Oldershaw perforated plate distillation

Transcription

1 NTNU Norwegian Universiy of Science and Technology Faculy of Naural Sciences and Technology Deparmen of Chemical Engineering Oldershaw perforaed plae disillaion Felleslab, TKP 4105 and TKP 4110 Tile: Oldershaw perforaed plaes Locaion: Trondheim Auhors: Anders Leirpoll & Kasper Linnesad Group: B16 Supervisor: Vladimiros Minasidis Version: Performed: a 8:15-13:00 Number of pages: Repor: Appendices: Absrac An oldershow perforaed plaes disillaion was performed on a waer-ehanol mixure using complee reflux o sudy seady sae, heoreical rays, column efficiency, flooding poin and weeping poin. The column efficiency was found o be highes wih a heaing duy of 60 %. The weeping poin was reached a a boiler power duy of 10%, while he column proved unable o reach he flooding poin. Jeg erklærer a arbeide er ufør selvsendig og i samsvar med NTNUs eksamensreglemen. Dae and signaures: Address Locaion Tel Sem Sælands vei 4 NO-7491 Trondheim Fax Org. no. NO

2 i Table of Conens 1 Purpose Theory Flooding poin Weeping poin McCabe-Thiele mehod Toal reflux Gas chromaography Experimenal Column sarup Time required o reach seady sae condiion Efficiency vs. vapor velociy Column shudown Resuls Discussion Conclusion... 8 References... 8 Symbols and abbreviaions... 8 Appendix A - Calculaions... A-1 A.1 Waer-ehanol mixure... A-1 A.2 Conversion beween mole fracion, volume fracion and mass fracion... A-1 Appendix B - Daa... B-1 Appendix C - MATLAB scrips... C-1 Appendix D - Assignmen calculaions... D-1 D.1 Pycnomeer... D-1 D.2 Vapor velociy... D-2

3 1 1 Purpose The purpose of he experimen was o be inroduced o he basic principles of seady sae, column efficiency, vapor velociy and heoreical rays, by performing an oldershaw perforaed plae disillaion. 2 Theory 2.1 Flooding poin In a disillaion column he vapor flows upwards and he liquid flows downwards. The flooding poin is referred o as he vapor velociy when liquid accumulaes in he column [1]. This happens when he vapor velociy ges oo high, and he vapor drags he liquid flow up he column. The flooding poin causes a pressure drop in he column, as well as reduced efficiency [2]. 2.2 Weeping poin A seady sae condiions he flow of liquid hrough he perforaions is sopped by vapor velociy hrough he perforaions [1]. Low vapor velociy causes he liquid o weep down hrough he perforaions, giving less vapor-liquid conac, resuling in a lower efficiency [2]. 2.3 McCabe-Thiele mehod The McCabe-Thiele mehod is a graphical mehod for analysis of disillaion by deerminaion of he number of heoreical rays needed for a given separaion [3]. I bases around he assumpion of consan molar flows. Using mass balances and vapor-liquid equilibrium (VLE) daa for componens, a McCabe-Thiele diagram can be consruced, and heoreical number of rays can be deermined [3]. An example is shown in Figure 8. The horizonal axis represens mole fracion of ligh componen in liquid phase, while verical axis represens mole fracion of ligh componen in gas phase. Ploing VLE daa gives he equilibrium line, while mass balance gives he enriching and sripping operaing lines. For he enriching secion of he column, he mole fracion of ligh componen in gas phase a ray,, is given by [3]: Where is he reflux raio, is he mole fracion of ligh componen in liquid phase a sep and is he mole fracion of ligh componen in he disillae. For he sripping secion of he column, he mole fracion of ligh componen in gas phase a ray,, is given by [3]: Where is he liquid flow from ray, is vapor flow from ray, is boom flow, is mole fracion of ligh componen in boom flow and is mole fracion of ligh componen in liquid phase a ray. In his experimen i is assumed consan molar flows, e.g. and. (2.1) (2.2)

