Fluid Phase Equilibria 520 (2020) 112660
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Fluid Phase Equilibria
j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / fl u i d
Elemental mercury partitioning in high pressure fluids part 1:
Literature review and measurements in single components
Antonin Chapoy a, *, Pezhman Ahmadi a, Richard Szczepanski b, Xiaohong Zhang b,
Alessandro Speranza b, Junya Yamada c, Atsushi Kobayashi c
a
b
c
Hydrates, Flow Assurance & Phase Equilibria Research Group, Institute of Petroleum Engineering, Heriot-Watt University, UK
KBC (A Yokogawa Company), 42-50 Hersham Road, Walton on Thames, KT12 1RZ, UK
Technical Research Center, INPEX Corporation, 9-23-30 Kitakarasuyama, Setagaya-ku, Tokyo, 157-0061, Japan
a r t i c l e i n f o
a b s t r a c t
Article history:
Received 22 April 2020
Received in revised form
19 May 2020
Accepted 19 May 2020
Available online 30 May 2020
Mercury in its elemental form is naturally present in most reservoir fluids. The presence of mercury can
lead to serious operational and safety/health problems. Knowledge of the maximum solubility of
elemental mercury with temperature and pressure in reservoir fluids is important to avoid mercury
dropping out during processing operations, as mercury is naturally present in hydrocarbon deposits.
In this work, a new experimental approach is presented to determine the mercury content in high
pressure gas and liquid systems. Mercury solubility in methane, ethane, propane, nitrogen and carbon
dioxide over a wide range of temperature and pressure (243.15e323.15K and up to 20 MPa) have been
measured. An extensive literature review has been conducted on the solubilities of mercury in gases and
liquid hydrocarbons. A critical evaluation of the literature data has been conducted to identify any inconsistencies in the reported data. The new experimental data generated in this work along with the
literature data have been used to tune the binary interaction parameters of the Peng-Robinson and the
Soave-Redlich-Kwong equations of state between mercury and the mentioned compounds.
© 2020 Elsevier B.V. All rights reserved.
Keywords:
Mercury
Methane
Ethane
Propane
Carbon dioxide
Nitrogen
Phase behaviour
Thermodynamic modelling
1. Introduction
Although not present in every gas or oil field, mercury
contamination has been reported in several locations worldwide.
Hotspots of mercury contamination appear to be spread globally,
with higher concentrations in Southeast Asia, North Europe (Germany/Netherlands) and the Middle East [1]. Mercury contamination represents a big risk for the oil and gas industry. Although
normally present in small amounts, its effects may be very
damaging for the industry. It is an obvious Health, Safety and
Environmental (HSE) hazard for the staff and the environment. If
not detected promptly and removed from the fluid, mercury can
easily be dispersed in the immediate environment, with tragic
consequences for the health of the workers on the plant and major
risks of contamination of the wider environment. Moreover, mercury is highly corrosive and its accumulation in pipelines or operating units, like heat exchangers or separators, may compromise
* Corresponding author.
E-mail address: a.chapoy@hw.ac.uk (A. Chapoy).
https://doi.org/10.1016/j.fluid.2020.112660
0378-3812/© 2020 Elsevier B.V. All rights reserved.
the integrity of the steel walls and cause leaks with associated risk
of fire and further risks of contamination from the dispersion of
hydrocarbons in the environment [2,3].
The strategies adopted to mitigate risks associated with mercury
are obviously very costly. While a conservative approach in design
and construction of the facilities is clearly necessary, the adoption
of excessive design margins may lead to excessive CAPEX and OPEX
or reduced operating capacity. For instance, the correct sizing and
positioning of a mercury removal unit may have a major impact on
the economics of the project. The ability to determine with
improved accuracy the risk of accumulation of mercury across the
plant and assess within safety margins, the correct sizing and
operating conditions of the mercury removal units would therefore
provide great benefit to the industry overall. With increased
modelling and simulations capabilities, engineers would be able to
assess more effectively the risks associated with mercury
contamination, maximize the effectiveness of capital and operational expenditure, and improve their general capability to operate
the plant within its actual productive limits, without compromising
the safety of the staff and the environment.
In this communication, we present experimental techniques,
2
A. Chapoy et al. / Fluid Phase Equilibria 520 (2020) 112660
equipment and thermodynamic modelling for investigating the
phase behaviour of systems in presence of mercury. Mercury contents in methane, ethane, propane, carbon dioxide and nitrogen
were measured at (243.15, 258.15, 273.15, 298.15 and 323.15) K and
pressures up to 20 MPa.
Finally, the PR78-EoS [4] and the SRK72-EoS [5] were used to
calculate the phase behaviour and the mercury distribution in fluid
phases. Binary interaction parameters were adjusted using obtained experimental data and the literature data. In this manuscript, all mercury content data from the literature and from this
work are reported in mole fraction (ppm: part per million, i.e. 106
mol fraction/ppb: part per billion, i.e. 10-9 mol fraction).
2. Literature review
Experimental data for solubility of mercury in various substances are scarce and limited to a few research groups. Among the
published works focusing on solubility data of mercury, the review
carried out by Clever [6] is one of the main references for experimental data measured before 1987. An updated literature review
for solubility of mercury in various alkanes, carbon dioxide and
nitrogen is described in this section. Furthermore, for all the data
points found in open literature, details including pressure, temperature and solubility of mercury have been tabulated in the
appendix.
