A method for calculating the conductivity of a supercritical fluid system NaCl-H 2 O-H 2 S

Abstract

The present invention relates to the technical field of calculating the ionic conductivity of solutions in supercritical fluid systems, and specifically discloses a method for calculating the conductivity of the supercritical fluid system NaCl-H2O-H2S. The calculation method includes the following steps: constructing an H2S model, an H2O model, and an NaCl model for the mixed system of the NaCl-H2O-H2S fluid to obtain the corresponding potential energy; using the LAMMPS code to perform molecular dynamics simulations on the inert gas in the NaCl-H2O-H2S system in an isobaric-isothermal system to obtain the output positions and velocities of the atoms, and calculating the atomic force values; using the Einstein relation to calculate the self-diffusion coefficient of the inert gas and deriving the ionic conductivity (σ e ) using the Green-Kubo relation. Compared with the obtained conductivity, there is no dielectric relaxation mechanism at lower frequencies, and the conductivity calculated using MD simulation corresponds to the same low-frequency range measured by electromagnetic experiments. This method clearly simulates the dynamics of ions and H2O molecules at different salt concentrations, temperatures, and pressures, overcomes the difficulties of experimental determination, and verifies the physical principles of conductivity.

Description

Technical Field

[0001] The present invention relates to the technical field of calculating the ionic conductivity of solutions in supercritical fluid systems, and specifically to a method for calculating the conductivity of NaCl-H 2 O-H 2 S in supercritical fluid systems. Background Technique

[0002] In molecular dynamics simulations, the SPC, SPC / E models proposed by Berendsen et al. and the TIP4P model proposed by Jorgensen et al. are widely used. A common feature of these models is that the oxygen atoms in water molecules have LJ contributions, while the hydrogen atoms do not. The contributions made by hydrogen atoms during the molecular dynamics simulation are only determined by the charges they carry.

[0003] During the simulation, the total number of simulation steps is 600,000. The first 300,000 steps are used to equilibrate the system, and the last 300,000 steps are used to statistically analyze the parameters. After the system reaches equilibrium, the thermodynamic properties of the system are statistically analyzed. Since the moment of inertia of H 2 S molecules is small and they may rotate rapidly, a smaller time step needs to be used to ensure the stability of solving the motion equations. Summary of the Invention

[0004] Aiming at the above problems of the prior art, the present invention provides a method for calculating the conductivity of NaCl-H 2 O-H 2 S in supercritical fluid systems and solves the problem of insufficient derivation of the ionic conductivity of solutions at present.

[0005] The technical solution adopted by the present invention is as follows:

[0006] A method for calculating the conductivity of NaCl-H 2 O-H 2 S in supercritical fluid systems, comprising the following steps:

[0007] S1. Use Materials Studio software to construct a model of the mixed system of NaCl-H 2 O-H 2 S fluid, specifically including the H 2 S model, the H 2 O model and the NaCl model, and then obtain the corresponding potential of interaction;

[0008] S2. Use the LAMMPS code to perform molecular dynamics simulations on the inert gas in the NaCl-H 2 O-H 2 S system in an isobaric-isothermal system to obtain the output positions and velocities of atoms, and calculate the atomic force values;

[0009] S3. Calculate the self-diffusion coefficient of inert gas in the NaCl-H 2 O-H 2 S system;

[0010] S4. Derive the ionic conductivity σ e using the Green-Kubo relation and calculate the conductivity under DC voltage; there is no dielectric relaxation mechanism at low frequencies, and the conductivity calculated using MD simulation corresponds to the same low-frequency range measured by electromagnetic experiments.

[0011] Preferably, in step S1, the obtained H 2 S model includes the following steps:

[0012] S11. Construct the H 2 S model using the Shyamal model and calculate the intermolecular interaction force;

[0013] S12. Calculate the solubility of H 2 S gas in water using the molality of the solution;

[0014] S13. Calculate the interaction within water molecules;

[0015] S14. Calculate the intermolecular coupling scale parameter ls and energy parameter ls according to the Lorentz-Berthelot mixing rule.

