source: branches/new_gui/my_folders/fogler/chap8/acetic_anhydride.mso @ 896

#*-------------------------------------------------------------------
* EMSO Model Library (EML) Copyright (C) 2004 - 2007 ALSOC.
*
* This LIBRARY is free software; you can distribute it and/or modify
* it under the therms of the ALSOC FREE LICENSE as available at
* http://www.enq.ufrgs.br/alsoc.
*
* EMSO Copyright (C) 2004 - 2007 ALSOC, original code
* from http://www.rps.eng.br Copyright (C) 2002-2004.
* All rights reserved.
*
* EMSO is distributed under the therms of the ALSOC LICENSE as
* available at http://www.enq.ufrgs.br/alsoc.
*
*---------------------------------------------------------------------
* Production of acetic anhydride
*----------------------------------------------------------------------
* Solved problem from Fogler (1999)
* Problem number: 8-7
* Page: 421 (Brazilian version, 2002)
*----------------------------------------------------------------------
*
*   Description:
*               The acetic anhydride is produced for thermal craking of the
*       acetone in a PFR:
*                       CH3COCH3 -> CH2CO + CH4
*               This sample calculates the molar conversion and temperature
*       as function of the length in the tubular reactor. In the case I 
*       the operation is adiabatic and in the case II the reactor is
*       jacketed.
*
*   Assumptions
*               * first-order reaction with respect to acetone
*               * steady-state
*       * gaseous phase
*
*       Specify:
*               * the inlet stream
*               * the kinetic parameters
*               * the parameters of components
*
*----------------------------------------------------------------------
* Author: Christiano D. W. Guerra and Rodolfo Rodrigues
* $Id: acetic_anhydride.mso 574 2008-07-25 14:18:50Z rafael $
*--------------------------------------------------------------------*#

using "types";


#*---------------------------------------------------------------------
* Model of the thermal craking of acetone
*--------------------------------------------------------------------*#

Model thermal_cracking
        PARAMETERS
        NComp           as Integer              (Brief="Number of components", Lower=1);
        stoic(NComp)as Real                     (Brief="Stoichiometric number");
        Pao             as pressure     (Brief="Input pressure of A");
        Tr                      as temperature  (Brief="Reference temperature");
        To                      as temperature  (Brief="Inlet temperature");
        Ta                      as temperature  (Brief="Internal temperature");
        Hr(NComp)       as enth_mol             (Brief="Enthalpy of component");
        R                       as Real                 (Brief="Universal gas constant", Unit='kPa*m^3/kmol/K', Default=8.314);
        U                       as Real                 (Brief="Heat transfer coefficient", Unit='J/m^2/K/s');
        a                       as Real                 (Brief="Heat transfer area per volume of tube", Unit='1/m');
        alpha(NComp)as cp_mol           (Brief="Alpha term of Cp expression");
        beta(NComp)     as Real                 (Brief="Beta term of Cp expression", Unit='J/mol/K^2');
        gamma(NComp)as Real                     (Brief="Gamma term of Cp expression", Unit='J/mol/K^3');
        
        VARIABLES
        Ca                      as conc_mol     (Brief="Molar concentration of A", DisplayUnit='kmol/m^3');
        Cao             as conc_mol     (Brief="Inlet molar concentration of A", DisplayUnit='mol/m^3');
        Fao             as flow_mol     (Brief="Inlet molar flow of A");
        vo                      as flow_vol     (Brief="Volumetric flow", DisplayUnit='m^3/s');
        r                       as reaction_mol (Brief="Rate of reaction", DisplayUnit='kmol/m^3/s');
        k                       as Real                 (Brief="Specific rate of reaction", Unit='1/s');
        T                       as temperature  (Brief="Temperature of reactor");
        X                       as fraction     (Brief="Molar conversion");
        V                       as volume               (Brief="Volume");
        eps                     as Real                 (Brief="Parameter epsilon");
        Cp(NComp)       as cp_mol               (Brief="Molar heat capacity", DisplayUnit='J/mol/K');
        DHr                     as enth_mol             (Brief="Enthalpy of reaction", DisplayUnit='kJ/mol');   
        
