基于流量校准的吸附测量方法及误差分析

doi:10.11949/0438-1157.20211630

摘要/Abstract

摘要：

多孔吸附材料广泛应用于分离提纯、气体储存和工业催化等领域，吸附等温线的测定对研究吸附性质具有重要意义。针对传统容积法易受管路温度均匀性影响的问题，介绍了一种基于流量校准的吸附测量方法。分析了两种方法的误差传递，并对比了结构参数、物性参数和仪表精度对测量结果的影响。分析结果显示，增大校准球体积和样品室容积可提升传统容积法测量精度，提升样品量、比过剩吸附量、密度和仪表精度，可提升两种方法的测量精度。相比传统容积法，基于流量校准的吸附测量方法误差因子数量更少，可实现更低的测量误差。研究成果对提升容积法吸附测量精度具有指导意义。

关键词: 吸附, 测量, 状态方程, 误差分析, 流量控制器, 不确定度

Abstract:

Porous adsorbents are widely used in separation and purification, gas storage, and industrial catalysis, and the determination of adsorption isotherms is of great significance for studying adsorption properties. Aiming at solving the difficulty that the traditional volumetric method is easily affected by the temperature distribution along the pipeline, the paper introduces an adsorption measurement method based on flow calibration. The error transfer of both methods is analyzed, and the influence of the structure parameters, physical parameters and instrument accuracy on the adsorption measurement is compared. The results show that increasing the calibration ball volume and sample chamber volume can improve the adsorption measurement accuracy of the traditional volumetric method, and increasing the sample volume, excess adsorption amount, skeleton density and instrument accuracy can improve the measurement accuracy of both methods. Compared to the traditional volumetric method, the method based on flow calibration has fewer error factors and can achieve lower measurement errors. The results can help improve the measurement accuracy of the volumetric method.

Key words: adsorption, measurement, equation of state, error analysis, mass flow controller, uncertainty

中图分类号:

O 647.32

刘碧强, 曹海山. 基于流量校准的吸附测量方法及误差分析[J]. 化工学报, 2022, 73(4): 1597-1605.

Biqiang LIU, Haishan CAO. Adsorption measurement method based on flow calibration and its error analysis[J]. CIESC Journal, 2022, 73(4): 1597-1605.

图/表 16

图1 容积法吸附测量装置原理图

Fig.1 The schematic diagram of volumetric adsorption measurement instrument

表1 吸附测量系统的各平衡状态

Table 1 Various equilibrium states of the adsorption measurement system

平衡状态	工质	状态	气体分配系统	校准腔	样品室(包括过渡段)	气体吸附量
1	氦气	气体分配系统充气	$p 1, T 1$	$0, T 1$	$0, T 1$	$0$
2	氦气	连通校准腔	$p 2, T 1$	$p 2, T 1$	$0, T 1$	$0$
3	氦气	校准腔内加入校准球	$p 3, T 1$	$p 3, T 1$	$0, T 1$	$0$
4	氦气	连通加入样品后的样品室	$p 4, T 1$	$0, T 1$	$p 4, T 1$	$0$
5	氦气	调节样品室温度至测量温度 $T t e s t$	$p 5, T 1$	$0, T 1$	$p 5, T e f f$	$0$
6	吸附气体	气体分配系统充气	$p 6, T 1$	$0, T 1$	$0, T 1$	$0$
7	吸附气体	连通加入样品的样品室，调节样品室温度至测量温度 $T t e s t$	$p 7, T 1$	$0, T 1$	$p 8, T e f f$	$n a d s$