4 2 The parameer represens he condiion of he feed and is defined as [3]: he needed o por e o e o eed ener ng ond on o r en he o por on o eed This is used in he diagram o plo he -line, wih slope, crossing he crossing-poin of he operaing lines and he line. To deermine number of heoreical sages required in a disillaion, seps are drawn in he diagram, saring a he op ray where. The seps are made by drawing horizonal and verical alernaing lines beween he equilibrium line and he operaing line, unil is reached. The number of seps in he diagram represen he number of heoreical rays required in he disillaion [3] Toal reflux Wih oal reflux he reflux raio is infiniely large, hence he operaing line can be found by aking he limi of (2.2) as approaches infiniy: (2.3) This resul can be used as he operaing in he McCabe-Thiele mehod wih oal reflux, consequenly he operaing line a oal reflux is given as he line. 2.4 Gas chromaography Gas chromaography (GC) is used for separaion and deecion of gasses and volaile componens in mainly organic soluions. This is an analyical soluion used o es he puriy of he sample or he relaive amoun of each componen of he es sample. [4] In gas chromaography here is a moving phase, usually an iner gas, and a saionary phase consising of a polymer or glass, called column. The sample will elue a differen imes on he column, called he reenion ime of he componen. Using his, he weigh fracion of each componen can be calculaed. [4] (2.4) 3 Experimenal 3.1 Column sarup The compuer and cooling waer were urned on, and he boom and disillae aps were closed. The oldershow perforaed plaes column was filled wih ehanol (11%, 5800 ml). The column was se o oal reflux, and he boilers power duy was se o 90%, wih a conrol box emperaure of. When he op emperaure or pressure changed subsanially he boiler was se o 50%. The ime when he vapor sream saed condensing was noed as zero ime,. In case of flooding he heaed was urned off, and in case of any emergency he heaer was urned off and he cooling lef running.

5 3 3.2 Time required o reach seady sae condiion Samples were aken from he op of he column every 5 minues unil 12 samples had been aken. A he ime of he 12 h sample, a sample was also aken from he boom of he column. Samples were analyzed using GC. 3.3 Efficiency vs. vapor velociy The power was se o 40%, and he column was lef alone unil i had reached seady sae. Samples (20 ml) were aken from op and boom, o be analyzed. This was performed for 5 differen boiler duies. Afer he las sample, weeping and flooding poins of he boiler were noed. 3.4 Column shudown Afer all samples were aken, he heaer was urned off, and he column was lef o cool. The column was empied, cooling waer and compuer were urned off. 4 Resuls The mole fracion of ehanol in disillae a a boiler duy of 40% was ploed agains ime in Figure 1. x e :00 05:00 10:00 15:00 20:00 25:00 30:00 35:00 40:00 45:00 50:00 55:00 [min:s] Figure 1: Mole fracion of ehanol in disillae, e, ploed agains ime,. I appears as if he daa poin a 15 min should have been higher, which would give a seady sae afer ~15 min, while he poin a 35 min is higher han i should be. In Figure 2, Figure 3, Figure 4, Figure 5 and Figure 6 he McCabe-Thiele diagrams are ploed for boiler duies of 40%, 50%, 60%, 70% and 80%, respecively.

6 y y The number of sages required is: 4.63 Wih a heaing duy of: 40 % Equilibrium line Operaing line x Figure 2: McCabe-Thiele diagram for a power duy of 40%. Here, x is he mole fracion of ehanol in he liquid phase and y is he mole fracion of ehanol in he gas phase. The plo is made wih Program code 1 in Appendix C - Malab scrips The number of sages required is: 6.24 Wih a heaing duy of: 50 % Equilibrium line Operaing line x Figure 3: McCabe-Thiele diagram for a power duy of 50%. Here, x is he mole fracion of ehanol in he liquid phase and y is he mole fracion of ehanol in he gas phase. The plo is made wih Program code 1 in Appendix C - Malab scrips.

