CN113591408A - Method for determining microscopic adsorption characteristic parameters of liquid sulfur in nano pores of carbonate rock - Google Patents

Method for determining microscopic adsorption characteristic parameters of liquid sulfur in nano pores of carbonate rock Download PDF

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CN113591408A
CN113591408A CN202110880418.6A CN202110880418A CN113591408A CN 113591408 A CN113591408 A CN 113591408A CN 202110880418 A CN202110880418 A CN 202110880418A CN 113591408 A CN113591408 A CN 113591408A
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张志伟
张广东
莫超平
张明迪
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Southwest Petroleum University
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Abstract

The invention discloses a method for determining microscopic adsorption characteristic parameters of liquid sulfur in carbonate rock nanopores, which comprises the steps of utilizing Monte Carlo simulation and molecular dynamics simulation to obtain the microscopic adsorption characteristic parameters; the microscopic adsorption characteristic parameters comprise adsorption molecular weight, excess adsorption capacity, adsorption heat, adsorption phase density, radial distribution function and diffusion coefficient. The method is highly targeted, can solve the problem that the adsorption characteristic parameters of the liquid sulfur in the carbonate rock are difficult to obtain, can disclose the microscopic adsorption mechanism of the liquid sulfur in a nanoscale, and can provide a theoretical reference basis for the prevention and treatment work of the on-site sulfur deposition.

Description

Method for determining microscopic adsorption characteristic parameters of liquid sulfur in nano pores of carbonate rock
Technical Field
The invention relates to the technical field of oil and gas field development, in particular to a method for determining microscopic adsorption characteristic parameters of liquid sulfur in carbonate rock nanopores.
Background
As the formation temperature is above the melting point of sulfur, the sulfur, once precipitated, becomes a liquid in the formation. The separated liquid sulfur is adsorbed on the wall surface of the pore and is continuously adsorbed and aggregated to cause damage to a reservoir, and the gas well is reduced in production and even forced to stop production in severe cases. At present, the phase state characteristics and the macroscopic seepage mechanism of the high-sulfur-content gas reservoir are relatively researched at home and abroad, a relatively mature research method is formed, and the research on the microscopic adsorption mechanism of the liquid sulfur in the high-sulfur-content carbonate gas reservoir is not reported. The unclear microscopic adsorption mechanism of the liquid sulfur deposition seriously restricts the development of the on-site sulfur deposition prevention and control work.
Disclosure of Invention
In view of the above problems, the present invention aims to provide a method for determining microscopic adsorption characteristic parameters of liquid sulfur in nano pores of carbonate rock.
The technical scheme of the invention is as follows:
a method for determining microscopic adsorption characteristic parameters of liquid sulfur in nanopores of carbonate rocks, wherein the microscopic adsorption characteristic parameters comprise adsorption molecular weight, excess adsorption capacity, adsorption heat, adsorption phase density, radial distribution function and diffusion coefficient, and the method for determining the microscopic adsorption characteristic parameters comprises the following steps:
s1: establishing a molecular model of a target rock sample;
s2: selecting an adsorption experimental surface of the molecular model, and cutting and expanding the molecular model along the adsorption experimental surface;
s3: combining and adjusting the expanded adsorption experimental surface to obtain a microscopic adsorption skeleton model according with a periodic mirror principle;
s4: setting a truncation radius according to the size of the microscopic adsorption skeleton model;
s5: calculating the total potential energy of the microscopic adsorption skeleton model by using a COMPASS II force field;
s6: setting a temperature and pressure interval gradient value during simulation calculation according to the formation pressure and temperature interval needing simulation calculation, and determining the step length of the simulation calculation;
s7: calculating the fugacity of the liquid sulfur simple substance molecules under different temperature and pressure;
s8: performing giant regular ensemble Monte Carlo simulation of an adsorption isotherm to obtain adsorption heat, adsorption molecular weight, adsorption isotherm and relative molecular concentration within a pressure interval at a certain set temperature;
s9: changing the set temperature according to the step length, and repeating the step S8 until the adsorption heat, the adsorption molecular weight, the adsorption isotherm and the relative molecular concentration in each pressure interval under all temperature intervals are obtained;
s10: calculating the adsorption phase density and the excess adsorption amount at each temperature according to the parameters obtained in the step S8 and the step S9;
s11: according to the adsorption isotherms at all temperatures, obtaining corresponding saturated pressure values when the saturated adsorption state is reached at all temperatures;
s12: respectively carrying out constant-pressure adsorption Monte Carlo simulation under the conditions of each saturated pressure value and corresponding temperature value, and screening out the molecular configuration with the lowest total energy of the system;
s13: carrying out volume optimization on the molecular configuration according to the system energy minimization to obtain a stable adsorption configuration;
s14: performing molecular dynamics simulation on the stable adsorption configuration to obtain a radial distribution function and mean square displacement;
s15: and drawing a relation curve of the mean square displacement and time, calculating the slope of the relation curve, and calculating according to the slope to obtain the diffusion coefficient.
Preferably, in step S4, the cutoff radius is one half of the minimum side length of the microscopic adsorption skeleton model.
