吉布斯系综模拟氮气—水和氧气—水的气液相平衡
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摘要
Monte Carlo 模拟(MC)是化工热力学中的一种现代研究方法。近年来随着
实验成本的增加,采用计算机来模拟实际体系越来越受到工业界和学术界相关领
域研究人员的关注。本论文先对 MC 模拟的起源、原理及发展作了简要讨论,对
现有的用来预测流体相平衡的 MC 模拟方法及涉及的不同系综作了较全面的论
述并对它们的优缺点、适用范围作了比较。结果表明,Gibbs 系综的 MC(GEMC)
方法为化工过程设计和开发中必不可少的流体相平衡的直接模拟提供了方便的
研究手段。本文利用 GEMC 模拟技术,对 Lennard-Jones(LJ)模型流体、用简
单 LJ 位能描述的真实气体 N2、O2、水及气体与水的混合物的平衡性质进行了研
究。主要包括以下几个方面:
对Lennard-Jones流体的汽液平衡性质进行了NVT-GEMC模拟并探讨了模拟
所用的初始条件对结果的影响:初始条件对平衡性质结果的影响在统计不确定误
差范围以内但对体系达到平衡的时间有一定的影响。只要体系中的粒子数足以描
述各相的性质,模拟应该尽量选取较少的粒子数。
对真实气体 N2、O2从接近三相点到临界点附近的汽液相平衡模拟得到了与
实验数据非常吻合的结果。而对用 MSPC/E 模型描述的水的模拟可知,仅当温度
升高到 550K 以上时,模拟结果才显示出与实验数据较大的偏差。
本论文用 NPT-GEMC 模拟了高度非理想性的含有氢键的混合物:N2-H2O 和
O2-H2O 体系。N2-H2O 体系的模拟在固定压力、不同温度下进行而 O2-H2O 体系
的模拟在固定温度、不同压力下进行。模拟中运用了精确描述纯组分汽液平衡性
质的位能模型,对于在混合物中具有重要作用的水采用了 MSPC/E 模型而气体则
用最简单的 LJ 势能模型。气体分子与水分子之间的相互作用使用不带任何可调
二元参数的 Lorentz-Berthelot 组合规则。模拟得到了混合物的结构性质和平衡性
质。通过与已有实验数据的比较发现:模拟得到的气体在液相中的溶解度虽然仅
在数量级上是可靠的但是却有与实验数据一致的趋势;对于 N2-H2O 体系的气相
性质,模拟结果与实验值吻合很好;对于氧气中的水含量,模拟值大于用模型计
算的结果是由于 O2-H2O 体系模拟的温度为 560.93K,已经接近 MSPC/E 水的临
I
摘 要
界温度。所以,只有精确预测相同温度和压力下混合物中各纯组分的汽液平衡性
质,用 GEMC 模拟混合物的平衡性质才可以得到较好的结果,达到定量的标准。
通过分析混合物体系的径向分布函数可知:高压下,温度对于流体结构性质的影
响较明显;而在高温下,压力的作用可以忽略。
Monte Carlo simulation technique is a modern method in chemical
thermodynamics. Recently, with the increase of the cost of experiments, more and
more researchers focus their interests on the technology of computer simulation. On
the brief review of the origin, principle and development of Monte Carlo techniques,
we discussed the advantages and disadvantages, scopes of application of different MC
methods for determination of phase equilibrium and the involved ensemble. Gibbs
ensemble Monte Carlo method based on simultaneous calculations in two regions
representing equilibrium phases is now commonly used for obtaining phase
equilibrium of fluids because of its simplicity and speed. The vapor-liquid equilibrium
of Lennard-Jones model fluid, real gas represented by simple LJ model such as
oxygen and nitrogen and water were investigated by NVT-GEMC; while coexistence
properties of highly non-ideal hydrogen bonding mixtures: nitrogen-water and
oxygen-water were calculated by NPT-GEMC. The main contents of this dissertation
are as follow:
Vapor-liquid phase equilibrium of the Lennard-Jones model fluid was simulated
by NVT-GEMC. Meantime, we discussed the effect of the initial conditions on the
coexistence property. The results showed that the coexistence property itself was not
influenced by these initial conditions. However, in view of the computational time,
less number of molecules but should be enough to represent each phase were much
better.
