Heat-Integrated Distillation Columns -Analysis and Modellingwith. Advanced Distillation as Supporting Subject

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1 Norwega Uversty Of Scece ad Techology Faculty of Egeerg ad Techology Uversty of Belgrade Faculty of Mechacal Egeerg Isttute for Eergy Techology The log-term co-operatve project Master Degree Program: Sustaable Eergy ad Evromet Serba Heat-Itegrated Dstllato Colums -Aalyss ad Modellgwth Advaced Dstllato as Supportg Subject M.Sc.- caddate Dmtrje R. Djordjevc Trodhem, Norway December 2003

2 Abstract I ths work, a dstllato system wth heat-tegrated prefractoator colums s aalysed. The equlbrum (theoretcal) stage cocept s used ad costat relatve volatlty was assumed. Usg short cut calculatos three terary mxtures, take from lterature, were cosdered. The most promsg mxture s cosdered further. Usg mathematcal model self-optmsato study was doe. Accordg to the results from the self-optmsato study, a cotrol structure was adopted, ad further aalysed. Dyamcal performace of the system for dfferet dsturbaces feed composto ad flow rate has bee smulated. Keywords. Heat-tegrated colums, prefractoator arragemet, optmal operato, self-optmsato study, cotrol structure smulato Faculty of Mechacal Egeerg 2

3 Ackowledgemet I wsh to thak Professor Truls Guderse for hs effort fdg me a project assgmet. For gudace ad help my work I wsh to thak my metor Norway Professor Sgurd Skogestad, metor Serba Professor Jacmovc Braslav, PhD studet Hlde Egele ad Dr Srbslav Gec. Faculty of Mechacal Egeerg 3

4 Cotets Nomeclature (5) Itroducto (6) 1. Basc Dstllato Theory 1.1 Equlbrum stage cotact (7) 1.2 Materal Balace o a Dstllato Stage (9) 1.3 Mmum Eergy Usage Ifte Number of Stages (11) 2. Model Descrpto (17) 3. Itroducto to Heat-Itegrated Dstllato System wth Prefractoator (21) 4. Itroducto to Self-Optmsato.(23) 5. Short Cut Calculato (28) 6. Fdg the Optmum Steady State Soluto 6.1. Optmum for Dfferet Pressures (33) 6.2. Optmum for Dfferet Feed Compostos (34) 7. Smulatos Results for Dsturbace Feed Compostos Cosderg Best Self Optmsato Value (38) 8. Smulato of Dyamcal Performace of System wth Prefractoator (45) 9. Coclusos (53) Refereces (54) Faculty of Mechacal Egeerg 4

5 Nomeclature x, - Composto lqud phase o tray for compoet y - Composto vapour phase o tray for compoet, M - Amout of lqud o tray F - Feed flow rate o tray D - Dstllate flow rate B - Bottom product flow rate z - Composto of feed for tray ad compoet, W - Sde stream flow rate for tray L - Lqud flow rate from tray V - Vapour flow rate from tray T - Temperature p - Pressure h l - Ethalpy of lqud phase h - Ethalpy of vapour phase v h sat D - Ethalpy of saturato Q - Heat flux o tray w - Molar flow rate of compoet above tray, r - Recovery factor a - Relatve volatlty of compoet f - Uderwood root t - Tme Faculty of Mechacal Egeerg 5

6 Itroducto Dstllato s a very mportat dustral separato techology. It s commoly used for hgh purty separato sce ay degree of separato ca be obtaed wth a fxed eergy cosumpto by creasg the umber of equlbrum stages. Dstllato colums are used for about 95% of lqud separatos ad the eergy use from ths process s estmated as 3% of the world eergy cosumpto [22]. Wth rsg eergy costs ad growg evrometal problems there s a eed to reduce the eergy use dustry. For the dstllato process there are potetals for large eergy savgs by applyg dfferet methods of heat tegrato. I ths work, a heat-tegrated dstllato system wth prefractoator was studed. Ths s a heattegrated soluto wth bg eergy savg potetals. Ths arragemet ca decrease eergy cosumpto wth more tha 50%, as show the short cut calculatos ths work. Ufortuately, systems wth heat-tegrated prefractoator are very dffcult to cotrol. I ths work self-optmsato study ad dyamcal aalyse of was doe. All aalyss was doe for a terary mxture. Faculty of Mechacal Egeerg 6

7 1. Basc Dstllato Theory 1.1 Equlbrum Stage Cocept I ths work, a dstllato system wth staged colums s aalysed. It s establshed that calculatos based o equlbrum stage cocept (wth the umber of stages adjusted approprately) fts data from most real colums very well [21]. The equlbrum (theoretcal) stage cocept s cetral dstllato. Fgure 1.1 shows a equlbrum stage. Fgure 1.1. Equlbrum stage cocept. We assume vapour-lqud equlbrum o each stage, phases are deally mxed. The stream, whch leaves the stage, has the same composto ad ethalpy as the lqud or vapour phase o the stage. I may cases, we ca assume costat relatve volatlty. I that case, equlbrum equatos become: y a x,, = N a C = å j a x j j, cost. (1.1) Where a s relatve volatlty, x, ad y, are compostos of compoet o stage the lqud ad vapour phase. Relatve volatlty s: a = y / x y / x (1.2) * * j j I equato (1.2) the heavest compoet s oted wth dex j, ad wth * equlbrum composto. Faculty of Mechacal Egeerg 7

8 For a bary mxture wth costat relatve volatlty the equlbrum curve s llustrated Fgure 1.2 Fgure 1.2. Equlbrum curve for deal bary mxture. Large relatve volatltes mply large dffereces bolg pots ad easy separato. Close bolg pots mply relatve volatltes closer to uty. As recommeded lterature [21], the temperature o a stage ca be estmated as: æx+ y ö T = å ç Tb çè 2 ø (1.3) I equato (1.3) Tb s bolg temperature for pure compoet. A suggested relatoshp betwee pressure ad bolg temperature for a mxture cosdered s [21]: p sat æ 1,5 3,0 6,0ö æ T ö æ b T ö æ b T ö æ b T ö b A 1- + B 1- + C 1- + D 1- ç T c T c T c T è ø ç è ø ç è ø ç è cø = pc exp Tb 1 - ç T c çè ø (1.4) Equatos of equlbrum (1.1), (1.3) ad (1.4) ca be easly used for computer calculato. Faculty of Mechacal Egeerg 8

9 1.2 Materal Balace o a Dstllato Stages Based o the equlbrum stage cocept, a dstllato colum secto s modelled as show Fgure 1.3. Note that we choose to umber the stages startg from the bottom of the colum. We assume perfect mxg both phase sde a stage. The mole fracto of speces the vapour leavg the stage wth V s y,, ad the mole fracto L s x,. Fgure 1.3 Staged dstllato O dstllato stage (see Fgure 1.3) the mass balace equato for compoet ca be expressed as: ( M x ) t, = F z - W x + V y - V y +,, -1, -1, + L x - L x + 1, + 1, (1.5) Every stage ca be addtoally heated or cooled (heatg flux s Q ). Eergy balace for stage s: l ( M h ) l v v l l = hf, F- W h + V- 1 h- 1- V h + L+ 1 h + 1- L h+ Q t (1.6) Faculty of Mechacal Egeerg 9

