Simulation of oxygen production via VPSA optimized based on MPC control strategy

doi:10.11949/0438-1157.20190857

Abstract

Abstract:

A rigorous mathematical model was established in the gPROMS software for vacuum PSA oxygen production. Based on the LiLSX adsorbent, a two-stage, eight-step vacuum PSA process was designed to produce O ₂ with a purity of 92%. Changes in feed flow rate as well as the decrease of the adsorption property were set as disturbances to make the simulation work more close to reality. Meanwhile, time duration was set to change consistently according to the feedback of O ₂ purity in product. The system identification model was then adopted and was used to predict the dynamic behavior of the VPSA process and to develop an MPC controller. Detailed performance under open-loop and closed-loop was listed and compared. The results demonstrated that the model shows an enhanced performance with the presence of random disturbances under closed-loop control. This suggested that the MPC control strategy can be implied to improve the oxygen-production process.

Key words: adsorption, oxygen production, VPSA simulation, optimization, model-predictive control

摘要：

针对真空变压吸附制氧在gPROMS软件中建立了严格的数学模型，基于LiLSX吸附剂设计了两塔八步的真空变压吸附流程生产纯度为92%的O ₂。对此流程进行优化，其纯度和回收率有了明显的改进。在此基础上，引入实际生产中经常存在的如进料流量的变化以及吸附性能降低等扰动因素，使模拟工作更接近实际。根据产品气中O ₂纯度的反馈，采用模型辨识技术设计了MPC控制器，用于预测控制VPSA过程的动态行为。开环和闭环控制结果的对比显示，流程在设计的MPC控制下展现出更好的结果，这表明MPC控制策略可以明显改善空气分离制氧的生产过程。

关键词: 吸附, 制氧, VPSA模拟, 优化, 模型预测控制

CLC Number:

TQ 028.1

Rui XING, Nan JIANG, Bing LIU, Yaxiong AN, Yayan WANG, Donghui ZHANG. Simulation of oxygen production via VPSA optimized based on MPC control strategy[J]. CIESC Journal, 2020, 71(2): 669-679.

邢瑞, 江南, 刘冰, 安亚雄, 汪亚燕, 张东辉. 基于MPC控制技术优化VPSA制氧工艺的模拟[J]. 化工学报, 2020, 71(2): 669-679.

Figures/Tables 16

Table 1 Fitting parameters of extended Langmuir model

Parameter	N ₂	O ₂	Ar
IP ₁/(kmol·kg ^-1·Pa ^-1)	7.107×10 ^-10	6.861×10 ^-9	6.254×10 ^-9
IP ₂/K	2910	1567	1334
IP ₃/Pa ^-1	2.563×10 ^-8	4.625×10 ^-8	4.374×10 ^-8
IP ₄/K	1612	441.3	450.6
Δ H/(kJ·mol ^-1)	-23.43	-13.22	-12.65

Table 2 Mass and heat transfer parameters

Parameter	Value
T_feed/K	298
c _p_g/(kJ·kg ^-1·K ^-1)	1.03
c _p_s/(kJ·kg ^-1·K ^-1)	1.21
R_p/m	8.5×10 ^-4
$D v, N 2$ /(m ²·s ^-1)	1.30×10 ^-4
$D v, O 2$ /(m ²·s ^-1)	1.29×10 ^-4
D, _v, _Ar/(m ²·s ^-1)	1.24×10 ^-4
h/(W·m ^-2·K ^-1)	0.3
k_g/(W·m ^-1·K ^-1)	0.02452
k_s/(W·m ^-1·K ^-1)	0.48

Table 2 Mass and heat transfer parameters

Parameter	Value
T_feed/K	298
c _p_g/(kJ·kg ^-1·K ^-1)	1.03
c _p_s/(kJ·kg ^-1·K ^-1)	1.21
R_p/m	8.5×10 ^-4
$D v, N 2$ /(m ²·s ^-1)	1.30×10 ^-4
$D v, O 2$ /(m ²·s ^-1)	1.29×10 ^-4
D, _v, _Ar/(m ²·s ^-1)	1.24×10 ^-4
h/(W·m ^-2·K ^-1)	0.3
k_g/(W·m ^-1·K ^-1)	0.02452
k_s/(W·m ^-1·K ^-1)	0.48

