Hybrid modeling and optimization of acetylene hydrogenation process

doi:10.11949/j.issn.0438-1157.20181082

Abstract

Abstract:

The mathematical model of the acetylene hydrogenation reactor established by traditional single modeling method does not meet the needs of industrial practical applications in predictive performance. This paper proposes a mechanism and neural network nesting modeling method, which fully utilizes the mechanism model. It makes full use of mass and energy balance information in mechanism model to reduce the degree of constraint violation of the neural network model, which can describe the process characteristics of industrial reactor well. The optimization problem which targets the operational profits as the objective function is studied basing on the hybrid model. The main decision variables include several key parameters, such as the reactor feed hydrogen-alkyne ratio, the feed temperature, and the two-stage reactor operating cycle and many more. For the long-term operation of the reactor, processing capacity of the reactor will decrease due to the decreased catalyst activity, and an improved optimizing strategy is proposed by adjusting the hydrogen-alkyne ratio as well as the reaction temperature simultaneously. The sequence method is used to discretize the operating cycle of the reactor. The two-stage difference algorithm is improved by introducing differential mutation strategy and potential solution alternative strategy. Then the optimization problem is solved by combining the incremental coding method with the improved two-stage difference algorithm. And the results confirm the effectiveness. Furthermore the optimal operating cycle and operating strategy of the reactor are given.

Key words: acetylene hydrogenation, dynamic model, control, algorithm, optimization

摘要：

针对传统单一建模方法所构建的乙炔加氢反应器数学模型存在预测性能无法满足工业实际应用需求的问题，提出了一种机理与神经网络嵌套的建模方法，充分利用机理模型包含的能质约束信息降低神经网络模型的约束违反度，得到了能够良好描述实际工业乙炔加氢反应过程特性的混合模型。基于反应器混合模型，研究了以运行效益为目标函数的优化问题。主要决策变量包括：一段反应器进料中氢气与乙炔的摩尔比（R _H/A）、进料温度和反应器运行周期等几个关键参数。针对反应器长期运行后，催化剂活性降低造成的处理能力下降的问题，提出了反应温度补偿机制和R _H/A并行调节的运行优化策略，并采用序列法对反应器运行周期进行离散化处理。通过引入差异化变异策略、潜在解替代策略对两阶段差分算法进行改进，采用增量式编码法结合改进两阶段差分算法，对优化问题进行求解。结果证实了优化策略与改进算法的有效性，并据此确定了反应器最佳运行方案。

关键词: 乙炔加氢, 动力学模型, 控制, 算法, 优化

CLC Number:

TP 18

Zhencheng YE, Huanlan ZHOU, Debao RAO. Hybrid modeling and optimization of acetylene hydrogenation process[J]. CIESC Journal, 2019, 70(2): 496-507.

叶贞成, 周换兰, 饶德宝. 乙炔加氢反应过程混合建模与优化[J]. 化工学报, 2019, 70(2): 496-507.

Figures/Tables 15

Fig.1 Schematic diagram of hydrid model structure

Fig.2 Schematic diagram of ANN structure

Table 1 Prediction error of different models/%

Parameters	Hybrid model	Mechanism model
acetylene	1.706	7.040
ethylene	0.025	1.119
temperature	0.429	0.985

Table 2 Factors and levels of orthogonal test

Level	Factor
Level	NP	β	NS	δ	R
1	70	0.1	4	0.8	0.1
2	80	0.2	5	0.85	0.2
3	90	0.3	6	0.9	0.3
4	100	0.4	7	0.95	0.4

Table 3 Analysis table of standard deviation

Problem	NP	β	NS	δ	R
C07	0.150	0.095	0.095	0.095	0.095
C08	3.553	1.474	3.010	1.635	3.354
C13	0.252	0.134	0.140	0.035	0.071
C15	3.688	3.588	3.588	3.688	3.588
C17	0.094	0.133	0.168	0.113	0.062
C18	0.307	0.446	0.240	0.409	0.252

Table 4 Time complexity analysis table

Dim	Algorithm	T ₁	T ₂	(T ₂-T ₁)/T ₁
10	TSDE	0.01240	0.18911	14.25080
10	RTSDE	0.01269	0.22084	16.40268
30	TSDE	0.02741	0.21881	6.98285
30	RTSDE	0.02786	0.24745	7.88191

Table 5 Comparison of best values

Pro	TSDE		εDEag		CO-CLPSO
Pro	10	30	10	30	10	30
C01	+	+	~	~	~	+
C02	+	+	~	+	~	~
C07	~	+	~	+	+	+
C08	~	+	~	+	+	+
C13	+	+	~	+	~	+
C14	~	+	~	+	+	+
C15	+	+	-	~	-	-
C16	+	+	+	~	~	~
C17	+	+	+	+	+	+
C18	+	+	+	+	+	+

Table 6 Comparison of mean values

Pro	TSDE		εDEag		ICTLBO		CO-CLPSO
Pro	10	30	10	30	10	30	10	30
C01	+	+	-	~	+	+	+	+
C02	+	+	+	+	+	+	+	+
C07	~	~	+	+	+	+	+	+
C08	+	-	+	-	+	+	+	+
C13	+	+	~	+	+	+	+	+
C14	+	~	+	+	+	+	+	+
C15	+	-	+	~	+	~	+	+
C16	+	+	-	~	+	+	~	+
C17	+	+	+	+	+	+	+	+
C18	+	+	+	+	+	+	+	+

