Equilibrium Ratios of Water in the Water-Triethylene
Glycol-Natural Gas System
FRANK R. SCAUZILLO
ABSTRACT
INTRODUCTION
During the last several years, the drying of natural
gas with aqueous triethylene-glycol (TEG) solutions
has become very prominent. Most users of TEG as a
drying agent have been satisfied with the performance of
TEG solutions at the conditions used; however, there
always has been some discussion of the drying ability
of TEG solutions at conditions not commonly encountered such as temperatures below 50° or 60 P, but more
particularly temperatures above 100 P, and pressures
above 1,000 psia. Today, when higher wellhead temperatures such as 120 P are more commonly encountered
many are skeptical of TEG's ability to dry sufficiently
well to provide dew points around 32°P, which is generally the maximum tolerable when attempting to dry a
gas to contract specifications of 7 Ib/MMscf.
These views probably have evolved to some extent
from the days when suppliers would not guarantee dewpoint depressions in excess of 65° to 75°P. Also, the
feelings about TEG drying may have arisen from the
lack of information about the equilibrium relation of
water in the drying operations.
Porter and Reid ' have reported equilibrium data for
a 95 per cent TEG solution, while Townsend' reported
0
0
0
Original manuscript received in Society of Petroleum Engineers
office July 13, 1960. Rovised manuscript received March 10, 1961.
Paper presented at 35th Annual Fall Meeting of SPE, Oct. 2-5.
1960, in Denver
lReferences given at end of paper.
JULY,
1961
SPE 1567-G
equilibrium data for 95, 98 and 100 per cent TEG
solutions. Townsend also presented a calculational
method which obtains activity coefficients in the liquid
phase and, subsequently, the equilibrium water content
of a saturated gas over glycol from published' atmospheric dew points. Wise, Puck and Pailey' present~d
activity data for the water-TEG system at atmosphenc
pressure.
In the past, the equilibrium ratios published for water
in a 95 per cent by weight aqueous TEG solution have
been used indiscriminately by many for all concentrations of TEG encountered in gas drying operations.
Since essentially all such gas operations require the use
of more concentrated TEG solutions, a study was undertaken to correlate the existing equilibrium data for
aqueous TEG and gas systems and to provide some
means of calculating the equilibrium ratio of water in
the natural gas-water-TEG system where TEG concentrations were other than 95 per cent. The data presented
herein consider only the equilibrium drying ability of
the TEG solutions and do not consider the effect of
temperature and pressure on the tray efficiency of contactors. In other words, this paper is concerned primarily with the development of the equilibrium relationship between water in the dried natural gas and the
water in the lean TEG entering the top tray of the
absorber.
BASIC EQUILIBRIUM RELATIONS
A relationship which relates the K value of water in
the natural gas-water-TEG system to the vapor pressure
of water at the system temperature, the total pressure
of the system and the activities of the liquid and gas
phases has been evaluated.
It is well known that, for any component of a mixture at equilibrium between a gas phase and a liquid
phase,
(1)
fv = fL and Yv Y fv ° = yr, X fLO
Y
YL fr,O
X
=
(2)
Yv---Y:O ,
and
I
V(p -
y
Yr,
p
)
I' e -~'~'1-
(3)
x
Yvvp
At the vapor pressure of water p', f' is essentially
equal to the vapor pressure, and
,
V(p - P )
yp
Xp'
-~R~1-
yL e
y.v
(4)
697
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Equilibrium data which should be useful in the design
and/or evaluation of glycol dehydration units were prepared from an analysis of various published data and
the correlation of these data by the use of the thermodynamic equilibrium ratio. The equilibrium ratios of
water are used to solve the glycol absorber problem;
such solutions are necessary to define the number of
trays and the glycol circulation rate needed to meet
drying requirements.
Activity coefficients were obtained which relate directly to the equilibrium ratios of water in the waterTEG-natural gas system. These activity coefficients have
been used to calculate the equilibrium dew points for
aqueous TEG concentrations of 60 to 99.9 weight per
cent for the temperature range of 40° to 120°F. They
also provide a means of calculating equilibrium ratios
for water in the water-TEG-natural gas system; this
applies to any desired TEG concentration and to the
temperature range from 40° to 120°F.