The method was also applied to the calculation of the coexistence envelope for
non-polar nitrogen and oxygen from the vicinity of the triple point to close to the
critical point. Good overall agreement with experimental data and previously
available literature results was obtained.
From the research for MSPC/E water, the deviation between simulated results
and experimental data increased obviously when temperature was higher than 550K.
NPT-GEMC simulations were used to calculate gas-liquid equilibrium of highly
non-ideal hydrogen bonding mixtures: nitrogen-water and oxygen-water.
Nitrogen-water simulations were performed from 323K to 503K at a fixed pressure;
oxygen-water simulations were performed from 105bar to 173bar at a fixed
temperature. The effective intermolecular potential models that describe accurately
i
ABSTRACT
the pure component (for water: MSPC/E; for nitrogen and oxygen; LJ) phase
equilibrium were applied. The interactions between gas and water were estimated
with the standard Lorentz-Berthelot combining rules without any adjustable binary
parameter. Simulated results were compared to experimental data. Predicted
properties in gas phase of nitrogen-water agreed well with experimental data.
Simulated liquid composition of coexisting phases showed the same trend as the
experimental data. For water content in gas phase for oxygen-water, the simulated
results were larger than the calculated value from a semi-empirical method because the
simulation was done at 560.93K which was in the vicinity of MSPC/E water critical point
602K. It showed that only the vapor-liquid equilibrium of pure components at the same
temperature and pressure was predicted accurately, good results could be got in the simulation
for mixture. Meanwhile, from the radial distribution functions of mixtures, the effect of
temperature on the structure of liquids was obvious while the effect of pressure could
be negligible in the investigated range of state.
GEMC method was a good tool to predict the phase behaviour of fluid and their mixtures
not only in quality but also in quantity.
实验成本的增加,采用计算机来模拟实际体系越来越受到工业界和学术界相关领
域研究人员的关注。本论文先对 MC 模拟的起源、原理及发展作了简要讨论,对
现有的用来预测流体相平衡的 MC 模拟方法及涉及的不同系综作了较全面的论
述并对它们的优缺点、适用范围作了比较。结果表明,Gibbs 系综的 MC(GEMC)
方法为化工过程设计和开发中必不可少的流体相平衡的直接模拟提供了方便的
研究手段。本文利用 GEMC 模拟技术,对 Lennard-Jones(LJ)模型流体、用简
单 LJ 位能描述的真实气体 N2、O2、水及气体与水的混合物的平衡性质进行了研
究。主要包括以下几个方面:
对Lennard-Jones流体的汽液平衡性质进行了NVT-GEMC模拟并探讨了模拟
所用的初始条件对结果的影响:初始条件对平衡性质结果的影响在统计不确定误
差范围以内但对体系达到平衡的时间有一定的影响。只要体系中的粒子数足以描
述各相的性质,模拟应该尽量选取较少的粒子数。
对真实气体 N2、O2从接近三相点到临界点附近的汽液相平衡模拟得到了与
实验数据非常吻合的结果。而对用 MSPC/E 模型描述的水的模拟可知,仅当温度
升高到 550K 以上时,模拟结果才显示出与实验数据较大的偏差。
本论文用 NPT-GEMC 模拟了高度非理想性的含有氢键的混合物:N2-H2O 和
O2-H2O 体系。N2-H2O 体系的模拟在固定压力、不同温度下进行而 O2-H2O 体系
的模拟在固定温度、不同压力下进行。模拟中运用了精确描述纯组分汽液平衡性
质的位能模型,对于在混合物中具有重要作用的水采用了 MSPC/E 模型而气体则
用最简单的 LJ 势能模型。气体分子与水分子之间的相互作用使用不带任何可调
二元参数的 Lorentz-Berthelot 组合规则。模拟得到了混合物的结构性质和平衡性
质。通过与已有实验数据的比较发现:模拟得到的气体在液相中的溶解度虽然仅
在数量级上是可靠的但是却有与实验数据一致的趋势;对于 N2-H2O 体系的气相
性质,模拟结果与实验值吻合很好;对于氧气中的水含量,模拟值大于用模型计
算的结果是由于 O2-H2O 体系模拟的温度为 560.93K,已经接近 MSPC/E 水的临
I
摘 要
界温度。所以,只有精确预测相同温度和压力下混合物中各纯组分的汽液平衡性
质,用 GEMC 模拟混合物的平衡性质才可以得到较好的结果,达到定量的标准。
通过分析混合物体系的径向分布函数可知:高压下,温度对于流体结构性质的影
响较明显;而在高温下,压力的作用可以忽略。
Monte Carlo simulation technique is a modern method in chemical
thermodynamics. Recently, with the increase of the cost of experiments, more and
more researchers focus their interests on the technology of computer simulation. On
