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Partition coefficients for alcohol tracers between nonaqueous-phase liquids and water from UNIFAC-solubility method
SO309-1708(96)00040-1
ELSEVIER
Advances in Warer Resources 21, No. 2, pp. 171-181, 1998 Copyright 0 1997 Elsevier Science Limited Printed in Great Britain. All rights reserved 0309-1708/98/517.00+0.00
Partition coefficients for alcohol tracers between nonaqueous-phase liquids and water from UNIFAC-solubility method Peng Wang, Varrldarajan Dwarakanath,
Bruce A. Rouse, Gary A. Pope & Kamy Sepehrnoori
Centre for Petroleum and Geosystems Engineering, The University of Texas at Austin, Austin, TX 78712, USA
(Received 9 October 1995; accepted 11 June 1996) In this work, we have applied a group-contribution activity-coefficient model, UNIFAC, and the solubility of alcohols in water to estimate partition coefficients for alcohol tracers between water and nonaqueous-phase liquids (NAPLs). The elects of temperature and mutual solubility between NAPL and aqueous phases on the estimation of partition coefficients were also investigated. By comparing the estimated results with experimental partition coefficients for 30 alcohol tracers between 10 NAPLs and water, we found that: i) the UNIFAC-solubility method, in which the UNIFAC model in its infinite-dilution form is applied to the NAPL phase and the solubility of tracers in water is used for estimation of the activity coefficient in the aqueous phase, works better than the UNIFAC model; ii) a linear relation between the logarithm of partition coefficients and the logarithm of tracer solubility in water is observed for those tracers having a similar chemical structure (i.e. the same number of branched methyl groups). This can serve as a meful tool for quick selection of the tracers that exhibit the desired partition coefficients; iii) the effect of mutual solubility between NAPL and aqueous phases can be neglected because such miscibility is very small, usually of the order of 10e3 mole/mole unit; and iv) temperature variation between 15”and 25°C does nlot significantly affect partition coefficients. Copyright 0 1997 Elsevier Science Limited Key wora!s: partition coefficients. alcohol tracer, NAPL, interwell tracer, UNIFAC.
1 INT.RODUCTION
that exhibit the desired partition coefficients’. We have made measurements on several common pure NAPLs such as trichloroethylene (TCE)7. However, most NAPLs are mixtures of many hydrocarbon and/or chlorocarbon components, and it would be very useful to have a method to predict the approximate partition coefficients for these mixtures to minimize the number of measurements required to select the appropriate tracers as well as for other purposes such as preliminary modeling of the aquifer test with compositional fluid flow models such as UTCHEM6 and subsequently inverse modeling to infer the saturations and composition of the field NAPL. Such a predictive model can also he used to help spot experimental errors. Finally, in some cases a sample of NAPL cannot be obtained from the field and yet it is useful to design a partitioning tracer test for the purpose of attempting to locate the NAPL. In such cases, an approximate composition of the NAPL can often be calculated from the contaminant concentrations in
The partitioning tracer technique has been successfully applied in the following two areas: ??
characterizing
residual saturations of oil in oilfield
reser~oir8;1,‘,14,21,22,24,26 ??
detecting and characterizing nonaqueous- hase P liquids (NAPL) in the subsurface.2~‘0~‘1~15~1812
An accurate determination of the partition coefficient for the partitioning tracer is one of the keys to the success of these applications. The partition coefficient is defined as the ratio of its concentration in a nonaqueous phase to its concentration in the aqueous phase. A reliable way of obtaining this partition coefficient is through laboratory experiments. This may be costly, time-consuming, and dilficult to conduct.13~20~27 Usually, for a given NAPL, several experiments with different tracers need to be performed to select several tracers 171
P. Wang et al.
172
water samples taken from the aquifer. Thus, the main objective of this work was to develop a thermodynamic model that is capable of predicting the partition coefficient for a wide range of partitioning alcohol tracers.
2 DEFINITION
OF PARTITION
COEFFICIENTS
The partition coefficient for a chemical component between NAPL and aqueous phases is defined as
i
XYN
K+i,
(1) 1
where Cy and Ct are the concentrations of component i in NAPL and aqueous phases, respectively, in units of moles per unit volume. When such a system is in thermodynamic equilibrium (liquid-liquid equilibrium), we can write the following equation for component i: ryxy
= yfxf,
(4
where 7; and 7” are the activity coefficients and xr and x4 are the mole fractions for component i in NAPL and aqeuous phases, respectively. Using eqn (2), eqn (1) may be rewritten as K, = ?4MAPN ’
$QppA
3.1 UNIFAC model The UNIFAC model employs a group-contribution concept in which each compound is considered as a collection of basic functional groups. Thus, a mixture of compounds is viewed as a mixture of these functional groups, and mixture properties are computed using functional group properties and their interactions. It is also assumed that any pair of the functional groups interacts in the same manner regardless of the presence of any other groups (i.e. for a given pair of groups the same value of interaction parameter is used). These features make this model one of the few predictive models available for estimation of the activity coefficients for each of the components in a polar mixture. In computing Tiyi,the UNIFAC model assumes that the logarithm of the activity coefficient is the sum of two contributions: lnyi = lny,C + lny”,
(4)
where superscript C denotes the combinatorial contribution coming from differences in size and shape of the compounds in the mixture, while superscript R stands for the residual part resulting from energy interactions. The combinatorial term is evaluated from
(3)
where M is molecular weight and p is density (g/cm3). Superscript A denotes the aqueous phase, while superscript N denotes the NAPL phase. When applying eqn (3) to tracers (which are very dilute components in solution), Ti becomes an infinite dilution activity coefficient, ry.
3 MODEL ESTIMATION Many models can be used to estimate activity coefficients at infinite dilution. However, groundwater contamination consists of a wide range of nonpolar and polar chemical components and strictly speaking, the calculation of partition coefficients for tracers in this work needs to be done through liquid-liquid equilibrium calculations. This limits the number of applicable models. A group-contribution model, UNIFAC, was used in this work because of its predictive capability and its power of handling both vapor-liquid and liquid-liquid equilibria for a large number of strongly polar chemical components. This model has been used by others for the estimation of octanol-water partition coefficients.3’4 As most of the alcohol tracers for groundwater application are at low concentrations, the applicability of the solubility of these tracers in water for the estimation of their activity coefficients in aqueous phase was also investigated.
where Bi is the molecular surface area fraction component i and is defined as
for
and $i is the molecular volume fraction for component i, which is computed from ++. c
rjqj
j=l
The van der Waals surface area, qi, and volume, ri, for molecule i are calculated from *s
ri =
c
v;Rk
k=l
(8) k=l
where v; means the number of group k in molecule i. Qk and RR are the surface area and volume for group k, which have been tabulated by Reid et aLI8 The average coordination number, z in eqn (5) is usually taken to be 10, and the parameter li is computed from li =
c(ri - qi) L
(ri - 1).
173
Partition coe#cients for alcohol tracers
The residual term in eqn (4) is computed from ln7” = ~7J(lnrt
- lnl?;),
(10)
be eliminated without a significant loss of accuracy of the above equation. So eqn (17) can be further simplified as
k=l
where the residual activity coefficient of group k is estimated from lnrk
If the solubility of tracer in water is small, this equation provides a reasonable estimate of 7:.
=
1
r
4 MUTUAL SOLUBILITY BETWEEN NAPL AND WATER where 0, is the surface area fraction of group m and is calculated from em=
,“,Qm . CQ
xn
(12)
n
?I=1
Some of the NAPL components may be partially miscible with water under aquifer conditions. When this occurs, the NAPL phase will contain a certain amount of water and the aqueous phase will contain some of the NAPL components. For a binary mixture, the thermodynamic criterion for this phase-splitting to happen can be written as
The mole fraction of group m in mixture, X,,,, is defined as
(13)
in eqn (11) is given by The parameter Xk’nm
(14)
*\E,, = exp(-F).
where a”,,, represents ,the interaction energy between groups m and n and is correlated using binary phase equilibrium data.7
(19) where g” is the molar excess Gibbs energy of the mixture and is easily computed using the UNIFAC model. Model1 and ReidI also give an expression for liquidliquid phase separation for multicomponent mixtures. If eqn (19) shows that the phase-splitting for a mixture at a given temperature and pressure is going to occur, we then simultaneously solve the following equations for the compositions of the two coexisting liquid phases:
N
N
c
3.2 Solubility method
RT
XI lnyixi
+x2 lncY2x2.
When such a mixture is saturated, equation should be satisfied:
(15) the following
i=l
lnrixi
-1nr2x2-1>=0.
