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作者简介:

赵东亚(1975-),男,教授,博士,博士生导师,研究方向为过程建模、优化与控制。E-mail:dyzhao@upc.edu.cn。

中图分类号:TQ015.9;TP391.9

文献标识码:A

文章编号:1673-5005(2021)02-0181-06

DOI:10.3969/j.issn.1673-5005.2021.02.022

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目录contents

    摘要

    针对再生塔反应精馏特点,基于再生塔机制模型,建立再生塔能耗优化模型。 运用非线性规划优化方法中的罚函数法及牛顿法,以进入再生塔的富液温度为决策变量,对再生塔能耗进行优化。 结果表明:在最优富液入塔温度条件下,返塔冷凝液温度和富液升温差的敏感性较差,将富液入塔温度作为决策变量可忽略其影响;再生塔塔底压力的增大有利于降低再生能耗;气相流率的减小有利于降低再生能耗;本文中提供的优化方法有效可靠。

    Abstract

    According to the characteristics of reactive distillation of regeneration tower, an optimization model was established on the basis of the mechanism model of regeneration tower. By using nonlinear programming optimization methods including penalty function method and Newton method, the regeneration consumption was optimized by taking the temperature of the rich liquid entering the regeneration tower as the decision variable. The results show that under the optimal temperature of the rich liquid entering the tower, the temperature of the condensate returning to the column and the temperature difference of the rich liquid are less sensitive. The influence of that can be ignored when the temperature of the rich liquid is used as the decision variable. The increase of the bottom pressure of the regeneration tower is beneficial to reduce the regeneration energy consumption. The reduction of gas flow rate is beneficial to the reduction of renewable energy consumption. The optimization method presented in this paper is effective and reliable.

  • 燃煤电厂是温室效应[1-3] 主要的碳排放源之一,对烟气中的CO2 进行捕集是缓解气候变化、促进人类社会可持续发展的重要方式之一[4-6]。化学吸收法[7]捕集效率较高[8],其中MEA吸收法具有吸收速率快、吸收效率高等优点。但MEA吸收工艺需要大量蒸汽提供解吸所需热量,导致捕集成本较高[9-10]。再生塔是单乙醇胺法CO2 捕集技术耗能最大的设备,降低CO2 解吸能耗的方法主要有采用新型吸收剂、优化工艺参数、改进吸收与解吸工艺。优化工艺参数具有成本低、操作难度小的特点。白亚开[11]分析了MEA法脱碳系统参数变动对脱碳能耗的影响,马嘉慧等[12] 对MEA溶液捕集CO2 的反应热进行实验研究,并利用自主开发的量热系统分析了负载率等参数的影响,RAO等[13] 借助化工模拟软件并利用线性回归方法建立捕集系统能耗模型及全流程成本数学模型,赵东亚等[14] 对再生塔能耗进行平衡级建模,利用MESH方程建立再生塔机制模型,借助化工模拟软件ProTreat建立工艺模型,并进行能耗敏感性分析。笔者基于再生塔能耗机制模型[14],运用非线性规划方法,以进入再生塔的富液的温度为决策变量,对再生塔能耗进行优化,得出参数变化时的最佳能耗,并进行案例对比分析,验证所述优化方法的有效性。

  • 1 再生塔单位能耗机制模型

  • 单乙醇胺法碳捕集工艺流程如图1所示。电厂烟气在水洗塔中清洁处理后,经压缩机加压发生吸收反应。反应后的烟气自吸收塔塔顶排出回流至烟道,塔底排出CO2 富液。 CO2 富液经贫富液换热器升温后从塔顶进入再生塔中完成富液的乙醇胺再生[14],其中再沸器提供CO2 解吸所需的热量。

  • 图1 碳捕集工艺流程

  • Fig.1 Process of carbon capture

  • 1.1 单乙醇胺法CO2 捕集工艺过程

  • CO2 吸收:

  • 2R-NH2+CO2R-NH3++R-NH-COO-;
    (1)
  • 乙醇胺的再生(CO2 解吸):

  • R-NH-COO-+R-NH3++(heat )CO2+2R-NH2
    (2)
  • 再生塔发生反应(2)完成MEA的再生,在再生塔的塔顶得到高浓度的CO2 产品,塔底排出高温的CO2 贫液[15-17]

  • 为分析能耗影响因素,对其进行机制建模[18]

