source: trunk/eml/stage_separators/tray_Eff.mso @ 593

Last change on this file since 593 was 593, checked in by Argimiro Resende Secchi, 15 years ago

Adding efficiency models in distillation column (by Josias)
File size: 25.5 KB
Line 
1#*-------------------------------------------------------------------
2* Models of tray with Efficiency Prediction
3* Author: Josias J. Junges
4*-------------------------------------------------------------------*#
5
6using "streams";
7using "tray";
8
9Model trayEffEmp as tray
10       
11        ATTRIBUTES
12        Pallete         = false;
13        Icon            = "icon/Tray";
14        Brief           = "Tray with Efficiency Prediction - Empiric Model";
15        Info =
16        "==Description==
17Prediciton based on Chan e Fair(1984) model, with entrainment correction.
18Multicomponent mixture treated with pseudo-binary approach.
19       
20        == References ==
21*Clear Liquid Height: Bennett et al. (1983).
22*Capacity Factor: Treybal(1968).
23*Flood Velocity: Fair(1961).
24*Liquid Mixing Models: Lewis(1936).
25*Eddy Diffusivity: Molnar(1974).
26*Entrainment Correction: Colburn(1936).
27*Fraction of entrained liquid: Zuiderweg(1982).
28
29General References:
30*CHAN, H.;FAIR, J. R. Prediction of Point Efficiencies on Sieve Trays. 1. Binary Systems. Ind. Eng. Chem. Process Des. Dev., v.23, n.4, p.814-9, 1984.
31*LOCKETT, M. J. Distillation Tray Fundamentals. Cambridge: Cambridge University Press, 1986.
32";
33        PARAMETERS
34       
35        z as length (Brief="Liquid flow path length");
36        d as length (Brief="Plate Diameter");
37        Aa as area (Brief="Active Area or Bubbling Area = Atray - 2*Adowncomer");
38        fi as fraction (Brief="Fractional perforated tray area(hole area/ bubbling area)");
39        Ts as length (Brief="Tray spacing");
40outer   iLK as Integer (Brief="Pseudo-binary ligth key index");
41outer   iHK as Integer (Brief="Pseudo-binary heavy key index");
42
43        VARIABLES
44       
45        Qv as flow_vol (Brief="Vapour volumetric flow");
46        Ql as flow_vol (Brief="Liquid volumetric flow");
47        Mv as flow_mass (Brief="Vapour mass flow", Lower=0);
48        Ml as flow_mass (Brief="Liquid mass flow", Lower=0);
49        Dv as diffusivity (Brief="Diffusivity on Vapour Phase");
50        Dl as diffusivity (Brief="Diffusivity on Liquid Phase");
51        sigma as surf_tens (Brief="Surface Tension");
52       
53        ua as velocity (Brief="Superficial velocity based on Aa");
54        fs as positive(Brief="Superficial factor", Unit='kg^.5/m^.5/s');
55        c as positive (Brief="Constant in eq. of Clear Liquid Height");
56        ae as fraction (Brief="Effective liquid volume fraction");
57        hcl as length (Brief="Clear Liquid Height");
58        tv as time_sec (Brief="Mean residence time of vapour in dispersion");
59        tl as time_sec (Brief="Mean residence time of liquid on tray");
60        us as velocity (Brief="Superficial velocity based on Ap");
61        fp as positive (Brief="Flow Parameter");
62        csb as positive (Brief="Capacity Factor");
63        uf as velocity (Brief="Flood velocity");
64        ff as positive (Brief="Flood factor");
65        lambda as Real (Brief="Stripping factor or ratio of slope of equilibrium line to slope of operating line");
66        m as Real (Brief="Slope of equilibrium line");
67       
68        VinLK as Real (Brief="Pseudo-binary key ");
69        VoutLk as Real (Brief="Pseudo-binary key");
70        LinLK as Real (Brief="Pseudo-binary key");
71        LoutLk as Real (Brief="Pseudo-binary key");
72       
73        NV as positive (Brief="Number of vapour phase transfer units");
74        NL as positive (Brief="Number of liquid phase transfer units");
75        NOG as positive (Brief="Number of overall vapour phase transfer units");
76        EOG as positive (Brief="Point Efficiency");
77       
78        De as Real (Brief="Eddy diffusivity for liquid mixing");
79        Pe as positive (Brief="Peclet Number");
80        n as Real (Brief="Constant");
81        Emv1 as positive (Brief="Murphree tray efficiency");
82       
83        hb as length (Brief="Height on spray regime");     
84        l as positive (Brief="Fraction of entrained liquid");   