1
(17)
If alcohol is used as a tracer, the last two terms may
XN - 1 = 0.
(21)
The UNIFAC model is again used in this work to compute the activity coefficients for each component in both NAPL and aqueous phases in eqn (20). The average molecular weights and densities for both phases used in eqn (3) are calculated using the following mixing rules: M = 2XiMi
Substituting eqn (15) into the above equation for alcohol (component l:)-water (component 2) binary mixtures and using the Gibbs-Duhem relation, the following equation results:
c
i=l
i=l
For a binary single-phase mixture, the molar Gibbs free energy of mixing may be written as Ag” -=
and
x:-1=0
(22)
N
c P=
XiMi
i=l
(23)
Nx& c i=l
Pi
because the UNIFAC density information.
model does not give us any
174
P. Wang et al. Table 1. Partition coefficients for alcohols between several DNAPLs
Alcohol Ethanol Iso-propanol Pentanol @-AmyI) 2-Methyl-Zbut. (r-amyl) Hexanol 2-Methyl- 1-pentan 3-Methyl-1-pentanol 2-Methyl-Zpentanol 3-Methyl-2-pentanol 4-Methyl- 1-pentanol 2-Methyl-3-pentanol 4-Methyl-Zpentanol 3-Methyl-3-pentanol 2-Ethyl-1-butanol 2,3-Dimethyl-2-butanol 3,3-Dimethyl-2-butanol 3,3-Dimethyl-1-butanol 3-Methyl-3-hexanol 2-Methyl-3-hexanol 3-Methyl-Zhexanol 2-Methyl-Zhexanol 5-Methyl-2-hexanol 3-Ethyl-3-pentanol 4,4-Dimethyl-2-pentanol 2,3-Dimethyl-3-pentanol 2,2-Dimethyl-3-pentanol PCE = tetrachloroethylene; TCM = tricholoromethane
and water at 25°C
PCE
TCE
TCA
CTET
TCM
DCB
0.0 0.0
0.0
0.1 0.1 3.1 0.7 15.2 11.6 9.7 5.1 8.2 12.8 9.7 7.4 4.4 10.8 4.4 8.9 6.7 20.6 35.4 42.2 21.8 39.8 23.9 37.6 23.8 45.1
0.0 0.0
0.3 1.1 10.8 3.1 51.5 36.7 41.2 19.7 32.5 58.9 32.6 30.2 18.3 37.3 16.4 31.5 25.9 68.3 81.2 70.1 554.1 99.2
0.0
0.1 3.8 1.3 18.6 14.5 12.8 6.3 11.3 16.0 13.2 10.2 4.5 13.0 6.3 9.6 9.5 27.9 43.2 56.9 28.1 55.3 31.9 51.3 29.0 80.2
1.4 0.4 6.8 5.4 4.7 2.6 6.2 5.7 5.2 3.8 2.2 9.6 2.8 4.5 3.8 11.8 20.0 19.2 10.9 17.1 13.9 22.6 12.3 26.4
1.9 0.9 11.0 7.8 6.5 3.4 5.9 8.5 7.7 5.1 3.3 7.5 3.3 6.5 4.1 15.9 29.8 30.0 16.1 30.4 17.1 24.7 17.6 39.1
TCE = trichloroethylene; TCA = 1, 1,l -tricholoethane; (chloroform); DCB = dichlorobenze.
81.6 292.5
CTET = carbon tetrachloride;
Table 2. Partition coefficients for five alcohols between TCE and water at 25°C
Alcohol i-Butanol 4-Methyl-2-pentanol 2-Methyl-3-pentanol 2-Ethyl-1-butanol 5-Methyl-2-hexanol
Exp K-value 0.8 10.2 13.2 13.0 55.3
UNIFAC(LLE) 1.22 12.82 12.82 12.82 41.50
UNIFAC(VLE) 1.31 13.73 13.73 13.73 44.56
Table 3. Partition coetlicients for five alcohols between benzene and water at 25°C
Alcohol i-Butanol 4-Methyl-2-pentanol 2-Methyl-3-pentanol 2-Ethyl-1-butanol 5-Methyl-Zhexanol
Exp K-value 1.2 7.9 9.8 11.6 41.5
UNIFAC(LLE) 6.87 28.27 28.27 28.18 103.18
UNIFAC(VLE) 1.91 15.33 15.33 15.33 49.30
Table 4. Partition coefficients for five alcohols between toluene and water at 25°C
Alcohol i-Butanol 3-Methyl-Zpentanol 4-Methyl- I-pentanol 2-Ethyl-1-butanol 5-Methyl-Zhexanol
Exp K-value O-6 9.4 11.4 10.2 34.7
UNIFAC(LLE) 1.09 22.01 22.01 22.01 81.20
0.1 2.2 0.7 13.2 9.0 8.4 3.4 6.0 9.2 7.1 4.9 3.2 7.7 3.0 5.8 4.4 14.4 23.8 29.3 14.9 33.7 16.4 22.1 15.8 32.4
UNIFAC(VLE) 1.62 11.22 11.22 11.22 36.12
Partition coeficients for alcohol tracers ‘l’able 5. Partition coefficients for five alcohols between decane and water at 25°C
Alcohol
Exp K-value
UNIFAC(LLE)
UNIFAC(VLE)
0.2 1.9 2.7 2.4 7.2
1.22 12.79 12.79 12.79 41.50
0.27 2.80 2.80 2.80 8.70
i-Butanol 3-Methyl-1-pentanol 4-Methyl-1-pentanol 2-Ethyl-1-butanol S-Methyl-2-hexanol
X
_. Alcohol solubility in water Fig.
UNIFAC-sdubolttymethod
0.1
1 Alcohol solubility
(weight %)
Partition coefficient between TCE and water for alcohols with one branched methyl group at 25°C.
1.
10 (weight %)
100
Fig. 3. Partition coefficients between tetrachloromethane and water for alcohols with 1 branched methyl group at 25°C.
ld
T
s
.
in water
0
E.V
+
UNIFAC I
$10’
2
.:
100 Alcohol solubility in water
(weight
%)
5 RESULTS AND DISCUSSION The UNIFAC model and the solubility method were used to estimate the partition coefficients for 30 alcohol tracers between 10 NAPLs and water and compared to the values measured in our laboratory. An infinitedilution form of the UNIFAC model was used hecause the concentration of tracers in the experiments was on the order of lOOOmg/l. The solubility of these alcohols in water was obtained from.” 5.1 Experimental measurements
experiments
conducted
were
static
or
1
0.1
i
_-L
1
0.1 Alcohol
Fig. 2. Partition coefficient between benzene and water for alcohols with one branched methyl group at 25°C.
The
8 s ._ .z a”
batch
solubility
10 in water
(weight
100 %)
Fig. 4. Partition coefficient between decane and water for alcohols with one branched methyl group at 25°C. equilibrium partition coefficient tests’. A lOm1 aliquot of a lOOOmg/l aqueous standard was placed in a separatory funnel with 10 ml of the NAPL. The samples were thoroughly shaken, allowed to separate for 1 h and re-shaken. This was repeated twice to ensure that the samples were at equilibrium. The samples were then allowed to separate for at least 12 h, were drained into centrifuge tubes and centrifuged at approximately IOOOg for 1 h to allow a complete separation of the phases to occur. Three aqueous aliquots on duplicate aqueous samples were then analyzed with a gas chromatograph for a total of six measurements of the alcohol concentrations in the aqueous phase. The
P. Wang et al.
176
1 o*
I
;
I
y-
I
L
i
E
.
E .$
s ..% a” E 8
.
10’
-r
++ (81
X
r
0 0 ;
e
IFAC IIFAC-solutnl+~method
I d
10 Alcohol solubility in water
(weight
Alcohol solubility in
%)
water (weight %)
Partition coefficient between chloroform and water for alcohols with one branched methyl group at 25°C.
Fig. 7. Partition coefficient between dichlorobenzene and water for alcohols with one branched methyl group at 25°C.
concentration of alcohol in the NAPL is then calculated from a mass balance on the sample. A summary of partition coefficients between these alcohol tracers and several common DNAPLs (dense nonaqueous phase liquids) is presented in Table 1. These measured partition coefficients were then compared to partition coefficients estimated using the UNIFAC-solubility method.
Both the VLE and LLE parameter tables available today in the literature are generated using binary equilibrium data in which components are not in dilute concentrations. Some degree of deviation from the experimental partition coefficients (measured at infinite dilution) is therefore observed. Surprisingly, the UNIFAC model with the LLE parameter table systematically overestimates the partition coefficients significantly, while the model with the VLE parameter table generally gives better predictions.
Fig.
5.