表1 吸附测量系统的各平衡状态

Table 1 Various equilibrium states of the adsorption measurement system

平衡状态	工质	状态	气体分配系统	校准腔	样品室(包括过渡段)	气体吸附量
1	氦气	气体分配系统充气	$p 1, T 1$	$0, T 1$	$0, T 1$	$0$
2	氦气	连通校准腔	$p 2, T 1$	$p 2, T 1$	$0, T 1$	$0$
3	氦气	校准腔内加入校准球	$p 3, T 1$	$p 3, T 1$	$0, T 1$	$0$
4	氦气	连通加入样品后的样品室	$p 4, T 1$	$0, T 1$	$p 4, T 1$	$0$
5	氦气	调节样品室温度至测量温度 $T t e s t$	$p 5, T 1$	$0, T 1$	$p 5, T e f f$	$0$
6	吸附气体	气体分配系统充气	$p 6, T 1$	$0, T 1$	$0, T 1$	$0$
7	吸附气体	连通加入样品的样品室，调节样品室温度至测量温度 $T t e s t$	$p 7, T 1$	$0, T 1$	$p 8, T e f f$	$n a d s$

图2 基于流量校准的吸附测量流程图

Fig.2 Flowchart of the adsorption measurement based on flow calibration

图3 各因素影响(a) 容积法;(b) 基于流量校准的吸附测量

Fig.3 Influence of various factors in volumetric adsorption measurement (a) and adsorption measurement based on flow calibration (b)

表2 两种方法测量不确定度表达式参数

Table 2 Parameters of measurement uncertainty expression in both methods

$A$	容积法		基于流量校准的容积法
$A$	$B i$	$l$	$B i$	$l$
$Z$ ^①	$p, T$
$V M$	$p 1$ , $p 2, p 3, Z 1, Z 2, Z 3, T 1, V c a l$	8	$p 1, p 4, Z 1, Z 4, T 1, m V M, ? H e$	6
$V S$	$p 1, p 4, Z 1, Z 4, V M$	5	$p 4, Z 4, T 1, m S, H e$	4
$T e f f$	$p 1, p 5, Z 1, Z 5, Z e f f, T 1, V M, V S$	8	$p 5, Z e f f, m T, H e, V S$	4
$x a d s$	$p 6, p 7, p 8, Z 6, Z 7, Z e f f, a d s, T 1, V M, V S$ , $T e f f$	10	$p 8, Z e f f, a d s, m a d s$ , $V S$ , $T e f f$	5

表2 两种方法测量不确定度表达式参数

Table 2 Parameters of measurement uncertainty expression in both methods

$A$	容积法		基于流量校准的容积法
$A$	$B i$	$l$	$B i$	$l$
$Z$ ^①	$p, T$
$V M$	$p 1$ , $p 2, p 3, Z 1, Z 2, Z 3, T 1, V c a l$	8	$p 1, p 4, Z 1, Z 4, T 1, m V M, ? H e$	6
$V S$	$p 1, p 4, Z 1, Z 4, V M$	5	$p 4, Z 4, T 1, m S, H e$	4
$T e f f$	$p 1, p 5, Z 1, Z 5, Z e f f, T 1, V M, V S$	8	$p 5, Z e f f, m T, H e, V S$	4
$x a d s$	$p 6, p 7, p 8, Z 6, Z 7, Z e f f, a d s, T 1, V M, V S$ , $T e f f$	10	$p 8, Z e f f, a d s, m a d s$ , $V S$ , $T e f f$	5

表3 基本参数设定

Table 3 Basic parameter set

参数	数值
恒温箱温度/K	$313.15$
校准腔容积/m³	$5.25 × 10 - 6$
气体分配管路系统容积/m³	$1.05 × 10 - 5$
压力测量误差限	±0.05%×量程
质量流量测量误差限	±0.2%×读数

表3 基本参数设定

Table 3 Basic parameter set

参数	数值
恒温箱温度/K	$313.15$
校准腔容积/m³	$5.25 × 10 - 6$
气体分配管路系统容积/m³	$1.05 × 10 - 5$
压力测量误差限	±0.05%×量程
质量流量测量误差限	±0.2%×读数

图4 气体分配系统容积相对不确定度与校准球体积的关系

Fig.4 Relationship between relative uncertainty of manifold volume and calibration ball volume