2.1. Mercury e alkanes
2.1.1. Methane
The most recent data in the literature reported for this system
have been measured by Yamada et al. [7]. They have measured the
solubility of mercury in methane between (268.15e303.15) K and
pressures up to 6 MPa. In addition, Butala et al. [8] measured the
solubility of mercury in methane at nine isotherms between
(253.15e293.15) K and pressure up to 6.9 MPa. The range of mercury content varies between 1.3 and 77 ppb M in the methane-rich
phase. The system has also been studied by McFarlane [9] at Texas
A&M University in the solid-liquid equilibrium (SLE). Later in 2016,
McFarlane published the results reported in his MSc thesis, with
additional experimental results in a journal paper by Marsh et al.
Fig. 1. Literature data for solubility of mercury in nC6. ( ): Okouchi & Sasaki [15], ( ):
Spencer & Voigt [18], ( ): Reichardt & Bonhoeffer [19], ( ): Kuntz & Mains [17], ( ):
Gallup & Bloom [16].
[10]. This article (Marsh et al. [10]) is used as the main reference of
the results published by McFarlane in this manuscript.
2.1.2. Ethane
The data set measured by Yamada et al. [7] is the most recent
reported measurements in the literature. Like the measured data
for methane, their measurements cover 8 isotherms between
(268.15e303.15) K and pressures up to 3.5 MPa. In addition, Koulocheris et al. [11] reported measurements for the solubility of
mercury in ethane at five isotherms of (273, 278, 283, 288 and 293)
K and pressures up to 8.2 MPa.
2.1.3. Propane
Three sources are available for the phase equilibrium data of
mercury-propane binary mixtures. Jepson et al. [12] reported
experimental vapour-liquid equilibrium (VLE) of the mercurypropane system. The VLE measurements were conducted at
(457.15, 491.15 and 529.15) K and pressures up to 3.3 MPa. The
solubility measurements were in a range of (800e10231) ppm. One
SLE measurement and few liquid-liquid equilibrium (LLE) data for
this binary mixture have been reported by Marsh et al. [10]. LLE
measurements were conducted at temperatures between
(233.15e343.15) K and pressures up to 2.6 MPa. The mercury concentration in their mixtures was in the range of 0.4e3369 ppb. In
addition, the single SLE measurement was carried out at 177.15 K
and 0.004 MPa. Finally, five solubility data points obtained at
(273.15, 278.15, 283.15, 288.15 and 293.15) K were reported by
Mentzelos [13] in 2015.
2.1.4. Butanes
For n-butane, 23 data points were found in the literature from
the works performed by Jepson et al. [12] and Richardson et al. [14].
Jepson et al. [12] measured VLE at (457.15e529.15) K and pressures
up to 3.1 MPa, with a range of mercury content between
(614e10448) ppm. The VLE measurements conducted by Richardson et al. focused on binary mixtures with mercury contents between (454e3860) ppm, at P-T ranges of (7e38) MPa and
(486e573) K, respectively.
For iso-butane, the only available data set in the literature is the
work reported by Butala et al. [8], where they obtained
Fig. 2. Reported data in the literature for the solubility of mercury in nC7. ( ): Okouchi
& Sasaki [15], ( ): Spencer & Voigt [18].
A. Chapoy et al. / Fluid Phase Equilibria 520 (2020) 112660
3
Table 1
Composition of the chemical used in this work (used without further purification).
Fig. 3. Literature data for solubility of mercury in nC8. ( ): Okouchi & Sasaki [15], ( ):
Spencer & Voigt [18], ( ): Marsh et al. [10], ( ): Vogel et al. [20], ( ): Gallup & Bloom
[16], ( ): Miedaner et al. [22], ( ): Migdisov et al. [21].
experimental mercury content data in the isobutane rich phase in
VLE and LLE conditions at (263.15, 268.15, 273.15, 278.15 and
283.15) K and pressures up to 8.3 MPa. In these measurements, the
mercury contents of the samples were in the range of (50e269)
ppb.
2.1.5. Pentanes
The available experimental data for solubility of mercury in
normal pentane were reported by Marsh et al. [10], Okouchi and
Sasaki [15], Butala et al. [8], Gallup and Bloom [16], and Kuntz and
Mains [17].
Marsh et al. reported mercury solubility in n-pentane for six
isotherms between 233 and 383 K. The obtained mercury content
in their experiments was in a range of (9e16161) ppb. Okouchi and
Sasaki [15] measured mercury concentration in HgeC5 mixtures at
Fig. 4. Mercury content in equilibrium with CO2 at different isotherms. Butala et al.
[8]; ( ): T ¼ 293.15, ( ):T ¼ 288.15, ( ):T ¼ 283.15, ( ): T ¼ 278.15, ( ): T ¼ 273.15.
Yamada et al. [7]; ( ): data at three isobars (~0.5, 1.5, and 2 MPa).
Chemical
Symbol
CASRN
Purity
Supplier
Mercury
Methane
Ethane
Propane
Carbon dioxide
Nitrogen
Hg
CH4
C2H6
C3H8
CO2
N2
7439-97-6
74-82-8
74-84-0
74-98-6
124-38-9
7727-37-9
99.9995 wt%
99.995 vol%
99.99 vol%
99.95 vol%
99.995 vol%
99.9992 vol%
Sigma-Aldrich
BOC
BOC
BOC
Air Product
Air Product
six isotherms of (278.15, 283.15, 293.15, 298.15, 303.15 and 313.15)
K. The minimum and maximum mercury concentration for these
binary mixtures were found to be 190 and 1600 ppb, respectively.
The other set of literature data generated by Butala et al. [8] covered
a temperature range of (258.15e293.15) K. In their measurements,
the mercury contents of the mixtures were found to be between 44
and 464 ppb. Comparison of the measured data from these three
works shows a reasonable agreement between their results. In
addition, the solubility of mercury in n-pentane at 298.15 K was
investigated in two different works performed by Gallup and Bloom
[16], and Kuntz and Mains [17]. The mercury contents were found
to be 793 ppb by Gallup and Bloom [16], and 674 ppb by Kuntz and
Mains [17].