Preferably, in step S5, the total potential energy is calculated by the following formula:
Figure BDA0003192042180000021
in the formula: e is total potential energy, kcal/mol;
Figure BDA0003192042180000022
is the sum of the stretching energy of the key;
Figure BDA0003192042180000023
is the sum of the bending energy of the key angle;
Figure BDA0003192042180000024
is the sum of the bond twisting energies;
Figure BDA0003192042180000025
the key corner out-of-plane bending energy;
Figure BDA0003192042180000026
key expansion-key expansion coupling function energy;
Figure BDA0003192042180000027
the key expansion-key angle bending coupling function energy is adopted;
Figure BDA0003192042180000028
a key angle bending-key angle bending coupling effect energy;
Figure BDA0003192042180000029
the key expansion-dihedral angle torsion coupling function energy;
Figure BDA00031920421800000210
the key angle bending-dihedral angle torsion coupling effect energy;
Figure BDA00031920421800000211
the coupling function of key angle bending-dihedral angle torsion-key angle bending;
Figure BDA00031920421800000212
is a non-bonding energy;
Kb1、Kb2and Kb3Is a key expansion force constant; b is bond length, nm; b0Is the initial value of bond length, nm; ka1、Ka2And Ka3Is the key angle bending force constant; θ is the key angle, °; theta0Initial key angle, °; kt1、Kt2And Kt3Is the dihedral torsional potential constant; phi is dihedral angle, °; kxIs the out-of-plane vibro potential constant; x is the vibration angle out of plane, °; x is the number of0Initial out-of-plane angle, °; kbbIs key expansion-key expansion coupling term constant; kbaIs a key expansion-key bending coupling term constant; b' is the bond length of the cross term, nm; b0' is the initial bond length of the cross term, nm; kaaIs the key bending-key bending coupling term constant; θ' is the cross-term key angle, °; theta0' is the cross term initial key angle, °; kbt1、Kbt2And Kbt3Is key stretch-key twist coupling term constant; kat1、Kat2And Kat3Is the key bending-key twisting coupling term constant; k is a bond bending-bond twisting-bond bending coupling term constant; epsiloni、εjIs a potential well of an atom or molecule i, j, kj/mol; epsilon0Dielectric constant, 8.854X 10-12F/M；σi、σjIs the collision diameter, nm, of an atom or molecule i, j; r isijIs the distance between charge i and charge j, nm; q. q.siIs the charge value of the charge acceptor, C; q. q.sjIs the charge value of the charge donor, C.
Preferably, in step S7, the fugacity is calculated by the following formula:
fl＝pl,vexp(Vl(p-pl,v)/RT) (2)
wherein:
pl,v＝pcexp(-9.741(1-T/Tc)+5.127(1-T/Tc)1.5-0.205(1-T/Tc)3+9.502(1-T/Tc)7)Tc/T (3)
when the temperature is less than 432.6K, wherein:
Vl＝115.708+0.06735T (4)
when the temperature is more than 432.6K and less than or equal to 577.96K, wherein:
Vl＝171.075-0.1442T+0.000193T2 (5)
in the formula: f. oflFugacity, Pa; p is a radical ofl,vIs the saturated vapor pressure, Pa; vlIs volume, cm3Per mol; p is pressure, Pa; r is an ideal gas constant of 8.314472 x 106cm3·Pa·mol-1·K-1(ii) a T is temperature, K; p is a radical ofcIs the critical pressure, 10.4209 MPa; t iscCritical temperature, 1115.0292K.
Preferably, in step S10, the adsorption phase density is calculated by the following formula:
Figure BDA0003192042180000031
in the formula: rhobAs adsorbed phase density, g/cm3(ii) a C is the relative concentration of molecules,%; n is a radical oftTo adsorb molecular weight, molecules/uc; m is the relative molecular mass of the liquid sulfur simple substance, 1; v is the simulated unit cell volume, cm3；NAIs an Avogastron constant without dimension;
the excess adsorption amount is calculated by the following formula:
Figure BDA0003192042180000032
in the formula: n isexExcess adsorption, mmol/g; vbVolume of adsorbed phase, cm3；MaMass of adsorbate molecule, g.
Preferably, in step S15, the diffusion coefficient is calculated by the following formula:
D＝a/6 (8)
in the formula: d is a diffusion coefficient and is dimensionless; a is the slope and is dimensionless.
Preferably, step S10 further includes the steps of calculating gibbs free energy from the parameters obtained in steps S8 and S9, and calculating entropy change in the adsorption process from the gibbs free energy;
the gibbs free energy is calculated by the following formula:
Figure BDA0003192042180000041
in the formula: Δ G is Gibbs free energy change, KJ/mol; Δ H is the heat of adsorption, KJ/mol; t is the absolute temperature of the adsorption process, K; p is the pressure of the adsorption process, MPa;
the entropy change is calculated by:
Figure BDA0003192042180000042
in the formula: delta S is the entropy change of the adsorption process, KJ (mol. K)-1。
Preferably, between step S10 and step S11, the method further comprises the following steps:
s11': judging the adsorption type according to the Gibbs free energy or the adsorption heat; and judging the type of the adsorption force according to the adsorption heat.
