Research progress in measurement methods in vapor-liquid critical properties of mixtures

doi:10.11949/0438-1157.20230075

Abstract

Abstract:

Near-critical and supercritical fluids have excellent transport and thermodynamic properties and can be widely used in fields such as chemical engineering, environment, machinery, and thermal energy utilization. Since the thermophysical properties including fluid density will change substantially near the critical point, it is of great significance to accurately determine the critical point of the fluid, including critical temperature, critical pressure and critical density data, to guide the optimization of thermodynamic cycle and system component design. Currently, experimental measurement is the most direct way to obtain high-precision critical parameters. This article first outlines the theory of gas-liquid critical points, the current research status of critical parameters, and their typical application scenarios. Secondly, it summarizes the main measurement methods of critical parameters, including constant volume method, variable volume method, flow method, pulse heating method, density line midpoint law method, pressure-volume-temperature (p-V-T) relationship method, quasi-static thermal analysis method, and physical property method. The advantages and disadvantages, scope of application, accuracy and main research institutions of these methods are summarized. Finally, the challenges and future development trends of critical parameter measurement methods are discussed.

Key words: critical parameters, thermodynamic properties, vapor-liquid equilibria, mixtures, supercritical fluid

摘要：

近、超临界流体具备优良的输运和热力学性质，可广泛应用于化工、环境、机械和热能利用等领域。由于临界点附近包括流体密度在内的热物性会发生大幅改变，因此准确确定流体的临界点，包括临界温度、临界压力和临界密度数据，对指导热力循环和系统部件设计优化有重要意义。目前实验测量是获取高精度临界参数的最直接方式。本文首先概述了气液临界点理论、临界参数的研究现状及其典型应用场景；其次，综述了目前临界参数主要的测量方法，包括定容法、变容法、流动法、脉冲加热法、密度直线中径定律法、压力-体积-温度（p-V-T）关系法、准静态热分析法和物理性质法等，总结了这些方法的优缺点、适用范围、准确性和主要研究机构；最后，探讨了临界参数测量方法当前面临的挑战和未来发展趋势。

关键词: 临界参数, 热力学性质, 汽液平衡, 混合物, 超临界流体

CLC Number:

TK 123

Xiaoyu YAO, Jun SHEN, Jian LI, Zhenxing LI, Huifang KANG, Bo TANG, Xueqiang DONG, Maoqiong GONG. Research progress in measurement methods in vapor-liquid critical properties of mixtures[J]. CIESC Journal, 2023, 74(5): 1847-1861.

姚晓宇, 沈俊, 李健, 李振兴, 康慧芳, 唐博, 董学强, 公茂琼. 流体气液临界参数测量方法研究进展[J]. 化工学报, 2023, 74(5): 1847-1861.

Figures/Tables 15

Fig.1 Schematic diagram of the constant-volume method apparatus[57-58]

Fig.2 Schematic diagram of the variable-volume method apparatus (Burrnet expansion method)[59]A—optical cell; B—variable-volume vessel; C—differential null-pressure detector; D—aluminum blocks; E—constant-temperature oil bath; F—impeller; G—temperature controller; H—platinum resistance thermometer; I—cold trap; J—quartz crystal pressure gauge; V1—cutoff valve; V2—separation valve

Fig.3 Schematic diagram of the variable-volume apparatus (metal-bellows method)[60-61]A—metal-bellows in pressure vessel; B—optical cell; C—thermostatic oil bath; D—platinum resistance thermometer; E1—heater (1.2 kW); E2—heater (0.3 kW); F—stirrer

Fig.4 Schematic diagram of the variable-volume apparatus (metal-bellows method) from the Technical Institute of Physics and Chemistry, Chinese Academy of Sciences[62]1—silicone oil bath; 2—metal-bellow volumeter; 3—platinum resistance thermometers; 4—refrigerator; 5—trirrer; 6—motor; 7—vacuum pump; 8—electronic balance; 9—gas cylinder; 10—pressure transducers; 11—pressure and temperature indicator; 12—bridge; 13—stabilized voltage supply; 14—equilibrium cell; 15—view windows; 16—electrical heater

