trunk/models/rachford.a4c

REQUIRE "atoms.a4l";
(* => atoms.a4l, measures.a4l, system.a4l, basemodel.a4l *)
PROVIDE "rachford.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
 * rachford.a4s.
 *)

(*
   Ascend model of the Rachford-Rice equation described by King.
-- Separation Process. Chemical Engineering series. 2nd. Edition, McGraw-
Hill, 77-79, 1980  --. The problem consists in a simple flash calculation
performed by solving the Rachford-Rice equation. There is a disjunctive
statement which extends the use of that equation for cases in which the
system has only one phase (liquid or vapor). That is, this model not only
copes with the liquid-vapor equilibrium case. The resulting system of
equations can be solved  with the ascend conditional solver CMSlv.

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

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

(* Components *)

MODEL component_constants;
	Tc			IS_A	critical_temperature;
	Pc			IS_A	critical_pressure;
	vpa, vpb, vpc, vpd	IS_A	vapor_pressure_constant;
END component_constants;

MODEL n_butane REFINES component_constants;
(*Constants *)
	Tc :== 425.2 {K};
	Pc :== 38.0 {bar};
	vpa :== -6.88709;
	vpb :== 1.15157;
	vpc :== -1.99873;
	vpd :== -3.13003;
END n_butane;

MODEL n_pentane REFINES component_constants;
(*Constants *)
        Tc :== 469.7 {K};
        Pc :== 33.7 {bar};
        vpa :== -7.28936;
        vpb :== 1.53679;
        vpc :== -3.08367;
        vpd :== -1.02456;
END n_pentane;

MODEL n_hexane REFINES component_constants;
(*Constants *)
         Tc :== 507.5 {K};
         Pc :== 30.1 {bar};
         vpa :== -7.46765;
         vpb :== 1.44211;
         vpc :== -3.28222;
         vpd :== -2.50941;
END n_hexane;

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

(* Flash calculation *)
(* Rachford Rice calculation when P and T are specified *)

MODEL simple_flash;
	components		IS_A set OF integer_constant;
	comp[components]	IS_A component_constants;
	VP[components]		IS_A pressure;
	K[components]		IS_A factor;
	z[components],
	x[components],
	y[components]		IS_A fraction;
	V,F			IS_A molar_rate;
	V_F			IS_A factor;
	T			IS_A temperature;
	P			IS_A pressure;
	G			IS_A factor;
	bol1,bol2		IS_A boolean_var;


			(* Component Data *)

	components :== [1..3];
	comp[1] IS_REFINED_TO n_butane;
        comp[2] IS_REFINED_TO n_pentane;
        comp[3] IS_REFINED_TO n_hexane;


(* Boundaries *)
	CONDITIONAL
	  cond1: G <= 0.0;
	  cond2: G <= 1.0;
	END CONDITIONAL;

	bol1 == SATISFIED(cond1,1e-08);
	bol2 == SATISFIED(cond2,1e-08);

(* Variant Equations*)
	eq1: V_F = 0.0;
	eq2: V_F = G;
	eq3: V_F = 1.0;

(* Disjunctive Statement*)
	WHEN (bol1,bol2)
          CASE TRUE,TRUE:
		USE eq1;
	  CASE FALSE,TRUE:
		USE eq2;
	  CASE FALSE,FALSE:
		USE eq3;
	  OTHERWISE:
	END WHEN;

(* Invariant Equations *)

	FOR i IN components CREATE

        (* Vapor pressure *)
          ln(VP[i]/comp[i].Pc)*T/comp[i].Tc*abs(comp[i].Tc - T) =
            (comp[i].vpa*abs(1.0 - T/comp[i].Tc) +
            (comp[i].vpb*abs(1.0 - T/comp[i].Tc)^1.5) +
            (comp[i].vpc*abs(1.0 - T/comp[i].Tc)^3.0) +
            (comp[i].vpd*abs(1.0 - T/comp[i].Tc)^6.0))*(comp[i].Tc - T);

        (* Equilibrium constant *)
	  K[i] = VP[i] / P;

	END FOR;

   (* Rachford-Rice *)

	SUM[ ( z[i] * ( K[i] - 1 ) ) / ( ((K[i]-1)* V_F) + 1 )
                                               | i IN components ] = G - V_F;

