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Solvation structure of supercritical CO2 and brine mixture for CO2 plume geothermal applications: A molecular dynamics study
Journal Pre-proof Solvation structure of supercritical CO2 and brine mixture for CO2 plume geothermal applications: A molecular dynamics study Zongliang Qiao, Yue Cao, Yuming Yin, Lingling Zhao, Fengqi Si
PII:
S0896-8446(20)30034-6
DOI:
https://doi.org/10.1016/j.supflu.2020.104783
Reference:
SUPFLU 104783
To appear in:
The Journal of Supercritical Fluids
Received Date:
12 July 2019
Revised Date:
5 February 2020
Accepted Date:
5 February 2020
Please cite this article as: Qiao Z, Cao Y, Yin Y, Zhao L, Si F, Solvation structure of supercritical CO2 and brine mixture for CO2 plume geothermal applications: A molecular dynamics study, The Journal of Supercritical Fluids (2020), doi: https://doi.org/10.1016/j.supflu.2020.104783
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Solvation structure of supercritical CO2 and brine mixture for CO2 plume geothermal applications: A molecular dynamics study Zongliang Qiao*, Yue Cao, Yuming Yin, Lingling Zhao, Fengqi Si Key Laboratory of Energy Thermal Conversion and Control of Ministry of Education,
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Southeast University, Nanjing, 210096, China
* Corresponding author: Zongliang Qiao*
Key Laboratory of Energy Thermal Conversion and Control of Ministry of Education,
E-mail address: [email protected]
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Graphical abstract
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Tel: +86 13770829247
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Southeast University, Nanjing, 210096, China
Highlights
Solvation structure of scCO2/brine mixture produced by CPG was investigated.
Molecular dynamics simulations were performed for different compositions.
Temperature and ion concentration affected the interaction of H2O and ion.
The scCO2/brine mixture was heterogeneous in the CPG application.
Abstract: This paper reports an investigation for solvation structure of supercritical CO2 (scCO2) and brine mixture for CO2 plume geothermal (CPG) applications. Molecular dynamics simulations are performed to calculate radial distribution function, coordination number and hydrogen-bond number for mixtures of different compositions. This study can help reveal the solvation structures of scCO2/brine
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mixture under different temperatures (373.15 K to 473.15 K) and ion concentrations (1 wt% to 10 wt%). Results show that H2O molecules bind more tightly to Na+ ion
than Cl- ion while scCO2 molecules seem have a uniform distribution in the
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scCO2/brine mixture. Both the interaction of Na+-H2O pairs and that of Cl--H2O pairs
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become stronger under higher temperature conditions. Besides, the increase of ion concentration not only reduces the number of H2O molecules in the solvation shell of
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Na+ ion, but also weakens the interaction of hydrogen bonds. Moreover, it seems that
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the scCO2/brine mixture is heterogeneous in the CPG application.
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KEYWORDS: Molecular dynamics simulation; scCO2/brine mixture; Solvation
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structure; Ion pair; CO2 plume geothermal.
Nomenclature
g(r)
radial distribution function
k
fraction of CO2 molecules
N
number of particles
number of hydrogen bonds
n(r)
coordination number
P(r)
probability
q
charge of particle (C)
r
distance (m)
r1
first minimum of RDF (m)
Tc,model
model critical temperature (K)
Tr,sim
reduced simulation temperature
Tsim
simulation temperature (K)
V
volume (m3)
Vc
Coulomb term of non-bonded interaction energy (J)
VLJ
Lennard-Jones term of non-bonded interaction energy (J)
Vij
non-bonded interaction energy (J)
XNaCl
NaCl mass fraction
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vaccum permittivity (C2 N-1 m-2)
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0
na
Greek letters
parameter of Lennard-Jones potential probability density parameter of Lennard-Jones potential
Subscripts A
solvent atom A
a
anion
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nHB
solute ion B
c
cation
Hw
hydrogen atom of H2O
i
particle i
j
particle j
Oc
oxygen atom of CO2
Ow
oxygen atom of H2O
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B
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1. Introduction
Modern coal-fired power plants are increasingly being combined with carbon
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capture and storage (CCS) systems, typically geological sequestration [1]. As
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supercritical carbon dioxide (scCO2) is a better working fluid for geothermal energy utilization than water [2], a novel CO2 plume geothermal (CPG) [3] power generation
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system is proposed to sequestrate CO2 and utilize geothermal energy simultaneously. The produced scCO2 has a pressure of (8 to 26) MPa and a temperature of (333.15 to
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473.15) K. However, this production may contain brine (about 10% mass fraction [4]),
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which is harm to the turbine and heat exchangers of the power generation system [5]. To solve this issue, properties of scCO2/brine mixture should be studied. A wide range of analyses for scCO2/brine mixture have been performed in recent
years, focusing on different aspects of properties. Duan and Zhang [6] studied the PVTx properties of CO2/H2O mixtures and proposed equations of state for H2O, CO2 and CO2/H2O. Yang et al. [7] conducted a molecular dynamics study to show PVT
properties of CO2/H2O mixture, in which the H2O is supercritical or near-critical. Chapoy et al. [8] focused on the thermophysical properties and phase behavior of a CO2-rich system. By their experimentally and theoretically investigation, the effect of water on density and viscosity of CO2/H2O mixture could be obtained. Zhao et al. [9, 10] presented investigations on the interfacial tension between supercritical CO2 and brine. They concluded these investigations would help directly predict interfacial
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tension in scCO2-complex electrolyte solution systems for practical applications.
Besides, other researchers mainly focused on the solubility of scCO2/brine mixture. Caumona et al. [11] developed an experimental platform for solubility measurement
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and obtained the solubility of water in CO2 with the pressure from 0.5 MPa to 20 MPa.
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Wang et al. [12] investigated the solubility of water in CO2 varying from 10 MPa to 50 MPa and 313.15 K to 473.15 K by the experimental method of in-situ quantitative
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Raman spectroscopy. This study indicated that the solubility of water in CO2 was
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greater under high temperature conditions. Aavatsmark and Kaufmann [13] proposed a function for solubility calculation of water in dense-phase CO2 by experimental data.
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It showed that the solubility of water first declined and then rose with the increase of pressure when the temperature was between 373.15 K and 473.15 K.
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To understand the microscopic characteristics of the scCO2/brine mixture, the
solvation structure of brine in scCO2 should also be studied. Keshri and Tembe [14] investigated the ion association in water/CO2 mixture by molecular dynamics simulations. Their study focused on the mixture of supercritical conditions of 673 K and 39.94 MPa while the temperature and pressure of CPG production were much
lower. Under the conditions of CPG applications, water is subcritical which means that the solvation structure may be different. Keshri et al. [15] also conducted molecular dynamics simulations for Na+-Cl- ion pair in both supercritical methanol and water-methanol mixtures. Moreover, similar study was carried out by Hidayat et al. [16] to investigate the preferential solvation of K(I) ion in water/ammonia mixture. Callsen et al. [17] studied the solvation structure of lithium ions in ether solution.
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Petrenko et al. [18] investigated solvate structures of salicylic acid and its derivatives
in supercritical carbon dioxide by molecular dynamics simulations. Prasetyo and Hofer [19] studied hydration free energy of carbon dioxide in aqueous solution and
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described the first hydration shell of CO2 in aqueous solution. Therefore, it indicates
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researchers have already focused on study solvation structure of mixtures. Moreover, based on former references, it seems that the molecular dynamics
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(MD) simulation is a viable option to investigate the solvation characteristics of
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scCO2/brine mixture. This is because molecular dynamics simulations consider the interactions between atoms and molecules at microscopic level, which are unavailable
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by experimental investigations. Yoon et al. [20] presented a molecular dynamics simulation on the local density distribution and solvation structure of supercritical
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carbon dioxide around naphthalene. Silveira et al. [21] conducted a molecular dynamics study on the solvation of carbon dioxide in the ionic liquids. Xue et al. [22] used the spatial distribution functions to describe the solvation structure of supercritical carbon dioxide around the ether group by molecular dynamics simulations. Qi et al. [23] investigated the solvation free energy of carbon dioxide in
the mixture of brine and CH4 through molecular dynamics simulations. Besides, a molecular dynamics simulation was conducted by Wang et al. [24] to show the difference of solvation structure between benzaldehyde and cinnamaldehyde by using radial distribution functions at different CO2 densities. Vaz et al. [25] presented a molecular dynamics simulation for structural properties of ketones in supercritical carbon dioxide at infinite dilution, which means each ketone was surrounded by
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carbon dioxide molecules only.
