基于拟牛顿法气-液直接接触式冷却塔设计实例研究
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摘要
最优化计算方法是能源与动力专业的基础课程,目前缺乏关于能源装备的实际案例。采用拟牛顿算法求解气-液接触式冷却塔设计问题。首先基于蒸发和冷凝物理过程构建常微分方程,进而采用拟牛顿法求解常微分方程,为改善迭代稳定性,开发一种基于液相温度最大值点的迭代更新算法,具有很好的收敛速度和稳定性。针对国外某台28MWe富氧燃烧电厂实际烟气计算所需冷却塔填料高度。研究发现:L/G对填料高度和烟气出口湿度的影响相似。过低的L/G大大增加填料高度和烟气出口湿度,而过高的L/G并不能有效降低填料高度和烟气出口湿度,存在最优L/G范围。降低液体温度提高了冷却塔出口烟气的冷凝效率,但温度低于10℃,冷凝效率的提升有限。根据L/G与液体温度的关系,获得最优的液体温度为10℃,相应的最优L/G范围为3.4～4.5。
Optimization method is the foundation course in the major of Energy and Power Engineering,and currently the real cases related to the energy equipment are scarce.A case study of design of gas-liquid direct contact condenser was performed by the Quasi-Newton method.Ordinary differential equations were firstly constructed based on evaporation and condensation processes,and then were solved by the Newton method.In order to improve the stability of iteration,a new updated method based on the maximum temperature of liquid phase was developed,and the convergence rate as well as the stability was improved.This method was used to calculate the packing height of direct contact condenser in a 28 MWe Oxyfuel combustion power plant.Results indicate that the influence of L/Gon the packing height is similar to flue gas humidity at the outlet of condenser.Low L/Gratio greatly increases packing height and flue gas humidity at the outlet of condenser,while high L/Gratio does not reduce packing height and humidity significantly.Therefore,optimumL/Gratio range may exist.Reducing liquid temperature increases the condensation efficiency for the outlet of condenser,but when the liquid temperature is lower than 10 ℃,the improvement on the water removal efficiency is limited.Based on the relationship between L/Gratio and liquid temperature,the optimum liquid temperature is 10 ℃,and its related optimum L/Gratio range is 3.4～4.5.
Optimization method is the foundation course in the major of Energy and Power Engineering,and currently the real cases related to the energy equipment are scarce.A case study of design of gas-liquid direct contact condenser was performed by the Quasi-Newton method.Ordinary differential equations were firstly constructed based on evaporation and condensation processes,and then were solved by the Newton method.In order to improve the stability of iteration,a new updated method based on the maximum temperature of liquid phase was developed,and the convergence rate as well as the stability was improved.This method was used to calculate the packing height of direct contact condenser in a 28 MWe Oxyfuel combustion power plant.Results indicate that the influence of L/Gon the packing height is similar to flue gas humidity at the outlet of condenser.Low L/Gratio greatly increases packing height and flue gas humidity at the outlet of condenser,while high L/Gratio does not reduce packing height and humidity significantly.Therefore,optimumL/Gratio range may exist.Reducing liquid temperature increases the condensation efficiency for the outlet of condenser,but when the liquid temperature is lower than 10 ℃,the improvement on the water removal efficiency is limited.Based on the relationship between L/Gratio and liquid temperature,the optimum liquid temperature is 10 ℃,and its related optimum L/Gratio range is 3.4～4.5.
引文
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[2]TREYBAL R E.Adiabatic Gas Absorption and Stripping in Packed Towers[J].Industrial&Engineering Chemistry,2002,61(7):36-41.
[3]LI J D,SARAIREH M,THORPE G.Condensation of vapor in the presence of non-condensable gas in condensers[J].International Journal of Heat&Mass Transfer,2011,54(17):4078-4089.
[4]LI Y,KLAUSNER J F,MEI R,et al.Direct contact condensation in packed beds[J].International Journal of Heat&Mass Transfer,2006,49(25–26):4751-4761.