85        uh as velocity (Brief="Gas velocity through holes");   
86        Emv2 as positive (Brief="Apparent Murphree tray efficiency"); 
87       
88        EQUATIONS
89       
90        "Vapour Volumetric Flow"
91        Qv=OutletV.F*vV;
92       
93        "Liquid Volumetric Flow"
94        Ql=OutletL.F*vL;
95       
96        "Vapour Mass Flow"
97        Mv=Qv*rhoV;
98       
99        "Liquid Mass Flow"
100        Ml=Ql*rhoL;
101       
102        "Superficial Velocity"
103        ua=Qv/Aa;
104       
105        "Superficial Factor"
106        fs=ua*rhoV^.5;
107       
108        "Constant c"
109        c=.5+0.438*exp(-137.8*'1/m'*hw);
110       
111        "Effective liquid volume fraction"
112        ae=exp(-12.55*(ua*'s/m'*(rhoV/(rhoL-rhoV))^0.5)^0.91); 
113       
114        "Clear Liquid Height"
115        hcl=ae*(hw*'1/m'+c*((Ql*'s/m^3')/(lw*'1/m'*ae))^.67)*'m';
116       
117        "Mean residence time of vapour in dispersion"
118        tv=(1-ae)*hcl/(ae*ua);
119       
120        "Mean residence time of liquid on tray"
121        tl=hcl*z*lw/Ql;
122       
123        "Superficial velocity based on Ap"
124        us*Ap=Qv;
125       
126        "Flow Parameter"
127        (fp*Mv)^2*rhoL=Ml^2*rhoV;
128       
129        "Capacity Factor"
130        csb=(0.0744*Ts*'1/m'+0.0117)*(log(abs(1/fp)))+0.0304*Ts*'1/m'+0.0153;
131       
132        "Flood velocity"
133        uf = csb*(sigma*'1/(N/m)'/0.02)^.2*(abs((rhoL-rhoV)/rhoV))^.5*(fi/.1)^.44*'m/s';
134       
135        "Flood Factor"
136        ff*uf=us;
137       
138        if NComp > 2 then
139               
140                "Pseudo-binary Approach"
141                VinLK=InletV.z(iLK)/(InletV.z(iLK)+InletV.z(iHK));
142                VoutLk=OutletV.z(iLK)/(OutletV.z(iLK)+OutletV.z(iHK));
143                LinLK=InletL.z(iLK)/(InletL.z(iLK)+InletL.z(iHK));
144                LoutLk=OutletL.z(iLK)/(OutletL.z(iLK)+OutletL.z(iHK));
145               
146        else
147                VinLK=1;
148                VoutLk=1;
149                LinLK=1;
150                LoutLk=1;
151               
152        end
153       
154        "Stripping factor or ratio of slope of equilibrium line to slope of operating line"
155        lambda=m*(OutletV.F/OutletL.F);
156       
157        #Chan e Fair(1984) Model#
158       
159        "Number of vapour phase transfer units"
160        NV*(abs(hcl)*'1/m')^.5=(10300-8670*ff)*ff*(Dv*'s/m^2')^0.5*tv*'1/s';
161       
162        "Number of liquid phase transfer units"
163        NL=19700*((Dl*'s/m^2')^.5)*(.4*fs*'1/(kg^.5/m^.5/s)'+.17)*tl*'1/s';
164       
165        "Number of overall vapour phase transfer units"
166        NV*NL=NOG*(NL+lambda*NV);
167       
168        "Point Efficiency"
169        EOG=1-exp(-NOG);
170       
171        #Liquid Mixing Models#
172       
173        "Eddy diffusivity for liquid mixing"
174        De=(0.0005+0.01285*ua*'s/m'+6.32*(Ql*'s/m^3'/(lw*'1/m'))+0.312*hw*'1/m')^2;
175       
176        "Peclet Number"
177        Pe=(OutletL.F*d)/(lw*hcl*(1/vL)*De*'m^2/s');
178       
179        "Constant n"
180        n=Pe/2*((1+4*lambda*EOG/Pe)^.5-1);
181
182        if Pe equal 0 then
183                Emv1=EOG;
184        else
185                if Pe < 20 then
186                        Emv1/EOG=(1-exp(-(n+Pe)))/((n+Pe)*(1+(n+Pe)/n))+(exp(n)-1)/(n*(1+n/(n+Pe)));
187                else
188                        lambda*Emv1=(exp(lambda*EOG)-1);
189                end
190        end
191       
192        #Entrainment Correction#
193       
194        "Height on spray regime"
195        hb=hcl*(265*((ua/(g*hcl)^.5)*(rhoV/rhoL)^.5)^1.7+1);
196       
197        "Gas velocity through hole"
198        uh=Qv/Ah;
199       
200        "Fraction of entrained liquid"
201        l=1e-8*(hb/Ts)^3*(uh/(Ql/Aa))^2;
202       
203        "Apparent Murphree tray efficiency"
204        Emv1=Emv2*(1+l*Emv1);
205
206        Emv=Emv2;
207       
208        end
209       
210Model trayEffFund as tray
211       
212        ATTRIBUTES
213        Pallete         = false;
214        Icon            = "icon/Tray";
215        Brief           = "Tray with Efficiency Prediction - Fundamental Model";
216        Info =
217        "==Description==
218Prediciton based on Prado(1986), Gracia and Fair(2000,2002) model, with entrainment and weeping correction.