Although much literature is available on solvation structure investigation for both carbon dioxide in solutions and solute in dense-phase supercritical carbon
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dioxide, limited work has been published on brine solvation structure in supercritical
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carbon dioxide. Moreover, within the temperature and pressure range of scCO2/brine mixture produced by CPG, carbon dioxide is supercritical while water is subcritical.
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This makes the solvation structure of scCO2/brine mixture more complicated and
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worthy of study. As solubility is a function of temperature and pressure, the mass fraction of solute brine in scCO2 will change with its temperature and pressure, which
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may result in different solvation structures. Therefore, to better understand this issue, the effects of thermodynamic parameters should be considered.
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In the present study, molecular dynamics simulations are performed to predict
solvation structure of scCO2/brine mixture produced by CPG. Results from this paper may present why solute brine in scCO2 has such solvation structure and offer what the effects of thermodynamic parameters on the solvation structure are. The investigation in this paper may help solve issues of CPG applications. The organization of this
paper is as follows. In Section 2, the computational methods are described and simulation conditions are presented, respectively. In Section 3, results for molecular dynamics simulations are provided and further discussion is made on the influence of simulation conditions. Then Section 4 presents concise conclusions.
2. Computational Methods
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2.1 Force field parameters
In the present MD simulation, non-bonded interactions of the force field include two terms: Lennard-Jones term (for repulsion and dispersion, i.e. van der Waals
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attractions) and Coulomb term (for electrostatic interactions). The equation for
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non-bonded interaction energy can be expressed as follows
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ij Vij (rij ) VLJ (rij ) Vc (rij ) 4 ij rij
12 6 ij 1 qi q j rij 4 0 rij
(1)
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where rij is the distance between particle i and particle j, q is charge of particle and ε0 is the vacuum permittivity. As the Lorentz-Berthelot rules used, εij and σij can be
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calculated by
ij ( ii jj )1/2 1 2
ij ( ii jj )
(2) (3)
The cut-off radius for the Lennard-Jones attractions is set to be 1.2 nm. For Coulomb interactions, a shifted potential is applied using the fourth order Particle Mesh Ewald (PME) with a cut-off radius of 1.2 nm.
Bonded interactions for CO2 and H2O are estimated by EPM2 [26] model and TIP3P [27] model, respectively. To valid these molecular models, the phase boundaries of CO2 and H2O were reproduced by simulation data, experimental data and equation of state (EOS) data, as shown in Table 1. Besides, Na+ and Cl- (main ions in brine) are modeled using the OPLS force field [28].
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2.2 Data analyses The radial distribution function (RDF) is a key evaluation parameter to reveal the solvation structure of scCO2/brine mixture, as it can present how the normal number
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density of solvent atoms (B) distribute around the solute ion (A) at different distances. Therefore, RDF gAB(r) is shown as
N A NB 1 V P(r ) 4 r 2 iA iB
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g AB (r )
(4)
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where V is volume, P(r) is the probability of finding a solvent atom at distance r from
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a solute ion.
Then the coordination number (CN) nAB, which represents the number of solvent
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atoms or molecules bonded to a central solute ion, is defined as r1
nAB 4 r 2 g AB (r ) B dr 0
(5)
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where r1 is the first minimum of RDF. Therefore, nAB is the area under the first peak of gAB(r).
The definition of hydrogen bond is based on geometric rules. Two water molecules are chosen as being hydrogen bonded only if their interoxygen distance is less than 3.5 Å, and simultaneously the O-H...O angle is less than 30° [35].
2.3 MD simulation system In this paper, the solvation structure of scCO2/brine mixture with variable temperature (373.15-473.15 K) and fixed pressure (20 MPa) was first studied. Under such simulation condition, CO2 is within supercritical region (critical point of 304.13 K and 7.377 MPa [31]) while H2O is within liquid region (critical point of 647.1 K
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and 22.064 MPa [34]). In CPG applications, brine was saturated in dense-phase
supercritical carbon dioxide. Therefore, compositions of scCO2/brine mixture would change with its temperature because brine solubility in scCO2 varied. Table 2 lists
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compositions of present MD simulation systems under different temperatures. For
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Case 1-3, the numbers of H2O molecules and CO2 molecules were determined by solubility of brine in scCO2 and mass fraction of NaCl in brine [12]. For Case 4-7,
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different amounts of ions were added into simulation system to investigate what the
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effect of ion concentration on the solvation structure of scCO2/brine mixture was.
2.4 Solution procedure
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All MD simulations were performed in the platform of GROMACS 5.1.4 [36].
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The simulation box for Case 1-3 was of a geometric parameter of 3.4 nm × 3.4 nm × 3.4 nm, as shown in Fig. S1. Case 4-7 had larger simulation boxes of 8 nm × 8 nm × 8 nm as more molecules were added. Initial positions for ions, CO2 and H2O molecules were random. The Newtonian equations of motion were integrated using leap-frog algorithm with a time step of 1 fs. Before MD simulations conducted, the process of energy minimization (EM) was done by the steepest decent algorithm to ensure the
MD simulation system had a reasonable starting structure. Then MD simulations were carried out under isothermal-isobaric NPT ensemble. The temperature and pressure for each simulation were controlled by the Nosé-Hoover thermostat [37, 38] and Parrinello-Rahman barostat [39], respectively. All MD simulations in this study were
3. Results and discussion 3.1 Radial distribution functions & coordination numbers
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calculated for 15 ns.
In this section, a MD simulation is first performed for Case 1 to show the radial
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distribution functions and coordination numbers of Na+ and Cl- ions at different
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distances. Figure 1 presents that the interactions of ions and CO2 molecules are quite different from those of ions and H2O molecules. The RDFs of Na+-Ow and Cl--Ow are
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maximum at 0.238 nm and 0.324 nm, respectively. Then they decline rapidly with the
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increase of particle distance. Although the RDFs of Na+-Oc and Cl--Oc have maximal values, the RDFs at r=1.6 nm vary less than 20% from their maxima. This is because
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polar molecules (H2O) gather around ions while nonpolar molecules (CO2) disperse in the whole space. Moreover, a greater maximum of g(r) and a smaller corresponding
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particle distance of Na+-Ow indicate that H2O molecules seem to bind more tightly to Na+ ion than Cl- ion in the scCO2/brine mixture. Results for coordination numbers of different particles are illustrated in Fig. 2. The variation trend of nNa-Ow(r) implies that there is a solvation shell for Na+ ion. Comparing with the particle distances of Na+-Ow and Cl--Ow at low CNs, it seems that
H2O molecules could gather closer to Na+ than Cl- in the scCO2/brine mixture. The variations of CNs of Na+-Oc and Cl--Oc show cubic polynomial increase trends. It is likely that ions have limited effect on the distribution of supercritical CO2 molecules. Therefore, it is inferred that scCO2 molecules may have a uniform distribution in the simulation space.
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3.2 Effect of thermodynamic parameter
In the application of CPG, the temperature not only influences compositions of
the scCO2/brine mixture but also affects its solvation structure. The compositions
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have already been calculated by the solubility of brine in scCO2 under three different
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temperatures varying from 393.15 K to 473.15 K, which are typical temperatures of CPG productions. Then three MD simulations are conducted to present what the effect
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of temperature on the solvation structure is. Since the critical temperature may be
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different for molecular models, the simulation temperatures are modified by the critical temperature of EPM2 CO2 and TIP3P H2O in this study. Therefore, the
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reduced simulation temperature Tr,sim is defined as the ratio of simulation temperature Tsim and model critical temperature Tc,model, as presented in Table S1.
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Figure 3 shows the variations of RDFs of Na+-Ow and Na+-Oc with different
temperatures. The results for Na+-Ow indicate the decline of temperature can reduce the maximum of g(r), which is further presented by the inset of Figure 3(a). As a consequence, the coordination numbers may be changed which will be discussed later. Figure 3(b) illustrates the decrease of temperature is favorable to enlarge the
maximum of RDF while this peak will appear at a larger particle distance. More supercritical CO2 molecules are added to the simulation system when the simulation temperature decreases. This is able to explain why a greater peak appears with the decrease of temperature. Moreover, the results for particle distances of these peaks imply the interactions of Na+ ion and H2O molecules are stronger under higher temperature conditions.