Fig.5 Schematic diagram of the variable-volume method apparatus (piston method) from Tianjin University[65]1—screw-driven pump; 2—pressure meter; 3—hall probe; 4—heat jacket; 5—autoclave; 6—position; 7—O-ring; 8—stirrer; 9—quartz window; 10—sampling valves; 11—pressure sensor; 12—thermocouple; 13—small steel vessel; 14—thermometer; 15—vacuum meter; 16—steel bulb

Fig.6 Schematic diagram of the variable-volume method apparatus (piston method) from University of Science and Technology of China[65]1—sample cylinder A; 2—sample cylinder B; 3-6—valves; 7—vacuum pump; 8—optical cell; 9—pressure transducer; 10—platinum resistance thermometer; 11—stirrer; 12—heater; 13—data acquisition instrument; 14—temperature controller; 15—computer; 16—gas chromatograph

Fig.7 Schematic diagram of the flow method apparatus[67]PS—pressurized source; VPr—volumetric press; SP—syringe pump; VP—vacuum pump; HE—heat exchanger; VC—view cell; AT—air thermostat bath (oven); TP—platinum resistance temperature probe; PT—pressure transducer; TR—temperature regulator; FV—flow regulation valve; DAS—data acquisition system; CPU—central processor unit; V—valve

Fig.8 Schematic diagram of the pulse-heating method apparatus[68]1—thermocouple; 2—ceramic thermal insulator; 3—furnace; 4—measuring probe; 5—liquid under study; 6—body; 7—flange; 8—confining liquid

Fig.9 Schematic diagram of the law of rectilinear diameter method[69]

Fig.10 A schematic diagram of the deviation between the critical density measured by rectilinear diameter law and the true critical density of fluid[72]

Fig.11 The near-critical region isotherms of argon[76]

Fig.12 Schematic diagram of the quasi-static thermograms method[39]1—piezometer; 2—air thermostat; 3—differential membrane separator; 4—valve; 5,8—platinum resistance thermometer; 6—digital micro-ohmmeter; 7—digital high precision temperature controller; 9—regulating heater; 10—fan; 11,12—platinum sensitive element; 13—multichannel analog-to-digital converter; 14-16—differential thermocouples; 17—digital voltmeter; 18—dead-weight pressure gauge; 19—capillary; 20—micro amperemeter

Fig.13 Schematic diagram of the acoustic method apparatus[79]A—amplifier; C—acoustic cell; HP—hand pump; HPB—high-pressure bomb; O—oscilloscope; P—pressure transducer; PG—pulse generator; R—acoustic receiver; S—acoustic sender; T—thermocouple

Table 1 Summary of measurement methods for critical p-ρ-T-x parameters

测量方法	测量范围	测量精度	优点	缺点
定容法	热稳定物质	较高	简单、可靠	主观性判定临界点，实验效率低
变容法	热稳定物质	较高	实验效率高	主观性判定临界点，系统复杂度高，需精密测量或计算体积
流动法	热不稳定物质	较高	能测量热不稳定物质	主观性判定临界点，不能测量临界密度，需确保流体均匀混合和流动
脉冲加热法	热不稳定物质	较低	能测量易受热分解物质	主观性判定临界点，不能测量临界密度，需确保流体均匀混合和流动，系统复杂度高
密度直线中径定律法	热稳定物质	较低	简单，能以气相和液相饱和密度数据拟合临界参数	近临界区数据受主观性观测影响大，拟合精度低，密度中径是否符合直线规律存在争议
压力-体积-温度（p-V-T）关系法	热稳定物质	较低	拟合精度高	需要拟合数据较多，效率低
准静态热分析法	热稳定物质	较高	判断临界点准确客观，能同时测量近临界区比定容热容	实验效率低
物理性质法	热不稳定物质	较低	判断临界点客观	发展不成熟，测量精度低

