185
8. MODEL TESTING
In order to test the model, calculations will be compared with experimental
data at conditions of interest for the users of the model. There exists a large
number of experimental data in the literature on solubilities at 25ºC at 1 atm.
However, the amount of solubility data for salts at high pressures and
temperatures in electrolyte solutions, is often very limited. In many cases, the
calculations will therefore be compared with data in one published paper
only.
8.1
Solubility of pH independent salts
8.1.1 NaCl
The solubility of NaCl in pure water and various electrolytes have been
investigated by several authors. Some of the published data are compared
with calculations in Fig. 8.1. The solubility of NaCl is predicted accurately in
the temperature range of practical interest.
186
11
Linke
Potter
Pitzer
Calculated
2
NaCl (mole/kgH O)
10
9
8
7
6
0
50
100
150
200
o
Temperature ( C)
250
300
Fig. 8.1. Solubility of NaCl in pure water. Data from Linke [1], Potter et
al.[2] and Pitzer et al.[3].
Clynne et al.[4] measured the solubility of NaCl in aqueous solutions
containing KCl, CaCl2 or MgCl2. The result are compared with calculations in
Figs. 8.2-8.4. The agreement between the measurements and model
calculations are within 2% for the KCl and MgCl2 solutions and for the CaCl2
solution up to 0.68 molal. For CaCl2 with higher concentrations, up to 1.85
molal, the error can be as high as 9%.
6.4
KCl
6
0.706m
2
NaCl (mole/kgH O)
6.2
5.8
5.6
1.492m
5.4
2.37m
5.2
5
4.8
0
20
40
60
o
Temperature ( C)
80
100
Fig. 8.2. Solubility of NaCl in solutions containing various concentrations of
KCl. Experimental data from Clynne et al.[4].
187
6.5
CaCl
6
2
0.184m
2
NaCl (mole/kgH O)
5.5
0.678m
5
4.5
1.228m
4
3.5
1.846m
3
2.5
0
20
40
60
o
Temperature ( C)
80
100
Fig. 8.3. Solubility of NaCl in solutions containing various concentrations of
CaCl2. Experimental data from Clynne et al.[4].
6
MgCl
2
0.552m
1.160m
2
NaCl (mole/kgH O)
5
4
1.854m
3
2
2.652m
1
0
0
20
40
60
o
Temperature ( C)
80
100
Fig. 8.4. Solubility of NaCl in solutions containing various concentrations of
MgCl2. Experimental data from Clynne et al. [4].
8.1.2 Anhydrite (CaSO4) and Gypsum (CaSO4⋅2H2O )
The calculated solubility of gypsum and anhydrite in pure water is compared
with literature data in Fig. 8.5. The solubility of anhydride is well described
in the whole temperature region, while there seems to be an overestimation of
188
the solubility of gypsum at temperature higher than 100ºC. The intersection
between the gypsum and the anhydrite solubility is 41ºC. This means that at
temperature below 41ºC, gypsum is the thermodynamic stable phase, and
above 41ºC, anhydrite is stable. It is, however, well known, that due to the
kinetics of the precipitation reactions, gypsum may be the initially
precipitating phase at temperatures much higher than 41ºC. The limit of 41ºC
is for the solubility of CaSO4 in pure water. In electrolyte solutions, this
transition temperature may vary because of variation in the water activity.
High ionic strengths gives lower water activity causing gypsum to be less
stable and the transition temperature is reduced.
M arshall
Bock
P osnjak
Hall
Booth
P artridge
Calculated
20
4
2
CaSO (m m ol/kgH O)
25
Gypsum
15
10
5
Anhydrite
0
0
50
100
150
200
o
Tem perature ( C)
250
300
Fig. 8.5. The solubility of gypsum and anhydrite in pure water as function of
temperature. Data from Marshall and Slusher [5], Bock [6], Posnjak
[7], Hall et al.[8], Booth and Bidwell [9] and Partridge and White
[10].
The solubility of gypsum in NaCl solutions is shown in Fig. 8.6. There is a
good fit between the calculated solubility and the literature data. The
solubility of gypsum at 25 and 70ºC is almost similar, see Fig. 8.5, but the
effect of increasing NaCl concentration at the two temperatures is different, at
least at high concentrations.
189
CaSO *2H O (m m ole/KgH O)
60
Gypsum
2
Gypsum
2
CaSO *2H O (m m ole/KgH O)
60
o
50
25 C
40
30
4
20
10
70 C
40
30
2
M arshall
Ostroff
Block
Calculated
20
4
2
M arshall
Bock
Tanji
Calculated
o
50
0
10
0
0
1
m
2
NaC l
3
4
(m ole/kgH O)
2
5
6
0
1
m
2
NaC l
3
4
(m ole/kgH O)
5
6
2
Fig. 8.6. Solubility of Gypsum in NaCl solutions at 25 and 70ºC. Data from
Marshall and Slusher [5], Bock [6], Tanji [11], Ostroff and Metler
[12] and Block and Waters [13].
The calculated solubility of Anhydrite in NaCl solutions at various
temperatures are compared with literature data in Fig. 8.7. Note the difference
in the y-axis at 25ºC and the other temperatures. There is a good fit between
the calculated and experimental solubility at 25ºC. At 100ºC, the calculated
solubility is within the experimental uncertainties. It is, however, reasonable
to believe that the data of Block and Waters [13] at 100ºC are too high since
also the solubility in pure water is to high. If so, the calculated Anhydrite
solubility is higher than the experimental at both 100 and 150ºC in the region
1-3 mole/kgH2O NaCl. At 200ºC, the calculated solubility is significantly
higher than the measured.
