source: branches/new_gui/my_folders/fogler/chap9/cstr_startup.mso @ 896

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1#*-------------------------------------------------------------------
2* EMSO Model Library (EML) Copyright (C) 2004 - 2007 ALSOC.
3*
4* This LIBRARY is free software; you can distribute it and/or modify
5* it under the therms of the ALSOC FREE LICENSE as available at
6* http://www.enq.ufrgs.br/alsoc.
7*
8* EMSO Copyright (C) 2004 - 2007 ALSOC, original code
9* from http://www.rps.eng.br Copyright (C) 2002-2004.
10* All rights reserved.
11*
12* EMSO is distributed under the therms of the ALSOC LICENSE as
13* available at http://www.enq.ufrgs.br/alsoc.
14*
15*---------------------------------------------------------------------
16* Hydrolysis of propylene glycol in a unsteady-state CSTR
17*----------------------------------------------------------------------
18* Solved problem from Fogler (1999).
19* Problem number: 9-4, 9-5, and 9-7
20* Page: 504 at 517 (Brazilian version, 2002)
21*----------------------------------------------------------------------
22*
23*   Description:
24*               The propylene glycol is produced for hydrolysis reaction of
25*       propylene oxide in a CSTR:
26*                       CH3(O)CHCH3 + H2O -> CH2(OH)CH2(OH)CH3
27*               This sample calculates the outlet molar concentration and
28*       temperature as function of the time in a CSTR jacketed. It is
29*       possible to identify the MSS (Multiple Steady-State).
30*
31*   Assumptions
32*               * elementary reactions
33*               * unsteady-state
34*               * heat exchange
35*       * isobaric system
36*       * gaseous phase
37*
38*       Specify:
39*               * the inlet stream
40*               * the kinetic parameters
41*               * the components parameters
42*
43*----------------------------------------------------------------------
44* Author: Christiano D. W. Guerra and Rodolfo Rodrigues
45* $Id: cstr_startup.mso 574 2008-07-25 14:18:50Z rafael $
46*--------------------------------------------------------------------*#
47
48using "types";
49
50
51#*---------------------------------------------------------------------
52* Example 9-4 : Startup of a CSTR
53*--------------------------------------------------------------------*#
54
55Model CSTR_startup
56        PARAMETERS
57        NComp           as Integer              (Brief="Number of components");
58        stoic(NComp)as Real             (Brief="Stoichiometric number");
59        UA              as Real             (Brief="Exchange heat", Unit='Btu/h/degR');
60        V               as volume           (Brief="Volume of the reactor");
61        Ta1             as temperature  (Brief="Cooling temperature");
62        DH              as enth_mol     (Brief="Molar reaction enthalpy");
63        rho(NComp)      as dens_mol     (Brief="Molar density");
64        cp(NComp)       as cp_mol               (Brief="Molar heat capacity");
65        # Rate of reaction
66        ko                      as frequency    (Brief="Frequency factor");
67        E                       as energy_mol   (Brief="Activation energy");
68        R                       as Real                 (Brief="Universal gas constant", Unit='Btu/lbmol/degR', Default=1.987);
69       
70        VARIABLES
71        C(NComp)        as conc_mol     (Brief="Molar concentration", DisplayUnit='lbmol/ft^3', Lower=0);
72        N(NComp)        as mol                  (Brief="Molar holdup", DisplayUnit='lbmol');
73        Co(NComp)       as conc_mol     (Brief="Initial molar concentration", DisplayUnit='lbmol/ft^3', Lower=0);
74        Fo(NComp)       as flow_mol     (Brief="Initial molar flow", DisplayUnit='lbmol/h');
75        T               as temperature  (Brief="Reactor temperature", DisplayUnit='degR');
76        To              as temperature  (Brief="Initial reactor temperature", DisplayUnit='degR');
77        Ta2             as temperature  (Brief="Temperature of heat exchange", DisplayUnit='degR');
78        r(NComp)        as reaction_mol (Brief="Rate of reaction", DisplayUnit='lbmol/ft^3/h');
79        k               as frequency    (Brief="Specific rate of reaction", DisplayUnit='1/h', Upper=1e5);
80        mc              as flow_mol     (Brief="Molar flow of cooling water", DisplayUnit='lbmol/h');
81        Q               as heat_rate    (Brief="Heat exchange", DisplayUnit='Btu/h');
82        Theta(NComp)as Real                     (Brief="Parameter Theta");
83        vo              as flow_vol     (Brief="Volumetric flow", DisplayUnit='ft^3/h');
84        tau             as time_h       (Brief="Residence time", DisplayUnit='h');
85
86        EQUATIONS
87        "Molar balance"
88        diff(C) = r + (Co - C)/tau;
89       
90        "Energy balance"
91        diff(T)*sumt(N*cp) = (Q - Fo(1)*sumt(Theta*cp)*(T - To) + DH*r(1)*V);
92       
93        "Rate of reaction"
