water dew point lines as a function of con-

tactor 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 TEGwater 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:

fLTEG= fVTEG (30)

fLw= fVw (31)

wherefi is the fugacity of component i in the solution. The

fugacity of component i is calculated from the TST equa-

tion 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 pres-

sureP and vapor-phase compositions. In the context of gas

dehydration, the equilibrium temperature Tis referred to asthe 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 tem-

perature 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

f0Lw (Td) = fVw (Td) (32)

where f0Lw (Td) is the liquid fugacity of pure water at the

water dew point temperatureTd and equilibrium pressure P

andfVw (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, 273.16K, 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.

(30) and (31)as discussed above. Rewrite Eq.(32)as

f0Lw (Td) = P0Lw (Td) = fVw (Td) = ywPVw(Td) (33)or

yw=0Lw (Td)

Vw(Td) (34)

whereywis the vapor mole fraction of water (without TEG)

in equilibrium with the TEG solution at equilibrium temper-

ature (contact temperature)T. The vapor and liquid fugacity

coefficients of water are calculated using the TST equation

of state atTd 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 giveyw= 1.0 in this case. Eq.(34)is used to solve for thewater dew point temperatureTd. After that, the liquid fugac-

ity of pure water atTd,f0Lw (Td), can then be calculated from

the equation of state.

When the value off0Lw (Td) at the water dew point temper-

atureTd is obtained, the water content in lbH2O/MMSCF at

standard condition ofT0= 60F (288.71 K) and the equilib-

rium pressureP can be calculated from the following equa-

tion:

n

V= PZ0RT0

(35)

whereZ0 is the gas compressibility factor at T0 andP, and

n the number of moles in vapor volume V. The number of

moles of water,nw, in the vapor then becomes

nw

V= yw

P

Z0RT0(36)

whereyw is themole fraction of waterin thegas phase without

TEG. Rewrite Eq.(36)using Eq.(33)and assuming that the

vapor fugacity coefficient of water is 1.0,

nw

V= ywPZ0RT0

fVw

Z0RT0(37)

Substituting Eq.(32)into Eq.(37), we obtain

nw

V= f

0Lw

Z0RT0(38)

Given T0= 60F (288.71 K),the gasconstantR and assuming

Z0=1.0, we obtain the water content in lbH2O/MMSCF in

terms off0Lw (Td) at the water dew point temperature Td,

Water content in lbH2O/MMSCF = 22272.23f0Lw (Td) (39)The water content in SI units is expressed in kg/106 scm:

Water content in kg/106 scm = 356765.00f0Lw (Td) (40)wheref0Lw (Td) is in the pressure unit of kPa. Since the water

content of lbH2O/MMSCF is commonly used in the US and

in the field, this unit is used inTable 6.

The typical application range is shown inTables 5 and 6.

Table 5shows the prediction of the water dew point temper-

atures of vapor in equilibrium with TEG solutions from the


8/9


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)

277.59 288.71 299.82 310.93 322.04 333.15 344.26

Water dew points of vapor (K)

GPSA 208.15 214.26 220.37 225.93 232.04 237.59 243.15TST 208.86 214.99 221.00 226.91 232.74 238.52 244.30

99.50 wt.% TEG

Contact temperature (K)

277.59 288.71 299.82 310.93 322.04 333.15 344.26

Water dew points of vapor (K)

GPSA 232.04 239.82 247.59 255.93 263.15 270.93 278.71

TST 232.66 240.47 248.16 255.75 263.22 270.58 277.84

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 arealso 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

lbH2O/MMSCF gas in equilibrium with 99.50 wt.% TEG.

The results predicted from the TSTequation of state are com-

pared with the reported data[13,14], which cover the range

of temperature from 222 to 277 K. The predicted water con-

tent 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 inTable 6.