190
30
50
40
20
15
4
CaSO
CaSO
4
30
20
Bock
Calculated
10
10
B lock
Calculated
0
0
1
m
2
NaCl
3
4
(m ole/kgH O)
5
6
0
1
2
30
m
2
NaCl
3
4
(m ole/kgH O)
5
6
2
30
Anhydrite
200°C
25
2
25
(m m ole/K gH O)
Anhydrite
150°C
2
(m m ole/K gH O)
Blount
5
0
20
20
15
4
15
4
10
Marshall
CaSO
CaSO
Anhydrite
100°C
25
2
(m m ole/K gH O)
Anhydrite
25°C
60
2
(m m ole/K gH O)
70
Blount
5
Calculated
10
Marshall
Blount
5
Calculated
0
0
0
1
m
2
NaCl
3
4
(m ole/kgH O)
2
5
6
0
1
m
2
NaCl
3
4
(m ole/kgH O)
5
6
2
Fig. 8.7. Solubility of Anhydrite in NaCl solutions at 25, 100, 150 and
200ºC. NB! Note the different y-axis at 25ºC. Literature data from:
Bock [6], Blount [18] and Block and Waters [13].
Several attempts have been made to model the solubility of CaSO4 in NaCl
solutions in the literature. The mixed electrolyte Pitzer parameters used to
calculate the CaSO4 solubility in this work is more or less based on the Pitzer
parameters obtained by Harvie et al.[14] who investigated the Na-K-Mg-CaSO4-Cl-H2O system at 25ºC. Main electrolyte parameters are from Pitzer
[15]. Møller [16] investigated the Na-Ca-Cl-SO4-H2O system in the
temperature range 25-250ºC. The parameters obtained by Møller are,
however, different from the parameters given by Harvie et al. Møller also
included the association complex CaSO D4 to improve the calculations. Using
the parameters given by Møller, a very good fit between measurements and
191
calculations was obtained at 200ºC. However, when the “Møller-parameters”
were used at lower temperatures, 25-100ºC, the solubilities of Gypsum and
Anhydrite in NaCl solutions were overestimated by ≈11%.
Fig. 8.8 shows the solubility of Gypsum at 25ºC in Na2SO4, CaCl2 and MgCl2
solutions. The solubility in Na2SO4 and MgCl2 solutions is well represented,
even at high concentrations. For CaCl2 solutions the only data found are those
from Tanji [11] up to 0.05 molar solutions. For this range, there is good
agreement between the measured and calculated solubility.
70
CaSO *2H O (m m ole/kgH O)
Gypsum
25 C
20
15
2
10
4
Block
Hill
Tanji
Calculated
5
0
Gypsum
25°C
60
M gCl
2
50
40
2
o
30
4
2
2
C aSO *2H O (m m ole/KgH O)
25
20
CaCl
10
Tanji
Linke
C alcu lated
2
0
0
0.5
m
Na2SO4
1
1.5
(m ole/kgH O)
2
2
0
0.5
1
1.5
Concentration (m ole/kgH O)
2
2
Fig. 8.8. Solubility of Gypsum in Na2SO4, CaCl2 and MgCl2 solutions. Data
from: Block and Waters [13], Hill and Wills [17], Tanji [11] and
Linke [1].
8.1.3 BaSO4
The solubility of barite in pure water is shown in Fig. 8.9. As can be seen
from the figure, the solubility is very low, less than 1.8⋅10-5 mole/kg⋅H2O.
This means that the ionic strength in the BaSO4-H2O system is very low, and
deviation from ideality is well represented by the Debye-Hückel limiting law.
A consequence is that varying Pitzer parameters have very little effect on the
calculated solubility.
192
Blount
Tem pleton
Linke
Calculated
0.015
2
(m m ol/kgH O)
0.02
BaS O
4
0.01
0.005
0
0
50
100
150
200
Tem perature (°C)
250
300
Fig. 8.9. The solubility of barite in pure water as function of temperature.
Data from: Blount [18], Templeton [19] and Linke [1].
The solubility of Barite in NaCl solutions is shown in Fig. 8.10. There is good
fit between the calculated and measured solubilities up to 80ºC. At 150ºC the
calculated solubility seems to be overestimated. A further investigation of the
data indicates that the solubilities reported by Blount [18] are too low. Fig.
8.11 shows the solubility of Barite in 2 and 4 molal NaCl solutions versus
temperature. It is a shift in the solubility from the data of Templeton [19] to
the data of Blount [18] at 100ºC. This explains why the calculations in Fig.
8.10 fits the data of Templeton, but overestimates the barite solubility relative
to the data of Blount.
193
Tem pleton
Blount
Calculated
0.6
BaS O
4
2
(m m ole/kgH O)
0.7
150°C
0.5
0.4
80°C
0.3
50°C
0.2
25°C
0.1
0
0
1
2
m
3
4
5
6
NaCl
Fig. 8.10. Solubility of Barite in NaCl solutions. Data from: Templeton [19]
and Blount [18].
4m
0.8
Shift in solubility
0.6
BaSO
2m
Data from
Templeton
4
(m m ol/kgH2O)
1
0.4
Data from
Blount
0.2
0
0
50
100
150
200
Tem perature (°C)
250
300
Fig. 8.11. Solubility of BaSO4 versus temperature in solutions containing 2
(lower curve) and 4 (upper curve) molal NaCl. Data from:
Templeton [19] and Blount [18].
