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REQUIRE "atoms.a4l"; |
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(* => atoms.a4l, measures.a4l, system.a4l, basemodel.a4l *) |
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PROVIDE "heatex.a4c"; |
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(* |
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* This file is part of the ASCEND Modeling Library and is released |
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* under the GNU Public License as described at the end of this file. |
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* |
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* Use of this module is demonstrated by the associated script file |
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* heatex.a4s. |
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*) |
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|
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|
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(* |
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Ascend model of the heat exchanger example presented by |
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Zaher -- Conditional Modeling. Ph.D. Thesis, Carnegie Mellon University, |
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Pittsburgh, PA, 15213. 1995 --. The problem represents the condensation |
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of vapor because the heat transfer between the vapor and cooling water in |
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a heat exchanger. There are two disjunctive statement which represent |
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the possible condensation of vapor in the different sections of the |
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heat exchanger. This example shows how we can represent a conditional model |
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containing differential equations. It represent a problem that we can |
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solve with the ascend conditional solver CMSlv. |
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|
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This model requires: |
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"system.a4l" |
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"atoms.a4l" |
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*) |
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|
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(* ************************************************* *) |
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|
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MODEL heatex; |
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|
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points IS_A set OF integer_constant; |
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components IS_A set OF symbol_constant; |
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k_terms IS_A set OF integer_constant; |
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z[components] IS_A fraction; |
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x[points][components] IS_A fraction; |
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y[points][components] IS_A fraction; |
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Tcr[components] IS_A critical_temperature; |
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Pcr[components] IS_A critical_pressure; |
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Hv[components] IS_A molar_energy_constant; |
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B[components][k_terms] IS_A factor_constant; |
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C[k_terms] IS_A factor_constant; |
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D[components][k_terms] IS_A molar_energy_constant; |
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E[k_terms] IS_A factor_constant; |
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phi[points] IS_A fraction; |
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eta[points] IS_A fraction; |
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A IS_A area; |
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Fc IS_A molar_rate; |
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Fh IS_A molar_rate; |
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P IS_A pressure; |
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Tc[points] IS_A temperature; |
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Th[points] IS_A temperature; |
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Hc[points] IS_A molar_energy; |
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Hh[points] IS_A molar_energy; |
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dQ[points] IS_A energy_rate; |
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erscale IS_A energy_rate; |
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entscale IS_A factor; |
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bolphaq[1..2] IS_A boolean_var; |
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|
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(* Boundaries *) |
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|
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CONDITIONAL |
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cond1: SUM[x[0][i] | i IN components] + phi[0] >= 1.0; |
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cond2: SUM[x[2][i] | i IN components] + phi[1] >= 1.0; |
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END CONDITIONAL; |
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|
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bolphaq[1] == SATISFIED(cond1,1e-08); |
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bolphaq[2] == SATISFIED(cond2,1e-08); |
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|
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(* Variant Equations *) |
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|
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sum0: SUM[x[0][i] | i IN components] = 1.0; |
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frac0: phi[0] = 0.0; |
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|
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sum2: SUM[x[2][i] | i IN components] = 1.0; |
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frac1: phi[1] = 0.0; |
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|
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p1: eta[1] = 0.5; |
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p2: eta[2] = 0.5; |
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|
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sum1: SUM[x[1][i] | i IN components] = 1.0; |
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p12: eta[1] = 0.0; |
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|
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(* Disjunctive Statements *) |
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|
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WHEN (bolphaq[1]) |
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CASE TRUE: |
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USE sum0; |
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USE sum1; |
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CASE FALSE: |
