CHAPTER 3 MODELLING OF DISTILLATION COLUMN

Transcription

1 4 CHAPTER 3 MODEIG O DISTIATIO COUM In ths chapter, the bass of dstllaton, need for dstllaton control and dfferent control technques are descrbed. Model of W and Skogestad column s presented. euro model and fuzzy model dentfcatons are also explaned. 3. DISTIATIO Dstllaton s one of the most mportant unt operatons n chemcal engneerng. The am of a dstllaton column s to separate a mxture of components nto two or more products of dfferent compostons. The physcal prncple of separaton n dstllaton s the dfference n the volatlty of the components. The separaton takes place n a vertcal column where heat s added to a reboler at the bottom and removed from condenser at the top. A stream of vapour produced n the reboler rses through the column and s forced nto contact wth a lqud stream from the condenser flowng downwards n the column. The volatle (lght) components are enrched n the vapour phase and the less volatle (heavy) components are enrched n the lqud phase. A product stream taken from the top of the column therefore manly contans lght components, whle a stream taken from the bottom contans heavy components.

2 Dstllaton Equpment A smple contnuous bnary tray dstllaton column for separatng a feed stream nto two fractons, an overhead dstllate product and a bottoms product s shown n gure 3.. The nsde of the column s normally provded wth horzontal plates or trays. The lqud mxture to be separated s ntroduced more or less centrally nto a vertcal cascade of trays. A reboler s provded at the bottom of the column to supply the heat requred for the vaporzaton nvolved n dstllaton and also to compensate for heat loss. A water-cooled or ar-cooled condenser s provded at the top of the column to condense and cool the overhead stream. The purty of the top product can be mproved by recyclng some of the externally condensed top product lqud as reflux from the upper part of the column. gure 3. Control scheme of bnary dstllaton column

3 43 The more reflux that s provded, the better s the column separaton of the lower bolng from the hgher bolng components of the feed. The feed tray dvdes column nto two parts namely rectfyng secton and strppng secton. In rectfyng secton, the vapour rsng s rectfed wth lqud flowng down from top to remove less volatle component and n strppng secton the lqud s strpped of volatle components by vapour produced at bottom by partal vaporzaton of bottom lqud n reboler. The condensed lqud that s removed from reflux drum s known as dstllate or top product and the lqud removed from reboler s known as bottom product eed for Dstllaton Control Dstllaton s used n many process ndustres for separatng feed streams and for purfcaton of fnal and ntermedate product streams. There are many reasons for the nterest n dstllaton control. rom an academc pont of vew dstllaton control s an nterestng multvarable problem, and from an ndustral pont of vew mproved dstllaton control has a potental to substantally ncrease the proft. Dstllaton accounts for approxmately 95% of the separaton systems used for refnng and n chemcal ndustres. It has a major mpact upon the product qualty, energy usage, and plant throughput of these ndustres. It consumes enormous amounts of energy, both n terms of coolng and heatng requrements. It can contrbute to more than 50% of plant operatng costs. The energy requrement may be reduced sgnfcantly through mproved operatons. Ths s acheved not only through optmal column desgn, but requres, n adon, a control system whch s able to mantan the optmal conons. Dstllaton control s a challengng endeavour due to () the nherent nonlnearty of dstllaton, (2) multvarable nteracton, (3) the nonstatonary behavor and, (4) the severty of dsturbances (Shnskey 984). Tghter control of dstllaton columns s consequently mportant for energy

4 44 savngs, and wll also yeld ncreased proft through mproved product recovery. The major benefts of mproved dstllaton control are reduced energy consumpton, ncreased yeld and hgher throughput Dstllaton Control Technques Dstllaton columns provde a very challengng example wthn the feld of process dynamcs and process control. Traonally PID controllers were used n the process ndustres for control of the dstllaton column. The man drawback of the conventonal feedback PID control s that correctve acton for dsturbances does not begn untl the controlled varable devates from the set pont (Skogestad 997). In ndustry, most of the columns are operated by SISO controllers and usually only one composton s automatcally controlled (one pont control). Ths leads to waste of valuable products and excessve energy. However, automatc control of both compostons may be very dffcult to obtan due to strong nteracton between top and bottom product compostons (Shnskey 984). Skogestad et al (988) have reported that hgh purty columns,.e. columns where both top and bottom compostons are very pure, suffer from strong nteracton whch makes the system very senstve to small changes n the manpulated varables (nput uncertanty). Wthout a rgorous method for dealng wth uncertanty t may be practcally mpossble to tune a two pont controller for a system wth strong nteracton. Ths may n fact be one of the reasons to why one pont control s so commonly used. Another dsadvantage wth such a decentralzed (multloop) control s that the control performance may serously deterorate f the system ht some constrants. or example, f a stablzng loop saturates, the system goes unstable. To avod ths, the plant has to be operated suffcently far away from the constrants, or facltes for reconfguraton have to be nstalled on-top of the SISO controllers (undstrom and Skogestad 995).