Fig.3 Comparison of convergence for test functions

Fig.4 Iterative curves of algorithms

Table 7 Comparison of algorithms results

R₁ cycle	R₂ cycle	DE	TSDE	RTSDE
300	100	1.038×10⁵	1.104×10⁵	1.146×10⁵
	120	1.035×10⁵	1.107×10⁵	1.145×10⁵
	140	9.911×10⁴	1.062×10⁵	1.105×10⁵
320	100	1.014×10⁵	1.114×10⁵	1.149×10⁵
	120	1.103×10⁵	1.081×10⁵	1.132×10⁵
	140	9.646×10⁴	1.103×10⁵	1.105×10⁵
340	100	9.783×10⁴	1.108×10⁵	1.134×10⁵
	120	9.460×10⁴	1.075×10⁵	1.115×10⁵
	140	9.272×10⁴	1.045×10⁵	1.098×10⁵

Fig.5 Curve of first reactor catalyst’s selectivity

Fig.6 Curve of first reactor outlet temperature

Fig.7 Curve of total flow rate increment of ethylene

a_i ,a_j	——反应i、j的失活系数
C_i	——i组分的工厂实测浓度值
C_i ^sim	——模型对i组分的模拟浓度值
C_pi	——气体的比定压热容，kJ·kg^-1·K^-1
E	——相对误差
E _a	——失活活化能，kJ·kmol^-1
E_i	——反应i的活化能，kJ·kmol^-1
F_i	——气体i的摩尔流率，kmol·h^-1
g(·)	——约束条件
ΔH_j	——反应j焓变，kJ·kmol^-1
$Δ I C 2 H 4$	——两段反应器总乙烯流率增量，kmol·h^-1
K_i	——气体i的吸附常数，kPa^-1
k_a	——失活指前因子，kmol·kg^-1·h^-1·kPa^-3
k ₀ _,i	——反应i的指前因子，kmol·kg^-1·h^-1·kPa^-3
$M C 2 H 4$	——乙烯的质量通量，kg·kmol^-1
n_i	——反应i的失活级数
$P C 2 H 4$ ,P _reg	——分别表示乙烯的价格和催化剂再生费用
p_i	——气体i的分压，kPa
R	——理想气体常数，kJ·kmol^-1·K^-1
r_i ,r_j	——反应i、j的速率，kmol·kg^-1·h^-1
S	——反应器横截面积，m²
T	——反应温度，K
T ₁	——CEC2010测试函数求解10000次所需的平均计算时间，s
T ₂	——算法对CEC2010测试函数求解10000次所需的总平均计算时间，s
ΔT _max	——工厂实际温度的最大温升，K
t _first,t _second	——分别表示一段、二段反应器总运行时间，d
t ₁,t ₂	——分别表示一段、二段反应器当前运行时间，d
z	——反应器长度，m
ρ	——催化剂填充密度，kg·m^-3
下角标
in,out	——分别表示反应器进、出口
R₁,R₂	——分别代表一、二段反应器

a_i ,a_j	——反应i、j的失活系数
C_i	——i组分的工厂实测浓度值
C_i ^sim	——模型对i组分的模拟浓度值
C_pi	——气体的比定压热容，kJ·kg^-1·K^-1
E	——相对误差
E _a	——失活活化能，kJ·kmol^-1
E_i	——反应i的活化能，kJ·kmol^-1
F_i	——气体i的摩尔流率，kmol·h^-1
g(·)	——约束条件
ΔH_j	——反应j焓变，kJ·kmol^-1
$Δ I C 2 H 4$	——两段反应器总乙烯流率增量，kmol·h^-1
K_i	——气体i的吸附常数，kPa^-1
k_a	——失活指前因子，kmol·kg^-1·h^-1·kPa^-3
k ₀ _,i	——反应i的指前因子，kmol·kg^-1·h^-1·kPa^-3
$M C 2 H 4$	——乙烯的质量通量，kg·kmol^-1
n_i	——反应i的失活级数
$P C 2 H 4$ ,P _reg	——分别表示乙烯的价格和催化剂再生费用
p_i	——气体i的分压，kPa
R	——理想气体常数，kJ·kmol^-1·K^-1
r_i ,r_j	——反应i、j的速率，kmol·kg^-1·h^-1
S	——反应器横截面积，m²
T	——反应温度，K
T ₁	——CEC2010测试函数求解10000次所需的平均计算时间，s
T ₂	——算法对CEC2010测试函数求解10000次所需的总平均计算时间，s
ΔT _max	——工厂实际温度的最大温升，K
t _first,t _second	——分别表示一段、二段反应器总运行时间，d
t ₁,t ₂	——分别表示一段、二段反应器当前运行时间，d
z	——反应器长度，m
ρ	——催化剂填充密度，kg·m^-3
下角标
in,out	——分别表示反应器进、出口
R₁,R₂	——分别代表一、二段反应器

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