Preferably, in step S11', the determining the adsorption type according to the gibbs free energy or the adsorption heat is specifically:
when the change amount of the Gibbs free energy is-20-0 KJ/mol or the absolute value of the adsorption heat is less than 40KJ/mol, the adsorption type is physical adsorption;
and when the change amount of the Gibbs free energy is-400 to-80 KJ/mol or the absolute value of the adsorption heat is 50 to 200KJ/mol, the adsorption type is chemical adsorption.
Preferably, in step S11', the determination of the type of the adsorption force based on the heat of adsorption is as follows:
when the adsorption heat is 4-10 KJ/mol, van der Waals force exists in adsorption acting force;
when the adsorption heat is 2-40 KJ/mol, hydrogen bonds exist in the adsorption acting force;
when the adsorption heat is 40KJ/mol, ligand exchange exists in the adsorption acting force;
when the adsorption heat is 2-29 KJ/mol, dipole interaction force exists in the adsorption action force;
when the heat of adsorption is greater than 60KJ/mol, the adsorption force is a chemical bond.
The invention has the beneficial effects that:
the method utilizes Monte Carlo simulation and molecular dynamics simulation, and can effectively obtain the quantized adsorption characteristic parameters of the liquid sulfur in the carbonate rock mineral adsorption process: the adsorption molecular weight, the excess adsorption capacity, the adsorption heat, the adsorption phase density, the radial distribution function, the diffusion coefficient and the like can solve the problem that the adsorption characteristic parameters of the liquid sulfur in the carbonate rock are difficult to obtain, can disclose the microscopic adsorption mechanism of the liquid sulfur in a nanoscale, and can provide a theoretical reference basis for the prevention and treatment work of the on-site sulfur deposition.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without creative efforts.
FIG. 1 is a schematic diagram of a scanning electron microscope result of a target rock sample according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a Monte Carlo simulation principle;
FIG. 3 is a graph showing adsorption results according to an embodiment of the present invention;
FIG. 4 is a graph showing the heat of adsorption results according to one embodiment of the present invention;
FIG. 5 is a graph showing the results of stabilizing an adsorption configuration according to an embodiment of the present invention;
FIG. 6 is a schematic diagram of a molecular dynamics simulation principle;
FIG. 7 is a graph illustrating the results of radial distribution functions according to one embodiment of the present invention;
FIG. 8 is a diagram illustrating the result of mean square shift according to an embodiment of the present invention.
Detailed Description
The invention is further illustrated with reference to the following figures and examples. It should be noted that, in the present application, the embodiments and the technical features of the embodiments may be combined with each other without conflict. It is noted that, unless otherwise indicated, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The use of the terms "comprising" or "including" and the like in the present disclosure is intended to mean that the elements or items listed before the term cover the elements or items listed after the term and their equivalents, but not to exclude other elements or items.
The invention provides a method for determining microscopic adsorption characteristic parameters of liquid sulfur in carbonate rock nanopores, wherein the microscopic adsorption characteristic parameters comprise adsorption molecular weight, excess adsorption quantity, adsorption heat, adsorption phase density, radial distribution function and diffusion coefficient, and the method for determining the microscopic adsorption characteristic parameters comprises the following steps:
s1: and establishing a molecular model of the target rock sample.
In a specific embodiment, taking a target rock sample of a deep sea phase high sulfur-containing carbonate rock as an example, firstly, analyzing the target rock sample by using a field emission scanning electron microscope, an atomic force microscope and other technologies to obtain the actual characteristics of the pore structure of the deep sea phase high sulfur-containing carbonate rock, wherein the scanning electron microscope result is shown in fig. 1; and establishing a carbonate rock mineral molecular model conforming to the target rock sample according to the obtained actual characteristics. It should be noted that, establishing a molecular model according to actual characteristics of a target rock sample is prior art, and specific steps are not described herein again.
S2: and selecting the adsorption experimental surface of the molecular model, and cutting and expanding the molecular model along the adsorption experimental surface.
S3: and combining and adjusting the expanded adsorption experimental surface to obtain a microscopic adsorption skeleton model according with the periodic mirror principle.
In one embodiment, the adsorption experimental plane of the molecular model is selected in step S2, and the radial combination adjustment of the expanded adsorption experimental plane in step S3 is performed by the selection and combination adjustment method in the prior art.
The establishment of the microscopic adsorption skeleton model adopts a periodic mirror principle, and the molecular configuration used in the simulation has periodic boundary conditions: during the forced movement of the particles in the simulation box, the particles can enter the simulation box from the opposite side after leaving from one side of the simulation box so as to ensure the constant number of the particles in the model system. The existence of the periodic mirror image can eliminate the influence of the boundary effect when the particles pass through the simulation box boundary on one hand, and can simulate the movement of an unlimited number of particles by using a limited number of particles on the other hand, thereby improving the precision of the simulation result.
S4: and setting a truncation radius according to the size of the microscopic adsorption skeleton model.
In a specific embodiment, the truncation radius is one-half of the smallest edge length of the microscopic adsorption scaffold model.
S5: and calculating the total potential energy of the microscopic adsorption skeleton model by using a COMPASS II force field.
