source: trunk/eml/stage_separators/tray_Eff.mso @ 607

Last change on this file since 607 was 607, checked in by Argimiro Resende Secchi, 15 years ago

Updating tray efficiency models.
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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        tray_type as Switcher (Valid = ["Dualflow", "Downcomer"], Default= "Downcomer");
257outer   iLK as Integer (Brief="Pseudo-binary ligth key index");
258outer   iHK as Integer (Brief="Pseudo-binary heavy key index");
259       
260        VARIABLES
261
262        Qv as flow_vol (Brief="Vapour volumetric flow");
263        Ql as flow_vol (Brief="Liquid volumetric flow");
264        Mv as flow_mass (Brief="Vapour mass flow");
265        Ml as flow_mass (Brief="Liquid mass flow");
266        Miv as viscosity (Brief="Vapour viscosity");
267        Mil as viscosity (Brief="Liquid viscosity");
268        Dl as diffusivity (Brief="Diffusivity on Liquid Phase");
269        Dv as diffusivity (Brief="Diffusivity on Vapour Phase");
270       
271        lambda as Real (Brief="Stripping factor or ratio of slope of equilibrium line to slope of operating line");
272        m as Real (Brief="Slope of equilibrium line");
273       
274        VinLK as Real (Brief="Pseudo-binary key ");
275        VoutLk as Real (Brief="Pseudo-binary key");
276        LinLK as Real (Brief="Pseudo-binary key");
277        LoutLk as Real (Brief="Pseudo-binary key");
278       
279        us as velocity (Brief="Superficial velocity based on Ap");
280        ua as velocity (Brief="Superficial velocity based on Aa");
281        fs as positive (Brief="Superficial factor", Unit='kg^.5/m^.5/s');
282        uh as velocity (Brief="Vapour velocity through holes");
283        fp as positive (Brief="Flow Parameter");
284        hcl as length (Brief="Clear Liquid Height");
285        hcld as length (Brief="Dynamic liquid head at tray floor");
286        hf as length (Brief="Froth Height");
287        e as positive (Brief="Porosity");
288        csb as positive(Brief="Capacity Factor");
289        uf as velocity (Brief="Flood velocity");
290        ff as positive (Brief="Flood factor");
291        sigma as surf_tens (Brief="Surface Tension");
292       
293        ftm as Real (Brief="General Factor in equations of Units of Mass Transfer", Unit='cm/s^.5');
294       
295        xf as fraction (Brief="Fraction of holes with vapour flow");
296        dj as length (Brief="Jet Diameter");
297        uj as velocity (Brief="Jet velocity");
298        Reh as positive (Brief="Reynolds number for vapour flow through hole");
299        hj as length (Brief="Jet lenght");
300        tg1 as time_sec (Brief="Residence time in Zone One");
301        NL1 as positive (Brief="Number of liquid phase transfer units in Zone One");
302
303        dbs as length (Brief="Small bubble diameter");
304        dbl as length (Brief="Large bubble diameter");
305        sigCSB as positive (Brief="Surface tension correction");
306        MilCSB as positive (Brief="Liquid viscosity correction");
307        fi3 as positive;
308        dbss as length (Brief="Small bubble Sauter diameter");
309        dbls as length (Brief="Large bubble Sauterdiameter");
310        eo as positive (Brief="Etvos number");
311        mo as positive (Brief="Morton number");
312        h as positive (Brief="Constant h");
313        j as positive (Brief="Constant j");
314        usb as velocity (Brief="Terminal velocity of small bubbles");
315        ubss as velocity (Brief="Terminal velocity of small bubbles using Sauter diameter");
316        aj as fraction (Brief="Fraction of small bubbles in froth");
317        ulb as velocity (Brief="Terminal velocity of large bubbles");