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USE frac0; |
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USE p12; |
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END WHEN; |
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|
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WHEN (bolphaq[2]) |
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CASE TRUE: |
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USE sum2; |
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USE p1; |
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CASE FALSE: |
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USE frac1; |
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USE p2; |
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END WHEN; |
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|
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(* Invariant Equations *) |
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|
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phi[2] = 0.0; |
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phi[3] = 0.0; |
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|
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FOR i IN points CREATE |
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FOR j IN components CREATE |
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phi[i]*x[i][j] + (1 - phi[i])*y[i][j] = z[j]; |
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END FOR; |
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END FOR; |
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|
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FOR i IN points CREATE |
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FOR j IN components CREATE |
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ln((y[i][j]*P)/(x[i][j]*Pcr[j])) = (Tcr[j]/Th[i])*( |
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SUM[B[j][k] *(1 - Th[i]/Tcr[j])^C[k] |
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| k IN k_terms] ); |
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END FOR; |
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END FOR; |
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|
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FOR i IN points CREATE |
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dQ[i]/erscale = 20{BTU/hour/ft^2/R}*(1 + 10*phi[i])* |
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A*(Th[i] - Tc[i])/erscale; |
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END FOR; |
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|
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FOR i IN [0..2] CREATE |
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Fh*(Hh[i+1] - Hh[i])/erscale = |
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Fc*(Hc[i+1] - Hc[i])/erscale; |
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|
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Fc*(Hc[i+1] - Hc[i])/erscale = 0.5*(dQ[i] + dQ[i+1])* |
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(eta[i+1] - eta[i])/erscale; |
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END FOR; |
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|
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FOR i IN points CREATE |
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Hc[i]/entscale = 9720{BTU/lb_mole}*(Tc[i]/540{R} - 1)/entscale; |
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END FOR; |
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|
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FOR j IN points CREATE |
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Hh[j]/entscale = (SUM[ z[i] *( |
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SUM[ D[i][k]*((Th[j]/540{R})^E[k] - 1)|k IN k_terms]) |
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- phi[j]*x[j][i]*Hv[i] | i IN components])/entscale; |
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END FOR; |
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|
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(* Definition of sets *) |
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|
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components :== ['B','P5','H']; |
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points :== [0..3]; |
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k_terms :== [1..4]; |
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|
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(* Constants *) |
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|
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Tcr['B'] :== 765.4 {R}; |
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Tcr['P5'] :== 845.3 {R}; |
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Tcr['H'] :== 913.3 {R}; |
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Pcr['B'] :== 37.5 {atm}; |
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Pcr['P5'] :== 33.3 {atm}; |
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Pcr['H'] :== 29.3 {atm}; |
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Hv['B'] :== 9634 {BTU/lb_mole}; |
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Hv['P5'] :== 11088{BTU/lb_mole}; |
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Hv['H'] :== 12413 {BTU/lb_mole}; |
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C[1] :== 1.0; |
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C[2] :== 1.5; |
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C[3] :== 3.0; |
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C[4] :== 6.0; |
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E[1] :== 1.0; |
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E[2] :== 2.0; |
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E[3] :== 3.0; |
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E[4] :== 4.0; |
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B['B'][1]:== -6.88709; |
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B['B'][2]:== 1.15157; |
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B['B'][3]:== -1.99873; |
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B['B'][4]:== -3.13003; |
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B['P5'][1]:== -7.28936; |
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B['P5'][2]:== 1.53679; |
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B['P5'][3]:== -3.08367; |
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B['P5'][4]:== -1.02456; |
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B['H'][1]:== -7.46765; |
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B['H'][2]:== 1.44211; |
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B['H'][3]:== -3.28222; |
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B['H'][4]:== -2.50941; |
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D['B'][1]:== 1224 {BTU/lb_mole}; |
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D['B'][2]:== 6410 {BTU/lb_mole}; |
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D['B'][3]:== -429 {BTU/lb_mole}; |
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D['B'][4]:== -2 {BTU/lb_mole}; |
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D['P5'][1]:== -468 {BTU/lb_mole}; |
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D['P5'][2]:== 9428 {BTU/lb_mole}; |
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D['P5'][3]:== -998 {BTU/lb_mole}; |
