[283] | 1 | #*--------------------------------------------------------------------- |
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| 2 | * EMSO Model Library (EML) Copyright (C) 2004 - 2007 ALSOC. |
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| 3 | * |
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| 4 | * This LIBRARY is free software; you can distribute it and/or modify |
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| 5 | * it under the therms of the ALSOC FREE LICENSE as available at |
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| 6 | * http://www.enq.ufrgs.br/alsoc. |
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| 7 | * |
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| 8 | * EMSO Copyright (C) 2004 - 2007 ALSOC, original code |
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| 9 | * from http://www.rps.eng.br Copyright (C) 2002-2004. |
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| 10 | * All rights reserved. |
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| 11 | * |
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| 12 | * EMSO is distributed under the therms of the ALSOC LICENSE as |
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| 13 | * available at http://www.enq.ufrgs.br/alsoc. |
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| 14 | * |
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| 15 | *---------------------------------------------------------------------- |
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| 16 | * 3. Vapor pressure data representation by polynomials and equations |
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| 17 | *---------------------------------------------------------------------- |
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| 18 | * |
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| 19 | * Description: |
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| 20 | * This problem is part of a collection of 10 representative |
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| 21 | * problems in Chemical Engineering for solution by numerical methods |
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| 22 | * developed for Cutlip (1998). |
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| 23 | * |
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| 24 | * Subject: |
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| 25 | * * Mathematical Methods |
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| 26 | * * Thermodynamics |
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| 27 | * |
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| 28 | * Concepts utilized: |
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| 29 | * Use of polynomials, a modified Clausis-Clapeyron, and the |
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| 30 | * Antoine equations to model vapor pressure versus temperature data. |
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| 31 | * |
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| 32 | * Numerical method: |
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| 33 | * * Nonlinear regression |
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| 34 | * |
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| 35 | * Reference: |
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| 36 | * * CUTLIP et al. A collection of 10 numerical problems in |
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| 37 | * chemical engineering solved by various mathematical software |
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| 38 | * packages. Comp. Appl. in Eng. Education. v. 6, 169-180, 1998. |
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| 39 | * * More informations and a detailed description of all problems |
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| 40 | * is available online in http://www.polymath-software.com/ASEE |
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| 41 | * |
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| 42 | *---------------------------------------------------------------------- |
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| 43 | * Author: Rodolfo Rodrigues |
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| 44 | * GIMSCOP/UFRGS - Group of Integration, Modeling, Simulation, |
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| 45 | * Control, and Optimization of Processes |
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| 46 | * $Id$ |
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| 47 | *--------------------------------------------------------------------*# |
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| 48 | using "types"; |
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| 49 | |
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| 50 | |
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| 51 | #*--------------------------------------------------------------------- |
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| 52 | * Simple polynomial equation |
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| 53 | *--------------------------------------------------------------------*# |
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| 54 | |
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| 55 | FlowSheet simple_polynomial |
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| 56 | PARAMETERS |
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| 57 | # N as Integer (Brief="Number of polynomial terms", Default=5); |
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| 58 | # a(N) as Real (Brief="Parameters (coefficients) to be determined", Default=1e-2); |
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| 59 | |
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| 60 | a1 as Real (Default=100); |
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| 61 | a2 as Real (Default=1); |
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| 62 | a3 as Real (Default=1e-2); |
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| 63 | a4 as Real (Default=1e-4); |
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| 64 | a5 as Real (Default=1e-6); |
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| 65 | |
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| 66 | VARIABLES |
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| 67 | P as pressure (Brief="Vapor pressure", DisplayUnit='mmHg', Upper=1e4); |
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| 68 | T as temperature (Brief="Temperature"); # T(K) |
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| 69 | |
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| 70 | EQUATIONS |
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| 71 | # "Polynomial expression" # P(mmHg) and T(K) |
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| 72 | # P/'mmHg' = sum(a*(T/'K' - 273.15)^[0:N-1]); |
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| 73 | |
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| 74 | "Polynomial expression" # P(mmHg) and T(K) |
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| 75 | # P/'mmHg' = a1 + (T/'K' - 273.15)*(a2 + (T/'K' - 273.15)*(a3 + |
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| 76 | # (T/'K' - 273.15)*(a4 + a5*(T/'K' - 273.15)))); |
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| 77 | P/'mmHg' = a1 + a2*(T/'K' - 273.15) + a3*(T/'K' - 273.15)^2 + |
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| 78 | a4*(T/'K' - 273.15)^3 + a5*(T/'K' - 273.15)^4; |
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| 79 | |
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| 80 | # SET |
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| 81 | # a = [100 1 1e-2 1e-4 1e-6]; |
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| 82 | |
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| 83 | SPECIFY |
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| 84 | T = 300*'K'; |
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| 85 | |
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| 86 | OPTIONS |
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| 87 | Dynamic = false; |
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| 88 | end |
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| 89 | |
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| 90 | |
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| 91 | #*--------------------------------------------------------------------- |
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| 92 | * Clausius-Clapeyron equation |
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| 93 | *--------------------------------------------------------------------*# |
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| 94 | |
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| 95 | FlowSheet clausius_clapeyron |
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| 96 | PARAMETERS |
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| 97 | A as Real (Brief="Parameters to be determined", Default=10); |
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| 98 | B as temperature (Brief="Parameters to be determined", Default=1e3); |
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| 99 | |
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| 100 | VARIABLES |
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| 101 | P as pressure (Brief="Vapor pressure", DisplayUnit='mmHg', Upper=1e4); |
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| 102 | T as temperature (Brief="Temperature"); # T(K) |
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| 103 | |
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| 104 | EQUATIONS |
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| 105 | "Clausis-Clapeyron equation" # P(mmHg) and T(°C) |
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| 106 | P/'mmHg' = exp(A - B/T); |
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| 107 | |
