# Operational Optimization of Ideal Internal Thermally Coupled Distillation Columns.

код для вставкиСкачатьDev. Chem Eng. Mineral Process., 9(lR).pp.133-142. 2001. Operational Optimization of Ideal Internal Thermally Coupled Distillation Columns Xing-Gao Liu* and Ji-Xin Qian National Laboratoiy of Industrial Control Technology, Institute of IndustriaI Process Control, Zhejiang University, Hangzhou 310027, RR.China Lack of the optimal operation parameters in operation is one of major diflculties associated with the we of advanced mew saving distillation methods. In this paper, the operational optimization of the ideal Internal Thermally Coupled Distillation Column (ITCDICJ is considered. An optimization model and the related simulation algorithm are proposed, An optimization and the related result analysis are cam'ed out, which pave the way forfirrther design studies and its practical application. Introduction Distillation consumes a Iarge percentage of the energy used in the chemical process industries. Consequently, there is a significant incentive to improve the energy efficiency of this widely applied separation process. Thee are various methods of reducing external energy q u t s by the effective use of heat energy in the distillation system [I-31,such as multi-effect columns, side cooler-side heater, heat pumps and secondary reflux and vaporization (SRV). Energy recovery by heat transfer from the rectifying section to the stripping section is an effective method for energy savings in distillation columns. This method, first proposed by Mah et al. [4], is called SRV method. Since thea, there are extensive studies of SRV [5-61. ITCDIC is a distillation column where energy savings are realized by SRV method, which has neither a reboiler nor a condenser and possesses large potential of energy reduction [7-91. However, one of the major difficulties associated with the use of such advanced energy saving columns is a lack of operational optimization in operation [IO], i.e., how to get the optimal operation parameters. This paper will address the operational optimization of ideal ITCDIC. First,an optimizationmodel of ideal ITCDIC is proposed, upon which the optimal operation parameters can be archived simultaneously guaranteeing both the product quality and the maximumenergy savings. A related simulation algorithm is presented The simulation and the result analysis of the steady state are carried out. Finally, the optimization and the optimization analysis are canied out. From our current knowledge, no one has worked in this area. Optimization Model Figure 1 shows the schematic diagram of the ideal ITCDIC.The rectifjmg section ~~ * Author for correspondence (e-mail: liuxinggao@263.net). Current Address: Institute of Process Control Engineering, Department of Automation, Tsinghua University, Beijing 1OOO84, l? R China. 133 X.-C. Liu and J.-X. Qian and the stripping section are separated into two columns. The manipulation of internal thermal coupling is accomplished through heat exchanger between the two sections. In order to provide the necessary temperature driving force for the heat transferred from the rectieing section to the stripping section, the former must be operated at a higher pressure than the latter. To adjust the pressure, a compressor and a throttling valve are installed between the two sections. Because of the internal t h e m 1 coupling, a certain amount of heat is transferred from the rectifying section to the stripping section and brings the downward reflux flow for the former and the upward vapor flow for the latter. As a result, a condenser and a reboiler are not required and energy savings are realized. Figure 1. Schematic diagram of ITCDIC. The optimization model of the ideal ITCDIC is derived by applying energy, component, and overall material balances, and vapor-liquid equilibrium under the following assumptions: (1) Negligible vapor holdups, liquid molar holdups on each tray being constant; (2) Perfect