219Multicomponent mixture treated with pseudo-binary approach.
220
221        == Options ==
222You can select the tray type: with downcomer or dualflow.
223       
224        == References ==
225*Clear Liquid Height (Downcomer): Dhulesia (1984).
226*Clear Liquid Height (Dualflow): Garcia e Fair(2002).
227*Froth Height: Todd & Van Winkle (1972).
228*Fraction of holes with vapour flow (Downcomer): Prado (1990).
229*Fraction of holes with vapour flow (Dualflow): Garcia e Fair (2002).
230*Fraction of active holes that are in jetting: Prado (1987), considering fj=60% when ua=uatp.
231*Capacity Factor (Downcomer): Treybal(1968).
232*Capacity Factor (Dualflow): Garcia e Fair(2002).
233*Flood Velocity: Fair(1961).
234*Liquid Mixing Models: Lewis(1936).
235*Eddy Diffusivity: Molnar(1974).
236*Entrainment Correction (Downcomer): Colburn(1936).
237*Fraction of entrained liquid (Downcomer): Zuiderweg(1982).
238
239General References:
240*GARCIA, J. A.; FAIR, J. R. A Fundamental Model for the Prediction of Distillation Sieve Tray Efficiency. 1. Database Development. Ind. Eng. Chem. Res., v.39, n.6, p. 1809-17,2000.
241*GARCIA, J. A.; FAIR, J. R. A Fundamental Model for the Prediction of Distillation Sieve Tray Efficiency. 2. Model Development and Validation. Ind. Eng. Chem. Res., v.39, n.6, p. 1818-25,2000.
242*GARCIA, J. A.; FAIR, J. R. Distillation Sieve Trays without Downcomers: Prediction of Performance Characteristics. Ind. Eng. Chem. Res., v.41, n.6, p. 1632-40,2002.
243*LOCKETT, M. J. Distillation Tray Fundamentals. Cambridge: Cambridge University Press, 1986.
244*PRADO, M.; FAIR, J. R. Fundamental Model for the Prediction of Sieve Tray Efficiency.  Ind. Eng. Chem. Res., v.29, n.6, p. 1031-42,1990.
245";
246
247        PARAMETERS
248       
249        d as length (Brief="Tray Diameter");
250        dh as length (Brief="Hole Diameter");
251        Aa as area (Brief="Case Downcomer: Active Area or Bubbling Area = Atray - 2*Adowncomer. Case dualflow: total tray area");
252        Ah as area (Brief="Area of Holes");
253        fi as fraction (Brief="Fractional perforated tray area(hole area/ bubbling area)");
254        Ts as length (Brief="Tray spacing");
255        T as length (Brief="Tray thickness");
256        psi as Real (Brief="Correction factor of liquid entrainment in dualflow trays");
257        psi1 as Real (Brief="Correction factor of weeping in dualflow trays");
258        tray_type as Switcher (Valid = ["Dualflow", "Downcomer"], Default= "Downcomer");
259outer   iLK as Integer (Brief="Pseudo-binary ligth key index");
260outer   iHK as Integer (Brief="Pseudo-binary heavy key index");
261       
262        VARIABLES
263
264        Qv as flow_vol (Brief="Vapour volumetric flow");
265        Ql as flow_vol (Brief="Liquid volumetric flow");
266        Mv as flow_mass (Brief="Vapour mass flow");
267        Ml as flow_mass (Brief="Liquid mass flow");
268        Miv as viscosity (Brief="Vapour viscosity");
269        Mil as viscosity (Brief="Liquid viscosity");
270        Dl as diffusivity (Brief="Diffusivity on Liquid Phase");
271        Dv as diffusivity (Brief="Diffusivity on Vapour Phase");
272       
273        lambda as Real (Brief="Stripping factor or ratio of slope of equilibrium line to slope of operating line");
274        m as Real (Brief="Slope of equilibrium line");
275       
276        VinLK as Real (Brief="Pseudo-binary key ");
277        VoutLk as Real (Brief="Pseudo-binary key");
278        LinLK as Real (Brief="Pseudo-binary key");
279        LoutLk as Real (Brief="Pseudo-binary key");
280       
281        us as velocity (Brief="Superficial velocity based on Ap");
282        ua as velocity (Brief="Superficial velocity based on Aa");
283        fs as positive (Brief="Superficial factor", Unit='kg^.5/m^.5/s');
284        uh as velocity (Brief="Vapour velocity through holes");
285        fp as positive (Brief="Flow Parameter");
286        hcl as length (Brief="Clear Liquid Height");
287        hcld as length (Brief="Dynamic liquid head at tray floor");
288        hf as length (Brief="Froth Height");