5 45 Confguraton selecton s an mportant aspect n the case of multloop controller desgn. Control confguraton for a dstllaton column can be selected from the knowledge of the thermodynamc parameters, reflux rato, vapor bol-up rate and dstllate to bottoms rato for bnary and multcomponent dstllaton (Stlchmar 995). Improper choce of manpulated/controlled varable parngs can result n poor control performance. Decouplers are ntroduced nto the multloop confguraton to compensate for the process nteractons and reduce the control loop nteractons. Hurowtz et al (2003) have used decouplers to control the top product composton usng reflux flow rate, bottom product composton usng vapour bol-up rate for the xylene/toluene column and the depropanzer. In both cases, the decouplers resulted n mproved control performance compared to the feedback controllers wthout a decoupler. The nsuffcent performance of SISO controllers lead to the development of specalzed sngle loop control strateges such as feed-forward control (roll et al 995), nferental control (Zhang and Agustryanto 200), cascade control (Kano et al 2000), adaptve control (atarajan et al 2006) etc. The abltes of the specalzed sngle-loop control strateges and multloop controllers were not satsfactory for ncreasngly strngent performance requrements of the chemcal processes whch led to the development of multvarable control technques Multvarable Controllers Processes whch are multvarable n nature,.e. processes where the varables to control and the varables avalable to manpulate cannot be separated nto ndependent loops, where one nput only would affect one output, consttute a major source of dffculty n process control. These processes show a certan degree of nteracton,.e. the change n process

6 46 varables of one control loop affects that of other loop. The complexty of the control problem ncreases as ths nteracton ncreases (uyben 992). Multvarable processes n ndustral and other applcatons are often of hgher order, where there are many, possbly tens or hundreds, of control loops nteractng (Postlethwate and Skogestad 996). The term multvarable control refers to the class of control strateges n whch each manpulated varable s adjusted on the bass of errors n all of the controlled varables, rather than the error n the sngle controlled varable, as n the case of multloop control. Multvarable control s partcularly well-suted for controllng processes wth several nteractng controls whch need to be smultaneously decoupled. An adequate model s generally consdered as a prerequste for multvarable controller desgn. The model s used to predct the behavour of the controlled varables wth respect to changes n the nput varables (Sagfors and Waller 998). Establshed multvarable control technques rely on the avalablty of the lnear system models. Ths s to ensure that the resultng control scheme s closely matched to the dynamcs of the process. The multvarable system must therefore frst be modelled ether analytcally usng set of dfferental equatons to descrbe the system behavour or emprcally by fttng expermentally obtaned data to an assumed structure of the process.e. black-box modellng. Obvously, how well the resultng control strategy performs depends on the accuracy of the model. In applcatons where the physcal and/or chemcal characterstcs of the system are well known, usually the former approach s adopted. In the process ndustres, where the hgher degree of uncertanty prevals about the process behavour, emprcal modellng approach s often employed. However for control system desgn purposes, the nput-output (transfer functon) model obtaned usng later