Fig.3 presents the water dew point predicted from the TST

equation of state developed in this work as a function of con-

Table 6

Prediction of the equilibrium water content in lbH2 O/MMSCF from TST equation of state in equilibrium with 99.50 wt.% TEG

Tdew (K) Reported by Predicted from TST equation of state

McKetta and Wehe[13] Bukacek[14] Water content Pressure (Pa)

277.59 390 396 393 838.0

266.48 170 176 174 370.0

255.37 70 72 71 151.0

244.26 28 27 26 56.1

233.15 9.2 9.1 9 18.7

222.04 2.4 2.8 2.6 6.0

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 con-

stant wt.% of TEG. This plot is similar to those presentedin 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 suc-

cessfully to represent the TEGwater binary, which is an in-

dustrial 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 forusing the TST equation of state to calculate water dew point

andwatercontent in natural gassystems.The infinite-dilution

and finite-concentration activity coefficients of water in TEG,

water dew point temperatures and water content over the en-

tire application range of temperature, pressure and composi-

tion encountered in a typical TEG dehydration unit predicted

from the TST equation of state match the reported data very

closely.

List of symbols

a, b cubic equation of state parameters

A Helmholtz energy

Aij,Aji,Bij,Bji NRTL binary interaction parameters


9/9


Cr defined in Eq.(20)

C1 defined in Eq.(19)

G Gibbs energy

kij binary interaction parameter

L,M,N parameters in the Twus function

P pressure

r reduced liquid volumeR gas constant

T temperature

xi liquid mole fraction of componenti

yi vapor mole fraction of componenti

Greek letters

cubic equation of state alpha function

ij NRTL binary interaction parameters

i activity coefficient of componenti

ij characteristic of the interaction between molecules

iandj

i the fugacity coefficient of componenti in the mix-

ture infinite pressure

Subscripts

c critical property

i, j property of componenti,j

ij interaction property between componentsiandj

vdw van der Waals

0 zero pressure

Superscripts

* reduced property

E excess property

L liquid phase

V vapor phase

References

[1] J.R. Cunningham, J.E. Coon, C.H. Twu, Estimation of aromatic hy-

drocarbon emissions from glycol dehydration units using process

simulation, in: Proceedings of the 72nd Annual Gas Processors As-

sociation Convention, San Antonio, TX, March 1517, 1993.

[2] W.R. Parrish, K.W. Won, M.E. Baltatu, Phase behavior of the triethy-

lene glycolwater system and dehydration/regeneration design for

extremely low dew point requirements, in: Proceedings of the 65th

Annual GPA Convention, San Antonio, TX, March 1012, 1986.

[3] GPSA Engineering Data Book, Tenth Edition, First Revision, Gas

Processors Suppliers Association, Tulsa, OK, 1994.

[4] M. Herskowitz, M. Gottlieb, J. Chem. Eng. Data 29 (1984) 173175.

[5] B. Bestani, K.S. Shing, Fluid Phase Equilib. 50 (1989) 209221.

[6] GPA Editorial Review Board, Recent developments in gas dehydra-

tion and hydrate inhibition, in: Proceedings of the Laurance Reid

Conference, Norman, Oklahoma, 1994.

[7] C.H. Twu, W.D. Sim, V. Tassone, Fluid Phase Equilib. 6574 (2001)183184.

[8] C.H. Twu, W.D. Sim, V. Tassone, Fluid Phase Equilib. 194197

(2002) 385399.

[9] G. Soave, Chem. Eng. Sci. 27 (1972) 11971203.

[10] D.Y. Peng, D.B. Robinson, Ind. Eng. Chem. Fundam. 15 (1976)

5864.

[11] C.H. Twu, D. Bluck, J.R. Cunningham, J.E. Coon, Fluid Phase Equi-

lib. 69 (1991) 3350.

[12] C.H. Twu, J.E. Coon, D. Bluck, B. Tilton, M. Rowland, Fluid Phase

Equilib. 153 (1998) 3944.

[13] J.J. McKetta, A.H. Wehe, GPA Engineering Data Book Fig. 15-10,

Ninth Edition, Fourth Revision, Gas Processors Suppliers Associa-

tions, Tulsa, OK, 1979.

[14] R.F. Bukacekm, Equilibrium moisture content of natural gases, Re-

search Bulletin 8, Institute of Gas Technology, Chicago, IL, 1955.

teg water equilibrium

Documents