六塔变压吸附制氧工艺的模拟与分析

doi:10.11949/0438-1157.20230978

摘要/Abstract

摘要：

采用13X分子筛作为吸附剂，设计了一种六塔变压吸附制氧工艺，可用于中型医用制氧机。通过静态容积法测定了氮氧气体在13X分子筛上的吸附等温线，建立了六塔变压吸附工艺的数学模型，包括吸附床模型和辅助设备的数学模型。利用Aspen Adsorption软件对工艺进行了数值模拟，分析了塔内的压力、温度和吸附相浓度分布。模拟结果表明，在吸附压力6 bar（1 bar=0.1 MPa）、步骤时长8 s、产品流量6 m³·h^-1的条件下，O₂产品纯度达93.83%，回收率46.85%，生产能力3.42×10^-2 m³·h^-1·kg^-1。相较于已有的两塔和四塔工艺，该工艺的回收率有所提高。探究了步骤时长、吸附压力和产品流量对氧气浓度、回收率和生产能力的影响。在4.5~7.5 m³·h^-1的产品流量范围内，该工艺均可以制得90%以上纯度的氧气，可应用于氧气纯度需求不同的场景。

关键词: 变压吸附, 数值模拟, 制氧, 13X分子筛, 吸附剂, 吸附

Abstract:

A six-bed PSA oxygen production process was designed by using 13X zeolite as adsorbent, which can be used in medium-sized medical oxygen concentrators. The adsorption isotherms of nitrogen and oxygen on 13X zeolite were measured by the static volumetric method. A mathematical model of the pressure swing adsorption process was developed, including the mathematical model of adsorption bed and auxiliary equipment. The process was simulated by using Aspen Adsorption software, and the pressure, temperature and solids concentration distribution within the column were analyzed. The simulations demonstrated that the purity of oxygen is as high as 93% with a recovery rate of 46.85%, and the production capacity is 3.42×10^-2 m³·h^-1·kg^-1 under 6 bar (1 bar=0.1 MPa), 8 s step duration and 6 m³·h^-1 product flow rate. Compared with the existing two-bed and four-bed processes, the recovery of this process has been improved. The effects of step duration, adsorption pressure, and product flow rate on oxygen concentration, recovery, and productivity were investigated. Moreover, as the product flow range expands to 4.5 m³·h^-1to 7.5 m³·h^-1, this process can produce oxygen with a purity of more than 90% and can be applied to scenarios with different oxygen purity requirements.

Key words: pressure swing adsorption, numerical simulation, oxygen production, 13X zeolite, adsorbents, adsorption

中图分类号:

TQ 028.1

孔德齐, 张莹莹, 武文玲, 马军, 宋振兴, 张东辉, 张彦军. 六塔变压吸附制氧工艺的模拟与分析[J]. 化工学报, 2023, 74(12): 4934-4944.

Deqi KONG, Yingying ZHANG, Wenling WU, Jun MA, Zhenxing SONG, Donghui ZHANG, Yanjun ZHANG. Simulation and analysis of oxygen production process by six-bed pressure swing adsorption process[J]. CIESC Journal, 2023, 74(12): 4934-4944.

图/表 17

图1 六塔PSA工艺结构图

Fig.1 Configuration diagram of six-bed PSA process

图2 PSA循环工艺示意图

Fig.2 Schematic diagram of PSA process

表1 六塔PSA工艺时序

Table 1 The schedule of six-bed PSA

步骤	塔1	塔2	塔3	塔4	塔5	塔6
1	AD1	ER1	ER3	BD	ED3	ED1
2	AD2	PR	ER2	PUR	CoD	ED2
3	ED1	AD1	ER1	ER3	BD	ED3
4	ED2	AD2	PR	ER2	PUR	CoD
5	ED3	ED1	AD1	ER1	ER3	BD
6	CoD	ED2	AD2	PR	ER2	PUR
7	BD	ED3	ED1	AD1	ER1	ER3
8	PUR	CoD	ED2	AD2	PR	ER2
9	ER3	BD	ED3	ED1	AD1	ER1
10	ER2	PUR	CoD	ED2	AD2	PR
11	ER1	ER3	BD	ED3	ED1	AD1
12	PR	ER2	PUR	CoD	ED2	AD2