In comparison to the data available for solubility of mercury in
nC5 mixtures, for iC5 experimental data is scarce, and only one
single point has been reported in the literature by Kuntz and Mains
[17] at 298.15 K. The mercury content for this point was found to be
645 ppb, which is less than the value reported for the solubility of
mercury in nC5.
2.1.6. Hexanes
The solubility of mercury in normal hexane has been measured
at temperatures between 273.15 and 336.15 K. Most experimental
results were reported by Okouchi and Sasaki [15], and Spencer and
Voigt [18]. Experiments conducted by Okouchi and Sasaki were
performed at six isotherms between 278.15 and 313.15 K. The
obtained mercury contents were found to be between 240 and
1900 ppb. Also, Spencer and Voigt, reported solubility measurements at five isotherms between 273.15 and 308.15 K. A close
agreement is seen by comparing the experimental results obtained from these works at similar isotherms (303.15 and
293.15 K). Measurements conducted by Reichardt and Bonhoeffer
[19] at 313.15 and 336.15 K, and two single-point measurements at
298.15 K conducted by Gallup and Bloom [16] and Kuntz and
Mains [17], are other available data in the open literature as shown
in Fig. 1.
For the different isomers of hexane, four sets of experimental
results were found in the literature. Kuntz and Mains reported
solubility measurements at 298.15 K for 3-methylpentane, 2,2dimethylbutane and 2,3-dimethylbutane. Also, Spencer and Voigt
performed similar measurements for 2,2-dimethylbutane at
different temperatures between 273.15 and 308.15 K, where the
measured mercury contents were found to be between 167 and
984 ppb.
2.1.7. Heptanes
Two data sets have been reported in the literature for LLE of
binary mixtures of Hg-nC7. The first set was reported by Spencer
and Voigt [18] and covers six isotherms between 273.15 and
308.15 K, with mercury content in the range of (200e1628) ppb.
The second set is the measurements conducted by Okouchi and
Sasaki [15] at six isotherms between 278.15 and 313.15 K. In their
work, the measured solubility of mercury in normal heptane varied
from (290e2200) ppb. The obtained results from the literature are
4
A. Chapoy et al. / Fluid Phase Equilibria 520 (2020) 112660
depicted in Fig. 2. As shown in this figure, except for the points
measured at 303.15 K, a similar trend can be seen from both sets of
measurements. For the different isomers of heptane, no data were
found in the open literature.
2.1.8. Octanes
In comparison to other alkanes, experimental results for n-octane are available over a wider temperature range. Spencer and
Voigt [18] obtained mercury solubility in equilibrium with nC8 at
six isotherms between (273.15e313.15) K. Okouchi and Sasaki [15]
conducted a similar study at temperatures between
(278.15e313.15) K. Among the measurements carried out in both
these works, three isotherms of (298.15, 303.15, 313.15) K are
similar. A deviation of up to 10% is seen by comparing the obtained
results of these works.
Gallup and Bloom [16] and Vogel et al. [20] have also reported
measurements at 298.15 K. Comparison of their results with those
obtained by Okouchi and Sasaki [15], Spencer and Voigt [18], and
Marsh et al. [10] show discrepancies of the experimental results
obtained at this temperature. In the experiments conducted by
Marsh et al. [10], five other isotherms between (233.15e413.15) K
were tested. In these measurements, the concentrations of mercury
were in a range of (14e41794) ppb.
For higher temperatures, two data sets were found in the literature. In the first one, Migdisove et al. [21] measured the mercury
content at (382e483) K, where the mercury contents were found to
be in a range of (17,267e314,026) ppb. In this work, the authors
have checked the reproducibility of results by repeating the measurements for three temperatures. Based on the available experimental results in the open literature, significant deviations
(between 32% and 46%) are observed between the repeated measurements. This can raise questions about the validity of the
method used for these measurements. In the second set, Miedaner
et al. [22] reported three data points measured at temperatures
between (373.15e473.15) K, with obtained solubilities from 54,000
to 821,000 ppb. Fig. 3 summarises the reported literature data for
normal octane. In this figure, the Y-axis (mercury content) is in a
Logarithmic scale to show all the reported data points.
To the best of our knowledge, among the different isomers of
octane, 2,2,4-trimethylpentane is the only one with available records in the literature. Vogel et al. [20] and Klehr and Voigt [23]
measured the mercury content at 298.15 K. Also, Spencer and Voigt
[18] conducted the measurements for seven temperatures in a
range of (273.15e308.15) K. The measured mercury contents in
their work were in a range of (164e1121) ppb.
2.1.11. Pentadecane/hexadecane
For the solubility of mercury in other alkanes with carbon
numbers more than 12, only two data points measured by Gallup
and Bloom [16] for n-pentadecane and n-hexadecane were found in
the literature. The solubility of mercury in C15 at 294.15 K, and in C16
at 294.85 K were reported to be 1371 and 1955 ppb, respectively.
2.2. Mercuryecarbon dioxide
The most recent published data in the literature were measured
by Yamada et al. [7]. Solubilities of mercury in CO2 were measured
at 8 isotherms between (268.15e303.15) K and pressures up to
2 MPa. Also, Butala et al. [8] measured mercury solubility at three
different pressures for five isotherms. Fig. 4 summarises all the
literature data.
2.3. Mercuryenitrogen
The only available data set in the literature are those reported by
Mentzelos [13], which includes six data points at 273.15 K. Similar
to other data points from this reference, due to the confidentiality
of the measured data, exact values of the results were not directly
available.
3. Experimental setup and procedures
3.1. Materials
The source and purity of gases used in this study are listed in
Table 1. Mercury purchased from Sigma-Aldrich used in all tests
was 99.9995 wt% pure. No further purification or analysis of the
composition of these substances was conducted.
