trunk/models/phaseq_comp.a4c

REQUIRE "atoms.a4l";
(* => atoms.a4l, measures.a4l, system.a4l, basemodel.a4l *)
PROVIDE "phaseq_comp.a4c";
(*
 * This file is part of the ASCEND Modeling Library and is released
 * under the GNU Public License as described at the end of this file.
 *
 * Use of this module is demonstrated by the associated script file
 * phaseq_comp.a4s.
 *)

(*
   Ascend model of the phase Equilibrium example presented by Zaher
-- Conditional Modeling. Ph.D. Thesis, Carnegie Mellon University,
Pittsburgh, PA, 15213. 1995 --. The problem consists of a phase equilibrium
calculation of a  multicomponent mixture. For each of the phases (3 phases
are possible: organic-liquid, inorganic-liquid, and vapor) there is a
disjunctive statement which represents whether the phase exists or not.
Each disjunctive statement is represented by using a complementarity
formulation, in such a way that we can solve the problem by using a
conventional nonlinear solver.

This model requires:
			"system.a4l"
		    	"atoms.a4l"
*)

(* ************************************************* *)

MODEL phaseq;

      phases			IS_A set OF symbol_constant;
      components      		IS_A set OF symbol_constant;
      k_terms      		IS_A set OF integer_constant;
      z[components]   		IS_A fraction;
      y[phases][components]	IS_A fraction;
      phi[phases]		IS_A fraction;
      exist[phases]		IS_A boolean_var;
      P				IS_A pressure;
      T				IS_A temperature;
      Pcr[components]  		IS_A pressure;
      Tcr[components] 		IS_A temperature;
      B[components][k_terms]    IS_A factor;
      C[k_terms]                IS_A factor;
      A[components][components] IS_A temperature;
      h1[phases],h2[phases]	IS_A fraction;

(* Definition of sets *)

      components :== ['B','E','W'];
      phases :== ['A','O','V'];
      k_terms :== [1..4];

(* Complementarity Equations *)

      FOR i IN phases CREATE
         SUM[y[i][j] | j IN components ] = 1.0 - h1[i];
         phi[i] = h2[i];
         h1[i] * h2[i] = 0;
      END FOR;

(* Invariant Equations *)

      FOR i IN components CREATE
         y['V'][i] = y['A'][i] * (Pcr[i]/P) * exp(
            ((1/T) *
               SUM[ ( A[i][j] - (0.5*
                 SUM[ A[j][k] * y['A'][k] | k IN components]
                 ) ) * y['A'][j]
                 | j IN components ])  +
             ((Tcr[i]/T) *
                SUM[ B[i][k] * ( (1 - (T/Tcr[i]))^C[k] ) | k IN k_terms] ) );

         y['V'][i] = y['O'][i] * (Pcr[i]/P) * exp(
             ((1/T) *
               SUM[ ( A[i][j] - (0.5*
                 SUM[ A[j][k] * y['O'][k] | k IN components]
                 ) ) * y['O'][j]
                 | j IN components ])  +
             ((Tcr[i]/T) *
                SUM[ B[i][k] * ( (1 - (T/Tcr[i]))^C[k] ) | k IN k_terms] ) );
      END FOR;

     FOR i IN components CREATE
        SUM[phi[j]*y[j][i] | j IN phases] = z[i];
     END FOR;


  METHODS

    METHOD specify;
	FIX P;
	FIX T;
	FOR i IN components DO
	    FIX z[i];
	    FIX Pcr[i];
	    FIX Tcr[i];
            FOR j IN components DO
	      FIX A[i][j];
            END FOR;
            FOR j IN k_terms DO
	      FIX B[i][j];
            END FOR;
        END FOR;
	FOR j IN k_terms DO
	   FIX C[j];
        END FOR;
    END specify;

    METHOD bound_self;
        FOR i IN components DO
            FOR j IN components DO
	      A[i][j].lower_bound := 0 {K};
            END FOR;
        END FOR;
    END bound_self;

    METHOD default_self;
        (* Constants *)
        Tcr['B'] := 562.2 {K};
        Tcr['E'] := 516.2 {K};
        Tcr['W'] := 647.4 {K};
        Pcr['B'] := 48.3 {atm};
        Pcr['E'] := 63.0 {atm};
        Pcr['W'] := 217.6 {atm};
        C[1] := 1.0;
        C[2] := 1.5;
        C[3] := 3.0;
        C[4] := 6.0;
        A['B']['B'] := 0.0{K};
        A['B']['E'] := 576.3 {K};
        A['B']['W'] := 1074.5 {K};
        A['E']['B'] := 576.3 {K};
        A['E']['E'] := 0.0 {K};
        A['E']['W'] := 351.8 {K};
        A['W']['B'] := 1074.5 {K};
        A['W']['E'] := 351.8 {K};
        A['W']['W'] := 0.0 {K};
        B['B'][1] := -6.98273;
        B['B'][2] := 1.33213;
        B['B'][3] := -2.62863;
        B['B'][4] := -3.33399;
        B['E'][1] := -8.51838;
        B['E'][2] := 0.34163;
        B['E'][3] := -5.73683;
        B['E'][4] := 8.32581;
        B['W'][1] := -7.76451;
        B['W'][2] := 1.45838;
        B['W'][3] := -2.77580;
        B['W'][4] := -1.23303;