194
8.1.4 SrSO4
The calculated solubility of celestite in pure water is shown in Fig. 8.12. The
celestite solubility is small, less than 6.6⋅10-4 mole/kg⋅H2O. This means that
the ionic strength in the SrSO4-H2O system is very low and the deviation
from ideality is well described by the Debye-Hückel limiting law. Variations
in the Pitzer parameters will therefore have small effects on the calculated
solubility.
Reardon
Strubel
Kohlraush
Booth
Howell
Calculated
0.6
S rS O
4
2
(mm ole/kgH O)
0.7
0.5
0.4
0.3
0.2
0.1
0
0
50
100
150
200
o
Tem perature ( C)
250
300
Fig. 8.12. The solubility of celestite in pure water as function of temperature.
Literature data from Reardon and Armstrong [20], Strubel [21],
Kohlraush [22], Booth [9], Howell et al.[23].
Fig. 8.13 shows the solubility of Celestite in NaCl solution. The calculated
solubilities agrees well with literature data at 25 and 50ºC, but at higher
temperatures the calculated solubility is higher than the measured.
195
6
6
SrSO
(m m ole/K gH O)
5
4
3
2
1
4
Brow er
How el
Reardon
Strubel
Calculated
SrSO
4
SrSO
4
0
1
m
2
NaC l
3
4
(m ole/kgH O)
5
3
2
How ell
Strubel
Calculated
1
0
1
2
m
2
NaCl
3
4
(m ole/kgH O)
5
6
2
6
5
SrSO
4
(m m ole/K gH O)
SrSO
5
4
150°C
2
100°C
2
(m m ole/K gH O)
4
6
6
4
3
4
2
SrSO
4
4
50°C
0
0
SrSO
5
2
25°C
2
(m m ole/KgH O)
SrSO
Strubel
Calculated
1
0
4
3
2
How ell
Calculated
1
0
0
1
2
m
NaCl
3
4
(m ole/kgH O)
2
5
6
0
1
2
m
NaCl
3
4
(m ole/kgH O)
5
6
2
Fig. 8.13. Solubility of Celestite in NaCl solutions. Data from: Brower and
Renault [24], Howell et al. [23], Reardon and Armstrong [20] and
Strubel [21].
The solubility of the pH dependent minerals CaCO3, FeCO3 and FeS will be
discussed in Chapter 8.4.
8.2
Gas fugacity
The fugacity coefficients are calculated with the Equation Of State. At high
pressures and low temperatures, there will be a substantial deviation from
ideal behaviour in the gas phase. This will again have a direct influence on
the calculated gas solubility. Fig. 8.14 shows the fugacity coefficients of the
water soluble hydrocarbons (CH4, CO2 and H2S) versus pressure at some
selected temperatures. There is excellent agreement between the calculated
196
fugacity coefficients and the reference values from Angus et al.[25,26]
(IUPAC tables) and Starling [27]
307°C
247°C
197°C
1.1
147°C
1
97°C
0.9
0.8
47°C
4
CH fugacity coefficient
1.2
17°C
0.7
0.6
200
300
400
Pressure (bar)
307°C
247°C
0.8
197°C
147°C
0.6
97°C
0.4
0.2
500
600
1
0.8
304°C
260°C
0.6
204°C
0.4
149°C
2
47°C
2
C0 fugacity coefficient
1
100
H S fugacity coefficient
0
17°C
0
93°C
0.2
49°C
15.5°C
4.4°C
0
0
100
200
300
400
Pressure (bar)
500
600
0
100
200
300
400
Pressure (bar)
500
600
Fig. 8.14. Fugacity coefficient of CO2, H2S and CH4 versus pressure for
selected temperatures. Data for CO2 and CH4 from Angus et al.
[25,26]. Data for H2S from Starling [27].
8.3
Gas solubility
8.3.1 Solubility of CO2
The solubility of CO2 in water and different electrolytes has been investigated
in several works during the century. It is, however, very difficult to measure
the CO2 solubility for several reasons; 1) CO2 dissociates and it is necessary
to separate between CO2 and the dissociation products, 2) it has to be
197
measured as function of both temperature and pressure, 3) it is necessary to
correct for non ideal behaviour of the gas phase. The solubility of CO2 in pure
water at relatively low pressures is shown in Fig. 8.15. Very good agreement
between the calculated and measured solubilities is observed.
0.8
2
CO (m ole/kgH2O)
0.7
Carroll
Aylw ard
Calculated
0.6
0.5
10 bar
0.4
5 bar
0.3
1.013 bar
0.2
2 bar
0.1
0
0
20
40
60
80
100
120
Tem perature (°C)
140
160
Fig. 8.15. Solubility of CO2 in pure water versus temperature at different
pressures. The given pressures are total pressures and the CO2
pressure is given by: PCO2 = Ptot − PH 2O . Data are from: Carroll et al.
[28] and Aylward and Findlay [29].
Fig. 8.16 shows the CO2 solubility in pure water at pressures up to 700 bar.
Again there is good agreement between measured and calculated solubilities.
Fig. 8.17 shows the CO2 solubility at 160 and 198ºC at pressures up to 100
bar. At 160ºC, the calculated solubility is in good agreement with the data of
Carroll et al.[28], but at both 160ºC and 198ºC the calculated solubilities are
systematically lower than the solubilities given by Nighswander et al.[32].