表2 PSA工艺数学模型

Table 2 The mathematical models of PSA process

数学模型	数学方程	序号
质量守恒方程	$- ε_{b} D_{a x, i} \frac{\partial^{2} c_{i}}{\partial z^{2}} + \frac{\partial (v_{g} c_{i})}{\partial z} + [ε_{b} + (1 - ε_{b}) ε_{p}] \frac{\partial c_{i}}{\partial t} + ρ_{s} (1 - ε_{b}) \frac{\partial q_{i}}{\partial t} = 0$	(1)
质量守恒方程	$D_{a x, i} = 0.73 D_{m, i} + \frac{v_{g} r_{p}}{ε_{b} (1 + 9.49 \frac{ε_{b} D_{m, i}}{2 v_{g} r_{p}})}$	(2)
能量守恒方程	$- k_{g} \frac{\partial^{2} T_{g}}{\partial z^{2}} + c_{v g} ν_{g} ρ_{g} \frac{\partial T_{g}}{\partial z} + ε_{b} c_{v g} ρ_{g} \frac{\partial T_{g}}{\partial t} + P \frac{\partial v_{g}}{\partial z} + h_{f} (T_{g} - T_{s}) + \frac{4 h_{w}}{D_{b}} (T_{g} - T_{w}) = 0$	(3)
	$\begin{matrix} - k_{s} \frac{\partial^{2} T_{s}}{\partial z^{2}} + c_{p s} ρ_{s} \frac{\partial T_{s}}{\partial t} + ρ_{s} \sum_{i = 1}^{n} (c_{p g, i} q_{i}) \frac{\partial T_{s}}{\partial t} + ρ_{s} \sum_{i = 1}^{n} Δ H_{i} \frac{\partial q_{i}}{\partial t} - h_{f} (T_{g} - T_{s}) = 0 \end{matrix}$	(4)
	$- k_{w} \frac{\partial^{2} T_{w}}{\partial z^{2}} + c_{p w} ρ_{w} \frac{\partial T_{w}}{\partial z} - h_{w} \frac{4 D_{b}}{{(D_{b} + W_{t})}^{2} - D_{b}^{2}} (T_{g} - T_{w}) + h_{a m b} \frac{4 {(D_{b} + W_{t})}^{2}}{{(D_{b} + W_{t})}^{2} - D_{b}^{2}} (T_{w} - T_{a m b}) = 0$	(5)
动量守恒方程（Ergun方程）	$- \frac{\partial P}{\partial z} = \frac{150 μ (1 - ε_{b})^{2}}{ε_{b}^{3} (2 r_{p} {ψ)}^{2}} v_{g} + 1.75 \frac{(1 - ε_{b})}{2 r_{p} ψ ε_{b}^{3}} \| v_{g} \| v_{g}$	(6)
吸附等温线方程	$q_{i}^{*} = \frac{I P_{1, i} e^{^{I P_{2, i} / T}} p_{i}}{1 + \sum_{i = 1}^{n} I P_{3, i} e^{^{I P_{4, i} / T}} p_{i}}$	(7)
LDF方程	$\frac{\partial q_{i}}{\partial t} = k_{L D F, i} (q_{i}^{*} - q_{i})$	(8)
压缩机模型	$\begin{matrix} d W = \frac{p_{c i n}}{η_{p}} \times \frac{γ}{γ - 1} [{(\frac{p_{c o u t}}{p_{c i n}})}^{\frac{γ - 1}{γ}} - 1] \\ W_{c y c l e} = \int_{0}^{t_{c y c l e}} d W \end{matrix}$	(9)
缓冲罐模型	$\begin{matrix} \frac{\partial T (\sum_{i = 1}^{n} n_{i} c_{ρ g, i})}{\partial t} = \sum_{b i n = 1}^{n} F_{b i n} T_{b i n} \sum_{i = 1}^{n} y_{i} c_{p g, i} - \sum_{b o u t = 1}^{n} F_{b o u t} T_{b o u t} \sum_{i = 1}^{n} y_{i} c_{p g, i} \\ \frac{\partial n_{i}}{\partial t} = \sum_{b i n = 1}^{n} F_{b i n} y_{i} - \sum_{b o u t = 1}^{n} F_{b o u t} y_{i} \end{matrix}$	(10)
线性阀门模型	$F = C_{V} (p_{v i n} - p_{v o u t})$	(11)