        RUN bound_self;
    END default_self;

    METHOD values;
(* fixed *)
        T := 340.0 {K};
        P := 1.0 {atm};
	z['B'] := 0.50;
	z['E'] := 0.15;
	z['W'] := 0.35;
(* initial values *)
	y['A']['B'] := 0.02;
	y['A']['E'] := 0.03;
	y['A']['W'] := 0.95;

	y['O']['B'] := 0.95;
	y['O']['E'] := 0.03;
	y['O']['W'] := 0.02;

	y['V']['B'] := 0.50;
	y['V']['E'] := 0.15;
	y['V']['W'] := 0.35;

	phi['A'] := 0.0;
	phi['O'] := 0.0;
	phi['V'] := 0.0;
    END values;

END phaseq;


(*
 *  phaseq_comp.a4c
 *  by Vicente Rico-Ramirez
 *  April 10, 1998
 *  Part of the ASCEND Library
 *  $Date: 1998/06/17 19:13:37 $
 *  $Revision: 1.3 $
 *  $Author: mthomas $
 *  $Source: /afs/cs.cmu.edu/project/ascend/Repository/models/phaseq_comp.a4c,v $
 *
 *  This file is part of the ASCEND Modeling Library.
 *
 *  Copyright (C) 1998 Carnegie Mellon University
 *
 *  The ASCEND Modeling Library is free software; you can redistribute
 *  it and/or modify it under the terms of the GNU General Public
 *  License as published by the Free Software Foundation; either
 *  version 2 of the License, or (at your option) any later version.
 *
 *  The ASCEND Modeling Library is distributed in hope that it will be
 *  useful, but WITHOUT ANY WARRANTY; without even the implied
 *  warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
 *  See the GNU General Public License for more details.
 *
 *  You should have received a copy of the GNU General Public License
 *  along with this program.  If not, see <http://www.gnu.org/licenses/>.
 *)
1	aw0a	1	REQUIRE "atoms.a4l";
2			(* => atoms.a4l, measures.a4l, system.a4l, basemodel.a4l *)
3			PROVIDE "phaseq_comp.a4c";
4			(*
5			* This file is part of the ASCEND Modeling Library and is released
6			* under the GNU Public License as described at the end of this file.
7			*
8			* Use of this module is demonstrated by the associated script file
9			* phaseq_comp.a4s.
10			*)
11
12			(*
13			Ascend model of the phase Equilibrium example presented by Zaher
14			-- Conditional Modeling. Ph.D. Thesis, Carnegie Mellon University,
15			Pittsburgh, PA, 15213. 1995 --. The problem consists of a phase equilibrium
16			calculation of a multicomponent mixture. For each of the phases (3 phases
17			are possible: organic-liquid, inorganic-liquid, and vapor) there is a
18			disjunctive statement which represents whether the phase exists or not.
19			Each disjunctive statement is represented by using a complementarity
20			formulation, in such a way that we can solve the problem by using a
21			conventional nonlinear solver.
22
23			This model requires:
24			"system.a4l"
25			"atoms.a4l"
26			*)
27
28			(* ************************************************* *)
29
30			MODEL phaseq;
31
32			phases IS_A set OF symbol_constant;
33			components IS_A set OF symbol_constant;
34			k_terms IS_A set OF integer_constant;
35			z[components] IS_A fraction;
36			y[phases][components] IS_A fraction;
37			phi[phases] IS_A fraction;
38			exist[phases] IS_A boolean_var;
39			P IS_A pressure;
40			T IS_A temperature;
41			Pcr[components] IS_A pressure;
42			Tcr[components] IS_A temperature;
43			B[components][k_terms] IS_A factor;
44			C[k_terms] IS_A factor;
45			A[components][components] IS_A temperature;
46			h1[phases],h2[phases] IS_A fraction;
47
48			(* Definition of sets *)
49
50			components :== ['B','E','W'];
51			phases :== ['A','O','V'];
52			k_terms :== [1..4];
53
54			(* Complementarity Equations *)
55
56			FOR i IN phases CREATE
57			SUM[y[i][j] \| j IN components ] = 1.0 - h1[i];
58			phi[i] = h2[i];
59			h1[i] * h2[i] = 0;
60			END FOR;
61
62			(* Invariant Equations *)
63
64			FOR i IN components CREATE
65			y['V'][i] = y['A'][i] * (Pcr[i]/P) * exp(
66			((1/T) *
67			SUM[ ( A[i][j] - (0.5*
68			SUM[ A[j][k] * y['A'][k] \| k IN components]
69			) ) * y['A'][j]