7 y y The number of sages required is: 9.09 Wih a heaing duy of: 60 % Equilibrium line Operaing line x Figure 4: McCabe-Thiele diagram for a power duy of 60%. Here, x is he mole fracion of ehanol in he liquid phase and y is he mole fracion of ehanol in he gas phase. The plo is made wih Program code 1 in Appendix C - Malab scrips The number of sages required is: 4.47 Wih a heaing duy of: 70 % Equilibrium line Operaing line x Figure 5: McCabe-Thiele diagram for a power duy of 70%. Here, x is he mole fracion of ehanol in he liquid phase and y is he mole fracion of ehanol in he gas phase. The plo is made wih Program code 1 in Appendix C - Malab scrips.

8 y The number of sages required is: 4.98 Wih a heaing duy of: 80 % Equilibrium line Operaing line x Figure 6: McCabe-Thiele diagram for a power duy of 80%. Here, x is he mole fracion of ehanol in he liquid phase and y is he mole fracion of ehanol in he gas phase. The plo is made wih Program code 1 in Appendix C - Malab scrips. In Table 1 he calculaed heoreical seps for each boiler duy is shown. Table 1: Calculaed heoreical seps for each boiler duy. Boiler duy # of heoreical seps Column efficiency 40 % % % % % The column efficiency was ploed agains vapor velociy in Figure 7.

9 Column efficiency 7 86% 84% 82% 80% 78% 76% 74% Vapor velociy [m s -1 ] Figure 7: Column efficiency ploed agains vapor velociy. The weeping poin was observed using a boiler duy of 10%, while maximum power duy was no enough o reach he flooding poin. 5 Discussion In Figure 1, i is observed ha he column reached an approximae seady sae afer abou 20 minues. Afer 20 minues he composiion in he disillae is relaively consan, which is an indicaion ha equilibrium has been aained in each sage, and herefore a seady sae, has been obained. While he sysem is operaing a oal reflux and consan power duy, he equilibriums will remain consan, hence also he composiion of he disillae. From daa obained from he GC, all samples were found o have a molar fracion lower han he azeorope of ehanol-waer mixures. The McCabe-Thiele diagrams show ha o ge closer o he azeorope would require more significanly more sages in he column, since he column efficiency is already high. The column efficiency seen in Figure 7 shows no rend; herefore i is difficul o draw any conclusion if column efficiency is influenced by vapor velociy. However if he 4 h poin is assumed o be oo low, an expeced rend appears. The efficiency as a funcion of vapor velociy should indeed have a maximum where maximum conac beween he phases is achieved. I looks like he column is mos effecive a 50-60% boiling power. The weeping poin was observed a 10% boiler hea duy, afer which he column gave no disillae. Even a 100% boiler hea duy he flooding poin was no observed, hough he vapor velociy did increase subsanially.

10 8 6 Conclusion The ime required o reach seady sae condiions was approximaely 20 minues. The column efficiency was found o be highes wih a heaing duy of 60 %. The weeping poin was observed a 10% boiler hea duy, while he flooding poin was no reached, even a 100% boiler hea duy. References [1 "Felles Lab: Disillaion Columns," Deparmen of Chemical Engineering, Norwegian Universiy of ] Technology and Science, Trondheim, Scrip [Online]. hp:// pions/disinsruc.pdf [2 Rober H. Perry and Don W. Green, Perry's Chemical Engineers' Handbook, 8h ed.: McGraw-Hill ] Professional, [3 Chrisie John Geankoplis, Transpor Processes and Separaion Process Principles, 4h ed. ] Wesford, Massachuses: Prenice Hall, [4 Raymond P. W. Sco, "Chrom-Ed Book Series," in Gas Chromaography.: Library for Science, LLC, ] 2003, vol. II. Symbols and abbreviaions Symbol Uni Descripion o Concenraion of componen Inner diameer of column GC Gas chromaography IS Inernal sandard Liquid flow a ray g o Molecular weigh of componen g Mass of componen Tray number mol The number of moles of componen Parameer for q-line Reflux raio Temperaure Time Volume of componen Toal volume Volume of sample in gas phase Vapor velociy Boom flow a ray Molefracion of componen in liquid phase Molefracion of componen in gas phase g Densiy of componen