图5 气体分配系统容积相对不确定度极小值与校准球体积的关系

Fig.5 Relationship between minimum relative uncertainty of manifold volume and calibration ball volume

图6 气体分配系统容积相对不确定度与校准腔容积的关系

Fig.6 Relationship between relative uncertainty of manifold volume and calibration chamber volume

图7 气体分配系统容积相对不确定度极小值与校准腔容积的关系

Fig.7 Relationship between minimum relative uncertainty of manifold volume and calibration chamber volume

图8 样品室容积相对不确定度与样品室容积的关系

Fig.8 Relationship between relative uncertainty of sample chamber volume and sample chamber volume

图9 样品室容积相对不确定度极小值与样品室容积的关系

Fig.9 Relationship between minimum relative uncertainty of sample chamber volume and its value

图10 比过剩吸附量相对不确定度与样品骨架体积占比的关系

Fig.10 Relationship between relative uncertainty of excess adsorption amount and sample skeleton volume

图11 比过剩吸附量相对不确定度和比过剩吸附量(a)、样品密度(b)的关系

Fig.11 Relationship between relative uncertainty of excess adsorption amount and excess adsorption amount (a), sample density (b)

图12 比过剩吸附量相对不确定度与压力测量精度(a)、温度测量精度(b)的关系

Fig.12 Relationship between relative uncertainty of excess adsorption amount and pressure measurement accuracy (a), temperature measurement accuracy (b)

图13 比过剩吸附量相对不确定度与质量流量测量精度的关系

Fig.13 Relationship between relative uncertainty of excess adsorption amount and mass flow measurement accuracy