SO CONY MOBIL OIL CO., INC.
DALLAS, TEX.
To solve Eq. 4, as it applies to the water-TEG system,
a knowledge of the activity coefficients of water in both
phases is required. This type of information for the
natural gas-water-TEG system is not easy to come by
experimentally. The problem deals with the determination of small amounts of water in the vapor phase, and
any absolute error in the water determination can conceivably result in a large error on a percentage basis.
It seems practical, then, to devise some manner of
calculating the equilibrium for water in the subject
system. The vapor phase in equilibrium with a glycol
solution contains essentially no TEG, and the liquid
phase contains very little methane or natural gas. Therefore, it appears that the activity of water in either phase
can be obtained independently of the other phase.
NON·IDEALITY OF WATER IN THE VAPOR PHASE
YP
xp'
'II,
aL
yLx -
Yu
ACTIVITY OF WATER IN THE LIQUID PHASE
The data used to evaluate the activity of water in
aqueous TEG solutions were taken from the experiments of Townsend' and of Wise, Puck and Failey.'
Townsend experimentally obtained the concentration
of water in the vapor phase of a natural gas in equilibrium with 95 and 9S weight per cent TEG glycol solutions and approximately 100 per cent TEG. The glycol
concentrations were reported accurate to 0.5 weight per
cent. Since 100 per cent TEG normally contains about
0.3 weight per cent water, it was decided to treat the
100 per cent glycol as a 99.5 per cent solution in this
evaluation.
Table 1 presents the experimental data of Townsend
and the equilibrium data calculated therefrom with Eqs.
7 and S. The temperatures investigated were 70°, Soo
and 90°F over the pressure range of approximately 500
to 2,500 psia. The data for all three temperatures were
averaged for each pressure level used in the experiments,
and the results are tabulated in Table 2. These data
reveal that the activity of water in glycol solutions is
essentially independent of the system pressure. There
were insufficient data to evaluate any temperature effect
on activity.
Wise, et aI, investigated the activities of aqueous TEG
solutions at atmospheric pressure and 70°, Soo and
90°F. The highest TEG concentration reported was
96.S per cent. The activities reported then were used to
determine the more useful variable, the activity coefficient. The activity coefficients for water in TEG concentrations greater than 96.S per cent were evaluated with
the aid of the binary Van Laar equations; namely,
A
logy, = -(~-AX'
where C is an empirical constant and equal to ~e
V(p -
p )
--RT-'
This eliminates evaluating the fugacity coefficient as a
separate variable. The value of C then can be evaluated
from existing data on the natural gas-water system, such
as the data of McCarthy, Boyd and Reid:
In the natural gas-water system, the liquid phase
will follow ideal behavior because the mol fraction of
methane in the liquid is very small even at high pressures
and YL ;:.:;: 1.0. The value of x (mol fraction of water)
can be assigned a value of 1.0 for all practical consideratioris. The only information then needed to evaluate
C is the water content of the water-saturated gas, the
total pressure and the vapor pressure of water at the
temperature of interest.
p'
(' = - - - ,
yp
(6)
and
c=
47500 p'
Wp
(7)
where W is the water content of the gas in Ib/MMscf.
(S)
Y
where aL is then the ratio of the concentration of water
in the dry gas to the concentration of water when gas
is saturated at the same pressure and temperature.
(5)
=C
=
),
(9)
BX2
and
B
logy, =
(1 + BX')'
(10)
Ax,
where A = logy, at x, = 0 and B = log '12 at x, =
1.0. Values of A and B were estimated from the activity
coefficients of water and TEG calculated from the experimental data of Wise, et al. The best agreement with
the experimental data was obtained for A = --OA05
and B = -0.356. The average deviation of the experimental data from the calculated data thus obtained was
about 0.3 per cent for water and 4 per cent for TEG.