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The variations of radial distribution functions of Cl- ion with the decrease of temperature are presented in Fig. 4. There exists a bias between the blue line and the
other two lines from r=0.4 nm to 1.0 nm in Fig. 4(a). This helps to explain that both
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Cl- ion and Na+ ion have stronger ability to bond H2O molecules under higher
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temperature conditions. In Fig. 4(b), the peaks of gCl-Oc(r) with the reduced simulation temperatures of 1.385 and 1.257 appear at a smaller particle distance comparing with
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those of gNa-Oc(r). If the particle distance differences of these peaks in Figure 4(b) are
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discussed, it can find that the temperature has limited effect on them. Former simulation results have already indicated that only Na+-Ow has an
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obvious solvation shell. Therefore, the numbers of H2O molecules in the first solvation shell of Na+ ion with different temperatures are presented in Table 3. The
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increase of temperature results in larger first solvation shell radius. The molecular thermal motion may be the main reason for this variation. It is definitely that molecules move more intensely under higher temperature conditions. Besides, more H2O molecules will stabilize at the first solvation shell of Na+ ion under low temperature conditions. These all imply the first solvation shell of Na+ ion will
become weaker with the increase of temperature.
Coordination numbers of the first solvation shell for the other three particle interactions in the scCO2/brine mixture are not presented because their first solvation shells are not obvious. But we can still discuss how the temperature affects their coordination numbers at specific radius. Table 3 further lists the results for these
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coordination numbers with different temperatures at the radius of 1.6 nm. It is
concluded that the coordination numbers of Na+-Oc and Cl--Oc are almost equal at any temperature. One reason for this phenomenon is that polar ions (Na+ and Cl-) have
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limited influence on nonpolar molecules of CO2, therefore CO2 molecules will
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distribute uniformly in the simulation space. The other reason is that Na+ ion and Clion may associate to an ion pair, which means they have approximate coordination
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numbers. Moreover, a fraction of CO2 molecules k is defined as the ratio of
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coordination number at 1.6 nm and total CO2 molecule number. Although the variations of coordination numbers indicate that CO2 molecules have intense
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distribution under low temperature conditions, the results of kNa-Oc and kCl-Oc imply more CO2 molecules distribute out of the sphere with a radius of 1.6 nm. The
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snapshot of scCO2/brine mixture under the condition of 393.15 K is illustrated in Fig. 5. This further validates a Na+-Cl- ion pair does associate under such simulation condition and there exists a stable solvation shell of H2O molecules around this ion pair. Therefore, it is concluded that the increase of temperature will make the first solvation shell of Na+-Cl- ion pair become weaker.
3.3 Effect of ion concentration Brine composition is another key parameter which may affect the solvation structure of scCO2/brine mixture. As the NaCl mass fraction of brine in CPG production may vary, the investigation of ion concentration effects becomes further significant. Firstly, a simulation is performed for Case 4, which is just a mixture of
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supercritical CO2 and water. This is selected as a reference for those cases with different ion concentrations.
Figure 6 shows the interactions of H2O molecules in the scCO2/H2O mixture.
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The variation curve of gOw-Ow(r) has an obvious peak and finally drops to zero. This
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implies H2O molecules may be clustered in the supercritical CO2 environment. The results for nOw-Ow(r) further prove this inference because nOw-Ow(r) is almost achieved
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300 at the radius of 3.2 nm. This is an interesting conclusion considering water is able
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to solvate in supercritical CO2. Therefore, it seems that the scCO2/H2O mixture is heterogeneous under the conditions of CPG application. Moreover, the results for
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gOw-Hw(r) in Fig. 6(a) can helps to explain the interaction of hydrogen bond (H-bond) in the scCO2/H2O mixture. The first peak of H-bond appears at the radius of 0.184 nm,
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which is consistent with the result of Ref. [40]. The first minimum of gOw-Hw(r) indicates that the number of hydrogen bonds per oxygen atom is 3.579. Then simulations are carried out for Case 5 and Case 7 to present what the effect of ion concentration on the interactions of Ow-Ow and Ow-Hw is. In Fig. 7(a), the peak of gOw-Ow(r) for Case 7 is much smaller, as well as the area under the variation curve
of gOw-Ow(r). This is because H2O molecules around the Na+ ion and Cl- ion will bind to them. Therefore, the coordination number of Ow-Ow will become smaller at the same time. The results for gOw-Hw(r) imply the interaction of hydrogen bond in the scCO2/H2O mixture will become weaker with the increase of ion concentration. Furthermore, the first minimum of gOw-Hw(r) for Case 7 indicates its number of hydrogen bonds per oxygen atom decreases to 3.194.
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The effects of ion concentration on the RDFs of Na+ ion and Cl- ion are illustrated in Figs. 8 and 9, respectively. A lower peak of gNa-Ow(r) achieves around
0.24 nm when the ion concentration goes up. Besides, the first minimum of gNa-Ow(r)
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reaches at larger radius with the increase of ion concentration. These both indicate
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that less H2O molecules are contained in the first solvation shell of Na+ ion. Table 4 lists the results for coordination numbers of Na+-Ow with different ion concentrations.
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This also suggests the number of H2O molecules in the first solvation shell of Na+ ion
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decreases with the increase of ion concentration. However, it cannot be inferred that H2O molecules bind to ions more tightly under higher ion concentration, because
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interactions between ions have not been discussed yet. Figure 8(b) indicates CO2 molecules are not able to form a solvation shell under any simulated ion concentration
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because of their nonpolarity. The RDF of Na+-Oc for Case 7 has a lower peak. As more Na+-Cl- ion pairs are contained in Case 7, it seems that the Na+-Cl- ion pairs are clustered together. Thus, ion pairs in the center may have fewer CO2 molecules around them while other ion pairs may be surrounded by more CO2 molecules. In general, their mean RDF of Na+-Oc shows such variation trend as Figure 8(b).
The results for gCl-Ow(r) present the first solvation shell of H2O molecules around Cl- ion only appears under quite low ion concentration conditions, as shown in Fig. 9(a). Considering the discussion above for H2O molecules clustering, it seems that the amount of H2O molecules is great enough so that the Na+-Cl- ion pair is dissolved into single Na+ ion and Cl- ion. This is the reason why the first solvation shell of H2O
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forms under such conditions. Besides, it also helps to explain why the first maxima of Case 5 in Figs. 8(b) and 9(b) are lower than those of Case 6. Furthermore, the curves
of gNa-Oc(r) and gCl-Oc(r) for Case 7 have similar variation trend, which implies ion
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pairs exist under high ion concentration conditions.
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Table 4 further presents the coordination numbers of cases with different ion concentrations at the radius of 3.2 nm. The variations of these coordination numbers
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indicate that ion interactions affect the interactions of Na+-H2O pairs and Cl--H2O
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pairs, as well as those between H2O molecules, resulting in smaller CNs at high ion concentration condition. Specifically, it seems the decrease of CN number has an
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approximate linear relation with the increase of ion concentration. Moreover, the solvation structure of Na+-Cl- ion pair with different ion
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concentration may be different when comparing results for RDF in Figs. 8(a) and 9(a). The peak value of RDF of Na+-Ow is quite different for Case 5 and Case 7. With the decrease of ion concentration, this peak value falls from 426.454 to 205.241. Results in Fig. 9(a) present the peak values of RDF of Cl--Ow for Case 5 and Case 7 are 227.003 and 76.927, respectively. These rapid decreases show more H2O molecules
occupy the space around Na+ ion and Cl- ion under low ion concentration condition. Therefore, it is likely that the distance of Na+-Cl- pair varies with the ion concentration. Fig. 10 illustrates the snapshot of scCO2/brine mixture for Case 7. It further indicates that the scCO2/brine mixture is heterogeneous under the condition of CPG application. Snapshot for other simulated cases are further presented in Fig. S2.
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3.4 Hydrogen bond analysis
Results for gOw-Hw(r) show ion concentration may influence the interactions of
hydrogen bonds. Therefore, further investigation is performed to present the
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relationship between ion concentration and number of hydrogen bonds, as listed in
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Table 5. The NaCl mass fraction XNaCl is calculated by compositions of scCO2/brine mixture. The results indicate the number of total hydrogen bonds nHB in the simulation
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system declines monotonically with the increase of XNaCl.