[5]OLANDER D.Design of Direct Contact Cooler-Condensers[J].Industrial&Engineering Chemistry,1961,53(2):121-126.
[6]KLAUSNER J F,LI Y,MEI R.Evaporative heat and mass transfer for the diffusion driven desalination process[J].Heat and Mass Transfer,2006,42(6):528-536.
[7]ALNAIMAT F,KLAUSNER J F,MEI R.Transient analysis of direct contact evaporation and condensation within packed beds[J].International Journal of Heat&Mass Transfer,2011,54(15):3381-3393.
[8]LLANO-RESTREPO M,MONSALVE-REYES R.Modeling and simulation of counterflow wet-cooling towers and the accurate calculation and correlation of mass transfer coefficients for thermal performance prediction[J].International Journal of Refrigeration,2017,74:45-70.
[9]LUCIA A,MACCHIETTO S.New approach to approximation of quantities involving physical properties derivatives in equation-oriented process design[J].AIChE Journal,1983,29(5):705-712.
[10]BROYDEN C G.A class of method for solving nonlinear simultaneous equation[J].Math Comp,1965,19(92):577-593.
[11]SCHUBERT L K.Modification of a quasi-Newton method for nonlinear equations with a sparse Jacobian[J].Mathematics of Computation,1970,24(109):27-30.
[12]BERNA T J,LOCKE M H,WESTERBERG A W.A new approach to optimization of chemical processes[J].AIChE Journal,1979,26(1):37-43.
[13]KUB CEK M,HLAV CEK V,PROCH SKA F.Global modular Newton-Raphson technique for simulation of an interconnected plant applied to complex rectification columns[J].Chemical Engineering Science,1976,31(4):277-284.
[14]SHACHAM M,MACCHIETO S,STUTZMAN L F,et al.Equation oriented approach to process flowsheeting[J].Computers&Chemical Engineering,1982,6(2):79-95.
[15]TAYLOR R,KRISHNAMURTHY R,FURNO J S,et al.Condensation of vapor mixtures.1.Nonequilibrium models and design procedures[J].Ind Eng Chem Process Des Dev,1986,25(1):83-97.
[16]SEIDER W D,BRENGEL D D,WIDAGDO S.Nonlinear analysis in process design[J].AIChE Journal,1991,37(1):1-38.
[17]MARWIL E.Convergence results for schubert's method for solving sparse nonlinear equations[J].SIAM Journal on Numerical Analysis,1979,16(4):588-604.
[18]SUN E T,STADTHERR M A.Issues in nonlinear equation solving in chemical engineering[J].Computers&Chemical Engineering,1988,12(11):1129-1139.
[19]LIU D,JIN J,GAO M,et al.A comparative study on the design of direct contact condenser for air and oxy-fuel combustion flue gas based on Callide Oxy-fuel Project[J].International Journal of Greenhouse Gas Control,2018,75:74-84.
[20]SPARROW E M,MINKOWYCZ W J,SADDY M.Forced convection condensation in the presence of noncondensables and interfacial resistance[J].International Journal of Heat&Mass Transfer,1967,10(12):1829-1845.
[21]SPERO C,YAMADA T,REES G,et al.Callide Oxyfuel Project:Overview of Commissioning Experience[C].OCC3.2013.
[22]FAIR J,STEINMEYER D,PENNEY W,et al.Gas absorption and gas-liquid system design[J].Engineering handbook New York:McGraw-Hill,1997,14-81.
[23]COKER A K.Packed towers[M].Ludwig's Applied Process Design for Chemical and Petrochemical Plants(Fourth Edition).Burlington;Gulf Professional Publishing.2007:483-678.
[24]LIU D,XIONG Z,JIN J,et al.Conceptual design of a packed bed for the removal of SO2in Oxy-fuel combustion prior to compression[J].International Journal of Greenhouse Gas Control,2016,53:65-78.
[25]PERRY R H,CHILTON C H.Chemical Engineers Handbook[M].Sixth edition ed.New York:McGraw-Hill Book Company,1984.