  • 1.2 再生热能耗的数学模型

  • 再生热能耗的数学模型[13]

  • Qreg=Qs+Qr+Qg
    (3)
  • 显热:

  • Qs=mscptreboil ab-trich =mscpΔt
    (4)
  • 式中,ms 为吸收剂溶液的循环量,kg/h;cp 为吸收剂溶液的比热容,kJ/( kg·K);Δt=treboil ab-tinab为富液升温差,K; tinab为进入再生塔的富液温度,K; treboil ab为贫液温度,K。

  • 1.3 分解反应热

  • Q=GCO2ΔqCO2
    (5)
  • 式中, ΔqCO2为再生反应生成单位CO2 所需平均反应热,kJ/(mol(CO2)); GCO2为塔顶CO2 流率,kg/h。

  • 1.4 汽化热

  • Qg=hCO2gGCO2+hH20gGH20-hH201lH20=hCO2gGCO2+γH20GCO2+hH201-hH2O0GCO2=hCO2gGCO2+γH20GCO2+ΔhH20GCO2.
    (6)
  • 式中, hCO2g为出塔温度toutab下CO2 的焓,kJ/kg; hH20g为出塔温度toutab下水的焓; γH20Pbottom 下水的汽化潜热,kJ/kg; hH201为出塔温度toutab下H2O的焓,kJ/kg; hH2O0为返塔冷凝液温度tinH2O下H2O的焓, kJ/kg; ΔhH20hH201hH2O0的焓差。

  • 基于上述分析可得再生塔单位能耗机制模型[13]

  • qreg=mscpΔtV1y1+ΔqCO2+hCO2g+γH20+ΔhH20
    (7)
  • 式中,V1 为气相流率,kg/h;y1 为示CO2 物质的量分率,%。

  • 2 优化设计

  • 基于再生塔能耗机制模型,运用非线性规划优化方法,以进入再生塔的富液温度为决策变量,对再生塔能耗进行优化。

  • 根据建立的单位能耗机制模型,结合工程实际得到的优化问题数学模型如下。

  • min qreg=mscpΔtV1y1+ΔqCO2+hCO2g+γH20+ΔhH20,s.t. tlowtinabthigh, tlow'tinH20thigh'.
    (8)
  • 式中, tinH20表示冷凝液返塔温度,K。

  • 式(8)描述的是复杂的非线性约束优化问题, 为便于求解,首先运用罚函数法将式(8) 转化为无约束优化问题,然后通过牛顿法进行求解。

  • 2.1 外罚函数内嵌牛顿迭代算法

  • 罚函数法是将约束最优化问题转化为求解无约束最优化问题的方法,分为外罚函数法和内罚函数法,其中外罚函数可用于等式和不等式约束的最优化问题,且能在可行域内、外搜索[19],因此本文中选择外罚函数法。

  • 外罚函数的形式为

  • Gt(i),σ(k)=mscpΔtV1y1+ΔqCo2+hCO2g+γH20+ΔhH20+σ(k)maxthigh-tinab,02+max-tlow -tinab,02.
    (9)
  • 牛顿法是最常用的无约束优化问题求解方法之一。它的基本思想是利用目标函数的二次泰勒展开,求极小值[19]。因此先选择罚函数法将约束优化问题转化为无约束优化问题,然后用牛顿法求解无约束优化问题。

  • 牛顿迭代公式为

  • t(i+1)=t(i)-Ht(i)-1φt(i).
    (10)
  • 其中Ht(i)φt(i)分别表示式(9) 的海塞矩阵和一阶导数,当φt(i)ε时,迭代停止。

  • 2.2 优化算法设计

  • 以进入再生塔的富液温度为决策变量,使用罚函数嵌套牛顿法,对再生塔能耗进行优化,优化程序流程如下。

  • (1)分析再生塔能耗,建立再生塔再生热计算式。

  • (2)在建立的温焓关系模型的基础上[20],建立能耗机制模型(7)。

  • (3)选择决策变量,即进入再生塔的富液温度tinab,固定出塔温度、水的汽化潜热等参数,对再生塔单位能耗 qreg 进行优化。

  • (4)选择初始罚因子 σ(0)、初始点 t(0)(即初始温度)、收敛精度 ε 和罚因子系数 c 构造罚函数,将约束优化问题转化为无约束优化问题。本程序分别取 σ(0)=2,t(0)=[273,273],ε=10-6,c=1.02。令初始迭代步数 k =0。

  • (5)选择牛顿法求解步骤(4)中形成的无约束优化问题min φ(t,σ(k))的极值点tinabσ(k)

  • (6)检验是否满足迭代终止准则:

  • tin abσ(k)-tinabσ(k-1)ε

  • 以及

  • ftinabσ(k)-ftinabσ(k-1)ftinabσ(k-1)ε.