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| 108 | SPECIFY |
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| 109 | T = 300*'K'; |
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| 110 | |
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| 111 | OPTIONS |
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| 112 | Dynamic = false; |
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| 113 | end |
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| 114 | |
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| 115 | |
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| 116 | #*--------------------------------------------------------------------- |
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| 117 | * Antoine equation |
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| 118 | *--------------------------------------------------------------------*# |
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| 119 | |
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| 120 | FlowSheet antoine |
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| 121 | PARAMETERS |
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| 122 | A as Real (Brief="Parameters to be determined", Default=10); |
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| 123 | B as temperature (Brief="Parameters to be determined", Default=1e3); |
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| 124 | C as temperature (Brief="Parameters to be determined", Default=20); |
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| 125 | |
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| 126 | VARIABLES |
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| 127 | P as pressure (Brief="Vapor pressure", DisplayUnit='mmHg', Upper=1e4); |
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| 128 | T as temperature (Brief="Temperature"); # T(K) |
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| 129 | |
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| 130 | EQUATIONS |
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| 131 | "Antoine equation" # P(mmHg) and T(K) |
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| 132 | P/'mmHg' = exp(A - B/(T + C)); |
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| 133 | |
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| 134 | SPECIFY |
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| 135 | T = 300*'K'; |
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| 136 | |
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| 137 | OPTIONS |
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| 138 | Dynamic = false; |
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| 139 | end |
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| 140 | |
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| 141 | |
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| 142 | #*--------------------------------------------------------------------- |
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| 143 | * Parameter estimation to simple polynomial equation |
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| 144 | *--------------------------------------------------------------------*# |
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| 145 | |
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| 146 | Estimation est_pol as simple_polynomial |
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| 147 | ESTIMATE |
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| 148 | # PAR START LOWER UPPER UNIT |
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| 149 | #* a(1) 100 0 1e3; |
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| 150 | a(2) 1 0 10; |
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| 151 | a(3) 1e-2 0 10; |
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| 152 | a(4) 1e-4 0 10; |
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| 153 | a(5) 1e-6 0 10; |
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| 154 | *# |
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| 155 | a1 100 0 1e3; |
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| 156 | a2 1 0 10; |
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| 157 | a3 1e-2 0 10; |
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| 158 | a4 1e-4 0 10; |
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| 159 | a5 1e-6 0 10; |
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| 160 | |
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| 161 | EXPERIMENTS |
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| 162 | # FILE WEIGTH |
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| 163 | "prob03.dat" 1; |
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| 164 | # Data from Perry (1999), Table 2-8 |
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| 165 | |
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| 166 | # Solution: a=[24.75, 1.61, 3.56e-2, 4.13e-4, 4.23e-6] |
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| 167 | |
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| 168 | OPTIONS |
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| 169 | NLPSolver( |
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| 170 | # File = "ipopt_emso", |
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| 171 | File = "complex", |
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[530] | 172 | ObjTol = 1e-6); |
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[283] | 173 | Dynamic = false; |
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| 174 | end |
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| 175 | |
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| 176 | |
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| 177 | #*--------------------------------------------------------------------- |
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| 178 | * Parameter estimation to Clausius-Clapeyron equation |
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| 179 | *--------------------------------------------------------------------*# |
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| 180 | |
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| 181 | Estimation est_clau as clausius_clapeyron |
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| 182 | ESTIMATE |
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| 183 | # PAR START LOWER UPPER UNIT |
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| 184 | A 10 -3 100; |
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| 185 | B 1e3 200 5e3 'K'; |
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| 186 | |
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| 187 | EXPERIMENTS |
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| 188 | # FILE WEIGTH |
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| 189 | "prob03.dat" 1; |
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| 190 | # Data from Perry (1999), Table 2-8 |
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| 191 | |
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| 192 | # Solution: A=8.75, B=2035.33K |
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| 193 | |
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| 194 | OPTIONS |
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| 195 | NLPSolver( |
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| 196 | File = "ipopt_emso", |
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| 197 | # File = "complex", |
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[530] | 198 | ObjTol = 1e-6); |
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[283] | 199 | Dynamic = false; |
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| 200 | end |
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| 201 | |
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| 202 | |
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| 203 | #*--------------------------------------------------------------------- |
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| 204 | * Parameter estimation to Antoine equation |
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| 205 | *--------------------------------------------------------------------*# |
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| 206 | |
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| 207 | Estimation est_ant as antoine |
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| 208 | ESTIMATE |
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| 209 | # PAR START LOWER UPPER UNIT |
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| 210 | A 10 -3 100; |
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| 211 | B 1e3 200 5e3 'K'; |
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| 212 | C 20 -200 200 'K'; |
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| 213 | |
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| 214 | EXPERIMENTS |
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| 215 | # FILE WEIGTH |
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| 216 | "prob03.dat" 1; |
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| 217 | # Data from Perry (1999), Table 2-8 |
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| 218 | |
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| 219 | # Solution: A=5.73, B=665.42, C=152.47-273.15 |
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| 220 | |
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| 221 | OPTIONS |
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| 222 | NLPSolver( |
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| 223 | File = "ipopt_emso", |
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| 224 | # File = "complex", |
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[530] | 225 | ObjTol = 1e-6); |
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[283] | 226 | Dynamic = false; |
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| 227 | end |
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