[0016] Preferably, the expression of the intermolecular interaction potential is:

[0017]

[0018] where and σ ij are the energy parameter and size parameter respectively, r ij represents the distance between the centroids of molecules i and j in the simulated fluid, q i and q j are both the charges on the atoms, is the vacuum permittivity;

[0019] H 2 The solubility calculation formula of H

[0020] where ρ i (z) is the density distribution of component i in the liquid phase, M i is the molar mass of component i, ρ j (z) is the density distribution of component j, and i represents H 2where \(S_j\) represents water, \(\rho(z)\) is the molecular number density, \(N(z)\) is the number of particles between \(z\) and \(z + \Delta z\), \(A = L_xL_y\) is the cross-sectional surface area, \(\Delta z\) is the slice thickness, and the curly brackets denote time averaging;

[0021] The interaction within the water molecule is the harmonic vibration of the bond and bond angle around its origin, and its calculation formula is:

[0022]

[0023] In the formula, \(r\) is the molecular diameter, \(\theta\) is the bond angle, \(r\) 0 and \(\theta\) 0 are respectively and \(109.47^{\circ}\), \(k\) b and \(k\) θ are respectively and \(92\ kcal / (mol\cdot rad^2)\);

[0024] The intermolecular coupling energy parameter \(l_s\) and the scale parameter \(l_s\) are respectively: \(\sigma\) ls \(= (\sigma\) l \cdot\sigma\) s ) / 2.

[0025] Preferably, in step S1, the SPC / E model is used to construct the water molecule model to obtain the interaction potential between atoms, and its formula is:

[0026]

[0027] In the formula, \(r\) is the distance between two \(i\)-type and \(j\)-type atoms, \(\varepsilon\) ij and \(\sigma\) ij are respectively the energy parameter and the size parameter, \(q\) i and \(q_j\) are both the electric charges on the atoms, is the vacuum permittivity.

[0028] Preferably, in step S1, the energy parameter \(\varepsilon\) ij and the size parameter \(\sigma\) ij between different types of atoms are obtained according to the Lorentz - Berthelot mixing rule, and its expression is:

[0029] Preferably, in step S2 during the simulation, periodic boundary conditions are used in the \(x\), \(y\), and \(z\) directions, the Berendsen method is used to control the temperature and pressure, the RATTLE algorithm is used to limit the bond length and bending angle, the LJ interaction is used for long - range correction, and the PPPM method is used to calculate the long - range electrostatic interaction.

[0030] Preferably, in step S2 during the simulation, the VelocityVerlet algorithm is used to integrate the equations of motion to obtain the time step and the positions of atoms at a certain moment.

[0031] Calculate The velocity at time is:

[0032] The calculated position at t+Δt is:

[0033] The calculated velocity at t+Δt is:

[0034] In the formula, r i (t) is the position at the initial moment, v i (t) is the velocity, F i (t) is the acting force, m i is the solubility.

[0035] Preferably, the formula for calculating the self-diffusion coefficient of the inert gas in step S3 is:

[0036]

[0037] In the formula, t is the time, <[r i (t)-r i (0)] 2 > is the average value of the molecule, r i (t) is the position of molecule i at time t.

[0038] Preferably, the ionic conductivity in step S4 is:

[0039]

[0040] In the formula, v is the volume of the unit cell, k b is the Boltzmann constant, T is the temperature, j el (t) is the current at time t, q i is the partial charge of ion i and q i is the velocity of ion i.

[0041] The present invention has the following characteristics and advantages:

[0042] The described calculation method clearly simulates the dynamics of ions and H 2 O molecules under different salt concentrations, temperatures and pressures, overcomes the difficulties of experimental determination, verifies the physical principle of conductivity, improves the efficiency of traditional experiments, reduces the R & D cost, and shortens the industrialization cycle. Description of the Drawings

[0043] Figure 1is a conductivity calculation method for the supercritical fluid system NaCl-H 2 O-H 2 S, and the molecular structure diagram of H 2 S;

[0044] Figure 2 is a conductivity calculation method for the supercritical fluid system NaCl-H 2 O-H 2 S, and the overall intermolecular flow chart;

[0045] Figure 3 is a conductivity calculation method for the supercritical fluid system NaCl-H 2 O-H 2 S, and the overall atomic flow chart. Specific implementation manners

[0046] The embodiments will be described below in conjunction with experimental data.