	FOR i IN components CREATE
   (* Liquid compositions *)
	  x[i] = z[i] / ( ((K[i]-1)* V_F) + 1 );

   (* Vapor compositions *)
	  y[i] = ( K[i] * z[i] ) / ( ((K[i]-1)* V_F) + 1 );
	END FOR;

   (* V/F  *)
	  V_F = V/F;


METHODS

    METHOD default_self;
    END default_self;

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

    METHOD values;

(* fixed values *)
     z[1] := 0.2;
     z[2] := 0.5;
     z[3] := 0.3;
     P := 10 {atm};
     T := 405 {K}; (* It obtains results in the complete range 150 - 830 *)
     F:= 200 {lb_mole/hour};
(* initial guesses *)
     K[1] := 2;
     K[2] := 1;
     K[3] := 0.5;
     V := 100 {lb_mole/hour};
     V_F:= 0.5;
     G := 0.5;

    END values;

END simple_flash;


(*
 *  rachford.a4c
 *  by Vicente Rico-Ramirez
 *  April 10, 1998
 *  Part of the ASCEND Library
 *  $Date: 1998/06/17 19:15:05 $
 *  $Revision: 1.3 $
 *  $Author: mthomas $
 *  $Source: /afs/cs.cmu.edu/project/ascend/Repository/models/rachford.a4c,v $
 *
 *  This file is part of the ASCEND Modeling Library.
 *
 *  Copyright (C) 1998 Carnegie Mellon Univesity
 *
 *  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 "rachford.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	* rachford.a4s.
10	*)
11
12	(*
13	Ascend model of the Rachford-Rice equation described by King.
14	-- Separation Process. Chemical Engineering series. 2nd. Edition, McGraw-
15	Hill, 77-79, 1980 --. The problem consists in a simple flash calculation
16	performed by solving the Rachford-Rice equation. There is a disjunctive
17	statement which extends the use of that equation for cases in which the
18	system has only one phase (liquid or vapor). That is, this model not only
19	copes with the liquid-vapor equilibrium case. The resulting system of
20	equations can be solved with the ascend conditional solver CMSlv.
21
22	This model requires:
23	"system.a4l"
24	"atoms.a4l"
25	*)
26
27	(* ************************************************* *)
28
29	(* Components *)
30
31	MODEL component_constants;
32	Tc IS_A critical_temperature;
33	Pc IS_A critical_pressure;
34	vpa, vpb, vpc, vpd IS_A vapor_pressure_constant;
35	END component_constants;
36
37	MODEL n_butane REFINES component_constants;
38	(Constants )
39	Tc :== 425.2 {K};
40	Pc :== 38.0 {bar};
41	vpa :== -6.88709;
42	vpb :== 1.15157;
43	vpc :== -1.99873;
44	vpd :== -3.13003;
45	END n_butane;
46
47	MODEL n_pentane REFINES component_constants;
48	(Constants )
49	Tc :== 469.7 {K};
50	Pc :== 33.7 {bar};
51	vpa :== -7.28936;
52	vpb :== 1.53679;
53	vpc :== -3.08367;
54	vpd :== -1.02456;
55	END n_pentane;
56
57	MODEL n_hexane REFINES component_constants;
58	(Constants )
59	Tc :== 507.5 {K};
60	Pc :== 30.1 {bar};
61	vpa :== -7.46765;
62	vpb :== 1.44211;
63	vpc :== -3.28222;
64	vpd :== -2.50941;
65	END n_hexane;
66
67	(* ************************************************* *)
68
69	(* Flash calculation *)
70	(* Rachford Rice calculation when P and T are specified *)
71
72	MODEL simple_flash;
73	components IS_A set OF integer_constant;
74	comp[components] IS_A component_constants;
75	VP[components] IS_A pressure;
76	K[components] IS_A factor;
77	z[components],
78	x[components],
79	y[components] IS_A fraction;
80	V,F IS_A molar_rate;
81	V_F IS_A factor;
82	T IS_A temperature;
83	P IS_A pressure;
84	G IS_A factor;
