Adsorption measurement method based on flow calibration and its error analysis

doi:10.11949/0438-1157.20211630

Abstract

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

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

CLC Number:

O 647.32

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

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.

Figures/Tables 16

Fig.1 The schematic diagram of volumetric adsorption measurement instrument

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 $T t e s t$	$p 7, T 1$	$0, T 1$	$p 8, T e f f$	$n a d s$

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 $T t e s t$	$p 7, T 1$	$0, T 1$	$p 8, T e f f$	$n a d s$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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