5.2 UNIFAC with VLE and LLE parameter tables As stated earlier, the estimations covered in this work belong to liquid-liquid equilibrium calculations. The UNIFAC model was, therefore, first used with the group-interaction parameter table that was correlated from binary liquid-liquid equilibrium (LLE) data.16 Some typical estimated partition coefficients using the UNIFAC model with this parameter table are shown in Tables 2-5. The calculations were repeated using a parameter table from binary vapor-liquid equilibrium (VLE) data.**19The results are also given in Tables 2-5 for comparison. For these calculations, the mutual solubility between the NAP1 and aqueous phases was ignored; its effect will be discussed later. -
. .
I
0
m
+
UNIFAC
Alcohol solubility
5.3 UNIFAC-solublllty method In this method, we only apply the UNIFAC model to compute the activity coefficients for tracers in the NAPL phase. The solubility data are used to estimate the tracer activity coefficients in the aqueous phase. Again, the partial miscibility between NAPL and aqueous phases is neglected. The estimated results using this method are shown in Figs 1-7, in which the partition coefficients of tracers are plotted versus their solubilities in water using loglog scales. From these figures it can be seen that the UNIFAC-solubility method works better than the UNIFAC model for estimation of the partition coefficients. The trend of increasing partition coefficients with decreasing solubility of the alcohols in water is better predicted using the UNIFAC-solubility method. This is because of the following reasons: Table 6. Mutual solubiity between NAPL(1) end water(t) from UNIFAC at 25°C NAPL
I
in water (weight %)
Fig. 6. Partition coefficient between tetrachloroethane and water for alcohols with one branched methyl group at 25°C.
Trichloroethylene Benzene Toluene Dichlorobenzene n-Octane n-Decane
x(2) in NAPL phase O+rOO80 0*00300 0+X)236 WO1856 0+0091 OM105
x(l) in aqueous phase OWOOO 0+0039 OMO14 OMOO4 O*OOOOl OWOOO
Partition coeficients for alcohol tracers
177 [
7_TT :
0' ++
f’
xx
0
x
I
1 ’ 0.1
1
1
10
Alcohol solubility in water (weight %)
‘F
X 0
1
x
1
.+.
!a
UNIFAC-wlubildy m&wd
1
I 0.1
L
Yj
1 Alcohol solubility in water (weight %)
10
Fig. 8. Partition coefficient between tetrachloroethylene and water for alcohols with two branched methyl groups at 25°C.
Fig. 10. Partition coefficient between tetrachloromethane and water for alcohols with two branched methyl groups at 25°C.
eqn (18) approxim.ates reasonably the true activity coefficients of tracers in the aqueous phase because of their low solubilities in water; the aqueous phase can be treated as pure water because of the very low solubility of the NAPLs in water (see Table 6); and the NAPL phase is much less nonideal than the aqueous phase. This probably makes the UNIFAC model applicable to infinite dilution. In other words, the paramleter table can be extended to infinite dilution with less error.
with two branched methyl groups to those measured in our laboratory. The comparisons are shown Figs 8-13. Again, it appears that the partition coefficients for these tracers can be correlated both experimentally and computationally in a linear manner versus their solubilities in water. This linear behaviour offers an alternative and valuable tool for quick selection of tracers that exhibit desired partition coefficients. For example, to locate an alcohol tracer with one branched methyl group and having a partition coefficient of 100 at 25°C and 1 atm between trichloroethylene and water, use Fig. 1 to extrapolate the calculated values (marked with crosses) to the point at which the partition coefficient is 100; the x-axis then gives us the corresponding solubility of 0.32 weight % for such an alcohol. Using these solubility data, one can easily identify a few candidate alcohols.
In case of dichlorobenzene, both the UNIFAC predictions of the partition coefficient and UNIFACsolubility method over predict the partition coefficients but the estimates using the UNIFAC-solubility method are much closer to the experimentally measured values. An important observation from these figures is that a linear relation of the logarithm of the partition coefficients of tracers to the logarithm of their solubilities in water exists folr those tracers having a similar chemical structure (i.e. the same number of the branched methyl groups). To further demonstrate this, we also compare the estimated partition coefficients for tracers
5.4 Effect of mutual solubility The partition coefficient for a tracer is usually not expected to be equal to the ratio of the tracer’s solubility in the NAPL phase to that in the aqueous phase. This is 100
lo2
1
.:: ::
/
I
i i::
‘/,ho:
10
:
-.-
i
;
.......,
n mahcd
1c
Alcohol solubility in water (weight %)
0.1
:
j
,x j,x f:
:
j : ,j: ._.:
6’ + .I .._......... ,. .g .+1...>.
;
::,.,i
X
UNIFAC-sohstilty m&cd
1
10k--------i’---------l
: :. :.
0
:
UNiFAMWbiMy
.i+:
; I
* 0.1
1 Alcohol
solubility
in water
10 (weight
%)
Fig. 9. Partition coefficient between benzene and water for
Fig. 11. Partition coefficient between octane and water for
alcohols with two bralnched methyl groups at 25°C.
alcohols with two branched methyl groups at 25°C.
P. Wang et al.
I !,,I,
I 1
/
10
1 Alcohol solubility
100
Alcohol solubility in water (weight %) Fig. 12. Partition coefficient between trichloroethane and water for alcohols with two branched methyl groups at 25°C.
because: the mutual
solubility would make each phase a mixture consisting of the compounds in another phase; and ?? the tracer may not be saturated in both phases. ??
10 in water (weight %)
100
Fig. 13. Partition coefficient between dichlorobenzene and water for alcohols with two branched methyl groups at 25°C.
To investigate this effect, we first used the UNIFAC model to calculate the mutual solubility between NAPL and aqueous phases by simultaneously solving eqn (2) and (21). Alcohol tracers were then introduced into this two-liquid-phase system (one phase is NAPL-rich and
Table 7. ym for 30 alcohol tracers from tbe UNIFAC model Toluene-water
Tracer
Dichlorobenzene-water
NMS m
Y 1,(1
Methanol Ethanol iPropano1 Propanol idutanol 2-Methyl-Zbutanol Pentanol 3-Methyl-3-pentanol 2,3-Dimethyl-2-butanol 2-Methyl-Zpentanol 4-Methyl-2-pentanol 3,3-Dimethyl-1-butanol 3,3-Dimethyl-2-butanol 3-Methyl-1-pentanol 2-Methyl-3-pentanol 2-Methyl- 1-pentanol CMethyl- 1-pentanol 3-Methyl-2-pentanol Hexanol 2-Ethyl- 1-butanol 2-Methyl-Zhexanol 3-Methyl-bhexanol 2,3-Dimethyl-3-pentanol 3-Ethyl-3-pentanol 5-Methyl-2-hexanol 3-Methyl-Zhexanol 2-Methyl-3-hexanol 4,4-Dimethyl-2-pentanol 2,2-Dimethyl-3-pentanol 2,4-Dimethyl-3-pentanol
2 8 20 20 54 139 148 382 382 382 409 382 382 409 409 409 409 409 408 409 1058 1058 1059 1058 1138 1138 1138 1059 1059 1140
NMS
MS 7TN
16.4 12.2 10-O 10.0 8.4 7.6 I.2 6.5 6.5 6-l 6.1 6.5 6.5 6.2 6.1 6.2 6.2 6.1 6.2 6.2 5.7 5.7 5.6 5.7 5.3 5.3 5.3 5.6 5.6 5.3
00 Y ,,a
2 8 20 20 54 140 149 386 387 386 414 386 387 413 414 413 413 414 412 413 1072 1072 1074 1072 1153 1153 1153 1074 1074 1155
YTN
15.6 12.0 9.8 9.8 8.3 7.5 7.0 6.4 6.4 6.4 6.0 6,4 6.4 6.0 6.0 6.0 6.0 6.0 6.1 6.0 5.5 5.5 5.5 5.5 5.2 5.2 5.2 5.5 5.5 5.2
r:
2 8 20 20 54 139 148 382 382 382 409 382 382 409 409 409 409 409 408 409 1058 1058 1059 1058 1138 1138 1138 1059 1059 1140
MS $N
12.6 4.8 4.3 4.3 3.9 3.9 3.6 3.6 3.6 3.6 3.3 3.6 3.6 3.3 3.3 3.3 3.3 3.3 3.3 3.3 3.3 3.3 3.3 3-3 3.1 3-l 3.1 3.3 3.3 3.1
m Y ,,(I
2 8 20 20 54 139 148 381 382 381 409 381 382 408 409 408 408 409 407 408 1055 1055 1057 1055 1135 1135 1135 1057 1057 1137
YTN
12.3 4.5 4.0 4-o 3.6 3.6 3.3 3.3 3.3 3.3 3.1 3.3 3.3 3.1 3.1 3.1 3.1 3.1 3.1 3.1 3.1 3.1 3.1 3.1 2.9 ;:; 3.1 3.1 2.9
MS = the mutual solubility is considered; NMS = the mutual solubility is ignored; rz = the activity coefficient of tracer in aqueous phase at infinite dilution; 77~ = the activity coefficient of tracer in NAPL phase at’infinite dilution.