198
2
2
CO
0.5
0
(m ole/kgH2O)
W iebe 40°C
W iebe 50°C
W iebe 75°C
W iebe 100°C
Prutton 101°C
Calculated
1.5
1
2
1
CO
1.5
2
(m ole/kgH2O)
120°C
Carroll
Prutton
Nighsw ander
Calculated
0.5
0
0
100
200
300
400
500
Pressure (bar)
600
700
0
100
200
300
400
500
Pressure (bar)
600
700
Fig. 8.16. Solubility of CO2 in pure water versus pressure at different
temperatures. The pressure is the total pressures and the CO2
pressure is given by: PCO2 = Ptot − PH 2O . Data are from Wiebe [30],
Prutton and Savage [31], Carroll et al.[28] and Nighswander et
al.[32].
0.8
Nighsw ander 160°C
Nighsw ander 198°C
Carroll 160°C
Calculated
0.6
0.5
160°C
0.4
0.3
CO
2
(m ole/kgH2O)
0.7
198°C
0.2
0.1
0
0
20
40
60
Pressure (bar)
80
100
Fig. 8.17. Solubility of CO2 in pure water versus pressure at 160 and 198ºC.
Data are from Nighswander et al.[32] and Carroll et al.[28].
199
The solubility of CO2 in some electrolytes is shown in Fig. 8.18. The
agreement between calculated and measured data is good up to 4-6 molar
solution at both 25 and 90ºC.
0.035
Yasunishi
M alinin
He
Calculated
0.025
CO
25°C
P =1.013 bar
0.02
tot
0.015
2
(m ole/kgH2O)
0.03
0.01
0.005
90°C
0
0
1
2
3
4
NaCl (m ole/kgH2O)
Yasunishi
He
Calculated
25°C
(m ole/kgH2O)
0.025
P =1.013 bar
tot
0.02
0.01
M alinin
0.025
Calculated
25°C
P =1.013 bar
0.02
tot
0.015
2
0.015
0.005
Yasunishi
0.03
CO
(m ole/kgH2O)
0.03
2
6
0.035
0.035
CO
5
0.01
0.005
90°C
0
0
0
1
2
M gCl
2
3
4
(m ole/kgH2O)
5
6
0
1
2
C aCl
2
3
4
(m ole/kgH2O)
5
6
Fig. 8.18. Solubility of CO2 in NaCl, MgCl2 at CaCl2 solutions at 25 and 90ºC
and 1.013 bar total pressure. Data from Yasunishi and Yoshdia
[33], Malinin and Savelyeva [34] and He and Morse [44].
8.3.2 Solubility of CH4
The solubility of CH4 in natural waters has been investigated by Duan et al.
[35]. Over 1700 measurement published this century was used to determine
the Henrys law constant and Pitzer parameters in the system CH4-H2O-Na-KCa-Mg-Cl-SO4. Fig. 8.19 shows a comparison between calculated CH4
solubility in pure water and NaCl solutions compared with solubilities
reported by Duan et al. Note that the solubility at 90ºC is lower than the
solubility at 30ºC.
200
1
210°C
30°C
4
2
150°C
1.5
270°C
1
210°C
4
1.5
0.5
1 m ole/kgH O NaCl
2
270°C
CH solubility (m ole/kgH O)
2
Pure w ater
2
CH solubility (m ole/kgH O)
2
0.5
30°C
150°C
90°C
90°C
0
0
0
200
400
600
Pressure (bar)
800
1000
0
400
600
Pressure (bar)
800
1000
6 m ole/kgH O NaCl
0.7
2
2
CH solubility (m ole/kgH O)
0.8
4 m ole/kgH O NaCl
270°C
0.6
0.5
0.4
210°C
4
0.3
30°C
0.2
150°C
0.1
2
0.6
30°C Exp
30°C Calculated
0.5
270°C
0.4
0.3
4
0.7
2
CH solubility (m ole/kgH O)
0.8
200
210°C
0.2
150°C
0.1
90°C
30°C
90°C
0
0
0
200
400
600
Pressure (bar)
800
1000
0
200
400
600
Pressure (bar)
800
1000
Fig. 8.19. Solubility of CH4 in pure water and NaCl solutions at different
temperatures. The pressure is the total pressure: PCH 4 + PH 2O Data
are from Duan et al.[35]. The lines are calculated
8.3.3 Solubility of H2S
Compared with the CO2–H2O and CH4-H2O systems, there are few published
solubility data for H2S-H2O system. For the solubility of H2S in electrolyte
solutions, only data for NaCl solutions are found. The solubility of H2S in
water is 3 times higher than the CO2 solubility at 25ºC. H2S is a polar
compound and it is therefore considerable deviations from ideality even in the
pure H2S-H2O system when the H2S concentration is high. Fig. 8.20 compares
calculated and measured solubilities as functions of temperature and pressure.
Good agreement is observed. Fig. 8.21 compares the calculated and measured
201
solubility of H2S in NaCl solutions. The agreement is satisfactory, though at
80ºC it seems as if the calculated solubilities are somewhat high.
