Study The Dynamic Behaviour Of Distillation Column With .

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Published by :http://www.ijert.orgInternational Journal of Engineering Research & Technology (IJERT)ISSN: 2278-0181Vol. 6 Issue 04, April-2017Study the Dynamic Behaviour of DistillationColumn with Fundamental Modelling andSimulation by MATLABGaurav ShuklaChemical Engineering Department,Aligarh Muslim UniversityAligarh, Uttar Pradesh 202001Abstract— Distillation columns are very substantial unitoperations in process industries. In the present work, wereviews some techniques of modelling and simulation ofdistillation columns and explain with the help of MATLABmodel for binary continuous distillation column. Simulationstudies are often used to examine the operational behaviour ofdistillation column. A rigorous model for the simulation of thesteady state behaviour of the distillation column. MESHequation, which actually represent the behaviour of thedistillation column has been solved through MATLAB, inorder to study the effect of different parameter. With theMATLAB software we study the dynamic behaviour of theproduct composition with the feed change with the time. In thispaper the effect of the feed condition and the feed compositionon the steady state behaviour. Developed code has been used tostudy the column and the result show that the compositionresponse to disturbance are close to the response of first ordersystem and also the response to change in feed composition haslarger gain than the response to change in feed flow rate.Validation of the developed code has been using by the otherauthor and is to be found in good agreement.Keywords- Binary Distillation Column, Relative Volatility,Modeling and Simulation, MATLABI. INTRODUCTIONDistillation column are most studied unit operation inchemical industries. Distillation is a process of separatingmixtures based on differences in their volatilities in a boilingliquid mixture. Distillation process may be classified in twocategories namely binary distillation and multicomponentdistillation. It is used to separate a mixture into itscomponents by the application and removal of heat. Itconsumes a huge amount of energy in both heating andcooling operations. There are many types of distillationcolumns based on different classifications such as: batch,conduct, tray, packed. In this paper we focus on continuousbinary distillation columns since continuous columns aremostly used in industry. The objective of analysismathematical model is to develop for binary distillationcolumn. The model is constructed based on the physicalproperties of the system, such as the preservation of mass,energy and momentum. The mathematical models rangefrom simple to rigorous models depending on the levels ofcomplexity and the assumptionsIJERTV6IS040665A continuous distillation column shown in Fig. 1. Thecolumn has N stages on which the vapor liquid equilibriumsoccur. The feed enters the column on the stage NF. This stagedivides the column into a rectifying section and a strippingsection. Near the bottom of the column is a reboiler whichprovides energy to the column. The mixture is heated toform a flow of vapor rising up inside the column. In thestripping section, the less volatile component is enrichedwhile in the rectifying section the more volatile componentis enriched. The top product is condensed by the condenserfrom which there is a reflux flow back to the top of thecolumn to enhance the purity of the product.In distillation column our main problem is to control itbecause of their highly nonlinear characteristics. It is definedas in distillation column in their multiple input and multipleoutput so there is several disturbance .We can easilyunderstand the non-linearity of distillation column. We canget if the product is purer the system become more nonlinear [3]. The term rectification is derived from the Latinwords rectefacere, meaning to improve. Modern distillationderives its ability to produce almost pure products from theuse of multi-stage contacting. In distillation columndisturbances comes from many side because the interactionoccurring the feed and the product are difficult to identify.The disturbance comes from either side i.e. the feed flowrate, feed composition, inside the column pressure, from thecooling water etc. From these disturbances number ofchallenge in running plant in control problem and so we cando lot of research in different discipline like electrical,mechanical and chemical.www.ijert.org(This work is licensed under a Creative Commons Attribution 4.0 International License.)800