Table 2 Active research institutions of critical p-ρ-T-x parameters measurement in recent 30 years and their measurement principles

测量方法	研究机构	国家	标准不确定度
定容法	奥尔登堡大学 ^[57-58]	德国	10 kPa （p_c）、0.1 K （T_c）、2% （ρ_c）、 0.0005 （x）
定容法	卡尔斯鲁厄大学 ^[84]	德国	6 kPa （p_c）、 0.06 K （T_c）、 2% （ρ_c）、 0.003 （x）
定容法	华东理工大学 ^[85]	中国	30 kPa （p_c）、 0.3 K （T_c）、 N/A （ρ_c）、 0.003 （x）
定容法	清华大学 ^[45]	中国	0.5 kPa （p_c）、 0.01 K （T_c）、 0.7% （ρ_c）、 N/A （x）
定容法	马来亚大学 ^[86]	马来西亚	50 kPa （p_c）、 0.2 K （T_c）、 N/A （ρ_c）、 0.015 （x）
定容法/直线法	达吉斯坦州立大学/俄罗斯科学院高温联合研究所^[87]	俄罗斯	0.05% （p_c）、 0.015 K （T_c）、 0.15% （ρ_c）、 N/A （x）
定容法/直线法	西安现代化学研究所 ^[88]	中国	24 kPa （p_c）、 0.21 K （T_c）、 6.4 kg/m³ （ρ_c）、 0.0009 （x）
定容法/流体p-V-T关系法	俄罗斯科学院油气研究所 ^[89]	俄罗斯	70 kPa （p_c）、 2 K （T_c）、 N/A （ρ_c）、 0.015 （x） 1.8 kPa （p）、 0.05 K （T）、 0.0003 cm³/g （V）、 0.25 （x）
变容法/流体p-V-T关系法	九州大学 ^[59,41]	日本	0.5 kPa （p_c）、 0.01 K （T_c）、 0.15% （ρ_c）、 0.005 （x）
变容法	庆应义塾大学 ^[61,60]	日本	1.6 kPa （p_c）、 0.016 K （T_c）、 0.18% （ρ_c）、 0.009 （x）
变容法	中国科学技术大学 ^[66]	中国	3.1 kPa （p_c）、 0.01 K （T_c）、 0.0015 （x）
变容法	丽水国立大学 ^[90]	韩国	30 kPa （p_c）、 0.1 K （T_c）、 0.001 （x）
变容法	天津大学 ^[65]	中国	100 kPa （p_c）、 0.1 K （T_c）、 N/A （ρ_c）、 N/A （x）
变容法	中国科学院理化技术研究所^[62]	中国	10.5 kPa （p_c）、 0.025 K （T_c）、 0.3% （ρ_c）、 0.005 （x）
流动法	洛林大学 ^[67]	法国	8 kPa （p_c）、 0.05 K （T_c）、 0.000015 （x）
流动法	西安交通大学 ^[46]	中国	5.2 kPa （p_c）、 0.2 K （T_c）、 0.006 （x）
流动法/流体p-V-T关系法	萨拉格萨大学 ^[91]	西班牙	34 kPa （p_c）、 0.32 K （T_c）、 0.1% （ρ_c）、 0.005 （x）
脉冲加热法	俄罗斯科学院乌拉尔分院 ^[68]	俄罗斯	80 kPa （p_c）、 0.1 K （T_c）、 N/A （x）
准静态热分析法	达吉斯坦州立大学/俄罗斯科学院高温联合研究所 ^[39]	俄罗斯	0.025% （p_c）、 0.075 K （T_c）、 0.25% （ρ_c）、 0.00005 （x）
声学法	诺丁汉大学 ^[78-79]	英国	10 kPa （p_c）、 0.1 K （T_c）、 N/A （ρ_c）、 N/A （x）