liquid and vapor mixing on each tray, the temperature and the composition on each iray being unifonq (3) Vapor-liquid equilibrium for streams leaving each tray; (4) Instantaneous heat transfer from the rectifying section to the stripping section and the transportation of liquid and vapor between trays; ( 5 ) Negligible pressure drop in each column; (6) Negligible hydraulic delay occuniug in the liquid flows; (7) Heat loss and heat capacity change of the separation process being negligible; (8) No time delay in column pressure changes and feed thermal condition; (9) Equal and constant latent heat of each component; (1O)The relative volatility is constant; (11)No vapor and liquid side-stream withdraw. For a separation process, the minimum amount of thermodynamic energy required to make a complete separation is given by the following equation: W,, = F (AH-TAS) For an ideal mixture, equation (1) can be expressed as: 134 (1) Ideal Internal Thermally Coupled Distillation Columns [X,,, (2) Wm,n is a thermodynamic term that is independent of any particular process. Actual processes operate with finite driving forces, whch are irreversible and consume more energy than the thermodynamic minimum. For conventional distillation columns (CDIC), minimum energy required for the separation process (Q,,,ln,con) is the minimumreboiler energy requirement. With the use of the McCabe-Thiele diagram, Qm,,,con for a binary mixture can be shown to be a function of the heat of vaporization of the bottom product, relative volatility, and feed composition. For complete separation, when feed thermal condition q=l, there is: Wmin = FRTqXfi Ua-1) 5 1 (3) The maximum thermodynamic efficiency (Em) is defined as the minimm thermodynamic energy ( W,,,,,) divided by minimum energy required for a separation process (Q,,,J,so for conventional distillation: Qmmcon = Fmb,v [ Em,con= Wmid Qmm.con = RT4xfi lflfi)/{ m b . v [ ll(a-1) (4) 51 } For the ideal ITCDIC, the energy required for the separation process (Qlcd)is composed of the heat for preheating feed and the work of compressor ( Wcmp),that is Qtcd = F(1-q)mjv + K o m p (5) We choose the compressor work as: wcomp = v/K/((K-~)RT,((P~/P,)(~-*~~ -1) (6) For gas mixture, 1/(K-1 ) = 4YJ(Kl- 1 ) ) (7) So we achieve thermodynamic efficiency of fully ideal ITCDIC (Et&): Etcd = wmd Qtcd = FR T 4 x , 1X,M F( 1 q)mjv+ Wcomp (8) 1 which has a profound impact on the overall cost of the separation process. Comparing with the the maximum thermodynamic efficiency of conventional distillation thermodynamic efficiency of ideal ITCDIC (Etc& we can know the energy saving effect of the ideal ITCDIC directly. The percentage of thennodynamic efficiency enhancement of the ideal ITCDIC (XJis defined as follows: x e = (Etcd - ~ m , c o n/)E m , c o n (9) For conventional distillation, energy required for the separation process under the minimumreflux ratio (Rmm)operation (Qmm,cm) can be calculated by: Qnnmcon = F ( 1 - q ) m j v +[ ( ~ r n i n + ~ ) ~ - ~ ( ~ - ~ ) I ~ b , v (10) where D is the top distillation product flow rate. The percentage of energy savings of the ideal ITCDIC is defined as follows: 135 X.-G. Liu and J.-X. Qian x,= (Qnnin.con-Qted) (11) 1Qnninxon which shows the energy saving effect directly. When the stages are numbered with the top as the stage 1 and the bottom as the stage n, the basic equations o f the ideal ITCDIC are presented as follows: Thermal coupling [4,7,9]: Qj = UA(I;-Tj+/.l) I;. = b/( a-LnPvi j=1,. ..,f- 1 )-c Mass balances: j=l,. ..,f-1 j=l,. ..,f-2 k=l Ln = F-Vl Vl = F( 1-4) 4*]= V1+Lj J=1,. ..,f-1 j=l,. ..,f-2 k=l Vapor-Liquid equilibrium relationships: I;= d j / [ ( a - l v j + l ] Component balances: Equations (1)-(25)consist of the dynamic mathematical model o f an ideal ITCDIC. For steady state studies, let: &/dt = 0 (26) the dynamic model then becomes steady state model. The mathematical models above including the dynamic and the steady state models provide an efficient