318        tg2s as time_sec (Brief="Residence time of small bubbles in Zone Two");
319        tg2l as time_sec (Brief="Residence time of large bubbles in Zone Two");
320        NL2S as positive (Brief="Number of liquid phase transfer units of small bubbles in Zone Two");
321        NL2L as positive (Brief="Number of liquid phase transfer units of large bubbles in Zone Two");
322        tg3 as time_sec (Brief="Residence time in Zone Three");
323        NL3 as positive (Brief="Number of liquid phase transfer units in Zone Three");
324        ulb3 as velocity (Brief="Terminal velocity of large bubbles in Zone Three");
325        tg4s as time_sec (Brief="Residence time of small bubbles in Zone Four");
326        tg4l as time_sec (Brief="Residence time of large bubbles in Zone Four");
327        NL4S as positive (Brief="Number of liquid phase transfer units of small bubbles in Zone Four");
328        NL4L as positive (Brief="Number of liquid phase transfer units of large bubbles in Zone Four");
329        tg5 as time_sec (Brief="Residence time in Zone Five");
330        NL5 as positive (Brief="Number of liquid phase transfer units in Zone Five");
331       
332        uatp as velocity (Brief="Superficial velocity based on Aa in the transition point of froth regime to spay regime");
333        fj as positive (Brief="Fraction of active holes that are in jetting");
334        flb as positive (Brief="Fraction of active holes that are producing small bubbles");
335        fsb as positive (Brief="Fraction of active holes that are producing large bubbles");
336       
337        ftmg as positive (Brief="General Factor in equations of Units of Mass Transfer");
338       
339        Rej as positive (Brief="Reynolds number of jet");
340        Scg as positive (Brief="Schmidt number of vapour phase");
341        kl1 as positive (Brief="Liquid phase mass transfer coefficient in Zone One");
342        kg1 as positive (Brief="Vapour phase mass transfer coefficient in Zone One");
343        NG1 as positive (Brief="Number of vapour phase transfer units in Zone One");
344       
345        Peg2s as positive (Brief="Peclet number of small bubbles in Zone Two");
346        Peg2l as positive (Brief="Peclet number of large bubbles in Zone Two");
347        Peg3 as positive (Brief="Peclet number in Zone Three");
348        Peg4s as positive (Brief="Peclet number of small bubbles in Zone Four");
349        Peg4l as positive (Brief="Peclet number of large bubbles in Zone Four");
350        Peg5 as positive (Brief="Peclet number in Zone Five");
351       
352        Sh2s as positive (Brief="Sherwood number of small bubbles in Zone Two");
353        Sh2l as positive (Brief="Sherwood number of large bubbles in Zone Two");
354        Sh3 as positive (Brief="Sherwood number in Zone Three");
355        Sh4s as positive (Brief="Sherwood number of small bubbles in Zone Four");
356        Sh4l as positive (Brief="Sherwood number of large bubbles in Zone Four");
357        Sh5 as positive (Brief="Sherwood number in Zone Five");
358       
359        kg2s as positive (Brief="Vapour phase mass transfer coefficient of small bubbles in Zone Two");
360        kg2l as positive (Brief="Vapour phase mass transfer coefficient of large bubbles in Zone Two");
361        kg3 as positive (Brief="Vapour phase mass transfer coefficient in Zone Three");
362        kg4s as positive (Brief="Vapour phase mass transfer coefficient of small bubbles in Zone Four");
363        kg4l as positive (Brief="Vapour phase mass transfer coefficient of large bubbles in Zone Four");
364        kg5 as positive (Brief="Vapour phase mass transfer coefficient in Zone Five");
365       
366        kl2s as positive (Brief="Liquid phase mass transfer coefficient of small bubbles in Zone Two");