In a specific embodiment, the total potential energy is a bond stretching energy, a bond angle bending energy, a dihedral torsion energy, a bond angle out-of-plane bending energy, a bond stretching energy, a bond angle bending energy, a dihedral torsion energy, a bond angle out-of-plane bending energy in the form of coupled motion, and a sum of electrostatic interaction forces and van der waals forces; optionally, the total potential energy is calculated by the following formula:
Figure BDA0003192042180000061
in the formula: e is total potential energy, kcal/mol;
Figure BDA0003192042180000071
is the sum of the stretching energy of the key;
Figure BDA0003192042180000072
is the sum of the bending energy of the key angle;
Figure BDA0003192042180000073
is the sum of the bond twisting energies;
Figure BDA0003192042180000074
the key corner out-of-plane bending energy;
Figure BDA0003192042180000075
key expansion-key expansion coupling function energy;
Figure BDA0003192042180000076
the key expansion-key angle bending coupling function energy is adopted;
Figure BDA0003192042180000077
a key angle bending-key angle bending coupling effect energy;
Figure BDA0003192042180000078
the key expansion-dihedral angle torsion coupling function energy;
Figure BDA0003192042180000079
the key angle bending-dihedral angle torsion coupling effect energy;
Figure BDA00031920421800000710
the coupling function of key angle bending-dihedral angle torsion-key angle bending;
Figure BDA00031920421800000711
is a non-bonding energy;
Kb1、Kb2and Kb3Is a key expansion force constant; b is bond length, nm; b0Is the initial value of bond length, nm; ka1、Ka2And Ka3Is the key angle bending force constant; θ is the key angle, °; theta0Initial key angle, °; kt1、Kt2And Kt3Is the dihedral torsional potential constant; phi is dihedral angle, °; kxIs the out-of-plane vibro potential constant; x is the vibration angle out of plane, °; x is the number of0Initial out-of-plane angle, °; kbbIs key expansion-key expansion coupling term constant；KbaIs a key expansion-key bending coupling term constant; b' is the bond length of the cross term, nm; b0' is the initial bond length of the cross term, nm; kaaIs the key bending-key bending coupling term constant; θ' is the cross-term key angle, °; theta0' is the cross term initial key angle, °; kbt1、Kbt2And Kbt3Is key stretch-key twist coupling term constant; kat1、Kat2And Kat3Is the key bending-key twisting coupling term constant; k is a bond bending-bond twisting-bond bending coupling term constant; epsiloni、εjIs a potential well of an atom or molecule i, j, kj/mol; epsilon0Dielectric constant, 8.854X 10-12F/M；σi、σjIs the collision diameter, nm, of an atom or molecule i, j; r isijIs the distance between charge i and charge j, nm; q. q.siIs the charge value of the charge acceptor, C; q. q.sjIs the charge value of the charge donor, C.
S6: and setting the gradient values of the temperature and the pressure interval during simulation calculation according to the formation pressure and the temperature interval which need to be simulated and calculated, and determining the step length of the simulation calculation.
S7: calculating the fugacity of the liquid sulfur elementary substance molecules under different temperature and pressure.
The fugacity is a physical quantity that represents the actual pressure of the gas by chemical thermodynamics and is used to replace the pressure in subsequent simulations. In one particular embodiment, the fugacity is calculated by the following equation:
fl＝pl,vexp(Vl(p-pl,v)/RT) (2)
wherein:
pl,v＝pcexp(-9.741(1-T/Tc)+5.127(1-T/Tc)1.5-0.205(1-T/Tc)3+9.502(1-T/Tc)7)Tc/T (3)
when the temperature is less than 432.6K, wherein:
Vl＝115.708+0.06735T (4)
when the temperature is more than 432.6K and less than or equal to 577.96K, wherein:
Vl＝171.075-0.1442T+0.000193T2 (5)
in the formula: f. oflFugacity, Pa; p is a radical ofl,vIs the saturated vapor pressure, Pa; vlIs volume, cm3Per mol; p is pressure, Pa; r is an ideal gas constant of 8.314472 x 106cm3·Pa·mol-1·K-1(ii) a T is temperature, K; p is a radical ofcIs the critical pressure, 10.4209 MPa; t iscCritical temperature, 1115.0292K.
S8: and carrying out giant regular ensemble Monte Carlo simulation of the adsorption isotherm to obtain the adsorption heat, the adsorption molecular weight, the adsorption isotherm and the relative molecular concentration in a pressure interval at a certain set temperature.
The Monte Carlo Method (MC) is a random simulation method based on statistical mechanics and combining ensemble to calculate the average value, and the Metropolis sampling method is used for sampling the generated random numbers so as to achieve the purpose of simplifying calculation and obtain the microstructure and the property of the substance. The Metropolis sampling method mainly constructs a Markov chain in a phase space so as to realize importance sampling, and the construction of the Markov chain needs to meet the following conditions: firstly, the point generated by random sampling must belong to one point in the set formed by the points in the system; second, the point generated by random sampling can only be correlated with the point immediately preceding the point, regardless of where the sampling began. The principle of the Metropolis Monte Carlo method is shown in FIG. 2.