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By fitting these simulation results, it is likely that the nHB has a quadratic polynomial decrease trend when the XNaCl goes up, which can be expressed as (6)
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nHB 1.8491( X NaCl )2 6.3494 X NaCl 368.3 1wt% X NaCl 10wt%
The rapid decrease of nHB implies the electrostatic interactions of ions and H2O
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molecules are stronger than the hydrogen bonding interactions between H2O molecules. Thus, much fewer hydrogen bonds form between H2O molecules under higher ion concentration condition. Moreover, MD simulation results for Case 4 show its number of hydrogen bonds is 359, which is less than that of Case 5. This maybe because the addition of ion pair makes the cluster of H2O molecules associate closely.
It means more H2O molecules are able to reach within the hydrogen bonding range of their neighbor H2O molecules. Under the combined effect of electrostatic interaction and hydrogen bonding interaction, the number of total hydrogen bonds in the scCO2/brine mixture presents the former variation trend.
4. Conclusions
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Molecular dynamics simulation was performed for the solvation structure of
scCO2/brine mixture produced by the CO2 plume geothermal system. Based on the analyses conducted in this investigation, the following conclusions may be drawn:
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(1) H2O molecules bind more tightly to Na+ ion than Cl- ion in the scCO2/brine
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mixture while supercritical CO2 molecules seem have a uniform distribution in the whole space. Besides, there is a solvation shell of H2O molecules around Na+ ion.
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(2) Both Na+ ion and Cl- ion have stronger ability to bind H2O molecules under higher
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temperature conditions. The increase of temperature will make the first solvation shell of Na+-Cl- ion pair become weaker.
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(3) Less H2O molecules are contained in the first solvation shell of Na+ ion under higher ion concentration conditions. Moreover, a first solvation shell of Cl- ion
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will appear under quite low ion concentration condition.
(4) It seems that the scCO2/brine mixture is heterogeneous under the conditions of CPG application. (5) The interaction of hydrogen bond in the scCO2/brine mixture becomes weaker with the increase of ion concentration. It is likely that the number of total
hydrogen bonds has a quadratic polynomial decrease trend when the ion concentration increases.
Declaration of interests 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.
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Acknowledgement The authors gratefully acknowledge the financial support by the National Natural
Science Foundation of China (Grant No. 51976031) and Qinglan Project of Jiangsu
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Province, China.
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ro of
Figure captions
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na
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(a)
(b) Fig. 1. Results for radial distribution functions of ions and molecules in scCO2/brine mixture of Case 1. (a) Blue line for Na+-Ow, red line for Cl--Ow; (b) blue line for
-p
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Na+-Oc, red line for Cl--Oc.
Jo
ur
na
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(a)
(b)
Fig. 2. Results for coordination numbers of ions and molecules in scCO2/brine mixture of Case 1. (a) Blue line for Na+-Ow, red line for Cl--Ow; (b) blue line for Na+-Oc, red line for Cl--Oc.
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(b)
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na
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-p
(a)
Fig. 3. Results for radial distribution functions of Na+ ion in scCO2/brine mixture with different reduced simulation temperatures. (a) Na+-Ow, (b) Na+-Oc. Blue solid line for Case 1; red dash line for Case 2; magenta dot line for Case 3.
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na
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-p
(a)
(b)
Fig. 4. Results for radial distribution functions of Cl- ion in scCO2/brine mixture with different reduced simulation temperatures. (a) Cl--Ow, (b) Cl--Oc. Blue solid line for Case 1; red dash line for Case 2; magenta dot line for Case 3.
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Fig. 5. Snapshot of Na+-Cl- ion pair and its first solvation shell in scCO2/brine mixture
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(a)
na
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-p
for Case 3.
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(b)
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Fig. 6. Results for interactions of H2O molecules in scCO2/H2O mixture. (a) Radial
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distribution functions, (b) coordination numbers. Blue solid line for Ow-Ow; red dash
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na
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line for Ow-Hw.
(a)
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(b)
-p
Fig. 7. Effect of ion concentration on radial distribution functions of H2O molecules
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in scCO2/brine mixture. (a) Ow-Ow, (b) Ow-Hw. Blue solid line for Case 4; red dash
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na
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line for Case 5; magenta dot line for Case 7.
(a)
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(b)
Fig. 8. Effect of ion concentration on radial distribution functions of Na+ ion in
-p
scCO2/brine mixture. (a) Na+-Ow, (b) Na+-Oc. Blue solid line for Case 5; red dash line
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na
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for Case 6; magenta dot line for Case 7.
(a)
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(b)
Fig. 9. Effect of ion concentration on radial distribution functions of Cl- ion in
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na
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for Case 6; magenta dot line for Case 7.
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scCO2/brine mixture. (a) Cl--Ow, (b) Cl--Oc. Blue solid line for Case 5; red dash line
Fig. 10. Snapshot of Na+-Cl- ion pair in scCO2/brine mixture for Case 7.
Table 1 Comparison among simulation data, experimental data and EOS data for critical parameters of CO2 and H2O. ρcrit/g·
pcrit/ Item
Tcrit/K cm-3
MPa 7.34 Simulation data [29]
312.8
0.453 0
Experimental
data
7.38
304.21 CO2
[30]
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EPM2
0.467
2
7.37
EOS data [31]
304.13
0.468
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-p
7
TIP3P
Experimental [33]
na
H2O
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Simulation data [32]
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EOS data [34]
12.6
578
0.272 0
data
22.0 647.1
0.322 64 22.0
647.1
0.322 64
Table 2 Compositions of MD simulation systems under different temperatures and ion concentrations. T/
p/
No.
NH2 Nc
K
NC
Ntot
Na
MPa
O
O2
al
473 1
20
1
1
20
1
1
20
1
1
30
116
148
433 2 .15 393 3
20
0
473 5
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.15
20
na
.15
re
473 4
30
275
307
30
646
678
116
146
-p
.15
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.15
1
0
300 0 116
1
20
ur
.15
0
Jo
.15
2 116
3
3
146
300 0
473
7
146
300
473
6
0
6 116
20
10
10
148
300 0
0
Table 3 MD simulation results for interactions of ions and molecules at first solvation shell and radius of 1.6 nm in Case 1, Case 2 and Case 3.
First solvation shell
Case 1
Case 2
Case 3
r1/nm
0.338
0.330
0.328
n(r)
3.856
4.075
4.294
NCO2
116
275
646
nNa-Oc(r)
83.791
102.816
121.383
kNa-Oc
0.722
0.374
0.188
nCl-Oc(r)
83.627
102.612
122.343
kCl-Oc
0.721
Radius of
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na
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-p
1.6 nm
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Item
0.373
0.189
Table 4 Results for coordination numbers of ions and molecules at first solvation shell and radius of 3.2 nm in Cases 4-7. Case
Case
Case
Case
Item 4
solvation shell
-
0.330
0.330
0.344
n(r)
-
5.259
5.028
4.056
nOw-Ow
296.1
296.0
294.8
279.3
84
59
nNa-Ow
81
298.5 -
(r)
32
298.5
-
67
Jo
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na
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r)
297.9
04
re
nCl-Ow(
85
-p
3.2 nm
7
r1/nm
(r) Radium of
6
ro of
First
5
290.2
22
297.9
49
290.3 11
Table 5 Results for number of hydrogen bonds of different ion concentrations in Cases 5-7. Case 5
Case 6
Case 7
Ion pair number
1
3
10
XNaCl (wt%)
1.071
3.145
9.765
nHB
373
370
254
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na
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ro of
Item
PII:
S0896-8446(20)30034-6
DOI:
https://doi.org/10.1016/j.supflu.2020.104783
Reference:
SUPFLU 104783
To appear in:
The Journal of Supercritical Fluids
Received Date:
12 July 2019
Revised Date:
5 February 2020
Accepted Date:
5 February 2020
Please cite this article as: Qiao Z, Cao Y, Yin Y, Zhao L, Si F, Solvation structure of supercritical CO2 and brine mixture for CO2 plume geothermal applications: A molecular dynamics study, The Journal of Supercritical Fluids (2020), doi: https://doi.org/10.1016/j.supflu.2020.104783
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Solvation structure of supercritical CO2 and brine mixture for CO2 plume geothermal applications: A molecular dynamics study Zongliang Qiao*, Yue Cao, Yuming Yin, Lingling Zhao, Fengqi Si Key Laboratory of Energy Thermal Conversion and Control of Ministry of Education,
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Southeast University, Nanjing, 210096, China
* Corresponding author: Zongliang Qiao*
Key Laboratory of Energy Thermal Conversion and Control of Ministry of Education,
E-mail address: [email protected]
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Graphical abstract
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Tel: +86 13770829247
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Southeast University, Nanjing, 210096, China
Highlights
Solvation structure of scCO2/brine mixture produced by CPG was investigated.