8;,* F1“““‘1 Partition coeficients for alcohol tracers
lo*
179 14 13
:c?o
10’
91. $3
.? ?
12
.
11
00
10
4
1
w
0 +
0
l-1 0
UNlFAc
>
”
“NlFACp50C)
1
10
/ 0.2
0
I
7
0.4
I 0.6
I 0.8
'6 1
Mole fraction of Octane
100
Alcohol solubility in water (weight %)
Fig. 17. Partition
coefficient for hexanot between water and NAPL (PCE-TCE-octane mixture).
14. Temperature
effect on partition coefficient from for alcohols with one branched methyl group.
UNIFAC
8
lM°C\
IO>1111
Fig.
9
lo*
10’
:
j
1
j 0.1
0.1
1
“,
V.
J
Ll
12.5 12.0 11.5
7.2 7.0
6.8
‘-
/
/
6.6
/’
/
,
10.0
i 3 0. 3 2
6.2
zi 0'
ii
0
6.0
0.2
0.4
0.6
0.8
1
5.0
' B F
!’ A
a
/
/
10.5
for two systems, toluene-water and dichlorobenzenewater, which exhibit the largest mutual solubility. It appears that the mutual solubility does not have a significant effect on yoo for all the tracers. We also noticed that the mutual-solubility effect on the average molecular weight and density for both phases is negligible. Therefore, one should not expect a significant
$ z z
6.4
/
/
11.0
1
’
0.1
Molesfraction of PCE
Fig.
100 %)
coefficient between a synthetic NAPL and water for alcohols with one branched methyl group.
// / I?-_ /
(weight
Fig. 18. Partition
the other is water-rich). The infinite dilution form of the UNIFAC model was again applied to estimate the partition coefficients of the tracers. Table 6 lists the typical mutual solubilities in mole fraction between six NAPLs and water predicted using the UNIFAC model with the LLE parameter table. Table 7 shows the UNIFAC activity coefficients of thirty alcohol tracers in both NAPL and aqueous phases
13.0
10
Alcohol solubility in water
Fig. 15. Temperature effect on K-value between trichloroethylene and water for alcohols with one branched methyl group.
13.5
1
0.1
100
10
Alcohol solubility in water (weight %)
14.0
I
16. Partition coefficient for hexanol between water and NAPL (PCE and TCE mixture).
Fig. 19. Partition
Soltihty method(pureTCE)
I 1
Alcohol solubility in water
10 (weight %)
coefficient between a synthetic NAPL and water for alcohols with two branched methyl groups.
180
P. Wang et al. Table 8. Composition of a synthetic NAPL Compound Methylene chloride 1, 1,l -Trichloroethane Trichloroethane Tetrachloroethane Dodecane
effect of mutual solubility for the tracers tested.
Mole fraction 0.42 6.22 84.29 4.51 4.56
on the partition
coefficients
5.5 Temperature effect One of the assumptions of the original UNIFAC model is that the group-interaction parameters are independent of temperature and this has been shown to be a good assumption when the temperature changes less than 30”C.7 In our investigation of the temperature effect on the
partition coefficient, we kept the parameter table unchanged with temperature. The effect was taken care of by the temperature term in eqn (14) for the UNIFAC model. For the solubility method, we used the alcohol solubility at each new temperature. Figures 14 and 15 show the effect of temperature on the partition coefficients for eight alcohol tracers between trichloroethylene and water. It can be seen that the computed results using either the UNIFAC model only or the UNIFAC-solubility method are not significantly affected by the temperature variation, although a slight influence is seen on the UNIFACsolubility method. For other alcohol tracers, the changes in their partition coefficients with temperature follow the same trend as observed in Figs 14 and 15. 5.6 Prediction of partition coefficients for NAPL mixtures
In this section, we present some of the theoretical predictions of the partition coefficients for NAPL mixtures. The mutual solubility between NAPL and aqueous phases is ignored. The molecular weight and density for the NAPL phase are averaged using eqns (22) and (23). Figure 16 shows the variation of the partition coefficient of n-hexanol between a tetrachloroethylene (PCE)-trichloroethylene (TCE) mixture and water. Clearly, an almost linear relationship for both activity and partition coefficients is obtained using the UNIFAC model. Figure 17 shows the result for a NAPL consisting of three components, PCE-TCE-octane with equimolar amounts of PCE and TCE. The partition coefficient trend is almost linear, but the activity coefficient trend is not in this case. Figures 18 and 19 demonstrate the calculated partition coefficients for alcohol tracers between a
synthetic DNAPL and water. The composition of this synthetic NAPL is listed in Table 8. This composition is similar to that of a field DNAPL that we have studied. We used n-dodecane to represent the less volatile component in this NAPL. A comparison with pure TCE is also shown on Figs 18 and 19. There is very little difference between the pure TCE and the synthetic DNAPL in this case because the chemical components are quite similar. This was found to be the case for the actual field DNAPL as well. Finally, it should be noted that the VLE and LLE parameter tables for the UNIFAC model used in this work are obtained from binary equilibrium data that are not at infinite dilution. We would expect an improvement in the partition coefficient estimates using the UNIFAC model with infinite dilution parameters, which can also be obtained from our own data and this is what we plan to do next.
6 CONCLUSIONS The UNIFAC-solubility method can reasonably predict the partition coefficients for alcohol tracers when the VLE parameter table is used. The UNIFAC model with the LLE parameter table significantly overestimates the partition coefficients for most of the 30 tracers examined. A linear relation between the logarithm of the partition coefficients and the logarithm of the solubility of alcohol tracers in water was observed. Effects of temperature and the mutual solubility between NAPL and aqueous phases can be neglected over the range of 15-25°C typical of many aquifers.
REFERENCES 1. Allison, S. B., Pope, G. A. & Sepehmoori, K., Analysis of field tracers for reservoir description. J. Pet. Sci. Engng, 1991, 5, 173. 2. Annable, M. D., Rao, P. S. C., Hatfield, K. & Graham, W. D., Use of partitioning tracers for measuring residual NAPL distribution in a contaminated aquifer: preliminary results from a field scale test. Proceedings of the Second Tracer Workshop, Center for Petroleum and Geosystems Engineering, The University of Texas at Austin, November 14-15, 1994. 3. Banerjee, S., Calculation of water solubility of organic components with UNIFAC-derived parameters. Environ. Sci. Technol., 1985, 19, 369. 4. Banerjee, S. & Howard, P. H., Improved estimation of solubility and partitioning through correlation of UNIFACderived activity coefficients. Environ. Sci. Technol., 1988, 22, 839. 5. Causin, E., Rochon, J. & Marzorati, D., Field measurements of remaining oil saturation, Paper SPE/DOE 20260. Proceedings of the SPE/DOE 7th Symposium on Enhanced Oil Recovery, Tulsa, OK, April 22-25, 1990. 6. Delshad, M., Pope, G. A. & Sepehmoori, K., A
Partition coejkients for alcohol tracers compositional simulator for modeling surfactant enhanced aquifer remediation. J. Contamin. Hydrol., 23,. 303-327. 7. Dwarakanath, V., Characterization and remediation of aquifers contaminated by non-aqueous phase liquids using partitioning traces and surfactants. PhD dissertation, May 1997. 8. Fredenslund, A., Gmehling, J. & Rasmussen, P., VaporLiquid Equilibria Us&g UNIFAC-A Method. Elsevier Scientific Publishing
Group-Contribution
Company, Amster-
dam, 1977. 9. Jin, M., Surfactant enhanced remediation and interwell tracer test for characterization of aquifers contaminated by NAPLs, Ph.D. dissertation, University of Texas at Austin, August 1995. 10. Jin, M., Delshad, M., McKinney, D. C., Pope, G. A., Sepehmoori, K., Tilburg, C. & Jackson, R. E., Subsurface NAPL contamination: partitioning tracer test for detection, estimation, and remediation performance assessment. Proceedings of the Annual Meeting of the American Institute of Hydrology, April 10-13, 1994.