70			\| j IN components ]) +
71			((Tcr[i]/T) *
72			SUM[ B[i][k] * ( (1 - (T/Tcr[i]))^C[k] ) \| k IN k_terms] ) );
73
74			y['V'][i] = y['O'][i] * (Pcr[i]/P) * exp(
75			((1/T) *
76			SUM[ ( A[i][j] - (0.5*
77			SUM[ A[j][k] * y['O'][k] \| k IN components]
78			) ) * y['O'][j]
79			\| j IN components ]) +
80			((Tcr[i]/T) *
81			SUM[ B[i][k] * ( (1 - (T/Tcr[i]))^C[k] ) \| k IN k_terms] ) );
82			END FOR;
83
84			FOR i IN components CREATE
85			SUM[phi[j]*y[j][i] \| j IN phases] = z[i];
86			END FOR;
87
88
89			METHODS
90
91			METHOD specify;
92	johnpye	576	FIX P;
93			FIX T;
94	aw0a	1	FOR i IN components DO
95	johnpye	576	FIX z[i];
96			FIX Pcr[i];
97			FIX Tcr[i];
98	aw0a	1	FOR j IN components DO
99	johnpye	576	FIX A[i][j];
100	aw0a	1	END FOR;
101			FOR j IN k_terms DO
102	johnpye	576	FIX B[i][j];
103	aw0a	1	END FOR;
104			END FOR;
105			FOR j IN k_terms DO
106	johnpye	576	FIX C[j];
107	aw0a	1	END FOR;
108			END specify;
109
110			METHOD bound_self;
111			FOR i IN components DO
112			FOR j IN components DO
113			A[i][j].lower_bound := 0 {K};
114			END FOR;
115			END FOR;
116			END bound_self;
117
118			METHOD default_self;
119			(* Constants *)
120			Tcr['B'] := 562.2 {K};
121			Tcr['E'] := 516.2 {K};
122			Tcr['W'] := 647.4 {K};
123			Pcr['B'] := 48.3 {atm};
124			Pcr['E'] := 63.0 {atm};
125			Pcr['W'] := 217.6 {atm};
126			C[1] := 1.0;
127			C[2] := 1.5;
128			C[3] := 3.0;
129			C[4] := 6.0;
130			A['B']['B'] := 0.0{K};
131			A['B']['E'] := 576.3 {K};
132			A['B']['W'] := 1074.5 {K};
133			A['E']['B'] := 576.3 {K};
134			A['E']['E'] := 0.0 {K};
135			A['E']['W'] := 351.8 {K};
136			A['W']['B'] := 1074.5 {K};
137			A['W']['E'] := 351.8 {K};
138			A['W']['W'] := 0.0 {K};
139			B['B'][1] := -6.98273;
140			B['B'][2] := 1.33213;
141			B['B'][3] := -2.62863;
142			B['B'][4] := -3.33399;
143			B['E'][1] := -8.51838;
144			B['E'][2] := 0.34163;
145			B['E'][3] := -5.73683;
146			B['E'][4] := 8.32581;
147			B['W'][1] := -7.76451;
148			B['W'][2] := 1.45838;
149			B['W'][3] := -2.77580;
150			B['W'][4] := -1.23303;
151
152			RUN bound_self;
153			END default_self;
154
155			METHOD values;
156			(* fixed *)
157			T := 340.0 {K};
158			P := 1.0 {atm};
159			z['B'] := 0.50;
160			z['E'] := 0.15;
161			z['W'] := 0.35;
162			(* initial values *)
163			y['A']['B'] := 0.02;
164			y['A']['E'] := 0.03;
165			y['A']['W'] := 0.95;
166
167			y['O']['B'] := 0.95;
168			y['O']['E'] := 0.03;
169			y['O']['W'] := 0.02;
170
171			y['V']['B'] := 0.50;
172			y['V']['E'] := 0.15;
173			y['V']['W'] := 0.35;
174
175			phi['A'] := 0.0;
176			phi['O'] := 0.0;
177			phi['V'] := 0.0;
178			END values;
179
180			END phaseq;
181
182
183			(*
184			* phaseq_comp.a4c
185			* by Vicente Rico-Ramirez
186			* April 10, 1998
187			* Part of the ASCEND Library
188			* $Date: 1998/06/17 19:13:37 $
189			* $Revision: 1.3 $
190			* $Author: mthomas $
191			* $Source: /afs/cs.cmu.edu/project/ascend/Repository/models/phaseq_comp.a4c,v $
192			*
193			* This file is part of the ASCEND Modeling Library.
194			*
195			* Copyright (C) 1998 Carnegie Mellon University
196			*
197			* The ASCEND Modeling Library is free software; you can redistribute
198			* it and/or modify it under the terms of the GNU General Public
199			* License as published by the Free Software Foundation; either
200			* version 2 of the License, or (at your option) any later version.
201			*
202			* The ASCEND Modeling Library is distributed in hope that it will be
203			* useful, but WITHOUT ANY WARRANTY; without even the implied
204			* warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
205			* See the GNU General Public License for more details.
206			*
207			* You should have received a copy of the GNU General Public License
208	jpye	2649	* along with this program. If not, see <http://www.gnu.org/licenses/>.
209	aw0a	1	*)