Fig. 1 presents the calculated curve for water. The
plotted points are the activity coefficients calculated
from the experimental data of Wise, et aI, and Townsend. Table 3 summarizes the activity coefficients and
activities of water at SO°F. These data are considered as
representative of the temperature range from 40° to
120°F since the effect of temperature in this range is
negligible.
The effect of temperature on the activity coefficient of
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In the vapor phase, TEG is normally present in
amounts up to 1 Ib/MMscf. This is a pretty well-accepted maximum for glycol units operating with a good
mist eliminator. Assuming all of the glycol lost overhead is in a true solution in the gas phase, this amounts
to a concentration of approximately 2.5 X 10- 6 mol
fraction TEG; for all practical considerations, the TEG
can be thought of as nonexistent in this phase. This
then leads to the natural gas-water system for which
there is sufficient information to define the behavior
of water in the vapor phase.
Considering the right side of Eq. 4 as it applies to
the natural gas-water system, all of the terms except
the activity coefficients YL and 'Iv are explicit functions
of the contact temperature and pressure, while the
activity coefficients are primarily functions of concentration. Since the water concentrations usually dealt with
fall in the range of approximately 7 to 120 Ib/MMscf
(the mol fractions being approximately 0.000147 to
0.00252), the systems are essentially at infinite dilution
and the activity coefficient of water in the vapor phase
can be taken as a constant value at any given temperature and pressure normally encountered. Therefore,
Eq. 4 can be rewritten as
If Eq. 6 is substituted into Eq. 5, the resulting equation can be used to determine the activity of the water
in the aqueous phase from experimental data.
TABLE l-VAPOR-liQUID EQUILIBRIA DATA FOR NATURAL GAS-AQUEOUS TRIETHYlENE GLYCOL SYSTEMS
Glycol
Mol
Concentration
Temp.
(Wt.%)
99_5
(0 F)
70
80
90
98
70
80
90
70
80
(psia)
~
2035
1555
1090
515
2515
1540
540
2565
1540
565
2545
2085
1555
1015
505
2515
2015
1535
990
455
2536
2055
1565
1005
575
2535
2040
1600
1015
435
2525
2095
1515
1015
485
p'
(psia)
0_3631
0.5069
0.6982
0.3631
0.5069
0.6982
0.3631
0.5069
W
(lb/MMscf)
14.0
15.5
18.5
23.5
42.0
19.2
25.0
54.0
24.7
34.0
73.0
14.0
15.1
18.5
24.7
42.0
19.2
21.5
25.0
34.0
62.0
24.9
28.0
34.0
47.0
72.0
13.9
15.2
18.5
24.7
48.0
19.3
21.0
26.0
34.0
59.0
Fraction
Water
Wu*
(lb/MMscf)
1.32
0.32
0
0.87
0.73
1.22
0.93
2.10
0.60
1.25
1.05
1.05
1.00
2.75
2.50
2.70
0.87
1.20
0.90
1.73
4.35
2.27
3.33
2.00
2.05
4.17
2.35
3.10
2.17
3.60
6.45
1.85
2.80
3.50
4.12
7.85
C
0.484
0.547
0.599
0.673
0.798
0.499
0.626
0.828
0.522
0.633
0.803
0.484
0.548
0.599
0.688
0.813
0.499
0.557
0.628
0.715
0.855
0.524
0.576
0.622
0.701
0.800
0.490
0.557
0.582
0.688
0.825
0.494
0.548
0.612
0.699
0.842
0.0391
0.0392
0.0393
0.0396
0.0399
0.0391
0.0393
0.0399
0.0391
0.0393
0.0399
0.1405
0.1410
0.1412
0.1420
0.1434
0.1405
0.1410
0.1412
0.1420
0.1434
0.1405
0.1410
0.1412
0.1420
0.1434
0.294
0.295
0.296
0.298
0.300
0.294
0.295
0.296
0.298
0.300
/,L/C
/,1,
~
0964
0
1.39
0.546
3.25
1.515
1.18
1.19
1.48
0.448
1.10
0.857
1.76
1.04
0.551
0.646
0.711
0.407
0.502
0.572
1.24
,1.47
0.669
0.438
0.504
L18
1.24
0.68
0.712
0.544
0.66
0.825
0.744
0.582
0.532
~
al
Tom-
0.528
0
0.935
0.436
1.62
0.949
0.977
0.621
0.936
0.359
0.538
0.469
1.055
0.716
0.448
0.322
0.396
0.256
0.359
0.489
0.650
0.847
0.416
0.307
0.403
0.578
0.691
0.396
0.490
0.449
0.326
0.452
0.455
0.407
0.448
0.0207
0
0.0370
0.0174
0.0635
0.0373
0.0390
0.0243
0.0368
0.0143
0.0750
0.0662
0.149
0.102
0.0643
0.0452
0.0558
0.0361
0.0510
0.0701
0.0913
0.119
0.0587
0.0436
0.0578
0.169
0.204
0.117
0.146
0.135
0.096
0.133
0.134
0.121
0.134
*Data of Townsend (Ref. 2). Above data for 99.5 per cent TEG was reported by Townsend as approximately 100 per cent.
