A novel method for solution of the one-dimensional dynamic mathematical model of PFR

doi:10.16085/j.issn.1000-6613.2019-1207

Abstract

Abstract: The volumetric flowrate of reactants (i.e. gas or liquid) is simplified as constant in dynamic modeling of the one-dimensional piston flow reactor (PFR). However, the volumetric flowrate of the gas is often easily effected by many factors such as temperature, pressure and molar flowrate. Therefore, the relative error of simulation results should be enlarged because of the simplification. To solve this problem, a novel method for solution of the dynamic model of PFR is presented in this work. In the novel method, the finite difference method is improved by introducing a mathematical expression for the flowrate of gaseous feedstock. To validate the method, the provided novel method and classic method of line (MOL) are applied in dynamic modeling PFR of the vapor-phase cracking of acetone to ketene and methane. Furthermore, the simulation results of different methods are compared and more accurate simulation results is obtained by the novel method.

Key words: dynamic simulation, piston flow reactors, finite difference, volumetric flow rate, algorithm

摘要： 目前对一维平推流反应器动态模型求解时，常将反应体系中气体的体积流量假设为恒定参数。由于实际过程中气体的体积流量会随着温度等相关参数的改变而不断变化，该假设会对模拟结果带来一定的误差。本文针对此问题提出一种新的求解方法：首先通过有限差分法将动态模型中的空间和时间变量均离散化得到相应的代数方程组，再结合气体状态方程，推导出浓度关于气体摩尔流量和温度的函数，然后联立方程组进行求解；此方法有效克服了动态模拟中由于气体的体积流量变化而导致模型方程难以求解的困难。将所提出的方法应用于丙酮气相裂解生成乙烯酮过程的动态模拟，并将所得到的模拟结果与线上法动态模拟的结果进行比较，结果表明所提出的求解方法得到的模拟结果更加精确。

关键词: 动态仿真, 平推流反应器, 有限差分法, 体积流量, 算法

CLC Number:

TQ015

QI Liang, ZHANG Bo, SHANG Qinyu, WANG Yanbing, CAO Zhikai, LI Wei, ZHOU Hua. A novel method for solution of the one-dimensional dynamic mathematical model of PFR[J]. Chemical Industry and Engineering Progress, 2019, 38(s1): 70-76.

祁亮, 张波, 尚秦玉, 王雁冰, 曹志凯, 李薇, 周华. 一维平推流反应器动态模型的新型求解方法[J]. 化工进展, 2019, 38(s1): 70-76.

