source: mso/eml/stage_separators/tray.mso @ 68

Last change on this file since 68 was 60, checked in by Argimiro Resende Secchi, 17 years ago

Fixed tray equilibrium with tray efficiency.
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1#*-------------------------------------------------------------------
2* Model of a tray
3*--------------------------------------------------------------------
4*       - Streams
5*               * a liquid outlet stream
6*               * a liquid inlet stream
7*               * a vapour outlet stream
8*               * a vapour inlet stream
9*               * a feed stream
10*
11*       - Assumptions
12*               * both phases (liquid and vapour) exists all the time
13*               * thermodymanic equilibrium (Murphree plate efficiency=1)
14*               * no entrainment of liquid or vapour phase
15*               * no weeping
16*               * the dymanics in the downcomer are neglected
17*
18*       - Tray hydraulics: Roffel B.,Betlem B.H.L.,Ruijter J.A.F. (2000)
19*                                               Computers and Chemical Engineering and
20*                                          The gPROMS Model Library
21*
22*       Specify:
23*               * the Feed stream
24*               * the Liquid inlet stream
25*               * the Vapour inlet stream excluding its flow
26*               * the Vapour outlet flow (Outlet.F)
27*
28*       Initial:
29*               * the plate temperature (OutletL.T)
30*               * the liquid height (hl)
31*               * (NoComps - 1) OutletL (or OutletV) compositions
32*
33*----------------------------------------------------------------------
34* Author: Paula B. Staudt
35* $Id: tray.mso 60 2006-11-21 10:48:57Z arge $
36*--------------------------------------------------------------------*#
37
38using "streams";
39
40Model trayBasic
41
42        PARAMETERS
43ext PP as CalcObject;
44ext NComp as Integer;
45        V as volume(Brief="Total Volume of the tray");
46        Q as heat_rate (Brief="Rate of heat supply");
47        Ap as area (Brief="Plate area = Atray - Adowncomer");
48       
49        VARIABLES
50in      Inlet as stream;
51in      InletL as stream;
52in      InletV as stream;
53out     OutletL as stream_therm;
54out     OutletV as stream_therm;
55
56        M(NComp) as mol (Brief="Molar Holdup in the tray");
57        ML as mol (Brief="Molar liquid holdup");
58        MV as mol (Brief="Molar vapour holdup");
59        E as energy (Brief="Total Energy Holdup on tray");
60        vL as volume_mol (Brief="Liquid Molar Volume");
61        vV as volume_mol (Brief="Vapour Molar volume");
62        Level as length (Brief="Height of clear liquid on plate");
63        yideal(NComp) as fraction;
64        Emv as Real (Brief = "Murphree efficiency");
65       
66        EQUATIONS
67        "Component Molar Balance"
68        diff(M)=Inlet.F*Inlet.z + InletL.F*InletL.z + InletV.F*InletV.z
69                - OutletL.F*OutletL.z - OutletV.F*OutletV.z;
70       
71        "Energy Balance"
72        diff(E) = ( Inlet.F*Inlet.h + InletL.F*InletL.h + InletV.F*InletV.h
73                - OutletL.F*OutletL.h - OutletV.F*OutletV.h + Q );
74       
75        "Molar Holdup"
76        M = ML*OutletL.z + MV*OutletV.z;
77       
78        "Energy Holdup"
79        E = ML*OutletL.h + MV*OutletV.h - OutletL.P*V;
80       
81        "Mol fraction normalisation"
82        sum(OutletL.z)= 1.0;
83        sum(OutletL.z)= sum(OutletV.z);
84       
85        "Liquid Volume"
86        vL = PP.LiquidVolume(OutletL.T, OutletL.P, OutletL.z);
87        "Vapour Volume"
88        vV = PP.VapourVolume(OutletV.T, OutletV.P, OutletV.z);
89       
90        "Chemical Equilibrium"
91        PP.LiquidFugacityCoefficient(OutletL.T, OutletL.P, OutletL.z)*OutletL.z =
92                PP.VapourFugacityCoefficient(OutletV.T, OutletV.P, yideal)*yideal;
93
94        "Murphree Efficiency"
95        OutletV.z = Emv * (yideal - InletV.z) + InletV.z;
96       
97        "Thermal Equilibrium"
98        OutletV.T = OutletL.T;
99       
100        "Mechanical Equilibrium"
101        OutletV.P = OutletL.P;
102       
103        "Geometry Constraint"
104        V = ML* vL + MV*vV;
105       
106        "vaporization fraction "
107        OutletV.v = 1.0;
108        OutletL.v = 0.0;
109       
110        "Level of clear liquid over the weir"
111        Level = ML*vL/Ap;
112end
113
114Model tray as trayBasic
115
116        PARAMETERS
117        Ah as area (Brief="Total holes area");
118        lw as length (Brief="Weir length");
119        g as acceleration (Default=9.81);
120        hw as length (Brief="Weir height");
121        beta as fraction (Brief="Aeration fraction");
122        alfa as fraction (Brief="Dry pressure drop coefficient");
123       
124        VARIABLES
125        rhoL as dens_mass;
126        rhoV as dens_mass;
127