a component in a solution of two completely miscible
liquids is approximated by the following equation.
H-H(l D. In y =--~~R----T;~
1) -
T
(11 )
where H - H is the average differential heat of solution
for the component in question for the temperatures considered. Table 4 is a tabulation of enthalpy data for the
water-TEO binary system compiled from the Union
Carbide Coos heat-capacity data on TEO solutions. The
partial enthalpy of water was obtained by applying the
method of intercepts to the solution heats calculated
from the heat-capacity data.
The differential heat of solution was found to be
positive in the temperature range from 40° to 120°F; as
such, the activity coefficient of water will decrease as
the temperature increases. The change in activity coefficient is about 3 per cent/40°F. Since drying at the
higher temperatures is of primary concern, the data of
Fig. 3 and Table 3 can be applied conservatively at
temperatures around 120°F without fear of any detrimental temperature effects.
data of natural gases after McCarthy, Boyd and Reid,'
and the activity coefficient at 80°F for water in a 98
weight per cent aqueous solution of TEO by solving
Eq. 5 for y/x or K.
The data of Fig. 2 present the K values of water in
the 98 per cent solution over the temperature range
from 40° to 120°F and over the pressure range from
14.7 to 2,500 psia. These data are considered accurate
through this temperature range because the effect of
temperature on the activity of the water phase in the
range is small. A relationship which relates K for any
concentration to the K for 98 per cent TEO is given
and allows the user to correct the plotted values to any
desired concentration with the use of the activity coefficients of water found in Fig. 1 and Table 3.
The values of K were found to decrease linearly as
the pressure increased to about 200 psia. Thereafter,
the incremental changes in the K value became smaller
1.0
C-'l
x
II
APPLICATIONS
EQUILIBRIUM RATIOS FOR WATER IN THE
WATER-TEG-NATURAL GAS SYSTEM
The vapor-liquid eqUilibrium ratios for water in this
basic system have been calculated and are suggested as
the values to be used in all dehydration calculations involving TEO. The K values for the system, 98 weight
per cent TEO-natural gas, are plotted in Fig. 2. These
values have been calculated from the water-content
TABLE 2-ACTIVITY AND ACTIVITY COEFFICIENTS FOR WATER IN THE
NATURAL GAS-AQUEOUS TRIETHYlENE GLYCOL SOLUTIONS
IN TEMPERATURE RANGE FROM 70° TO 90°F'
95 WI % TEG
98 WI % TEG
99.5 WI % TEG
Pressure
(psia)
"IL
aI,
"IL
aJ,
OL
"IL
~ 0.448
0.134
0.447
0.0641
0.591
0.0236
1000
0.448
0.134
0.461
0.0655
0.935
0.0370
1500
0.426
0.126
0.576
0.0813
0.628
0.0247
2000'
0.572
0.169
0.571
0.0805
0.528
0.0207
2500
0,452
0.136
0.502
1.550
0.0705
0.0606
Average
0.469
0.140
0.511
0.0724
0.846
0.0333
*From data of Townsend (Ref. 2).