7 47 approach s generally adequate. Multvarable controls strateges can also be developed that nclude ntegral, dervatve and feed-forward control acton. Among the multvarable controllers, MPC s an mportant advanced control technque whch can be used for dffcult multvarable control problems (Perez et al 200). 3.2 MODE O DISTIATIO COUM In the present work, two dstllaton column models are taken for case study. The frst example s Wood and erry (W) column whch s n the form of transfer functon model and second example s based on Skogestad model Wood and erry (W) Model The frst 2 x 2 MIMO process s presented by Wood and erry (973). The study was performed on a 9 nch dameter, 8 tray column equpped wth a total condenser and a basket type reboler. The requred control acton for the manpulatve varables n the composton loops, reflux and steam flow, were cascaded to the set ponts of the approprate flow controllers. The transfer functon characterzng the column dynamcs were establshed by pulse testng. Parameters of the assumed frst order plus tme delay transfer functon were determned from the transent data. The tme delays were establshed and the gans and tme constants are determned by least squares ft employng Rosenbrok s drect search technque. The process transfer functon matrx of the dstllaton process s gven by G(s) X (s) D X (s) s 2.8e 8.9e 6.7s 2s 7s 3s 3s 6.6e 9.4e 0.9s 4.4s R(s) S(s) (3.)

8 48 where X D (s) and X (s) are the overhead and bottom compostons of methanol, respectvely. R(s) s the reflux flow rate and S(s) s the steam flow rate to the reboler, (s) s the feed flow rate, a load dsturbance Skogestad Dstllaton Column Model The dstllaton column used n ths work s based on Skogestad model (Skogestad 997). The column conssts of stages (trays), numbered from bottom to top. The feed enters the column at stage, wth < <. The feed flow, s a saturated lqud wth feed composton z [mole fracton] and feed lqud fracton q. T denotes the reflux flow rate of the condenser; s the bolup flow rate of the reboler. The top product conssts of a dstllate flow rate D, wth composton X D. kewse the bottom product conssts of a bottom flow rate, wth composton X. The stages postoned above the feed stage defne the enrchng secton and those below are the strppng secton of the column. The materal balance equatons for the feed stage and the stages n the strppng secton of the column are affected by the contnuous flow to the column and the wthdrawal of the bottom product from the reboler. The vapour flow rates are assumed to be constant molar flows wth no vapour dynamcs. They are gven by ( q ) (3.2) ( q ) for for (3.3)

9 49 The constant q s the feed lqud fracton and s determned by the feed thermal qualty. The lqud flow rates n the strppng and enrchng secton assume lnearzed tray hydraulcs wth a tme constant. They are defned as T * * M M M * M * top of column enrchng secton strppng secton (3.4) where M*() s some nomnal stage holdup at tray, * [kmol / mn] s a nomnal reflux flow n the enrchng secton and * q * * [kmol / mn] s a nomnal lqud flow n the strppng secton. The dstllate and bottom product flow rates are * D T T (3.5) et and [kmol / mn] denote the lqud and vapour flow on stage I of the column. Denote by X and Y the lqud and vapour compostons of the lght component on stage, respectvely. urther, let M, denote the lqud hold-up on the -th stage. The vapour-lqud equlbrum descrbes the relaton between the vapour and lqud compostons Y and X on each stage of the column and s gven by the non-lnear expresson Y X, ( ) X,..., (3.6) where s the so called relatve volatlty (dependent on the product) the total materal balance on the varous stages s gven by the dfferental equatons

10 50 dm dm dm dm dm 2 D condensor stage enrchng secton feeder stage strppng secton reboler stage (3.7) here = T, = T and M = M T at the top of the column and =, =, M = M at the bottom of the column. gven as follows. The materal balances for the component holdup of the column are dm T dm X dm X dm X dm X X X X X 2 Y ( D) X 2 X X Y Y X X Y Y Y Y X Y z condensorstage feed stage rebolerstage (3.8) usng the chan rule for dfferentaton, the lqud composton X on the -th stage then satsfes dx d( M X ) X, M d( M X ),..., (3.9) n Table 3.. The dstllaton column specfcatons used for ths study are lsted

11 5 Table 3. Dstllaton column data umber of trays 40 Relatve volatlty between lght and heavy component.5 eed tray (numberng from the bottom) 2 eed composton (lght component molar fracton) 0.5 Dstllate composton (mole fracton) 0.99 ottoms composton (mole fracton) 0.0 eed flow rate (kmol/mn) Dstllate flow rate (kmol/mn) 0.5 ottom flow rate (kmol/mn) 0.5 Reflux flow rate (kmol/mn) olup flow rate (kmol/mn) Condenser holdup (kmol) 0.9 Reboler holdup (kmol) 5.8 racton of lqud n feed Average tray holdup (kmol) eural Modellng of the Dstllaton Column Pror to desgn of the neuro-fuzzy controller an dentfcaton process s accomplshed n order to predct the plant dynamcs (ernandez et al 2000). A smulated bnary dstllaton column plant based on the nonlnear equatons has been used to obtan representatve data for tranng process, and an R neural network has been used as an dentfcaton model of the dstllaton column shown n gure 3.2.

