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;
	P.fixed := TRUE;
	T.fixed := TRUE;
	FOR i IN components DO
	    z[i].fixed := TRUE;
	    Pcr[i].fixed := TRUE;
	    Tcr[i].fixed := TRUE;
            FOR j IN components DO
	      A[i][j].fixed := TRUE;
            END FOR;
            FOR j IN k_terms DO
	      B[i][j].fixed := TRUE;
            END FOR;
        END FOR;
	FOR j IN k_terms DO
	   C[j].fixed := TRUE;
        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 the program; if not, write to the Free Software
 *  Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139 USA.  Check
 *  the file named COPYING.
 *)
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	P.fixed := TRUE;
93	T.fixed := TRUE;
94	FOR i IN components DO
95	z[i].fixed := TRUE;
96	Pcr[i].fixed := TRUE;
97	Tcr[i].fixed := TRUE;
98	FOR j IN components DO
99	A[i][j].fixed := TRUE;
100	END FOR;
101	FOR j IN k_terms DO
102	B[i][j].fixed := TRUE;
103	END FOR;
104	END FOR;
105	FOR j IN k_terms DO
106	C[j].fixed := TRUE;
107	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	* along with the program; if not, write to the Free Software
209	* Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139 USA. Check
210	* the file named COPYING.
211	*)