使用无迹卡尔曼滤波估计缩合反应中催化剂活性

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"本文探讨了在苯酚(A)缩合反应中使用无迹卡尔曼滤波器(unscented Kalman filter, UKF)估计催化剂活性的方法。" 文章详细阐述了一种用于在线估计催化活性的新方法，特别是在苯酚A(BPA)生产过程中，随着阳离子交换树脂使用时间的增长，其催化活性会逐渐降低。为了实现在线估计，作者研究了一个催化失活模型，该模型基于反应器轴向温度分布和反应器入口处的丙酮浓度提出了状态方程和观测方程。首先，为了提高估计精度，文章构建了一个混合状态方程。这种混合模型结合了不同物理或化学过程的特性，旨在更准确地模拟催化活性的变化。接着，利用样本数据计算观测方程中的未知参数，这是对实际系统进行建模的关键步骤，因为它确保了模型能够反映实际操作条件。然后，文章引入无迹卡尔曼滤波算法(UKF)进行在线催化活性的估计。UKF是一种非线性滤波方法，它通过近似概率密度函数来处理非线性问题，比传统的卡尔曼滤波器更适合处理复杂的动态系统。UKF可以在不知道完整系统动力学的情况下，有效地估计系统的状态，并且对于非线性系统的估计性能优越。实验结果显示，使用UKF进行在线估计能有效地跟踪催化活性的变化，对于实时监控和控制反应过程具有重要意义。这种估计方法可以提供实时反馈，帮助操作者了解催化剂的性能变化，及时调整操作条件，从而提高BPA的生产效率和产品质量。此外，该研究对化工过程系统工程和工艺安全领域具有广泛的应用价值，因为它为复杂化工过程的动态监测和控制提供了新的工具和策略。通过这种方法，可以提前预测催化剂的衰退，避免因催化剂性能下降导致的生产效率降低或产品质量问题，从而优化整个生产过程。总结来说，这篇研究论文介绍了如何利用无迹卡尔曼滤波技术来估计苯酚A生产中催化剂的活性，通过建立精确的模型和应用高级滤波算法，提高了在线监测和控制催化过程的能力，为化工行业的工艺优化和安全性提供了有力支持。

Process Systems Engineering and Process Safety

Estimation of catalytic activity using an unscented Kalman ﬁltering in

condensation reaction

☆

Wentao Cang, Huizhong Yang

⁎

Key Laboratory of Advanced Process Control for Light Industry, Ministry of Education, Jiangnan University, Wuxi 214122, China

abstractarticle info

Article history:

Received 19 May 2015

Received in revised form 23 June 2015

Accepted 1 July 2015

Available online 10 November 2015

The catalytic activity of cation exchange resins will be continuously reduced with its use time in a condensation

reaction for bisphenol A (BPA). For online estimation of the catalytic activity, a catalytic deactivation model is

studied for a production plant of BPA, state equation and observation equation are proposed based on the axial

temperature distribution of the reactor and the acetone concentration at reactor entrance. A hybrid model of

state equation is constructed for improving estimation precision. The unknown parameters in observation

equation are calculated with sample data. The unscented Kalman ﬁltering algorithm is then used for on-line

estimation of the catalytic activity. The simulation results show that this hybrid model has higher estimation

accuracy than the mechanism model and the model is effective for production process of BPA.

Keywords:

Unscented Kalman ﬁltering

Catalyst deactivation

Soft sensor

Hybrid modeling

1. Introduction

In a chemical reaction process, catalyst activity determines the

chemi cal reaction rate. However, it may de cline with time or even

completely failure in the process, reducing the production efﬁciency.

For example, bisphenol A (BPA) is synthesiz ed by condensation of

acetone and ph enol in proper proportions at sui table temperature

with the catalys t of acidic ion exc hange resin. Wi th long-term high

temperature in the reactor and continuous ﬂush of reactant ﬂuid, the

catalyst activity of ion exchange resin decreases gradually. The produc-

tion conditions must be adjusted accordingly, otherwise the production

stability and product quality may be affected. This paper focuses on soft

sensor development for online prediction of the catalyst activity in the

synthesis of BPA, which has important practical signiﬁcance.

Catalyst activity of BPA synthesis has been widely studied in recent

years [1–5]. Various catalyst deactivation kinetics models have been re-

ported because of the complexities of BPA synthesis. For example,

Biswal et al. have studied the catalytic activity, kinetics and reusability

of catalyst 60CsTPA-ZTP and found that it is an effective and re-usable

catalyst for the synthesis of BPA [6]. An improved linear discriminant

analysis algorithm has been proposed to estimate BPA concentration

with ion exchange resin as catalyst [7]. Shimizu and Kontani presented

an effective design of solid acid catalysts fo r synthesis of BPA with

organic–inorganic dual modiﬁcation of heteropolyacids [8]. Wang

et al. derived the kinetic equation for the synthesis of BPA with ZnCl

modiﬁed ion exchange resin as an efﬁcient catalyst and estimated the

catalyst activity based on its relationship with acetone conversion rate

at the reactor outlet [9]. However, the acetone conversion rate is highly

dependent on operation conditions and cannot be measured online in

the majority of industrial processes. Therefore, this paper establishes a

state -space model for estimation of the catalyst acti vity with the

temperature distribution in the reactor and acetone concentration at

the reactor inlet as variables, so that the BPA synthesis can be described

by a nonlinear distribution parameter model.

As a nonlinear estimation method, the extended Kalman ﬁlter (EKF)

is widely used in state estimation [10–14 ]. The method has som e

deﬁciencies, including the requirement of differentiability of state

dynamics and susceptibility to bias and divergence in state estimates

[15]. On the other hand, the unscented Kalman ﬁlter (UKF) uses the

nonlinear model directly inst ead of linearizing it [16], improving the

effect of nonlinear system ﬁltering by approximating the probability

distribution of nonlinear functions and the posterior probability density

of state based on a series of deterministic samples. UKF is accurate to the

second-order Taylor series expansion for arbitrary nonlinearity while

the accuracy of EKF is of the ﬁ rst order [17]. In this paper, UKF is

employed in state estimation and the simulation results are provided

to demonstrate the effectiveness of the proposed method.

2. Catalyst Deactivation Model

BPA, an important starting material for p roduction of epoxy and

polycarbonates, is produced by mixing phenol and acetone in certain

proportion at proper temperature with cation exchange resin as

catalyst. The main reaction is

A þ B

→

P þ −ΔHðÞ

Chinese Journal of Chemical Engineering 23 (2015) 1965–1969

☆

Supported by the National Natural Science Foundation of China (60674092).

⁎ Corresponding author.

E-mail address: yhz_jn@163.com (H. Yang).

http://dx.doi.org/10.1016/j.cjche.2015.11.008

Contents lists available at ScienceDirect

Chinese Journal of Chemical Engineering

journal homepage: www.elsevier.com/locate/CJChE

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