11. Jin, M., Delshad, M., Dwarakanath, V., McKinney, D. C., Pope, G. A., Sepehmoori, K., Tilburg, C. E. &Jackson, R. E., Partitioning tracer test for detection, estimation, and remediation performance assessment of subsurface nonaqueous phase liquids. Water Resour. Res., May 1995, 31(5), 1201. 12. Kertes, A. S. and Barton, A. F. M., Solubility Data Series: Alcohols with Water. Pergamon Press, New York, 1984.
13. Knaepen, W. A. I., Tijssen, R. & Bergen, E. A. v.d., Experimental aspects of partitioning tracer tests for residual oil saturation determination FIA-based laboratory equipment. SPE 12eser. Engng, May 1990, 239-244. 14. Lichtenberger, G. J., Field applications of interwell tracers for reservoir characterization of enhanced oil recovery pilot areas, Paper SPE 21652 presented at the Production Operations Symposium in Oklahoma City, OK, April 7-9, 1991. 15. Mackay, D. M. & Wilson, R. D., Direct detection of residual nonaqueous phase liquid in the saturated zone using SF, as a partitioning tracer. Environ, Sci. Technol., 1995, 29, 1256-1258.
181
16. Magnussen, T., Rasmussen, P. & Fredenslund, A., UNIFAC parameter table for prediction of liquid-liquid equilibria. Ind. Engng Chem. Proc. Des. Dev., 1981,20, 331. 17. Modell, M. & Reid, R. C., Thermodynamics and Its Applications.Prentice-Hall Inc., Englewood Cliffs, NJ, 1983. 18. Pope, G. A., Jin, M., Dwarakanath, V., Rouse, B. A. & Sepehrnoori, K., Partitioning tracer tests to characterize organic contaminants. Proceedings of the Second Tracer Workshop, Center for Petroleum and Geosystems Engineering, The University of Texas at Austin, November 1415, 1994. 19. Reid, R. C., Prausnitz, J. M. & Poling, B. E., The Book Properties of Gases & Liquids. McGraw-Hill Company, New York, 1988. 20. Sandler, S. I., Chemical and Engineering Thermodynamics. John Wiley & Sons, Inc., New York, 1989. 21. Tang, J. S., Interwell tracer test to determine residual oil saturation to waterllood at Judy Creek BHL ‘A’ Pool. J. Can. Petrol. Tech., 1991, 31(8), 61. 22. Tang, J. S., Partitioning tracers and in-situ fluid saturation measurements. SPE Form. Eval., March 1995, 33-39. 23. Tang, J. S. & Harker, B., Interwell tracer test to determine residual oil saturation in a gas-saturated reservoir. Part I: Theory and design. J. Can. Pet. Tech., 1991, M(3), 76. 24. Tang, J. S. & Harker, B., Interwell tracer test to determine
residual oil saturation in a gas saturated reservoir. Part II: Field applications. J. Can. Pet. Tech., 1992, M(4), 34. 25. Whitley, Jr, G. A., Pope, G. A., McKinney, D. C., Rouse, B. A. & Mariner, P. E., Vadose zone nonaqueous-phase liquid characterization using partitioning gas tracers. Proceedings of the Third International Symposium on In Situ and On-Site Bioreclamation, San Diego, CA, April
24-27, 1995. 26. Wood, K. N., Tang, J. S. & Luckasavitch, R. J., Inter-well residual oil saturation at Leduc miscible pilot, Paper SPE 20543. Proceedings of the 65th SPE Annual Technical and Exhibition, New Orleans, LA, Sept. 23-26, 1990. 27. Zemel, B., Tracers in the Oil Field, Developments in Petroleum Science, 43, Elsevier Science, New York, 1995.
ELSEVIER
Advances in Warer Resources 21, No. 2, pp. 171-181, 1998 Copyright 0 1997 Elsevier Science Limited Printed in Great Britain. All rights reserved 0309-1708/98/517.00+0.00
Partition coefficients for alcohol tracers between nonaqueous-phase liquids and water from UNIFAC-solubility method Peng Wang, Varrldarajan Dwarakanath,
Bruce A. Rouse, Gary A. Pope & Kamy Sepehrnoori
Centre for Petroleum and Geosystems Engineering, The University of Texas at Austin, Austin, TX 78712, USA
(Received 9 October 1995; accepted 11 June 1996) In this work, we have applied a group-contribution activity-coefficient model, UNIFAC, and the solubility of alcohols in water to estimate partition coefficients for alcohol tracers between water and nonaqueous-phase liquids (NAPLs). The elects of temperature and mutual solubility between NAPL and aqueous phases on the estimation of partition coefficients were also investigated. By comparing the estimated results with experimental partition coefficients for 30 alcohol tracers between 10 NAPLs and water, we found that: i) the UNIFAC-solubility method, in which the UNIFAC model in its infinite-dilution form is applied to the NAPL phase and the solubility of tracers in water is used for estimation of the activity coefficient in the aqueous phase, works better than the UNIFAC model; ii) a linear relation between the logarithm of partition coefficients and the logarithm of tracer solubility in water is observed for those tracers having a similar chemical structure (i.e. the same number of branched methyl groups). This can serve as a meful tool for quick selection of the tracers that exhibit the desired partition coefficients; iii) the effect of mutual solubility between NAPL and aqueous phases can be neglected because such miscibility is very small, usually of the order of 10e3 mole/mole unit; and iv) temperature variation between 15”and 25°C does nlot significantly affect partition coefficients. Copyright 0 1997 Elsevier Science Limited Key wora!s: partition coefficients. alcohol tracer, NAPL, interwell tracer, UNIFAC.
1 INT.RODUCTION
that exhibit the desired partition coefficients’. We have made measurements on several common pure NAPLs such as trichloroethylene (TCE)7. However, most NAPLs are mixtures of many hydrocarbon and/or chlorocarbon components, and it would be very useful to have a method to predict the approximate partition coefficients for these mixtures to minimize the number of measurements required to select the appropriate tracers as well as for other purposes such as preliminary modeling of the aquifer test with compositional fluid flow models such as UTCHEM6 and subsequently inverse modeling to infer the saturations and composition of the field NAPL. Such a predictive model can also he used to help spot experimental errors. Finally, in some cases a sample of NAPL cannot be obtained from the field and yet it is useful to design a partitioning tracer test for the purpose of attempting to locate the NAPL. In such cases, an approximate composition of the NAPL can often be calculated from the contaminant concentrations in
The partitioning tracer technique has been successfully applied in the following two areas: ??
characterizing
residual saturations of oil in oilfield
reser~oir8;1,‘,14,21,22,24,26 ??
detecting and characterizing nonaqueous- hase P liquids (NAPL) in the subsurface.2~‘0~‘1~15~1812
An accurate determination of the partition coefficient for the partitioning tracer is one of the keys to the success of these applications. The partition coefficient is defined as the ratio of its concentration in a nonaqueous phase to its concentration in the aqueous phase. A reliable way of obtaining this partition coefficient is through laboratory experiments. This may be costly, time-consuming, and dilficult to conduct.13~20~27 Usually, for a given NAPL, several experiments with different tracers need to be performed to select several tracers 171
P. Wang et al.
172
water samples taken from the aquifer. Thus, the main objective of this work was to develop a thermodynamic model that is capable of predicting the partition coefficient for a wide range of partitioning alcohol tracers.
2 DEFINITION
OF PARTITION
COEFFICIENTS
The partition coefficient for a chemical component between NAPL and aqueous phases is defined as
i
XYN
K+i,
(1) 1
where Cy and Ct are the concentrations of component i in NAPL and aqueous phases, respectively, in units of moles per unit volume. When such a system is in thermodynamic equilibrium (liquid-liquid equilibrium), we can write the following equation for component i: ryxy
= yfxf,
(4
where 7; and 7” are the activity coefficients and xr and x4 are the mole fractions for component i in NAPL and aqeuous phases, respectively. Using eqn (2), eqn (1) may be rewritten as K, = ?4MAPN ’
$QppA
3.1 UNIFAC model The UNIFAC model employs a group-contribution concept in which each compound is considered as a collection of basic functional groups. Thus, a mixture of compounds is viewed as a mixture of these functional groups, and mixture properties are computed using functional group properties and their interactions. It is also assumed that any pair of the functional groups interacts in the same manner regardless of the presence of any other groups (i.e. for a given pair of groups the same value of interaction parameter is used). These features make this model one of the few predictive models available for estimation of the activity coefficients for each of the components in a polar mixture. In computing Tiyi,the UNIFAC model assumes that the logarithm of the activity coefficient is the sum of two contributions: lnyi = lny,C + lny”,
(4)
where superscript C denotes the combinatorial contribution coming from differences in size and shape of the compounds in the mixture, while superscript R stands for the residual part resulting from energy interactions. The combinatorial term is evaluated from
(3)
where M is molecular weight and p is density (g/cm3). Superscript A denotes the aqueous phase, while superscript N denotes the NAPL phase. When applying eqn (3) to tracers (which are very dilute components in solution), Ti becomes an infinite dilution activity coefficient, ry.