Molecular dynamics simulations were performed for different compositions.
Temperature and ion concentration affected the interaction of H2O and ion.
The scCO2/brine mixture was heterogeneous in the CPG application.
Abstract: This paper reports an investigation for solvation structure of supercritical CO2 (scCO2) and brine mixture for CO2 plume geothermal (CPG) applications. Molecular dynamics simulations are performed to calculate radial distribution function, coordination number and hydrogen-bond number for mixtures of different compositions. This study can help reveal the solvation structures of scCO2/brine
ro of
mixture under different temperatures (373.15 K to 473.15 K) and ion concentrations (1 wt% to 10 wt%). Results show that H2O molecules bind more tightly to Na+ ion
than Cl- ion while scCO2 molecules seem have a uniform distribution in the
-p
scCO2/brine mixture. Both the interaction of Na+-H2O pairs and that of Cl--H2O pairs
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become stronger under higher temperature conditions. Besides, the increase of ion concentration not only reduces the number of H2O molecules in the solvation shell of
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Na+ ion, but also weakens the interaction of hydrogen bonds. Moreover, it seems that
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the scCO2/brine mixture is heterogeneous in the CPG application.
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KEYWORDS: Molecular dynamics simulation; scCO2/brine mixture; Solvation
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structure; Ion pair; CO2 plume geothermal.
Nomenclature
g(r)
radial distribution function
k
fraction of CO2 molecules
N
number of particles
number of hydrogen bonds
n(r)
coordination number
P(r)
probability
q
charge of particle (C)
r
distance (m)
r1
first minimum of RDF (m)
Tc,model
model critical temperature (K)
Tr,sim
reduced simulation temperature
Tsim
simulation temperature (K)
V
volume (m3)
Vc
Coulomb term of non-bonded interaction energy (J)
VLJ
Lennard-Jones term of non-bonded interaction energy (J)
Vij
non-bonded interaction energy (J)
XNaCl
NaCl mass fraction
Jo
-p
vaccum permittivity (C2 N-1 m-2)
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re
0
na
Greek letters
parameter of Lennard-Jones potential probability density parameter of Lennard-Jones potential
Subscripts A
solvent atom A
a
anion
ro of
nHB
solute ion B
c
cation
Hw
hydrogen atom of H2O
i
particle i
j
particle j
Oc
oxygen atom of CO2
Ow
oxygen atom of H2O
ro of
B
-p
1. Introduction
Modern coal-fired power plants are increasingly being combined with carbon
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capture and storage (CCS) systems, typically geological sequestration [1]. As
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supercritical carbon dioxide (scCO2) is a better working fluid for geothermal energy utilization than water [2], a novel CO2 plume geothermal (CPG) [3] power generation
na
system is proposed to sequestrate CO2 and utilize geothermal energy simultaneously. The produced scCO2 has a pressure of (8 to 26) MPa and a temperature of (333.15 to
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473.15) K. However, this production may contain brine (about 10% mass fraction [4]),
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which is harm to the turbine and heat exchangers of the power generation system [5]. To solve this issue, properties of scCO2/brine mixture should be studied. A wide range of analyses for scCO2/brine mixture have been performed in recent
years, focusing on different aspects of properties. Duan and Zhang [6] studied the PVTx properties of CO2/H2O mixtures and proposed equations of state for H2O, CO2 and CO2/H2O. Yang et al. [7] conducted a molecular dynamics study to show PVT
properties of CO2/H2O mixture, in which the H2O is supercritical or near-critical. Chapoy et al. [8] focused on the thermophysical properties and phase behavior of a CO2-rich system. By their experimentally and theoretically investigation, the effect of water on density and viscosity of CO2/H2O mixture could be obtained. Zhao et al. [9, 10] presented investigations on the interfacial tension between supercritical CO2 and brine. They concluded these investigations would help directly predict interfacial
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tension in scCO2-complex electrolyte solution systems for practical applications.
Besides, other researchers mainly focused on the solubility of scCO2/brine mixture. Caumona et al. [11] developed an experimental platform for solubility measurement
-p
and obtained the solubility of water in CO2 with the pressure from 0.5 MPa to 20 MPa.
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Wang et al. [12] investigated the solubility of water in CO2 varying from 10 MPa to 50 MPa and 313.15 K to 473.15 K by the experimental method of in-situ quantitative
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Raman spectroscopy. This study indicated that the solubility of water in CO2 was
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greater under high temperature conditions. Aavatsmark and Kaufmann [13] proposed a function for solubility calculation of water in dense-phase CO2 by experimental data.
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It showed that the solubility of water first declined and then rose with the increase of pressure when the temperature was between 373.15 K and 473.15 K.
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To understand the microscopic characteristics of the scCO2/brine mixture, the
solvation structure of brine in scCO2 should also be studied. Keshri and Tembe [14] investigated the ion association in water/CO2 mixture by molecular dynamics simulations. Their study focused on the mixture of supercritical conditions of 673 K and 39.94 MPa while the temperature and pressure of CPG production were much
lower. Under the conditions of CPG applications, water is subcritical which means that the solvation structure may be different. Keshri et al. [15] also conducted molecular dynamics simulations for Na+-Cl- ion pair in both supercritical methanol and water-methanol mixtures. Moreover, similar study was carried out by Hidayat et al. [16] to investigate the preferential solvation of K(I) ion in water/ammonia mixture. Callsen et al. [17] studied the solvation structure of lithium ions in ether solution.
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Petrenko et al. [18] investigated solvate structures of salicylic acid and its derivatives
in supercritical carbon dioxide by molecular dynamics simulations. Prasetyo and Hofer [19] studied hydration free energy of carbon dioxide in aqueous solution and
-p
described the first hydration shell of CO2 in aqueous solution. Therefore, it indicates
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researchers have already focused on study solvation structure of mixtures. Moreover, based on former references, it seems that the molecular dynamics
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(MD) simulation is a viable option to investigate the solvation characteristics of
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scCO2/brine mixture. This is because molecular dynamics simulations consider the interactions between atoms and molecules at microscopic level, which are unavailable
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by experimental investigations. Yoon et al. [20] presented a molecular dynamics simulation on the local density distribution and solvation structure of supercritical
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carbon dioxide around naphthalene. Silveira et al. [21] conducted a molecular dynamics study on the solvation of carbon dioxide in the ionic liquids. Xue et al. [22] used the spatial distribution functions to describe the solvation structure of supercritical carbon dioxide around the ether group by molecular dynamics simulations. Qi et al. [23] investigated the solvation free energy of carbon dioxide in
the mixture of brine and CH4 through molecular dynamics simulations. Besides, a molecular dynamics simulation was conducted by Wang et al. [24] to show the difference of solvation structure between benzaldehyde and cinnamaldehyde by using radial distribution functions at different CO2 densities. Vaz et al. [25] presented a molecular dynamics simulation for structural properties of ketones in supercritical carbon dioxide at infinite dilution, which means each ketone was surrounded by
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carbon dioxide molecules only.
Although much literature is available on solvation structure investigation for both carbon dioxide in solutions and solute in dense-phase supercritical carbon
-p
dioxide, limited work has been published on brine solvation structure in supercritical
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carbon dioxide. Moreover, within the temperature and pressure range of scCO2/brine mixture produced by CPG, carbon dioxide is supercritical while water is subcritical.
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This makes the solvation structure of scCO2/brine mixture more complicated and
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worthy of study. As solubility is a function of temperature and pressure, the mass fraction of solute brine in scCO2 will change with its temperature and pressure, which
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may result in different solvation structures. Therefore, to better understand this issue, the effects of thermodynamic parameters should be considered.
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In the present study, molecular dynamics simulations are performed to predict
solvation structure of scCO2/brine mixture produced by CPG. Results from this paper may present why solute brine in scCO2 has such solvation structure and offer what the effects of thermodynamic parameters on the solvation structure are. The investigation in this paper may help solve issues of CPG applications. The organization of this
paper is as follows. In Section 2, the computational methods are described and simulation conditions are presented, respectively. In Section 3, results for molecular dynamics simulations are provided and further discussion is made on the influence of simulation conditions. Then Section 4 presents concise conclusions.