Published by :http://www.ijert.orgInternational Journal of Engineering Research & Technology (IJERT)ISSN: 2278-0181Vol. 6 Issue 04, April-2017and half vaporized, with the design and operation of thecolumn remaining unchanged. By running the simulationsfor the distillation, it has been actually tried to establish thethermal condition of the feed that leads to a greater methanolconcentration in the liquid phase inside the column. Thesimulation calculations indicate that the latter is obtained bymeans of feeding a saturated liquid feed. It is alsoeconomical to feed the saturated liquid feed to the column,which is beneficial from two viewpoints, i.e., from theviewpoint of separation as can be seen from the graphs andalso from the heat economy viewpoint. To make the modelfrom this method advantage is global validity, accuracy.This method of modeling has the advantage of globalvalidity, accuracy. However, this method is quite complexfor controller design with huge amount of computation andsimplifications are often needed [1].Figure 1. A Two-product Distillation ColumnTo study the behaviour of distillation column first we shouldmake the model for distillation column. We can easilyunderstand behaviour of column by modelling , can guessnext reaction and therefore devise a control structure for thecolumn. In the present work study some importanttechniques in distillation column modeling. These MESHequations have been solved by making use of the solver‘fsolve’ in MATLAB, which can solve various non-linearequations simultaneously. The model has been simulatedunder different simulating conditions, viz., different feedconditions (saturated vapour, half vaporized and (saturatedliquid) and different feed compositions. A MATLAB codehas been developed in order to simulate the model fordifferent simulating conditions in order to study the impactof the different parameters on the steady-state performance.A brief outline of the work presented in we made the modelof continuous distillations in part II, the modeling of ourdistillation column is detailed in part III, the simulationresults are shown in part IV, and the conclusion and futurework are presented in part V of this paper. Objective of thepresented work to develop the code in MATLAB fordistillation column, to validate the code with available data,to study affect the operating variable.II.MODELING OF CONTINUOUS DISTILLATIONCOLUMNSWe can distinguish the modeling of distillation column inthree group: fundamental modeling, empirical modeling andhybrid modeling [1]. In fundamental modeling, we made themodel on conservation of physical properties such as mass,energy and momentum and ii depend on the accuracy ofassumption we use simple to rigorous model.Simulation calculations for the distillation column have beenmade in order to study its behaviour when feed of differenttypes are fed, for example, saturated liquid, saturated vaporIJERTV6IS040665In the empirical modeling uses the data from the running ofthe column to build the relationship between the input andthe output. With this method we do not need to understandthe inner dynamics of the column, and the computation canbe reduced. But in using this method we have to carry outexperiments on the real column, and the results may not beapplied for other column, even the results from one columncan be different if the column’s conditions are differentbetween the experiment and the actual operation of thecolumn.In the hybrid modeling, as we know the word hybrid, it iscombines the fundamental modeling and the empiricalmodeling. As it is hybrid modeling, it has advantages of theother two, but for that we need well structural model for thatwhich part of model model to use fundamental techniqueand which part to use empirical data. We made our modelwith fundamental modeling, but empirical model isdominantly use in industries. It is used because of that it iseasy to understand the dynamics The reasons that we wantto understand the dynamics of the distillation columns, andsince the empirical model may not be used to predict thebehaviour of the system at other operating conditions” [4].Martin-Sanchez (1976) developed the adaptive predictivecontrol system which is related to the traditional dead-beatcontrol idea of bringing a system to its final state or set pointin minimum time. It is characterized by the followingprinciples:(1) At each step a future desired process output is generated,and the control input is computed in order to make thepredicted process output equal to the desired process output.(2) The predicted output is based on an adaptive predictive(AP) model, whose parameters are estimated by a recursiveestimation law the objective of minimizing the predictionerror.(3) The previously mentioned desired process outputbelongs to a desired output trajectory, that satisfies a certainperformance criterion, e.g., this trajectory can start from thecurrent 'state' of the plant and evolve according to somechosen dynamics to the final desired set point.www.ijert.org(This work is licensed under a Creative Commons Attribution 4.0 International License.)801

