Process simulation of stream circulation system based on stability:

doi:10.11949/0438-1157.20211472

Abstract

Abstract:

The sequential modular method, which is widely used in process simulation, has many difficulties in dealing with stream circulation system, such as the selection of tearing stream and the convergence of iterative equations. Based on the stability theory, this paper solves the process simulation problem of stream circulation system. First, according to the model equation, chemical plants are identified as forward model and backward model, and the variables in stream circulation are defined as iterative variables and convergence variables respectively. Then, the stream circulation is broken at the convergence variables, and the convergence variables are calculated from the iterative variables by the forward model and the backward model respectively; the convergence errors are used for the correction of iterative variables through the gain coefficients, and then the iterative equation is obtained. Finally, the stability theory in control theory is used to determine the gain coefficient of the iterative equation, the iterative equation is linearized, and the Routh criterion is used to determine the stable range of the gain coefficient; when the gain coefficients is within the stable range, the iterative equation must converge. The reaction and regeneration system of FCCU is a typical stream circulation system because of catalyst circulation. The reactor is treated as the forward model and the regenerator is treated as the backward model. The temperature and carbon content of regenerator are treated as iteration variables to build the iterative equation of process simulation for FCCU reaction and regeneration system. The stability range of the gain coefficients is found by using the stability theory to ensure the convergence of the simulation calculation, and the feasibility and effectiveness of this method are verified.

Key words: stream circulation, process system, process simulation, FCCU, stability

摘要：

过程流程模拟中广泛应用的序贯模块法处理循环物流系统存在很多困难，如断裂流股的选择、迭代方程的收敛性等。基于稳定性理论解决循环物流系统的流程模拟问题，首先根据化工单元装置的模型方程将其分为正向模型和反向模型，并将循环物流中的变量定义为迭代变量和收敛变量；然后在收敛变量处将循环物流的流股断裂，迭代变量分别通过正向模型和反向模型计算收敛变量，二者的偏差通过增益系数对迭代变量进行修正，进而得到迭代方程；最后，利用控制理论中的稳定性理论来确定迭代方程的增益系数，将迭代方程线性化，采用劳斯判据确定增益系数的稳定范围，当增益系数位于稳定范围以内时，迭代方程必然收敛。催化裂化装置反应-再生系统因催化剂循环的存在而成为典型的循环物流系统，本文将反应器作为正向模型，再生器作为反向模型，以再生温度和再生催化剂含碳量作为迭代变量，构造了催化裂化装置反应-再生系统流程模拟的迭代方程，利用稳定性理论找到增益系数的稳定范围，保证流程模拟计算必定达到收敛，验证了该方法的可行性和有效性。

关键词: 循环物流, 过程系统, 流程模拟, 催化裂化装置, 稳定性

CLC Number:

TQ 021.8

Senshan CAO, Feng XU, Xionglin LUO. Process simulation of stream circulation system based on stability:[J]. CIESC Journal, 2022, 73(3): 1256-1269.

曹森山, 许锋, 罗雄麟. 基于稳定性的循环物流系统流程模拟——以催化裂化反应-再生系统为例[J]. 化工学报, 2022, 73(3): 1256-1269.

Figures/Tables 16

Fig.1 Forward model

Fig.2 Backward model

Fig.3 Information flow diagram with stream circulation

Fig.4 Information flow diagram of stream circulation system after tearing stream

Fig.5 The flow chart for obtaining convergence module

Table 1 Rolls table

$w n$	$a n$	$a n - 2$	$a n - 4$	$a n - 6$	…
$w n - 1$	$a n - 1$	$a n - 3$	$a n - 5$	$a n - 7$	…
$w n - 2$	$b 1$	$b 2$	$b 3$	$b 4$	…
$w n - 3$	$c 1$	$c 2$	$c 3$	$c 4$	…
$w n - 4$	$d 1$	$d 2$	$d 3$	$d 4$	…
$?$	$?$	$?$	$?$	$?$	$?$
$w 2$	$e 1$	$e 2$
$w 1$	$f 1$	0
$w 0$	$g 1$	0

Table 1 Rolls table

$w n$	$a n$	$a n - 2$	$a n - 4$	$a n - 6$	…
$w n - 1$	$a n - 1$	$a n - 3$	$a n - 5$	$a n - 7$	…
$w n - 2$	$b 1$	$b 2$	$b 3$	$b 4$	…
$w n - 3$	$c 1$	$c 2$	$c 3$	$c 4$	…
$w n - 4$	$d 1$	$d 2$	$d 3$	$d 4$	…
$?$	$?$	$?$	$?$	$?$	$?$
$w 2$	$e 1$	$e 2$
$w 1$	$f 1$	0
$w 0$	$g 1$	0