94        r = stoic*k*C(1);
95       
96        "Specific rate of reaction"
97        k = ko*exp(-E/(R*T));
98       
99        "Residence time"
100        tau = V/vo;
101       
102        "Volumetric flow"
103        vo = sumt(Fo/rho);
104       
105        "Temperature of heat exchange"
106        Ta2 =  T - (T - Ta1)*exp(-UA/(cp(2)*mc));
107       
108        "Exchange Heat"
109        Q = mc*cp(2)*(Ta1 - Ta2);
110       
111        "Inlet Concentration"
112        Co = Fo/vo;
113       
114        "Molar holdup"
115        N = C*V;
116       
117        "Relation among molar fractions of components"
118        Theta = Fo/Fo(1);
119       
120        SET
121        NComp = 4; # A, B, C and M
122        stoic = [-1, -1, 1, 0]; # A + 2B -> C + D
123       
124        UA      = 16000*'Btu/h/degR';
125        V       = 500*'gal';
126        Ta1     = (60 + 460)*'degR';
127        DH      =-3.6e4*'Btu/lbmol';
128        rho     = [0.923, 3.45, 1, 1.54]*'lbmol/ft^3';
129        cp      = [35, 18, 46, 19.5]*'Btu/lbmol/degR';
130       
131        ko = 16.96e12*'1/h';
132        E  = 32400*'Btu/lbmol';
133end
134
135
136FlowSheet CSTR_stopped
137        DEVICES
138        CSTR as CSTR_startup;
139       
140        SPECIFY
141        CSTR.Fo = [80, 1000, 0, 100]*'lbmol/h';
142        CSTR.To = (75 + 460)*'degR';
143        CSTR.mc = 1e3*'lbmol/h';
144
145        INITIAL
146        "Molar concentration"
147        CSTR.C  = [0, 3.45, 0, 0]*'lbmol/ft^3';
148        "Reactor temperature"
149        CSTR.T  = CSTR.To;
150
151        OPTIONS
152        TimeStep = 0.05;
153        TimeEnd = 4;
154        TimeUnit = 'h';
155end
156
157
158#*---------------------------------------------------------------------
159* Example 9-5 : Falling off the upper steady-state
160*--------------------------------------------------------------------*#
161
162Model CSTR_ss as CSTR_startup
163        VARIABLES
164        X                       as fraction             (Brief="Molar conversion");
165        XMB                     as fraction             (Brief="Molar conversion of Material balance");
166        XEB                     as fraction             (Brief="Molar conversion of Energy balance");
167
168        EQUATIONS
169        "Molar conversion"
170        X       = 1 - C(1)/Co(1);
171       
172        "Molar conversion of Material balance"
173        XMB = tau*k/(1 + tau*k);
174       
175        "Molar conversion of Energy balance"
176        XEB = (sumt(Theta*cp)*(T - To) + Q/Fo(1))/(-DH);
177end
178
179
180FlowSheet CSTR_stopped2
181        DEVICES
182        CSTR as CSTR_ss;
183       
184        SPECIFY
185        CSTR.Fo = [80, 1000, 0, 100]*'lbmol/h';
186        CSTR.To = (70 + 460)*'degR'; # Reduction of temperature: 75°F to 70°F
187        CSTR.mc = 1e3*'lbmol/h';
188
189        INITIAL
190        "Molar concentration"
191        CSTR.C = [0.039, 2.12, 0.143, 0.226]*'lbmol/ft^3'; # Final values of SS in 9-4
192        "Reactor temperature"
193        CSTR.T = (138.5 + 460)*'degR'; # Final values of SS in 9-4
194
195        OPTIONS
196        TimeStep = 0.05;
197        TimeEnd = 4;
198        TimeUnit = 'h';
199end
200
201
202#*---------------------------------------------------------------------
203* Example 9-7 : PI Controller
204*--------------------------------------------------------------------*#
205
206Model CSTR_control_PI as CSTR_startup
207        PARAMETERS
208        Tsp                     as temperature  (Brief="Reference temperature");
209        mco             as flow_mol     (Brief="Molar flow of cooling water");
210        kc                      as Real                 (Brief="Gain", Unit='lbmol/degR/h');
211       
212        VARIABLES
213        I                       as Real                 (Brief="Integral action", Unit='degR*h');
214        X                       as fraction             (Brief="Fraction conversion");
215       
216        EQUATIONS
217        "Integral action"
218        diff(I) = T - Tsp;
219       
220        "Molar flow of cooling water"
221        mc = mco + kc/tau*I + kc*(T - Tsp);
222       
223        "Molar conversion"
224        X = 1 - C(1)/Co(1);
225end
226
227
228FlowSheet CSTR_stopped3
229        DEVICES
230        CSTR as CSTR_control_PI;
231       
232        SET
233        CSTR.mco = 1000*'lbmol/h';
234        CSTR.Tsp = (138 + 460)*'degR';
235        CSTR.kc = 8.5*'lbmol/degR/h';
236
237        SPECIFY
238        CSTR.Fo = [80, 1000, 0, 100]*'lbmol/h';
239        CSTR.To = (70 + 460)*'degR';
240
241        INITIAL
242        "Molar concentration"
243        CSTR.C = [0.03789, 2.12, 0.143, 0.2265]*'lbmol/ft^3';
244        "Reactor temperature"
245        CSTR.T = (138.53 + 460)*'degR';
246        "Integral action"
247        CSTR.I = 0*'degR*h';
248
249        OPTIONS
250        TimeStep = 0.01;
251        TimeEnd = 4;
252        TimeUnit = 'h';
253end
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