[0047] A conductivity calculation method for the supercritical fluid system NaCl-H 2 O-H 2 S includes the following steps:

[0048] S1. Use the MaterialsStudio software to construct a model for the mixed system of the NaCl-H 2 O-H 2 S fluid, specifically including the H 2 S model, the H 2 O model, and the NaCl model, and then obtain the corresponding potential energy;

[0049] Common models include: the Jorgensen model, the Forester model, the Kristof model, and the Shyamal model. Among them, the Jorgensen model and the Shyamal model are three-point interaction models, and the Forester model and the Kristof model are four-point interaction models.

[0050] The potential energy function models of the Jorgensen model, the Forester model, and the Kristof model are expressed as follows:

[0051]

[0052] The right side of the equation represents the sum of the long-range electrostatic interaction and the short-range Lennard-Jones interaction, which constitutes the potential energy of the H 2 S molecule;

[0053] In the formula, U represents the intermolecular interaction force of the H 2 S molecule; r ijThe simulated fluid represents the distance between the centroids of molecule i and molecule j. → Ω i and Ω j → are the azimuthal angles describing molecule i and j respectively. is the electric charge quantity at the α position of the i-th molecule, N α is the number of interaction points of a hydrogen sulfide molecule in the model. For the Jorgensen model, N α = 3, for the Forester model and Kristof model, N α = 4. is the distance between the α interaction point of molecule i and the β interaction point of molecule j, ε ss and σ are the energy and size parameters of the LJ potential energy respectively.

[0054] The potential energy parameters of the four models are shown in the following table:

[0055] Table 1 Potential energy parameters of the four models

[0056]

[0057] In step S1, H obtained 2 The S model includes the following steps:

[0058] S11 uses the Shyamal model to construct the H 2 S model, calculates the intermolecular interaction force. The intermolecular interaction force is divided into short-range van der Waals force and long-range Coulomb force. The intermolecular interaction potential function is:

[0059]

[0060] In the formula, ε ij and σ ij are the energy parameter and size parameter respectively, r ij The simulated fluid represents the distance between the centroids of molecule i and molecule j, q i and q j are both the electric charges on the atoms. is the vacuum permittivity;

[0061] The energy parameter ε ij and size parameter σ ij between like atoms are shown in the following table:

[0062] Table 2 Energy parameter and size parameter table between like atoms

[0063]

[0064] S12 calculates H using the molality of the solution. 2The solubility of gas S in water, and its formula is:

[0065]

[0066] In the formula, ρ i (z) is the density distribution of component i in the liquid phase, M i is the molar mass of component i, ρ j (z) is the density distribution of component j, i represents H 2 S, j represents water, ρ(z) is the number density of molecules, N(z) is the number of particles between z and z + Δz, A = LxLy is the cross-sectional surface area, Δz is the slice thickness, and the curly brackets represent the time average;

[0067] S13 calculates the interaction within a water molecule, and the interaction within a water molecule is the harmonic vibration of bonds and bond angles around its origin:

[0068]

[0069] In the formula, r 0 and θ 0 are respectively and 109.47°, k b and k θ are respectively and 92 kcal / (mol·rad2);

[0070] S14 calculates the intermolecular coupling energy parameter ls and the scale parameter ls according to the Lorentz-Berthelot mixing rule, and its expression is: σ ls =(σ l ·σ s ) / 2;

[0071] A water molecule model is constructed using the SPC / E model. This model uses rigid molecules. In this model, the hydrogen bond length r 0 is 0.1 nm, the bond angle θ 0 between H - O - H is 109.47°, and the interaction potential between atoms is composed of the Lennard-Jones potential and the Coulomb interaction, that is, the interaction potential U ij between two i-type and j-type atoms with a distance of r is:

[0072]