References

[1] 王健红, 陈晓春. 化工装置动态模拟与优化工艺软件平台[J]. 化工进展, 1997, 16(4):49-51. WANG J H, CHRN X C. Dynamic simulation and optimization platform for chemical process[J]. Chemical Industry and Engineering Progress, 1997, 16(4):49-51.
[2] 赵毅, 李超, 田健辉. 实时优化技术在乙烯装置在线优化中的应用[J]. 化工进展, 2016, 35(3):679-684. ZHAO Y, LI C, TIAN J H. Application of real-time optimization in on-line optimization of ethylene plant[J]. Chemical Industry and Engineering Progress, 2016, 35(3):679-684.
[3] 吕媛媛, 张岩, 刘蕾. 先进控制在烯烃厂碳二加氢反应器的应用[J]. 化工进展, 2011, 30(s1):457-461. LÜ Y Y, ZHANG Y, LIU L. Industrial application of advanced process control in hydrogenation reactor of olefin plant[J]. Chemical Industry and Engineering Progress, 2011, 30(s1):457-461.
[4] 吴斯侃, 曹志凯, 周华, 等. 一种用于二维稳态固定床的通用计算方法[J]. 厦门大学学报(自然科学版), 2016, 55(6):830-835. WU S K, CAO Z K, ZHOU H, et al. General calculation method for two-dimensional fixed-bed at steady state[J]. Journal of Xiamen University(Natural Science), 2016, 55(6):830-835.
[5] MOHAMMAD O, ERLING R, MAGNE H. Evaluation of kinetic models for Fischer-Tropsch cobalt catalysts in a plug flow reactor[J]. Chemical Engineering Research and Design, 2016, 114:236-246.
[6] GEERT H, TSILLA B. Comprehensive Fischer-Tropsch reactor model with non-ideal plug flow and detailed reaction kinetics[J]. Computers & Chemical Engineering, 2016, 84(4):281-289.
[7] LI Y F, MARIA S, BAO J. A dynamic plug flow reactor model for a vanadium redox flow battery cell[J]. Journal of Power Sources, 2016, 31(15):57-67.
[8] SAVVAS S, JOANNE D, TIM P, et al. Biological methanation of CO₂ in a novel biofilm plug-flow reactor:a high rate and low parasitic energy process[J]. Applied Energy, 2017, 202(15):238-247.
[9] K&OUML;NIG S, SURIYAH M R, LEIBFRIED T. A plug flow reactor model of a vanadium redox flow battery considering the conductive current collectors[J]. Journal of Power Sources, 2017, 360(31):221-231.
[10] DONG X J, HE Y J, SHEN J N, et al. Multi-zone parallel-series plug flow reactor model with catalyst deactivation effect for continuous catalytic reforming process[J]. Chemical Engineering Science, 2018, 175(16):306-319.
[11] FOGLER H S. Essentials of chemical reaction engineering[M]. 4nd ed. New York:Pearson Education, 2010:504-508.
[12] LUYBEN W L. Process modeling, simulation and control for chemical engineers[M]. 2nd ed. New York:McGraw-Hill Higher Education, 1989:19-25.
[13] 李复, 吴慧雄, 解娅男. 硫磺回收工艺的动态模拟[J]. 北京化工大学学报(自然科学版), 2015, 42(6):37-41. LI F, WU H X, XIE Y N. Dynamic simulation of the sulfur recovery process[J]. Journal of Beijing University of Chemical Technology (Natural Science), 2015, 42(6):37-41.
[14] ALOPAEUS V, LAAVI H, AITTAMAA J. A dynamic model for plug flow reactor state profiles[J]. Computers & Chemical Engineering, 2008, 32(7):1494-1506.
[15] ROININEN J, ALOPAEUS V. The moment method for one-dimensional dynamic reactor models with axial dispersion[J]. Computers & Chemical Engineering, 2011, 35(3):423-433.
[16] 解娅男, 李复. Gsp气化炉建模与动态模拟[J]. 计算机与应用化学, 2017, 34(6):465-470. XIE Y N, LI F. Modeling and dynamic simulation of Gsp gasifier[J]. Computers and Applied Chemistry, 2017, 34(6):465-470.
[17] XU Y L, ZHOU J L, QU Y Y, et al. Dynamics and oxygen transfer of a novel vertical tubular biological reactor for wastewater treatment[J]. Chemical Engineering Journal, 2010, 156(1):92-97.
[18] INGHAM J, DUNN I J, HEINZLE E, et al. Chemical engineering dynamics:an introduction to modelling and computer simulation[M]. 3nd ed. Ontario:John Wiley & Sons, 2008:340-344.
[19] 刘永康, 张树增, 王健红. 光气合成反应器动态仿真[J]. 计算机仿真, 2005, 22(10):280-283. LIU Y K, ZHANG S Z, WANG J H. Dynamic simulation of phosgene synthesis reactor[J]. Computer Simulation, 2005, 22(10):280-283.
[20] 李绍芬. 反应工程[M]. 3版. 北京:化学工业出版社, 2012. LI S F. Reaction engineering[M]. 3nd ed. Beijing:Chemical Industry Press, 2012.
[21] 陈涛, 张国亮. 化工传递过程基础[M]. 3版. 北京:化学工业出版社, 2001. CHEN T, ZHANG G L. Fundamental of transport phenomena for chemical process[M]. 3nd ed. Beijing:Chemical Industry Press, 2001.
[22] DANCKWERTS P V. Continuous flow systems:distribution of residence times[J]. Chemical Engineering Science, 1953, 2(1):1-13.
[23] 陆金甫, 关治. 偏微分方程数值解法[M]. 2版. 北京:清华大学出版社, 2003. LU J F, GUAN Z. Numeric solution for partial difference equations[M]. 2nd ed. Beijing:Tsing University Press, 2003.
[24] 易大义, 蒋叔豪, 李有法. 数值方法[M]. 杭州:浙江科学技术出版社, 1984. YI D Y, JIANG S H, LI Y F. Numerical method[M]. Hangzhou:Zhejiang Science & Technology Press, 1984.
[25] 王正烈, 周亚平. 物理化学[M]. 4版. 北京:高等教育出版社, 2001. WANG Z L, ZHOU Y P. Phisical chemistry[M]. 4nd ed. Beijing:Higher Education Press, 2001.