3 MODEL ESTIMATION Many models can be used to estimate activity coefficients at infinite dilution. However, groundwater contamination consists of a wide range of nonpolar and polar chemical components and strictly speaking, the calculation of partition coefficients for tracers in this work needs to be done through liquid-liquid equilibrium calculations. This limits the number of applicable models. A group-contribution model, UNIFAC, was used in this work because of its predictive capability and its power of handling both vapor-liquid and liquid-liquid equilibria for a large number of strongly polar chemical components. This model has been used by others for the estimation of octanol-water partition coefficients.3’4 As most of the alcohol tracers for groundwater application are at low concentrations, the applicability of the solubility of these tracers in water for the estimation of their activity coefficients in aqueous phase was also investigated.
where Bi is the molecular surface area fraction component i and is defined as
for
and $i is the molecular volume fraction for component i, which is computed from ++. c
rjqj
j=l
The van der Waals surface area, qi, and volume, ri, for molecule i are calculated from *s
ri =
c
v;Rk
k=l
(8) k=l
where v; means the number of group k in molecule i. Qk and RR are the surface area and volume for group k, which have been tabulated by Reid et aLI8 The average coordination number, z in eqn (5) is usually taken to be 10, and the parameter li is computed from li =
c(ri - qi) L
(ri - 1).
173
Partition coe#cients for alcohol tracers
The residual term in eqn (4) is computed from ln7” = ~7J(lnrt
- lnl?;),
(10)
be eliminated without a significant loss of accuracy of the above equation. So eqn (17) can be further simplified as
k=l
where the residual activity coefficient of group k is estimated from lnrk
If the solubility of tracer in water is small, this equation provides a reasonable estimate of 7:.
=
1
r
4 MUTUAL SOLUBILITY BETWEEN NAPL AND WATER where 0, is the surface area fraction of group m and is calculated from em=
,“,Qm . CQ
xn
(12)
n
?I=1
Some of the NAPL components may be partially miscible with water under aquifer conditions. When this occurs, the NAPL phase will contain a certain amount of water and the aqueous phase will contain some of the NAPL components. For a binary mixture, the thermodynamic criterion for this phase-splitting to happen can be written as
The mole fraction of group m in mixture, X,,,, is defined as
(13)
in eqn (11) is given by The parameter Xk’nm
(14)
*\E,, = exp(-F).
where a”,,, represents ,the interaction energy between groups m and n and is correlated using binary phase equilibrium data.7
(19) where g” is the molar excess Gibbs energy of the mixture and is easily computed using the UNIFAC model. Model1 and ReidI also give an expression for liquidliquid phase separation for multicomponent mixtures. If eqn (19) shows that the phase-splitting for a mixture at a given temperature and pressure is going to occur, we then simultaneously solve the following equations for the compositions of the two coexisting liquid phases:
N
N
c
3.2 Solubility method
RT
XI lnyixi
+x2 lncY2x2.
When such a mixture is saturated, equation should be satisfied:
(15) the following
i=l
lnrixi
-1nr2x2-1>=0.
1
(17)
If alcohol is used as a tracer, the last two terms may
XN - 1 = 0.
(21)
The UNIFAC model is again used in this work to compute the activity coefficients for each component in both NAPL and aqueous phases in eqn (20). The average molecular weights and densities for both phases used in eqn (3) are calculated using the following mixing rules: M = 2XiMi
Substituting eqn (15) into the above equation for alcohol (component l:)-water (component 2) binary mixtures and using the Gibbs-Duhem relation, the following equation results:
c
i=l
i=l
For a binary single-phase mixture, the molar Gibbs free energy of mixing may be written as Ag” -=
and
x:-1=0
(22)
N
c P=
XiMi
i=l
(23)
Nx& c i=l
Pi
because the UNIFAC density information.
model does not give us any
174
P. Wang et al. Table 1. Partition coefficients for alcohols between several DNAPLs
Alcohol Ethanol Iso-propanol Pentanol @-AmyI) 2-Methyl-Zbut. (r-amyl) Hexanol 2-Methyl- 1-pentan 3-Methyl-1-pentanol 2-Methyl-Zpentanol 3-Methyl-2-pentanol 4-Methyl- 1-pentanol 2-Methyl-3-pentanol 4-Methyl-Zpentanol 3-Methyl-3-pentanol 2-Ethyl-1-butanol 2,3-Dimethyl-2-butanol 3,3-Dimethyl-2-butanol 3,3-Dimethyl-1-butanol 3-Methyl-3-hexanol 2-Methyl-3-hexanol 3-Methyl-Zhexanol 2-Methyl-Zhexanol 5-Methyl-2-hexanol 3-Ethyl-3-pentanol 4,4-Dimethyl-2-pentanol 2,3-Dimethyl-3-pentanol 2,2-Dimethyl-3-pentanol PCE = tetrachloroethylene; TCM = tricholoromethane
and water at 25°C
PCE
TCE
TCA
CTET
TCM
DCB
0.0 0.0
0.0
0.1 0.1 3.1 0.7 15.2 11.6 9.7 5.1 8.2 12.8 9.7 7.4 4.4 10.8 4.4 8.9 6.7 20.6 35.4 42.2 21.8 39.8 23.9 37.6 23.8 45.1
0.0 0.0
0.3 1.1 10.8 3.1 51.5 36.7 41.2 19.7 32.5 58.9 32.6 30.2 18.3 37.3 16.4 31.5 25.9 68.3 81.2 70.1 554.1 99.2
0.0
0.1 3.8 1.3 18.6 14.5 12.8 6.3 11.3 16.0 13.2 10.2 4.5 13.0 6.3 9.6 9.5 27.9 43.2 56.9 28.1 55.3 31.9 51.3 29.0 80.2
1.4 0.4 6.8 5.4 4.7 2.6 6.2 5.7 5.2 3.8 2.2 9.6 2.8 4.5 3.8 11.8 20.0 19.2 10.9 17.1 13.9 22.6 12.3 26.4
1.9 0.9 11.0 7.8 6.5 3.4 5.9 8.5 7.7 5.1 3.3 7.5 3.3 6.5 4.1 15.9 29.8 30.0 16.1 30.4 17.1 24.7 17.6 39.1
TCE = trichloroethylene; TCA = 1, 1,l -tricholoethane; (chloroform); DCB = dichlorobenze.
81.6 292.5
CTET = carbon tetrachloride;
Table 2. Partition coefficients for five alcohols between TCE and water at 25°C
Alcohol i-Butanol 4-Methyl-2-pentanol 2-Methyl-3-pentanol 2-Ethyl-1-butanol 5-Methyl-2-hexanol
Exp K-value 0.8 10.2 13.2 13.0 55.3
UNIFAC(LLE) 1.22 12.82 12.82 12.82 41.50
UNIFAC(VLE) 1.31 13.73 13.73 13.73 44.56
Table 3. Partition coetlicients for five alcohols between benzene and water at 25°C
Alcohol i-Butanol 4-Methyl-2-pentanol 2-Methyl-3-pentanol 2-Ethyl-1-butanol 5-Methyl-Zhexanol
Exp K-value 1.2 7.9 9.8 11.6 41.5
UNIFAC(LLE) 6.87 28.27 28.27 28.18 103.18
UNIFAC(VLE) 1.91 15.33 15.33 15.33 49.30
Table 4. Partition coefficients for five alcohols between toluene and water at 25°C
Alcohol i-Butanol 3-Methyl-Zpentanol 4-Methyl- I-pentanol 2-Ethyl-1-butanol 5-Methyl-Zhexanol
Exp K-value O-6 9.4 11.4 10.2 34.7
UNIFAC(LLE) 1.09 22.01 22.01 22.01 81.20
0.1 2.2 0.7 13.2 9.0 8.4 3.4 6.0 9.2 7.1 4.9 3.2 7.7 3.0 5.8 4.4 14.4 23.8 29.3 14.9 33.7 16.4 22.1 15.8 32.4
UNIFAC(VLE) 1.62 11.22 11.22 11.22 36.12
Partition coeficients for alcohol tracers ‘l’able 5. Partition coefficients for five alcohols between decane and water at 25°C
Alcohol
Exp K-value
UNIFAC(LLE)
UNIFAC(VLE)
0.2 1.9 2.7 2.4 7.2
1.22 12.79 12.79 12.79 41.50
0.27 2.80 2.80 2.80 8.70
i-Butanol 3-Methyl-1-pentanol 4-Methyl-1-pentanol 2-Ethyl-1-butanol S-Methyl-2-hexanol
X
_. Alcohol solubility in water Fig.