The Monte Carlo simulation is mainly implemented in the invention by the following steps:
(1) building a mineral skeleton model, and ensuring that the mineral skeleton model is reasonable in structure;
(2) selecting an ensemble; different calculation results can be caused by using different ensembles for calculation, and the currently commonly used ensembles comprise several ensembles such as giant regular, Gibbs, micro regular, isothermal, isobaric and constant stress-isothermal;
(3) randomly generating a molecular configuration of elemental sulfur molecules distributed in a pore structure according to a random variable distribution mode and an ensemble rule in the model;
(4) setting the implementation mode of calculation, and determining physical quantity data (such as adsorption quantity, equivalent adsorption heat, configuration energy and the like) to be obtained;
(5) random changes to the particle in molecular configuration, such as generation, disappearance, translation, and rotation;
(6) and (3) comparing the energy change before and after the change by calculating the energy of each new configuration:
if the energy of the new configuration is lower than that of the original configuration, receiving the new configuration, and repeatedly performing next iterative computation on the new configuration;
if the energy of the new configuration is higher than that of the original configuration, calculating a boltzmann factor of the new configuration, and generating a random number:
if the generated random number is smaller than the calculated Boltzmann factor, receiving a current new configuration;
if the random number is larger than the Boltzmann factor, abandoning the configuration for the next repeated calculation;
(7) ending the calculation until all configurations lower than the given energy condition are searched out finally;
(8) the statistical analysis is performed on the balance simulation result, and it should be noted that the result is not related to the initial condition, otherwise, the result is invalid.
In the invention, the giant regular ensemble is selected in the step (2) when the ensemble is selected. The megaregularized ensemble monte carlo method includes three types of particle motion, which are insertion, deletion, and movement of particles, respectively.
(1) Particle insertion
Randomly inserting a particle in the particle source at any location in the simulation box, the particle being randomly selected, the probability of the particle being accepted for insertion into the box being a function of the chemical potential in the particle source:
Figure BDA0003192042180000091
in the formula: v' is the volume of the simulation box, m3(ii) a Λ is the de broglie wavelength of the particle, m; k is a radical ofBBoltzmann constant; mu is the chemical potential of the particle source, J/mol; u is the total energy of the systemJ, J; n is the particle sequence.
(2) Particle deletion
In the simulated box after the insertion of the particle, a particle in the box is randomly deleted, and the probability of the particle being accepted for deletion is also a function of the chemical potential in the particle source:
Figure BDA0003192042180000092
(3) movement and rotation of particles
Randomly selecting the inserted particle in the simulation box, moving to a new position or rotating the particle, wherein the probability that the particle movement or rotation is accepted is as follows:
P(s→s′)＝min(1,exp{-β[U(s′)-U(s)]}) (13)
wherein s and s' are the states of the particles in the system before and after movement and rotation.
In one specific embodiment, the giant canonical ensemble Monte Carlo simulation results are shown in FIG. 3 at a temperature of 403.15K and a pressure of 45 MPa.
S9: and changing the set temperature according to the step length, and repeating the step S8 until the adsorption heat, the adsorption molecular weight, the adsorption isotherm and the relative concentration of molecules in each pressure interval under all temperature intervals are obtained.
In a specific embodiment, the heat of adsorption in each pressure interval for all temperature intervals of the target rock sample is shown in fig. 4.
S10: based on the parameters obtained in step S8 and step S9, the adsorbed phase density and the excess adsorption amount at each temperature are calculated.
In a specific embodiment, the adsorbed phase density is calculated by the formula:
Figure BDA0003192042180000093
in the formula: rhobAs adsorbed phase density, g/cm3(ii) a C is the relative concentration of molecules,%; n is a radical oftTo adsorb molecular weight, molecules/uc; m is the relative molecular mass of the liquid sulfur simple substance, 1; v is the simulated unit cell volume, cm3；NAIs an Avogastron constant without dimension;
the excess adsorption amount is calculated by the following formula:
Figure BDA0003192042180000094
in the formula: : n isexExcess adsorption, mmol/g; vbVolume of adsorbed phase, cm3；MaMass of adsorbate molecule, g.
In addition, when the adsorption molecular weight obtained in step S8 and step S9 is an absolute adsorption amount, and the excess adsorption amount is calculated from the adsorption molecular weight by equation (7), the adsorption molecular weight is converted into units, specifically, the units are converted by the following equation:
Figure BDA0003192042180000101
s11: and obtaining a corresponding saturated pressure value when the saturated adsorption state is reached at each temperature according to the adsorption isotherm at each temperature.
S12: and respectively carrying out constant-pressure adsorption Monte Carlo simulation under the conditions of each saturated pressure value and the corresponding temperature value, and screening out the molecular configuration with the lowest total energy of the system.
S13: and carrying out volume optimization on the molecular configuration according to the system energy minimization to obtain a stable adsorption configuration.
It should be noted that, in steps S11-S13, obtaining a saturation pressure value, performing a constant pressure adsorption monte carlo simulation, screening a molecular configuration with the lowest total energy, and optimizing the system energy minimization volume are all the prior art, and the specific method is not described herein again. In a specific embodiment, the stable adsorption configuration is shown in fig. 5.
S14: and performing molecular dynamics simulation on the stable adsorption configuration to obtain a radial distribution function and mean square displacement.
The Molecular Dynamics (MD) simulation method is a simulation method used to calculate the equilibrium and transport properties of a classical multi-body system in which the motion of the particles satisfies the newtonian law of motion.
