trunk/models/phaseq.a4c

REQUIRE "atoms.a4l";
(* => atoms.a4l, measures.a4l, system.a4l, basemodel.a4l *)
PROVIDE "phaseq.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.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.
It represent a problem which we can represent as a conditional model and
solve  with the ascend conditional solver CMSlv.

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 critical_pressure;
      Tcr[components] 		IS_A critical_temperature;
      B[components][k_terms]    IS_A factor_constant;
      C[k_terms]                IS_A factor_constant;
      A[components][components] IS_A temperature_constant;

(* Definition os sets *)

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

(* Boundaries *)
      CONDITIONAL
        FOR i IN phases CREATE
           cond[i]: SUM[y[i][j] | j IN components ]+ phi[i] >= 1.0;
        END FOR;
      END CONDITIONAL;


      FOR i IN phases CREATE
(* Variant Equations *)
         sum[i]: SUM[y[i][j] | j IN components ] = 1.0;
         frac[i]: phi[i] = 0.0;
         exist[i] == SATISFIED(cond[i],1e-08);
(* Disjunctive statement *)
         WHEN (exist[i])
	   CASE TRUE:
	      USE sum[i];
	   CASE FALSE:
              USE frac[i];
         END WHEN;

      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;

(* 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;

  METHODS

    METHOD default_self;
    END default_self;

    METHOD specify;
	P.fixed := TRUE;
	T.fixed := TRUE;
	FOR i IN components DO
	    z[i].fixed := TRUE;
        END FOR;
    END specify;

    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 for reals *)
	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;

(* initial values for booleans *)
        FOR i IN phases DO
         exist[i] := SATISFIED(cond[i],1e-08);
        END FOR;
    END values;

END phaseq;