        EQUATIONS
        "Change time in V"
        V = time*'m^3/s';
        
        "Molar balance"
        diff(X) = (-r)/Fao*'m^3/s';
        
        "Rate of reaction"
        r = -k*Ca;
        
        "Specific rate of reaction"
        k = exp(34.34)*exp(-34222*'K'/T)*'1/s';
        
        "Concentration of component A"
        Ca = Cao*(1 - X)/(1 + eps*X)*To/T;
        
        "Parameter epsilon"
        eps = sum(stoic); # yAo = 1
        
        "Inlet molar concentration of A"
        Cao = Pao/(R*To);
        
        "Volumetric flow"
        Fao = Cao*vo;
        
        "Energy balance"
        diff(T)*(Fao*(Cp(1) + X*sumt(stoic*Cp))) = (U*a*(Ta - T) + (-r)*(-DHr))*'m^3/s';

        "Enthalpy of reaction"
        DHr = sumt(stoic*Hr) + sumt(stoic*alpha)*(T - Tr) + sumt(stoic*beta)/2*(T^2 - Tr^2) 
                +  sumt(stoic*gamma)/3*(T^3 - Tr^3);
        
        "Molar heat capacity"
        Cp  = alpha + beta*T + gamma*T^2;
end


#*---------------------------------------------------------------------
* Case I: In an adiabatic PFR
*--------------------------------------------------------------------*#

FlowSheet adiabatic_reactor
        DEVICES
        R as thermal_cracking;
        
        SET
        R.NComp = 3; # A: acetone, B: ketene and C: methane
        R.stoic = [-1.0, 1.0, 1.0]; # A -> B + C
        
        R.Pao = 162*'kPa';
        
        R.alpha = [26.63,  20.04, 13.39]*'J/mol/K';
        R.beta  = [0.183, 0.0945, 0.077]*'J/mol/K^2';
        R.gamma = [-45.86e-6, -30.95e-6, -18.71e-6]*'J/mol/K^3';
        
        R.Hr = [-216.67, -61.09, -74.81]*'kJ/mol';
        R.Tr = 298*'K';
        R.To = 1035*'K';
        R.Ta = 1150*'K';
        R.U  = 0.0*'J/m^2/K/s';
        R.a  = 150*'1/m';
        
        SPECIFY
        R.Fao = (8000/58)*'kmol/h';
        
        INITIAL
        "Molar conversion"
        R.X = 0.0;
        "Temperature"
        R.T = 1035*'K';
        
        OPTIONS
        TimeStep = 0.05;
        TimeEnd = 5;
        TimeUnit = 's';
end


#*---------------------------------------------------------------------
* Case II: In an jacketed PFR
*--------------------------------------------------------------------*#

FlowSheet jacketed_reactor
        DEVICES
        R as thermal_cracking;
        
        SET
        R.NComp = 3; # A: acetone, B: ketene and C: methane
        R.stoic = [-1.0, 1.0, 1.0]; # A -> B + C
        
        R.Pao = 162*'kPa';
        
        R.alpha = [26.63,  20.04, 13.39]*'J/mol/K';
        R.beta  = [0.183, 0.0945, 0.077]*'J/mol/K^2';
        R.gamma = [-45.86e-6, -30.95e-6, -18.71e-6]*'J/mol/K^3';
        
        R.Hr = [-216.67, -61.09, -74.81]*'kJ/mol';
        R.Tr = 298*'K';
        R.To = 1035*'K';
        R.Ta = 1150*'K';
        R.U  = 110*'J/m^2/K/s';
        R.a  = 150*'1/m';
        
        SPECIFY
        R.Fao = (18.8*2e-3)*'mol/s';
        
        INITIAL
        "Molar conversion"
        R.X = 0.0;
        "Temperature"
        R.T = 1035*'K';
        
        OPTIONS
        TimeStep = 1e-5;
        TimeEnd = 1e-3;
        TimeUnit = 's';
end