A method for extrapolating hydrate dissociation time under high methane concentration conditions

Abstract

The application provides a method for extrapolating hydrate dissociation time under high methane concentration conditions, which is based on the sequence consistency and time self-similarity principle of cage structure rupture events in the hydrate dissociation process. Under the premise of consistency between the initial and final dissociation states, the absolute rate of dissociation is mainly modulated by the concentration of the methane aqueous solution, and the relative time proportion of different spatial layers / structure stages in the total dissociation process remains unchanged. Without performing microsecond to tens of microsecond full-range molecular dynamics simulation, the long-time dissociation behavior of hydrates under high concentration and near-equilibrium conditions can be efficiently predicted. Compared with the traditional method, the application can retain the phased non-uniform speed characteristics of the dissociation process, significantly reduce the calculation cost and extrapolation deviation, and improve the capture ability and result reliability of the sudden increase of dissociation time under near-equilibrium and high concentration conditions.

Description

Technical Field

[0001] This invention relates to the field of molecular simulation technology, and in particular to a method for extrapolating the dissociation time of hydrates under high methane concentration conditions. Background Technology

[0002] Natural gas hydrates are widely found in seafloor sediments, permafrost regions, and deep-sea oil and gas environments. They also form and dissociate during natural gas extraction, subsea pipeline transportation, and the operation of wellbore and gas production systems. The formation and dissociation of hydrates significantly affect flow safety, recovery efficiency, and engineering risk assessment. Therefore, accurately characterizing the dissociation kinetics of hydrates under different temperature, pressure, and liquid methane concentration conditions is of great significance.

[0003] Currently, molecular dynamics simulations have become an important tool for studying hydrate dissociation mechanisms because they can resolve microscopic processes such as hydrate cage structure rupture, interface evolution, and gas diffusion at the molecular scale. However, as the concentration of liquid methane increases and approaches equilibrium, the hydrate dissociation time exhibits a significant nonlinear increase, often extending from nanoseconds to microseconds or even longer timescales. Since classical molecular dynamics simulations are limited by affordable computational costs, directly simulating the complete dissociation of the target region under high methane concentration conditions typically requires substantial computational resources, making it difficult to obtain reliable statistical results through sufficient repetition of trajectories. This limits the systematic study of dissociation dynamics in near-equilibrium high-concentration regions.

[0004] Furthermore, when constructing a hydrate-aqueous solution interface model, rapid transient collapse often occurs near the initial interface due to excessively high interfacial energy, forming an unstable boundary layer. Directly incorporating this boundary layer into kinetic statistics introduces unsteady-state disturbances and reduces the comparability and repeatability between different trajectories. Existing methods generally lack effective isolation of this transient effect and standardized definition of the target study region, further weakening the reliability of dissociation kinetic data under high concentration conditions. On the other hand, hydrate dissociation is not uniform. Actual trajectories often exhibit alternating slow phases dominated by structurally intact cages and rapid phases dominated by partially open / defective interfaces, making it impossible to linearly extrapolate the dissociation time from initial short-term data.

[0005] Therefore, there is an urgent need for a method that can automatically and robustly extrapolate the complete dissociation time of the target study region, especially under near-equilibrium conditions, by utilizing available local dissociation information without the need for ultra-long-duration direct molecular dynamics (MD) simulations. Summary of the Invention

[0006] In view of this, the present invention aims to propose a method for extrapolating the dissociation time of hydrates under high methane concentration conditions. This method is based on the principle of kinetic similarity scaling to solve the problems existing in current hydrate dissociation studies, such as excessively long dissociation times under high methane concentration conditions, high computational costs of direct molecular dynamics simulations, difficulty in obtaining sufficient repeated sampling, and systematic underestimation in the near-equilibrium high-concentration range by traditional fitting extrapolation. The present invention utilizes the stability of the cage structure rupture event sequence and the principle of temporal self-similarity during hydrate dissociation: under the premise that the initial and final dissociation states are consistent, the liquid-phase methane concentration mainly changes the absolute rate of dissociation, while the relative time proportion of different spatial layers / structural stages in the total dissociation process remains unchanged. By obtaining the spatial layer dissociation time proportion in the low-concentration reference trajectory and explicitly simulating only the dissociation time of reachable sub-regions in the high-concentration estimated trajectory, the present invention can reliably extrapolate the complete dissociation time of the target study region under high concentration (especially near-equilibrium) conditions without performing full-process simulations on microsecond or even longer time scales, thereby reducing computational costs, reducing extrapolation bias, and improving the repeatability and engineering applicability of the results.