(*
 *  phaseq.a4c
 *  by Vicente Rico-Ramirez
 *  April 10, 1998
 *  Part of the ASCEND Library
 *  $Date: 1998/06/17 19:13:16 $
 *  $Revision: 1.3 $
 *  $Author: mthomas $
 *  $Source: /afs/cs.cmu.edu/project/ascend/Repository/models/phaseq.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.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.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	It represent a problem which we can represent as a conditional model and
20	solve with the ascend conditional solver CMSlv.
21
22	This model requires:
23	"system.a4l"
24	"atoms.a4l"
25	*)
26
27	(* ************************************************* *)
28
29	MODEL phaseq;
30
31	phases IS_A set OF symbol_constant;
32	components IS_A set OF symbol_constant;
33	k_terms IS_A set OF integer_constant;
34	z[components] IS_A fraction;
35	y[phases][components] IS_A fraction;
36	phi[phases] IS_A fraction;
37	exist[phases] IS_A boolean_var;
38	P IS_A pressure;
39	T IS_A temperature;
40	Pcr[components] IS_A critical_pressure;
41	Tcr[components] IS_A critical_temperature;
42	B[components][k_terms] IS_A factor_constant;
43	C[k_terms] IS_A factor_constant;
44	A[components][components] IS_A temperature_constant;
45
46	(* Definition os sets *)
47
48	components :== ['B','E','W'];
49	phases :== ['A','O','V'];
50	k_terms :== [1..4];
51
52	(* Boundaries *)
53	CONDITIONAL
54	FOR i IN phases CREATE
55	cond[i]: SUM[y[i][j] \| j IN components ]+ phi[i] >= 1.0;
56	END FOR;
57	END CONDITIONAL;
58
59
60	FOR i IN phases CREATE
61	(* Variant Equations *)
62	sum[i]: SUM[y[i][j] \| j IN components ] = 1.0;
63	frac[i]: phi[i] = 0.0;
64	exist[i] == SATISFIED(cond[i],1e-08);
65	(* Disjunctive statement *)
66	WHEN (exist[i])
67	CASE TRUE:
68	USE sum[i];
69	CASE FALSE:
70	USE frac[i];
71	END WHEN;
72
73	END FOR;
74
75	(* Invariant Equations *)
76
77	FOR i IN components CREATE
78	y['V'][i] = y['A'][i] * (Pcr[i]/P) * exp(
79	((1/T) *
80	SUM[ ( A[i][j] - (0.5*
81	SUM[ A[j][k] * y['A'][k] \| k IN components]
82	) ) * y['A'][j]
83	\| j IN components ]) +
84	((Tcr[i]/T) *
85	SUM[ B[i][k] * ( (1 - (T/Tcr[i]))^C[k] ) \| k IN k_terms] ) );
86
87	y['V'][i] = y['O'][i] * (Pcr[i]/P) * exp(
88	((1/T) *
89	SUM[ ( A[i][j] - (0.5*
90	SUM[ A[j][k] * y['O'][k] \| k IN components]
91	) ) * y['O'][j]
92	\| j IN components ]) +
93	((Tcr[i]/T) *
94	SUM[ B[i][k] * ( (1 - (T/Tcr[i]))^C[k] ) \| k IN k_terms] ) );
95	END FOR;
96
97	FOR i IN components CREATE
98	SUM[phi[j]*y[j][i] \| j IN phases] = z[i];
99	END FOR;
100
101	(* Constants *)
102	Tcr['B'] :== 562.2 {K};
103	Tcr['E'] :== 516.2 {K};
104	Tcr['W'] :== 647.4 {K};
105	Pcr['B'] :== 48.3 {atm};
106	Pcr['E'] :== 63.0 {atm};
107	Pcr['W'] :== 217.6 {atm};
108	C[1] :== 1.0;
109	C[2] :== 1.5;
110	C[3] :== 3.0;
111	C[4] :== 6.0;
112	A['B']['B'] :== 0.0{K};
113	A['B']['E'] :== 576.3 {K};
114	A['B']['W'] :== 1074.5 {K};
115	A['E']['B'] :== 576.3 {K};
116	A['E']['E'] :== 0.0 {K};
117	A['E']['W'] :== 351.8 {K};
118	A['W']['B'] :== 1074.5 {K};
119	A['W']['E'] :== 351.8 {K};
120	A['W']['W'] :== 0.0 {K};
121	B['B'][1] :== -6.98273;
122	B['B'][2] :== 1.33213;
123	B['B'][3] :== -2.62863;
124	B['B'][4] :== -3.33399;
125	B['E'][1] :== -8.51838;
126	B['E'][2] :== 0.34163;
127	B['E'][3] :== -5.73683;
128	B['E'][4] :== 8.32581;
129	B['W'][1] :== -7.76451;
130	B['W'][2] :== 1.45838;
131	B['W'][3] :== -2.77580;
132	B['W'][4] :== -1.23303;
133
134	METHODS
135
136	METHOD default_self;
137	END default_self;
138
139	METHOD specify;
140	P.fixed := TRUE;
141	T.fixed := TRUE;
142	FOR i IN components DO
143	z[i].fixed := TRUE;
144	END FOR;
145	END specify;
146
147	METHOD values;
148	(* fixed *)
149	T := 340.0 {K};
150	P := 1.0 {atm};
151	z['B'] := 0.50;
152	z['E'] := 0.15;
153	z['W'] := 0.35;
154	(* initial values for reals *)
155	y['A']['B'] := 0.02;
156	y['A']['E'] := 0.03;
157	y['A']['W'] := 0.95;
158
159	y['O']['B'] := 0.95;
160	y['O']['E'] := 0.03;
161	y['O']['W'] := 0.02;
162
163	y['V']['B'] := 0.50;
164	y['V']['E'] := 0.15;
165	y['V']['W'] := 0.35;
166
167	phi['A'] := 0.0;
168	phi['O'] := 0.0;
169	phi['V'] := 0.0;
170
171	(* initial values for booleans *)
172	FOR i IN phases DO
173	exist[i] := SATISFIED(cond[i],1e-08);
174	END FOR;
175	END values;
176
177	END phaseq;
178
179
180	(*
181	* phaseq.a4c
182	* by Vicente Rico-Ramirez
183	* April 10, 1998
184	* Part of the ASCEND Library
185	* $Date: 1998/06/17 19:13:16 $
186	* $Revision: 1.3 $
187	* $Author: mthomas $
188	* $Source: /afs/cs.cmu.edu/project/ascend/Repository/models/phaseq.a4c,v $
189	*
190	* This file is part of the ASCEND Modeling Library.
191	*
192	* Copyright (C) 1998 Carnegie Mellon University
193	*
194	* The ASCEND Modeling Library is free software; you can redistribute
195	* it and/or modify it under the terms of the GNU General Public
196	* License as published by the Free Software Foundation; either
197	* version 2 of the License, or (at your option) any later version.
198	*
199	* The ASCEND Modeling Library is distributed in hope that it will be
200	* useful, but WITHOUT ANY WARRANTY; without even the implied
201	* warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
202	* See the GNU General Public License for more details.
203	*
204	* You should have received a copy of the GNU General Public License
205	* along with the program; if not, write to the Free Software
206	* Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139 USA. Check
207	* the file named COPYING.
208	*)