UNIFAC-sdubolttymethod
0.1
1 Alcohol solubility
(weight %)
Partition coefficient between TCE and water for alcohols with one branched methyl group at 25°C.
1.
10 (weight %)
100
Fig. 3. Partition coefficients between tetrachloromethane and water for alcohols with 1 branched methyl group at 25°C.
ld
T
s
.
in water
0
E.V
+
UNIFAC I
$10’
2
.:
100 Alcohol solubility in water
(weight
%)
5 RESULTS AND DISCUSSION The UNIFAC model and the solubility method were used to estimate the partition coefficients for 30 alcohol tracers between 10 NAPLs and water and compared to the values measured in our laboratory. An infinitedilution form of the UNIFAC model was used hecause the concentration of tracers in the experiments was on the order of lOOOmg/l. The solubility of these alcohols in water was obtained from.” 5.1 Experimental measurements
experiments
conducted
were
static
or
1
0.1
i
_-L
1
0.1 Alcohol
Fig. 2. Partition coefficient between benzene and water for alcohols with one branched methyl group at 25°C.
The
8 s ._ .z a”
batch
solubility
10 in water
(weight
100 %)
Fig. 4. Partition coefficient between decane and water for alcohols with one branched methyl group at 25°C. equilibrium partition coefficient tests’. A lOm1 aliquot of a lOOOmg/l aqueous standard was placed in a separatory funnel with 10 ml of the NAPL. The samples were thoroughly shaken, allowed to separate for 1 h and re-shaken. This was repeated twice to ensure that the samples were at equilibrium. The samples were then allowed to separate for at least 12 h, were drained into centrifuge tubes and centrifuged at approximately IOOOg for 1 h to allow a complete separation of the phases to occur. Three aqueous aliquots on duplicate aqueous samples were then analyzed with a gas chromatograph for a total of six measurements of the alcohol concentrations in the aqueous phase. The
P. Wang et al.
176
1 o*
I
;
I
y-
I
L
i
E
.
E .$
s ..% a” E 8
.
10’
-r
++ (81
X
r
0 0 ;
e
IFAC IIFAC-solutnl+~method
I d
10 Alcohol solubility in water
(weight
Alcohol solubility in
%)
water (weight %)
Partition coefficient between chloroform and water for alcohols with one branched methyl group at 25°C.
Fig. 7. Partition coefficient between dichlorobenzene and water for alcohols with one branched methyl group at 25°C.
concentration of alcohol in the NAPL is then calculated from a mass balance on the sample. A summary of partition coefficients between these alcohol tracers and several common DNAPLs (dense nonaqueous phase liquids) is presented in Table 1. These measured partition coefficients were then compared to partition coefficients estimated using the UNIFAC-solubility method.
Both the VLE and LLE parameter tables available today in the literature are generated using binary equilibrium data in which components are not in dilute concentrations. Some degree of deviation from the experimental partition coefficients (measured at infinite dilution) is therefore observed. Surprisingly, the UNIFAC model with the LLE parameter table systematically overestimates the partition coefficients significantly, while the model with the VLE parameter table generally gives better predictions.
Fig.
5.
5.2 UNIFAC with VLE and LLE parameter tables As stated earlier, the estimations covered in this work belong to liquid-liquid equilibrium calculations. The UNIFAC model was, therefore, first used with the group-interaction parameter table that was correlated from binary liquid-liquid equilibrium (LLE) data.16 Some typical estimated partition coefficients using the UNIFAC model with this parameter table are shown in Tables 2-5. The calculations were repeated using a parameter table from binary vapor-liquid equilibrium (VLE) data.**19The results are also given in Tables 2-5 for comparison. For these calculations, the mutual solubility between the NAP1 and aqueous phases was ignored; its effect will be discussed later. -
. .
I
0
m
+
UNIFAC
Alcohol solubility
5.3 UNIFAC-solublllty method In this method, we only apply the UNIFAC model to compute the activity coefficients for tracers in the NAPL phase. The solubility data are used to estimate the tracer activity coefficients in the aqueous phase. Again, the partial miscibility between NAPL and aqueous phases is neglected. The estimated results using this method are shown in Figs 1-7, in which the partition coefficients of tracers are plotted versus their solubilities in water using loglog scales. From these figures it can be seen that the UNIFAC-solubility method works better than the UNIFAC model for estimation of the partition coefficients. The trend of increasing partition coefficients with decreasing solubility of the alcohols in water is better predicted using the UNIFAC-solubility method. This is because of the following reasons: Table 6. Mutual solubiity between NAPL(1) end water(t) from UNIFAC at 25°C NAPL
I
in water (weight %)
Fig. 6. Partition coefficient between tetrachloroethane and water for alcohols with one branched methyl group at 25°C.
Trichloroethylene Benzene Toluene Dichlorobenzene n-Octane n-Decane
x(2) in NAPL phase O+rOO80 0*00300 0+X)236 WO1856 0+0091 OM105
x(l) in aqueous phase OWOOO 0+0039 OMO14 OMOO4 O*OOOOl OWOOO
Partition coeficients for alcohol tracers
177 [
7_TT :
0' ++
f’
xx
0
x
I
1 ’ 0.1
1
1
10
Alcohol solubility in water (weight %)
‘F
X 0
1
x
1
.+.
!a
UNIFAC-wlubildy m&wd
1
I 0.1
L
Yj
1 Alcohol solubility in water (weight %)
10
Fig. 8. Partition coefficient between tetrachloroethylene and water for alcohols with two branched methyl groups at 25°C.
Fig. 10. Partition coefficient between tetrachloromethane and water for alcohols with two branched methyl groups at 25°C.
eqn (18) approxim.ates reasonably the true activity coefficients of tracers in the aqueous phase because of their low solubilities in water; the aqueous phase can be treated as pure water because of the very low solubility of the NAPLs in water (see Table 6); and the NAPL phase is much less nonideal than the aqueous phase. This probably makes the UNIFAC model applicable to infinite dilution. In other words, the paramleter table can be extended to infinite dilution with less error.
with two branched methyl groups to those measured in our laboratory. The comparisons are shown Figs 8-13. Again, it appears that the partition coefficients for these tracers can be correlated both experimentally and computationally in a linear manner versus their solubilities in water. This linear behaviour offers an alternative and valuable tool for quick selection of tracers that exhibit desired partition coefficients. For example, to locate an alcohol tracer with one branched methyl group and having a partition coefficient of 100 at 25°C and 1 atm between trichloroethylene and water, use Fig. 1 to extrapolate the calculated values (marked with crosses) to the point at which the partition coefficient is 100; the x-axis then gives us the corresponding solubility of 0.32 weight % for such an alcohol. Using these solubility data, one can easily identify a few candidate alcohols.
In case of dichlorobenzene, both the UNIFAC predictions of the partition coefficient and UNIFACsolubility method over predict the partition coefficients but the estimates using the UNIFAC-solubility method are much closer to the experimentally measured values. An important observation from these figures is that a linear relation of the logarithm of the partition coefficients of tracers to the logarithm of their solubilities in water exists folr those tracers having a similar chemical structure (i.e. the same number of the branched methyl groups). To further demonstrate this, we also compare the estimated partition coefficients for tracers
5.4 Effect of mutual solubility The partition coefficient for a tracer is usually not expected to be equal to the ratio of the tracer’s solubility in the NAPL phase to that in the aqueous phase. This is 100
lo2
1
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10
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.......,
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Alcohol solubility in water (weight %)
0.1
:
j
,x j,x f:
:
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;
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UNIFAC-sohstilty m&cd
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: :. :.
0
:
UNiFAMWbiMy
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; I
* 0.1
1 Alcohol
solubility
in water
10 (weight
%)
Fig. 9. Partition coefficient between benzene and water for
Fig. 11. Partition coefficient between octane and water for
alcohols with two bralnched methyl groups at 25°C.
alcohols with two branched methyl groups at 25°C.
P. Wang et al.
I !,,I,
I 1
/
10
1 Alcohol solubility
100
Alcohol solubility in water (weight %) Fig. 12. Partition coefficient between trichloroethane and water for alcohols with two branched methyl groups at 25°C.
because: the mutual
solubility would make each phase a mixture consisting of the compounds in another phase; and ?? the tracer may not be saturated in both phases. ??
