Experimental and modelling study of the solubility of CO2 in various CaCl2 solutions at different temperatures and pressures
The Journal of Supercritical Fluids.
Experimental and modelling study of the solubility of CO in various CaCl solutions at 2 2 different temperatures and pressures
Alireza Bastami 1 2
Mohammad Allahgholi 1 2
Peyman Pourafshary 0 1
0 Institute of Petroleum Engineering, School of Chemical Engineering, Faculty of Engineering, University of Tehran, Now with Department of Petroleum and Chemical Engineering, Sultan Qaboos University
1 China University of Petroleum (Beijing) and Springer-Verlag Berlin Heidelberg 2014
2 Institute of Petroleum Engineering, School of Chemical Engineering, Faculty of Engineering, University of Tehran
Study of the thermodynamic behaviour of CaCl2-H2O-CO2 systems is important in different H2O-CO2 is a common system in CO2 also appears as the spent acid. Hence, study of the behaviour of this system and the solubility of CO2 in CaCl2 brine in different thermodynamic conditions is critical. In this study, CO2 solubility in 0, 1.90 and 4.80 mol/L CaCl2 solutions at 328.15 to 375.15 K and 68.9 to 206.8 bar were measured. These values are normal for oil reservoirs. A popular thermodynamic model is available in the literature for estimating the CO2 solubility in pure water and NaCl solutions. In 2 as well. Based on the measured data, the component interaction parameters in the base model were adjusted for a CaCl2-H2O-CO2 system. The developed model could predict CO2 solubility in different conditions improvement is up to 65% better than in the base model. This model can be used in Darcy scale models
Solubility of CO2-CaCl2 solubility measurement
In recent years some researchers have been paying
attention to environmental issues such as CO2 capture
and geological storage in deep saline aquifers or depleted
hydrocarbon reservoirs. Consequently, CO2 solubility in
pure water and brine has been widely studied. A variety of
of CO2 in brine, especially with NaCl, has been accomplished.
Since the major salt in aquifers is NaCl, the CO2-H2O-NaCl
a limited number of studies of the solubility of CO2 in other
electrolyte solutions. A detailed description of the available
2 in different
electrolyte solutions is presented by Springer et al (2012). The
main purpose of these studies is the estimation of the soluble
CO2 mole fraction in pure or saline water.
The CaCl2-H2O-CO2 system is a common compositional
(HCl) is one of the most common acids used during carbonate
2, water and CaCl2 are produced from the
reaction of HCl and calcite.
Hence, the solubility of CO2 in CaCl2 solutions is
carbonate formations. The produced CO2 may remain in the
solution in a specific range of temperatures and pressures
or may release and form a separate phase which affects
2 can have some
effects on the performance of wormholing during carbonate
and calcite reaction and retard the reaction between acid and
as a retarding agent. On the other hand, the formation of a
separate CO2 phase can prevent the movement of the acid
of the relative permeability effect between fresh/spent acid
and CO2 phases. Hence, formation of a separate CO2 phase
can change wormholing performance and also the depth of
There are several methods on different scales for
study the mechanism of wormholing and the effect of
different parameters on this complicated phenomenon. A
comprehensive model is one which properly estimates the
predicts the wormholing regime. Darcy models can be used
equations of continuity, velocity, concentration and porosity
simultaneously. They facilitate the design of an acid job.
Nevertheless, the previous Darcy scale models proposed for
can be applied together with the above-mentioned equations
in acid jobs. Thus, it can be used to improve the accuracy
the solubility of CO2 for this case, the models resulting from
2 with some
correction factors. The results of a study of CO2 solubility
in different ranges of pressure and temperature was reported
amount of CO2
much greater than the solubility of CO2 in spent acid in the
operational ranges of temperature and pressure.
In contrast to the attention paid to NaCl solutions, the
number of publications on the CaCl2-H2O-CO2 system is
very limited. This is readily apparent in Table 1, where the
2 solubility in CaCl2 solutions by
different authors are shown.