367        kl2l as positive (Brief="Liquid phase mass transfer coefficient of large bubbles in Zone Two");
368        kl3 as positive (Brief="Liquid phase mass transfer coefficient in Zone Three");
369        kl4s as positive (Brief="Liquid phase mass transfer coefficient of small bubbles in Zone Four");
370        kl4l as positive (Brief="Liquid phase mass transfer coefficient of large bubbles in Zone Four");
371        kl5 as positive (Brief="Liquid phase mass transfer coefficient in Zone Five");
372       
373        NG2S as positive (Brief="Number of Vapour phase transfer units of small bubbles in Zone Two");
374        NG2L as positive (Brief="Number of Vapour phase transfer units of large bubbles in Zone Two");
375        NG3 as positive (Brief="Number of Vapour phase transfer units in Zone Three");
376        NG4S as positive (Brief="Number of Vapour phase transfer units of small bubbles in Zone Four");
377        NG4L as positive (Brief="Number of Vapour phase transfer units of large bubbles in Zone Four");
378        NG5 as positive (Brief="Number of Vapour phase transfer units in Zone Five");
379       
380        NGFJ as positive (Brief="Number of Vapour phase transfer units of jetting");
381        NGFLB as positive (Brief="Number of Vapour phase transfer units of large bubbles");
382        EOG as positive (Brief="Point Efficiency");
383       
384        De as Real (Brief="Eddy diffusivity for liquid mixing");
385        Pe as positive (Brief="Peclet Number");
386        n as Real (Brief="Constant");
387        Emv1 as positive (Brief="Murphree tray efficiency");
388       
389        psi as Real (Brief="Correction factor of liquid entrainment in dualflow trays");
390        psi1 as Real (Brief="Correction factor of weeping in dualflow trays");
391       
392        hb as length (Brief="Height on spray regime");     
393        l as positive (Brief="Fraction of entrained liquid");     
394        Emv2 as positive (Brief="Apparent Murphree tray efficiency");
395        Emv3 as positive (Brief="Apparent Murphree tray efficiency");
396       
397
398        EQUATIONS
399       
400        "Vapour volumetric flow"
401        Qv=OutletV.F*vV;
402       
403        "Liquid volumetric flow"
404        Ql=OutletL.F*vL;
405
406        "Vapour mass flow"
407        Mv=Qv*rhoV;
408       
409        "Liquid mass flow"
410        Ml=Ql*rhoL;
411       
412        "Vapour viscosity"
413        Miv=PP.VapourViscosity(OutletL.T, OutletL.P, OutletL.z);
414       
415        "Liquid viscosity"
416        Mil=PP.LiquidViscosity(OutletL.T, OutletL.P, OutletL.z);
417
418        if NComp > 2 then
419               
420                "Pseudo-binary Approach"
421                VinLK=InletV.z(iLK)/(InletV.z(iLK)+InletV.z(iHK));
422                VoutLk=OutletV.z(iLK)/(OutletV.z(iLK)+OutletV.z(iHK));
423                LinLK=InletL.z(iLK)/(InletL.z(iLK)+InletL.z(iHK));
424                LoutLk=OutletL.z(iLK)/(OutletL.z(iLK)+OutletL.z(iHK));
425               
426        else
427                VinLK=1;
428                VoutLk=1;
429                LinLK=1;
430                LoutLk=1;
431               
432        end
433       
434        "Stripping factor or ratio of slope of equilibrium line to slope of operating line"
435        lambda=m*(OutletV.F/OutletL.F);
436       
437        "Superficial velocity based on Ap"
438        us=Qv/Ap;
439       
440        "Superficial velocity based on Aa"
441        ua=Qv/Aa;
442       
443        "Superficial factor"
444        fs=ua*rhoV^.5;
445       
446        "Vapour velocity through holes"
447        uh=Qv/Ah;
448       
449        "Flow parameter"
450        (fp*Mv)^2*rhoL=Ml^2*rhoV;
451       