[0073] Among them, ε ij and σ ij are respectively the energy parameter and the size parameter, q i and q j are both the electric charges on the atoms, is the vacuum permittivity;

[0074] The energy parameter ε between like atoms ij and the size parameter σ ij are shown in the following table:

[0075] Table 3 Energy and Size Parameters between Like Atoms

[0076] Atom <![CDATA[ε i kJ·mol -1 > <![CDATA[σ i nm]]> <![CDATA[q i e]]> O 125.89 0.370 0 H 269 0.369 0 <![CDATA[Na + > 250 0.373 0 <![CDATA[Cl - > 250 0.372 3.9

[0077] The ε between unlike atoms ij and σ ij are obtained according to the Lorentz - Berthelot mixing rule:

[0078] S2. Use the LAMMPS code to perform molecular dynamics simulations on the inert gases in the NaCl - H 2 O - H 2 S system in the isobaric - isothermal ensemble to obtain the output positions and velocities of the atoms, and calculate the atomic force values;

[0079] In step S2 during the simulation, periodic boundary conditions are adopted in the x, y, and z directions. During the simulation, the VelocityVerlet algorithm is used to integrate the equations of motion to obtain the time step and the positions of the atoms at a certain moment.

[0080] H 2 The simulation time step of the S molecule is 0.8 fs, and the VelocityVerlet algorithm is used to calculate the velocity at time: The calculated position at time t + Δt is: The calculated velocity at time t + Δt is: where r i (t) is the position at the initial moment, v i (t) is the velocity, F i (t) is the force, m i is the solubility.

[0081] In step S2, the Berendsen thermostat and the barostat are used respectively to keep the temperature and pressure constant. Let p D be the target pressure of the system, p(t) be the instantaneous pressure, and the size of the unit cell can be changed in the following way: V(t) → V(t)·η(t),

[0082] where Γ p is the relaxation time of the system pressure, γ is the compressibility, when p(t) > pD When η(t) > 1, conversely, η(t) < 1. It is the overall value that serves as the input parameter.

[0083] In step S2, the RATTLE algorithm is used to restrict the bond length and bond angle, the long-range correction of the LJ interaction is used, and the particle-particle and particle-mesh (PPPM) method is used to calculate the long-range electrostatic interaction.

[0084] In LAMMPS, the bond length and bond angle are restricted through the fix restrain command, restricting the movement of atoms or molecules, enabling the force field parameters to vary linearly with time. With this kind of constraint, several constrained atoms appear in a certain topological form, and its molecular structure still has a certain degree of movement flexibility. The second type of rigid constraint is the reaction force constraint, which fixes an atom at a specific configuration by applying a reaction force to the atom.

[0085] S3. Calculate the self-diffusion coefficient of noble gases in the NaCl-H 2 O-H 2 S system using the Einstein relation. The calculation formula is:

[0086] In the formula, t is time, <[r i (t) - r i (0)] 2 > is the average value of the molecule, and r i (t) is the position of molecule i at time t;

[0087] S4. Deduce the ionic conductivity (σ e ) using the Green-Kubo relation and calculate the conductivity under direct current (DC). The calculation formula is: and

[0088] In the formula, v is the volume of the unit cell, k b is the Boltzmann constant, T is the temperature, j el (t) is the current at time t, q i is the partial charge of ion i and q i is the velocity of ion i.

[0089] By confirming the convergence of the autocorrelation function, the equation is integrated up to 1 ps; there is no dielectric relaxation mechanism at lower frequencies, and the conductivity calculated using MD simulation corresponds to the same low-frequency range measured by electromagnetic experiments.

[0090] Therefore, a method of the present invention clearly simulates ions and H 2The dynamics of O molecules under different salt concentrations, temperatures, and pressures overcome the difficulties of experimental determination, verify the physical principles of conductivity, improve the efficiency of traditional experiments, reduce R & D costs, and shorten the industrialization cycle.

[0091] The embodiments described above are only descriptions of the preferred embodiments of the present invention and do not limit the scope of the present invention. Without departing from the design spirit of the present invention, various deformations and improvements made by those of ordinary skill in the art to the technical solutions of the present invention shall fall within the protection scope determined by the claims of the present invention.