2. Computational Methods
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2.1 Force field parameters
In the present MD simulation, non-bonded interactions of the force field include two terms: Lennard-Jones term (for repulsion and dispersion, i.e. van der Waals
-p
attractions) and Coulomb term (for electrostatic interactions). The equation for
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non-bonded interaction energy can be expressed as follows
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ij Vij (rij ) VLJ (rij ) Vc (rij ) 4 ij rij
12 6 ij 1 qi q j rij 4 0 rij
(1)
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where rij is the distance between particle i and particle j, q is charge of particle and ε0 is the vacuum permittivity. As the Lorentz-Berthelot rules used, εij and σij can be
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calculated by
ij ( ii jj )1/2 1 2
ij ( ii jj )
(2) (3)
The cut-off radius for the Lennard-Jones attractions is set to be 1.2 nm. For Coulomb interactions, a shifted potential is applied using the fourth order Particle Mesh Ewald (PME) with a cut-off radius of 1.2 nm.
Bonded interactions for CO2 and H2O are estimated by EPM2 [26] model and TIP3P [27] model, respectively. To valid these molecular models, the phase boundaries of CO2 and H2O were reproduced by simulation data, experimental data and equation of state (EOS) data, as shown in Table 1. Besides, Na+ and Cl- (main ions in brine) are modeled using the OPLS force field [28].
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2.2 Data analyses The radial distribution function (RDF) is a key evaluation parameter to reveal the solvation structure of scCO2/brine mixture, as it can present how the normal number
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density of solvent atoms (B) distribute around the solute ion (A) at different distances. Therefore, RDF gAB(r) is shown as
N A NB 1 V P(r ) 4 r 2 iA iB
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g AB (r )
(4)
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where V is volume, P(r) is the probability of finding a solvent atom at distance r from
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a solute ion.
Then the coordination number (CN) nAB, which represents the number of solvent
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atoms or molecules bonded to a central solute ion, is defined as r1
nAB 4 r 2 g AB (r ) B dr 0
(5)
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where r1 is the first minimum of RDF. Therefore, nAB is the area under the first peak of gAB(r).
The definition of hydrogen bond is based on geometric rules. Two water molecules are chosen as being hydrogen bonded only if their interoxygen distance is less than 3.5 Å, and simultaneously the O-H...O angle is less than 30° [35].
2.3 MD simulation system In this paper, the solvation structure of scCO2/brine mixture with variable temperature (373.15-473.15 K) and fixed pressure (20 MPa) was first studied. Under such simulation condition, CO2 is within supercritical region (critical point of 304.13 K and 7.377 MPa [31]) while H2O is within liquid region (critical point of 647.1 K
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and 22.064 MPa [34]). In CPG applications, brine was saturated in dense-phase
supercritical carbon dioxide. Therefore, compositions of scCO2/brine mixture would change with its temperature because brine solubility in scCO2 varied. Table 2 lists
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compositions of present MD simulation systems under different temperatures. For
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Case 1-3, the numbers of H2O molecules and CO2 molecules were determined by solubility of brine in scCO2 and mass fraction of NaCl in brine [12]. For Case 4-7,
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different amounts of ions were added into simulation system to investigate what the
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effect of ion concentration on the solvation structure of scCO2/brine mixture was.
2.4 Solution procedure
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All MD simulations were performed in the platform of GROMACS 5.1.4 [36].
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The simulation box for Case 1-3 was of a geometric parameter of 3.4 nm × 3.4 nm × 3.4 nm, as shown in Fig. S1. Case 4-7 had larger simulation boxes of 8 nm × 8 nm × 8 nm as more molecules were added. Initial positions for ions, CO2 and H2O molecules were random. The Newtonian equations of motion were integrated using leap-frog algorithm with a time step of 1 fs. Before MD simulations conducted, the process of energy minimization (EM) was done by the steepest decent algorithm to ensure the
MD simulation system had a reasonable starting structure. Then MD simulations were carried out under isothermal-isobaric NPT ensemble. The temperature and pressure for each simulation were controlled by the Nosé-Hoover thermostat [37, 38] and Parrinello-Rahman barostat [39], respectively. All MD simulations in this study were
3. Results and discussion 3.1 Radial distribution functions & coordination numbers
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calculated for 15 ns.
In this section, a MD simulation is first performed for Case 1 to show the radial
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distribution functions and coordination numbers of Na+ and Cl- ions at different
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distances. Figure 1 presents that the interactions of ions and CO2 molecules are quite different from those of ions and H2O molecules. The RDFs of Na+-Ow and Cl--Ow are
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maximum at 0.238 nm and 0.324 nm, respectively. Then they decline rapidly with the
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increase of particle distance. Although the RDFs of Na+-Oc and Cl--Oc have maximal values, the RDFs at r=1.6 nm vary less than 20% from their maxima. This is because
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polar molecules (H2O) gather around ions while nonpolar molecules (CO2) disperse in the whole space. Moreover, a greater maximum of g(r) and a smaller corresponding
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particle distance of Na+-Ow indicate that H2O molecules seem to bind more tightly to Na+ ion than Cl- ion in the scCO2/brine mixture. Results for coordination numbers of different particles are illustrated in Fig. 2. The variation trend of nNa-Ow(r) implies that there is a solvation shell for Na+ ion. Comparing with the particle distances of Na+-Ow and Cl--Ow at low CNs, it seems that
H2O molecules could gather closer to Na+ than Cl- in the scCO2/brine mixture. The variations of CNs of Na+-Oc and Cl--Oc show cubic polynomial increase trends. It is likely that ions have limited effect on the distribution of supercritical CO2 molecules. Therefore, it is inferred that scCO2 molecules may have a uniform distribution in the simulation space.
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3.2 Effect of thermodynamic parameter
In the application of CPG, the temperature not only influences compositions of
the scCO2/brine mixture but also affects its solvation structure. The compositions
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have already been calculated by the solubility of brine in scCO2 under three different
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temperatures varying from 393.15 K to 473.15 K, which are typical temperatures of CPG productions. Then three MD simulations are conducted to present what the effect
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of temperature on the solvation structure is. Since the critical temperature may be
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different for molecular models, the simulation temperatures are modified by the critical temperature of EPM2 CO2 and TIP3P H2O in this study. Therefore, the
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reduced simulation temperature Tr,sim is defined as the ratio of simulation temperature Tsim and model critical temperature Tc,model, as presented in Table S1.
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Figure 3 shows the variations of RDFs of Na+-Ow and Na+-Oc with different
temperatures. The results for Na+-Ow indicate the decline of temperature can reduce the maximum of g(r), which is further presented by the inset of Figure 3(a). As a consequence, the coordination numbers may be changed which will be discussed later. Figure 3(b) illustrates the decrease of temperature is favorable to enlarge the
maximum of RDF while this peak will appear at a larger particle distance. More supercritical CO2 molecules are added to the simulation system when the simulation temperature decreases. This is able to explain why a greater peak appears with the decrease of temperature. Moreover, the results for particle distances of these peaks imply the interactions of Na+ ion and H2O molecules are stronger under higher temperature conditions.
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The variations of radial distribution functions of Cl- ion with the decrease of temperature are presented in Fig. 4. There exists a bias between the blue line and the
other two lines from r=0.4 nm to 1.0 nm in Fig. 4(a). This helps to explain that both
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Cl- ion and Na+ ion have stronger ability to bond H2O molecules under higher
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temperature conditions. In Fig. 4(b), the peaks of gCl-Oc(r) with the reduced simulation temperatures of 1.385 and 1.257 appear at a smaller particle distance comparing with
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those of gNa-Oc(r). If the particle distance differences of these peaks in Figure 4(b) are
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discussed, it can find that the temperature has limited effect on them. Former simulation results have already indicated that only Na+-Ow has an
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obvious solvation shell. Therefore, the numbers of H2O molecules in the first solvation shell of Na+ ion with different temperatures are presented in Table 3. The
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increase of temperature results in larger first solvation shell radius. The molecular thermal motion may be the main reason for this variation. It is definitely that molecules move more intensely under higher temperature conditions. Besides, more H2O molecules will stabilize at the first solvation shell of Na+ ion under low temperature conditions. These all imply the first solvation shell of Na+ ion will
become weaker with the increase of temperature.