10 Summarzed equatos (1.5) for stage ad all compoets wth respect to x = 1 y = 1 å å, gves the overall balace: ( M ) t = F - W + V - V + L -L (1.7) Usually we ca assume costat vapour ad lqud phase ethalpy: h h l v = cost. = cost. (1.8) Wth these assumptos Equato (1.6) becomes: ( M ) h = h F - W h + h ( V - V ) + h ( L - L ) + Q t l F, l v - 1 l + 1 (1.9) Equatos (1.5), (1.7) ad (1.9) descrbe the dyamcal behavour of dstllato colums. For (...) steady state = 0, so equatos (1.5), (1.7) ad (1.9) become: t 0 F z, W x, V -1 y, - 1 V y, L+ 1 x, + 1 L x, = (1.10) ( ) ( ) = h F - W h + h V - V + h L - L + Q (1.11) 0 F, l v - 1 l F W V - 1 V L + 1 L = (1.12) Equatos (1.11) ad (1.12) ca be rearraged to: V = V + F - q + q (1.13) ˆ -1 (1 ) L = L + W - + q F + q (1.14) ˆ 1 I (1.13) ad (1.14) q h - h Q = Dh vsat, F, = ad ˆ D hsat sat q Equatos (1.10), (1.13) ad (1.14) represet a closed system of equatos ad completely descrbe the steady state behavours of dstllato colums. But, sce the equato of equlbrum (1.1) s hgher degree the oe, ths system of equatos ca ot be solved a closed form. To get accurate soluto from ths system of equatos t s ecessary to use some umercal method. Faculty of Mechacal Egeerg 10

11 1.3 Mmum Eergy Usage Ifte Number of Stages Let us cosder a smple colum wth oe feed, ad wthout sde stream ad addtoal heatg, as show o Fgure 1.4. Equato (1.12) ca be rearraged as: Fgure 1.4. Smple dstllato colum 1 L w, = y, - x, + 1 (1.15) V V where w, s the molar flow rate of compoet above tray umber. For the top ad bottom sectos, w, ca be calculated from the mass balace for the colum: w = D x cotour K1 (1.16) top, D, w = D x - F z =- B x cotour K2 (1.17) bottom, D, F, B, Note that w, bottom s egatve, accordg to axes drecto. Faculty of Mechacal Egeerg 11

12 After multplyg Equato (1.15) wth tray: a åa x, ad summg for every compoet for each 2 a x, 1 a w å a -f L a x å = - å V a - f a x V a -f,, + 1 å, (1.18) Let left sde (1.18) to be equal to 1: V = a w, å (1.19) a -f Equato (1.19) ca be used to calculate f. The umber of dfferet solutos for f s the same as the umber of compoets. Substtutg Equato (1.19) to Equato (1.18) gves: f å å a x, a - f L a x = å a x V a -f,, + 1 (1.20) Equatos (1.20) ad (1.19) are kow as Uderwood s equatos ad f as the Uderwood s roots [1]. Equato (1.20) ca be wrtte for each tray ad t s vald for ay of the Uderwood roots, so f we assume costat molar flow ad dvde oe equato wth root f k wth equato for root f j, we have the followg expresso: å å a x a x a f æf ö å - a -f = a x ç çèf ø a x å a -f a -f, + 1, k k k, + 1 j, j j (1.21) From equato (1.21) the followg equato ca be developed: å å a x a x a f æf ö å - a -f = a x ç çèf ø a x å a -f a -f, + m, m k k k, + m j, j j (1.22) Equato (1.22) s oly vald for trays wth costat molar flows. Ths equato ca be used to calculate the umber of stages. Faculty of Mechacal Egeerg 12

13 Uderwood showed that the top secto (wth Nc compoet) the roots (f ) obey: a1> f1> a2> f2 >... > anc > fnc, (1.23) ad for bottom secto: y1> a1> y2> a2 >... > ync > anc (1.24) I (1.24) wthy s deoted Uderwood s root bottom secto as wthf top secto. For theoretcally fte umber of stages we have mmum flow rate trough the colum. I that case, we have: V Vm Þ f y + 1 (1.25) Equato (1.19) for top ad bottom secto s: V T = a w, å (1.26) a-fj V B = a w, å (1.27) a-yj Eergy ad mass balace for colum Fgure 1.4 gves: a w a w (1- q) F = V - V = - T B top, bottom, å å (1.28) a-fj a-yj I case of fte umber of stages ad mmum vapour flow rate we may wrte: V V Þ f y q º f = y (1.29) m I expresso (1.29) q s the commo root. If we use commo roots (1.28): a ( wtop, - wbottom, ) a zf, å å (1.30) (1- q) F = = F a -q a -q j j If we dvded left ad rght sde of (1.30) wth F we obta what s called the feed equato: (1- q) = a z F, å (1.31) a-qj Equato (1.31) s oly vald for mmum vapour flow rate (fte umber of stages). Usg equato (1.31) we ca fd the commo Uderwood roots. Equato (1.27) ca the be used to calculate the mmum vapour flow rate for dfferet recovery fracto. Faculty of Mechacal Egeerg 13

14 For a mxture wth three compoets the mmum vapour flow rates top secto ad bottom secto are: V top,m 3 a 3 wtop, a rd, zf, = = F a -q a -q å å (1.32) = 1 j = 1 j V bottom,m 3 a 3 wbottom, - a rb, zf, = = F a -q a -q å å (1.33) = 1 j = 1 j For sharp AB/BC separato, whch meas that we do ot have ay lght compoet the bottom product ad heavy compoet the top product, we heave: r = 1 r = r = 0 (1.34) AD, BD, CD, r = 0 r = r = 1 (1.35) AB, BB, CB, Substtutg for the recoveres Equatos (1.32) ad (1.33) the become: V a z a r z = + F a -q a -q top,m A FA, B BD, FB, A j B j (1.36) V a r z a z =- - F a -q a -q bottom,m B BB, FB, C FC, B j C j (1.37) The dstllate flow rate ca be expressed as fucto of recovery fracto: D F = å rd, zf, (1.38) For sharp separato AB/BC (1.38) s equvalet to: D z r z FA, BD, FB, F = + (1.39) D z z r ( 1 ) FA, FB, BB, F = + - (1.40) Usg equatos (1.39) ad (1.40) equatos (1.36) ad (1.37) leads to: a æ ö = + ç - ø Vtop,m A zfa, ab ç D z FA, F aa-qj ab-q çè j F (1.40) Faculty of Mechacal Egeerg 14

15 Vbottom,m ac zfc, ab ç D z FA, z FB, F ac -qj ab-q çè j F æ ö =- + ç - - ø (1.41) Mmum vapour flow trough the colum s: ævtop,m V ö bottom,m Vm = max, F ç F F çè ø (1.42) I case of a bary mxture, the mmum flow rate ca be calculated usg Kg s formula [21], here gve for lqud feed (q=1): L V r - a r LD, H, D top,m = r a-1 - a r F H, B LB, bottom,m = a-1 F (1.43) (1.44) Kg s formula ca be developed from Uderwood s equatos (1.26), (1.27) ad (1.31). For sharp separatos ad bary mxtures we get: 1 VB m = F+ D (q=1) a- 1 (1.45) All equatos show above ca be represeted D - V m F F, so called as Vm dagram [21]. V dagram equatos (1.40) ad (1.42) are les ad wth respect to expresso (1.42) we I m get le as show o Fgure 1.6, le betwee pots PAB-PAC- PBC. All other les o Fgure (1.5) are obtaed the same way. O Fgure (1.5) are show regos wth dfferet type of separatos. O le PAB-PAC- PBC we have sharp separato AB/BC wth mmum eergy cosumpto. At pot P AB we have sharp separato A/BC ad at pot P BC sharp separato AB/C, both wth mmum eergy cosumpto. Above ths pot, as show wth dashed les we stll have proper sharp separato, but wth more eergy cosumpto tha the mmum. Pot P AC s called the preferred sharp AB/BC separato. I that pot, eergy used for sharp separato AB/BC s at a mmum. Recovery factor P AC ca be calculated from equato: a z a r z a z a r z + = + a -q a -q a -q a -q A FA, B BD, FB, A FA, B BD, FB, A j B j A k B k (1.46) Faculty of Mechacal Egeerg 15