Table 2 Active research institutions of critical p-ρ-T-x parameters measurement in recent 30 years and their measurement principles

测量方法	研究机构	国家	标准不确定度
定容法	奥尔登堡大学 ^[57-58]	德国	10 kPa （p_c）、0.1 K （T_c）、2% （ρ_c）、 0.0005 （x）
定容法	卡尔斯鲁厄大学 ^[84]	德国	6 kPa （p_c）、 0.06 K （T_c）、 2% （ρ_c）、 0.003 （x）
定容法	华东理工大学 ^[85]	中国	30 kPa （p_c）、 0.3 K （T_c）、 N/A （ρ_c）、 0.003 （x）
定容法	清华大学 ^[45]	中国	0.5 kPa （p_c）、 0.01 K （T_c）、 0.7% （ρ_c）、 N/A （x）
定容法	马来亚大学 ^[86]	马来西亚	50 kPa （p_c）、 0.2 K （T_c）、 N/A （ρ_c）、 0.015 （x）
定容法/直线法	达吉斯坦州立大学/俄罗斯科学院高温联合研究所^[87]	俄罗斯	0.05% （p_c）、 0.015 K （T_c）、 0.15% （ρ_c）、 N/A （x）
定容法/直线法	西安现代化学研究所 ^[88]	中国	24 kPa （p_c）、 0.21 K （T_c）、 6.4 kg/m³ （ρ_c）、 0.0009 （x）
定容法/流体p-V-T关系法	俄罗斯科学院油气研究所 ^[89]	俄罗斯	70 kPa （p_c）、 2 K （T_c）、 N/A （ρ_c）、 0.015 （x） 1.8 kPa （p）、 0.05 K （T）、 0.0003 cm³/g （V）、 0.25 （x）
变容法/流体p-V-T关系法	九州大学 ^[59,41]	日本	0.5 kPa （p_c）、 0.01 K （T_c）、 0.15% （ρ_c）、 0.005 （x）
变容法	庆应义塾大学 ^[61,60]	日本	1.6 kPa （p_c）、 0.016 K （T_c）、 0.18% （ρ_c）、 0.009 （x）
变容法	中国科学技术大学 ^[66]	中国	3.1 kPa （p_c）、 0.01 K （T_c）、 0.0015 （x）
变容法	丽水国立大学 ^[90]	韩国	30 kPa （p_c）、 0.1 K （T_c）、 0.001 （x）
变容法	天津大学 ^[65]	中国	100 kPa （p_c）、 0.1 K （T_c）、 N/A （ρ_c）、 N/A （x）
变容法	中国科学院理化技术研究所^[62]	中国	10.5 kPa （p_c）、 0.025 K （T_c）、 0.3% （ρ_c）、 0.005 （x）
流动法	洛林大学 ^[67]	法国	8 kPa （p_c）、 0.05 K （T_c）、 0.000015 （x）
流动法	西安交通大学 ^[46]	中国	5.2 kPa （p_c）、 0.2 K （T_c）、 0.006 （x）
流动法/流体p-V-T关系法	萨拉格萨大学 ^[91]	西班牙	34 kPa （p_c）、 0.32 K （T_c）、 0.1% （ρ_c）、 0.005 （x）
脉冲加热法	俄罗斯科学院乌拉尔分院 ^[68]	俄罗斯	80 kPa （p_c）、 0.1 K （T_c）、 N/A （x）
准静态热分析法	达吉斯坦州立大学/俄罗斯科学院高温联合研究所 ^[39]	俄罗斯	0.025% （p_c）、 0.075 K （T_c）、 0.25% （ρ_c）、 0.00005 （x）
声学法	诺丁汉大学 ^[78-79]	英国	10 kPa （p_c）、 0.1 K （T_c）、 N/A （ρ_c）、 N/A （x）

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