JULY, 1961
-'
O.9
•
0.8
)0
0.7
~
z
W
0.6
U
LL.
LL.
0.5
W
0
•
u
>>
~
o WISE, ET AL
0.4
• TOWNSEND
~
u
ex
o
0.2
0.4
0.6
0.8
1.0
MOL FRACTION WATER IN TEG SOLUTION
FIG. I-ACTIVITY COEFFICIENTS OF WATER IN TRIETHYLENEGLYCOL SOLUTIONS AT 80°F.
699
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95
Pressure
by McCarthy, et ai: Eq. 12 enables one to evaluate K
from any source of water-content data he might choose.
If the water-content data of McCarthy, et ai, is used,
the K's obtained from Eq. 12 will be consistent with K's
evaluated from Fig. 1.
A sample dehydration calculation which explains the
use of the water equilibrium ratio is presented in the
Appendix. This problem solves for the circulation rate
of lean glycol when given the inlet temperature
and pressure, the lean glycol concentration, tray efficiency and the number of trays in the contactor. The
problem can be amended to solve for anyone of these
variables as the unknown.
6
4
2
"'1"
0.001
8
6
II
"
4
2
1000
PRESSURE, psi a
WATER-VAPOR DEW POINTS
WITH TEG SOLUTIONS
FIG. 2-VAPOR-LIQUID EQUILIBRIUM RATIO FOR WATER IN 98
WEIGHT PER CENT TRIETHYLENE-GLYCOL SOLUTIONS.
K
v
= -=
x
(2.105) (10") (W) (YL)
(12)
The equilibrium ratios presented herein have been
based on the water content of natural gases as presented
TABLE 3-ACTIVITY OF WATER IN AQUEOUS TRIETHYLENE GLYCOL
SOLUTIONS AT 80°F
Mol Fraction
TEG
Water
(Wt%l
"II,
aL
0.02
99.76
0.410
0.0082
0.05
99.37
0.434
0.0217
0.10
98.68
0.475
0.0475
0.15
97.93
0.520
0.0780
0.20
97.08
0.113
0.565
95.1
0.654
0.196
0.30
0.40
92.6
0.295
0.738
0.50
89.3
0.815
0.408
0.60
84.7
0.880
0.528
78.1
0.935
0.656
0.70
67.5
0.776
0.80
0.970
0.90
48.0
0.891
0.990
1.00
1.000
1.000
o
TABLE 4-ENTHALPY DATA FOR AQUEOUS TRI ETHYLENE
GLYCOL SOLUTIONS
40°F
86° F
122°F
Mol Fraction
Water
H,
H1
H.,
H,
H.o
H,
0
0.01
0.02
0.05
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
0.95
0.98
1.00
577.2
573.8
570.5
560.2
541.2
502.3
461
418
374
330
284
238
192
168
154
144
254
253
241
221
204
187
177
169
163
158
154
150
147
145
144
144
4018
3995
3968
3888
3754
3473
3183
2887
2590
2285
1975
1655
1323
1150
1042
972
1550
1514
1462
1368
1282
1192
1147
1098
1067
1042
1022
1002
988
980
975
972
68-'8
6820
6772
6652
6430
5952
5445
4929
4400
3887
3350
2796
2230
1940
1780
1620
2840
2841
2720
2505
2320
2120
2000
1910
18<0
1785
1735
1695
1655
1638
1623
1620
H.~
= enthalpy of solution, Btu/mol solution.
"'H';" =
partial enthalpy water, Btu/mol water.
Enthalpy datum
700
=
32°F.
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as the pressure increased, and K neared a limiting value
as the pressure approached 10,000 psia. The latter is
inherent in the way the K values were calculated because equilibrium water contents over glycol solutions
were related directly to the water content of a gas over
pure water, and the water content of a gas over water
tends to approach a limiting value as pressures around
10,000 psia are reached.