3.2. Setup
The equipment in principle is similar to the setup used by Butala
et al. [8]. The equipment is comprised of two saturation cells, coiled
tubing and a set-up for measuring the mercury content of the
equilibrated fluids flowing out of the cell. The two saturation cells
are made of stainless steel 316 with inner volume of 50 cm3. The
maximum working pressure of these cell is 30 MPa. A schematic of
the set-up is shown in Fig. 5. Initially, the test fluid enters the
system through a needle valve and passes through coiled tubing
(15 m of 1/1600 stainless steel pipe) into the first saturation cell (presaturation), the temperature of the bath (bath 1) in which this cell is
immersed is set 5 K higher than the temperature of the bath (bath
2) of the main saturation cell. The test fluid passes then through
2.1.9. Decane
Klehr and Voigt [23] measured LLE of Hg-nC10 binary mixtures
between (273.15e318.15) K. In their measurements, the concentration of mercury in equilibrium with normal decane was found to
be in a range of (401e1077) ppb. Kuntz and Mains [17] measured
the solubility of mercury in decane at 298.15 K. In their work, the
mercury content was found to be 1077 ppb, 300 ppb less than the
value obtained by Klehr and Voigt at this temperature.
2.1.10. Dodecane
For binary mixtures of HgeC12, two sets of data points were
found in the literature. First, the measurements performed by
Gallup and Bloom [16] at 294.65 K and 298.15 K, with reported
mercury contents of 1341 and 1600 ppb, respectively. Second, the
measured data points reported by Miedaner et al. [22] at five isotherms between (383.15e498.15) K with mercury contents ranging
between (76e1049) ppm.
Fig. 5. Schematic illustration of the Dynamic Mercury Content Equilibrium Cell.
A. Chapoy et al. / Fluid Phase Equilibria 520 (2020) 112660
another coiled tubing (15 m of 1/16” stainless steel pipe) into the
second saturation cell. It is therefore assumed that the fluid is
therefore supersaturated when it enters the second cell and excess
mercury will drop out and the fluid will be saturated at the temperature of the main saturation cell.
Both bath temperatures are measured using a PRT (Platinum
Resistance Thermometer). The pressure of the setup is measured
using a Quartzdyne pressure transducer mounted on the main
saturation cell. The outlet from the setup is connected to a temperature (T ¼ 363.15 K) control choke valve and then connected to
the gas inlet of an atomic absorption spectroscopy (AAS) setup from
Mercury Instruments (VM-3000 - UV absorption is measured at a
wavelength of 253.7 nm). For each P/T point around 10 1-L samples
are analyzed until the readings are stable and repeatable.
The temperatures in the two baths are measured by platinum
probe (100 U). The temperature probes were calibrated against a
Prema 3040 precision calibrator. Temperature calibration uncertainty is estimated to be 0.05 K, in the temperature range
243.15e323.15 K. A precise pressure transducer (Quartzdyne
QS10KeB, pressure range 0e69 MPa) is used to measure system
pressure during the measurements. This transducer calibrated
regularly using a Budenberg deadweight tester. Pressure calibration
uncertainty is estimated to be 0.01 MPa. The mercury analyzer was
calibrated against a MC-3000 Mercury calibrator using nitrogen.
The mercury content uncertainty is Ucal(yHg) ¼ 2%.
5
Fig. 6. Calculated vapour pressure, Psat, of mercury using the PR-EoS with the MathiasCopeman alpha function [24] e Comparison with Huber et al. [20].
PR=SRK
bi
¼ Ub
RTC
with Ub ¼ 0:08664ðSRKÞ or 0:077796ðPRÞ
PC
(2)
The temperature dependency of the attractive term (1), a, is
defined using a Soave type temperature dependency:
4. Thermodynamic modelling
In this work, the PR78-EoS [4] and SRK72-EoS [5] were chosen
to calculate the phase behaviour and the mercury distribution in all
fluid phases. These equations are given below:
P¼
8 RT
aSRK
ðTÞ
i
>
ðSRKÞ
>
>
SRK
>
>
v v þ bSRK
< v bi
i
>
>
>
>
>
:
(1)
aPR ðTÞ
i
ðPRÞ
PR
PR
v bi
þ bPR
v bPR
v v þ bi
i
i
RT
a ¼ a0 aðTÞ
(3)
h
8
pffiffiffiffiffi i2
>
a
ðTÞ
¼
1
þ
m
1
Tr
>
<
Where
2 2
>
>
: a ¼ Ua R Tc with U ¼ 0:42748ðSRKÞ or 0:457240 ðPRÞ
a
0
Pc
(4)
where m is directly related to the acentric factor of the components
8
< SRK : 0:480 þ 1:574u 0:176u2
mðuÞ ¼ aa
0:37464 þ 1:54226u 0:26992u2 if u 0:491
: PR :
0:379642 þ 1:48503u 0:164423u2 þ 0:016666u3 if u > 0:491
The co-volume b for the SRK and PR EoS is given below:
(5)
To improve the calculation of the vapour pressure of mercury,
the Mathias-Copeman (MC) alpha function [24] with three
adjustable parameters was also used for this compound:
Table 2
Critical parameters, acentric factor and Mathias-Copeman [24] adjusted parameters for mercury and other compounds.
Compound
Mercury
c
Methane
Ethane
Propane
Nitrogen
CO2
a
b
Tc/Ka
Pc/MPaa
ua
c1b
c2b
c3b
EoS
1735
160.803
0.16445
190.56
305.32
369.89
126.19
304.13
4.5592
4.8722
4.2512
3.3958
7.3773
0.01142
0.0995
0.1521
0.0372
0.22394
0.23606
0.14738
e
e
e
e
e
0.2293
0.1564
e
e
e
e
e
0.16092
0.133982
e
e
e
e
e
SRK72
PR78
e
e
e
e
e
DIPPR801.