16 Equato (1.46) s developed from equatos (1.42) usg two dfferet commo roots, ow recovery factor P AC s: r BD, ( ) ( ) ( ) ( ) aa zf, A ab- qk ab-qj =- (1.47) a z a - q a - q B FB, A k A j Vapour flow rate ca be calculated wth equatos (1.36) ad (1.37) for a specfc recovery. Fgure 1.6. Regos of dstrbutg feed compoet as fucto of (D/F) ad (V/F) Le (0,0)- P AB represets separato A/ABC. Le PBC -(1,1-q) represet separato ABC/C. Les (0,0)- P AC ad PAC -(1,1-q) represet separatos AB/ABC ad ABC/BC. Faculty of Mechacal Egeerg 16

17 2. Model Descrpto Steady state behavour of colums s descrbed wth equatos (1.10), (1.13) ad (1.14). These equatos are ot lear, ad that ca be a problem for calculatos. However, for solvg these equatos, umercal methods are very good. MatLab has a tool fsolve for solvg system of lear ad o-lear matrx equatos. Fsolve uses a teratve method kow as the Gauss Newto method. For usg ths tool, all equatos have to be wrtte as: F( X ) = 0 (2.1) I equato (2.1) X s a matrx varable, ad fucto s a matrx fucto. I addto, t s ecessary to defe the Jacoba of fucto F. If we have Nt trays ad a mxture wth Nc compoets, the for oe colum matrx X ca be the lqud composto o each tray. The dmeso of the matrx that case wll be [Nc, Nt+2]. Two addtoal members are reserved for vapour ad lqud composto, whch are comg colum o top ad bottom. For oe tray, wth steady state operato, the mass balace equato wll be: f = G y - G y + L x - L x + F z - W x (2.2), -1, - 1, + 1, + 1,,, Fucto f, s member matrx F( X ), s compoet umber ad s tray umber. Jacoba of matrx F( X ) s calculated as partal dervatve of all f, members wth respect to all varables matrx X. Jacoba s matrx J wth dmeso ( Nt 2, Nc ( Nt 2) ) matrx J ca be calculated as: + +. Members of f f y f y f = + + x y x y x x,,,,, -1, km,, km,, -1 km, km, (2.3) The composto the vapour phase s a fucto of the compostos lqud phase, ad ths fucto, for equlbrum assumpto, s gve by (1.1). A other way to solve steady the state equatos are to use equatos for the dyamcal model, ad smulate log eough, utl steady state operato s reached. Dyamcal behavour s descrbed by a system of dfferetal equatos. It s hgher rak of equatos the oe, ad t depeds o the umber of compoets. Oly case of oe compoet, systems of dfferetal equatos become to be lear. Order of equatos s oe (frst order system). Ths system of equatos for three compoet mxture s mpossble to be solved closed form, but wth umercal calculato, we ca get solutos very close to correct oes. To solve sets of equatos gve by (1.5), (1.7) ad (1.9) we may use some hybrd method. I all umercal methods, tme dervate s dscretsed. Let cosder smple equato: (,, t) f xy t (,, ) = g f xy (2.4) Faculty of Mechacal Egeerg 17

18 Where f s a ukow fucto ad g s a kow fucto. If we wat to solve equato (2.4) wth some umercal method we should frst dscretsed left sde the equato (2.4): (,, t) (,, t t) (,, t) f xy f xy +D - f xy» t Dt (2.5) Rght sde the equato (2.4) s kow fucto ad basc problem umercal soluto s should we use f o the rght sde the equato (2.4) future momet or past momet. However, we may use both future momet ad past momet as: (,, t+dt) - (,, t) f xy f xy Dt (,, ) ( 1 ) g( x, y, ) = b g x y t+d t + - b t (2.6) I the equato (2.6) b s a umber betwee 0 ad 1. I Fgure (2.7) ths problem s represeted graphcally. Black pots are varables the past tme step, ad red pots are varables the future tme step. Wth arrows s represeted, whch varables we eed to calculate a ukow varable A. If b the equato (2.6) s equal to 0 the varable A depeds oly o varables past tme steep, blue arrows Fgure 1.7 a). If b the equato (2.6) s equal to 1 the varable A depeds oly o varables future tme steep, gree arrows Fgure 1.7 b). If b s betwee 0 ad 1 the varable A depeds o varables the past tme step ad future tme step Fgure 1.7 c). Fgure 2.7. Numercal method Faculty of Mechacal Egeerg 18

19 Faculty of Mechacal Egeerg 19 Equatos (1.5) ad (1.9), ow ca be wrtte as: ( ) ( ) ( ) ( ) ( ) o o o o F W V V L L F W V V L L M M t t t t t t t t t t b b t - + = +D - + = = +D = = - = D (2.7) ( ) ( ) τ β β τ τ τ τ τ τ τ τ τ τ = = = + = = = ,,, 1, 1, 1, 1,,, 1, 1, 1, 1,, ) ( ) (1 ) ( x M x M x L x L y V y V x W z F x L x L y V y V x W z F (2.8) I Equatos (2.7) ad (2.8) the value b descrbes whch method s used. Term b are varables future tme step ad they are ot kow each calculato. Term ( ) 1 b - are varables past tme step ad they are kow each calculato. If 0 b = the we have back tme method. I that case we calculate ew compostos ad flow rates oly cosderg varables past tme step. If 1 b = the we have forward tme method. If 0 1 b < < the we have hybrd method, where the case 0,5 b = s kow as Crak Ncholso method or scheme, whch s used these smulatos. Equatos (2.7) ad (2.8) are ot lear equatos, o-lear terms those equatos are: vapour compostos, ad amout of lqud o trays. These terms ca be learsed usg Talor s expaso (or polyomal). If we develop vapour composto usg Talor s expaso, we get: ( ) ( )... 2! * * * * * = = = C N C j j j j N j j j j x x x y x x x y y y (2.9) I equato (2.9) (*) deotes varables past tme step, other varables are future ext tme step. Members after secod member o left sde (2.9) ca be eglected, ad the we have lear equato stead equato (2.9). That lear equato ca be wrtte as: ( ) = + = N C j j j j j j x x x y y x y y y 1 * * * * * * * δ (2.10) Lqud flow rate ca be calculated usg Fracs Wer formula. If amout of lqud o tray s M, the lqud flow rate s: ( ) m L k M M w = - (2.11)

20 where M w s the amout of lqud uder the tray wer, ad t s assumed costat. Coeffcets k ad m are also costat. From equato (2.11) we ca develop: 1 m L M = Mw + (2.12) k Now the amout of lqud o each tray ca be expressed usg Talor s polyomal: * æ M ö 1 æ M ö 2 M = M + ç ( L - L ) + ç L - L +... ( ) * * * ç L 2! L è ø çè ø (2.13) As equato (2.9) the terms after the secod member o the left sde of (2.13) ca be eglected, gvg lear equato stead of equato (2.13): ( ) 1 -m * L m * * = + - M M ( L L ) mk (2.14) Usg (2.10) ad (2.14) equatos (2.7) ad (2.8) become lear equatos, whch ca be easly solved. For steady state calculato, we may use the same model as for dyamcal calculatos. I that case we ca separately calculate flow rates, ad keep them costat, for amout of lqud o tray we may use some costat umber. It does ot have to be correct amout of lqud o tray. I that case, we do ot have to use equato (2.8). Equato (2.7) ca be solved, as we solved the dyamcal model. The ed of teratos s whe two followg teratos dfferece compostos s small eough. Faculty of Mechacal Egeerg 20