表2 PSA工艺数学模型

Table 2 The mathematical models of PSA process

数学模型	数学方程	序号
质量守恒方程	$- ε_{b} D_{a x, i} \frac{\partial^{2} c_{i}}{\partial z^{2}} + \frac{\partial (v_{g} c_{i})}{\partial z} + [ε_{b} + (1 - ε_{b}) ε_{p}] \frac{\partial c_{i}}{\partial t} + ρ_{s} (1 - ε_{b}) \frac{\partial q_{i}}{\partial t} = 0$	(1)
质量守恒方程	$D_{a x, i} = 0.73 D_{m, i} + \frac{v_{g} r_{p}}{ε_{b} (1 + 9.49 \frac{ε_{b} D_{m, i}}{2 v_{g} r_{p}})}$	(2)
能量守恒方程	$- k_{g} \frac{\partial^{2} T_{g}}{\partial z^{2}} + c_{v g} ν_{g} ρ_{g} \frac{\partial T_{g}}{\partial z} + ε_{b} c_{v g} ρ_{g} \frac{\partial T_{g}}{\partial t} + P \frac{\partial v_{g}}{\partial z} + h_{f} (T_{g} - T_{s}) + \frac{4 h_{w}}{D_{b}} (T_{g} - T_{w}) = 0$	(3)
	$\begin{matrix} - k_{s} \frac{\partial^{2} T_{s}}{\partial z^{2}} + c_{p s} ρ_{s} \frac{\partial T_{s}}{\partial t} + ρ_{s} \sum_{i = 1}^{n} (c_{p g, i} q_{i}) \frac{\partial T_{s}}{\partial t} + ρ_{s} \sum_{i = 1}^{n} Δ H_{i} \frac{\partial q_{i}}{\partial t} - h_{f} (T_{g} - T_{s}) = 0 \end{matrix}$	(4)
	$- k_{w} \frac{\partial^{2} T_{w}}{\partial z^{2}} + c_{p w} ρ_{w} \frac{\partial T_{w}}{\partial z} - h_{w} \frac{4 D_{b}}{{(D_{b} + W_{t})}^{2} - D_{b}^{2}} (T_{g} - T_{w}) + h_{a m b} \frac{4 {(D_{b} + W_{t})}^{2}}{{(D_{b} + W_{t})}^{2} - D_{b}^{2}} (T_{w} - T_{a m b}) = 0$	(5)
动量守恒方程（Ergun方程）	$- \frac{\partial P}{\partial z} = \frac{150 μ (1 - ε_{b})^{2}}{ε_{b}^{3} (2 r_{p} {ψ)}^{2}} v_{g} + 1.75 \frac{(1 - ε_{b})}{2 r_{p} ψ ε_{b}^{3}} \| v_{g} \| v_{g}$	(6)
吸附等温线方程	$q_{i}^{*} = \frac{I P_{1, i} e^{^{I P_{2, i} / T}} p_{i}}{1 + \sum_{i = 1}^{n} I P_{3, i} e^{^{I P_{4, i} / T}} p_{i}}$	(7)
LDF方程	$\frac{\partial q_{i}}{\partial t} = k_{L D F, i} (q_{i}^{*} - q_{i})$	(8)
压缩机模型	$\begin{matrix} d W = \frac{p_{c i n}}{η_{p}} \times \frac{γ}{γ - 1} [{(\frac{p_{c o u t}}{p_{c i n}})}^{\frac{γ - 1}{γ}} - 1] \\ W_{c y c l e} = \int_{0}^{t_{c y c l e}} d W \end{matrix}$	(9)
缓冲罐模型	$\begin{matrix} \frac{\partial T (\sum_{i = 1}^{n} n_{i} c_{ρ g, i})}{\partial t} = \sum_{b i n = 1}^{n} F_{b i n} T_{b i n} \sum_{i = 1}^{n} y_{i} c_{p g, i} - \sum_{b o u t = 1}^{n} F_{b o u t} T_{b o u t} \sum_{i = 1}^{n} y_{i} c_{p g, i} \\ \frac{\partial n_{i}}{\partial t} = \sum_{b i n = 1}^{n} F_{b i n} y_{i} - \sum_{b o u t = 1}^{n} F_{b o u t} y_{i} \end{matrix}$	(10)
线性阀门模型	$F = C_{V} (p_{v i n} - p_{v o u t})$	(11)