Adjusted Mathias-Copeman parameters between 234.3 and 573.15 K (Eq. (6)).
6
A. Chapoy et al. / Fluid Phase Equilibria 520 (2020) 112660
Table 3
Adjusted kij and temperature range of regression for the PR78-EoS.
Compound
k0
k1
k2
Tmin/K
Tmax/K
Phase
CO2
Nitrogen
Methane
Ethane
Propane
n-pentane
n-hexane
n-heptane
n-octane
n-nonane
n-decane
n-dodecane
n-pentadecane
n-hexadecane
i-butane
i-pentane
n-butane*
1.2406
0.2218
0.1150
0.0428
0.1121
0.0461
0.0115
0.00881
0.02667
0.05516
0.07711
0.10537
0.15205
0.21116
0.04318
0.03560
0.1093
1.253E-02
e
e
4.965E-04
6.272E-04
e
e
e
e
e
e
e
e
e
e
e
2.429E-05
e
e
e
e
e
e
e
e
e
e
e
e
e
e
e
243.15
243.15
243.15
253.15
233.15
233.15
273.15
273.15
233.15
273.15
273.15
273.15
294
294
263.15
298.15
258.15
323.15
323.15
323.15
323.15
343.15
383.15
336.15
313.15
413.15
336.15
318.15
473.15
294
294
283.15
298.15
293.15
L&SC
SC
SC
L&SC
L
L
L
L
L
L
L
L
L
L
L
L
L
*Adjusted using n-butane þ n-pentane þ n-hexane ternary system from Butala et al. [8].
8
>
>
>
>
>
ifT < TC;
>
>
<
2
aðTÞ ¼ 41 þ c1
sffiffiffiffiffi !
sffiffiffiffiffi !2
sffiffiffiffiffi !3 32
T
T
T
5
þ c2 1 þ c3 1 1
TC
TC
TC
>
sffiffiffiffiffi !#2
"
>
>
>
>
T
>
>
: otherwise aðTÞ ¼ 1 þ c1 1 TC
where c1, c2 and c3 are the three adjustable parameters. These parameters are listed in Table 2. These parameters were adjusted
using the correlation developed by Huber et al. [25]. They estimated
that their correlation has an uncertainty (k ¼ 2) of 1% between
273.15 and 400 K, 0.15% from 400 K to the boiling point (629.77K)
and 3% above the triple point (TT ¼ 234.3156 K [26]). Their correlation has the following form:
h
i
p
T
ln
¼
a1 t þ a2 t1:89 þ a3 t2 þ a4 t8 þ a5 t8:5 þ a6 t9
pc
Tc
(7)
where
pc ¼ 167MPa; Tc ¼ 1764K; a1 ¼ 4:57618368; a2 ¼
1:40726277; a3 ¼ 2:36263541; a4 ¼ 31:0889985; a5 ¼
58:0183959; a6 ¼ 27:6304546.
The average deviation between 234.3 and 573.15 K is 0.4% (for
both EoS). The comparison between the correlation and the model
calculations is shown in Fig. 6.
For multicomponent systems, the classical van der Waals mixing
rules were used:
pffiffiffiffiffiffiffiffi
aij ¼ 1 kij
ai aj
bij ¼
bi þ bj
2
(8)
(9)
where kij is the binary interaction parameters, in this work the kij is
symmetrical, i.e. kij ¼ kji and equal to zero when j ¼ i. For some
systems the following temperature dependency was assumed for
the binary interaction parameters:
kij ¼ k0 þ k1 T þ k2 T 2
(10)
(6)
It is also assumed that the solubility of components in elemental
mercury is negligible and the mercury phase is therefore considered pure (Helium solubility in mercury was measured to have an
upper limit (most likely lower) of 1.108 mol fraction at 101.3 kPa
and near ambient temperature [27]).
5. Results and discussions
The binary interaction parameters between mercury and gases,
liquid hydrocarbons and carbon dioxide (Equation (10)) were
adjusted using the gathered solubility data through a Simplex algorithm using the objective function, OF, displayed in equation
(11):
OF ¼
Nexp
1 X xexp xcal
N 1
xexp
(11)
where x is the solubility of mercury, N is the number of data points.
The adjusted parameters are reported in Table 3 and Table 4 for the
PR78-EoS and the SRK72-EoS, respectively.
5.1. Methane
As reported in the literature review, only three sources are
available for methane, and the data are limited to pressure lower
than 7 MPa. Our new data expand the range both in term of temperature and pressure. The new data are reported in Table 5. The
model can reproduce the mercury solubility in the vapour phase
with a single binary interaction parameter, as seen in Fig. 7. The
optimised kijs are 0.115 and 0.069 for the PR-EoS and SRK-EoS,
respectively. The OF (defined in equation (11)) is equal to 5.8%
and 5.7% for the PR-EoS and SRK-EoS, respectively. At low pressure
A. Chapoy et al. / Fluid Phase Equilibria 520 (2020) 112660
7
Table 4
Adjusted kij and temperature range of regression for the SRK72-EoS.