Scharlin and Cargill (1996) and Springer et al (2012)
reviewed the few published studies of the CaCl2-H2O-CO2
(1877), Setchenow (1892), Kobe and Williams (1935),
(1993) are not particularly relevant as regards the reservoir
conditions owing to low pressure and temperature values.
The most significant paper published on CO2 solubility in
CaCl2 solutions is that of Prutton and Savage (1945), since
the range of temperatures, pressures and salt concentrations
important parameters of Darcy scale models.
The systems containing CaCl2
studied as widely as NaCl-containing solutions. To calculate
conditions. They measured the CO2 solubility in CaCl2
solutions at 348.65, 374.15, 394.15 K and pressures from
15.2 to 709.28 bar.
Temperature range, K
Pressure range, bar
In this paper, the CaCl2-H2O-CO2 system at different
ranges of pressure, temperature and CaCl2 molality, which
are consistent with reservoir conditions, is studied to measure
and model the solubility of CO2
models in Darcy scale.
The purpose of t 2
solubility in different CaCl2 solutions. The temperature and
pressure ranges consi
as the normal conditions of s
The purity of CO2 was 99.99%. The anhydrous CaCl2
2.2 Apparatus and procedures
Fig. 1 shows a schematic of apparatus used in this study
to estimate the solubility of CO2 in CaCl2 solutions. This
apparatus is similar to the one used by Bando et al (2003) and
cm3/h in constant pressure mode, a high pressure cylinder
with a volume of 500 cm3
of 689 bar, a stainless steel pycnometer, high pressure transfer
and 0.1 K precision, a pressure transducer for the 1-620 bar
range with 0.007 bar precision, a densitometer, and a vacuum
An agitating pump system as shown in Fig. 2 was
designed to agitate the high pressure cylinder in the oven. The
First of all, the high pressure cylinder was opened and
washed with distilled water and evacuated by a vacuum
pump. CaCl2 solution and CO2 were then pumped into
agitated at the desired temperature for 3 hours. The effects of
agitating time were investigated for 1.9 mol/L CaCl2 solution
at 137.9 bar and 351.65 K (Fig. 3). In this study, the soluble
CO2 mole fraction changed negligibly for data acquired in
ensure equilibrium, the samples were agitated for 3 hours. As
the pressure changed during the agitating period, the pressure
was adjusted again.
The concentration of the injected CO2 was more than its
saturation concentration to ensure reaching the saturation
concentration of CO2 in solution. Thus, there was a separate
supercritical CO2 phase in the high pressure cylinder after
reaching equilibrium. Since the high pressure cylinder had
was transferred gradually through lines to a pycnometer.
W 1) at the
final temperature and pressure. Knowing the weight of the
evacuated pycnometer (W0) and its volume means that we can
determine the solution density. To determine the amount of
CO2 dissolved in this solution, the pycnometer must be aged
for 1 hour under room conditions to reach room temperature.
Then, the pycnometer valve was opened and the gas was
released slowly from the top of the pycnometer until no
more gas was released and the weight of the cylinder did not
change. Immediately, the pycnometer valve was closed to
maintain the gas phase equilibrium. Finally, the pycnometer
with the remaining solution was weighed (W2). All of the
The total volume of soluble CO2 consisted of the CO2
released in the gas phase when the temperature and pressure
were reduced to atmospheric conditions (VC(1O)2), CO2 remaining
in the gas phase in the pycnometer after its valve was opened
(VC(O2)2), and CO2 remaining in the liquid phase at atmospheric
presTshueredainffderreonocme tbeemtwpeeerantuWre1 (aVnCd(O3)2 W).2 is the amount of CO2
in the gas phase which is released while the valve of the
pycnometer is being opened. Hence,
where CO2 is the CO2 density, g/cm3 brine is the CaCl2 brine
density, g/cm V cylinder is the volume of the pycnometer, cm3.