21 3. Itroducto to Heat-Itegrated Dstllato System wth Prefractoator For terary separatos there are three classcal separatos schemes: drect splt, drect splt ad the prefractoator arragemet. I the Fgures 3.1, 3.2 ad 3.3,below all three schemes are show. Fgure 3.1 Drect splt scheme Fgure 3.2 Idrect splt scheme Fgure 3.3 Prefractoator arragemet scheme I all three schemes mult-effect heat tegrato s possble. The colums are tegrated by combg the codeser of oe colum wth the reboler of aother colum. I that case, colums have to work o dfferet pressures to keep suffcet temperature dfferece for heat trasport. I lterature, may works are publshed wth subject whch arragemet s the best oe [12,13,14,15,17,18,21]. For savg eergy heat tegrated prefractoator arragemet has the best possblty. Accordg to lterature data [12,13], t s possble to save up to 70% of eergy usg heat tegrated prefractoator arragemet. Colums ca be tegrated forward or backward. I case of forward tegrato, the frst colum s ru at a hgher pressure tha the secod colum. For the backward tegrato, the secod colum s ru at a hgher pressure tha the frst colum. Faculty of Mechacal Egeerg 21

22 I ths work the forward tegrated prefractoator arragemet s studed. Fgure 3.4 below shows a smplfed scheme for ths arragemet. Fgure 3.4 Forward heat tegrated prefractoator arragemet The codeser for the frst colum ad the evaporator for the secod colum s combed the same heat exchager. I ths work the possble eergy savg, optmum operato ad selfoptmsato cotrol ad dyamcal behavours was studed for ths system. Faculty of Mechacal Egeerg 22

23 4. Itroducto to Self-Optmsg Cotrol The method of self-optmsg cotrol volves a search for the varables that, whe kept costat, drectly lead to ear-optmal operato wth acceptable loss. The procedure cossts of sx steps: 1) a degree of freedom (DOF) aalyss, 2) defto of cost fucto, 3) detfcato of the most mportat dsturbaces, 4) optmsato, 5) detfcato of caddate cotrolled varables ad 6) evaluato of loss wth costat set pot. For the two-colum scheme as show Fgure 3.3 (left fgure), there are seve degrees of freedom steady state work. For the frst colum, there are three degrees of freedom. Those are the reflux rato, dstllate flow rato ad the pressure. For the secod colum, there are four degrees of freedom, the reflux rato, the dstllate, the pressure ad duty of codeser. If the two colums are heat tegrated, as Fgure 3.4, the vapour flow the secod colum depeds o the vapour flow frst colum, so we have oe degree of freedom less tha two o-tegrated colums. I ths work feed mxtures wth hgh purty products (99% mole fracto) are cosdered. I that case flow rate of fal products are almost costat ad approxmately: D = F z (4.1) p, F, Accordg to equato (4.1) secod colum we have two degrees of freedom less. Fally we have 7 3 = 4 degrees of freedom for heat tegrated prefractoator arragemet wth hgh purty products (99%). I ths work for optmal operato aalyss depedet varables are: the pressure frst colum ad the pressure secod colum; the reflux rato frst colum ad the dstllate flow rate betwee two colums. The objectve fucto for ths system ca be expressed as: J = pd D+ ps S+ pb B- pf F- pv V (4.2) The prces for fal ( pd, ps, p B) products are costat, accordg to hgh purty. Prce for feed s, also costat. The equato (4.2) ca be wrtte as: J = Cost- pv V (4.3) Optmal operato s whe the objectve fucto s at maxmum, ad the the proft s at maxmum. If we chose costat pressure of heatg steam, whch we ca f the pressure the frst colum s costat, the maxmum of the objectve fucto J wll be whe the vapour flow trough frst colum s mmum. The optmsato problem ca the be formulated as fdg mmum vapour flow rate for the frst colum, but at the same tme, achevg a purty of products equal to or hgher tha 99% (the system costras). Faculty of Mechacal Egeerg 23

24 Accordg to theory from chapter 1, we ca cosder heat-tegrated colums case of fte umber of trays, usg D/F Vm/F dagram. If we have a system of two colums, as show Fgure 3.5 below, we may draw D/F Vm/F dagrams for both colums oe fgure. Fgure 4.1 Prefractoator arragemet The secod colum Fgure 4.1 above s splt to two colum sectos (colum II ad III). Betwee secto II ad III we take medum compoet product. Ths scheme s equvalet to the scheme show Fgure 3.3, but s clearer for cosderg. I colum II we have sharp separato of A/B ad colum III we have sharp separato of B/C. I the frst colum, colum I, we have sharp separato betwee A ad C. We ca calculate the mmum flow rate DI sectos II ad III as fucto of dstllate flow rate from colum I ( ). I the secod F colum (sectos II ad III) we wll use equatos for bary mxtures. Fgure 4.2 below shows Vm dagram for the system Fgure 4.1. The dot le represets mmum flow rate for colum III, ad poted le represets mmum flow rate for colum II. The sold le s for colum I, ths le s descrbed o Fgure 1.6. Possble workg order for ths sharp separato cocept s: DI zfa, zf, A+ zfb, (4.4) F Fgure 3.6 ca be used to easly establsh the mmum eergy cosumpto for the system wth ot-tegrated colums: {( ) {( ) ( ) }} Q =D H m V + max V, V (4.5) m vap. m I m II m III Faculty of Mechacal Egeerg 24

25 Ths method ca be used ad for tegrated colums, the (4.5) becomes: { {( ) ( ) ( ) }} Q =D H m max V, V, V (4.6) m vap. m II m III m I I equatos (4.5) ad (4.6) vapour flow rate s fucto of 4.2 s for fte umber of stages. DI F. Dagram represeted Fgure Fgure 4.2 D/F V/F dagram system wth prefractoator Fgure 4.3, o the ext page, shows how we ca calculated mmum flow rate for tegrated colums usg D/F V/F dagram. Faculty of Mechacal Egeerg 25

26 Fgure 4.3. Several examples for usg dagram for calculato Vm Whe colums are heat tegrated, some colums work wth more vapour flow rate tha they eed, for requred separato. I Fgure 4.3 a) for example colums II ad III work wth more vapour flow rate, case b) colum I receves a hgher vapour flow ad case c) colum III receves a hgher vapour flow the requred. For real colum show dagrams o Fgures above, are ot vald. It s ow terestg, ca we draw some same kd of dagram for real colums. I real colums, we ca ot make sharp separato, but f composto of a compoet s lower tha some value e, we may say that the separato s sharp. The value of e depeds o product purty, for example f the product purty should be 99%, the e s about 1%. Descrbed compoet s for example heavest compoet B colum II (Fgure 4.1) were we have sharp A/B, or compoet C colum I where we have sharp A/C. Accordg to smulato results, dagram D/F Vm/F for real colums s represeted by the dot le Fgure 4.4. The sold le represets mmum flow rate for fte umber of stages. Mmum vapour flow rate for case show Fgure 4.4 s approxmately above mmum flow rate for fte umber of trays, but dstllate flow rate for both cases (fte ad fte umber of stages) these case are equvalet. If we crease the umber of stages the secod colum (colums II ad III o Fgure 4.1), the the eergy cosumpto wll ot be decreased, but captal costs wll crease. If we crease umber of stages the frst colum (colum I o Fgure 4.1), eergy cosumpto wll decrease. For low products purty, dotted le ca be below the sold le. Faculty of Mechacal Egeerg 26