12 52 z R Dstllaton Column x x D TD + - x eural Identfer x D gure 3.2 euro Identfcaton scheme of dstllaton column To obtan representatve data, varyng feed flows, ntal lqud composton values both n the column, reboler and condenser along wth nput values for the control actons were mposed on the model. The dentfcaton model has been carred out usng R gven by y [ k ] ( y[ k], u[ k]), wth belongng to the class traned wth the Orthogonal east Square (OS) algorthm, usng 750 patterns for u [ k] [ R[ k], [ k]] and y[ k] [ x [ k], xd[ k]] regularly spaced, coverng the operatng range of the state varables. The neural dentfer has been utlsed to approxmate the Jacoban of the plant n order to adjust the neuro-fuzzy controller s parameter.

13 uzzy Modellng of the Dstllaton Column uzzy ogc does not deal wth dynamc elements lke other conventonal logc, and therefore careful consderaton s requred for desgners to construct such model rule forms that can express reasonably dynamc elements of tme-varyng systems Along wth ths consderaton, an unque model s developed that mtates verbal understandng of operators aganst dynamc behavours of process (Yamazak 996). The rule form used represents explctly the relaton between past control actons as causes and process responses as results, and the control actons are defned by three fuzzy varables, long past, medum past and short past actons. Another consderaton n the model rule s the partal parng of j-th nput and k-th output among J sets of nputs and K sets of outputs n order to prevent an explosve ncrease n the total number of model rules requred for MIMO systems. The uzzy varables U j [n+l] and Z j [n] denote a change n the j-th control acton and a change n the past j-th control acton respectvely. Y j,k [n+l In] and E k [n] denote a predcted change n k-th process by U j and a control error. The symbol [n] denotes a samplng nstance, and Y[n+l n] represents the change n the -samplng future predcted at n-samplng nstance. j k The uzzy labels ( A j, j, C j ) denote fuzzy labels of Z={z}, and Q, denotes fuzzy labels of Y=(y}. Here, a fuzzy lnear relaton s assumed between fuzzy labels j k Q, and { A j, j, C j } The Past control actons z T, are classfed n accordance wth fuzzy labels T (T l =S, T 2 =M, T 3 =). Superscrpts, M, and S on Z denote the change n long, medum and short past control actons respectvely.

14 54 calculated by Each past control acton z T correspondng to fuzzy labels s M M z [ n] { u[ n m]. ( m)} / ( m ) (3.0) T m 0 m 0 T y means of ncluson of U[n+l] nto the short past control acton Z S [n+l], the -th rule for j-th process nput and k-th process output among sets of rules s gven by (3.) R j, k) ( : If ( Z j [n+l ] = A j, M Z j [n+l ] = j, S Z j [n+l ] = C j then Y, [n+l n] = j k Q j, k (3.) Q j, k = { G j, k * A j, M G j, k * j + S G j, k * j C } where G,, M G,, S G, are scalar and the symbols + and * j k j k j k represent fuzzy sum and multplcaton respectvely. ow, for the calculaton of predcted process change from the model rules above defned, Sugeno's smplfed method can be appled as follows: 0 Q j, k [ n n] 0 G j, k * X j [n+] (3.2) and the degree of compatblty of the above rule s defned as X n A z n z n C z n (3.3) [ ] mn{ ( [ ]), ( M [ ]), ( S j j j j j j j [ ])} The predcted k-th process output nferred from all the rules of j-th nput s calculated by 0 Y j, k j 0 j, k [ n n] { Q [ n n] X [ n]/ X [ n]} (3.4) j j j

15 COCUSIO In ths chapter, the need for dstllaton column control, dfferent control technques used are presented. The mathematcal model of dstllaton column used n ths work s also gven. The W column s presented n transfer functon form and Skogestad column s gven n state space form. The neural and fuzzy modellng approach s also brefly explaned.