2.5
0.25
Pure w ater
0.2
H S (m ole/kgH2O)
Barrett
Carroll
Calculated
P =1.013 bar
0.15
tot
71°C
2
30°C
120°C
1.5
180°C
1
2
0.1
2
H S (m ole/kgH2O)
Pure w ater
0.5
0.05
Lee and M ather
Calculated
0
0
0
20
40
60
Tem perature (°C)
80
100
0
10
20
30
40
50
Total pressure (bar)
60
70
Fig. 8.20. Solubility of H2S in pure water. The H2S pressure is given by
PH 2 S = PTot − PH 2O in both graphs. Data are from Barrett et al.[36]
and Carroll and Mather [37] and Lee and Mather [38].
0.1
25°C
0.06
0.04
60°C
2
H S (m ole/kgH2O)
0.08
PH 2 S = PTot − PH 2O
80°C
0.02
0
0
1
2
3
4
NaCl (m ole/kgH2O)
5
6
Fig. 8.21. Solubility of H2S in NaCl solutions at 25, 60 and 80ºC and 1.013
bar total pressure. Data are from Barrett et al.[36]. Lines are
calculated.
202
8.4
Solubility of the pH dependent minerals: CaCO3, FeCO3 and FeS
It is far more complicated to model the solubility of these minerals than the
solubility of the sulphates because it is necessary to simultaneously model all
the equilibria in the carbonate/sulphide systems. This also includes pH
calculations. Since the mineral solubilities in some cases are strongly
dependent on the CO2/H2S activities it was necessary first to check that that
the solubilities of these gases were correctly modelled. This was done in
Chapter 8.3.1. Secondly, it is necessary to calculate pH in carbonate/sulphide
solutions. In Chapter 7 it was shown that the present model is capable of
calculating pH with an accuracy of typically ±0.05 pH unit, also at very high
pressures, temperatures and ionic strengths.
8.4.1 pH in carbonate solutions
Plummer and Busenberg [39] have measured pH in solutions containing HCl,
K2CO3 and CaCl2. Some of the experimental data are compared with
calculations in Table 8.1. The agreement is within 0.02 pH units.
Table 8.1. Measured and calculated pH in solutions containing HCl, K2CO3
and CaCl2. Experimental data from Plummer and Busenberg [39].
*
Temperature (ºC)
HCl*
K2CO3*
CaCl2*
5
25
40
60
80
2.737
2.737
2.739
2.754
2.744
2.621
2.689
2.62
2.649
2.621
3.221
3.051
3.833
3.237
3.529
pH
pH
Measured Calculated
9.794
9.027
9.47
9.052
8.979
9.799
9.042
9.4651
9.048
8.985
: The concentrations are given as –log(molality).
Plummer and Busenberg also measured CaCO3 (calcite) solubilities in pure
water at temperatures from 0 to 90ºC. Unfortunately, the measurements are
not made at constant CO2 pressures or CO2 pressures defined by the total
203
pressure and the vapour pressure. A graphical comparison is therefore
difficult, and the measurements are compared with calculations in Table 8.1.
There is very good agreement between the pH calculated by Plummer and
Busenberg and the pH calculated with the present model. The deviation is less
than 0.02 pH units in the temperature range 0-90ºC. The calculated CaCO3
solubilities are, however, on an average 5.6% too low.
Table 8.2. Calcite solubility in pure water.
Temperature
(ºC)
0.1
10.0
25.0
45.0
73.0
89.7
PCO 2
(atm)
0.9892
0.9720
0.9478
0.8849
0.6382
0.3082
Total Ca2+ Calculated pH
(mmol/kgH2O Plummer and
Busenberg[39]
)
Plummer [39]
14.37
11.93
9.10
6.22
3.325
1.92
6.060
6.033
6.016
6.029
6.134
6.363
Calculated
Ca2+
This model
Calculated pH
This model
13.42
11.16
8.527
5.897
3.198
1.819
6.062
6.038
6.020
6.027
6.121
6.334
8.4.2 Solubility of CaCO3
Fig. 8.22 shows the solubility of CaCO3 i pure water versus CO2 pressure at
75, 100, 125, 150 and 200ºC. There is good agreement between the measured
and calculated solubilities for all temperatures and pressures except at 75ºC
for CO2 pressures above 15 bar where the calculated solubility is up to 22%
higher than the measured data. Fig. 8.23 shows the solubility of CaCO3 in
pure water versus temperature at different CO2 pressures. The agreement
between calculated and measured data are good except at temperatures above
200ºC at 62 bar CO2 pressure where the calculated solubilities seem to be too
high.
204
15
75°C
10
100°C
CaCO
3
(m m ole/kgH2O)
20
125°C
5
150°C
200°C
0
0
10
20
30
40
50
CO pressure (bar)
60
70
80
2
Fig. 8.22. Solubility of CaCO3 in pure water versus CO2 pressure at various
temperatures. All the data are from Segnit et al.[40].
8
1 atm
4 atm
12 atm
62 atm
Calculated
CaCO
3
(m m ole/kgH2O)
7
6
5
4
3
2
1
0
100
150
200
Temperature (°C)
250
300
Fig. 8.23. Solubility of CaCO3 in pure water versus temperature at different
CO2 pressures. All the data are from Ellis [41].