[0007] To achieve the above objectives, the technical solution of the present invention is implemented as follows:

[0008] A method for extrapolating the dissociation time of hydrates under high methane concentration conditions, the method comprising the following steps:

[0009] S1. Construct an initial molecular dynamics model containing both a methane hydrate phase and a methane aqueous solution phase, setting the external temperature, pressure, and concentration of the methane aqueous solution phase, and determining the initial solid-liquid interface position; based on the initial solid-liquid interface, divide the space into layers along the normal direction, including at least an unstable boundary layer R0, a reference region R1, and the target study region R. target R1 and R target The effective study region after removing R0;

[0010] S2. Molecular dynamics simulations of the reference trajectory were performed under low concentration conditions (methane molar fraction ≤ 0.1%) in the methane aqueous solution phase, continuously tracking R1 and R2. target The dissociation process of R1 was recorded, and the characteristic time of complete dissociation of R1 was recorded respectively. and R target Characteristic time of complete dissociation ;

[0011] The total simulation time for the reference trajectory molecular dynamics simulation is around 500 ns, which is considered a medium-cost simulation.

[0012] S3. Perform trajectory molecular dynamics simulations under high concentration conditions of methane molar fraction ≥0.3% in the methane aqueous solution phase, simulating only until R1 complete dissociation, and record the characteristic time of complete R1 dissociation. ;

[0013] The total simulation time for the trajectory molecular dynamics simulation exceeds 1000 ns, which is considered an extremely computationally expensive simulation.

[0014] When the estimated trajectory is R target If complete dissociation is unattainable within the acceptable simulation duration, proceed to the scaling extrapolation step;

[0015] S4. Based on the time self-similarity assumption of the hydrate dissociation process, the relative time proportion of each spatial layer in the total dissociation process does not change with the liquid phase methane concentration. The following scaling relationship is established:

[0016] ;

[0017] Based on this, R was calculated under high methane concentration conditions. target Total dissociation time R, as the target research area under high methane concentration conditions target The dissociation time prediction results.

[0018] Furthermore, in the constructed "hydrate-aqueous solution" interface model, due to the high initial interface energy, the hydrate layer near the interface exhibits rapid transient collapse in the early stages of the simulation. Through trajectory observation or cross-sectional analysis of the cage structure quantity / order parameter along the normal direction, it was confirmed that this unstable collapse layer is confined to a half-cell scale. The unstable boundary layer R0 is defined as the hydrate layer within the range of 0-0.6 nm from the initial solid-liquid interface, and is not included in the kinetic statistics; R1 and R... target To determine the effective study region after eliminating the unstable boundary layer R0, R1 is located within the range of 0.6-1.2 nm from the initial solid-liquid interface. target Located within 0.6-1.8 nm from the initial solid-liquid interface. This ensures that statistical data originates from stable and comparable structural evolution processes.

[0019] Eliminating unstable boundary layers can avoid the interference of transient collapse on dissociation time statistics, so that the dissociation dynamics of different concentrations and trajectories have a consistent starting point and comparability.

[0020] Furthermore, the initial solid-liquid interface location is determined using any of the following methods:

[0021] a. Locations where abrupt changes occur in the water density, methane density, or local order parameter profile along the interface normal;

[0022] b. Identify the transitional positions of the hydrate cage structure distribution from high to low using the crystal nucleus identification algorithm;

[0023] c. Interface plane obtained by fitting the geometric boundaries of the hydrate lattice layer in the initial configuration.

[0024] Since hydrate dissociation is characterized by stages and non-uniformity, the determination of complete dissociation is based on "structural milestones" rather than extrapolation of a single linear trend, in order to improve the characterization ability of the later slow stages.

