source: branches/gui/sample/miscellaneous/tenprobs/prob01.mso @ 697

#*---------------------------------------------------------------------
* EMSO Model Library (EML) Copyright (C) 2004 - 2007 ALSOC.
*
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* 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.
*
*----------------------------------------------------------------------
* 1. Thermodynamic properties from van der Waals equation
*----------------------------------------------------------------------
*
*   Description:
*      This problem is part of a collection of 10 representative
*       problems in Chemical Engineering for solution by numerical methods
*       developed for Cutlip (1998).
*
*   Subject:
*       * Introduction to Chemical Engineering
*               * Thermodynamics
*
*       Concepts utilized:
*               Use of the van der Waals equation of state to calculate molar
*       volume and compressibility factor for a gas.
*
*       Numerical method:
*               * Single nonlinear algebraic equation
*
*   Reference:
*       * CUTLIP et al. A collection of 10 numerical problems in 
*       chemical engineering solved by various mathematical software 
*       packages. Comp. Appl. in Eng. Education. v. 6, 169-180, 1998. 
*       * More informations and a detailed description of all problems
*       is available online in http://www.polymath-software.com/ASEE
* 
*----------------------------------------------------------------------
* Author: Rodolfo Rodrigues
* GIMSCOP/UFRGS - Group of Integration, Modeling, Simulation, 
*                                       Control, and Optimization of Processes
* $Id$
*--------------------------------------------------------------------*#
using "types";



#*---------------------------------------------------------------------
*       Equation of state
*--------------------------------------------------------------------*#

Model van_der_waals
        PARAMETERS
outer Pc                as pressure             (Brief="Critical pressure");
outer Tc                as temperature  (Brief="Critical temperature");
        R                       as Real                 (Brief="Gas constant", Default=0.08206, Unit='atm*l/mol/K');
        
        
        VARIABLES
        P                       as pressure             (Brief="Pressure");
        V                       as volume_mol   (Brief="Molar volume", DisplayUnit='l/mol');
        T                       as temperature  (Brief="Temperature");
        
        a                       as Real                 (Brief="Parameter a of van der Waals equation", Unit='atm*(l/mol)^2');
        b                       as volume_mol   (Brief="Parameter b of van der Waals equation", DisplayUnit='l/mol');
        
        
        EQUATIONS
        "Van der Waals equation"
        (P + a/V^2)*(V - b) = R*T;
        
        "Parameter a"
        a = (27/64)*(R^2*Tc^2)/Pc;
        
        "Parameter b"
        b = R*Tc/(8*Pc);
end



#*---------------------------------------------------------------------
*       Thermodynamic properties calculation (question a)
*--------------------------------------------------------------------*#

FlowSheet properties
        PARAMETERS
        Pc                                      as pressure;
        Tc                                      as temperature;
        
        
        VARIABLES
        equation_of_state       as van_der_waals;
        Pr                                      as Real (Brief="Reduced pressure");
        Z                                       as Real (Brief="Compressibility factor");
        
        
        EQUATIONS
        # Thermodynamic properties
        "Reduced pressure"
        Pr = equation_of_state.P/Pc;
        
        "Compressibility factor"
        Z = equation_of_state.P*equation_of_state.V/(equation_of_state.R*equation_of_state.T);
        
        
        SET
        Pc = 111.3*'atm'; # for ammonia
        Tc = 405.5*'K'; # for ammonia

        
        SPECIFY
        equation_of_state.P = 56*'atm';
        equation_of_state.T = 450*'K';
        
        
        OPTIONS
        Dynamic = false;
end



#*---------------------------------------------------------------------
*       Variation of properties with Pr (question b and c)
*--------------------------------------------------------------------*#

FlowSheet variation_of_properties
        PARAMETERS
        Pc                                      as pressure;
        Tc                                      as temperature;
        
        
        VARIABLES
        equation_of_state       as van_der_waals;
        Pr                                      as Real (Brief="Reduced pressure");
        Z                                       as Real (Brief="Compressibility factor");
        
        
        EQUATIONS
        "Change time in Pr"
        Pr = time/'s';
        
        # Thermodynamic properties
        "Reduced pressure"
        Pr = equation_of_state.P/Pc;
        
        "Compressibility factor"
        Z = equation_of_state.P*equation_of_state.V/(equation_of_state.R*equation_of_state.T);
        
        
        SET
        Pc = 111.3*'atm'; # for ammonia
        Tc = 405.5*'K'; # for ammonia

        
        SPECIFY
        equation_of_state.T = 450*'K';
        
        
        OPTIONS
        TimeStart = 1;
        TimeStep = 0.5;
        TimeEnd = 20;
end