Model simplification strategy of cracking furnace coking based on adaptive spectroscopy method

doi:10.11949/0438-1157.20230582

Abstract

Abstract:

Furnace tube coking is an important operation of ethylene cracking furnace, and accurate coking model is an important prerequisite for optimizing the control of the scorching process and improving the scorching efficiency. The common scorching process mechanism model is in the form of partial differential equation, which has the characteristics of infinite dimensionality and space-time coupling, and has high computational complexity, which is difficult to meet the requirements of lightweight models for real-time optimization and control. Therefore, a lightweight modeling strategy for the coking process of ethylene cracker based on adaptive spectroscopy method is proposed. Firstly, according to the characteristics of the change of coke layer in the coke and coking process of the furnace tube, the furnace tube is adaptively divided into focal section and non-focal section. Secondly, the Legendre polynomial is used as the spatial basis function to approximate the dimensionality reduction of the distribution parameters of the focal segment and the non-focal section, and the concentrated parameter model of the time dimension coefficients of the coke layer thickness distribution and temperature distribution in the furnace tube control input and the furnace tube is established to avoid the problem of large error caused by directly using the spectral method to approximate the distribution parameter system with local features.

Key words: ethylene cracking furnace coking, distribution parameters, adaptive, spectral method, model simplification

摘要：

炉管烧焦是乙烯裂解炉的重要操作，准确的烧焦模型是优化控制烧焦过程、提高烧焦效率的重要前提。常见的烧焦过程机理模型为偏微分方程的形式，具有无穷维、时空耦合的特点，计算复杂度高，难以满足实时优化和控制对轻量级模型的需求。为此提出一种基于自适应谱方法的乙烯裂解炉烧焦过程轻量级模型化策略。首先，针对炉管生焦与烧焦过程焦层变化特点，将炉管自适应划分为有焦段和无焦段。其次，使用Legendre多项式作为空间基函数分别对有焦段和无焦段分布参数近似降维，建立烧焦过程控制输入与炉管内焦层厚度分布、温度分布的时间维系数的集中参数模型，避免因直接使用谱方法近似拟合带局部特征的分布参数系统而产生较大误差的问题。

关键词: 乙烯裂解炉烧焦, 分布参数, 自适应, 谱方法, 模型简化

CLC Number:

TP 272

Hao WANG, Zhenlei WANG. Model simplification strategy of cracking furnace coking based on adaptive spectroscopy method[J]. CIESC Journal, 2023, 74(9): 3855-3864.

王浩, 王振雷. 基于自适应谱方法的裂解炉烧焦模型化简策略[J]. 化工学报, 2023, 74(9): 3855-3864.

Figures/Tables 13

Table 1 Parameter description

参数	含义	单位	参数	含义	单位
$r_{O_{2}}$	氧反应速率	$k m o l / (m^{2} \cdot s)$	$ρ_{g}$	气体密度	$k g / m^{3}$
$r_{H_{2} O}$	水蒸气反应速率	$k m o l / (m^{2} \cdot s)$	$g$	重力加速度	$m / s^{2}$
$P_{O_{2}}$	氧气分压	MPa	$D$	炉管内径	mm
$R$	摩尔气体常数	J/(mol·K)	$δ$	焦层厚度	mm
$T_{s}$	炉管内壁温度	K	$c_{p g}$	气体比定压热容	$k J / (k g \cdot K)$
$P_{H_{2} O}$	水蒸气分压	MPa	$T_{g}$	气体温度	K
$P_{O_{2}}^{s}$	氧气表面分压	MPa	$h$	对流传热系数	$k J / (m^{2} \cdot s \cdot K)$
$P_{H_{2} O}^{s}$	水蒸气表面分压	MPa	${(k_{g})}_{O_{2}}$	氧的传质系数	$m / s$
$G$	气相质量流量	$k g / (m^{2} \cdot s)$	${(k_{g})}_{H_{2} O}$	水蒸气的传质系数	$m / s$
$M_{m}$	气体的平均分子量	kg/kmol	$P_{t}$	气体总压	MPa
$L_{A}$	几何因数	—	$C_{E}$	综合辐射系数	W/(m²·g·K⁴)
$C_{0}$	黑体辐射系数	W/(m²·g·K⁴)	$v$	介质流动速度	m/s
$ρ_{s}$	焦炭密度	$k g / m^{3}$	$d$	炉管外径	mm

Table 1 Parameter description

参数	含义	单位	参数	含义	单位
$r_{O_{2}}$	氧反应速率	$k m o l / (m^{2} \cdot s)$	$ρ_{g}$	气体密度	$k g / m^{3}$
$r_{H_{2} O}$	水蒸气反应速率	$k m o l / (m^{2} \cdot s)$	$g$	重力加速度	$m / s^{2}$
$P_{O_{2}}$	氧气分压	MPa	$D$	炉管内径	mm
$R$	摩尔气体常数	J/(mol·K)	$δ$	焦层厚度	mm
$T_{s}$	炉管内壁温度	K	$c_{p g}$	气体比定压热容	$k J / (k g \cdot K)$
$P_{H_{2} O}$	水蒸气分压	MPa	$T_{g}$	气体温度	K
$P_{O_{2}}^{s}$	氧气表面分压	MPa	$h$	对流传热系数	$k J / (m^{2} \cdot s \cdot K)$
$P_{H_{2} O}^{s}$	水蒸气表面分压	MPa	${(k_{g})}_{O_{2}}$	氧的传质系数	$m / s$
$G$	气相质量流量	$k g / (m^{2} \cdot s)$	${(k_{g})}_{H_{2} O}$	水蒸气的传质系数	$m / s$
$M_{m}$	气体的平均分子量	kg/kmol	$P_{t}$	气体总压	MPa
$L_{A}$	几何因数	—	$C_{E}$	综合辐射系数	W/(m²·g·K⁴)
$C_{0}$	黑体辐射系数	W/(m²·g·K⁴)	$v$	介质流动速度	m/s
$ρ_{s}$	焦炭密度	$k g / m^{3}$	$d$	炉管外径	mm

Fig.1 Spatiotemporal decomposition of distributed parameter systems

Fig.2 Flow curves of scorched air and water vapor during the scorching process

Fig.3 Temperature sampling outside the furnace tube during the production process

Fig.4 Comparison of the collected data of the scorching process with the output data of model

Fig.5 Change of wall temperature in low-order model

Fig.6 Temperature distribution error in low-order model

Fig.7 The change of coke thickness distribution in low-order model

Fig.8 Thickness distribution error of inlet tube focal layer in low-order model

Fig.9 Focal layer thickness distribution error of spectral method

Table 2 Modeling error of spectral method and adaptive spectral method

方法	温度分布最大误差/K	温度分布最大相对误差/%	焦层厚度分布最大误差/mm	焦层厚度分布最大相对误差/%
谱方法	11.42338	1.05285	0.10773	15.03873
自适应谱方法	1.69512	0.15623	3.41223×10^-3	0.47633

Fig.10 Thickness distribution error of outlet tube focal layer in low-order model

Table 3 Modeling error of adaptive spectral method

项目	最大误差	最大相对误差	入口管有焦段始端最大误差	出口管有焦段始端最大误差
温度分布/K	1.69512	0.15623%	1.69512	0.66372
焦层厚度分布/mm	0.00617	0.12851%	7.00860×10^-3	3.63016×10^-4

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