[0025] Furthermore, R1 is completely dissociated from R target Complete dissociation is determined using at least one of the following structural criteria:

[0026] a. The number of intact hydrate cage structures in the region has been reduced to zero;

[0027] b. The tetrahedral order parameter of water molecules in the region decreases to the liquid threshold F4 = -0.04;

[0028] c. The characteristic peaks of the hydrate lattice in the region disappear, or the density / potential energy in the region reaches and stabilizes at the liquid plateau;

[0029] d. Determine complete disintegration by assessing molecular connectivity or cage network connectivity within the region.

[0030] Furthermore, the time self-similarity assumption is constrained by the consistency of the sequence of cage structure rupture events during hydrate dissociation, which includes at least: destruction of intact cages at the lattice interface, increase in the proportion of partially opened cages, disintegration of cage network connectivity, and complete liquefaction of regions; and this consistency ensures that the relative time proportions remain unchanged under different methane concentrations.

[0031] Under different methane aqueous solution phase concentrations, the structural evolution of hydrate dissociation follows a consistent cage rupture event sequence, namely, from the destruction of the ordered interface dominated by intact cages, to an accelerated stage with an increase in partially opened cages, until the disintegration of cage network connectivity and complete liquefaction of regions; therefore, although the absolute duration of each stage in the methane aqueous solution phase changes, the relative time proportion of each stage in the total dissociation process remains unchanged, thus making the scaling relationship hold.

[0032] Furthermore, the time self-similarity assumption for the hydrate dissociation process in both reference trajectory molecular dynamics simulations and estimated trajectory molecular dynamics simulations must satisfy the following conditions:

[0033] a. Both use the same initial geometry, temperature, and pressure conditions, differing only in the concentration of liquid methane.

[0034] b. The initial dissociation state and the final dissociation state of both are consistent, and the final dissociation state includes at least R. target Complete dissociation;

[0035] c. The concentration of the methane aqueous solution selected for the reference trajectory molecular dynamics simulation must ensure that R... target Complete the dissociation within a tolerable computation time to obtain a complete [process / structure]. .

[0036] Furthermore, the molecular dynamics simulations in S2 and S3 employ an isothermal and isobaric ensemble, where temperature and pressure are stabilized using temperature and pressure control algorithms. The time steps are on the order of femtoseconds, and periodic boundary conditions are used. The simulation duration covers at least R0 in the reference trajectory molecular dynamics simulation. target Complete dissociation is required, and at least R1 complete dissociation must be covered in trajectory molecular dynamics simulations.

[0037] Furthermore, it also includes repeatability statistics of the molecular dynamics simulation process of the reference trajectory: performing multiple independent molecular dynamics simulations of the reference trajectory under the same temperature, pressure, and concentration conditions, and statistically analyzing each simulation. The mean and dispersion, and from this, we obtain The result.

[0038] Compared with existing technologies, the method for extrapolating hydrate dissociation time under high methane concentration conditions described in this invention has the following advantages:

[0039] (1) Breaking through the timescale limitations of molecular dynamics, this invention enables efficient prediction of long-term dissociation times at high methane concentrations. Based on the principle of time self-similarity, this invention combines the "calculable local dissociation process" (R1) with the "non-calculable target dissociation process" (R2). target By establishing a scaling relationship, R can be calculated simply by explicitly simulating until R1 is completely dissociated under high methane concentration conditions. target The complete dissociation time avoids the need for full-process molecular dynamics simulations on microsecond or even longer timescales under high concentration or near-equilibrium conditions, significantly reducing computational costs and improving feasibility.

[0040] (2) Avoiding the bias of traditional fitting extrapolation while retaining the phased non-uniform dynamic characteristics of the dissociation process. Existing methods often rely on low-concentration, short-time molecular dynamics simulation data for linear or simple nonlinear fitting extrapolation, which is difficult to reflect the phased changes in the hydrate dissociation process, especially when approaching the equilibrium concentration, which is prone to systematic underestimation. This invention uses the consistency of structural evolution milestones for scaling, without relying on a preset function form, which can effectively capture the nonlinear growth and order-of-magnitude transitions of dissociation time in the high-concentration range, improving the credibility and physical rationality of the extrapolation results.