Published by :http://www.ijert.orgInternational Journal of Engineering Research & Technology (IJERT)ISSN: 2278-0181Vol. 6 Issue 04, April-2017Cott et al. (1986) presented selection techniques forapproximate models of process model based controllers fordistillation columns. In their article they state what thequalities of an ideal model ought to be and then go on todevelop a selection procedure using the followingguidelines:the rigorous model. The simplifications are aimed to thevapor dynamics, to the energy balance and to the liquid flowdynamics. The paper recommends not neglecting liquiddynamics (i.e. not assuming constant liquid holdups) due tothe fact that the initial response, an important factor infeedback control, is largely affected by the liquid holdups.(1) Model AccuracyB. Wittgens and S. Skogestad carried out an evaluation ofdynamic models of distillation columns with emphasis onthe initial response. They found out that the most importantparameters are the liquid holdup, the liquid hydraulic timeconstant and the vapor constant that represent the initialeffect of a change in vapor flow on liquid flow.(2) Model Selection Procedure(3) Model Parameter Update.Luyben et al. extensively covers the dynamics ofmulticomponent distillation columns, and presents analgorithm using Euler's method to solve the differentialequations. In his approach almost all possible nonlinearitiesare eliminated by local linearization, using the followingAssumptions:(1) There is one feed plate onto which vapour and liquid feedare introduced.(2) Pressure is constant on each tray but varies linearly upthe column.(3) Coolant and steam dynamics are negligible in condenserand reboiler.(4) Vapor and liquid products are taken off the reflux drumand in equilibrium. Dynamics of vapor space in reflux drumare negligible.(5) Liquid hydraulics are calculated from the Francis weirformula.(6) Volumetric holdups in the reflux drum and column baseare held constant by changing the bottoms and distillaterates.(7) Dynamic changes in internal energy on trays arenegligible compared with latent-heat effects, so the energyequation on each tray is just algebraic. Luyben also presentsa code for the algorithm in his text. However, with theavailability of some differential equation solving packages,Euler's method is inefficient by contrast.Sourisseau and Doherty (1982) studied various differentdynamic models and classified them according to the statevariables employed. Following their definitions, a model inwhich the state vector consists of only liquid compositionswas called the C-model. If both compositions and enthalpiesare included, the CE-model results. The most complexmodel is the CHE-model and has a differential equation foreach state variable on each tray (composition, holdup andenthalpy). The constant molar-overflow model (CMOmodel), assumes fast holdup and energy changes as well asfixed liquid and vapor rates at all times.S. Skogestad did a critical survey of literature on dynamicsand control of distillation columns up until 1991. The papersummarized the simplifications of the rigorous model sinceno references had been found on solving all the equations ofIJERTV6IS040665Abdulla et al. have done a quite complete review on therecent nonlinear modeling applications in continuousdistillation column. The summary states that the empiricalmodeling has been preferred in industry because of itssimplicity compared to the fundamental model; and thecurrent development focuses on hybrid models, which canexploit the advantages of both fundamental model andempirical model; and that the neural network method is usedthe most to combine with the fundamental model inempirical modeling.In the case of fundamental modeling, the model is oftensimulated to understand the column’s dynamic behaviour.The development of distillation column’s simulation hasbeen going along with the growth of computing capacity. Asof 1930s and 1940s only graphical methods andSimple short-cut models were used to get insights of thesteady-state behaviour of the distillation columns. The fastgrowing of computing power has allowed the use of morecomplex and rigorous models. Computer programming andthe numerical methods to solve the differential equationsplay an important role.A MATLAB code has been developed in order to simulatethe model for different simulating conditions in order tostudy the impact of the different parameters on the steadystate performanceIII. MODELING OF THE APCThe APC (Advanced Process Control) column is a pilotdistillation column that has 15 trays and equipped with aDCS control system. The feed is positioned at tray 7. In themodel the following assumptions are made:1. Binary mixture, the feed contains only two components2. The pressure inside the column is fixed by controlling thecooling water3. Constant relative volatility, α 1.54. Constant molar flows5. No vapor holdup, the vapor holdup on each tray isnegligible6. Linear liquid dynamics7. Equilibrium on all stages8. Total condenser, there is no vapor holdup in thecondenserwww.ijert.org(This work is licensed under a Creative Commons Attribution 4.0 International License.)802