205
Fig. 8.24 shows the solubility of CaCO3 in NaCl and KCl solutions at 10, 25
and 60ºC compared with experimental data from Wolf et al.[42]. Wolf et al.
measured both the alkalinity and the total Ca2+ concentration. The total
alkalinity will be twice the CaCO3 solubility since CaCO3 is the only alkaline
source, (see Chapter 5). In Fig. 8.24, both solubility measured as total
calcium and total alkalinity are shown. There is good agreement between
measured and calculated solubilities, except for the data at 10ºC in solutions
containing more than 3 molal KCl
4
10°C
3
25°C
10°C
4
25°C
3
2
60°C
3
2
60°C
CaCO
CaCO
(m m ole/kgH2O)
5
3
(m m ole/kgH2O)
5
1
0
1
0
0
1
2
3
4
N aCl (m ole/kgH2O)
5
6
0
1
2
3
4
KCl (m ole/kgH2O)
5
6
Fig. 8.24. Solubility of CaCO3 in NaCl and KCl solutions at 10, 25 and 60ºC.
All the data are from Wolf et al.[42]. The open symbols give
solubilities from measurements of total calcium while the full
symbols are from alkalinity measurements. PCO2 = 1atm − PH 2O
Fig. 8.25 shows a comparison of calculated and measured CaCO3 solubilities
at temperatures above 100ºC at 12 bar CO2 pressure in NaCl solutions. There
is good agreement between calculated and measured solubilities, at least up to
250ºC. In 0.5 and 1 molal NaCl solutions, the calculated solubilities increases
at temperatures above 250ºC. This is probably not correct. The reason may be
incorrect Pitzer parameters which have been extrapolated from data below
100ºC.
206
15
CO2
=12atm
Pure w ater
0.2M NaCl
0.5M NaCl
1.0M NaCl
Calculated
10
3
CaCO (m m ole/kgH2O)
P
5
0
100
150
200
Temperature (°C)
250
300
Fig. 8.25. Solubility of CaCO3 in water containing 0-1 molar NaCl versus
temperature at 12 bar CO2. Data are from Ellis [43].
He and Morse [44] have measured the CaCO3 solubility in synthetic
formation waters. The water compositions are given in Table 8.3. They report
solubility as both total Ca2+ and as total alkalinity. Calculated solubilities are
compared with experimental data in Fig. 8.26. For the two Colbey waters,
good agreement between measured and calculated solubilities are observed.
In these waters, there is good agreement between the solubilities measured as
total calcium and those obtained from the total alkalinity. For the Kennedy
water, however, there is large differences in the CaCO3 solubilities measured
with the two methods. The reason is probably that the amount of calcium in
the synthetic formation water is ≈500 times higher than the amount of
dissolved CaCO3 at 25ºC. An error of only 0.2% in the analysed calcium
concentration will therefore give an error of 100% in the CaCO3 solubility.
The alkalinity analysis is, however, not influenced by the large calcium
concentration and is expected to be more accurate. The solubilities obtained
from alkalinity measurements agree well with the calculated solubility.
207
Table 8.3. Composition of synthetic formation waters from He and Morse
[44]. Concentrations are given in mole/kgH2O.
Water
Na+
K+
Ca2+
Mg2+
Cl-
SO 24−
Colbey 12
Colbey 18
Kennedy 1
1.103
1.592
3.438
0.012
0.019
0.132
0.040
0.023
0.655
0.010
0.175
0.037
1.137
1.915
4.954
0.0387
0.0457
0.0
CaCO
3
(m m ole/kgH 2O)
2.5
Kennedy 1
2+
2
From e tot Ca
From A
T
Calculated
1.5
1
0.5
0
0
25
50
75
90
Tem perature (°C)
20
25
Colbey 18
(m m ole/kgH2O)
2+
From tot Ca
From A
15
T
Calculated
CaCO
CaCO
2+
From tot Ca
From A
20
T
Calculated
15
10
3
10
3
(m m ole/kgH2O)
Colbey 12
5
0
5
0
0
20
40
60
Tem perature (°C)
80
100
0
20
40
60
Tem perature (°C)
80
100
Fig. 8.26. Solubilities of CaCO3 in synthetic formation waters at 1 atm total
pressure. The water compositions are given in Table 8.3 and the
experimental data are from He and Morse [44].
208
G reenberg and Tom son
Calculated
2
(2.990)
Pure w ater
1.5
(2.867)
1
FeCO
Pure w ater
30°C
4
3
Sm ith
Calculated
3
(2.624)
(2.508)
0.5
0
FeCO
(3.053)
3
(m m ole/kgH2O)
2.5
(m m ole/kgH2O)
8.4.3 Solubility of FeCO3
The available data for the solubility of FeCO3 are limited to temperatures
below 100ºC and low pressures. Fig. 8.27 shows a comparison of
experimental and calculated solubilities in pure water. Fig. 8.28 shows a
comparison of experimental and calculated solubilities in various electrolyte
solutions.
2
1
25
43
62
Tem perature (°C)
83
94
0
5
10
15
20
25
CO pressure (bar)
30
35
2
Fig. 8.27. Solubility of FeCO3 in pure water. The CO2 pressure is given in
parenthesis above each column. Data from Greenberg and Tomson
[45] and Smith [46].
Fig. 8.27 shows relatively good agreement between the measured and the
calculated solubilities. Fig. 8.28 shows that most of the calculated solubilities
in electrolyte solutions are on an average 10% lower than the experimental
data given by Bardy and Péré [47].