289        e as positive (Brief="Porosity");
290        csb as positive(Brief="Capacity Factor");
291        uf as velocity (Brief="Flood velocity");
292        ff as positive (Brief="Flood factor");
293        sigma as surf_tens (Brief="Surface Tension");
294       
295        ftm as Real (Brief="General Factor in equations of Units of Mass Transfer", Unit='cm/s^.5');
296       
297        xf as fraction (Brief="Fraction of holes with vapour flow");
298        dj as length (Brief="Jet Diameter");
299        uj as velocity (Brief="Jet velocity");
300        Reh as positive (Brief="Reynolds number for vapour flow through hole");
301        hj as length (Brief="Jet lenght");
302        tg1 as time_sec (Brief="Residence time in Zone One");
303        NL1 as positive (Brief="Number of liquid phase transfer units in Zone One");
304
305        dbs as length (Brief="Small bubble diameter");
306        dbl as length (Brief="Large bubble diameter");
307        sigCSB as positive (Brief="Surface tension correction");
308        MilCSB as positive (Brief="Liquid viscosity correction");
309        fi3 as positive;
310        dbss as length (Brief="Small bubble Sauter diameter");
311        dbls as length (Brief="Large bubble Sauterdiameter");
312        eo as positive (Brief="Etvos number");
313        mo as positive (Brief="Morton number");
314        h as positive (Brief="Constant h");
315        j as positive (Brief="Constant j");
316        usb as velocity (Brief="Terminal velocity of small bubbles");
317        ubss as velocity (Brief="Terminal velocity of small bubbles using Sauter diameter");
318        aj as fraction (Brief="Fraction of small bubbles in froth");
319        ulb as velocity (Brief="Terminal velocity of large bubbles");
320        tg2s as time_sec (Brief="Residence time of small bubbles in Zone Two");
321        tg2l as time_sec (Brief="Residence time of large bubbles in Zone Two");
322        NL2S as positive (Brief="Number of liquid phase transfer units of small bubbles in Zone Two");
323        NL2L as positive (Brief="Number of liquid phase transfer units of large bubbles in Zone Two");
324        tg3 as time_sec (Brief="Residence time in Zone Three");
325        NL3 as positive (Brief="Number of liquid phase transfer units in Zone Three");
326        ulb3 as velocity (Brief="Terminal velocity of large bubbles in Zone Three");
327        tg4s as time_sec (Brief="Residence time of small bubbles in Zone Four");
328        tg4l as time_sec (Brief="Residence time of large bubbles in Zone Four");
329        NL4S as positive (Brief="Number of liquid phase transfer units of small bubbles in Zone Four");
330        NL4L as positive (Brief="Number of liquid phase transfer units of large bubbles in Zone Four");
331        tg5 as time_sec (Brief="Residence time in Zone Five");
332        NL5 as positive (Brief="Number of liquid phase transfer units in Zone Five");
333       
334        uatp as velocity (Brief="Superficial velocity based on Aa in the transition point of froth regime to spay regime");
335        fj as positive (Brief="Fraction of active holes that are in jetting");
336        flb as positive (Brief="Fraction of active holes that are producing small bubbles");
337        fsb as positive (Brief="Fraction of active holes that are producing large bubbles");
338       
339        ftmg as positive (Brief="General Factor in equations of Units of Mass Transfer");
340       
341        Rej as positive (Brief="Reynolds number of jet");
342        Scg as positive (Brief="Schmidt number of vapour phase");
343        kl1 as positive (Brief="Liquid phase mass transfer coefficient in Zone One");
344        kg1 as positive (Brief="Vapour phase mass transfer coefficient in Zone One");
345        NG1 as positive (Brief="Number of vapour phase transfer units in Zone One");
346       
347        Peg2s as positive (Brief="Peclet number of small bubbles in Zone Two");
348        Peg2l as positive (Brief="Peclet number of large bubbles in Zone Two");
349        Peg3 as positive (Brief="Peclet number in Zone Three");