11 A-1 Appendix A - Calculaions A.1 Waer-ehanol mixure The mole fracion of componen,, is given by: where is moles of componen and is he oal number of moles. Moles of componen is given by: Where is volume of componen and is he molar mass of componen. In a mixure of only waer and ehanol, moles of waer is given by: (A.1) (A.2) (A.3) Where index w is for waer, e is for ehanol and (A.3) and (A.2)o (A.1): is he oal volume of he mixure. By applying (A.4) Insering values,, and he volume of ehanol is obained as. This is he amoun of pure ehanol needed. In 96% ehanol his is equal o: (A.5) Giving Making he waer required. The amoun of waer is hen: (A.6) A.2 Conversion beween mole fracion, volume fracion and mass fracion The mole fracion of componen A in a binary mixure is given as: o Where and is he number of moles of componen A and B respecively and o is he oal number of moles. The mass fracion is of componen A in a binary mixure given by: o Where and is he mass of componen A and B respecively and o is he oal mass of he mixure. Similarly he volume fracion of componen A can be found by: (A.7) (A.8)

12 A-2 o (A.9) Where and is he volume of componen A and B respecively and o is he oal volume of he mixure. By uilizing ha he mass of componen A is he number of moles of componen A muliplied wih he molecular weigh, (A.8) can be rewrien as Where is he molecular weigh of componen A. Solving for, doing he exac same operaions wih respec o componen B, and insering ino(a.7) yields: Here he fac ha he sum of he mass fracions is equal o one. (A.11) provides he means o conver from mass fracion o mole fracion. Rewriing (A.9) wih respec o : By noing ha he mass of componen A is equal o is volume imes is densiy (A.13) is obained: o (A.10) In he las sep he number of moles of componen A is found by dividing is mass by is molecular weigh. A similar derivaion can be performed wih respec o B, and insering hese resuls ino (A.7) yields: (A.14) enables calculaion of he mole fracion when he volume fracion is known. (A.11) (A.12) (A.13) (A.14)

13 B-1 Appendix B - Daa The daa obained during he experimen wih differen power duies are summarized in Table 2. Table 2: Daa from he experimen wih differen power duies, he composiions are given as volume fracions and were obained from a GC analysis. Power duy Reflux rae Temperaure Top composiion Boom composiion 40 % % % % % The daa used o deermine he ime i ook he column o reach seady sae are displayed in Table 3. Table 3: Daa obained o deermine he ime i ook for he column o reach seady sae. The op composiion is given as a volume fracion and were obained from a GC analysis Time Top composiion 00: : : : : : : : : : : :