The equilibrium ratios for water in the water-TEGnatural gas system also can be evaluated directly from
the water content of the saturated gas at the temperature and pressure of interest and the activity coefficient of the water in the glycol solution. The data of
Townsend reveal that the ratio of the water content of
the gas over a glycol solution to the water content of
the saturated gas is essentially constant for any given
glycol concentration and is equal to the activity of the
water in the glycol solution, or W g = WaL. Then,
The equilibrium dew points available with glycol concentrations of 60 to 99.9 per cent by weight in the
temperature range 40° to 120°F are presented in Fig. 3.
These have been obtained by calculating the water content of the gas at the dew point as equal to the product
of the activity and the water content of the gas saturated
with water at the contact temperature and pressure. The
dew-point temperature then was taken directly from the
water-content chart of McCarthy, et ai,' by entering
the chart with the water concentration at the dew point
and the contact pressure.
The temperature of contact affects the dew point
such that the dew-point depression, or the difference in
the contact temperature and the dew-point temperature,
at a temperature of 40°F is approximately 75 per cent
of the dew-point depression theoretically possible at
120°F.
Pressure was found to have no effect on the equilibrium dew point. The dew points of Fig. 3 represent
data calculated over the pressure range from 14.7 to
2,500 psia. These dew points for any given contact
temperature were found to agree within 1°F throughout this range of pressures.
Data such as shown in Fig. 3 have limited application
in the design of glycol units. One bit of information obtained from it is the minimum glycol concentration
which can be used to obtain a certain dew point. For
example, if a 32°F dew point at a contact temperature
of 100°F is desired, the lowest lean glycol concentration
which will suffice is approximately 97 per cent TEG.
If it is assumed the desired dew point will be about
20°F above the equilibrium dew point (quite often expressed as an approach to equilibrium of 20°F), the
lean glycol concentration should be one which gives a
dew point of 32 minus 20, or 12°F. This sets the desired lean glycol concentration at approximately 98.5
per cent TEG.
Another application of Fig. 3 is to use the glycol
concentration shown as the average concentration in the
dehydrator. Then the dew point obtained in this manner
will approximate the dew point which is obtained in the
actual operation. Nothing has been said about rates,
and this information cannot be obtained without performing the more detailed analysis illustrated in the
Appendix.
During the last several years, the gas engineer has
become more aware of the fact that dew-point depressions in excess of 100°F are needed and that depressions of this magnitude are possible only if the lean
glycol is stripped to very small water concentrations. At
a contact temperature of 120°F and using a lean glycol
concentration of 99.7 per cent TEG, a dew-point de-
of a dried natural gas, (2) a more critical look at dehydrator performance and (3) a more accurate prediction of rate and tray requirements.
80
L1..
60
0
~
IZ
NOMENCLATURE
40
(/,. = activity of water in liquid phase
0
Q.
20
3:
w
0
~
::::>
0::
CD
...J
99 9
::::>
0 -60
W
-80
20
40
60
80
100
120
CONTACT TEMPERATURE, of
FIG. 3-WATER-VAPOR DEW POINTS OBTAINED BY
DRYING NATURAL GAS WITH TRIETHYLENE-GLYCOL
SOLUTIONS.
pression of 133°P is theoretically possible. However,
the theoretical dew point (based on the concentration
of the incoming lean glycol) is never obtained in field
operations due to the enriching of the glycol with water
on the top tray and the inefficiency of the gas-liquid
contact in the absorber. The approach to equilibrium
dew point is often 20 P or less, and this approach can
always be improved by increasing the circulation rate
or by adding more trays. In the problem in the Appendix, an 18°P approach to equilibrium is obtained. The
dew point of the dried gas is 28°P, and the theoretical
dew point for the stated conditions is lOoP. At the same
circulation rate with an extra tray added, the dew point
of the dried gas will be approximately 22°P to give
a 12°P approach to equilibrium. If the circulation were
approximately doubled, and with five trays, the approach
to equilibrium would be approximately lOOP.
Consider drying a natural gas at 600 psi a and 120 P.