To estimate the CO2 solubility, it is required to estimate
the amount of soluble CO2 in CaCl2 solutions at atmospheric
pressure and room temperature. With reference to the method
CO2 in aqueous electrolyte solutions can be estimated by the
log L0 L
L VG VL
VL A and B are
empirical constants dependent upon the particular solute
present, as shown in Table 2, L/mol. These constants were
different electrolyte solutions such as CaCl2-H2O using the
method of least squares.
The absolute value of soluble CO2 volume in solution is
then calculated from Eq. (8).
The CO2 solubility in terms of molality is then given by
by VCO2 22.414Wwater , in which Wwater can be calculated by
2 soluble in the solution
can be calculated by Eq. (10):
where xCO2 is the total mole fraction of CO2
mCO2 is the molality of CO2 in the liquid phase, mol/L.
2.3 Experimental results
pure water are listed in Table 3 and also depicted in Fig. 4.
study at different temperatures. Koschel et al (2006) measured
the CO2 solubility in pure water at 323.15 K and 373.15 K
not the same, this comparison confirms the accuracy of the
study are listed in Tables 4 and 5. These data show the trend
of changes in CO2 solubility in solution with changing
pressure and temperature.
These data indicate that at low pressures the solubility
of CO2 in CaCl2 solutions increased directly with pressure.
At high pressures, however, the effect of pressure on CO2
solubility faded and the rate of increase in CO2 solubility
reduced with an increase in pressure. This observation was
et al, 2012). On the other hand, the temperature and CaCl2
concentrations had inverse effects on CO2 solubility.
3 Model development
The solubility of CO2 in pure water and brine at reservoir
for conditions up to 373.15 K and 1,000 bar, by Duan and
Sun (2003) for conditions up to 533.15 K and 2,000 bar and
K and 600 bar. Duan and Sun (2003) presented a popular
thermodynamic model for the estimation of CO2 solubility in
pure water and aqueous NaCl solutions. They stated, however,
is possible to use it to predict CO2 solubility in other systems
The method of CO2 solubility estimation proposed by
Duan and Sun (2003) is based on the balance between
chemical potentials between CO2 in liquid and gas phases.
This balance results in Eq. (11).
2 CO2 -Na
ln yCO2 CO2 P
CO2 -Na-ClmCl mNa
where yCO2 is the mole fraction of CO2
R is the universal gas constant,
0.08314 bar·L·mol-1·K-1 T
is the chemical potential and mSO42 is the molality of SO42- in
the liquid phase (if any), mol/L.
2H2O-NaCl system in the conditions of the study, it is assumed
that the water vapor pressure of H2
to the pure water saturation pressure. Based on the study of
Duan and Sun (2003), this assumption may lead to errors
(up to 5%) for Cl(O02) RT . They stated that these errors have
a negligible effect on the calculation of CO2 solubility. Thus,
yCO2 can be calculated by yCO2 P PH2O P . Duan and
Sun suggested an empirical equation for calculating PH2O as:
where c is the critical pressure of water, Pc Tc
is the critical temperature of water, Tc PH2O is the
t T Tc Tc and the parameters of
Eq. (12), c1-c5, are listed in Table 6.
Duan et al (1992) also developed an equation of state for
supercritical CO2, as in Eq. (13).
predicting the CO2 solubility in CaCl2-H2O system. They
concluded that the model developed by the interaction
parameters for NaCl solutions, can be applied for CaCl2
solutions as well. The parameters ’s and ,s for Na+ and
Cl and also the standard chemical potential of CO2 in the
liquid phase are essential to calculate the CO2 solubility as a
function of temperature, pressure and salinity. On the other
hand, measurements can only be made in electrically neutral
To calculate Vr, the reduced temperature and pressure
should be calculated and substituted in the EOS developed by
Duan et al (1992) as in Eq. (13). The parameters of Eq. (13)
are listed in Table 7.
interaction parameters are estimated by Eq. (14), with the
constants listed in Table 8.