  • 若满足, 则停止迭代, 输出最优温度tinab=tinabσ(k);如果不满足此条件,则转步骤(7)。

  • (7)取σ(k+1)=cσ(k),t(0)=tinabσ(k),k=k+1,转步骤(5)。

  • 根据步骤(1)~(7),运用MATLAB软件进行仿真模拟。最终迭代次数为1 737次,得出最优富液进入再生塔温度为358K。

  • 3 案例分析

  • 以胜利电厂100t/d CO2 捕集工程为案例,工程采用MEA复合胺吸收工艺,吸收液循环量为120m 3/h,吸收温度313K,解吸温度375K,捕集率为85%。其中电厂烟气物流参数:温度为313K,体积流率为18 863Nm 3/h,物质的量流率为796.2kmol/h。式(8)所需基本参数可由现场调研、文献[21-22] 和热工软件Refprop提供:ms 为407.862,cp 为4.087kJ/(kg·K), toutab为382.981K, ΔqCo2为84.85kJ/(mol( CO2)), GCO2为110 563.2kg/h, γH2O为2 257.2kJ/kg, hH201为338.17kJ/kg, hH200为147.17kJ/kg,y1 为4.32%。再生塔相关参数:塔径为1.2m,塔板数(折算)为22,进料位置为第2块塔板,工作压力为0.12MPa,塔总高(包括裙座等) 为16.7m,操作温度(塔顶) 为365K,操作温度为(塔底) 378K。

  • 3.1 敏感性分析

  • 基于能耗基本参数、最优温度,以其他参数的变化对单位能耗的影响进行敏感性分析,验证所提优化方法的工程有效性。

  • 以上述参数为标准.将返塔冷凝液温度的数值分别减少或增加5%、10%,其他参数值不变,对二氧化碳捕集系统单位再生能耗变化率进行计算,结果见图2。

  • 图2 返塔冷凝液温度变化率对单位能耗变化率的影响

  • Fig.2 Influence of temperature change rate of condensate returning to column on unit energy consumption

  • 由图2可知,返塔冷凝液温度增大时,二氧化碳捕集系统单位再生能耗变化率呈下降趋势;返塔冷凝液温度在参照温度下,增加(或减少) 10%,能耗将增加(或减少) 0.2%;返塔冷凝液温度在参照温度下,增加( 或减少) 5%, 能耗将增加( 或减少) 0.01%。因此在优化所得最优富液入塔温度下,返塔冷凝液温度敏感性较低,能耗变化率较低。

  • 将富液升温差的数值分别减少或增加5%、 10%,其他参数值不变,对二氧化碳捕集系统单位再生能耗变化率进行计算,结果见图3。

  • 图3 富液升温差变化率对单位能耗变化率的影响

  • Fig.3 Influence of change rate of temperature difference of rich liquid on unit energy consumption

  • 由图3可知,富液升温差增大时,二氧化碳捕集系统单位再生能耗变化率呈下降趋势;富液升温差在参照数值下,增加(或减少)10%,能耗将增加(或减少) 5%;富液升温差在参照温度下,增加(或减少)5%,能耗将增加(或减少)2.5%。即在优化所得最优富液入塔温度下,富液升温差敏感性较低,能耗变化率较低。

  • 因此将富液入塔温度作为决策变量可忽略返塔冷凝液温度和富液升温差的影响,即优化具有工程意义,验证了所得最优富液入塔温度的工程有效性。

  • 3.2 对比分析

  • 为进一步验证本文优化方法的有效性,以胜利电厂100t/d CO2 捕集工程为背景及数据来源,将本文提出的优化方法所得能耗与中石化节能环保工程科技有限公司利用室内试验研究经验和工程经验(以下简称经验法)设计的CO2 捕集工艺所得能耗进行比较。比较方法是固定基本参数,将优化法与经验法的两个结果分别应用于Aspen HYHSY进行模拟[23],数值模型如图4所示。