tool for operation studes, and can be used for further control, design and optimization studies. We select X, as the objective function. For Merent product qualities, such as top 136 Ideal Internal Thermally Coupled Distillation Columns product composition Y l 2 96%, bottom product composition Xnl5% or Ylr 98%, Xn14%, there should be Merent optimizing results of energy savings. So a constraint should be set on product qualities, such as top product composition Y1296%, bottom product compositionXn15%. For total separation effect, we have: FZy 2 V IYI (27) The equality constraints are equations (1)+26). The optimization goal is to find the optimal operating parameters Pr and q so that the energy saving is maximum compared with the energy required of CDIC under the minimum reflux ratio and the product qualities are guaranteed simultaneously. The energy saving optimization model of the ideal ITCDIC is derived as following: ITCDIC min. f (Pr,(I)= -X, (MOPT1) Eqs. (1-26) Product quality constraints (such as: Y,298%, Xn s 4%) V,YyFZ’SO 0.1013MPa S Pr 5 1.013MPa ~.t. O l q l l OlX*Il o q < 1 It is a nonlinear programming (Np) constrained optimization problem. The optimization program is programmed using the “Matlab Language”. The optimization a l g o r i h used is the Sequential Quadratic Programming (SQP)method. Simulation and Analysis In following simulation and optimization,a 30-stage ideal ITCDIC is considered as an ihstrative example, where a binary mixhue of benzene-toluene is separated. Its detailed operation conditions are shown in Table 1. Table I . Given operating conditionsfor the simulation. Stage number Feed stage Feed flow rate Feed composition (Benzene) (Toluene) Feed thermal condition Pressure of rectifying section Pressure of stripping section Heat transfer rate Latent heat of vaporization Relative volatility 30 16 100 Ian0l.K’ 0.5 0.5 0-1 0.1013-1 .O 13MPa 0.1013MPa 9803 W K ’ 30001.1 kJ.kmor’ 2.317 137 X.-G. L ~ and u J.-X. Qian The adiabatic index number ( K ) calculation uses the heat capacity equation of an ideal gas. The physical data used in simulation are listed in Table 2. Table 2. Physical data used in the simulation. Antoine constants: a b C Benzene Toluene 15.9008 2788.51 -52.36 16.0137 3096.52 -53.67 Ideal gas heat capacity equation parameters: A -8.101 B 1.1 33E-1 C -7.206E-5 D 1.703E-8 -5.817 1.224E-1 -6.605E-5 1.173E-8 The simulation programs are programmed using "Matlab Language". The steady state simulation procedure is illustrated as follows: 1. give operation condition and physical data : N J l?f i Ps. ZJ q, UA; a, b, c; A, B, C,D ; 2. give termination criteria (E) that is a measure of the worst case precision required of the independent variables; 3. give initial values ofX,(k). 4. calculate I;@), T&), P,~(k).Qj(k), LjF)?Q(k) from Eqs. (lW21); from Eqs. (22)-(26); 5. calculate 4(k+l) 6. when /q(k+I)-q(k) /<E, go to step (7); if not,q(k+I)+(k,), and go to step 4; 7. calculate Qmin.con , Q r C d , X, from Eqs. (5)47), (9)4 11); 8. calculate E,cd X,from Eqs. ( 1 ) ( 4 ) , (8)-(9). We choose PI and q as manipulated variables to inspect the system and its energy savings. Some simulation results are shown in Table 3.For conventional distillation, the maximum thermodynamic efficiency of the Benzene-Toluene system is 5.1 1%. But for the ideal ITCDIC, inTable4 the minimum thermodynamic efficiency is Table 3. Simulation results of the Benzene-Toluene system. N o 1 2 3 4 5 6 7 8 9 Manipulating Parameters 4 0.25 0.25 0.25 0.5 0.5 0.5 0.75 0.75 0.75 pr E-.cm 4.c~ Xe 0.1519 0.2532 0.3545 0.1519 0.2532 0.3545 0.1519 0.2532 0.3545 0.6373/0.0880 0.6666/0.0003 0.6667/0.oooO 0.770810.2292 0.9384/0.0616 0.9887/0.0113 0.909U0.3636 0.999710.3334 1.0000/0.3333 0.0511 0.0511 0.051 1 0.051 1 0.051I 0.05 11 0.0511 0.0511 0.0511 0.0813 0.0736 0.0692 0.1173 0.1019 0.0936 0.2103 0.1656 0.1447 59.26 44.19 35.48 129.69 99.60 83.29 311.79 224.17 183.23 Pr is m a ; Q is kWx106 138 System Characteristic Performance