Fig.6 Schematic diagram of the reaction-separation cycle for the oxidation of toluene to benzoic acid

Fig.7 Information flow diagram for reaction-separation

Fig.8 Comparison simulation of four iterative methods for reaction-separation cycle of the toluene oxidation

Fig.9 Schematic diagram of FCCU

Table 2 Process data of FCCU

压力/kPa		温度/℃
反应器顶	再生器顶	提升管出口	再生器密相床
244.95	274.38	500	700
催化剂藏量/ kg	主风流量/ (m³/h)	新鲜原料量/ (kg/h)	催化剂循环量/ (kg/h)
27000	45500	75000	410000

Fig.10 Information flow diagram of the FCCU reaction-regeneration system

Fig.11 Information flow diagram of the FCCU reaction-regeneration system after tearing stream

Fig.12 Iterative convergence curves for the main variables in riser and strip section

Fig.13 Iterative convergence curves for the main variables in regenerator

Table 3 Comparison of simulated steady-state values and production data from this paper

各单元出口变量	模拟结果稳态值	生产数据	误差/%
再生剂含碳量/%(mass)	0.18	0.1875	4.00
再生温度/℃	699.85	700	0.02
再生烟气氧含量/%(mol)	2.66	2.77	3.97
反应温度/℃	503.39	500.0855	0.66
待生催化剂活性	0.2071	0.2030	0.02
汽提段出口焦炭含量/%(mass)	1.03	1	3.00
回炼油生成量/(t/h)	14.756	14.9500	1.30
回炼油油浆生成量/(t/h)	8.3908	8.5500	1.86
焦炭产率/%(mass)	4.7696	5.0104	4.81
柴油产率/%(mass)	39.9028	38.6386	3.27
汽油产率/%(mass)	39.5864	41.2439	4.02
气体产率/%(mass)	11.5450	12.1089	4.66