Fig.1 Simulation of two-bed, eight-step VPSA process

Table 3 Schedule of VPSA process

时间 /s	BED1	BED2
6	AD ₁	VU ₂
3	AD ₂	PUR
3	ED	ER
10	VU ₁	FR
6	VU ₂	AD ₁
3	PUR	AD ₂
3	ER	ED
10	FR	VU ₁

Fig.2 Schematic diagram of cycle sequence

Table 4 Model equations of VPSA process

方程	方程表达式
组分质量方程	$- ε b D a x ? 2 y i ? z 2 + ? (v g c i) ? z + ε b + 1 - ε b ε p ? c i ? t + ρ p 1 - ε b ? q i ? t = 0$ (1)
总质量方程	$? (v g c) ? z + ε b + 1 - ε b ε p ? c ? t + ρ p 1 - ε b ? q ? t = 0$ (2)
能量衡算方程	$ε b + 1 - ε b ε p ∑ i = 1 N c i c p g, i - R + 1 - ε b ρ p c p s + 1 - ε b ρ p ∑ i = 1 N q i c p g, i - R ? T ? t + v g ρ g$ $∑ i = 1 N c p g, i ? T ? z + 1 - ε b ρ p ∑ i = 1 N ? q i ? t H i + 2 h T - T w R b - ε b + 1 - ε b ε p ? P ? t - k g ? 2 T ? z 2 = 0$ (3)
动量方程	$? p ? z = - 150 μ 1 - ε b 2 ε b 3 (2 R p) 2 v g + 1.75 1 - ε b ρ g 2 R p ε b 3 v g v g$ (4)
Langmuir 吸附等温方程	$q i * = I P 1 e I P 2 T P i 1 + ∑ i I P 3, i e I P 4, i T P i$ (5)
线性推动力方程	$? q i ? t = 15 D c, i R p 2 q i * - q i$ (6)
扩散系数	$D a x = 0.73 D m + v g R P ε b 1 + 9.49 ε b D m 2 v g R P; D c, i = ε p τ D k, i D m D k, i + D m D k, i = 48.5 D p T M i; D m = 0.1013 T 1.75 1 M A + 1 M B P (D v, A 1 / 3 + D v, B 1 / 3) 2$ (7)
边界条件	$z = 0 → v g, z ≥ 0, ? T z = T i n, ? y i, z = y i n, i; ? e l s e, ? ? T z ? z = 0, ? ? y i, z ? z = 0 z = H b → v g, z < 0, ? T z = T o u t, ? y i, z = y i n, i; e l s e, ? ? T z ? z = 0, ? ? y i, z ? z = 0$ (8)
阀门方程	$u n i d i r e c t i o n : ? i f ? P i n > P o u t, ? t h e n ? F = c v (P i n - P o u t) 106; e l s e, ? t h e n ? F = 0 b i d i r e c t i o n : ? F = c v (P i n - P o u t) 106$ (9)

Table 4 Model equations of VPSA process

方程	方程表达式
组分质量方程	$- ε b D a x ? 2 y i ? z 2 + ? (v g c i) ? z + ε b + 1 - ε b ε p ? c i ? t + ρ p 1 - ε b ? q i ? t = 0$ (1)
总质量方程	$? (v g c) ? z + ε b + 1 - ε b ε p ? c ? t + ρ p 1 - ε b ? q ? t = 0$ (2)
能量衡算方程	$ε b + 1 - ε b ε p ∑ i = 1 N c i c p g, i - R + 1 - ε b ρ p c p s + 1 - ε b ρ p ∑ i = 1 N q i c p g, i - R ? T ? t + v g ρ g$ $∑ i = 1 N c p g, i ? T ? z + 1 - ε b ρ p ∑ i = 1 N ? q i ? t H i + 2 h T - T w R b - ε b + 1 - ε b ε p ? P ? t - k g ? 2 T ? z 2 = 0$ (3)
动量方程	$? p ? z = - 150 μ 1 - ε b 2 ε b 3 (2 R p) 2 v g + 1.75 1 - ε b ρ g 2 R p ε b 3 v g v g$ (4)
Langmuir 吸附等温方程	$q i * = I P 1 e I P 2 T P i 1 + ∑ i I P 3, i e I P 4, i T P i$ (5)
线性推动力方程	$? q i ? t = 15 D c, i R p 2 q i * - q i$ (6)
扩散系数	$D a x = 0.73 D m + v g R P ε b 1 + 9.49 ε b D m 2 v g R P; D c, i = ε p τ D k, i D m D k, i + D m D k, i = 48.5 D p T M i; D m = 0.1013 T 1.75 1 M A + 1 M B P (D v, A 1 / 3 + D v, B 1 / 3) 2$ (7)
边界条件	$z = 0 → v g, z ≥ 0, ? T z = T i n, ? y i, z = y i n, i; ? e l s e, ? ? T z ? z = 0, ? ? y i, z ? z = 0 z = H b → v g, z < 0, ? T z = T o u t, ? y i, z = y i n, i; e l s e, ? ? T z ? z = 0, ? ? y i, z ? z = 0$ (8)
阀门方程	$u n i d i r e c t i o n : ? i f ? P i n > P o u t, ? t h e n ? F = c v (P i n - P o u t) 106; e l s e, ? t h e n ? F = 0 b i d i r e c t i o n : ? F = c v (P i n - P o u t) 106$ (9)

Table 5 Upper and lower bounds, initial and optimal value of decision variables and optimization objectives

变量	初始值	下限值	上限值	优化值
决策变量
进料流量/(m ³·h ^-1)	3.0	1.0	15.0	4.2
终升压流量/(m ³·h ^-1)	4.8	1.0	15.0	6.0
抽真空流量/(m ³·h ^-1)	7.2	1.0	30.0	18.6
吸附出口阀门开度/(mol·(bar·s) ^-1)	0.2	0.01	100.0	0.97
均压步骤阀门开度/(mol·(bar·s) ^-1)	0.2	0.01	10.0	0.86
冲洗步骤阀门开度/(mol·(bar·s) ^-1)	0.2	0.01	30.0	2.6
优化目标
纯度/%	90.2	92	100	92.03
回收率/%	58.7	60	100	60.5
能耗/(kW·h·m ^-3)	0.42	0.31

Fig.3 Comparison of N 2 axial gas phase distribution before and after optimization

Fig.4 Influence of adsorption time (a) and pressurization time (b) on purity

Fig.5 N 2 gas and solid phase distribution in tower at end of adsorption step and pressurization step

Fig.6 Comparison of state space model and original data

Fig.7 Pressure changes inside tower before and after disturbance

Fig.8 Comparison of product purity change with and without control under Case 1

Fig.9 N 2 and O 2 adsorption isotherms on LiLSX zeolite

Fig.10 Oxygen purity under different adsorption performance conditions

Fig.11 Comparison of purity O 2 in two cases disturbance without control and adding MPC controller after disturbance

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