[0041] (3) Eliminate unsteady-state interference from transient interface collapse to improve the stability and repeatability of kinetic statistics. This invention identifies and excludes the rapid transient collapse layer (unstable boundary layer) near the initial solid-liquid interface caused by high interfacial energy, and uniformly defines the target study area as a stable hydrate layer within a certain range from the interface, thereby avoiding the miscalculation of unsteady initial events into the dissociation time and improving the comparability, repeatability and statistical reliability of kinetic data under different trajectories and concentrations.

[0042] (4) The method and process are standardized and the parameters are highly portable, making it suitable for evaluating the dissociation kinetics of hydrates under multiple conditions and in multiple systems. This invention achieves dissociation time extrapolation through the process of "reference trajectory - estimated trajectory - scaling - statistical verification". The required inputs are clear and the implementation path is clear, making it easy to be compatible and extended with different temperature, pressure, concentration conditions and different types of hydrate systems (different guest gases or gas mixtures). At the same time, it supports the statistical analysis and cross-validation of multiple independent trajectories, which helps to form a dissociation time database that can be applied in engineering.

[0043] (5) Enhance engineering prediction capabilities at the application level to support hydrate risk assessment and development safety decisions. This invention can be extended to high methane concentration or near-equilibrium regions within the current computing resource capacity, obtaining long-term dissociation timescales that are difficult to cover by traditional molecular dynamics simulations. It provides key kinetic basis for natural gas hydrate development safety assessment, subsea pipeline and wellbore hydrate blockage risk prediction, and gas-containing hydrate phase change process control and parameter adjustment, and has significant engineering value and promotion significance. Attached Figure Description

[0044] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings:

[0045] Figure 1 This is a schematic diagram illustrating the process principle of the method of the present invention;

[0046] Figure 2 This is the initial model when the methane molar fraction is 0.1%;

[0047] Figure 3 For reference, the hydrate decomposition trajectory at a low methane concentration (0.1%), which can be obtained entirely through MD calculations, is shown. (a) represents the decomposition time in region R0, (b) represents the decomposition time in region R1, and (c) represents the decomposition time in region R2. target Domain decomposition time;

[0048] Figure 4 The hydrate decomposition trajectory at a high methane concentration (0.3%) is used for estimation, and only R1 can be obtained through MD calculation. (a) is the decomposition time of region R0, and (b) is the decomposition time of region R1. Detailed Implementation

[0049] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0050] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0051] Example 1

[0052] Using the trajectory of low methane concentration under hydrate depressurization extraction conditions at 285K and 45bar as a reference trajectory, the study area R is solved under high methane concentration conditions. target The dissociation time. Using the method of this invention, the kinetics of hydrate decomposition were simulated using the GROMACS software package. Figure 1 A schematic diagram illustrating the process principle of the method of this invention is provided.

[0053] The method for extrapolating the hydrate dissociation time under high methane concentration conditions includes the following steps:

[0054] S1. Establish the initial system architecture, comprising a methane hydrate phase of 3.5×3×3 sI (Structure I = Type I cage hydrate) single cell, an aqueous methane solution phase with methane molar fractions of 0.1% and 0.3%, and 3119 water molecules. Water molecules are described by the TIP4P / ICE force field, methane by the OLAS-UA force field, using the NPT ensemble, with constant temperature and pressure of 285 K and 45 bar; the system considers periodic boundary conditions.

[0055] Determine the initial solid-liquid interface location:

[0056] The transitional positions of the hydrate cage structure distribution from high to low were identified using a crystal nucleus identification algorithm; the identified interface model is as follows: Figure 2 As shown, the left side represents the methane hydrate phase, and the right side represents the methane aqueous solution phase.

[0057] Based on the initial solid-liquid interface, spatial layers are divided along the normal direction. The unstable boundary layer R0 is defined as the hydrate layer within the range of 0-0.6 nm from the initial solid-liquid interface, and is not included in the kinetic statistics; R1 and R target To determine the effective study region after eliminating the unstable boundary layer R0, R1 is located within the range of 0.6-1.2 nm from the initial solid-liquid interface. target It is located within the range of 0.6-1.8 nm from the initial solid-liquid interface.

[0058] S2. After the unstable boundary layer R0 at a distance of 0-0.6 nm from the initial solid-liquid interface rapidly decomposes, the simulated trajectory is tracked.