Coordination numbers of the first solvation shell for the other three particle interactions in the scCO2/brine mixture are not presented because their first solvation shells are not obvious. But we can still discuss how the temperature affects their coordination numbers at specific radius. Table 3 further lists the results for these
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coordination numbers with different temperatures at the radius of 1.6 nm. It is
concluded that the coordination numbers of Na+-Oc and Cl--Oc are almost equal at any temperature. One reason for this phenomenon is that polar ions (Na+ and Cl-) have
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limited influence on nonpolar molecules of CO2, therefore CO2 molecules will
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distribute uniformly in the simulation space. The other reason is that Na+ ion and Clion may associate to an ion pair, which means they have approximate coordination
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numbers. Moreover, a fraction of CO2 molecules k is defined as the ratio of
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coordination number at 1.6 nm and total CO2 molecule number. Although the variations of coordination numbers indicate that CO2 molecules have intense
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distribution under low temperature conditions, the results of kNa-Oc and kCl-Oc imply more CO2 molecules distribute out of the sphere with a radius of 1.6 nm. The
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snapshot of scCO2/brine mixture under the condition of 393.15 K is illustrated in Fig. 5. This further validates a Na+-Cl- ion pair does associate under such simulation condition and there exists a stable solvation shell of H2O molecules around this ion pair. Therefore, it is concluded that the increase of temperature will make the first solvation shell of Na+-Cl- ion pair become weaker.
3.3 Effect of ion concentration Brine composition is another key parameter which may affect the solvation structure of scCO2/brine mixture. As the NaCl mass fraction of brine in CPG production may vary, the investigation of ion concentration effects becomes further significant. Firstly, a simulation is performed for Case 4, which is just a mixture of
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supercritical CO2 and water. This is selected as a reference for those cases with different ion concentrations.
Figure 6 shows the interactions of H2O molecules in the scCO2/H2O mixture.
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The variation curve of gOw-Ow(r) has an obvious peak and finally drops to zero. This
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implies H2O molecules may be clustered in the supercritical CO2 environment. The results for nOw-Ow(r) further prove this inference because nOw-Ow(r) is almost achieved
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300 at the radius of 3.2 nm. This is an interesting conclusion considering water is able
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to solvate in supercritical CO2. Therefore, it seems that the scCO2/H2O mixture is heterogeneous under the conditions of CPG application. Moreover, the results for
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gOw-Hw(r) in Fig. 6(a) can helps to explain the interaction of hydrogen bond (H-bond) in the scCO2/H2O mixture. The first peak of H-bond appears at the radius of 0.184 nm,
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which is consistent with the result of Ref. [40]. The first minimum of gOw-Hw(r) indicates that the number of hydrogen bonds per oxygen atom is 3.579. Then simulations are carried out for Case 5 and Case 7 to present what the effect of ion concentration on the interactions of Ow-Ow and Ow-Hw is. In Fig. 7(a), the peak of gOw-Ow(r) for Case 7 is much smaller, as well as the area under the variation curve
of gOw-Ow(r). This is because H2O molecules around the Na+ ion and Cl- ion will bind to them. Therefore, the coordination number of Ow-Ow will become smaller at the same time. The results for gOw-Hw(r) imply the interaction of hydrogen bond in the scCO2/H2O mixture will become weaker with the increase of ion concentration. Furthermore, the first minimum of gOw-Hw(r) for Case 7 indicates its number of hydrogen bonds per oxygen atom decreases to 3.194.
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The effects of ion concentration on the RDFs of Na+ ion and Cl- ion are illustrated in Figs. 8 and 9, respectively. A lower peak of gNa-Ow(r) achieves around
0.24 nm when the ion concentration goes up. Besides, the first minimum of gNa-Ow(r)
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reaches at larger radius with the increase of ion concentration. These both indicate
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that less H2O molecules are contained in the first solvation shell of Na+ ion. Table 4 lists the results for coordination numbers of Na+-Ow with different ion concentrations.
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This also suggests the number of H2O molecules in the first solvation shell of Na+ ion
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decreases with the increase of ion concentration. However, it cannot be inferred that H2O molecules bind to ions more tightly under higher ion concentration, because
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interactions between ions have not been discussed yet. Figure 8(b) indicates CO2 molecules are not able to form a solvation shell under any simulated ion concentration
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because of their nonpolarity. The RDF of Na+-Oc for Case 7 has a lower peak. As more Na+-Cl- ion pairs are contained in Case 7, it seems that the Na+-Cl- ion pairs are clustered together. Thus, ion pairs in the center may have fewer CO2 molecules around them while other ion pairs may be surrounded by more CO2 molecules. In general, their mean RDF of Na+-Oc shows such variation trend as Figure 8(b).
The results for gCl-Ow(r) present the first solvation shell of H2O molecules around Cl- ion only appears under quite low ion concentration conditions, as shown in Fig. 9(a). Considering the discussion above for H2O molecules clustering, it seems that the amount of H2O molecules is great enough so that the Na+-Cl- ion pair is dissolved into single Na+ ion and Cl- ion. This is the reason why the first solvation shell of H2O
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forms under such conditions. Besides, it also helps to explain why the first maxima of Case 5 in Figs. 8(b) and 9(b) are lower than those of Case 6. Furthermore, the curves
of gNa-Oc(r) and gCl-Oc(r) for Case 7 have similar variation trend, which implies ion
-p
pairs exist under high ion concentration conditions.
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Table 4 further presents the coordination numbers of cases with different ion concentrations at the radius of 3.2 nm. The variations of these coordination numbers
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indicate that ion interactions affect the interactions of Na+-H2O pairs and Cl--H2O
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pairs, as well as those between H2O molecules, resulting in smaller CNs at high ion concentration condition. Specifically, it seems the decrease of CN number has an
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approximate linear relation with the increase of ion concentration. Moreover, the solvation structure of Na+-Cl- ion pair with different ion
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concentration may be different when comparing results for RDF in Figs. 8(a) and 9(a). The peak value of RDF of Na+-Ow is quite different for Case 5 and Case 7. With the decrease of ion concentration, this peak value falls from 426.454 to 205.241. Results in Fig. 9(a) present the peak values of RDF of Cl--Ow for Case 5 and Case 7 are 227.003 and 76.927, respectively. These rapid decreases show more H2O molecules
occupy the space around Na+ ion and Cl- ion under low ion concentration condition. Therefore, it is likely that the distance of Na+-Cl- pair varies with the ion concentration. Fig. 10 illustrates the snapshot of scCO2/brine mixture for Case 7. It further indicates that the scCO2/brine mixture is heterogeneous under the condition of CPG application. Snapshot for other simulated cases are further presented in Fig. S2.
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3.4 Hydrogen bond analysis
Results for gOw-Hw(r) show ion concentration may influence the interactions of
hydrogen bonds. Therefore, further investigation is performed to present the
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relationship between ion concentration and number of hydrogen bonds, as listed in
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Table 5. The NaCl mass fraction XNaCl is calculated by compositions of scCO2/brine mixture. The results indicate the number of total hydrogen bonds nHB in the simulation
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system declines monotonically with the increase of XNaCl.
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By fitting these simulation results, it is likely that the nHB has a quadratic polynomial decrease trend when the XNaCl goes up, which can be expressed as (6)
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nHB 1.8491( X NaCl )2 6.3494 X NaCl 368.3 1wt% X NaCl 10wt%
The rapid decrease of nHB implies the electrostatic interactions of ions and H2O
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molecules are stronger than the hydrogen bonding interactions between H2O molecules. Thus, much fewer hydrogen bonds form between H2O molecules under higher ion concentration condition. Moreover, MD simulation results for Case 4 show its number of hydrogen bonds is 359, which is less than that of Case 5. This maybe because the addition of ion pair makes the cluster of H2O molecules associate closely.
It means more H2O molecules are able to reach within the hydrogen bonding range of their neighbor H2O molecules. Under the combined effect of electrostatic interaction and hydrogen bonding interaction, the number of total hydrogen bonds in the scCO2/brine mixture presents the former variation trend.
4. Conclusions
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Molecular dynamics simulation was performed for the solvation structure of
scCO2/brine mixture produced by the CO2 plume geothermal system. Based on the analyses conducted in this investigation, the following conclusions may be drawn:
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(1) H2O molecules bind more tightly to Na+ ion than Cl- ion in the scCO2/brine
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mixture while supercritical CO2 molecules seem have a uniform distribution in the whole space. Besides, there is a solvation shell of H2O molecules around Na+ ion.