Compound
k0
k1
k2
Tmin/K
Tmax/K
Phase
CO2
Nitrogen
Methane
Ethane
Propane
n-pentane
n-hexane
n-heptane
n-octane
n-nonane
n-decane
n-dodecane
n-pentadecane
n-hexadecane
i-butane
i-pentane
n-butane*
1.4174
0.1105
0.0690
0.0436
0.1092
0.0527
0.0251
0.0076
0.0082
0.0344
0.0554
0.10537
0.12721
0.1856
0.04963
0.03560
0.1142
1.390E-02
e
e
4.866E-04
6.272E-04
e
e
e
e
e
e
e
2.6899-05
e
e
e
e
e
e
e
e
e
e
e
e
e
e
e
243.15
243.15
253.15
253.15
233.15
233.15
273.15
273.15
233.15
273.15
273.15
273.15
294
294
263.15
298.15
258.15
323.15
323.15
293.15
293.15
343.15
383.15
336.15
313.15
413.15
336.15
318.15
473.15
294
294
283.15
298.15
293.15
L&SC
SC
SC
L&SC
L
L
L
L
L
L
L
L
L
L
L
L
L
*Adjusted using the n-butane þ n-pentane þ n-hexane ternary system from Butala et al. [8].
Table 5
Mercury solubility in methane.
Npts
T/K
P/MPa
yHg/ppb
stdev
uc(y)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
244.35
244.55
244.55
245.15
246.15
258.15
258.15
258.15
258.15
258.15
273.15
273.15
273.15
273.15
278.15
283.15
288.15
293.15
298.15
298.15
298.15
298.15
298.15
323.15
323.15
323.15
1.03
2.07
3.45
6.89
10.34
15.51
10.55
5.27
2.59
1.34
2.50
5.09
8.41
18.62
1.03
0.93
1.05
0.80
8.79
2.56
4.90
4.83
1.03
5.17
8.69
2.76
1.43
1.01
0.59
0.51
0.81
2.14
1.95
2.12
2.99
5.42
14.64
9.06
7.87
8.25
45.93
84.24
113.89
226.93
60.66
125.29
77.04
79.94
285.54
491.48
406.58
758.14
0.080
0.020
0.010
0.016
0.034
0.024
0.028
0.018
0.090
0.065
0.056
0.599
0.130
0.080
0.663
0.056
1.156
0.230
0.203
0.401
0.598
0.693
0.373
3.212
0.725
1.072
0.260
0.248
0.246
0.247
0.249
0.251
0.251
0.251
0.270
0.281
0.394
0.674
0.321
0.316
1.116
1.541
2.309
3.688
1.050
2.120
1.426
1.510
4.616
7.713
5.886
10.683
Standard uncertainites are u(T) ¼ 0.005K and u(P) ¼ 0.01 MPa. Stdev is the standard
deviation.
uc(y) q
isffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
the
combined
standard
uncertainty
and
defined
as
uc ðyÞ ¼ usys 2 þ uca 2 þ urepeat 2 where usys, uca, and urepeat stand for standard uncertainties of the system (device), the calibration procedure and reproducibility of
the results, respectively.
for both systems, the mercury content is directly reducing
following a Raoult's law (Psat/P). The model is predicting the mercury content at higher pressure (~6 MPa) to slightly increase with
pressure similar to what is observed for the methanol or ethanol
content in the methane system [28].
5.2. Ethane
The data for the solubility of mercury in ethane are reported in
Table 6 and plotted in Fig. 8. The measurements were carried out
with ethane below its critical temperature and below the vapour-
Fig. 7. Experimental and calculated mercury solubilities in methane at 243.15, 258.15,
263.15, 268.15, 273.15, 278.15, 283.15, 288.15, 293.15, 298.15, 303.15 and 323.15 K;
experimental data from Butala et al. [8]: ( ); Yamada et al. [7]: ( ); this work: ( ):
243.15 K; ( ): 258.15 K; ( ): 273.15 K; ( ): 298.15 K; ( ): 323.15 K; Black lines: PR78
with kij reported in Table 3.
liquid (ethane)eliquid (Hg) locus, in the liquid region and for isotherms above ethane critical temperature. Two data sets are
available for the solubility of mercury in ethane, however only 5
points were reported in the liquid region. At low pressure
(P < 2 MPa) in the vapour phase, predictions of the model are
hardly affected by the value of the binary interaction parameters as
seen in Fig. 9. Predictions using parameters between 0.1 and 0.3
yield close predictions in the vapour region but large difference in
the liquid region. It is therefore recommended to tune the model
using mercury data in the liquid region. For this reason, only our
data were used to optimise the binary interaction parameters. The
kijs were found to have a slight temperature dependence as highlighted in Tables 3 and 4.
The absolute average deviations (AAD) between the model and
the experimental are 5.3% for both EoS (3.8%(SRK)/4.16%(PR) for
this work/7.1%/5.9% for [13] and 6.4%/6.4% for [7]) see Fig. 8. Below
saturation, the expected trend is observed for this system, the
mercury content is decreasing with pressure and the temperature
dependency is closely related to the vapour pressure of mercury,
however in the liquid region, different trends are observed, an
increase in the solubility of mercury in the liquid region is
observed.
8
A. Chapoy et al. / Fluid Phase Equilibria 520 (2020) 112660
Table 6
Mercury solubility in ethane.
Table 7
Mercury solubility in propane.