  • 压力的变化会直接影响汽液的平衡关系[24-25], 从而单位能耗也会受到影响(图5)。由图5可知, 当再生塔塔底压力相同时,优化方法的能耗低于经验法,同一压力下,两种方法的富液流入再生塔温度不同,其中所提优化方法能够获得最优温度,因此优化所得能耗低于经验法所得能耗。当再生塔塔底压力增大时,优化能耗和经验法能耗都逐渐降低。但基于经验法的能耗下降速度较快,而优化方法的能耗下降速度较缓。

  • 图4 Aspen HYSYS流程模拟

  • Fig.4 Aspen Hysys process simulation

  • 图5 塔底压力变化条件下能耗对比

  • Fig.5 Comparison of energy consumption under condition of change of tower bottom pressure

  • 由图6可知,当气相流率相同时,优化后所得能耗低于经验法的能耗,同一气相流率下,两种方法的富液流入再生塔温度不同,其中所提优化方法能够获得最优温度,因此优化所得能耗低于经验法所得能耗。当气相流率增大时,优化能耗与经验法能耗都随之增大,一方面是因为气相流率增大时,要求分离的CO2 也增多,因此能耗随之增大;另一方面是由于离开再生塔顶部的气体大部分是CO2 和水汽, 而水蒸气中的能量也较多,若气相流率增大,则会导致水汽量也增大,会将更多的能量带出再生塔,导致单位能耗的快速增大。因此可以通过适当减少气相流率以达到降低能耗的目的。

  • 图6 气相流率变化条件下能耗对比

  • Fig.6 Comparison of energy consumption under condition of change of gas flow rate

  • 4 结论

  • (1)在最优富液入塔温度条件下,返塔冷凝液温度和富液升温差的敏感性较差,将富液入塔温度作为决策变量可忽略其影响。

  • (2)再生塔塔底压力的增大有利于降低再生能耗;气相流率的减小有利于降低再生能耗。

  • (3)本文中提供的优化方法有效可靠。

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    • [24] 秦锋,王淑娟,HALLVARD F S,等.氨法脱碳系统再生能耗的研究 [J].化工学报,2010,61(5):1233-1240.QIN Feng,WANG Shujuan,HALLVARD F S,et al.Study on regenerative energy consumption of ammonia decarbonization system[J].Journal of Chemical Engineering,2010,61(5):1233-1240.

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  • 参考文献

    • [1] TIAN Qunhong,ZHAO Dongya,LI Zhaomin,et al.Robust and stepwise optimization design for CO2 pipeline transportation [J].International Journal of Greenhouse Gas Control,2017,58:10-18.

    • [2] ZHAO Dongya,TIAN Qunhong,LI Zhaomin,et al.A new stepwise and piecewise optimization approach for CO2 pipeline [J].International Journal of Greenhouse Gas Control,2016,49:192-200.

    • [3] TIAN Qunhong,ZHAO Dongya,LI Zhaomin,et al.A two-step co-evolutionary particle swarm optimization approach for CO2 pipeline design with multiple uncertainties [J].Carbon Management,2018,9(4):1-14.

    • [4] MIN K,CHOI W,KIM C,et al.Oxidation-stable amine-containing adsorbents for carbon dioxide capture [J].Nature Communications,2018,9(1):726.

    • [5] TIAN Qunhong,ZHAO Dongya,LI Zhaomin,et al.Modelling and evaluating CCUS:a survey [J].International Journal of Computer Applications in Technology,2016,53(1):1-12.

    • [6] 张军,房体明,王业飞,等.烷烃油滴在超临界二氧化碳中溶解的分子动力学模拟[J].中国石油大学学报(自然科学版),2015,39(2):124-129.ZHANG Jun,FANG Timing,WANG Yefei,et al.Molecular dynamics simulation of dissolution of n-alkanes droplets in supercritical carbon dioxid [J].Journal of China University of Petroleum(Edition of Natural Science),2015,39(2):124-129.

    • [7] RUBIN E S,RAO A B.A Technical economic and environment assessment of amine-based CO2 capture technology for power plant greenhouse gas control [J].Environ Sci Technol,2002,36(20):4467-4475.

