source: mso/sample/reactors/fogler/chap8/acetic_anhydride.mso @ 63

Last change on this file since 63 was 63, checked in by Rodolfo Rodrigues, 16 years ago

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1#*---------------------------------------------------------------------
2* Production of acetic anhydride
3*----------------------------------------------------------------------
4* Solved problem from Fogler (1999)
5* Problem number: 8-7
6* Page: 421 (Brazilian version, 2002)
7*----------------------------------------------------------------------
8*
9*   Description:
10*               The acetic anhydride is produced for thermal craking of the
11*       acetone in a PFR:
12*                       CH3COCH3 -> CH2CO + CH4
13*               This sample calculates the molar conversion and temperature
14*       as function of the length in the tubular reactor. In the case I
15*       the operation is adiabatic and in the case II the reactor is
16*       jacketed.
17*
18*   Assumptions
19*               * first-order reaction with respect to acetone
20*               * steady-state
21*       * gaseous phase
22*
23*       Specify:
24*               * the inlet stream
25*               * the kinetic parameters
26*               * the parameters of components
27*
28*----------------------------------------------------------------------
29* Author: Christiano D. W. Guerra and Rodolfo Rodrigues
30* GIMSCOP/UFRGS - Group of Integration, Modeling, Simulation,
31*                                       Control and Optimization of Processes
32* $Id$
33*--------------------------------------------------------------------*#
34
35using "types";
36
37
38#*---------------------------------------------------------------------
39* Model of the thermal craking of acetone
40*--------------------------------------------------------------------*#
41
42Model thermal_cracking
43        PARAMETERS
44        NComp           as Integer              (Brief="Number of components", Lower=1);
45        stoic(NComp)as Real                     (Brief="Stoichiometric number");
46        Pa0             as pressure     (Brief="Input pressure of A");
47        Tr                      as temperature  (Brief="Reference temperature");
48        T0                      as temperature  (Brief="Inlet temperature");
49        Ta                      as temperature  (Brief="Internal temperature");
50        Hr(NComp)       as enth_mol             (Brief="Enthalpy of component");
51        R                       as Real                 (Brief="Universal gas constant", Unit="kPa*m^3/kmol/K", Default=8.314);
52        U                       as Real                 (Brief="Heat transfer coefficient", Unit="J/m^2/K/s");
53        a                       as Real                 (Brief="Heat transfer area per volume of tube", Unit="1/m");
54        alpha(NComp)as cp_mol           (Brief="Alpha term of Cp expression");
55        beta(NComp)     as Real                 (Brief="Beta term of Cp expression", Unit="J/mol/K^2");
56        gamma(NComp)as Real                     (Brief="Gamma term of Cp expression", Unit="J/mol/K^3");
57       
58        VARIABLES
59        Ca                      as conc_mol     (Brief="Molar concentration of A", Unit="kmol/m^3");
60        Ca0             as conc_mol     (Brief="Inlet molar concentration of A", Unit="mol/m^3");
61        Fa0             as flow_mol     (Brief="Inlet molar flow of A");
62        v0                      as flow_vol     (Brief="Volumetric flow", Unit="m^3/s");
63        r                       as reaction_mol (Brief="Rate of reaction", Unit="kmol/m^3/s");
64        k                       as Real                 (Brief="Specific rate of reaction", Unit="1/s");
65        T                       as temperature  (Brief="Temperature of reactor", Unit="K");