图3 静态容积法吸附等温线测定实验装置

Fig.3 Experimental device for adsorption isotherms measurements by static volumetric method

图4 N2、O2在13X分子筛上的吸附等温线

Fig.4 Adsorption isotherms of nitrogen and oxygen on 13X zeolite

表3 扩展型Langmuir 2型方程拟合参数

Table 3 Fitting parameters of extended Langmuir 2 model

参数	N₂	O₂
IP₁/(mol·kg^-1·bar^-1)	7.895×10^-4	1.224×10^-2
IP₂/K	1750	626.5
IP₃/bar^-1	6.220×10^-3	6.737×10^-3
IP₄/K	721.2	174.1
R²	0.9989	0.9982
ΔH/(kJ·mol^-1)	-15.82	-5.03

表4 吸附剂和吸附床参数

Table 4 Parameters of adsorbent and adsorption bed

参数	数值
ρ_b/(kg·m^-3)	626.0
c_p_s/(kJ·kg^-1·K^-1)	0.92
r_p/m	0.00194
ε_b	0.38
ε_p	0.384
k_s/(W·m^-1·K^-1)	0.349
$k_{L D F, N_{2}}$ /s^-1	2.05
$k_{L D F, O_{2}}$ /s^-1	4.98
H_b/m	1.23
W_t/m	0.003
D_b/m	0.213
ρ_w/(kg·m^-3)	7850
c_p_w/(kJ·kg^-1·K^-1)	0.46
h_w/(W·m^-2·K^-1)	60
k_w/(W·m^-1·K^-1)	45.3
T_amb/K	293.15
T_feed/K	293.15

表4 吸附剂和吸附床参数

Table 4 Parameters of adsorbent and adsorption bed

参数	数值
ρ_b/(kg·m^-3)	626.0
c_p_s/(kJ·kg^-1·K^-1)	0.92
r_p/m	0.00194
ε_b	0.38
ε_p	0.384
k_s/(W·m^-1·K^-1)	0.349
$k_{L D F, N_{2}}$ /s^-1	2.05
$k_{L D F, O_{2}}$ /s^-1	4.98
H_b/m	1.23
W_t/m	0.003
D_b/m	0.213
ρ_w/(kg·m^-3)	7850
c_p_w/(kJ·kg^-1·K^-1)	0.46
h_w/(W·m^-2·K^-1)	60
k_w/(W·m^-1·K^-1)	45.3
T_amb/K	293.15
T_feed/K	293.15

表5 工艺性能评价指标

Table 5 Process performance indicator

指标	计算公式	序号
纯度( $P u r i t y_{O_{2}}$ )	$\frac{\int_{0}^{t_{c y c l e}} F_{o u t} y_{o u t, O_{2}} d t}{\int_{0}^{t_{c y c l e}} F_{o u t} d t}$	(12)
回收率( $R e c o v e r y_{O_{2}}$ )	$\frac{\int_{0}^{t_{c y c l e}} F_{o u t} y_{o u t, O_{2}} d t}{\int_{0}^{t_{c y c l e}} F_{i n} y_{i n, O_{2}} d t}$	(13)
生产能力( $P r o d u c t i v i t y_{O_{2}}$ )	$3600 \frac{\int_{0}^{t_{c y c l e}} F_{o u t} y_{o u t, O_{2}} d t}{t_{c y c l e} m_{a d s o r b e n t s}}$	(14)