452        switch tray_type
453                case "Downcomer":
454                "Clear Liquid Height"
455        hcl=0.42*(Ql*'1/m'/(lw*ua)*(rhoL/rhoV)^.5)^.33*(hw*'1/m')^.67*'m';
456                case "Dualflow":
457                "Clear Liquid Height"
458        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';
459       
460        end
461       
462        "Dynamic liquid head at tray floor"
463        hcld=hcl-ua*rhoV*(uh-ua)/(rhoL*g);
464       
465        "Froth Height"
466        hf=0.076*'m'+32.6*'m'*(fs*'1/(kg^.5/m^.5/s)')^2/((rhoL-rhoV)*'m^3/kg')+0.82*hcld;
467       
468        "Porosity"
469        e=1-hcl/hf;
470       
471        switch tray_type
472                case "Downcomer":
473                "Capacity factor"
474        csb=(0.0744*Ts*'1/m'+0.0117)*(log(abs(1/fp)))+0.0304*Ts*'1/m'+0.0153;
475                case "Dualflow":
476                "Capacity factor"
477        csb=(0.1317*fp^2-0.1747*fp+0.1124)*(0.6649*Ts*'1/m'+0.5667);
478        end
479       
480        "Flood velocity"
481        uf = csb*(sigma*'1/(N/m)'/0.02)^.2*(abs((rhoL-rhoV)/rhoV))^.5*(fi/.1)^.44*'m/s';
482       
483        switch tray_type
484                case "Downcomer":
485                "Flood Factor"
486        ff=us/uf;
487                case "Dualflow":
488                "Flood Factor"
489        ff=ua/uf;
490        end
491               
492       
493        #Prado, Garcia and Fair Model#
494       
495                #Liquid Phase#
496       
497        "General Factor in equations of Units of Mass Transfer"
498        ftm=(rhoL*Mv*Dl^.5)/(3.1416^.5*rhoV*Ml);
499       
500                        #Zone One#
501       
502        switch tray_type
503                case "Downcomer":
504                "Fraction of holes with vapour flow"
505        xf=0.9;
506                case "Dualflow":
507                "Fraction of holes with vapour flow"
508        xf=0.4668*(fi/0.2)^.8*(Ts*'1/m'/0.61)^.2*exp(-0.35*(abs(ff*100-90)/45));
509        end
510       
511       
512        "Jet diameter"
513        dj=1.1*dh+0.25*hcl;
514       
515        "Jet velocity"
516        uj=(uh*dh^2)/(xf*dj^2);
517       
518        "Reynolds number for vapour flow through hole"
519        Reh=dh*uh*rhoV/Miv;
520       
521        "Jet Height"
522        hj=1.1e-3*(dh*'1/m')^.2*Reh^.46*'m';
523       
524        "Residence time in Zone One"
525        tg1=hj/uj;
526       
527        "Number of vapour phase transfer units in Zone One"
528        NL1=(8*ftm*tg1^.5)/dj;
529       
530                        #Zone Two#
531       
532        "Small Bubble Diameter"
533        dbs=3.34/(ua*'s/m'*9.8)^.4*(sigma*'m/N'/(rhoL*'m^3/kg'))^.6*(Mil/Miv)^.1*'m';
534       
535        "Large Bubble Diameter"
536        dbl=dbs*(0.83+41.5*((sigma*'m/N')^.6*(Mil*'1/cP'/(rhoV*'m^3/kg'))^.1));
537       
538        if sigma > 5e-3 then
539                sigCSB=1;
540        else
541                sigCSB=3*(sigma*'m/N')^.6;
542        end
543        if Mil > .6e-3 then
544                MilCSB=4.13*(Mil*'1/cP')^1.5;
545        else
546                MilCSB=1;
547        end
548       
549        fi3=1*MilCSB*sigCSB;
550       
551        "Sauter diameters"
552        dbls=fi3*.605*(dh*'1/m')^.84*(uh*'s/m')^.18/((Ql*'s/m^3')/(lw*'1/m')^.07)*'m';
553        dbss=fi3*.660*(dh*'1/m')^.84*(uh*'s/m')^.085/((Ql*'s/m^3')/(lw*'1/m')^.08)*'m';
554       
555        "Eotvos Number"
556        eo=g*(rhoL-rhoV)*dbs^2/sigma;
557       
558        "Morton Number"
559        mo=g*Mil^4*(rhoL-rhoV)/(rhoL^2*sigma^3);
560       
561        "Constant h"
562        h=4/3*eo*mo^-0.149*((Mil*'1/cP')/9.12e-4)^-.14;
563       
564        if h > 59.3 then
565                j=3.42*h^.441;
566        else