References 41

1	张新强, 邱泽刚, 李志勤. 工艺流程模拟计算中循环物流的处理方法[J]. 化工设计通讯, 2019, 45(12): 129, 175.
	Zhang X Q, Qiu Z G, Li Z Q. Processing method for recycle materials in process simulation convergence[J]. Chemical Engineering Design Communications, 2019, 45(12): 129, 175.
2	Nikolopoulou A, Ierapetritou M G. Optimal design of sustainable chemical processes and supply chains: a review[J]. Computers & Chemical Engineering, 2012, 44: 94-103.
3	赵文, 周传光, 孙淑燕, 等. 反应-分离循环系统最佳工艺条件的确定[J]. 高校化学工程学报, 1999, 13(3): 245-251.
	Zhao W, Zhou C G, Sun S Y, et al. Optimal process condition of reaction-separation recycle system[J]. Journal of Chemical Engineering of Chinese Universities, 1999, 13(3): 245-251.
4	Jorissen F, Wetter M, Helsen L. Simplifications for hydronic system models in modelica[J]. Journal of Building Performance Simulation, 2018, 11(6): 639-654.
5	Adegbege A A, Heath W P. A framework for multivariable algebraic loops in linear anti-windup implementations[J]. Automatica, 2017, 83: 81-90.
6	Kozlowski A, Yamaguchi K. The homotopy type of the space of algebraic loops on a toric variety[J]. Topology and Its Applications, 2021, 300: 107705.
7	耿华, 杨耕. 控制系统仿真的代数环问题及其消除方法[J]. 电机与控制学报, 2006, 10(6): 632-635.
	Geng H, Yang G. Algebraic loop problems in simulations of control systems and the methods to avoid it[J]. Electric Machines and Control, 2006, 10(6): 632-635.
8	张毅超, 白建云. 一种改进型Smith预估补偿控制算法及其应用[J]. 自动化技术与应用, 2016, 35(10): 1-3, 13.
	Zhang Y C, Bai J Y. An improved Smith compensation control algorithm and its application[J]. Techniques of Automation and Applications, 2016, 35(10): 1-3, 13.
9	Hillestad M, Hertzberg T. Dynamic simulation of chemical engineering systems by the sequential modular approach[J]. Computers & Chemical Engineering, 1986, 10(4): 377-388.
10	Cao Y, He B S, Yan L B. Process simulation of a dual fluidized bed chemical looping air separation with Mn-based oxygen carrier[J]. Energy Conversion and Management, 2019, 196: 286-295.
11	Asadi-Saghandi H, Sheikhi A, Sotudeh-Gharebagh R. Sequence-based process modeling of fluidized bed biomass gasification[J]. ACS Sustainable Chemistry & Engineering, 2015, 3(11): 2640-2651.
12	王雅琳, 黎良伟, 桂卫华, 等. 序贯模块法在选矿流程模拟中的应用与实现[J]. 计算机工程与应用, 2009, 45(7): 224-226, 243.
	Wang Y L, Li L W, Gui W H, et al. Realization and application of mineral processing simulator using sequential modular approach[J]. Computer Engineering and Applications, 2009, 45(7): 224-226, 243.
13	占志良. 基于联立方程模型的乙烯淤浆聚合过程模拟与优化[D]. 杭州: 浙江大学, 2012.
	Zhan Z L. Simulation and optimization of an industrial HDPE slurry process based on equation oriented models[D]. Hangzhou: Zhejiang University, 2012.
14	俞裕国, 王长英. 氨合成回路的模拟分析与多目标优化的探讨[J]. 化工学报, 1988, 39(2): 129-136.
	Yu Y G, Wang C Y. Simulation and multi-objective optimization of ammonia synthesis loop[J]. Journal of Chemical Industry and Engineering (China), 1988, 39(2): 129-136.
15	刘广杰, 孙晓岩, 毕荣山, 等. 复杂炼油塔模拟的改进联立方程内外层算法[J]. 化工学报, 2020, 71(5): 2118-2127.
	Liu G J, Sun X Y, Bi R S, et al. Improved equation oriented inside-out method of complex crude distillation column simulation[J]. CIESC Journal, 2020, 71(5): 2118-2127.
16	胡仰栋, 刘芳芝, 周传光, 等. 联立方程法模拟多循环流程的新解算策略[J]. 化工学报, 1991, 42(1): 104-108.
	Hu Y D, Liu F Z, Zhou C G, et al. A new algorithm for simulation of multi-cycle processes by simultaneous equations method[J]. Journal of Chemical Industry and Engineering (China), 1991, 42(1): 104-108.
17	李云涛. 实际化工模拟过程有效切割算法的研究[J]. 炼油与化工, 2004, 15(2): 27-29, 45.
	Li Y T. Research on effective cutting algorithm during real chemical analog[J]. Refining and Chemicals, 2004, 15(2): 27-29, 45.
18	范超. 化工过程系统分隔与切断排序方法研究[D]. 北京: 北京化工大学, 2016.
	Fan C. Research on the method for partitioning and tearing sort of chemical process systems[D]. Beijing: Beijing University of Chemical Technology, 2016.
19	唐强. 精馏过程稳态模拟计算方法分析[J]. 化工设计通讯, 2020, 46(11): 81-82.
	Tang Q. Analysis of steady-state simulation of distillation process[J]. Chemical Engineering Design Communications, 2020, 46(11): 81-82.
20	Aliyu M D S. Iterative computational approach to the solution of the Hamilton-Jacobi-Bellman-Isaacs equation in nonlinear optimal control[J]. Control Theory and Technology, 2018, 16(1): 38-48.