Npts
T/K
P/MPa
yHg/ppb
stdev
uc(y)
Phases
Npts
T/K
P/MPa
yHg/ppb
stdev
uc(y)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
244.10
243.99
244.10
258.15
258.15
258.15
258.15
258.15
258.15
258.15
258.15
273.15
273.15
273.15
273.15
273.15
273.15
273.15
298.15
298.15
298.15
298.15
298.15
323.15
323.15
323.15
0.83
3.86
6.55
0.76
1.21
1.44
2.31
3.59
4.48
6.95
9.23
0.7
1.38
2.04
3.31
4.00
7.27
9.93
1.72
3.59
5.52
7.38
10.69
3.45
8.96
11.38
1.60
6.31
6.36
7.86
5.68
4.62
16.14
17.75
16.97
17.67
19.20
37.24
21.13
18.02
43.45
45.26
47.94
48.54
178.52
112.00
190.49
213.24
230.81
629.11
734.81
783.54
0.105
0.164
0.060
0.107
0.110
0.143
0.098
0.273
0.150
0.204
0.392
0.41
0.14
0.057
0.972
0.855
0.685
0.706
2.758
0.797
0.000
0.299
1.861
1.081
1.302
0.833
0.269
0.324
0.277
0.320
0.297
0.303
0.445
0.539
0.445
0.476
0.601
0.885
0.492
0.44
1.327
1.269
1.204
1.225
4.518
1.514
3.818
4.282
4.983
12.631
14.756
15.695
V-LHg
L-LHg
L-LHg
V-LHg
V-LHg
V-LHg
L-LHg
L-LHg
L-LHg
L-LHg
L-LHg
V-LHg
V-LHg
V-LHg
L-LHg
L-LHg
L-LHg
L-LHg
V-LHg
V-LHg
L-LHg
L-LHg
L-LHg
V-LHg
V-LHg
V-LHg
1
2
3
4
5
6
7
246.65
252.94
263.02
272.89
282.78
297.40
307.69
1.03
1.03
1.03
1.03
1.72
3.45
3.45
14.46
24.86
51.08
88.25
180.40
396.52
624.95
0.455
0.82
0.719
0.098
0.204
3.12
1.16
0.609
1.01
1.501
1.977
4.212
8.52
12.56
Standard uncertainites are u(T) ¼ 0.005K and u(P) ¼ 0.01 MPa; V: vapour; L: Liquid;
LHg: liquid mercury.
Standard uncertainites are u(T) ¼ 0.005K and u(P) ¼ 0.01 MPa.
Table 8
Mercury solubility in CO2.
Npts
T/K
P/MPa
yHg/ppb
stdev
uc(y)
Phases
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
243.15
243.15
243.15
243.15
243.15
243.15
258.15
258.15
258.15
258.15
258.15
258.15
273.15
273.15
273.15
273.15
298.15
298.15
298.15
298.15
298.19
323.15
323.15
323.15
0.39
0.68
1.05
1.69
2.45
7.24
0.74
1.39
2.07
2.30
3.45
8.69
1.41
2.11
3.46
7.93
2.77
4.34
7.24
11.72
1.77
5.39
9.51
13.79
2.40
1.29
0.94
1.04
1.06
1.08
7.23
4.55
3.08
3.75
3.83
3.92
22.28
15.97
9.77
12.67
111.90
76.35
85.76
88.89
176.89
429.47
371.43
437.93
0.054
0.049
0.006
0.012
0.006
0.006
0.211
0.079
0.094
0.060
0.060
0.060
0.131
0.150
0.072
0.177
0.717
1.401
1.41
0.12
1.813
1.005
3.720
2.637
0.252
0.251
0.246
0.246
0.246
0.246
0.362
0.277
0.272
0.28
0.282
0.283
0.568
0.457
0.336
0.303
0.758
1.422
1.43
0.27
1.829
1.034
3.720
2.648
V-LHg
V-LHg
V-LHg
L-LHg
L-LHg
L-LHg
V-LHg
V-LHg
V-LHg
L-LHg
L-LHg
L-LHg
V-LHg
V-LHg
V-LHg
L-LHg
V-LHg
V-LHg
L-LHg
L-LHg
L-LHg
V-LHg
V-LHg
V-LHg
Standard uncertainites are u(T) ¼ 0.005K and u(P) ¼ 0.01 MPa.
5.3. Propane
Fig. 8. Experimental and calculated mercury solubilities in ethane; experimental data
from Mentzelos [13] also discussed/reported in Ref. [11] ( ); Yamada et al. [7]: ( ); this
work: ( ): 244.15 K; ($$$): 258.15 K; ( ) 273.15 K; ( ): 298.15 K; ( ): 323.15 K; Black
lines: PR-78 with kij reported in Table 3.
The mercury content in propane measured in this work are
listed in Table 7 and shown in Fig. 10. Four independent data sets
(including ours) are available for the solubility of mercury in liquid
propane. Like for ethane, the kijs were also found to have a slight
temperature dependence (Table 3 & Table 4). The deviations between the model and the experimental are 2.9% for both EoSs.
Fig. 9. Impact of Interaction Parameters - Experimental and calculated mercury solubilities in ethane at 273.15 K; experimental data from Mentzelos [13] also discussed/reported in
Ref. [11] ( ); Yamada et al. [7]: ( ); this work: ( ); Dashed and solid lines: PR-78.
A. Chapoy et al. / Fluid Phase Equilibria 520 (2020) 112660
9
Table 9
Mercury solubility in nitrogen.
Fig. 10. Experimental and calculated mercury solubilities in liquid propane; experimental data from Butala et al. [8] ( ); Marsh et al. [10] ( ); Mentzelos [13] also discussed/reported in Refs. [11] ( ) and this work ( ). Dashed grey lines PR-78 (kij ¼ 0)/
Black lines: PR-78 with kij reported in Table 3.
5.4. Carbon dioxide
Three data sets (including these new data) are available for the
solubility of mercury in carbon dioxide (Fig. 11). The new data are
listed in Table 8. As for ethane and propane, only the data in the
liquid region and data above the critical points of carbon dioxide
were used to optimise the parameters. The kijs were also found to
have a slight temperature dependence as reported in Tables 3 and 4.
The behaviour is very similar to ethane: (i) in the CO2 vapour
region, the mercury content is decreasing with pressure and the
temperature dependency is closely related to the vapour pressure
of mercury, (ii) in the liquid region, different trends are observed,
an increase in the solubility of mercury in the liquid region is
observed, however the differences in mercury content between the
vapour and liquid region are not as pronounced as for ethane.