Bardy
Calculated
2
(m m ole/kgH2O)
1
FeCO
4
(0.86)
(0.97)
3
(0.84)
FeCO
Bardy
Calculated
4
(1.03)
3
(0.91)
2
(1.29)
(0.89)
(0.91)
3
(0.87)
(0.92)
3
(m m ole/kgH2O)
209
0
1
0
0.01
0.05
0.1
0.2
NaCl (m ole/kgH2O)
0.4
0.0033
0.0167
0.033
0.067
M gCl (m ole/kgH2O)
2
(m m ole/kgH2O)
1
FeCO
(0.81)
(0.85)
3
(0.84)
FeCO
(0.93)
Bardy
Calculated
4
(0.92)
(0.85)
3
(0.83)
(0.78)
2
3
(0.90)
3
(m m ole/kgH2O)
(0.68)
Bardy
Calculated
4
0.133
2
0
1
0
0.0033
0.0167
0.0333
0.0667
Na SO (m ole/kgH2O)
2
4
0.1333
0.0025
0.0125
0.025
0.05
M gSO (m ole/kgH2O)
0.1
4
Fig. 8.28. Solubility of FeCO3 in various electrolyte solutions at 20ºC. The
CO2 pressure is given in parenthesis above the column. All the data
are from Bardy and Pèrè [47].
8.4.4 Solubility of FeS
The amount of data for the solubility of FeS is very limited. Table 8.4 shows
a comparison between solubility data given by Berner [48] and calculation
with the present model. In distilled water, there is very good agreement
between the model and experimental data. In the KCl solution, however, the
solubility given by Berner is almost 6 times larger than the solubility in pure
water. This large increase in solubility by adding only 0.01 m KCl to the
water is not reasonable compared to the effect of ionic strength on other
minerals. The corresponding increase in CaCO3 solubility is only 1.05 times.
210
He has also found that the pH in the KCl solution is lower which is not
reasonable since the alkalinity is higher. The calculated solubility in the KCl
solution is only 1.2 times larger than in distilled water.
Experimental solubility data at higher temperatures and in other electrolyte
solutions have not been found.
Table 8.4. Solubility of FeS at 25ºC under 1 atm H2S pressure.
System
Fe2+
(mole/kgH2O)
Berner [48]
pH
Berner [48]
Fe2+
(mole/kgH2O)
This model
pH
This model
Distilled water
7.36⋅10-5
4.26
7.23⋅10-5
4.276
-5
3.97
8.88⋅10-5
4.30
0.01 m KCl
42.5⋅10
The data from Berner are average data of 3 different measurements in distilled water and 2
measurements in the KCl solution.
8.5
Prediction of PvT behaviour
To test the PvT predictions of the present model, calculated phase equilibria
can be compared to experimental multicomponent phase equilibrium data.
Unfortunately, such data have not been found in the literature. The PvT model
will therefore be compared to PvT reports obtained from Norwegian oil
companies.
A reprint of two PvT reports from two North Sea oil fields are given in
Appendix G. Oilfield A is a typical heavy oil while oilfield B is a very light
oil or a condensate system.
211
8.5.1 PvT predictions with oil from Oilfield A
The oil analysis is given in Appendix G, section G.1.1. After grouping, the
input composition of the flashed oil was:
-----------------------------------------------------------Compound
Liquid
Gas
Temperature: 20ºC
mole%
mole%
Pressure
: 1 bar
---------------------------------GOR
: 100.8
CO2
0.00
1.02
H2S
0.00
0.00
Bubblepoint: 130.8 bar
CH4
0.13
56.91
at: 99ºC
C2
1.99
28.27
C5
14.73
12.96
C8
28.71
0.84
+frac
54.44
0.00
Density of liquid oil: 837.00 kg/M3
------------------------------------------------------------
The result from a single point flash calculation to the flash analysis conditions
gave:
SINGLE POINT FLASH CALCULATION AT:
TEMPERATURE:
PRESSURE
:
20.00 C
1.00 bar
AMOUNT OF GAS:
4.19 mole
AMOUNT OF OIL:
4.92 mole
GAS FRACTION :
0.46
GAS COMPRESSIBILITY:
0.99
*********************************************************************
OIL PHASE
GAS PHASE
X
FUG
Y
FUG
K=Y/X
*********************************************************************
CO2
0.00017
58.17150
0.00993
0.99650
58.37598
H2S
0.00000
16.75579
0.00000
0.99361
16.86348
CH4
0.00259
217.50811
0.56379
0.99943
217.63300
C2
0.00811
36.08657
0.29479
0.99223
36.36923
C5
0.14584
0.87897
0.13144
0.97526
0.90127
C8
0.00193
0.01998
0.00004
0.95755
0.02086
C10
0.00272
0.00181
0.00001
0.94606
0.00192
C16
0.00729
0.00000*
0.00000
0.91144
0.00000
C20
0.01404
0.00000*
0.00000
0.88834
0.00000
C32
0.10032
0.00000*
0.00000
0.81730
0.00000
C44
0.71700
0.00000*
0.00000
0.74211
0.00000
H2O
0.00000
4.55787
0.00000
0.99310
4.58955
*********************************************************************
1.0000
1.0000
212
*********************************************************************
“FUG” is the fugacity coefficient. *: The fugacity coefficients are not zero, but very small
Table 8.5 shows a comparison between calculated and measured phase
compositions of the lightest hydrocarbons. There is very good agreement
between the measured and the calculated gas phase composition. For the
liquid phase, the error is 50% for the lightest hydrocarbons. The solubility of
the lightest hydrocarbons in the stabilised oil is, however, very small, and
good agreement could not be expected. The calculated concentration of C5 in
the liquid phase agrees well with the measured.
Table 8.5. Measured and calculated phase composition at oil flash analysis,
20ºC and 1bar, for oil A given in Appendix G. Data as mole%.