27 Fgure 4.4 Dagram D/F V/F for real colums Wth ths kowledge, the dagrams Fgure 4.4 ca be used for desg of heat-tegrated systems. I Fgure 4.5 s represeted bad desged system, where secod colum has fewer trays. Fgure 3.9 Bad desged colums Whole that the aalyss ca be doe for mxtures wth more tha three compoets ad systems wth more tha two colums. Faculty of Mechacal Egeerg 27

28 5. Short Cut Calculato All short cut calculatos are based o fte umber of trays, both for the frst ad secod colum. I that case, sharp separato ca be acheved, whch s mpossble real colums. Usg short cut calculatos three, terary mxtures were cosdered (Table 5.1), these mxtures are take from lterature [12,13, 15,17,18]. \ Mxture 1 Mxture 2 Mxture 3 Compoet A bezee -petae Ethaol Compoet B Toluee -hexae -propaol Compoet C m-xylee heptae -butaol Composto [0.25; 0.5; 025] [1/3; 1/3; 1/3] [0.4; 0.4; 0.2] Table 5.1. Feed data for mxtures The most promsg mxture wll be studed further. Characterstcs of the mxtures, such as relatve volatlty at two dfferet pressure levels, are calculated usg a commercal smulato tool HYSYS. Results are show Table 5.2, 5.3 ad 5.4. Mxture 1 / α sat H t m 100 kpa [5.57; 2.29; 1.00] MJ/mol 124/139 o C 600 kpa [3.58; 1.88; 1.00] MJ/mol 152/168 o C Table 5.2. Mxture 2 / α sat H t m 100 kpa [7.26; 2.64; 1.00] MJ/mol 84/98 o C 600 kpa [4.50; 2.08; 1.00] MJ/mol 101/120 o C Table 5.3. Mxture 3 / α sat H t m 100 kpa [4.55; 2.22; 1.00] 94.2 MJ/mol 108/118 o C 600 kpa [3.52; 1.94; 1.00] 39.7 MJ/mol 131/142 o C Table 5.4 The results of short cut calculato are represeted Fgures ad Tables above. Faculty of Mechacal Egeerg 28

29 Mxture 1 Fgure 5.1 Vm-dagram for terary feed mxture 1, frst colum at 6 bar, secod colum at 1bat pressure. Fgure 5.2 Vm-dagram for terary feed mxture 1, frst colum at 1 bar, secod colum at 6 bar pressure. Mxture 1 ot tegrated tegrated forward tegrated backward DS IS PF 1, (D/F=0.4195) (D/F=0.4975) Table 5.5 Vm/F for dfferet cofguratos. Faculty of Mechacal Egeerg 29

30 Results Table 5.5, ca be compared wth drect splt cofgurato wthout heat tegrato. These results are show Table 5.6, below. Mxture 1 ot tegrated tegrated forward tegrated backward DS 100% 60,7% 71,5% IS 112,1 % 78,1% 71,1% PF 76,6% 42,5% 43,6% Table 5.6 Comparg eergy cosumpto dfferet cofgurato based o short cut calculato. The best possblty for savg eergy s cofgurato wth heat-tegrated prefractoator (forward tegrated). Mxture 2 Fgure 5.3 Vm-dagram for terary feed mxture 2, frst colum at 6 bar, secod colum at 1 bar pressure. 1.4 Mxture 2 (backward tegrated) Vm/F D/F Fgure 5.4 Vm-dagram for terary feed mxture 2, frst colum o 1 bar, secod colum o 6 bar pressure. Faculty of Mechacal Egeerg 30

31 Mxture 2 ot tegrated tegrated forward tegrated backward DS 1, IS PF (D/F=0.4203) (D/F=0.5212) Table 5.7 Vm/F for dfferet cofguratos. Results Table 5.7, ca be compared wth drect splt cofgurato wthout heat tegrato. These results are show Table 5.8, below. Mxture 2 Not tegrated tegrated forward tegrated backward DS 100% 65,1% 63,9% IS 119,9% 87,6% 72,0% PF 79,3% 48,5% 52,5% Table 5.8 Comparg eergy cosumpto dfferet cofgurato based o short cut calculato. The best possblty for savg eergy s cofgurato wth heat-tegrated prefractoator (forward tegrated). Mxture 3 Fgure 5.5 Vm-dagram for terary feed mxture 3, frst colum at 6 bar, secod colum at 1bar pressure. Faculty of Mechacal Egeerg 31

32 Fgure 5.6 Vm-dagram for terary feed mxture 3, frst colum at 1 bar, secod colum at 6 bar pressure. Mxture 3 ot tegrated tegrated forward tegrated backward DS 2,231 1,4304 1,1970 IS 2, ,3823 PF 1,7400 0,9453 (D/F= ) (D/F=0.4770) Table 5.9 Vm/F for dfferet cofguratos. Results Table 5.9, ca be compared wth drect splt cofgurato wthout heat tegrato. These results are show Table 5.10, below. Mxture 3 ot tegrated tegrated forward tegrated backward DS 100% 64,1% 53,7% IS 118,1% 69,3% 62,0% PF 80,0% 42,4% 44,2% Table 5.10 Comparg eergy cosumpto dfferet cofgurato based o short cut calculato. The best possblty for savg eergy s cofgurato wth heat-tegrated prefractoator (backward tegrated). Faculty of Mechacal Egeerg 32

33 6. Fdg the Optmum Steady State Soluto I ths chapter, wth MatLab smulato, optmum workg order was calculated for dfferet pressures the hgh pressure colum ad dfferet feed composto. MatLab model s descrbed Chapter Optmum for Dfferet Pressures For omal feed composto (0,25 0,5 0,25), costat pressure the secod colum, ad for varous pressure levels the frst colum (from 4 bar to 15 bar), optmum (mmum) eergy cosumpto are gve Fgure 6.1 below. As t s show Fgure 6.1 below, wth creasg pressure the frst colum, eergy cosumpto s decreasg. Wth creasg pressure the frst colum, relatve volatlty s decreasg, whch causes hgher eergy cosumpto. However, whe creasg the pressure the frst colum, heat of vaporzato s decreasg, whch causes the eergy cosumpto to decrease. Obvously, the frst colum, for chose mxture ad pressure level, heat of vaporzato has a bgger fluece o heat cosumpto tha relatve volatlty. I Fgure 6.1 temperature dfferece the commo heat exchager for the frst ad secod colum s also show. Ths temperature dfferece s chose to be hgher or equal to 10 o C. For pressure the frst colum hgher tha 5,25 bar the requred temperature dfferece s acheved. Whe creasg the pressure the hgh-pressure colum (frst colum) the eergy cosumpto s decreasg, but captal costs are creasg, so t s ecoomcal to keep the pressure the frst colum low. I ths work 6 bar was chose the frst colum, ad 1,5 bar secod colum for further aalyses. Faculty of Mechacal Egeerg 33

34 Fgure 6.1 Temperature dfferece ad heat cosumpto for dfferet pressure frst colum 6.2. Optmum for Dfferet Feed Compostos For each feed composto there s dfferet optmum (mmum) cosumpto of heat eergy. Mmum heat cosumpto ths case s geerally fucto of feed composto, feed flow rate ad demad for products purty: m ( f,, m ) Q = f Z F Xp (6.1) All other teral varables, e.g. reflux, dstllate flow rate, are fuctos of composto, feed flow rate ad demad for products purty case of mmum eergy cosumpto. I the cosdered case the requred product purty s 99% ad t s costat for calculato. I ths model all teral flow rates, optmum workg codtos, are lear fucto of feed flow rate, so t s ot terestg to ru smulato for dfferet feed flow rate. For dfferet feed compostos optmum (.e. mmum) heat cosumpto s show Table 6.1. Results are calculated usg MatLab smulato. Faculty of Mechacal Egeerg 34