350        Peg4s as positive (Brief="Peclet number of small bubbles in Zone Four");
351        Peg4l as positive (Brief="Peclet number of large bubbles in Zone Four");
352        Peg5 as positive (Brief="Peclet number in Zone Five");
353       
354        Sh2s as positive (Brief="Sherwood number of small bubbles in Zone Two");
355        Sh2l as positive (Brief="Sherwood number of large bubbles in Zone Two");
356        Sh3 as positive (Brief="Sherwood number in Zone Three");
357        Sh4s as positive (Brief="Sherwood number of small bubbles in Zone Four");
358        Sh4l as positive (Brief="Sherwood number of large bubbles in Zone Four");
359        Sh5 as positive (Brief="Sherwood number in Zone Five");
360       
361        kg2s as positive (Brief="Vapour phase mass transfer coefficient of small bubbles in Zone Two");
362        kg2l as positive (Brief="Vapour phase mass transfer coefficient of large bubbles in Zone Two");
363        kg3 as positive (Brief="Vapour phase mass transfer coefficient in Zone Three");
364        kg4s as positive (Brief="Vapour phase mass transfer coefficient of small bubbles in Zone Four");
365        kg4l as positive (Brief="Vapour phase mass transfer coefficient of large bubbles in Zone Four");
366        kg5 as positive (Brief="Vapour phase mass transfer coefficient in Zone Five");
367       
368        kl2s as positive (Brief="Liquid phase mass transfer coefficient of small bubbles in Zone Two");
369        kl2l as positive (Brief="Liquid phase mass transfer coefficient of large bubbles in Zone Two");
370        kl3 as positive (Brief="Liquid phase mass transfer coefficient in Zone Three");
371        kl4s as positive (Brief="Liquid phase mass transfer coefficient of small bubbles in Zone Four");
372        kl4l as positive (Brief="Liquid phase mass transfer coefficient of large bubbles in Zone Four");
373        kl5 as positive (Brief="Liquid phase mass transfer coefficient in Zone Five");
374       
375        NG2S as positive (Brief="Number of Vapour phase transfer units of small bubbles in Zone Two");
376        NG2L as positive (Brief="Number of Vapour phase transfer units of large bubbles in Zone Two");
377        NG3 as positive (Brief="Number of Vapour phase transfer units in Zone Three");
378        NG4S as positive (Brief="Number of Vapour phase transfer units of small bubbles in Zone Four");
379        NG4L as positive (Brief="Number of Vapour phase transfer units of large bubbles in Zone Four");
380        NG5 as positive (Brief="Number of Vapour phase transfer units in Zone Five");
381       
382        NGFJ as positive (Brief="Number of Vapour phase transfer units of jetting");
383        NGFLB as positive (Brief="Number of Vapour phase transfer units of large bubbles");
384        EOG as positive (Brief="Point Efficiency");
385       
386        De as Real (Brief="Eddy diffusivity for liquid mixing");
387        Pe as positive (Brief="Peclet Number");
388        n as Real (Brief="Constant");
389        Emv1 as positive (Brief="Murphree tray efficiency");
390       
391        hb as length (Brief="Height on spray regime");     
392        l as positive (Brief="Fraction of entrained liquid");     
393        Emv2 as positive (Brief="Apparent Murphree tray efficiency");
394        Emv3 as positive (Brief="Apparent Murphree tray efficiency");
395       
396
397        EQUATIONS
398       
399        "Vapour volumetric flow"
400        Qv=OutletV.F*vV;
401       
402        "Liquid volumetric flow"
403        Ql=OutletL.F*vL;
404
405        "Vapour mass flow"
406        Mv=Qv*rhoV;
407       
408        "Liquid mass flow"
409        Ml=Ql*rhoL;
410       
411        "Vapour viscosity"
412        Miv=PP.VapourViscosity(OutletL.T, OutletL.P, OutletL.z);
413       
414        "Liquid viscosity"
415        Mil=PP.LiquidViscosity(OutletL.T, OutletL.P, OutletL.z);
416
417        if NComp > 2 then
418               
419                "Pseudo-binary Approach"
420                VinLK=InletV.z(iLK)/(InletV.z(iLK)+InletV.z(iHK));
421                VoutLk=OutletV.z(iLK)/(OutletV.z(iLK)+OutletV.z(iHK));