Basic principles of molecular dynamics simulation methods: and solving a Newton's equation of motion to obtain relevant parameters of the system at any moment, and then carrying out statistical averaging to obtain thermodynamic parameters of the system. The principle of the MD simulation method is shown in fig. 6.
The main implementation steps of the MD simulation in the invention are as follows:
(1) on the basis of the mineral-sulfur lowest energy configuration, the initial conditions are given: initial position r (0), v (0);
(2) the potential energy of the system is calculated according to the position of the sulfur molecule and the potential energy function, and the acting force and the acceleration of the sulfur molecule at the time t are calculated according to the Newton's second law;
(3) calculating the position of the sulfur molecule at the t + delta t moment, and solving the speed and the system potential energy;
(4) repeating the steps until all sulfur molecule information in a given time step is recorded, recording the sulfur molecule information at each time, and generating a motion track;
(5) based on the movement locus of sulfur molecules, the radial distribution function, the mean square displacement, the free energy and the like of the sulfur molecules can be calculated to analyze the adsorption property of the elemental sulfur molecules on the surface of the mineral.
The method for solving the particle motion equation comprises a Verlet method, a Leap frog method, a Beeman method, a Velocity-Verlet method, a Predictor-corrector method and the like. The Verlet algorithm is the most basic and the simplest algorithm in solving the newton equation of motion, and the core of the algorithm is as follows:
the position of each particle at a certain time (for example, t + Δ t time) in the system is subjected to Taylor expansion to obtain:
Figure BDA0003192042180000111
similarly, Taylor expansion of the position of the particle at time t- Δ t yields:
Figure BDA0003192042180000112
the two equations are added to obtain:
Figure BDA0003192042180000116
ignoring higher order terms can result in:
Figure BDA0003192042180000113
as can be seen from the above equation, when the position of the initial particle, the position of the particle at the next time, and the acceleration are known, the position of the particle at the new time can be predicted. The motion speed of the particle can be obtained by subtracting the two equations and neglecting the high-order term:
Figure BDA0003192042180000114
other algorithms for solving newtonian equations of motion are more accurate or efficient to perform in predicting the position of the particle and calculating the velocity of motion of the particle. Different algorithms have different advantages, such as that the Verlet method can directly calculate the total energy of the system compared with the Leap frog method, which cannot, but has higher precision in calculating the speed of the particles. In actual use, different algorithms can be selected according to needs.
Radial Distribution Function (RDF) is a generally applicable method for describing the aggregation order of the particles in the system structure, and is also an important method for researching the thermodynamic properties of the system.
RDF is the ratio of the probability of finding another target particle within the region of r to r + dr from a central atom and the probability of the other target particle appearing within this region, and is a physical quantity characterizing the microstructure of the liquid. The radial distribution function of the system is equal to the algebraic mean of the radial distribution functions of all atoms in the entire system. Defining a radial distribution function g (r) as:
Figure BDA0003192042180000115
in the formula: dN represents the number of target particles found in the region of r to dr from the central atom, and ρ' is the density of the target particles.
In a specific embodiment, the radial distribution function is shown in FIG. 7 and the mean square displacement is shown in FIG. 8.
S15: drawing a relation curve of the mean square displacement and time, calculating the slope of the relation curve, and calculating according to the slope to obtain a diffusion coefficient, wherein the diffusion coefficient is calculated according to the following formula:
D＝a/6 (8)
in the formula: d is a diffusion coefficient and is dimensionless; a is the slope and is dimensionless.
In a specific embodiment, step S10 further includes the steps of calculating gibbs free energy according to the parameters obtained in steps S8 and S9, and calculating entropy change in the adsorption process according to the gibbs free energy;
the gibbs free energy is calculated by the following formula:
Figure BDA0003192042180000121
in the formula: Δ G is Gibbs free energy change, KJ/mol; Δ H is the heat of adsorption, KJ/mol; t is the absolute temperature of the adsorption process, K; p is the pressure of the adsorption process, MPa.
The entropy change is calculated by:
Figure BDA0003192042180000122
in the formula: delta S is the entropy change of the adsorption process, KJ (mol. K)-1。
In a specific embodiment, between step S10 and step S11, the method further includes the following steps:
s11': judging the adsorption type according to the Gibbs free energy or the adsorption heat; judging the type of adsorption force according to the adsorption heat; specifically, the method comprises the following steps:
when the change amount of the Gibbs free energy is-20-0 KJ/mol or the absolute value of the adsorption heat is less than 40KJ/mol, the adsorption type is physical adsorption; when the change amount of the Gibbs free energy is-400 to-80 KJ/mol or the absolute value of the adsorption heat is 50 to 200KJ/mol, the adsorption type is chemical adsorption;
when the adsorption heat is 4-10 KJ/mol, van der Waals force exists in adsorption acting force; when the adsorption heat is 2-40 KJ/mol, hydrogen bonds exist in the adsorption acting force; when the adsorption heat is 40KJ/mol, ligand exchange exists in the adsorption acting force; when the adsorption heat is 2-29 KJ/mol, dipole interaction force exists in the adsorption action force; when the heat of adsorption is greater than 60KJ/mol, the adsorption force is a chemical bond.