the brief review of the origin, principle and development of Monte Carlo techniques,
we discussed the advantages and disadvantages, scopes of application of different MC
methods for determination of phase equilibrium and the involved ensemble. Gibbs
ensemble Monte Carlo method based on simultaneous calculations in two regions
representing equilibrium phases is now commonly used for obtaining phase
equilibrium of fluids because of its simplicity and speed. The vapor-liquid equilibrium
of Lennard-Jones model fluid, real gas represented by simple LJ model such as
oxygen and nitrogen and water were investigated by NVT-GEMC; while coexistence
properties of highly non-ideal hydrogen bonding mixtures: nitrogen-water and
oxygen-water were calculated by NPT-GEMC. The main contents of this dissertation
are as follow:
Vapor-liquid phase equilibrium of the Lennard-Jones model fluid was simulated
by NVT-GEMC. Meantime, we discussed the effect of the initial conditions on the
coexistence property. The results showed that the coexistence property itself was not
influenced by these initial conditions. However, in view of the computational time,
less number of molecules but should be enough to represent each phase were much
better.
The method was also applied to the calculation of the coexistence envelope for
non-polar nitrogen and oxygen from the vicinity of the triple point to close to the
critical point. Good overall agreement with experimental data and previously
available literature results was obtained.
From the research for MSPC/E water, the deviation between simulated results
and experimental data increased obviously when temperature was higher than 550K.
NPT-GEMC simulations were used to calculate gas-liquid equilibrium of highly
non-ideal hydrogen bonding mixtures: nitrogen-water and oxygen-water.
Nitrogen-water simulations were performed from 323K to 503K at a fixed pressure;
oxygen-water simulations were performed from 105bar to 173bar at a fixed
temperature. The effective intermolecular potential models that describe accurately
i
ABSTRACT
the pure component (for water: MSPC/E; for nitrogen and oxygen; LJ) phase
equilibrium were applied. The interactions between gas and water were estimated
with the standard Lorentz-Berthelot combining rules without any adjustable binary
parameter. Simulated results were compared to experimental data. Predicted
properties in gas phase of nitrogen-water agreed well with experimental data.
Simulated liquid composition of coexisting phases showed the same trend as the
experimental data. For water content in gas phase for oxygen-water, the simulated
results were larger than the calculated value from a semi-empirical method because the
simulation was done at 560.93K which was in the vicinity of MSPC/E water critical point
602K. It showed that only the vapor-liquid equilibrium of pure components at the same
temperature and pressure was predicted accurately, good results could be got in the simulation
for mixture. Meanwhile, from the radial distribution functions of mixtures, the effect of
temperature on the structure of liquids was obvious while the effect of pressure could
be negligible in the investigated range of state.
GEMC method was a good tool to predict the phase behaviour of fluid and their mixtures
not only in quality but also in quantity.
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