422                LinLK=InletL.z(iLK)/(InletL.z(iLK)+InletL.z(iHK));
423                LoutLk=OutletL.z(iLK)/(OutletL.z(iLK)+OutletL.z(iHK));
424               
425        else
426                VinLK=1;
427                VoutLk=1;
428                LinLK=1;
429                LoutLk=1;
430               
431        end
432       
433        "Stripping factor or ratio of slope of equilibrium line to slope of operating line"
434        lambda=m*(OutletV.F/OutletL.F);
435       
436        "Superficial velocity based on Ap"
437        us=Qv/Ap;
438       
439        "Superficial velocity based on Aa"
440        ua=Qv/Aa;
441       
442        "Superficial factor"
443        fs=ua*rhoV^.5;
444       
445        "Vapour velocity through holes"
446        uh=Qv/Ah;
447       
448        "Flow parameter"
449        (fp*Mv)^2*rhoL=Ml^2*rhoV;
450       
451        switch tray_type
452                case "Downcomer":
453                "Clear Liquid Height"
454        hcl=0.42*(Ql*'1/m'/(lw*ua)*(rhoL/rhoV)^.5)^.33*(hw*'1/m')^.67*'m';
455                case "Dualflow":
456                "Clear Liquid Height"
457        hcl=(0.01728*((Ml*'1/(kg/s)')^(4.3*(fi^1.5))*(ua*'1/(m/s)'*(rhoV/rhoL)^.5)^1))/(rhoL*'1/(kg/m^3)'*fi^1.5*(T/(dh*1000*1000))^.42)*'m';
458       
459        end
460       
461        "Dynamic liquid head at tray floor"
462        hcld=hcl-ua*rhoV*(uh-ua)/(rhoL*g);
463       
464        "Froth Height"
465        hf=0.076*'m'+32.6*'m'*(fs*'1/(kg^.5/m^.5/s)')^2/((rhoL-rhoV)*'m^3/kg')+0.82*hcld;
466       
467        "Porosity"
468        e=1-hcl/hf;
469       
470        switch tray_type
471                case "Downcomer":
472                "Capacity factor"
473        csb=(0.0744*Ts*'1/m'+0.0117)*(log(abs(1/fp)))+0.0304*Ts*'1/m'+0.0153;
474                case "Dualflow":
475                "Capacity factor"
476        csb=(0.1317*fp^2-0.1747*fp+0.1124)*(0.6649*Ts*'1/m'+0.5667);
477        end
478       
479        "Flood velocity"
480        uf = csb*(sigma*'1/(N/m)'/0.02)^.2*(abs((rhoL-rhoV)/rhoV))^.5*(fi/.1)^.44*'m/s';
481       
482        switch tray_type
483                case "Downcomer":
484                "Flood Factor"
485        ff=us/uf;
486                case "Dualflow":
487                "Flood Factor"
488        ff=ua/uf;
489        end
490               
491       
492        #Prado, Garcia and Fair Model#
493       
494                #Liquid Phase#
495       
496        "General Factor in equations of Units of Mass Transfer"
497        ftm=(rhoL*Mv*Dl^.5)/(3.1416^.5*rhoV*Ml);
498       
499                        #Zone One#
500       
501        switch tray_type
502                case "Downcomer":
503                "Fraction of holes with vapour flow"
504        xf=0.9;
505                case "Dualflow":
506                "Fraction of holes with vapour flow"
507        xf=0.4668*(fi/0.2)^.8*(Ts*'1/m'/0.61)^.2*exp(-0.35*(abs(ff*100-90)/45));
508        end
509       
510       
511        "Jet diameter"
512        dj=1.1*dh+0.25*hcl;
513       
514        "Jet velocity"
515        uj=(uh*dh^2)/(xf*dj^2);
516       
517        "Reynolds number for vapour flow through hole"
518        Reh=dh*uh*rhoV/Miv;
519       
520        "Jet Height"
521        hj=1.1e-3*(dh*'1/m')^.2*Reh^.46*'m';
522       
523        "Residence time in Zone One"
524        tg1=hj/uj;
525       
526        "Number of vapour phase transfer units in Zone One"
527        NL1=(8*ftm*tg1^.5)/dj;
528       
529                        #Zone Two#
530       
531        "Small Bubble Diameter"
532        dbs=3.34/(ua*'s/m'*9.8)^.4*(sigma*'m/N'/(rhoL*'m^3/kg'))^.6*(Mil/Miv)^.1*'m';
533       
534        "Large Bubble Diameter"
535        dbl=dbs*(0.83+41.5*((sigma*'m/N')^.6*(Mil*'1/cP'/(rhoV*'m^3/kg'))^.1));
536       
537        if sigma > 5e-3 then
538                sigCSB=1;
539        else
540                sigCSB=3*(sigma*'m/N')^.6;
541        end
542        if Mil > .6e-3 then
543                MilCSB=4.13*(Mil*'1/cP')^1.5;
544        else
545                MilCSB=1;
546        end
547       
548        fi3=1*MilCSB*sigCSB;
549       