Although the Gibbs free energy, entropy change, adsorption type and adsorption acting force type are not necessary microscopic adsorption characteristic parameters of the liquid sulfur in the nano pores of the carbonate rock, the Gibbs free energy, entropy change, adsorption type and adsorption acting force type have great help for analyzing the adsorption mechanism of the liquid sulfur.
The method can quantitatively obtain the adsorption characteristic parameters of the liquid sulfur in the carbonate rock minerals: compared with the prior art, the adsorption molecular weight, the excess adsorption capacity, the adsorption heat, the adsorption phase density, the radial distribution function and the diffusion coefficient have remarkable progress.
Although the present invention has been described with reference to a preferred embodiment, it should be understood that various changes, substitutions and alterations can be made herein without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (10)

1. A method for determining microscopic adsorption characteristic parameters of liquid sulfur in nanopores of carbonate rocks is characterized in that the microscopic adsorption characteristic parameters comprise adsorption molecular weight, excess adsorption capacity, adsorption heat, adsorption phase density, radial distribution function and diffusion coefficient, and the determination method comprises the following steps:
s1: establishing a molecular model of a target rock sample;
s2: selecting an adsorption experimental surface of the molecular model, and cutting and expanding the molecular model along the adsorption experimental surface;
s3: combining and adjusting the expanded adsorption experimental surface to obtain a microscopic adsorption skeleton model according with a periodic mirror principle;
s4: setting a truncation radius according to the size of the microscopic adsorption skeleton model;
s5: calculating the total potential energy of the microscopic adsorption skeleton model by using a COMPASS II force field;
s6: setting a temperature and pressure interval gradient value during simulation calculation according to the formation pressure and temperature interval needing simulation calculation, and determining the step length of the simulation calculation;
s7: calculating the fugacity of the liquid sulfur simple substance molecules under different temperature and pressure;
s8: performing giant regular ensemble Monte Carlo simulation of an adsorption isotherm to obtain adsorption heat, adsorption molecular weight, adsorption isotherm and relative molecular concentration within a pressure interval at a certain set temperature;
s9: changing the set temperature according to the step length, and repeating the step S8 until the adsorption heat, the adsorption molecular weight, the adsorption isotherm and the relative molecular concentration in each pressure interval under all temperature intervals are obtained;
s10: calculating the adsorption phase density and the excess adsorption amount at each temperature according to the parameters obtained in the step S8 and the step S9;
s11: according to the adsorption isotherms at all temperatures, obtaining corresponding saturated pressure values when the saturated adsorption state is reached at all temperatures;
s12: respectively carrying out constant-pressure adsorption Monte Carlo simulation under the conditions of each saturated pressure value and corresponding temperature value, and screening out the molecular configuration with the lowest total energy of the system;
s13: carrying out volume optimization on the molecular configuration according to the system energy minimization to obtain a stable adsorption configuration;
s14: performing molecular dynamics simulation on the stable adsorption configuration to obtain a radial distribution function and mean square displacement;
s15: and drawing a relation curve of the mean square displacement and time, calculating the slope of the relation curve, and calculating according to the slope to obtain the diffusion coefficient.
2. The method for determining the microscopic adsorption characteristic parameters of liquid sulfur in the nanopores of carbonate rock according to claim 1, wherein in step S4, the truncation radius is one half of the minimum side length of the microscopic adsorption skeleton model.
3. The method for determining the microscopic adsorption characteristic parameter of liquid sulfur in the nanopores of carbonate rock according to claim 1, wherein in step S5, the total potential energy is calculated by the following formula:
Figure FDA0003192042170000021
in the formula: e is total potential energy, kcal/mol;
Figure FDA0003192042170000022
is the sum of the stretching energy of the key;
Figure FDA0003192042170000023
is the sum of the bending energy of the key angle;
Figure FDA0003192042170000024
is the sum of the bond twisting energies;
Figure FDA0003192042170000025
the key corner out-of-plane bending energy;
Figure FDA0003192042170000026
key expansion-key expansion coupling function energy;
Figure FDA0003192042170000027
the key expansion-key angle bending coupling function energy is adopted;
Figure FDA0003192042170000028
a key angle bending-key angle bending coupling effect energy;
Figure FDA0003192042170000029
the key expansion-dihedral angle torsion coupling function energy;
Figure FDA00031920421700000210
the key angle bending-dihedral angle torsion coupling effect energy;
Figure FDA00031920421700000211
the coupling function of key angle bending-dihedral angle torsion-key angle bending;
Figure FDA00031920421700000212
is a non-bonding energy;
Kb1、Kb2and Kb3Is a key expansion force constant; b is bond length, nm; b0Is the initial value of bond length, nm; ka1、Ka2And Ka3Is the key angle bending force constant; θ is the key angle, °; theta0Initial key angle, °; kt1、Kt2And Kt3Is a dihedral angle knobA transition constant; phi is dihedral angle, °; kxIs the out-of-plane vibro potential constant; x is the vibration angle out of plane, °; x is the number of0Initial out-of-plane angle, °; kbbIs key expansion-key expansion coupling term constant; kbaIs a key expansion-key bending coupling term constant; b' is the bond length of the cross term, nm; b0' is the initial bond length of the cross term, nm; kaaIs the key bending-key bending coupling term constant; θ' is the cross-term key angle, °; theta0' is the cross term initial key angle, °; kbt1、Kbt2And Kbt3Is key stretch-key twist coupling term constant; kat1、Kat2And Kat3Is the key bending-key twisting coupling term constant; k is a bond bending-bond twisting-bond bending coupling term constant; epsiloni、εjIs a potential well of an atom or molecule i, j, kj/mol; epsilon0Dielectric constant, 8.854X 10-12F/M；σi、σjIs the collision diameter, nm, of an atom or molecule i, j; r isijIs the distance between charge i and charge j, nm; q. q.siIs the charge value of the charge acceptor, C; q. q.sjIs the charge value of the charge donor, C.