参考文献 23

1	Zhou D D, Chen P, Wang C . et al. Intermediate-sized molecular sieving of styrene from larger and smaller analogues[J]. Nature Materials, 2019, 18: 994-998.
2	Finsy V, Ma L, Alaerts L, et al. Separation of CO₂/CH₄ mixtures with the MIL-53(Al) metal–organic framework[J]. Microporous Mesoporous Materials, 2009, 120: 221-227.
3	Li H, Li L B, Lin R B, et al. Porous metal-organic frameworks for gas storage and separation: status and challenges[J]. EnergyChem, 2019, 1(1): 10006.
4	Dinca M, Long J R, Hydrogen storage in microporous metal-organic frameworks with exposed metal sites[J]. Angewandte Chemie International Edition, 2008, 47: 6766-6779.
5	Rowsell J L C, Millward A R, Park K S, et al. Hydrogen sorption in functionalized metal-organic frameworks[J]. Journal of the American Chemical Society, 2004, 126: 5666–5667.
6	Vo T S, Hossain M M, Jeong H M, et al. Heavy metal removal applications using adsorptive membranes[J]. Nano Convergence, 2020, 7: 36.
7	Piumetti Marco. A brief history of the science of catalysis (Ⅰ): From the early concepts to single-site heterogeneous catalysts[J]. Chimica Oggi, 2014, 32(6): 22-27.
8	赵振国. 吸附作用应用原理[M]. 北京: 化学工业出版社, 2005: 11.
	Zhao Z G. Principle of Application of Adsorption[M]. Beijing: Chemical Industry Press, 2005: 11.
9	Tzabar N, Nitrogen Grossman G., methane, and ethane sorption on activated carbon[J]. Cryogenics, 2011, 51: 499-508.
10	Tzabar N, ter Brake H J M. Adsorption isotherms and Sips models of nitrogen, methane, ethane, and propane on commercial activated carbons and polyvinylidene chloride[J]. Adsorption, 2016, 22: 901-914.
11	Brandani S, Mangano E, Net Sarkisov L., excess and absolute adsorption and adsorption of helium[J]. Adsorption, 2016, 22: 261-276.
12	Liu J H, Cao H S, Shi Y X, et al. Enhanced methane delivery in MIL-101(Cr) by means of subambient cooling[J]. Energy & Fuels, 2021, 35: 6898-6908.
13	张辉, 刘应书, 李永玲, 等. 基于容量法的高压静态吸附仪的研制与应用[J]. 低温与特气, 2010, 28(5): 20-23.
	Zhang H, Liu Y S, Li Y L, et al. Manufacture and application of the volumetric adsorption analyzer at high pressure[J]. Low Temperature and Specialty Gases, 2010, 28(5): 20-23.
14	周尚文, 薛华庆, 郭伟, 等. 基于重量法的页岩气超临界吸附特征实验研究[J]. 煤炭学报, 2016, 41(11): 2806-2812.
	Zhou S W, Xue H Q, Guo W, et al.Supercritical isothermal adsorption characteristics of shale gas based on gravimetric method[J].Journal of China Coal Society, 2016, 41(11): 2806-2812.
15	俞凌杰, 范明, 陈红宇, 等. 富有机质页岩高温高压重量法等温吸附实验[J]. 石油学报, 2015, 36(5): 557-563.
	Yu L J, Fan M, Chen H Y, et al. Isothermal adsorption experiment of organic-rich shale under high temperature and pressure using gravimetric method[J]. Acta Petrolei Sinica, 2015, 36(5): 557-563.
16	汤进华, 梁晓怿, 龙东辉, 等. 活性炭孔结构和表面官能团对吸附甲醛性能影响[J]. 炭素技术, 2007(3): 21-25.
	Tang J H, Liang X Y, Long D H, et al. Effects of micropore and functional groups of activated carbon on adsorption behavior of formaldehyde[J]. Carbon Techniques, 2007(3): 21-25.
17	Gregg S J, Sing K S W. Adsorption, Surface Area and Porosity[M]. London: Academic Press, 1982.
18	中华人民共和国国家质量监督检验检疫总局, 中国国家标准化管理委员会. 气体吸附BET法测定固态物质比表面积: [S]. 北京: 中国标准出版社, 2017.
	General Administration of Quality Supervision, Inspection and Quarantine of the People's Republic of China. Determination of the specific surface area of solids by gas adsorption using the BET method: [S]. Beijing: Standards Press of China, 2017.
19	近藤精一, 石川达雄, 安部郁夫. 吸附科学[M]. 2版. 李国希, 译. 北京: 化学工业出版社, 2006: 185.
	Kondo S, Ishikawa T, Abe I. Adsorption Science[M]. 2nd ed. Li G X, trans. Beijing: Chemical Industry Press, 2006: 185.
20	赵会民, 林丹, 杨刚, 等. 有机胺修饰具有较大孔径介孔材料的二氧化碳吸附性能[J]. 物理化学学报, 2012, 28(4): 985-992.
	Zhao H M, Lin D, Yang G, et al. Adsorption capacity of carbon dioxide on amine modified mesoporous materials with larger pore sizes[J]. Acta Phys. -Chim. Sin., 2012, 28(4): 985-992.
21	汤涛, 张淑华. 用IR-电子天平重量吸附法快速测定催化剂表面酸度[J]. 分析试验室, 2004(6): 57-59.
	Tang T, Zhang S H. Determination of surface acidity on catalysts by IR-electronic balance with mass adsorption[J]. Chinese Journal of Analysis Laboratory, 2004(6): 57-59.
22	周尚文, 王红岩, 薛华庆, 等. 页岩过剩吸附量与绝对吸附量的差异及页岩气储量计算新方法[J]. 天然气工业, 2016, 36(11): 12-20.
	Zhou S W, Wang H Y, Xue H Q, et al. Difference between excess and absolute adsorption capacity of shale and a new shale gas reserve calculation method[J]. Natural Gas Industry, 2016, 36(11): 12-20.
23	Belmabkhout Y, Frere M, Weireld G D. High-pressure adsorption measurements: a comparative study of the volumetric and gravimetric methods[J]. Measurement Science and Technology, 2004, 15: 848-858.

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