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(2) Both Na+ ion and Cl- ion have stronger ability to bind H2O molecules under higher
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temperature conditions. The increase of temperature will make the first solvation shell of Na+-Cl- ion pair become weaker.
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(3) Less H2O molecules are contained in the first solvation shell of Na+ ion under higher ion concentration conditions. Moreover, a first solvation shell of Cl- ion
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will appear under quite low ion concentration condition.
(4) It seems that the scCO2/brine mixture is heterogeneous under the conditions of CPG application. (5) The interaction of hydrogen bond in the scCO2/brine mixture becomes weaker with the increase of ion concentration. It is likely that the number of total
hydrogen bonds has a quadratic polynomial decrease trend when the ion concentration increases.
Declaration of interests 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.
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Acknowledgement The authors gratefully acknowledge the financial support by the National Natural
Science Foundation of China (Grant No. 51976031) and Qinglan Project of Jiangsu
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Province, China.
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18 (1989) 1537-1564. https://doi.org/10.1063/1.555836.
ro of
the melting line to 1273 K at pressures up to 25 000 MPa, J. Phys. Chem. Ref. Data,
[34] W. Wagner, A. Pruss, The IAPWS formulation 1995 for the thermodynamic
-p
properties of ordinary water substance for general and scientific use, J. Phys. Chem.
re
Ref. Data, 31 (2002) 387-535. https://doi.org/10.1063/1.1461829.
[35] A.K. Soper, M.G. Phillips, A new determination of the structure of water at 25 ℃,
lP
Chem. Phys., 107 (1986) 47-60. https://doi.org/10.1016/0301-0104(86)85058-3.
na
[36] M.J. Abraham, T. Murtola, R. Schulz, S. Páll, J.C. Smith, B. Hess, E. Lindahl, GROMACS: High performance molecular simulations through multi-level parallelism laptops
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supercomputers,
Softwarex,
1-2
(2015)
19-25.
ur
from
https://doi.org/10.1016/j.softx.2015.06.001.
Jo
[37] S. Nosé, A unified formulation of the constant temperature molecular dynamics methods, J. Chem. Phys., 81 (1984) 511-519. https://doi.org/10.1063/1.447334. [38] W.G. Hoover, Canonical dynamics: Equilibrium phase-space distributions, Phys. Rev. A, 31 (1985) 1695-1697. https://doi.org/10.1103/physreva.31.1695. [39] M. Parrinello, A. Rahman, Polymorphic transitions in single crystals: A new
molecular
dynamics
method,
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Appl.
Phys.,
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(1981)
7182-7190.
https://doi.org/10.1063/1.328693. [40] A. Botti, F. Bruni, R. Mancinelli, M.A. Ricci, F. Celso, Lo, R. Triolo, F. Ferrante, A.K. Soper, Study of percolation and clustering in supercritical water-CO2 mixtures, J.
Jo
ur
na
lP
re
-p
ro of
Chem. Phys., 128 (2008) 6-48. https://doi.org/10.1063/1.2898538.
-p
ro of
Figure captions
Jo
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na
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re
(a)
(b) Fig. 1. Results for radial distribution functions of ions and molecules in scCO2/brine mixture of Case 1. (a) Blue line for Na+-Ow, red line for Cl--Ow; (b) blue line for
-p
ro of
Na+-Oc, red line for Cl--Oc.
Jo
ur
na
lP
re
(a)
(b)
Fig. 2. Results for coordination numbers of ions and molecules in scCO2/brine mixture of Case 1. (a) Blue line for Na+-Ow, red line for Cl--Ow; (b) blue line for Na+-Oc, red line for Cl--Oc.
ro of
Jo
(b)
ur
na
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re
-p
(a)
Fig. 3. Results for radial distribution functions of Na+ ion in scCO2/brine mixture with different reduced simulation temperatures. (a) Na+-Ow, (b) Na+-Oc. Blue solid line for Case 1; red dash line for Case 2; magenta dot line for Case 3.
ro of
Jo
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na
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re
-p
(a)
(b)
Fig. 4. Results for radial distribution functions of Cl- ion in scCO2/brine mixture with different reduced simulation temperatures. (a) Cl--Ow, (b) Cl--Oc. Blue solid line for Case 1; red dash line for Case 2; magenta dot line for Case 3.
ro of
Fig. 5. Snapshot of Na+-Cl- ion pair and its first solvation shell in scCO2/brine mixture
ur
Jo
(a)
na
lP
re
-p
for Case 3.
ro of
(b)
-p
Fig. 6. Results for interactions of H2O molecules in scCO2/H2O mixture. (a) Radial
re
distribution functions, (b) coordination numbers. Blue solid line for Ow-Ow; red dash
Jo
ur
na
lP
line for Ow-Hw.
(a)
ro of
(b)
-p
Fig. 7. Effect of ion concentration on radial distribution functions of H2O molecules
re
in scCO2/brine mixture. (a) Ow-Ow, (b) Ow-Hw. Blue solid line for Case 4; red dash
Jo
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line for Case 5; magenta dot line for Case 7.
(a)
ro of
(b)
Fig. 8. Effect of ion concentration on radial distribution functions of Na+ ion in
-p
scCO2/brine mixture. (a) Na+-Ow, (b) Na+-Oc. Blue solid line for Case 5; red dash line
Jo
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na
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re
for Case 6; magenta dot line for Case 7.
(a)
ro of -p
(b)
Fig. 9. Effect of ion concentration on radial distribution functions of Cl- ion in
Jo
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na
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for Case 6; magenta dot line for Case 7.
re
scCO2/brine mixture. (a) Cl--Ow, (b) Cl--Oc. Blue solid line for Case 5; red dash line
Fig. 10. Snapshot of Na+-Cl- ion pair in scCO2/brine mixture for Case 7.
Table 1 Comparison among simulation data, experimental data and EOS data for critical parameters of CO2 and H2O. ρcrit/g·
pcrit/ Item
Tcrit/K cm-3
MPa 7.34 Simulation data [29]
312.8
0.453 0
Experimental
data
7.38
304.21 CO2
[30]
ro of
EPM2
0.467
2
7.37
EOS data [31]
304.13
0.468
re
-p
7
TIP3P
Experimental [33]
na
H2O
lP
Simulation data [32]
Jo
ur
EOS data [34]
12.6
578
0.272 0
data
22.0 647.1
0.322 64 22.0
647.1
0.322 64
Table 2 Compositions of MD simulation systems under different temperatures and ion concentrations. T/
p/
No.
NH2 Nc
K
NC
Ntot
Na
MPa
O
O2
al
473 1
20
1
1
20
1
1
20
1
1
30
116
148
433 2 .15 393 3
20
0
473 5
lP
.15
20
na
.15
re
473 4
30
275
307
30
646
678
116
146
-p
.15
ro of
.15
1
0
300 0 116
1
20
ur
.15
0
Jo
.15
2 116
3
3
146
300 0
473
7
146
300
473
6
0
6 116
20
10
10
148
300 0
0
Table 3 MD simulation results for interactions of ions and molecules at first solvation shell and radius of 1.6 nm in Case 1, Case 2 and Case 3.
First solvation shell
Case 1
Case 2
Case 3
r1/nm
0.338
0.330
0.328
n(r)
3.856
4.075
4.294
NCO2
116
275
646
nNa-Oc(r)
83.791
102.816
121.383
kNa-Oc
0.722
0.374
0.188
nCl-Oc(r)
83.627
102.612
122.343
kCl-Oc
0.721
Radius of
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-p
1.6 nm
ro of
Item
0.373
0.189
Table 4 Results for coordination numbers of ions and molecules at first solvation shell and radius of 3.2 nm in Cases 4-7. Case
Case
Case
Case
Item 4
solvation shell
-
0.330
0.330
0.344
n(r)
-
5.259
5.028
4.056
nOw-Ow
296.1
296.0
294.8
279.3
84
59
nNa-Ow
81
298.5 -
(r)
32
298.5
-
67
Jo
ur
na
lP
r)
297.9
04
re
nCl-Ow(
85
-p
3.2 nm
7
r1/nm
(r) Radium of
6
ro of
First
5
290.2
22
297.9
49
290.3 11
Table 5 Results for number of hydrogen bonds of different ion concentrations in Cases 5-7. Case 5
Case 6
Case 7
Ion pair number
1
3
10
XNaCl (wt%)
1.071
3.145
9.765
nHB
373
370
254
Jo
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na
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ro of
Item