4. The method for determining microscopic adsorption characteristic parameters of liquid sulfur in carbonate nanopores according to claim 1, wherein in step S7, the fugacity is calculated by the following formula:
fl＝pl,vexp(Vl(p-pl,v)/RT) (2)
wherein:
pl,v＝pcexp(-9.741(1-T/Tc)+5.127(1-T/Tc)1.5-0.205(1-T/Tc)3+9.502(1-T/Tc)7)Tc/T (3)
when the temperature is less than 432.6K, wherein:
Vl＝115.708+0.06735T (4)
when the temperature is more than 432.6K and less than or equal to 577.96K, wherein:
Vl＝171.075-0.1442T+0.000193T2 (5)
in the formula: f. oflFugacity, Pa; p is a radical ofl,vIs the saturated vapor pressure, Pa; vlIs volume, cm3Per mol; p is pressure, Pa; r is an ideal gas constant of 8.314472 x 106cm3·Pa·mol-1·K-1(ii) a T is temperature, K; p is a radical ofcIs the critical pressure, 10.4209 MPa; t iscCritical temperature, 1115.0292K.
5. The method for determining microscopic adsorption characteristic parameters of liquid sulfur in carbonate nanopores according to claim 1, wherein in step S10, the adsorption phase density is calculated by the following formula:
Figure FDA0003192042170000031
in the formula: rhobAs adsorbed phase density, g/cm3(ii) a C is the relative concentration of molecules,%; n is a radical oftTo adsorb molecular weight, molecules/uc; m is the relative molecular mass of the liquid sulfur simple substance, 1; v is the simulated unit cell volume, cm3；NAIs an Avogastron constant without dimension;
the excess adsorption amount is calculated by the following formula:
Figure FDA0003192042170000032
in the formula: n isexExcess adsorption, mmol/g; vbVolume of adsorbed phase, cm3；MaMass of adsorbate molecule, g.
6. The method for determining microscopic adsorption characteristic parameters of liquid sulfur in carbonate nanopores according to claim 1, wherein in step S15, the diffusion coefficient is calculated by the following formula:
D＝a/6 (8)
in the formula: d is a diffusion coefficient and is dimensionless; a is the slope and is dimensionless.
7. The method for determining the microscopic adsorption characteristic parameters of liquid sulfur in the nanopores of carbonate rock according to any one of claims 1 to 6, wherein the method further comprises the steps of calculating Gibbs free energy according to the parameters obtained in the steps S8 and S9, and calculating the entropy change in the adsorption process according to the Gibbs free energy in step S10;
the gibbs free energy is calculated by the following formula:
Figure FDA0003192042170000041
in the formula: Δ G is Gibbs free energy change, KJ/mol; Δ H is the heat of adsorption, KJ/mol; t is the absolute temperature of the adsorption process, K; p is the pressure of the adsorption process, MPa;
the entropy change is calculated by:
Figure FDA0003192042170000042
in the formula: delta S is the entropy change of the adsorption process, KJ (mol. K)-1。
8. The method for determining the microscopic adsorption characteristic parameters of liquid sulfur in the nanopores of carbonate rock according to claim 7, wherein between the step S10 and the step S11, the method further comprises the following steps:
s11': judging the adsorption type according to the Gibbs free energy or the adsorption heat; and judging the type of the adsorption force according to the adsorption heat.
9. The method for determining microscopic adsorption characteristic parameters of liquid sulfur in carbonate rock nanopores according to claim 8, wherein in step S11', the judgment of adsorption type according to gibbs free energy or adsorption heat is specifically as follows:
when the change amount of the Gibbs free energy is-20-0 KJ/mol or the absolute value of the adsorption heat is less than 40KJ/mol, the adsorption type is physical adsorption;
and when the change amount of the Gibbs free energy is-400 to-80 KJ/mol or the absolute value of the adsorption heat is 50 to 200KJ/mol, the adsorption type is chemical adsorption.
10. The method for determining microscopic adsorption characteristic parameters of liquid sulfur in carbonate rock nanopores according to claim 8, wherein in step S11', the determination of the adsorption force type according to the adsorption heat is specifically as follows:
when the adsorption heat is 4-10 KJ/mol, van der Waals force exists in adsorption acting force;
when the adsorption heat is 2-40 KJ/mol, hydrogen bonds exist in the adsorption acting force;
when the adsorption heat is 40KJ/mol, ligand exchange exists in the adsorption acting force;
when the adsorption heat is 2-29 KJ/mol, dipole interaction force exists in the adsorption action force;
when the heat of adsorption is greater than 60KJ/mol, the adsorption force is a chemical bond.
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