In an average four-tray contactor, a 100 P dew-point
depression could be made by circulating approximately
20 gal of 99.7 per cent TEG/lb of water in the inlet
gas. Increasing the number of trays by two to a sixtray unit at the same conditions, a 120 P dew-point
depression would be possible at only one-third of the
same circulation rate. The point to remember is that
drying to meet some requirements at higher temperatures can be done, although an extra tray or two may
be required as well as more complete regeneration of
the glycol. More complete regeneration of glycol is
being accomplished by the use of stripping gas as part
of the regeneration system.
In years past, the rule of thumb was 3 gal of glycol
circulated/lb of water in the wet gas. This rule probably
does very well at temperatures below 90 0 P and pressures above 600 psia, but it is not a recommended
practice. The absorber-type analysis such as presented
in the Appendix should be used to properly define drying needs.
R = gas constant = 10.71 (psia) (cu ft)
(lb mol) (OR)
0
1.99
T
V
V" " 1
W
W"
X,X,
x"
y
Yo
0
0
0
CONCLUSIONS
The application of the data presented herein should
permit (1) a more accurate estimate of the dew point
JULY,
1961
y"
+
I
Y,
y"
Y" YL
Yv
v
Btu
(lb mol) (OR)
= absolute temperature, OR
= molal volume of water, cu ft/mol
= inlet gas, mol
= water content of water-saturated gas, lb/
MMscf
= water content of gas over glycol solution,
Ib/MMscf
= mol fraction of water in the liquid phase
= mol fraction of water in lean glycol
= mol fraction of water in water-saturated gas
= mol fraction of water in the vapor phase
over glycol solution
= mol fraction of water in wet inlet gas
= mol fraction of water in dry outIet gas
= mol fraction of water in outIet gas in equilibrium with lean glycol
= activity coefficient of water in liquid phase
= activity coefficient of water in vapor phase
= fugacity coefficient of pure water at temperature and pressure of system.
ACKNOWLEDGMENT
The author wishes to thank the Socony Mobil Oil
Co. for permission to publish these data and to thank
E. B. Elfrink, Ovid Baker and Will Swerdloff of the
Socony Mobil Oil Co. for their critical reviews of this
paper.
REFERENCES
1. Porter, J. A. and Reid, L. S.: Trans. AIME (1950) 139,
235.
'
2. Townsend, F. M.: "Equilibrium Water Contents of Natural
10[
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o
A = absorption factor for water
A, = absorption factor for methane
r = fugacity of pure liquid water at its vapor
pressure, psia
r = fugacity of pure component in standard
state taken as temperature and pressure of
systems, psia
II. = fugacity of liquid water at system conditions,
psia
Iv = fugacity of water vapor at system conditions,
psia
H = partial enthalpy, Btu/mol
H = enthalpy of pure component, Btu/mol
K = equilibrium ratio of water
K, = equilibrium ratio of methane
L" = rich glycol rate, mol rich solution/mol inlet
gas
L" = lean glycol rate, mol lean solution/mol inlet
gas
p' = vapor pressure of water at system temperature, psia
p = system pressure, psia
~ IOOr---------~~------._~r_T1~
o
.....
n = NUMBER
THEORETICAL
TRAYS
U
<l
50
Z
o
30
.....
20
LL
a..
o
~
a::
10
<l
TABLE 5-APPROXIMATE EQUILIBRIUM RATIOS FOR METHANE IN
TRIETHYlENE GLYCOL SOLUTIONS'
PSIA
50°F
80°F
120°F
150
152
100
150
126
122
150
126
110
106
200
III
96
99
250
100
87
91
94
300
76
79
400
82
66
70
500
72
58
62
600
66
54
57
60
700
48
51
800
53
44
48
49
900
39
43
44
1000
29
33
34
1500
27
31
32
2000
*Calculated from data given in Ref. 1.
W
>
5
U
W
3
.....
LL
LL
W
<l
=
Yn+1 - y,
2
~~~----~------~~~--------~
0.7
0.8
0.9
1.0
EQUILIBRIUM FRACTION ABSORBED
n+1
Y
n+1
-
Y
-
Y
0
=A
A
n+ 1
n+1
-A
-I
FIG. 4---KREMSER·BROWN ABSORPTION FACTOR FOR ABSORB,ERS.