14 C-1 Appendix C - MATLAB scrips Program code 1: McCabeThiele.m %This scrip plos he equilibrium line for a binary mixure of ehanol and %waer, and calculaes he number of seps needed o reach a cerain %concenraion wih oal reflux. %PART 1 - Ploing he equilibrium line and he operaing line xy = impordaa(['c:\users\kasper Linnesad\Dropbox\KasperTL\Felleslab\',... 'Oldershaw\Daa\VLE.x']); x = xy(:,1); y = xy(:,2); %This is given as a mass fracions, and have o be convered o mole fracions x = x./(x+(1-x).*( / )); y = y./(y+(1-y).*( / )); %x is he mole fracion of ehanol in he liquid phase, and y is he mole %fracion of ehanol in he gas phase. %Fi a polynomial of enh degree, p, o fi he daa p = polyfi(x,y,10); %Disillae composiion, xd and boom composiion, xb xd = [ ]; xb = [ ]; %PART2 - Calculaing and ploing each heoreical sage for k=1:lengh(xd) xs = []; ys = []; i = 1; xs(i) = xd(k); ys(i) = xd(k); %A couner, i; The composiion on each sage, xs(i) and ys(i) f =@(x,y)(p(1)*x^10+p(2)*x^9+p(3)*x^8+p(4)*x^7+p(5)*x^6+p(6)*x^5+... p(7)*x^4+p(8)*x^3+p(9)*x^2+p(10)*x^1+p(11) - y); %Solve he above equaion for each sep, and plo he sages in he %McCabe-Thiele diagram %plo p and he operaing line y = x fig=figure(k); se(fig,'name','mccabe-thiele','posiion',[50 150, 800, 500]); hold on eq = plo(0:0.001:1,polyval(p,0:0.001:1)); se(eq, 'Color','red','LineWidh',1.5) op = line([0 1],[0 1]); se(op, 'Color','green','Linewidh',1.5) axis([ ]); xlabel('x'); ylabel('y'); legend('equilibrium line', 'Operaing line','locaion','eas');

15 C-2 while xs(i)>xb(k) xs(i+1) = fzero(f,0.5,[],ys(i)); if xs(i+1)>xb(k) line([xs(i) xs(i+1)],[ys(i) ys(i)],'color','blue','linewidh',1.5); else line([xs(i) xb(k)],[ys(i) ys(i)],'color','blue','linewidh',1.5); end ys(i+1) = xs(i+1); if xs(i+1)>xb(k) line([xs(i+1) xs(i+1)],[ys(i) ys(i+1)],'color','blue',... 'LineWidh',1.5); end i = i+1; end for j=1:i-1 if xs(j+1)>xb(k) plo(xs(j+1),ys(j),'-.kx','markersize',15,'linewidh',1.5) else plo(xb(k),ys(j),'-.kx','markersize',15,'linewidh',1.5) end end %Add a exbox wih he number of sages required N=i-2+(xb(k)-xs(i-1))/(xs(i)-xs(i-1)); sr ={['The number of sages required is: ', num2sr(n,3)],... ['Wih a heaing duy of: ',num2sr(30+10*k),' %']}; sbox = annoaion('exbox',[ ],'Sring',sr,... 'LineSyle','none'); name = [num2sr(30+10*k) '%.emf']; prin(fig,name,'-dmea'); end

16 D-1 Appendix D - Assignmen calculaions D.1 Pycnomeer The volume of pycnomeer can be calculaed by he following: (D.1) Where is he volume of pycnomeer ; is he weigh of pycnomeer filled wih pure waer; is he weigh of pycnomeer and is he densiy of pure waer a. The densiy of each sample can be deermined by: p e p e (D.2) Where p e is he weigh of pycnomeer filled wih he sample and p e is he densiy sample. The composiion can hen be found by comparing he calculaed densiy wih values from a able from he lieraure. The values given in he assignmen is summarized in Table 4 ogeher wih values calculaed by uilizaion of (D.1) and (D.2). The densiy of waer was found in Geankoplis [3]. The weigh percenage of each sample was found by he daa from Green and Perry [2]. The resuls are lised in Table 4. The mole fracion of a binary mixure is given as: 4 o Where is he number of moles of componen is he number of moles of componen ; is he mole fracion of componen and o is he oal number of moles. This can be rewrien in erms of mass and molecular weigh which leads o: (D.3) (D.4) Where is he mole fracion of ehanol; is he mass of ehanol, is he molecular weigh of ehanol; is he mass of waer; is he molecular weigh of waer; is he weigh percenage of ehanol and is he weigh percenage of waer. The molecular weighs are obained from [2]. This enables he calculaion of he mole fracion of ehanol in each sample, and he resul is presened in Table 4. Table 4: The values calculaed Pycnomeer # p e p e [ ] % %