35 Zfc\Zfa 0,2 0,21 0,22 0,23 0,24 0,25 0,26 0,27 0,28 0,29 0,3 0,2 2,4885 2,4824 2,4729 2,4788 2,4602 2,4888 2,4685 2,4965 2,4996 2,5021 2,504 0,21 2,4663 2,4596 2,4435 2,4496 2,4552 2,4602 2,4646 2,4471 2,4496 2,4768 2,4785 0,22 2,4441 2,4296 2,4368 2,4263 2,4316 2,4363 2,4404 2,4441 2,4471 2,4516 2,4768 0,23 2,4135 2,4071 2,4141 2,3974 2,4029 2,4316 2,4363 2,4404 2,4224 2,4496 2,4496 0,24 2,3916 2,3996 2,3846 2,3913 2,3974 2,3843 2,3885 2,4163 2,4196 2,4471 2,4471 0,25 2,383 2,3696 2,3621 2,3685 2,3743 2,3796 2,3843 2,3885 2,4163 2,4196 2,4441 0,26 2,3524 2,3477 2,3552 2,3621 2,3685 2,3743 2,3796 2,3843 2,4124 2,4163 2,4404 0,27 2,331 2,3396 2,3257 2,333 2,3396 2,3457 2,3513 2,3796 2,3843 2,4124 2,4163 0,28 2,3219 2,3096 2,3038 2,3257 2,333 2,3396 2,3457 2,3743 2,3796 2,3885 2,4124 0,29 2,2913 2,2882 2,2963 2,3038 2,3257 2,333 2,3396 2,3457 2,3743 2,3843 2,4079 0,3 2,2813 2,2796 2,2882 2,2963 2,3038 2,3107 2,333 2,3396 2,3513 2,3796 2,3843 Table 6.1 Optmum eergy cosumpto for dfferet feed composto. Ut s 10^4 kj per 1 mol of feed. Nomal composto s [ 0,25 0,50 0,25] Z =, ad for omal composto mmum eergy f 4 cosumpto s 2, kj 1. Results from Table 6.1, are show o Pcture 6.1. mol feed Pcture 6.1 Mmum eergy cosumpto for dfferet feed composto For omal feed composto [0,25 0,50 0,25] ad optmal eergy cosumpto compostos of the lqud phase o each tray s show Fgure 6.2 for the frst colum ad Fgure 6.3 for the secod colum. Fgure 6.4 shows temperature o each tray. Those data are take from smulatos, whch s doe for system show Fgure 8.1 chapter 8, for steady state operato. Faculty of Mechacal Egeerg 35

36 Fgure 6.2 Compostos the frst colum Fgure 6.3 Compostos the secod colum Faculty of Mechacal Egeerg 36

37 Fgure 6.4 Temperature the frst ad the secod colum I Fgure 6.3 we ca see that the secod colum has more trays the eeded. Wth same eergy cosumpto we ca reach product purty wth less trays the secod colum. I parts betwee trays umber 16 to 20; from 35 to 50 ad from 55 to 59 we do ot have mass ad heat trasport, sce composto ad temperature le o dagrams above s horzotal ths parts. Those trays ca be removed, ad system operato, othg wll happe. However, ths cocluso s vald oly for omal feed composto. If we have some dsturbaces the feed composto or feed flow rate ths creased umber of trays may be used. Faculty of Mechacal Egeerg 37

38 7. Smulatos Results for Dsturbace Feed Compostos Cosderg Best Self Optmsato Value As s descrbed Chapter 3 ths system has two degrees of freedom (f we assume costat pressures the frst ad secod colum). Oe depedet varable ca be used as selfoptmsato varable ad kept costat. I that case, oe depedet varable s left for achevg adequate product purty. I ths chapter fve caddates for self-optmsato are cosdered: -flow rate of dstllate from the frst to the secod colum, -temperature of lqud o the bottom the frst colum, -temperature of lqud o the top the frst colum, -composto of lght compoet o the bottom the frst colum, -composto of heavy compoet the top the frst colum. Smulatos were steady state, wthout cosderg trays effcecy ad tray behavour. Chages the feed flow rate wll chage optmal varables learly, so dsturbace the feed flow rate ths case was ot studed. Dsturbace feed composto were about 10% of omal compostos. Other possble self-optmsato caddates, for example compostos o the bottom the frst colums, temperatures ad compostos the secod colum, are ot cosdered ths work, but results that case ca be estmated accordg to results these smulatos. For each caddate ad each smulated dsturbaces feed composto, eergy cosumpto s show Table 7.1. Self-optmsato varables are set o optmum value for feed composto [0,25 0,50 0,25], whch s omal composto for feed flow. Because of that, Table 7.1 for omal composto heat cosumpto has to be same as optmal cosumpto for omal composto. Dffereces these heat cosumptos are cosequece of umercal accuracy of calculatos. Reflux rato the frst colum s ot cosdered, accordg to smulato results, chages reflux have bgger fluece o composto products the chages flow rate of dstllate from frst to the secod colum (ths results are ot represeted ths work). I tables below all heat cosumptos are gve 10^4 kj/s for 1 mol/sec of feed flow rate (or 10^4 kj/1 mol of feed). Q rel s relatve heat cosumpto ad t s gve as: Q rel Q-Qopt = 100% (7.1) Q opt Where Qopt s optmum eergy cosumpto for gve feed composto. Ths varable s show Table 6.1 Chapter 6. Relatve eergy cosumpto gves creasg heat cosumpto from optmal eergy cosumpto, ad t s good for choosg best self-optmsato varables. For deal self-optmsato varable relatve eergy cosumpto wll be zero for all dsturbaces. Faculty of Mechacal Egeerg 38