567                j=0.94*h^.757;
568        end
569       
570        "Terminal velocity of small bubbles"
571        usb=Mil/(rhoL*dbs)*mo^-.149*(j-0.857);
572       
573        "Terminal velocity of small bubbles using Sauter diameter"
574        ubss=Mil/(rhoL*dbs)*mo^-.149*(j-0.857);
575       
576        "Fraction of small bubbles in froth"
577        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;
578       
579        "Terminal velocity of large bubbles"
580        ulb =  us/((1 - aj)*e) - usb*aj/(1-aj);
581 
582        if hf > hj then
583         tg2s = (hf-hj)/usb;
584         tg2l = (hf-hj)/ulb;
585        else
586         tg2s = hf/usb;
587         tg2l = hf/ulb;
588        end
589 
590        "Number of liquid phase transfer units in Zone Two"
591        NL2S = 12*ftm*tg2s^0.5/dbs;
592        NL2L = 12*ftm*tg2l^0.5/dbl;
593 
594                        #Zone Three#
595       
596    "Terminal velocity of large bubbles in Zone Three"
597        ulb3 = us/e;
598       
599        "Residence time in Zone Three"
600        tg3 = dbls/ulb3;
601 
602    "Number of liquid phase transfer units in Zone Three"
603        NL3 = 12*ftm*tg3^0.5/dbls;
604 
605                        #Zone Four#
606       
607        if hf > dbls then
608                tg4s = (hf-dbls)/usb;
609                tg4l = (hf-dbls)/ulb;
610        else
611                tg4s = hf/usb;
612                tg4l = hf/ulb;
613        end
614 
615    "Number of liquid phase transfer units in Zone Four"
616        NL4S=12*ftm*tg4s^0.5/dbs;
617        NL4L=12*ftm*tg4l^0.5/dbl;
618 
619                        #Zone Five#
620       
621        "Residence time in Zone Five"
622        tg5=hf/ulb3;
623       
624        "Number of liquid phase transfer units in Zone Five"
625        NL5=12*ftm*tg5^0.5/dbss;
626       
627        #Fraction of holes in jet regime estimation
628
629        "Superficial velocity based on Aa in the transition point of froth regime to spay regime"
630        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';       
631   
632        "Fraction of active holes that are in jetting"
633        fj=ua*0.6/uatp;
634 
635        "Fraction of active holes that are producing small bubbles"
636        fsb=165.65*(dh*'1/m')^1.32*fi^1.33;
637       
638        "Fraction of active holes that are producing large bubbles"
639        flb=1-fj-fsb;
640       
641                #Vapour Phase#
642       
643        "General Factor in equations of Units of Mass Transfer"
644        ftmg=(Ml*rhoV)/(Mv*rhoL);
645 
646                        #Zone One#
647    "Reynolds number of jet"
648        Rej=uj*dj*rhoV/Miv;
649 
650    "Schimdt number on vapour phase"
651        Scg=Miv/(rhoV*Dv);
652 
653        "Vapour phase mass transfer coefficient in Zone One"
654        kg1=0.046*((Dv*'s/m^2')/(dj*'1/m'))*Rej^0.96*Scg^0.44;
655 
656    "Liquid phase mass transfer coefficient in Zone One"
657        kl1=1.13*((Dl*'s/m^2')/(tg1*'1/s'))^0.5;
658 
659    "Number of vapour phase transfer units in Zone One"
660        NG1=ftmg*kg1*NL1/kl1;
661       
662                        #Zones Two,Three, Four and Five#
663       
664        "Peclet number"
665        Peg2s=dbs*usb/Dv;
666        Peg2l=dbl*ulb/Dv;
667        Peg3=dbls*ulb3/Dv;
668        Peg4s=dbs*usb/Dv;
669        Peg4l=dbl*ulb/Dv;
670        Peg5=dbss*ubss/Dv;
671       
672        if Peg2s > 200  then
673         Sh2s=17.9;
674        else
675                 Sh2s=-11.878+25.879*log(Peg2s)-5.640*(log(Peg2s))^2;
676        end
677       
678        if Peg2l > 200  then
679         Sh2l=17.9;
680        else
681                 Sh2l=-11.878+25.879*log(Peg2l)-5.640*(log(Peg2l))^2;
682        end
683       
684        if Peg3 > 200  then