[0059] Molecular dynamics simulations of the reference trajectory were performed under low concentration conditions of 0.1% methane in an aqueous phase. The simulation duration was 500 ns, and R1 and R2 were continuously tracked. target The dissociation process of R1 was recorded, and the characteristic time of complete dissociation of R1 was recorded respectively. and R target Characteristic time of complete dissociation ;

[0060] R1 completely dissociates and R target The criterion for determining complete dissociation is:

[0061] The tetrahedral order parameter of water molecules in the region drops to the liquid threshold F4 = -0.04.

[0062] To ensure the reliability of the results, multiple independent molecular dynamics simulations of reference trajectories were performed under the same temperature, pressure, and concentration conditions, and the results were statistically analyzed. The mean and dispersion.

[0063] And based on this, the average value is obtained. 34.6 ns, dispersion = 3.4 ns;

[0064] average value 264ns, dispersion = 18.6ns.

[0065] Figure 3 The trajectory of hydrate decomposition at a low methane concentration (0.1%) is shown. Figure 3 (a) Figure 3 (b) Figure 3 (c) corresponds to the decomposition time of region R0, region R1, and region R, respectively. target The state at the moment of domain decomposition.

[0066] S3. Perform trajectory molecular dynamics simulations under high concentration conditions of 0.3% methane in an aqueous methane solution. The simulation duration is 3000 ns, simulating only until R1 completes dissociation, and recording the characteristic time of complete R1 dissociation. =2600ns;

[0067] R1 completely dissociates and R target The criterion for determining complete dissociation is:

[0068] The tetrahedral order parameter of water molecules in the region drops to the liquid threshold F4 = -0.04.

[0069] Figure 4 The trajectory of hydrate decomposition under high methane concentration (0.3%) is shown. Figure 4 (a) Figure 4 (b) corresponds to the states at the decomposition times of region R0 and region R1, respectively.

[0070] S4. Based on the time self-similarity assumption of the hydrate dissociation process, the relative time proportion of each spatial layer in the total dissociation process does not change with the liquid phase methane concentration. The following scaling relationship is established:

[0071] ;

[0072] Based on this, R was calculated under high methane concentration conditions. target Total dissociation time ≈19838.15 ns, representing the target study region R under high methane concentration conditions. target The dissociation time prediction results.

[0073] Example 2

[0074] To verify the feasibility of this method, at a concentration point where the entire process can be run directly, such as a low concentration of 0.1% in the methane aqueous solution phase, the estimated results of this method are compared with the dissociation time observed by the corresponding direct molecular simulation. When the deviation between the two is within the preset range, it is confirmed that the scaling relationship is applicable to the corresponding concentration range, thereby supporting extrapolation to higher concentrations or near-equilibrium conditions.

[0075] Example 1 yielded the characteristic times for reference trajectory molecular dynamics simulations using a 0.1% methane aqueous solution phase: 34.6ns, 264 ns; then, a molecular dynamics simulation of the estimated trajectory was performed on a 0.1% methane aqueous solution phase, yielding... 35.3ns.

[0076] According to the formula ;

[0077] =269.34ns.

[0078] This shows that the actual molecular simulation time (264 ns) and the estimated time (269.34 ns) are in good agreement, indicating that the estimation method is accurate and reasonable.

[0079] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for extrapolating the dissociation time of hydrates under high methane concentration conditions, characterized in that, The method includes the following steps: S1. Construct an initial molecular dynamics model containing both a methane hydrate phase and a methane aqueous solution phase, setting the external temperature, pressure, and concentration of the methane aqueous solution phase, and determining the initial solid-liquid interface position; based on the initial solid-liquid interface, divide the space into layers along the normal direction, including at least an unstable boundary layer R0, a reference region R1, and the target study region R. target R1 and R target The effective study region after removing R0; S2. Molecular dynamics simulations of the reference trajectory were performed under low concentration conditions (methane molar fraction ≤ 0.1%) in the methane aqueous solution phase, continuously tracking R1 and R2. target The dissociation process of R1 was recorded, and the characteristic time of complete dissociation of R1 was recorded respectively. and R target Characteristic time of complete dissociation ; S3. Perform trajectory molecular dynamics simulations under high concentration conditions of methane molar fraction ≥0.3% in the methane aqueous solution phase, simulating only until R1 complete dissociation, and record the characteristic time of complete R1 dissociation. ; S4. Based on the time self-similarity assumption of the hydrate dissociation process, the relative time proportion of each spatial layer in the total dissociation process does not change with the liquid phase methane concentration. The following scaling relationship is established: ； Based on this, R was calculated under high methane concentration conditions. target Total dissociation time R, as the target research area under high methane concentration conditions target The dissociation time prediction results.