Parameters Product quality Yllxn 9% Qrnin.m. 4.9122 4.9122 4.9122 4.4928 4.4928 4.4928 4.1562 4.1562 4.1562 Qtcd 2.6042 2.8764 3.0613 1.8057 2.0779 2.2628 1.0072 1.2794 1.4643 Xs ,% 46.99 41.44 37.68 59.81 53.75 49.64 75.71 69.22 64.77 Ideal Internal Thermally Coupled Distillation Columns Table 4. Optimization results of the Benzene-Toluene system. Product quality constrains Y,2 XnS Achieved optimal operation Pc MPa parameters 9 System characteristics under Yl optimal operation parameters Xn Qmin.con. l 0 k W 1 0 % ~ elc,+ Maximum energy savings X,, % 96% 5% 0.2826 0.5111 0.9705 0.0500 4.3933 2.0803 52.65 98% 4% 0.3006 0.5107 0.9800 0.0400 4.4768 2.1375 52.25 6.92%, enhancing 35.48%, and the related energy saving percentage is 37.68%; the maximum thermodynamic efficiency is 2 1.03%, enhancing 3 11.79%, and the related energy saving percentage is 75.77%. Obviously, the ideal ITCDIC can save more energy than conventional distillation, and the effect of energy savings is marked. When the feed thermal condhon, q, is 0.25, 0.5, 0.75 and pressure of rectifying section, Pr, is 0.15 19MPa, 0.2532MPa, 0.3545MPaYrespectively, the product qualities change from 63.73% to 100.00% for Yl, and from 0.00% to 36.36% for Xn. The performance parameter ElCdchanges from 6.92% to 2 1.03%; X, changes from 35.48% to 311.79%; and X, changes from 37.68% to 75.77%. It shows that there are very complicated relations and very large changes among energy saving, X,,manipulation parameters, h,q, and product quality, Xn, Y,. Hence, there should be an optimization between operation parameters and system characteristics. Optimization Result and Discussion The optimization results of operation variables of the ideal ITCDIC are shown in Table 4. For the Benzene-Toluene system, when top product composition Y, 2 98%, bottom product composition Xn I4%, the optimal operation variables and the maximum energy savings are achieved. The rectifying section pressure Pr, 0.3006MPa, the feed thermal condition q, 0.5107, the other operation conditions are the same as in Table 2. Under the above operation conditions, the percentage of energy savings of ideal ITCDIC is 52.25%. Table 5 lists other study results. Comparing the results of Table 5 with those of Table 4, it is seen that the ideal ITCDIC method saves more energy. Energy recovery by heat transfer from the Table 5. Results of other studies. Author Energy savings Studied system ethyl benzene/ dimethyl benzene non-ideal mixtureof Li [12], 1995 33.14% ethanol, ether etc. ethylend ethane etc. Mah [4], 1977 54%* Finn 1131, 1993 16% i-butand n-butane *Indicate relative steam consumption Yang [ I l l , 1990 50% Column construction Compared with petlyuk actual CDlC petlyuk actual CDlC SRV. actual CDlC direct sequence rectifier side rectifier 139 X.-G.Liu and J. -X.Qian rectifying section to the stripping section is an effective method for energy savings in distillation columns. Figure 2 shows the operating line contrast figure of the ideal ITCDIC under one of the optimal operating conditions, Pr, 0.2826MPa and q, 0.5111. For a conventional distillation column under the minimum operating reflux ratio, product quality requirements are the same as those of the ideal ITCDIC. Other parameters are the same as those in Table 1. 0 02 04 0.6 lqud mnpostmnX 08 Figure 2. Operating line contrast figure, P ~ 0 . 2 8 2 6q=O.5111. , Owing to the internal thermal coupllng between the rectifying and stripping sections where the operating line is very close to the equilibrium line. Especially, near the top and the bottom stage number, the driving forces of mass and heat transfer of ITCDIC have been significantly reduced compared with the conventional distillation columns (even under minimum reflux operation). Hence the process irreversibilityhas been sigmfkantly reduced. From the viewpoint of thermodynamics, large energy losses for the separation process usually occur due to the irreversibility of processes. The result is that either