Gas Dehydrated by Aqur.ous Diethylene and Triethylene
Glycol Solutions at Various Temperatures and Pressures",
PhD dissertation, The U. of Oklahoma (1955).
3. Union Carbide Co.: Gas Treating Chemicals.
4. Wise, H., Puck, T. T. and Failey, C. F.: Jour. Phys. Chem.
(1950) 54, 734.
5. McCarty, E. L., Boyd, W. L. and Reid, L. S.: Trans., AIME
(1950) 189, 241.
equilibrium fraction to be absorbed
0.001515 - 0.000147
0.001515 - 0.0000772
= 0.951.
Past experience has indicated trays in glycol units
to be approximately 25 per cent efficient. Then assume
25 per cent efficiency for each tray and n, the number
of theoretical trays, = 5 (.25) = 1.25 theoretical trays.
Refer to Fig. 4 and find the absorption factor A = 10.6
for 1.25 trays and an absorbed fraction = 0.951.
Then the circulation rate of rich glycol,
L.
=
(A) (Vn+1) (K)
= (10.6) (1.0) (0.000728)
= 0.00772 mol rich glycol/mol inlet gas
A, = absorption factor of methane or natural
gas
APPENDIX
= ~ = 0.00772 = 0.000154,
SAMPLE DEHYDRATION CALCULATIONS
where K, is equilibrium ratio of methane in glycol solutions (Table 5) .
Since the gas phase consists mainly of methane (C,),
the absorption factor will approximate the moles of
natural gas absorbed when using 1 mol of gas as basis,
or
moles C absorbed = 0.000154 mol/mol inlet
gas;
moles water absorbed =0.001515 - 0.000147
= 0.001368 mol/mol inlet
gas.
Then the circulation rate of lean glycol,
Lo = L. - (mol C, absorbed + mol water absorbed)
= 0.00772 - (0.000154 + 0.001368)
= 0.0062 mol lean glycol/mol inlet gas.
Molecular weight
(MW) of lean glycol = mol fraction water (MW
water) + mol fraction TEO
(MW TEO)
= 0.106 (18) + 0.894 (150)
= 136.
Density of lean glycol = 9.3 lb/ gal.
Therefore,
_
(mOl lean gIYCOI)(2637 mol gas)
Lo - 0.0062
.
M
f
mol mlet gas
Msc gas
136 gal TEO)
( 9.3 mol TEO
239 galjMMscf
= 0.166 gal/min / MMscflD
= 3.32 gal/lb water in inlet gas.
Calculate the circulation rate of 98.6 weight per cent
TEO solution required to dry 1 MMscfjD of gas at
800 psi a and 100°F so as to make a dry gas containing
7 IbjMMscf. The contactor has five trays.
COMPUTATION OF K
K from water content of natural gas and the activity
coefficient of water in the 98.6 weight per cent solution
can be calculated by either of the following methods.
Method 1
K =
~ = (2.105) (lO·') (W)
(y[,)
(24)
x
where W = water content of saturated gas = 72 lbj
MMscf.
YL = activity coefficient of water = 0.481 (Fig.
1) and (2.105) 10" is a constant converting water concentration from IbjMMscf
to mol fraction.
K = (2.105) (10") (72) (0.481) = 0.000728.
Method 2
K from Fig. 2 and YL
K",. = (K,,) (1.94) (YL)
= (0.00079) (1.94) (0.481) = 0.000728.
CIRCULATION RATE
Yn+1 = mol fraction water in wet gas
(72) (2.105) 10-' = 0.001515.
y, = mol fraction water in dry gas
(7) (2.105) 10-' = 0.000147.
Yo = mol fraction water in dry gas
= at equilibrium (Yo = Kxo)
702
=
KYn+1
50(1)
***
JOURNAL OF PETROLEUM TECHNOLOGY
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Y
Yn+l - Yo
(0.000728) (0.106) =0.0000772.