5.5. Nitrogen
Mercury content in nitrogen has been measured from 243.15 to
423.15 K and up to 19 MPa. The new data are listed in Table 9. Only
one source is available for nitrogen, and the data are limited to
273.15 K and pressure lower than 6.9 MPa. Our new data expand
the range both in term of temperature and pressure. The model can
reproduce the mercury solubility in the vapour phase with a single
Figure 11. Experimental and calculated mercury solubilities in Carbon Dioxide at
243.15, 258.15, 268.15, 273.15, 278.15, 283.15, 288.15, 293.15, 298.15, 303.15 and
323.15 K; experimental data from Butala et al. [8]: ( ); Yamada et al. [7]: ( ); this
work: ( ): 243.15 K; ( ): 258.15 K; ( ): 273.15 K; ( ): 298.15 K; ): 323.15 K; Black
lines: PR-78 with kij reported in Table 3.
Npts
T/K
P/MPa
yHg/ppb
stdev
uc(y)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
244.35
244.35
244.35
244.35
258.15
258.15
258.15
258.15
258.15
273.15
273.15
273.15
273.15
273.15
298.26
298.26
298.28
298.26
298.28
298.15
323.18
323.18
323.18
323.18
0.74
1.42
3.81
5.99
1.23
2.68
5.26
10.41
16.48
1.07
2.62
5.01
8.79
14.34
0.70
1.23
2.49
5.08
9.69
17.25
2.90
5.29
10.20
17.28
1.75
1.04
0.56
0.46
5.22
2.81
1.81
1.27
0.94
25.02
12.43
7.45
5.47
4.58
383.96
231.28
125.40
74.49
51.15
38.57
670.31
416.19
258.06
186.13
0.022
0.047
0.008
0.006
0.275
0.020
0.027
0.015
0.037
0.060
0.360
0.052
0.021
0.051
0.353
1.098
0.373
0.332
0.488
0.353
0.247
1.152
1.721
4.840
0.250
0.251
0.246
0.246
0.387
0.254
0.251
0.248
0.249
0.610
0.516
0.301
0.275
0.271
6.350
3.978
2.117
1.297
1.005
0.768
9.391
5.944
4.009
5.502
Standard uncertainites are u(T) ¼ 0.005K and u(P) ¼ 0.01 MPa.
binary interaction parameter as seen in Fig. 12. The optimised kijs
are 0.222 and 0.111 for the PR-EoS and SRK-EoS, respectively. The OF
(defined in equation (10)) is equal to 13.1% and 12.8% for the PR-EoS
and SRK-EoS, respectively. It is worth noting that the experimental
uncertainties for the 243.15 K isotherm are greater than the actual
measurements hence the relatively high objective function.
5.6. Comparison
As seen in Fig. 13, the mercury solubility at the same pressure and
temperature conditions is higher in liquid hydrocarbons than in
vapour hydrocarbon and non-hydrocarbon gases. The following
ranking in term of solubility can be established C3H8>C2H6>CH4>N2
and with the solubility in CO2 very close to N2 in the vapour region
and higher in the liquid region but significantly lower than in ethane.
In general, for liquid hydrocarbons, it can be observed that the
mercury content is increasing with the carbon number.
Fig. 12. Experimental and calculated mercury solubilities in nitrogen at 243.15, 258.15,
273.15, 298.15 and 323.15 K; experimental data from Mentzelos [13] also discussed/
reported in Ref. [11]: ( ); this work: ( ): 243.15 K; ( ): 258.15 K; ( ): 273.15 K; ( ):
298.15 K; ( ): 323.15 K; Black lines: PR-78 with kij reported in Table 3.
10
A. Chapoy et al. / Fluid Phase Equilibria 520 (2020) 112660
References
Fig. 13. Experimental and calculated mercury solubilities at 273.15 in methane, ethane,
propane, N2, and CO2 e Lines were calculated using the PR-EoS (ideal model ¼ PsatHg/
P).
6. Conclusion
In this work, the mercury contents in single component fluids
have been measured over a wide range of pressure and temperature.
From this work, it can be concluded that at intermediate pressure
(P < 7 MPa) and in the vapour region, the solubility of mercury is
decreasing with pressure. The measurements also show that the
mercury solubility in the liquid region is higher than in the gas region, and is higher in liquid hydrocarbons than liquid carbon dioxide. Using the adjusted parameters, the models can provide accurate
predictions of mercury partitionning, across a wide range of pressure and temperature. Further measurements for multicomponent
mixtures are nevertheless required to validate the model.
Declaration of competing interest
The authors declare that they have no known competing
financial interests or personal relationships that could have
appeared to influence the work reported in this paper.
CRediT authorship contribution statement
Antonin Chapoy: Investigation, Data curation, Software, Writing
- review & editing. Pezhman Ahmadi: Investigation, Visualization.
Richard Szczepanski: Supervision, Visualization, Writing - review
& editing. Xiaohong Zhang: Writing - review & editing. Alessandro
Speranza: Project administration, Writing - review & editing. Junya
Yamada: Project administration, Supervision, Writing - review &
editing. Atsushi Kobayashi: Writing - review & editing.
Acknowledgments
This work was part of a OGIC (Oil & Gas Innovation Centre)
project (https://www.ogic.co.uk/mercury-related-risk/) conducted
at the Institute of Petroleum Engineering, Heriot Watt University.
The project was supported by KBC (A Yokogawa Company), INPEX
Corporation and OGIC, which is gratefully acknowledged.
Appendix A. Supplementary data
Supplementary data to this article can be found online at
https://doi.org/10.1016/j.fluid.2020.112660.
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