21	Carson E, Higham N J. Accelerating the solution of linear systems by iterative refinement in three precisions[J]. SIAM Journal on Scientific Computing, 2018, 40(2): A817-A847.
22	Evans C, Pollock S, Rebholz L G, et al. A proof that Anderson acceleration improves the convergence rate in linearly converging fixed-point methods (but not in those converging quadratically)[J]. SIAM Journal on Numerical Analysis, 2020, 58(1): 788-810.
23	Li Y, Guo X P. Multi-step modified Newton-HSS methods for systems of nonlinear equations with positive definite Jacobian matrices[J]. Numerical Algorithms, 2017, 75(1): 55-80.
24	苏涛. 化工间歇过程的迭代学习控制方法[D]. 青岛: 青岛科技大学, 2014.
	Su T. Iterative learning control of chemical batch processes[D]. Qingdao, China: Qingdao University of Science & Technology, 2014.
25	Zhou W J, Shen D M. Convergence properties of an iterative method for solving symmetric non-linear equations[J]. Journal of Optimization Theory and Applications, 2015, 164(1): 277-289.
26	Geng Z Q, Wei C Y, Han Y M, et al. Pipeline network simulation calculation based on improved Newton Jacobian iterative method[C]//Proceedings of the 2019 International Conference on Artificial Intelligence and Computer Science. New York, USA: ACM, 2019: 219-223.
27	周游, 赵成业, 刘兴高. 一种求解化工动态优化问题的迭代自适应粒子群方法[J]. 化工学报, 2014, 65(4): 1296-1302.
	Zhou Y, Zhao C Y, Liu X G. An iteratively adaptive particle swarm optimization approach for solving chemical dynamic optimization problems[J]. CIESC Journal, 2014, 65(4): 1296-1302.
28	Kuo M T, Rubin D I. Optimization study of chemical processes[J]. The Canadian Journal of Chemical Engineering, 1962, 40(4): 152-156.
29	Shacham M, Kehat E. Converging interval methods for the iterative solution of a non-linear equation[J]. Chemical Engineering Science, 1973, 28(12): 2187-2193.
30	Motard R L, Shacham M, Rosen E M. Steady state chemical process simulation[J]. AIChE Journal, 1975, 21(3): 417-436.
31	Naseem A, Rehman M A, Abdeljawad T. Some new iterative algorithms for solving one-dimensional non-linear equations and their graphical representation[J]. IEEE Access, 2021, 9: 8615-8624.
32	汪德友, 崔艳雨, 李旭光, 等. 基于牛顿迭代法的复杂机坪管网水力计算[J]. 油气储运, 2020, 39(12): 1394-1400.
	Wang D Y, Cui Y Y, Li X G, et al. Hydraulic calculation for complicated apron pipeline network based on Newton iteration method[J]. Oil & Gas Storage and Transportation, 2020, 39(12): 1394-1400.
33	管慧莹. 求解非线性方程的两种迭代算法[D]. 哈尔滨: 哈尔滨理工大学, 2020.
	Guan H Y. Two iterative algorithms for solving nonlinear equations[D]. Harbin: Harbin University of Science and Technology, 2020.
34	王晓锋. 两类修正的3阶收敛的牛顿迭代格式[J]. 哈尔滨理工大学学报, 2011, 16(1): 113-115.
	Wang X F. Two classes of Newton's iteration methods with third-order convergence[J]. Journal of Harbin University of Science and Technology, 2011, 16(1): 113-115.
35	Fang X W, Ni Q, Zeng M L. A modified quasi-Newton method for nonlinear equations[J]. Journal of Computational and Applied Mathematics, 2018, 328: 44-58.
36	Bublitz S, Esche E, Tolksdorf G, et al. Analysis and decomposition for improved convergence of nonlinear process models in chemical engineering[J]. Chemie Ingenieur Technik, 2017, 89(11): 1503-1514.
37	罗雄麟. 前置烧焦罐式高效再生器催化裂化装置动态模拟与操作分析[D]. 北京: 中国石油大学, 1997.
	Luo X L. Dynamic modeling and operation analysis of FCCU(fluid catalytic cracking unit) with high efficient regenerator[D]. Beijing: China University of Petroleum, 1997.
38	罗雄麟, 袁璞, 林世雄. 催化裂化装置动态机理模型 (Ⅰ): 反应器部分[J]. 石油学报(石油加工), 1998, 14(1): 34
	Luo X L, Yuan P, Lin S X. Dynamic Model of Fluid Catalytic Cracking(Ⅰ): Reactor Section[J]. Acta Petrolei Sinica (Petroleum Processing Section), 1998, 14(1): 34
39	Zheng Y Y. Dynamic modeling and simulation of a catalytic cracking unit[J]. Computers & Chemical Engineering, 1994, 18(1): 39-44.
40	罗雄麟, 袁璞, 林世雄. 催化裂化装置动态机理模型 (Ⅱ): 再生器部分[J]. 石油学报(石油加工), 1998, 14(2): 34
	Luo X L, Yuan P, Lin S X. Dynamic Modeling of Fcc (Ⅱ): regenerator　section[J]. Acta Petrolei Sinica (Petroleum Processing Section), 1998, 14(2): 34
41	罗雄麟, 张建芳. 催化裂化高效再生器多级混合模型及其应用[J]. 石油炼制与化工, 1992, 23(8): 34-40.
	Luo X L, Zhang J F. A tanks-in-series model for the FCC regenerator with fast fluidization and its applications[J]. Petroleum Processing and Petrochemicals, 1992, 23(8): 34-40.

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