    • [8] 黄宏,杨思宇.一种低能耗捕集 CO2 煤基甲醇和电力联产过程设计[J].化工学报,2017(10):3860-3869.HUANG Hong,YANG Siyu.Design of a low energy consumption CO2 capture cogeneration process of coal-based methanol and electric power[J].Journal of Chemical Industry and Engineering,2017(10):3860-3869.

    • [9] SRIVASTAVA R K,HUANG S S,DONG Mingzhe.Comparative effectiveness of CO2,and flue gas for enhanced heavy-oil recovery [J].SPE Reservoir Enal & Eng,1999,2(3):238-247.

    • [10] ISLAM M R,CHAKMA A.Storage and utilization of CO2 in petroleum reservoirs:a simulation study [J].Energy Conversion and Managemen,1993,34(9/10/11):1205-1210.

    • [11] 白亚开.基于乙醇胺法与氨水法碳捕集能耗特性分析与系统优化[D].北京:华北电力大学,2016.BAI Yakai.Analysis and system optimization of carbon capture energy consumption based on ethanolamine method and ammonia method[D].Beijing:North China Electric Power University,2016.

    • [12] 马嘉慧,张建,李玉星,等.MEA 溶液捕集 CO2 的反应热实验研究 [J].天然气化工(C1 化学与化工),2017,42(3):28-32.MA Jiahui,ZHANG Jian,LI Yuxing,et al.Experimental study on reaction heat of CO2 capture by MEA solution [J].Chemical Engineering of Natural Gas(C1 Chemistry and Chemical Engineering),2017,42(3):28-32.

    • [13] RAO A B,RUBIN E S.A technical,economic,and environmental assessment of amine-based CO2 capture technology for power plant greenhouse gas control[J].Environmental Science & Technology,2002,36(20):4467-4475.

    • [14] 赵东亚,揭超,李兆敏.醇胺法碳捕集工艺解吸塔能耗分析[J].中国石油大学学报(自然科学版),2016,40(6):150-155.ZHAO Dongya,JIE Chao,LI Zhaomin.Energy consumption analysis of desorption column in amine-based CO2 capture process [J].Journal of China University of Petroleum(Edition of Natural Science),2016,40(6):150-155.

    • [15] ELMER D.Post-combustion CO2 separation technology [M].Oxford:Elsevier,2005:91-97.

    • [16] LIANG Zhiwu,WICHITPAN R W,LIU Helei,et al.Recent progress and new developments in post-combustion carbon-capture technology with amine based solvents[J].International Journal of Greenhouse Gas Control,2015,40:26-54.

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    • [18] 周雷皓,刘桂莲.复杂反应的代数分析建模方法[J].化工学报,2017,69(3):1030-1037.ZHOU Leihao,LIU Guilian.An algebraic analytical modeling method for complex reactions [J].Journal of Chemical Engineering,2017,69(3):1030-1037.

    • [19] 袁亚湘,孙文瑜.最优化理论与方法[M].北京:科学出版社,1997:467-478.

    • [20] 陈则韶.高等工程热力学[M].合肥:中国科学技术大学出版社,2014:86-98.

    • [21] 李静.16 万吨/年MTBE装置催化精馏塔的建模与控制仿真[D].青岛:中国石油大学(华东),2010.LI Jing.Modeling and control simulation of catalytic distillation column in 160,000 tons/year MTBE unit[D].Qingdao:China University of Petroleum(East China),2010.

    • [22] LUO Xiaobo,WANG Meihong.Improving prediction accuracy of a rate-based model of an MEA-based carbon capture process for large-scale commercial deployment [J].Engineering,2017,3(2):232-243.

    • [23] 孙兰义,张骏驰,石宝明,等.过程模拟实训:Aspen HYSYS 教程 [ M].北京:中国石化出版社,2015:121-135.

    • [24] 秦锋,王淑娟,HALLVARD F S,等.氨法脱碳系统再生能耗的研究 [J].化工学报,2010,61(5):1233-1240.QIN Feng,WANG Shujuan,HALLVARD F S,et al.Study on regenerative energy consumption of ammonia decarbonization system[J].Journal of Chemical Engineering,2010,61(5):1233-1240.

    • [25] ROSARIO P,GRAEME W,OCONE R.Aspen Plus simulations of fluidised beds for chemical looping combustion[J].Fuel,2014,136:46-56.

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