Oil
Gas
Component
Exp
Calc
Exp
Calc
CO2
CH4
C2
C5
0.00
0.13
1.99
14.73
0.02
0.26
0.81
14.58
1.02
56.91
28.27
12.96
0.99
56.38
29.48
13.14
GOR can be calculated from the above results and data from Appendix G.
VGas =
VOil =
N Gas ZRT 4.19 ⋅ 0.99 ⋅ 8.314 ⋅ 293.15
= 0.1011m 3
=
5
P
1 ⋅ 10
N Oil M Oil
GOR =
ρ
=
4.92 ⋅ 194.3 ⋅ 10 −3
= 1.142 ⋅ 10 −3
837
3
VGas
0.1011m 3
=
= 88.5 m 3
−3
3
m
VOil 1.142 ⋅ 10 m
The calculated GOR is only 12% lower than the measured.
(8.1)
(8.2)
(8.3)
213
8.5.2 PvT predictions with oil from Oilfield B
There are several ways to enter the oil data for Oilfield B. It is possible to
enter the recombined reservoir fluid, or it is possible to use the data from the
flash. In the calculation example below, it was decided to use the measured
data only instead of any recombined data. When an oil sample from the
separator was flashed, the GOR was 8.2 and the phase composition given
below was measured. Since the oil is in equilibrium with gas at the separator,
it must be at its bubblepoint. The bubblepoint conditions used for tuning of
the +fraction was therefore set equal to the separator conditions. The gas
phase on the separator was entered as a free gas phase. The input data were:
Oil analysis: Appendix G
-----------------------------------------------------------Oil data at analysis conditions:
GOR
:
8.20 M3/M3
Temperature: 20.00 C
Pressure
:
1.00 bar
Compound
Liquid
Gas
mole%
mole%
-----------------------------------------------------------CO2
0.00
4.26
H2S
0.00
0.00
CH4
0.03
54.13
C2
1.55
30.90
C5
13.27
10.09
C8
39.76
0.62
+frac
45.39
0.00
Density of liquid oil: 805.00 kg/M3
-----------------------------------------------------------A free gasphase is added. GLR=
1600.00 M3/M3
GLR measured at: 1.00 bar
and
: 20.00 C
-----------------------------------------------------------CO2 :
3.44 mole%
H2S :
0.00 mole%
CH4 : 85.14 mole%
C2 :
9.24 mole%
C5 :
1.89 mole%
214
C8 :
0.30 mole%
------------------------------------------------------------
The results from the calculations was:
SINGLE POINT FLASH CALCULATION AT:
TEMPERATURE:
29.00 C
PRESSURE
:
9.30 bar
AMOUNT OF GAS:
65.69 mole
AMOUNT OF OIL:
4.81 mole
GAS FRACTION :
0.93
GAS COMPRESSIBILITY:
0.98
*********************************************************************
OIL PHASE
GAS PHASE
X
FUG
Y
FUG
K=Y/X
*********************************************************************
CO2
0.00445
7.46764
0.03438
0.96728
7.72027
H2S
0.00000
2.26996
0.00000
0.95211
2.38414
CH4
0.03914
21.50276
0.85311
0.98649
21.79732
C2
0.02350
3.76185
0.09345
0.94612
3.97607
C5
0.14257
0.10711
0.01779
0.85831
0.12480
C8
0.32157
0.00284
0.00118
0.77468
0.00366
C10
0.23746
0.00029
0.00010
0.72483
0.00041
C16
0.12392
0.00000
0.00000
0.59266
0.00000
C20
0.08003
0.00000
0.00000
0.51686
0.00000
C32
0.02155
0.00000
0.00000
0.33457
0.00000
C44
0.00580
0.00000
0.00000
0.20366
0.00000
H2O
0.00000
0.58442
0.00000
0.95777
0.61018
*********************************************************************
1.0000
1.0000
*********************************************************************
The calculated phase compositions are compared to the measured
compositions in Table 8.6. The agreement between the calculated and
measured gas phase composition is very good. The agreement for the liquid
phase is better this time. The reason is that this system is a gas condensate
system and the composition of the stabilised oil is lighter. The concentration
215
of methane in the liquid oil phase is 3.6 mole% compared to the last example
where it was only 0.13 mole%.
Table 8.6. Measured and calculated phase composition at separator. Data are
given as mole%.
Oil
Component
Exp
CO2
CH4
C2
C5
C8
0.28
3.61
3.49
13.06
37.17
Gas
Calc
Exp
Calc
0.445 3.441 3.438
3.914 85.135 85.311
2.350 9.236 9.345
14.257 1.892 1.779
32.157 0.296 0.118
From the amount of gas and oil, the calculated GOR at the separator,
recalculated to 1 bar and 20ºC is:
VGas =
VOil =
N Gas ZRT 65.69 ⋅ 0.98 ⋅ 8.314 ⋅ 293.15
=
= 1.569m 3
P
1 ⋅ 10 5
N Oil M Oil
GOR =
ρ
=
4.81 ⋅ 163.9 ⋅ 10 −3
= 1.008 ⋅ 10 −3
782
3
VGas
1.569m 3
=
= 1556 Sm 3
3
−3
m
VOil 1.008 ⋅ 10 m
(8.4)
(8.5)
(8.6)
The calculated GOR is 1556 Sm3/m3 which is only 3% lower than the
measured GOR of 1600 Sm3/m3.
8.6
References Chapter 8
216
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