17 D-2 Table 4 display ha he mole fracions calculaed by (D.4) is in grea viciniy of he ones lised in he scrip [1] D.2 Vapor velociy The vapor velociy,, is given by: g (D.5) where is he volumeric flow of he gas phase, is he cross secion area of he column and is he inner diameer of he column. In his experimen he reflux rae is given as a volumeric liquid flow, and hus has o be convered o a volumeric gas flow. This is done by firs convering he liquid flow o a mole flow, hen he mole flow is convered o a vapor flow using he ideal gas law. u d is he molar flow rae; u d is he volume flow of he reflux, e.g. he reflux rae; is he volume fracion of ehanol; is he densiy of ehanol; is he densiy of waer; is he molecular weigh of ehanol and is he molecular weigh of waer. The volumeric gas flow can hen be found by he ideal gas law; u d (D.6) g ( u d u d ) (D.7) Where is he gas consan; is he emperaure and is he pressure. Using he daa from he scrip [1] and insering (D.7) ino (D.5) he vapor velociy was found o be

18 D-3 Program code 2: McCabeThiele1.m %This scrip plos he equlibrium line for a binary mixure of ehanol and %waer, and calculaes he number of seps needed o reach a cerain %concenraion wih oal reflux. %PART 1 - Ploing he equilibrium line and he operaing line xy = impordaa(['c:\users\kasper Linnesad\Dropbox\KasperTL\Felleslab\',... 'Oldershaw\Daa\VLE.x']); x = xy(:,1); y = xy(:,2); %This is given as a mass fracions, and have o be convered o mole fracions x = x./(x+(1-x).*( / )); y = y./(y+(1-y).*( / )); %x is he mole fracion of ehanol in he liquid phase, and y is he mole %fracion of ehanol in he gas phase. %Fi a polynom of enh degree, p, o fi he daa p = polyfi(x,y,10); %plo p and he operaing line y = x figure('name','mccabe-thiele','posiion',[50 150, 800, 500]); hold on eq = plo(0:0.001:1,polyval(p,0:0.001:1)); se(eq, 'Color','red','LineWidh',1.5) op = line([0 1],[0 1]); se(op, 'Color','green','Linewidh',1.5) axis([ ]); xlabel('x'); ylabel('y'); legend('equilibrium line', 'Operaing line','locaion','easouside'); %Disillae composiion, xd and boom composiion, xb xd = 0.744; xb = 0.033;

19 D-4 %PART2 - Calculaing and ploing each heoreical sage xs = []; ys = []; i = 1; xs(i) = xd; ys(i) = xd; %A couner, i; The composiion on each sage, xs(i) and ys(i) f =@(x,y)(p(1)*x^10+p(2)*x^9+p(3)*x^8+p(4)*x^7+p(5)*x^6+p(6)*x^5+... p(7)*x^4+p(8)*x^3+p(9)*x^2+p(10)*x^1+p(11) - y); %Solve he above equaion for each sep, and plo he sages in he %McCabe-Thiele diagram while xs(i)>xb xs(i+1) = fzero(f,0.5,[],ys(i)); line([xs(i) xs(i+1)],[ys(i) ys(i)],'color','blue','linewidh',1.5); ys(i+1) = xs(i+1); if xs(i+1)>xb line([xs(i+1) xs(i+1)],[ys(i) ys(i+1)],'color','blue','linewidh',1.5); end i = i+1; end for j=1:i-1 plo(xs(j+1),[ys(j)],'-.kx','markersize',15,'linewidh',1.5) end %Add a exbox wih he number of sages required sr={'the number of sages required is:', num2sr(i-1)}; sbox = annoaion('exbox',[ ],'Sring',sr,'LineSyle','none'); Running Program code 2 yields Figure 8 and i is obained ha five heoreical sages is required o achieve he desired concenraions.

20 y D The number of sages required is: Equilibrium line Operaing line x Figure 8: A McCabe-Thiele diagram for a binary mixure of ehanol and waer a 1 bar. The number of heoreical sages is calculaed wih Program code 2