128        EQUATIONS
129        "Liquid Density"
130        rhoL = PP.LiquidDensity(OutletL.T, OutletL.P, OutletL.z);
131        "Vapour Density"
132        rhoV = PP.VapourDensity(InletV.T, InletV.P, InletV.z);
133
134        if (Level > (beta * hw)) then
135                "Francis Equation"
136                OutletL.F = 1.84*"m^0.5/s"*lw*((Level-(beta*hw))/(beta))^1.5/vL;
137        else
138                "Low level"
139                OutletL.F = 0 * "mol/h";
140        end
141
142end
143
144#*-------------------------------------------------------------------
145* Model of a tray with reaction
146*-------------------------------------------------------------------*#
147Model trayReact
148
149        PARAMETERS
150ext PP as CalcObject;
151ext NComp as Integer;
152        V as volume(Brief="Total Volume of the tray");
153        Q as power (Brief="Rate of heat supply");
154        Ap as area (Brief="Plate area = Atray - Adowncomer");
155       
156        Ah as area (Brief="Total holes area");
157        lw as length (Brief="Weir length");
158        g as acceleration (Default=9.81);
159        hw as length (Brief="Weir height");
160        beta as fraction (Brief="Aeration fraction");
161        alfa as fraction (Brief="Dry pressure drop coefficient");
162
163        stoic(NComp) as Real(Brief="Stoichiometric matrix");
164        Hr as energy_mol;
165        Pstartup as pressure;
166       
167        VARIABLES
168in      Inlet as stream;
169in      InletL as stream;
170in      InletV as stream;
171out     OutletL as stream_therm;
172out     OutletV as stream_therm;
173
174        yideal(NComp) as fraction;
175        Emv as Real (Brief = "Murphree efficiency");
176
177        M(NComp) as mol (Brief="Molar Holdup in the tray");
178        ML as mol (Brief="Molar liquid holdup");
179        MV as mol (Brief="Molar vapour holdup");
180        E as energy (Brief="Total Energy Holdup on tray");
181        vL as volume_mol (Brief="Liquid Molar Volume");
182        vV as volume_mol (Brief="Vapour Molar volume");
183        Level as length (Brief="Height of clear liquid on plate");
184        Vol as volume;
185       
186        rhoL as dens_mass;
187        rhoV as dens_mass;
188        r as reaction_mol (Brief = "Reaction rate", Unit = "mol/l/s");
189        C(NComp) as conc_mol (Brief = "Molar concentration", Lower = -1); #, Unit = "mol/l");
190       
191        EQUATIONS
192        "Molar Concentration"
193        OutletL.z = vL * C;
194       
195        "Component Molar Balance"
196        diff(M)=Inlet.F*Inlet.z + InletL.F*InletL.z + InletV.F*InletV.z
197                - OutletL.F*OutletL.z - OutletV.F*OutletV.z + stoic*r*ML*vL;
198       
199        "Energy Balance"
200        diff(E) = ( Inlet.F*Inlet.h + InletL.F*InletL.h + InletV.F*InletV.h
201                - OutletL.F*OutletL.h - OutletV.F*OutletV.h + Q ) + Hr * r * vL*ML;
202       
203        "Molar Holdup"
204        M = ML*OutletL.z + MV*OutletV.z;
205       
206        "Energy Holdup"
207        E = ML*OutletL.h + MV*OutletV.h - OutletL.P*V;
208       
209        "Mol fraction normalisation"
210        sum(OutletL.z)= 1.0;
211       
212        "Liquid Volume"
213        vL = PP.LiquidVolume(OutletL.T, OutletL.P, OutletL.z);
214        "Vapour Volume"
215        vV = PP.VapourVolume(OutletV.T, OutletV.P, OutletV.z);
216
217        "Thermal Equilibrium"
218        OutletV.T = OutletL.T;
219       
220        "Mechanical Equilibrium"
221        OutletV.P = OutletL.P;
222       
223        "vaporization fraction "
224        OutletV.v = 1.0;
225        OutletL.v = 0.0;
226       
227        "Level of clear liquid over the weir"
228        Level = ML*vL/Ap;
229
230        Vol = ML*vL;
231       
232        "Liquid Density"
233        rhoL = PP.LiquidDensity(OutletL.T, OutletL.P, OutletL.z);
234        "Vapour Density"
235        rhoV = PP.VapourDensity(InletV.T, InletV.P, InletV.z);
236
237        if (Level > (beta * hw)) then
238                "Francis Equation"
239                OutletL.F = (1.84*"m^0.5/s"*lw*((Level-(beta*hw))/(beta))^1.5/vL);
240        else
241                "Low level"
242                OutletL.F = 0 * "mol/h";
243        end
244
245               
246        "Pressure Drop through the tray"
247        OutletV.F = (1 + tanh(1 * (OutletV.P - Pstartup)/"Pa"))/2 *
248                Ah/vV * sqrt(2*(OutletV.P - InletL.P + 1e-8 * "atm") / (alfa*rhoV) );
249       
250
251        "Chemical Equilibrium"
252        PP.LiquidFugacityCoefficient(OutletL.T, OutletL.P, OutletL.z)*OutletL.z =
253                PP.VapourFugacityCoefficient(OutletV.T, OutletV.P, yideal)*yideal;
254       
255        OutletV.z = Emv * (yideal - InletV.z) + InletV.z;
256       
257        sum(OutletL.z)= sum(OutletV.z);
258       
259        "Geometry Constraint"
260        V = ML* vL + MV*vV;
261end
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