fewer stages are needed to accomplish the same separation, or better separation effect is obtained with the same number of stages at the same energy consumption, and energy savings occur in the ideal ITCDIC process. Conclusions This paper gives an effective method to obtain the optimal operation parameters of the ' ideal ITCDIC. The illustrative example shows its validity. For other systems, such as non-ideal mixture separation, the optimization model can be also applied, the only thing needed is to change the given conditions, physical data and vapor-liquid equilibrium relationships. Based on the study in h s paper, we have developed the relative s o h a r e "ENORM", which is very useful for future research on ITCDIC and its practical application. Further investigation is underway to study the control and design of ITCDIC. I40 Ideal Internal Thermally Coupled Distillation Columns Acknowledgment The authors thank the National Environmental Protect Bureau of P. R. China (HuanKe-Ke, 1997, No. 006, Project 14) for financial support. Nomenclature Thermodynamic efficiency Percent energy saving Percent thermodynamic efficiency enhancement x e Feed F Stage holdups H Adiabatic index number of gas K Liquid flow rate L Number of total stages n Vapor saturation pressure Atp Pressure of rectifying sectiona pr Pressure of stripping section Ps Representation of either Pr or Ps P Feed thermal condition 4 Energy require Q General gas constant R Minimum reflux ratio Rmin Time t Absolute temperature T Heat transfer rate UA Vapor flow rate V Thermodynamic work W Mole fraction of liquid X Mole fraction of vapor Y Mole fiaction of feed 5 Change in enthalpy and entropy AH,ds Relative volatility a latent heat. A E 4 (kJ/lanol) Subscripts b Bottom comp Compressor con Conventional distillation column f Feed stage 1 Component j Stage number maX Maximum amount min Minimum amount rmin Minimumrefluxratio tcd The ideal ITCDIC V Vaporization I41 X.-G. Liu and J.-X. Qian References Lang, L. 1996. Dynamic Behavior and Operational Aspects of Heat-Integrated Distillation Processes. Chem. Eng. Tech., 19,498-497. 2. Umeda, T., Niida, K., and Shiroko, K. 1979. A Thermodynamic Approach to Heat Integration in Distillation Systems. AlChE J., 25(3), 423-429. 3. Linnhoff, B. 1993. Pinch Analysis - A State of the Art Review. Trans. IChemE., 71A, 503-51 1. 4. Mah, R.S.H.,Nicholas, J.J., and Wodnik, RB. 1977. Distillation with Secondary Reflux and Vaporization: A Comparative Evaluation. AlChE J., 23(5), 651-658. 5. Shimizu, K., Holt, B.R., et al. 1985. Assessment of Control Structures for Binary Distillation Columns with Secondary Reflux and Vaporization. Ind. Eng. Chem. Pro. Des.Dev., 24,852-858. 6. Fitmwrris, RE., and Mah, R.S.H. 1980. Improving Distillation Columns Design Using ThermodynamicAvailability Analysis. AIChE J., 26(2), 265-273. 7. Humg, K.J., Qian, Ji-Xin, et al. 1997. Steady-state operation analysis of an ideal heat integrated distillation column. Chinese J. Chem. Eng., 5(4), 325-336. 8. Lueprasitsakul, V., Hasebe, S., et al. 1990. Analyses of the characteristics of a binary packed distillation column with internal heat integration. J. Chem. Eng. Japan, 23(6), 686-691. 9. Lestak, F., Smith, R., and Dhole, V.R 1994. Heat Transfer Across the Wall of Dividing Wall Columns. Trans.IChemE., 72(A9), 639-644. 10. Glinos, K., and Malone, M.F. 1988. Optimality regions for complex column alternatives in distillation systems. Chem. h g . R ~ s D~s., . 66,229-240. 11. Yang, Y. Q. 1990. Simulation Study of Operational Performance of Thermally Coupled Distillation. J. Chern. Ind Eng. (Chinese), 41(4), 491-497. 12. Li, F. H.,Fan, X. S., and Yao,P. J. 1995. Study on the Feasibility of Employing Thermally Coupled Distillation Tower to Save Energy. Shi You Hua Gong (Chinese), 24(1 I), 783-798. 13. Finn, A.J. 1993. Consider Thermally Coupled Distillation. Chem. Eng. Pro., Oct., 41-45 1. Received: 28 October 1999; Accepted afier revision: 24 May 2000. I42

1/--страниц