Published by :http://www.ijert.orgInternational Journal of Engineering Research & Technology (IJERT)ISSN: 2278-0181Vol. 6 Issue 04, April-2017STEADY-STATE MODELING OF A DISTILLATIONCOLUMNA rigorous steady-state column model was developedusing MESH equations which actually represent thebehaviour of the column where xi and yi is thecomposition of the light component and heavycomponent on tray i respectively. At the feed stage(NF 7). We have Figure shows the schematic of aseparation stage. The model consists of mass balance,equilibrium relation, summation equations and energybalance, which are collectively known as MESHequationsEnergy BalanceThe total energy balance for ‘jth’ stage is given by:Lj-1 hLj-1 Vj 1 hvj 1 FjhF,j – ( Lj Vj) hLj – ( Vj Wj)hvj – Qj 0 7The composition of the heavy component is related to thecomposition of the light component via the relativevolatility formula𝛼𝑥𝑖𝑦𝑖 1 (𝛼 1)𝑥𝑖 .8The liquid flow dynamics is considered due to its importanteffect on the initial response of the column. The formulasfor the liquid holdup are:Li L0,b 𝑀𝑖 𝑀𝑜,𝑖Li L0,b 𝜏𝑀𝑖 𝑀0,𝑖𝜏 ( Vi-1- V0) α .9 ( Vi-1- V0) α .10for i from NF 1 to NT-1 where L0 is the nominal reflux flowand M0i is the nominal reboiler holdup (kmol) on stage i.These values are achieved after we do steady statesimulation (see Table 1). τ is the time constant for liquiddynamics, in this model it is chosen to be 0.063 (min), and λrepresents the effect of vapor flow on liquid flow. In thesimulation we ignore this effect by setting λ 0.Mass BalanceL0b L0 qF0F0The model equations for a general ‘j ’ stage and ‘i ’component are represented as:thLj-1 xj-1,I Vj 1yj 1i FZj,i- (Vj 𝑠𝑗𝑣 ) y j,I – (Lj 𝑠𝑗𝑙 ) 0 .1And in terms of the flow rate of components, aboveequation can be written as:lj-1,I Vj 1,i ,fji – vj,i - 𝑠𝑗𝑙 𝑙𝑗, 𝑖 𝑠𝑗𝑖𝑣 0 2whereli,j Lj xij 3Vi,j Vjyij .4Vj 𝑐𝑖 1 𝑉𝑖, 𝑗 .5Equilibrium RelationshipThe compositions of the streams leaving a stage are inequilibrium. Therefore, the mole fractions of the com ponent‘i’ in the liquid and vapor streams leaving stage ‘j’ arerelated by the equilibrium relation shown in the equationgiven below:y j,i Kj,i xj,IIJERTV6IS040665 .(11)th .6in which F0 1(kmol/min) is the nominal feed rate,qF0 1 is the nominal fraction of liquid in the feed.IV. SIMULATION RESULTS AND DISCUSSIONThe main objective is to modelling and simulation is tocheck the response of distillation column. In the presentwork we want to see how the column respond when thechange due to disturbance in feed and output composition.We found that the our main focus is to control thedistillation column because it effect the dynamic of column.We do the simulation with the help of MATLAB. We runthe program till the steady state. The steady state data isshown in figure.TABLE I. STEADY STATE DATA OF THE COLUMNZFΑNNFXDXwDB0.52.10940.920.070.50.5After simulating, when we get the steady state, we check thecomposition under different disturbance. We choose a stepchange in feed flow rate because of most frequentdisturbance. We check the response in the composition ofthe light component at the reboiler (XB) and at the condenser(XD) when the magnitude of the step change. We must thelevel distillate and bottom tank kept constant simulating bychanging the distillate and bottom (B) flows. In our modelboth level control by PI control with gain equal to 8.www.ijert.org(This work is licensed under a Creative Commons Attribution 4.0 International License.)803

Published by :http://www.ijert.orgInternational Journal of Engineering Research & Technology (IJERT)ISSN: 2278-0181Vol. 6 Issue 04, April-2017Fig. 2 shows the changes in compositions due to 1% increases in feed flow rate.Figure 2. Composition responses to 1% step increase in feedflow rate For 1% increase in feed flow rate, the response ofXD has a time constant of about 17 minutes while theresponse of XB has a time constant of 11 minutes. Theoutput result showing in the curve is the response of a firstorder system in varying the time constants as we know the(the value of reaches 63.2 percent of its ultimate value whenthe time elapsed is equal to one time constant), which is gooddeal with the other author.[7],[8].simulate our model with two step change 1% to 20% . Theoutput result shown in table II.Table II . Time constants (in minutes) of the compositionchanges due to different feed flow rate perturbations1%10%15%20%XD22201615XW16171310In digram 3 , after the simulating when we increase the feedflow rate 10% which are 15 minutes and 10 minutesrespectively. We can see the responses in this case are fasterthan in the case of 1% increase in feed flow rate. WeFigure 3. Composition responses to 10% step increase in feed flow rateIJERTV6IS040665www.ijert.org(This work is licensed under a Creative Commons Attribution 4.0 International License.)804

Published by :http://www.ijert.orgInternational Journal of Engineering Research & Technology (IJERT)ISSN: 2278-0181Vol. 6 Issue 04, April-2017After the simulating from the simulation results it is easilyobserved that the slow respond of the composition of thedistillation columns which has been in

Study the Dynamic Behaviour of Distillation Column with Fundamental Modelling and Simulation by MATLAB . Gaurav Shukla . Chemical Engineering Department, Aligarh Muslim University . Aligarh, Uttar Pradesh 202001 . Abstract— A continuous distillation column shown in Fig.

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