550        "Sauter diameters"
551        dbls=fi3*.605*(dh*'1/m')^.84*(uh*'s/m')^.18/((Ql*'s/m^3')/(lw*'1/m')^.07)*'m';
552        dbss=fi3*.660*(dh*'1/m')^.84*(uh*'s/m')^.085/((Ql*'s/m^3')/(lw*'1/m')^.08)*'m';
553       
554        "Eotvos Number"
555        eo=g*(rhoL-rhoV)*dbs^2/sigma;
556       
557        "Morton Number"
558        mo=g*Mil^4*(rhoL-rhoV)/(rhoL^2*sigma^3);
559       
560        "Constant h"
561        h=4/3*eo*mo^-0.149*((Mil*'1/cP')/9.12e-4)^-.14;
562       
563        if h > 59.3 then
564                j=3.42*h^.441;
565        else
566                j=0.94*h^.757;
567        end
568       
569        "Terminal velocity of small bubbles"
570        usb=Mil/(rhoL*dbs)*mo^-.149*(j-0.857);
571       
572        "Terminal velocity of small bubbles using Sauter diameter"
573        ubss=Mil/(rhoL*dbs)*mo^-.149*(j-0.857);
574       
575        "Fraction of small bubbles in froth"
576        aj=1-0.463*((sigma*'m/N')/0.07282)^0.6*((Mil/9.12e-4)*(1.845e-5/Miv))^0.1*(994.7/(rhoL*'m^3/kg'))^0.6*(1.183/(rhoV*'m^3/kg'))^0.1;
577       
578        "Terminal velocity of large bubbles"
579        ulb =  us/((1 - aj)*e) - usb*aj/(1-aj);
580 
581        if hf > hj then
582         tg2s = (hf-hj)/usb;
583         tg2l = (hf-hj)/ulb;
584        else
585         tg2s = hf/usb;
586         tg2l = hf/ulb;
587        end
588 
589        "Number of liquid phase transfer units in Zone Two"
590        NL2S = 12*ftm*tg2s^0.5/dbs;
591        NL2L = 12*ftm*tg2l^0.5/dbl;
592 
593                        #Zone Three#
594       
595    "Terminal velocity of large bubbles in Zone Three"
596        ulb3 = us/e;
597       
598        "Residence time in Zone Three"
599        tg3 = dbls/ulb3;
600 
601    "Number of liquid phase transfer units in Zone Three"
602        NL3 = 12*ftm*tg3^0.5/dbls;
603 
604                        #Zone Four#
605       
606        if hf > dbls then
607                tg4s = (hf-dbls)/usb;
608                tg4l = (hf-dbls)/ulb;
609        else
610                tg4s = hf/usb;
611                tg4l = hf/ulb;
612        end
613 
614    "Number of liquid phase transfer units in Zone Four"
615        NL4S=12*ftm*tg4s^0.5/dbs;
616        NL4L=12*ftm*tg4l^0.5/dbl;
617 
618                        #Zone Five#
619       
620        "Residence time in Zone Five"
621        tg5=hf/ulb3;
622       
623        "Number of liquid phase transfer units in Zone Five"
624        NL5=12*ftm*tg5^0.5/dbss;
625       
626        #Fraction of holes in jet regime estimation
627
628        "Superficial velocity based on Aa in the transition point of froth regime to spay regime"
629        uatp=((0.04302*(rhoV*'m^3/kg')^(-0.5)*(rhoL*'m^3/kg')^0.692*(sigma*'m/N')^0.06*fi^0.25*((Ql*'s/m^3')/(lw*'1/m'))^.05*(dh*'1/m')^(-0.1))*(2.58717*(hw*'1/m')+0.86))*'m/s';       
630   
631        "Fraction of active holes that are in jetting"
632        fj=ua*0.6/uatp;
633 
634        "Fraction of active holes that are producing small bubbles"
635        fsb=165.65*(dh*'1/m')^1.32*fi^1.33;
636       
637        "Fraction of active holes that are producing large bubbles"
638        flb=1-fj-fsb;
639       
640                #Vapour Phase#
641       
642        "General Factor in equations of Units of Mass Transfer"
643        ftmg=(Ml*rhoV)/(Mv*rhoL);
644 
645                        #Zone One#
646    "Reynolds number of jet"
647        Rej=uj*dj*rhoV/Miv;
648 
649    "Schimdt number on vapour phase"
650        Scg=Miv/(rhoV*Dv);
651 
652        "Vapour phase mass transfer coefficient in Zone One"
653        kg1=0.046*((Dv*'s/m^2')/(dj*'1/m'))*Rej^0.96*Scg^0.44;
654 
655    "Liquid phase mass transfer coefficient in Zone One"
656        kl1=1.13*((Dl*'s/m^2')/(tg1*'1/s'))^0.5;
657 
658    "Number of vapour phase transfer units in Zone One"
659        NG1=ftmg*kg1*NL1/kl1;
660       
661                        #Zones Two,Three, Four and Five#
662       
663        "Peclet number"
664        Peg2s=dbs*usb/Dv;
665        Peg2l=dbl*ulb/Dv;
666        Peg3=dbls*ulb3/Dv;
667        Peg4s=dbs*usb/Dv;
668        Peg4l=dbl*ulb/Dv;
669        Peg5=dbss*ubss/Dv;
670       