39 Feed composto [mol/mol] Optmal eergy cosumpto Dstllate flow rate s costat Temperature o bottom s costat Temperature o top s costat Composto of lght compoet o top s costat X fa X fb X fc Q opt Q Q rel Q Q rel Q Q rel Q Q rel 0,2 0,5 0,3 2,3396 2, ,4977 2, ,8743 2,4268 3,7271 2,4854 6,2318 0,21 0,5 0,29 2,2882 2, ,9395 2,634 15,1123 2,4125 5,4322 2,4721 8,0369 0,22 0,5 0,28 2,3038 2,5142 9,1327 2, ,5678 2,4073 4,4926 2,4532 6,4849 0,23 0,5 0,27 2,333 2,467 5,7437 2,5039 7,3253 2,3923 2,5418 2,4421 4,6764 0,24 0,5 0,26 2,3457 2,4434 4,1651 2,4387 3,9647 2,384 1,6328 2,4245 3,3593 0,25 0,5 0,25 2,3796 2,3961 0,6934 2,368-0,487 2,374-0,235 2,4029 0,9792 0,26 0,5 0,24 2,3885 2,4198 1,3104 2,4395 2,1352 2,4685 3,3494 2,3949 0,268 0,27 0,5 0,23 2,4163 2,4906 3,0749 2,5274 4,5979 2,5735 6,5058 2,4996 3,4474 0,28 0,5 0,22 2,4471 2,5614 4,6708 2,6142 6,8285 2,6852 9,7299 2,5976 6,1501 0,29 0,5 0,21 2,4516 2,6558 8,3293 2, ,1437 2, ,0609 2, ,0139 0,3 0,5 0,2 2,4796 2,7266 9,9613 2, ,5669 2, ,0389 2, ,4415 0,2 0,55 0,25 2,383 2,585 8,4767 2,4146 1,3261 2,6044 9,2908 2, ,9639 0,21 0,54 0,25 2,3696 2,5378 7,0982 2,3959 1,1099 2,5454 7,419 2, ,3055 0,22 0,53 0,25 2,3621 2,5142 6,4392 2,388 1,0965 2,5033 5,9777 2,5638 8,539 0,23 0,52 0,25 2,3685 2,467 4,1588 2,383 0,6122 2,4588 3,8125 2,5052 5,7716 0,24 0,51 0,25 2,3513 2,4434 3,917 2,3628 0,4891 2,4071 2,3732 2,4574 4,5124 0,25 0,5 0,25 2,3796 2,3961 0,6934 2,368-0,487 2,374-0,235 2,4029 0,9792 0,26 0,49 0,25 2,3843 2,3961 0,4949 2,3821-0,092 2,4685 3,5314 2,406 0,9101 0,27 0,48 0,25 2,3885 2,4198 1,3104 2,3961 0,3182 2,5863 8,2813 2,5288 5,874 0,28 0,47 0,25 2,4124 2,467 2,2633 2,4221 0,4021 2, ,3953 2,6349 9,2232 0,29 0,46 0,25 2,4163 2,4906 3,0749 2,4482 1,3202 2, ,6272 2, ,2061 0,3 0,45 0,25 2,4441 2,5378 3,8337 2,484 1,6325 2, ,4444 2, ,0304 0,25 0,55 0,2 2,4646 2,5378 2,9701 3, ,0766 2,5083 1,7731 2, ,6596 0,25 0,54 0,21 2,4404 2,4906 2,057 2,852 16,8661 2,4788 1,5735 2, ,8784 0,25 0,53 0,22 2,4363 2,467 1,2601 2, ,438 2,4494 0,5377 2, ,3049 0,25 0,52 0,23 2,4079 2,4198 0,4942 2,5621 6,4039 2,4201 0,5067 2,483 3,1189 0,25 0,51 0,24 2,3843 2,3961 0,4949 2,4646 3,3679 2,397 0,5327 2,4487 2,701 0,25 0,5 0,25 2,3796 2,3961 0,6934 2,3736-0,252 2,368-0,487 2,4029 0,9792 0,25 0,49 0,26 2,3743 2,3961 0,9182 2,4636 3,7611 2,368-0,265 2,3686-0,24 0,25 0,48 0,27 2,3457 2,3961 2,1486 2,5554 8,9398 2,368 0,9507 2,3514 0,243 0,25 0,47 0,28 2,3396 2,3961 2,4149 2, ,6902 2,368 1,2139 2,3456 0,2565 0,25 0,46 0,29 2,333 2,4198 3,7205 2, ,8153 2,3853 2,2417 2,3513 0,7844 0,25 0,45 0,3 2,3107 2,4198 4,7215 2,82 22,0409 2,3796 2,9818 2,3626 2,2461 Table 7.1 Eergy cosumpto for dfferet self-optmsato varables ( Q [ ] rel % ; Qé10 kj 4 êë molúû ) For better uderstadg, results Table 7.1 are show Fgures below. I Fgure 7.1 comparso of heat cosumptos for frst group of dsturbace feed compostos where composto of medum compoet s costat ad equal to 0,5 s show. I Fgure 7.2 comparso of heat cosumptos for secod group of dsturbace feed compostos where composto of heavy compoet s costat ad equal to 0,25 s show. I Fgure 7.3 comparso of heat cosumptos for secod group of dsturbace feed compostos where composto of lght compoet s costat ad equal to 0,25 s show. ù Faculty of Mechacal Egeerg 39

40 I Fgures below (Fgure 7.1, Fgure 7.2 ad Fgure 7.3 ) the sold le s for costat dstllate flow rate, the dash le s for costat composto of the lght compoet o the top frst colum, the dash-dot s for costat temperature o the top frst colum ad the dot le s for costat temperature the bottom the frst colum. Fgure 7.1 Eergy cosumptos for dfferet self-optmsato varables (composto of the lght compoet feed s costat) Fgure 7.2 Eergy cosumptos for dfferet self-optmsato varables (composto of the medum compoet feed s costat) Fgure 7.3 Eergy cosumptos for dfferet self-optmsato varables (composto of the heavy compoet feed s costat) Faculty of Mechacal Egeerg 40

41 As t s show the fgures above, there s o best varable for self-optmsato cotrol, for all dsturbaces. Some varables are good for oe type of dsturbaces, for example creasg the heavest compoet composto, but bad for other type of dsturbaces. For fal cocluso from Table 6.1 ext dsturbaces are cosdered: [0,22 0,5 0,28]; [0,28 0,5 0,22]; [0,25 0,53 0,22]; [0,25 0,47 0,28]; [0,22 0,53, 0,25]; [0,28 0,47 0,25]. For those feed compostos, each caddate creased eergy cosumptos from optmum are summarzed. Results are Table 7.2 ad Fgure 7.4. \ [0,22 0,5 [0,28 0,5 [0,25 0,53 [0,25 0,47 [0,22 0,53 [0,28 0,47 0,28] 0,22] 0,22] 0,28] 0,25] 0,25] S D=cost. 2,5142 2,5614 2,5142 2,467 2,467 2,3961 0,6186 Ttop=cost 2,5703 2,6142 2,388 2,4221 2,6906 2,6365 1,0204 Tbottom=cost 2,4073 2,6852 2,5033 2,6873 2,4494 2,368 0,7992 Xa top=cost 2,4532 2,5976 2,5638 2,6349 2,8579 2,3456 1,1517 Table 7.2 Summarzed heat cosumptos for dfferet self-optmsato varables 1,2 1 0,8 0,6 0,4 D Tbottom Ttop Xa top 0,2 0 - Fgure 7.4. Results from Table 6.2, summarzed heat cosumptos for dfferet self-optmsato varables The best varable for self-optmsato cotrol, accordg to results show Fgure 7.4 above s dstllate flow rate the frst colum. The worst self-optmsato varable s composto of lght compoet o top of frst colum. Composto of heavy compoet o the top frst colum was also cosdered. These results are show Table 7.3, below. Ufortuately, accuracy was ot hgh eough, so results are scattered. Results from Table 7.3, are compared wth results for costat dstllate flow rate. Comparsos are showed Fgures 7.4, 7.5 ad 7.6. Faculty of Mechacal Egeerg 41