10 in water (weight %)
100
Fig. 13. Partition coefficient between dichlorobenzene and water for alcohols with two branched methyl groups at 25°C.
To investigate this effect, we first used the UNIFAC model to calculate the mutual solubility between NAPL and aqueous phases by simultaneously solving eqn (2) and (21). Alcohol tracers were then introduced into this two-liquid-phase system (one phase is NAPL-rich and
Table 7. ym for 30 alcohol tracers from tbe UNIFAC model Toluene-water
Tracer
Dichlorobenzene-water
NMS m
Y 1,(1
Methanol Ethanol iPropano1 Propanol idutanol 2-Methyl-Zbutanol Pentanol 3-Methyl-3-pentanol 2,3-Dimethyl-2-butanol 2-Methyl-Zpentanol 4-Methyl-2-pentanol 3,3-Dimethyl-1-butanol 3,3-Dimethyl-2-butanol 3-Methyl-1-pentanol 2-Methyl-3-pentanol 2-Methyl- 1-pentanol CMethyl- 1-pentanol 3-Methyl-2-pentanol Hexanol 2-Ethyl- 1-butanol 2-Methyl-Zhexanol 3-Methyl-bhexanol 2,3-Dimethyl-3-pentanol 3-Ethyl-3-pentanol 5-Methyl-2-hexanol 3-Methyl-Zhexanol 2-Methyl-3-hexanol 4,4-Dimethyl-2-pentanol 2,2-Dimethyl-3-pentanol 2,4-Dimethyl-3-pentanol
2 8 20 20 54 139 148 382 382 382 409 382 382 409 409 409 409 409 408 409 1058 1058 1059 1058 1138 1138 1138 1059 1059 1140
NMS
MS 7TN
16.4 12.2 10-O 10.0 8.4 7.6 I.2 6.5 6.5 6-l 6.1 6.5 6.5 6.2 6.1 6.2 6.2 6.1 6.2 6.2 5.7 5.7 5.6 5.7 5.3 5.3 5.3 5.6 5.6 5.3
00 Y ,,a
2 8 20 20 54 140 149 386 387 386 414 386 387 413 414 413 413 414 412 413 1072 1072 1074 1072 1153 1153 1153 1074 1074 1155
YTN
15.6 12.0 9.8 9.8 8.3 7.5 7.0 6.4 6.4 6.4 6.0 6,4 6.4 6.0 6.0 6.0 6.0 6.0 6.1 6.0 5.5 5.5 5.5 5.5 5.2 5.2 5.2 5.5 5.5 5.2
r:
2 8 20 20 54 139 148 382 382 382 409 382 382 409 409 409 409 409 408 409 1058 1058 1059 1058 1138 1138 1138 1059 1059 1140
MS $N
12.6 4.8 4.3 4.3 3.9 3.9 3.6 3.6 3.6 3.6 3.3 3.6 3.6 3.3 3.3 3.3 3.3 3.3 3.3 3.3 3.3 3.3 3.3 3-3 3.1 3-l 3.1 3.3 3.3 3.1
m Y ,,(I
2 8 20 20 54 139 148 381 382 381 409 381 382 408 409 408 408 409 407 408 1055 1055 1057 1055 1135 1135 1135 1057 1057 1137
YTN
12.3 4.5 4.0 4-o 3.6 3.6 3.3 3.3 3.3 3.3 3.1 3.3 3.3 3.1 3.1 3.1 3.1 3.1 3.1 3.1 3.1 3.1 3.1 3.1 2.9 ;:; 3.1 3.1 2.9
MS = the mutual solubility is considered; NMS = the mutual solubility is ignored; rz = the activity coefficient of tracer in aqueous phase at infinite dilution; 77~ = the activity coefficient of tracer in NAPL phase at’infinite dilution.
8;,* F1“““‘1 Partition coeficients for alcohol tracers
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7
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I 0.6
I 0.8
'6 1
Mole fraction of Octane
100
Alcohol solubility in water (weight %)
Fig. 17. Partition
coefficient for hexanot between water and NAPL (PCE-TCE-octane mixture).
14. Temperature
effect on partition coefficient from for alcohols with one branched methyl group.
UNIFAC
8
lM°C\
IO>1111
Fig.
9
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for two systems, toluene-water and dichlorobenzenewater, which exhibit the largest mutual solubility. It appears that the mutual solubility does not have a significant effect on yoo for all the tracers. We also noticed that the mutual-solubility effect on the average molecular weight and density for both phases is negligible. Therefore, one should not expect a significant
$ z z
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coefficient between a synthetic NAPL and water for alcohols with one branched methyl group.
// / I?-_ /
(weight
Fig. 18. Partition
the other is water-rich). The infinite dilution form of the UNIFAC model was again applied to estimate the partition coefficients of the tracers. Table 6 lists the typical mutual solubilities in mole fraction between six NAPLs and water predicted using the UNIFAC model with the LLE parameter table. Table 7 shows the UNIFAC activity coefficients of thirty alcohol tracers in both NAPL and aqueous phases
13.0
10
Alcohol solubility in water
Fig. 15. Temperature effect on K-value between trichloroethylene and water for alcohols with one branched methyl group.
13.5
1
0.1
100
10
Alcohol solubility in water (weight %)
14.0
I
16. Partition coefficient for hexanol between water and NAPL (PCE and TCE mixture).
Fig. 19. Partition
Soltihty method(pureTCE)
I 1
Alcohol solubility in water
10 (weight %)
coefficient between a synthetic NAPL and water for alcohols with two branched methyl groups.
180
P. Wang et al. Table 8. Composition of a synthetic NAPL Compound Methylene chloride 1, 1,l -Trichloroethane Trichloroethane Tetrachloroethane Dodecane
effect of mutual solubility for the tracers tested.
Mole fraction 0.42 6.22 84.29 4.51 4.56
on the partition
coefficients
5.5 Temperature effect One of the assumptions of the original UNIFAC model is that the group-interaction parameters are independent of temperature and this has been shown to be a good assumption when the temperature changes less than 30”C.7 In our investigation of the temperature effect on the
partition coefficient, we kept the parameter table unchanged with temperature. The effect was taken care of by the temperature term in eqn (14) for the UNIFAC model. For the solubility method, we used the alcohol solubility at each new temperature. Figures 14 and 15 show the effect of temperature on the partition coefficients for eight alcohol tracers between trichloroethylene and water. It can be seen that the computed results using either the UNIFAC model only or the UNIFAC-solubility method are not significantly affected by the temperature variation, although a slight influence is seen on the UNIFACsolubility method. For other alcohol tracers, the changes in their partition coefficients with temperature follow the same trend as observed in Figs 14 and 15. 5.6 Prediction of partition coefficients for NAPL mixtures
In this section, we present some of the theoretical predictions of the partition coefficients for NAPL mixtures. The mutual solubility between NAPL and aqueous phases is ignored. The molecular weight and density for the NAPL phase are averaged using eqns (22) and (23). Figure 16 shows the variation of the partition coefficient of n-hexanol between a tetrachloroethylene (PCE)-trichloroethylene (TCE) mixture and water. Clearly, an almost linear relationship for both activity and partition coefficients is obtained using the UNIFAC model. Figure 17 shows the result for a NAPL consisting of three components, PCE-TCE-octane with equimolar amounts of PCE and TCE. The partition coefficient trend is almost linear, but the activity coefficient trend is not in this case. Figures 18 and 19 demonstrate the calculated partition coefficients for alcohol tracers between a
synthetic DNAPL and water. The composition of this synthetic NAPL is listed in Table 8. This composition is similar to that of a field DNAPL that we have studied. We used n-dodecane to represent the less volatile component in this NAPL. A comparison with pure TCE is also shown on Figs 18 and 19. There is very little difference between the pure TCE and the synthetic DNAPL in this case because the chemical components are quite similar. This was found to be the case for the actual field DNAPL as well. Finally, it should be noted that the VLE and LLE parameter tables for the UNIFAC model used in this work are obtained from binary equilibrium data that are not at infinite dilution. We would expect an improvement in the partition coefficient estimates using the UNIFAC model with infinite dilution parameters, which can also be obtained from our own data and this is what we plan to do next.
6 CONCLUSIONS The UNIFAC-solubility method can reasonably predict the partition coefficients for alcohol tracers when the VLE parameter table is used. The UNIFAC model with the LLE parameter table significantly overestimates the partition coefficients for most of the 30 tracers examined. A linear relation between the logarithm of the partition coefficients and the logarithm of the solubility of alcohol tracers in water was observed. Effects of temperature and the mutual solubility between NAPL and aqueous phases can be neglected over the range of 15-25°C typical of many aquifers.
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