671        if Peg2s > 200  then
672         Sh2s=17.9;
673        else
674                 Sh2s=-11.878+25.879*log(Peg2s)-5.640*(log(Peg2s))^2;
675        end
676       
677        if Peg2l > 200  then
678         Sh2l=17.9;
679        else
680                 Sh2l=-11.878+25.879*log(Peg2l)-5.640*(log(Peg2l))^2;
681        end
682       
683        if Peg3 > 200  then
684         Sh3=17.9;
685        else
686                 Sh3=-11.878+25.879*log(Peg3)-5.640*(log(Peg3))^2;
687        end
688       
689        if Peg4s > 200  then
690         Sh4s=17.9;
691        else
692                 Sh4s=-11.878+25.879*log(Peg4s)-5.640*(log(Peg4s))^2;
693        end
694       
695        if Peg4l > 200  then
696         Sh4l=17.9;
697        else
698                 Sh4l=-11.878+25.879*log(Peg4l)-5.640*(log(Peg4l))^2;
699        end
700       
701        if Peg5 > 200  then
702         Sh5=17.9;
703        else
704                 Sh5=-11.878+25.879*log(Peg5)-5.640*(log(Peg5))^2;
705        end
706       
707        "Vapour phase mass transfer coefficient"
708        kg2s=Sh2s*(Dv*'s/m^2')/(dbs*'1/m');
709        kg2l=Sh2l*(Dv*'s/m^2')/(dbl*'1/m');
710        kg3=Sh3*(Dv*'s/m^2')/(dbls*'1/m');
711        kg4s=Sh4s*(Dv*'s/m^2')/(dbs*'1/m');
712        kg4l=Sh4l*(Dv*'s/m^2')/(dbl*'1/m');
713        kg5=Sh5*(Dv*'s/m^2')/(dbss*'1/m');
714 
715    "Liquid phase mass transfer coefficient"
716        kl2s=1.13*((Dl*'s/m^2')/(tg2s*'1/s'))^0.5;
717        kl2l=1.13*((Dl*'s/m^2')/(tg2l*'1/s'))^0.5;
718        kl3=1.13*((Dl*'s/m^2')/(tg3*'1/s'))^0.5;
719        kl4s=1.13*((Dl*'s/m^2')/(tg4s*'1/s'))^0.5;
720        kl4l=1.13*((Dl*'s/m^2')/(tg4l*'1/s'))^0.5;
721        kl5=1.13*((Dl*'s/m^2')/(tg5*'1/s'))^0.5;
722       
723        "Number of vapour phase transfer units"
724        NG2S=ftmg*kg2s*NL2S/kl2s;
725        NG2L=ftmg*kg2l*NL2L/kl2l;
726        NG3=ftmg*kg3*NL3/kl3;
727        NG4S=ftmg*kg4s*NL4S/kl4s;
728        NG4L=ftmg*kg4l*NL4L/kl4l;
729        NG5=ftmg*kg5*NL5/kl5;
730       
731        "Number of Vapour phase transfer units of jetting"
732        NGFJ=NG1-ln(1e-8+abs(1-(aj*(1-exp(-NG2S))+(1-aj)*(1-exp(-NG2L)))));
733       
734        "Number of Vapour phase transfer units of large bubbles"
735        NGFLB= NG3-ln(1e-8+abs(1-(aj*(1-exp(-NG4S))+(1-aj)*(1-exp(-NG4L)))));
736   
737        "Point Efficiency"
738        EOG=fj*(1-exp(-NGFJ))+flb*(1-exp(-NGFLB))+fsb*(1-exp(-NG5));
739       
740        #Liquid Mixing Models#
741       
742        "Eddy diffusivity for liquid mixing"
743        De=(0.0005+0.01285*ua*'s/m'+6.32*(Ql*'s/m^3'/(lw*'1/m'))+0.312*hw*'1/m')^2;
744       
745        "Peclet Number"
746        Pe=(OutletL.F*d)/(lw*hcl*(1/vL)*De*'m^2/s');
747       
748        "Constant n"
749        n=Pe/2*((1+4*lambda*EOG/Pe)^.5-1);
750
751        if Pe equal 0 then
752                Emv1=EOG;
753        else
754                if Pe < 20 then
755                        Emv1/EOG=(1-exp(-(n+Pe)))/((n+Pe)*(1+(n+Pe)/n))+(exp(n)-1)/(n*(1+n/(n+Pe)));
756                else
757                        lambda*Emv1=(exp(lambda*EOG)-1);
758                end
759        end
760       
761        #Entrainment and Weeping Correction#
762       
763        "Height on spray regime"
764        hb=hcl*(265*((ua/(g*hcl)^.5)*(rhoV/rhoL)^.5)^1.7+1);
765       
766        "Fraction of entrained liquid"
767        l=1e-8*(hb/Ts)^3*(uh/(Ql/Aa))^2;
768       
769        switch tray_type
770                case "Downcomer":
771                "Apparent Murphree tray efficiency"
772        Emv1=Emv2*(1+l*Emv1);
773                case "Dualflow":
774                "Apparent Murphree tray efficiency"
775        Emv1=Emv2*(1+Emv1*psi/(1-psi));
776       
777        end
778       
779        switch tray_type
780                case "Downcomer":
781                "Apparent Murphree tray efficiency"
782        Emv2=Emv3;
783                case "Dualflow":
784                "Apparent Murphree tray efficiency"
785        Emv2=Emv3*(1+Emv2*psi1/(1-psi1));
786       
787        end
788
789        Emv=Emv3;
790end
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