85	bol1,bol2 IS_A boolean_var;
86
87
88	(* Component Data *)
89
90	components :== [1..3];
91	comp[1] IS_REFINED_TO n_butane;
92	comp[2] IS_REFINED_TO n_pentane;
93	comp[3] IS_REFINED_TO n_hexane;
94
95
96	(* Boundaries *)
97	CONDITIONAL
98	cond1: G <= 0.0;
99	cond2: G <= 1.0;
100	END CONDITIONAL;
101
102	bol1 == SATISFIED(cond1,1e-08);
103	bol2 == SATISFIED(cond2,1e-08);
104
105	(* Variant Equations*)
106	eq1: V_F = 0.0;
107	eq2: V_F = G;
108	eq3: V_F = 1.0;
109
110	(* Disjunctive Statement*)
111	WHEN (bol1,bol2)
112	CASE TRUE,TRUE:
113	USE eq1;
114	CASE FALSE,TRUE:
115	USE eq2;
116	CASE FALSE,FALSE:
117	USE eq3;
118	OTHERWISE:
119	END WHEN;
120
121	(* Invariant Equations *)
122
123	FOR i IN components CREATE
124
125	(* Vapor pressure *)
126	ln(VP[i]/comp[i].Pc)T/comp[i].Tcabs(comp[i].Tc - T) =
127	(comp[i].vpa*abs(1.0 - T/comp[i].Tc) +
128	(comp[i].vpb*abs(1.0 - T/comp[i].Tc)^1.5) +
129	(comp[i].vpc*abs(1.0 - T/comp[i].Tc)^3.0) +
130	(comp[i].vpdabs(1.0 - T/comp[i].Tc)^6.0))(comp[i].Tc - T);
131
132	(* Equilibrium constant *)
133	K[i] = VP[i] / P;
134
135	END FOR;
136
137	(* Rachford-Rice *)
138
139	SUM[ ( z[i] * ( K[i] - 1 ) ) / ( ((K[i]-1)* V_F) + 1 )
140	\| i IN components ] = G - V_F;
141
142	FOR i IN components CREATE
143	(* Liquid compositions *)
144	x[i] = z[i] / ( ((K[i]-1)* V_F) + 1 );
145
146	(* Vapor compositions *)
147	y[i] = ( K[i] * z[i] ) / ( ((K[i]-1)* V_F) + 1 );
148	END FOR;
149
150	(* V/F *)
151	V_F = V/F;
152
153
154	METHODS
155
156	METHOD default_self;
157	END default_self;
158
159	METHOD specify;
160	FOR i IN components DO
161	z[i].fixed := TRUE;
162	END FOR;
163	F.fixed := TRUE;
164	P.fixed := TRUE;
165	T.fixed := TRUE;
166	END specify;
167
168	METHOD values;
169
170	(* fixed values *)
171	z[1] := 0.2;
172	z[2] := 0.5;
173	z[3] := 0.3;
174	P := 10 {atm};
175	T := 405 {K}; (* It obtains results in the complete range 150 - 830 *)
176	F:= 200 {lb_mole/hour};
177	(* initial guesses *)
178	K[1] := 2;
179	K[2] := 1;
180	K[3] := 0.5;
181	V := 100 {lb_mole/hour};
182	V_F:= 0.5;
183	G := 0.5;
184
185	END values;
186
187	END simple_flash;
188
189
190	(*
191	* rachford.a4c
192	* by Vicente Rico-Ramirez
193	* April 10, 1998
194	* Part of the ASCEND Library
195	* $Date: 1998/06/17 19:15:05 $
196	* $Revision: 1.3 $
197	* $Author: mthomas $
198	* $Source: /afs/cs.cmu.edu/project/ascend/Repository/models/rachford.a4c,v $
199	*
200	* This file is part of the ASCEND Modeling Library.
201	*
202	* Copyright (C) 1998 Carnegie Mellon Univesity
203	*
204	* The ASCEND Modeling Library is free software; you can redistribute
205	* it and/or modify it under the terms of the GNU General Public
206	* License as published by the Free Software Foundation; either
207	* version 2 of the License, or (at your option) any later version.
208	*
209	* The ASCEND Modeling Library is distributed in hope that it will be
210	* useful, but WITHOUT ANY WARRANTY; without even the implied
211	* warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
212	* See the GNU General Public License for more details.
213	*
214	* You should have received a copy of the GNU General Public License
215	* along with the program; if not, write to the Free Software
216	* Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139 USA. Check
217	* the file named COPYING.
218	*)