685         Sh3=17.9;
686        else
687                 Sh3=-11.878+25.879*log(Peg3)-5.640*(log(Peg3))^2;
688        end
689       
690        if Peg4s > 200  then
691         Sh4s=17.9;
692        else
693                 Sh4s=-11.878+25.879*log(Peg4s)-5.640*(log(Peg4s))^2;
694        end
695       
696        if Peg4l > 200  then
697         Sh4l=17.9;
698        else
699                 Sh4l=-11.878+25.879*log(Peg4l)-5.640*(log(Peg4l))^2;
700        end
701       
702        if Peg5 > 200  then
703         Sh5=17.9;
704        else
705                 Sh5=-11.878+25.879*log(Peg5)-5.640*(log(Peg5))^2;
706        end
707       
708        "Vapour phase mass transfer coefficient"
709        kg2s=Sh2s*(Dv*'s/m^2')/(dbs*'1/m');
710        kg2l=Sh2l*(Dv*'s/m^2')/(dbl*'1/m');
711        kg3=Sh3*(Dv*'s/m^2')/(dbls*'1/m');
712        kg4s=Sh4s*(Dv*'s/m^2')/(dbs*'1/m');
713        kg4l=Sh4l*(Dv*'s/m^2')/(dbl*'1/m');
714        kg5=Sh5*(Dv*'s/m^2')/(dbss*'1/m');
715 
716    "Liquid phase mass transfer coefficient"
717        kl2s=1.13*((Dl*'s/m^2')/(tg2s*'1/s'))^0.5;
718        kl2l=1.13*((Dl*'s/m^2')/(tg2l*'1/s'))^0.5;
719        kl3=1.13*((Dl*'s/m^2')/(tg3*'1/s'))^0.5;
720        kl4s=1.13*((Dl*'s/m^2')/(tg4s*'1/s'))^0.5;
721        kl4l=1.13*((Dl*'s/m^2')/(tg4l*'1/s'))^0.5;
722        kl5=1.13*((Dl*'s/m^2')/(tg5*'1/s'))^0.5;
723       
724        "Number of vapour phase transfer units"
725        NG2S=ftmg*kg2s*NL2S/kl2s;
726        NG2L=ftmg*kg2l*NL2L/kl2l;
727        NG3=ftmg*kg3*NL3/kl3;
728        NG4S=ftmg*kg4s*NL4S/kl4s;
729        NG4L=ftmg*kg4l*NL4L/kl4l;
730        NG5=ftmg*kg5*NL5/kl5;
731       
732        "Number of Vapour phase transfer units of jetting"
733        NGFJ=NG1-ln(1e-8+abs(1-(aj*(1-exp(-NG2S))+(1-aj)*(1-exp(-NG2L)))));
734       
735        "Number of Vapour phase transfer units of large bubbles"
736        NGFLB= NG3-ln(1e-8+abs(1-(aj*(1-exp(-NG4S))+(1-aj)*(1-exp(-NG4L)))));
737   
738        "Point Efficiency"
739        EOG=fj*(1-exp(-NGFJ))+flb*(1-exp(-NGFLB))+fsb*(1-exp(-NG5));
740       
741        #Liquid Mixing Models#
742       
743        "Eddy diffusivity for liquid mixing"
744        De=(0.0005+0.01285*ua*'s/m'+6.32*(Ql*'s/m^3'/(lw*'1/m'))+0.312*hw*'1/m')^2;
745       
746        "Peclet Number"
747        Pe=(OutletL.F*d)/(lw*hcl*(1/vL)*De*'m^2/s');
748       
749        "Constant n"
750        n=Pe/2*((1+4*lambda*EOG/Pe)^.5-1);
751
752        if Pe equal 0 then
753                Emv1=EOG;
754        else
755                if Pe < 20 then
756                        Emv1/EOG=(1-exp(-(n+Pe)))/((n+Pe)*(1+(n+Pe)/n))+(exp(n)-1)/(n*(1+n/(n+Pe)));
757                else
758                        lambda*Emv1=(exp(lambda*EOG)-1);
759                end
760        end
761       
762        #Entrainment and Weeping Correction#
763       
764        "Height on spray regime"
765        hb=hcl*(265*((ua/(g*hcl)^.5)*(rhoV/rhoL)^.5)^1.7+1);
766       
767        "Fraction of entrained liquid"
768        l=1e-8*(hb/Ts)^3*(uh/(Ql/Aa))^2;
769       
770        switch tray_type
771                case "Downcomer":
772                "Apparent Murphree tray efficiency"
773        Emv1=Emv2*(1+l*Emv1);
774                case "Dualflow":
775                "Apparent Murphree tray efficiency"
776        Emv1=Emv2*(1+Emv1*psi/(1-psi));
777       
778        end
779       
780        switch tray_type
781                case "Downcomer":
782                "Apparent Murphree tray efficiency"
783        Emv2=Emv3;
784                case "Dualflow":
785                "Apparent Murphree tray efficiency"
786        Emv2=Emv3*(1+Emv2*psi1/(1-psi1));
787       
788        end
789
790        Emv=Emv3;
791end
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