2. The method for extrapolating the hydrate dissociation time under high methane concentration conditions according to claim 1, characterized in that, The unstable boundary layer R0 is a hydrate layer in the range of 0-0.6 nm from the initial solid-liquid interface, and R1 and R target To determine the effective study region after eliminating the unstable boundary layer R0, R1 is located within the range of 0.6-1.2 nm from the initial solid-liquid interface. target It is located within the range of 0.6-1.8 nm from the initial solid-liquid interface.

3. The method for extrapolating the dissociation time of hydrates under high methane concentration conditions according to claim 1, characterized in that, The initial solid-liquid interface location can be determined using any of the following methods: a. Locations where abrupt changes occur in the water density, methane density, or local order parameter profile along the interface normal; b. Identify the transitional positions of the hydrate cage structure distribution from high to low using the crystal nucleus identification algorithm; c. Interface plane obtained by fitting the geometric boundaries of the hydrate lattice layer in the initial configuration.

4. The method for extrapolating the hydrate dissociation time under high methane concentration conditions according to claim 1, characterized in that, R1 completely dissociates and R target Complete dissociation is determined using at least one of the following structural criteria: a. The number of intact hydrate cage structures in the region has been reduced to zero; b. The tetrahedral order parameter of water molecules in the region decreases to the liquid threshold F4 = -0.04; c. The characteristic peaks of the hydrate lattice in the region disappear, or the density / potential energy in the region reaches and stabilizes at the liquid plateau; d. Determine complete disintegration by assessing molecular connectivity or cage network connectivity within the region.

5. The method for extrapolating the dissociation time of hydrates under high methane concentration conditions according to claim 1, characterized in that, The time self-similarity assumption is constrained by the consistency of the sequence of cage structure rupture events during hydrate dissociation, which includes at least: complete cage destruction at the lattice interface, an increase in the proportion of partially open cages, disintegration of cage network connectivity, and complete liquefaction of regions; and this consistency ensures that the relative time proportions remain unchanged under different methane concentrations.

6. The method for extrapolating the hydrate dissociation time under high methane concentration conditions according to claim 5, characterized in that, The time self-similarity assumption for hydrate dissociation processes in both reference trajectory molecular dynamics simulations and estimated trajectory molecular dynamics simulations must satisfy the following conditions: a. Both use the same initial geometry, temperature, and pressure conditions, differing only in the concentration of liquid methane. b. The initial dissociation state and the final dissociation state of both are consistent, and the final dissociation state includes at least R. target Complete dissociation; c. The concentration of the methane aqueous solution selected for the reference trajectory molecular dynamics simulation must ensure that R... target Complete the dissociation within a tolerable computation time to obtain a complete [process / structure]. .

7. The method for extrapolating the dissociation time of hydrates under high methane concentration conditions according to claim 1, characterized in that, The molecular dynamics simulations in S2 and S3 employ an isothermal and isobaric ensemble, with temperature and pressure maintained stable through temperature and pressure control algorithms. The time steps are on the order of femtoseconds, and periodic boundary conditions are used. The simulation duration covers at least R0 in the reference trajectory molecular dynamics simulation. target Complete dissociation is required, and at least R1 complete dissociation must be covered in trajectory molecular dynamics simulations.

8. The method for extrapolating the dissociation time of hydrates under high methane concentration conditions according to claim 1, characterized in that, This also includes repeatability statistics of the molecular dynamics simulation process of the reference trajectory: performing multiple independent molecular dynamics simulations of the reference trajectory under the same temperature, pressure, and concentration conditions, and statistically analyzing each simulation. The mean and dispersion, and from this, we obtain The result.

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