Claims

1. A method for calculating the conductivity of a supercritical fluid system NaCl-H2O-H2S, characterized in that: The following steps are involved: S1. Use MaterialsStudio software to build a model for the mixed system of NaCl-H2O-H2S fluids, including H2S model, H2O model and NaCl model, and then obtain the corresponding potential; Obtaining the H2S model in step S1 includes the following steps: S11 uses the Shyamal model to construct the H2S model and calculate the intermolecular interaction force; S12 uses the mass molar concentration of the solution to calculate the solubility of H2S gas in water; S13 calculates the interactions within water molecules; S14 Calculation of intermolecular coupling scaling parameters based on the Lorentz-Berthelot mixing rule and energy parameters ; Step S1 uses the SPC / E model to construct a water molecule model and obtain the interaction potential between atoms, the formula of which is: ； In the formula, r is two Class and The distance between atoms, and are energy parameters and size parameters respectively, qi and qj are the charges on atoms, is the dielectric constant of vacuum; S2. Use LAMMPS code to perform molecular dynamics simulation on the inert gas in the NaCl-H2O-H2S system in an isobaric-isothermal system to obtain the output position and velocity of the atoms and calculate the atomic force values; S3. Calculate the self-diffusion coefficient of noble gases in the NaCl-H2O-H2S system using the Einstein relation; S4. Derivation of ionic conductivity using the Green-Kubo relationship , and calculate the conductivity under direct current voltage DC; at lower frequencies there is no dielectric relaxation mechanism, and the conductivity calculated using MD simulations corresponds to the same low-frequency range measured by electromagnetic experiments.

2. The method according to claim 1, characterized in that The H2S model obtained in step S1 includes the following calculation process and formula: The intermolecular interaction force is calculated by the calculation formula of the intermolecular potential: ； In the formula, and are the energy parameter and size parameter respectively, The simulated fluid represents the distance between the center of mass of molecules i and j, q i and q j are the charges on the atoms, is the dielectric constant of vacuum; The solubility calculation formula of H2S gas in water is: ， ； In the formula, is the density distribution of component i in the liquid phase, M i is the molar mass of component i, is the density distribution of component j, i represents H2S, j represents water, is the molecular number density, N(z) is the molecular number density from z to The number of particles between them, A=LxLy is the cross-sectional surface area, is the slice thickness, and curly brackets indicate time averaging; The interaction within the water molecule is the simple harmonic vibration of the bond and bond angle around its origin, and its calculation formula is: ； In the formula, r is the molecular diameter, θ is the bond angle, r0, θ0, k b , are the bond and angle constants, respectively; The intermolecular coupling energy parameter and scale parameter They are: , .

3. The method according to claim 1, characterized in that Energy parameters between heterogeneous atoms in step S1 and size parameters According to the Lorentz-Berthelot mixing regulation, its expression is: , .

4. The method according to claim 1, characterized in that In step S2, periodic boundary conditions are used in the x, y, and z directions during the simulation, the Berendsen method is used to control temperature and pressure, the RATTLE algorithm is used to restrict bond length and bending angle, the LJ interaction is used for long-range correction, and the PPPM method is used to calculate long-range electrostatic interactions.

5. The method according to claim 1, characterized in that Step S2: During the simulation, the VelocityVerlet algorithm is used to integrate the equation of motion, calculate the time step, and obtain the position of the atom at a certain moment; calculate The speed at this moment is: , Calculated The position at the moment is: , Calculated The speed at this moment is: , In the formula, is the initial position, For speed, is the force, For solubility.

6. The method according to claim 1, characterized in that The calculation formula of the inert gas self-diffusion coefficient in step S3 is: , Where t is time, is the average value of the numerator, is the position of molecule i at time t.

7. The method according to claim 1, characterized in that The ionic conductivity in step S4 is: ， Where v is the volume of the unit cell, k b is the Boltzmann constant, T is the temperature, is the current at time t, q i are the partial charges i and q of the ions i is the velocity of ion i.

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