表5 工艺性能评价指标

Table 5 Process performance indicator

指标	计算公式	序号
纯度( $P u r i t y_{O_{2}}$ )	$\frac{\int_{0}^{t_{c y c l e}} F_{o u t} y_{o u t, O_{2}} d t}{\int_{0}^{t_{c y c l e}} F_{o u t} d t}$	(12)
回收率( $R e c o v e r y_{O_{2}}$ )	$\frac{\int_{0}^{t_{c y c l e}} F_{o u t} y_{o u t, O_{2}} d t}{\int_{0}^{t_{c y c l e}} F_{i n} y_{i n, O_{2}} d t}$	(13)
生产能力( $P r o d u c t i v i t y_{O_{2}}$ )	$3600 \frac{\int_{0}^{t_{c y c l e}} F_{o u t} y_{o u t, O_{2}} d t}{t_{c y c l e} m_{a d s o r b e n t s}}$	(14)

表6 六塔PSA模拟结果

Table 6 The simulation results of six-bed PSA process

模拟工况	吸附压力/bar	步骤时长/s	产品流量/(m³·h^-1)	O₂纯度/%	O₂回收率/%	生产能力/(m³·h^-1·kg^-1)
1	6	7	6	95.38	40.45	3.48×10^-2
2	6	8	6	93.83	46.85	3.42×10^-2
3	6	9	6	91.87	52.00	3.35×10^-2
4	6	10	6	89.17	57.26	3.25×10^-2
5	6	11	6	86.03	60.58	3.14×10^-2
6	6	12	6	82.46	62.95	3.01×10^-2
7	4	8	6	80.53	57.67	2.94×10^-2
8	4.5	8	6	86.24	55.09	3.14×10^-2
9	5	8	6	89.74	53.16	3.27×10^-2
10	5.5	8	6	92.19	50.44	3.36×10^-2
11	6	8	6	93.83	46.85	3.42×10^-2
12	6	8	4.5	96.19	37.31	2.63×10^-2
13	6	8	5	95.27	40.94	2.89×10^-2
14	6	8	5.5	94.73	43.85	3.16×10^-2
15	6	8	6	93.83	46.85	3.42×10^-2
16	6	8	6.5	92.81	49.64	3.66×10^-2
17	6	8	7	91.62	52.21	3.90×10^-2
18	6	8	7.5	90.31	54.53	4.11×10^-2
19	6	8	8	88.85	56.60	4.32×10^-2

表7 本文与已有文献的工艺性能对比

Table 7 Comparison of process performance between this work and existing literatures

流程	吸附剂	纯度/%	回收率/%	产品流量	文献
两塔PSA	LiLSX	92	40	13.57 L·min^-1	[36]
两塔PSA	13X	94	33	40 L·min^-1	[37]
两塔PSA	LiLSX	93.59	40.7	6 m³·h^-1(标准状况)	[38]
两塔PSA	LiX	95.5	36	104 L·min^-1	[39]
六塔PSA	13X	93.83	46.85	6 m³·h^-1	本文

图5 PSA吸附塔压力分布

Fig.5 Pressure distribution of PSA adsorption bed

图6 PSA吸附塔气相温度分布

Fig.6 Gas temperature distribution diagram of PSA adsorption bed

图7 各步骤结束时N2、O2在轴向上的吸附相浓度分布

Fig.7 Axial distribution of N2 and O2 on adsorbed phase at the end of each step

图8 步骤时长对PSA工艺性能的影响

Fig.8 The effect of step time on PSA process performance

图9 吸附压力对PSA工艺性能的影响

Fig.9 The effect of adsorption pressure on PSA process performance

图10 产品流量对PSA工艺性能的影响

Fig.10 The effect of product flowrate on PSA process performance

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