66        X                       as fraction     (Brief="Molar conversion", Lower=0);
67        V                       as volume               (Brief="Volume", Unit="m^3");
68        eps                     as Real                 (Brief="Parameter epsilon");
69        Cp(NComp)       as cp_mol               (Brief="Molar heat capacity", Unit="J/mol/K");
70        DHr                     as enth_mol             (Brief="Enthalpy of reaction", Unit="kJ/mol"); 
71       
72        EQUATIONS
73        "Change time in V"
74        V = time*"m^3/s";
75       
76        "Molar balance"
77        diff(X) = (-r)/Fa0*"m^3/s";
78       
79        "Rate of reaction"
80        r = -k*Ca;
81       
82        "Specific rate of reaction"
83        k = exp(34.34)*exp(-34222*"K"/T)*"1/s";
84       
85        "Concentration of component A"
86        Ca = Ca0*(1 - X)/(1 + eps*X)*T0/T;
87       
88        "Parameter epsilon"
89        eps = sum(stoic); # yAo = 1
90       
91        "Inlet molar concentration of A"
92        Ca0 = Pa0/(R*T0);
93       
94        "Volumetric flow"
95        Fa0 = Ca0*v0;
96       
97        "Energy balance"
98        diff(T)*(Fa0*(Cp(1) + X*sumt(stoic*Cp))) = (U*a*(Ta - T) + (-r)*(-DHr))*"m^3/s";
99
100        "Enthalpy of reaction"
101        DHr = sumt(stoic*Hr) + sumt(stoic*alpha)*(T - Tr) + sumt(stoic*beta)/2*(T^2 - Tr^2)
102                +  sumt(stoic*gamma)/3*(T^3 - Tr^3);
103       
104        "Molar heat capacity"
105        Cp  = alpha + beta*T + gamma*T^2;
106end
107
108
109#*---------------------------------------------------------------------
110* Case I: In an adiabatic PFR
111*--------------------------------------------------------------------*#
112
113FlowSheet adiabatic_reactor
114        DEVICES
115        R as thermal_cracking;
116       
117        SET
118        R.NComp = 3; # A: acetone, B: ketene and C: methane
119        R.stoic = [-1.0, 1.0, 1.0]; # A -> B + C
120       
121        R.Pa0 = 162*"kPa";
122       
123        R.alpha = [26.63,  20.04, 13.39]*"J/mol/K";
124        R.beta  = [0.183, 0.0945, 0.077]*"J/mol/K^2";
125        R.gamma = [-45.86e-6, -30.95e-6, -18.71e-6]*"J/mol/K^3";
126       
127        R.Hr = [-216.67, -61.09, -74.81]*"kJ/mol";
128        R.Tr = 298*"K";
129        R.T0 = 1035*"K";
130        R.Ta = 1150*"K";
131        R.U  = 0.0*"J/m^2/K/s";
132        R.a  = 150*"1/m";
133       
134        SPECIFY
135        "Inlet molar flow"
136        R.Fa0 = (8000/58)*"kmol/h";
137       
138        INITIAL
139        "Molar conversion"
140        R.X = 0.0;
141        "Temperature"
142        R.T = 1035*"K";
143       
144        OPTIONS
145        time = [0:0.05:5];
146end
147
148
149#*---------------------------------------------------------------------
150* Case II: In an jacketed PFR
151*--------------------------------------------------------------------*#
152
153FlowSheet jacketed_reactor
154        DEVICES
155        R as thermal_cracking;
156       
157        SET
158        R.NComp = 3; # A: acetone, B: ketene and C: methane
159        R.stoic = [-1.0, 1.0, 1.0]; # A -> B + C
160       
161        R.Pa0 = 162*"kPa";
162       
163        R.alpha = [26.63,  20.04, 13.39]*"J/mol/K";
164        R.beta  = [0.183, 0.0945, 0.077]*"J/mol/K^2";
165        R.gamma = [-45.86e-6, -30.95e-6, -18.71e-6]*"J/mol/K^3";
166       
167        R.Hr = [-216.67, -61.09, -74.81]*"kJ/mol";
168        R.Tr = 298*"K";
169        R.T0 = 1035*"K";
170        R.Ta = 1150*"K";
171        R.U  = 110*"J/m^2/K/s";
172        R.a  = 150*"1/m";
173       
174        SPECIFY
175        "Inlet molar flow"
176        R.Fa0 = (18.8*2e-3)*"mol/s";
177       
178        INITIAL
179        "Molar conversion"
180        R.X = 0.0;
181        "Temperature"
182        R.T = 1035*"K";
183       
184        OPTIONS
185        time = [0:1e-5:1e-3];
186end
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