42 Feed composto Optmal eergy cosumpto Composto of heavy compoet o top s costat X fa X fb X fc Q opt Q Q rel 0,2 0,5 0,3 2,3396 2,3096-0, ,21 0,5 0,29 2,2882 2,2902 0, ,22 0,5 0,28 2,3038 2,3455 0, ,23 0,5 0,27 2,333 2,3631 0, ,24 0,5 0,26 2,3457 2,3784 0, ,25 0,5 0,25 2,3796 2,3973 0, ,26 0,5 0,24 2,3885 2,4173 0, ,27 0,5 0,23 2,4163 2,4352 0, ,28 0,5 0,22 2,4471 2,4518 0, ,29 0,5 0,21 2,4516 2,4695 0, ,3 0,5 0,2 2,4796 2,4855 0, ,2 0,55 0,25 2,383 2,3777-0, ,21 0,54 0,25 2,3696 2,3788 0, ,22 0,53 0,25 2,3621 2,3871 0, ,23 0,52 0,25 2,3685 2,3893 0, ,24 0,51 0,25 2,3513 2,3937 0, ,25 0,5 0,25 2,3796 2,3973 0, ,26 0,49 0,25 2,3843 2,4031 0, ,27 0,48 0,25 2,3885 2,4112 0, ,28 0,47 0,25 2,4124 2,4159 0, ,29 0,46 0,25 2,4163 2,4228 0, ,3 0,45 0,25 2,4441 2,4318-0, ,25 0,55 0,2 2,4646 2,5786 0, ,25 0,54 0,21 2,4404 2,5014 0, ,25 0,53 0,22 2,4363 2,4247-0, ,25 0,52 0,23 2,4079 2,4203 0, ,25 0,51 0,24 2,3843 2,4118 0, ,25 0,5 0,25 2,3796 2,3973 0, ,25 0,49 0,26 2,3743 2,3853 0, ,25 0,48 0,27 2,3457 2,3731 0, ,25 0,47 0,28 2,3396 2,3604 0, ,25 0,46 0,29 2,333 2,3477 0, ,25 0,45 0,3 2,3107 2,3318 0, Table 7.3 Eergy cosumpto for heavy compoet o the top frst colum as self-optmsato varable 4 ( Q [%] ; Qé10 kj ù rel êë molúû Faculty of Mechacal Egeerg 42

43 Fgure 7.4 Eergy cosumptos for dfferet self-optmsato varables (composto of lght compoet feed s costat) Fgure 7.5 Eergy cosumptos for dfferet self-optmsato varables (composto of medum compoet feed s costat) Fgure 7.6 Eergy cosumptos for dfferet self-optmsato varables (composto of heavy compoet feed s costat) I Fgures above, sold le s for costat dstllate flow rate betwee colums, ad dash le s for costat composto o the top the frst colum. Faculty of Mechacal Egeerg 43

44 Fgure 7.7 s the same fgure as Fgure 7.4 but oly for costat dstllate flow rate ad for costat heavy compoet o the top frst colum. As t s show o the Fgure 7.7 below, the best self-optmsato varable s heavy compoet composto o the top the frst colum. Sce ths composto s very low, frst colum separato s close to sharp separato, due to hgh purty of fal products. 0,7 0,6 0,5 0,4 0,3 D Xheavy top 0,2 0,1 0 - Fgure 7.7 Summarzed heat cosumptos for self-optmsato varables (costat dstllate flow rate ad costat heavy compoet composto o the top frst colum) As represeted o Fgure 7.7 ad 7.4 the best self-optmsato varable s the composto of the heavest compoet o the top the frst colum. If ths varable s kept costat, accordg to Fgure 7.4, 7.5 ad 7.5, the the crease of heat cosumpto wll be low compared to the optmal cosumpto. From smulato results, composto of heavest compoet o the top frst colum should be mol/mol o the top tray. I Chapter 4 s descrbes sharp separato real colums, ad we ca coclude that the frst colum should work as sharp AB/BC. Wth keepg top composto of heavest compoet the frst colum eough low, we have sharp AB/BC, ad we are close to optmum performace of dstllato system. Ths cocluso s used ext chapter, where dyamcal behavour of system s cosdered. Faculty of Mechacal Egeerg 44

45 8. Smulato of Dyamcal Performace of System wth Prefractoator As s descrbed Chapter 7, the best self-optmsato varable for the system cosdered s composto of the heavest compoet o the top the frst colum. Ths composto, accordg results from smulatos, should be 0,0144 mol/mol o the top tray. If we keep ths composto costat, we are very close to optmal eergy cosumpto (Fgure 7.4, Fgure 7.5 ad Fgure 7.6). Whe keepg costat composto of heavest compoet, the frst colum (prefractoator) works as sharp AB/BC. Fgure 8.1 shows haw oe possble solutos, for the mplemetato of a cotrol scheme, based o the above results. The cotrol scheme preseted Fgure 8.1 has bee used for the dyamc smulatos. Fgure 8.1 The cotrol scheme Faculty of Mechacal Egeerg 45

46 Composto of the product C s cotrolled wth the vapour flow rate cotrol valve the bottom of frst colum. Composto of product B s cotrolled, usg cotrol of flow rate of sde stream. Composto of product A s cotrolled chagg reflux the secod colum. Composto of heavest compoet the dstllate from the frst colum s also cotrolled usg reflux. Ths cotrol loop s chose accordg results from self-optmsato study. The most dffcult cotrol loop ths system s the coecto betwee composto of the bottom product ad evaporator duty for the frst colum. Ths s because of the erta of the system ad t s very mportat case of perodc dsturbaces. Evaporator duty for frst colum s cotrolled usg pressure cotrol valve for steam supply The smulato model s smplfed. It s assumed that all level cotrols work perfect. Pressure cotrol frst colum was assumed perfect. Smplfed model, smulated ths work s show o Fgure 8.2. Fgure 8.2 Smplfed model Nomal feed composto the smulato was [ ] ad omal feed flow rate was 0.1 mol/s. Smulato was doe for two dsturbaces composto: [ ] ad [ ] ad for two dsturbaces feed flow rate 0.9 ad 0.11 m/s. All dsturbaces Faculty of Mechacal Egeerg 46

47 happeed 100 secod after startg momet. Before dsturbaces, performace was steady for omal composto ad omal feed flow rate. O Fgure 8.3 ad Fgure 8.4, below s gve result for dsturbaces feed composto. Fgure 8.3 Product composto. Dsturbace feed composto [ ] Faculty of Mechacal Egeerg 47

48 Fgure 8.4 Product composto. Dsturbace feed composto s [ ] Accordg to results show o fgures above, after about 300 secod, we have composto of fal product hgher tha 98%, whch s acceptable, for dsturbaces [ ], ad after 2300 secod for dsturbace [ ]. I smulato PI cotrollers were used. Proportoal ga was twce hgher for compostos above Result for dsturbaces feed flow rates are show Fgure 8.5 ad Fgure 8.6, o the ext page. Faculty of Mechacal Egeerg 48

49 Fgure 8.5 Product composto. Dsturbace feed flow rate, 0.9 mol/s Fgure 8.6 Product composto. Dsturbace feed flow rate, 0.11 mol/s Accordg results Fgures above, dsturbaces feed flow rate do ot have bg fluece o products composto. Faculty of Mechacal Egeerg 49

50 Accordg to smulato results, we may coclude that t s possble to cotrol ths system ad keep product composto at 99%. Dsturbaces feed flow rate, as s show o Fgure 8.5 ad Fgure 8.6 do ot make bg dsturbaces products composto. I smulated cases, feed + 0,05% dsturbaces dd ot make bgger chages products compostos tha. Dsturbaces -0,91% feed compostos, as s show o Fgure 8.3 ad Fgure 8.4, made bg chages product composto, but oly temporally. A bggest dsturbace product composto that case was + 1,01%. -8,59% I Fgure 8.7 results for smulato whch the set pot for composto of products are chaged from 90% o 99% are show. Before chagg the set pots the system was workg at steady wth composto of products at 90%. Fgure 8.7 Chagg set compostos products As t s show the Fgure, steady workg order s reached after approxmately 2500 secods. I Fgure 8.8 below results of smulato wth perodcal dsturbaces s show. Composto of the heavest ad lght compoet feed flow rate was chaged as sus fucto betwee 0.22 ad 0.28 mol/mol every 1600 secods. Same smulato, but for slower chages feed composto (every 3600 secods), was doe ad results are show Fgure 8.9. Fgure 8.8 Perodcal chages feed composto Faculty of Mechacal Egeerg 50