Par T , P
c8 P T
and the data reported by Prutton and Savage (1945), the
interaction parameters of Duan and Sun’s solubility model
are modified for CaCl2 solutions. The constants of Eq. (14)
CO2 -Ca and CO2 -Ca-Cl , in comparison with the ones presented
by Duan and Sun (2003) for NaCl solutions, are shown
in Table 9. As can be seen from the table, Cl(O02) RT is not
changed, because it is independent of the solvent in the
4 Results and discussion
T h e m o d e l p r o p o s e d b y D u a n a n d S u n ( 2 0 0 3 )
overestimates the CO2 solubility in high molality solutions
and also at high pressures as well. This observation was
and Hilal, 2010). A comparison between the CO2 solubility
estimation by the base and modified models has been
L CaCl2 solutions. The model is more accurate for higher
concentration of CaCl2 and higher pressures as well.
L solutions is reduced. Hence, the developed model is more
accurate. The comparison between CO2 mole fractions
is illustrated in Fig. 5.
CO2 solubility estimations for the 1.90 mol/L CaCl2
seen in Fig. 5 for 4.80 mol/L CaCl2 solutions, however. This
indicates that this improvement has more meaning for high
concentrations of CaCl2 solutions.
Prutton and Savage (1945) proves that predictions of the new
All plots of Fig. 6 show this improvement for different
values of temperature, pressure and CaCl2 concentrations.
2 solubility estimations
are reduced by about 14%, 53% and 65% on the basis of the
Prutton and Savage (1945) results for 1.01, 2.28 and 3.90
have been improved about 25% for 4.80 mol/L CaCl2
be concluded that the modified model shows a significant
as well. Fig. 6 shows a comparison between data estimated
(c) T= 368.15 K
(a) T=328.15 K
(b) T=348.15 K
improvement in CO2 mole fraction estimations. The model
presents better results for high concentration solutions.
reduction, but that for the 1.90 mol/L solution is almost
CO2 mole fraction in CaCl2 solutions in better agreement with
increase with pressure, temperature and CaCl2 molality.
Adding more CaCl2 to the solution results in decreasing CO2
solubility within the system. The base model cannot match
T=348.15 K, 1.01 mol/L CaCl2
T=373.15 K, 1.01 mol/L CaCl2
T=393.15 K, 1.01 mol/L CaCl2
Modified Duan model
Modified Duan model
2 solubility based on data from Prutton and Savage (1945)
Modified Duan model
this behaviour, but the new developed model can predict the
behaviour of the system more precisely. This comparison
2 solubility prediction in
3.90 mol/L CaCl2 solutions compared with the Duan model,
as shown in Fig. 6.
Since the range of CaCl2 concentrations in this study is
improvement in estimating the soluble CO2 mole fraction is
noteworthy in wormhole propagation models. The original
form of the Duan model overestimates CO2 solubility in spent
presented in this study gives more reasonable estimates of
CO2 solubility in spent acid. This solubility model can be
used in an integrated study on wormhole propagation during
1) The solubility of CO2 in saline water is of particular
importance regarding environmental issues such as CO2
capture and geological storage. Hence, the thermodynamic
behavior of CO2-H2
contrast, CO2-H2O-CaCl2 has only been studied to a limited
CO2 in CaCl2 solutions.
was prepared and the solubility of CO2 in 0, 1.90 and 4.80
mol/L CaCl2 solutions at 328.15 to 375.15 K and 68.9 to 206.8
that CO2 solubility decreases with increasing concentration,
increasing temperature and decreasing pressure. The effect of
pressure, however, diminishes at higher pressures.
3) A modified model was developed by refitting the
interaction parameters to predict the CO2 solubility in CaCl2
solutions. The modified model can predict solubility better
than the available Duan and Sun thermodynamic model.
This improvement is up to 65% better than the Duan and
Sun model. In addition, the modified model estimates the
CO2 solubility in high concentration solutions and also high
pressures with noticeable accuracy. Prediction by this model
4) Darcy models on the basis of core scale predict
In the course of reactions between acid and carbonates
physically affect the performance of an acid job, it is of
2 is not
soluble in the solution (spent acid) and can form a separate
study can be applied in Darcy scale wormhole propagation
models to improve the accuracy of their predictions.
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Spycher N and Pruess K. CO2-H2
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