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D['P5'][4]:== 46 {BTU/lb_mole}; |
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D['H'][1]:== -569 {BTU/lb_mole}; |
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D['H'][2]:== 11260 {BTU/lb_mole}; |
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D['H'][3]:== -1207 {BTU/lb_mole}; |
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D['H'][4]:== 57 {BTU/lb_mole}; |
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|
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METHODS |
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|
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METHOD default_self; |
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END default_self; |
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|
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METHOD specify; |
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FOR j IN components DO |
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z[j].fixed := TRUE; |
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END FOR; |
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A.fixed := TRUE; |
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P.fixed := TRUE; |
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Fc.fixed := TRUE; |
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Fh.fixed := TRUE; |
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erscale.fixed := TRUE; |
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entscale.fixed := TRUE; |
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eta[0].fixed := TRUE; |
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eta[3].fixed := TRUE; |
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Tc[0].fixed := TRUE; |
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Th[3].fixed := TRUE; |
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END specify; |
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|
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METHOD values; |
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(* fixed *) |
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P := 1.0{atm}; |
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z['B'] := 0.2; |
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z['P5'] := 0.5; |
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z['H'] := 0.3; |
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Fh := 250.0{lb_mole/hour}; |
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Tc[0] := 540.0{R}; |
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Th[3] := 600.0{R}; |
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erscale := 1.0e6{BTU/hour}; |
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entscale := 1000.0 ; |
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|
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(* initial guess *) |
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A := 379.12{ft^2}; |
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Fc := 1104.13{lb_mole/hour}; |
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x[0]['B'] := 0.04183; |
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x[0]['P5'] := 0.32735; |
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x[0]['H'] := 0.58922; |
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x[1]['B'] := 0.04183; |
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x[1]['P5'] := 0.32735; |
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x[1]['H'] := 0.58922; |
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x[2]['B'] := 0.03558; |
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x[2]['P5'] := 0.27044; |
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x[2]['H'] := 0.47211; |
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x[3]['B'] := 0.03153; |
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x[3]['P5'] := 0.23457; |
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x[3]['H'] := 0.40038; |
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y[0]['B'] := 0.2; |
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y[0]['P5'] := 0.5; |
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y[0]['H'] := 0.3; |
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y[1]['B'] := 0.2; |
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y[1]['P5'] := 0.5; |
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y[1]['H'] := 0.3; |
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y[2]['B'] := 0.2; |
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y[2]['P5'] := 0.5; |
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y[2]['H'] := 0.3; |
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y[3]['B'] := 0.2; |
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y[3]['P5'] := 0.5; |
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y[3]['H'] := 0.3; |
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phi[0] := 0.0; |
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phi[1] := 0.0; |
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phi[2] := 0.0; |
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phi[3] := 0.0; |
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eta[0] := 0.0; |
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eta[1] := 0.0; |
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eta[2] := 0.5; |
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eta[3] := 1.0; |
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Tc[1] := 540.000{R}; |
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Tc[2] := 559.820{R}; |
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Tc[3] := 575.386{R}; |
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Th[0] := 579.932{R}; |
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Th[1] := 579.932{R}; |
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Th[2] := 591.242{R}; |
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Hc[0] := 0000.0{BTU/lb_mole}; |
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Hc[1] := 0000.0{BTU/lb_mole}; |
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Hc[2] := 356.768{BTU/lb_mole}; |
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Hc[3] := 636.948{BTU/lb_mole}; |
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Hh[0] := 1212.93{BTU/lb_mole}; |
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Hh[1] := 1212.93{BTU/lb_mole}; |
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Hh[2] := 1569.7{BTU/lb_mole}; |
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Hh[3] := 1849.88{BTU/lb_mole}; |
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dQ[0] := 199658{BTU/hour}; |
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dQ[1] := 199658{BTU/hour}; |
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dQ[2] := 157110{BTU/hour}; |
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dQ[3] := 123070{BTU/hour}; |
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eta[1].upper_bound := 0.5; |
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eta[2].lower_bound := 0.5; |
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eta[2].upper_bound := 1.0; |
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|
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(* Initial value for booleans *) |
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bolphaq[1] := SATISFIED(cond1,1e-08); |
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bolphaq[2] := SATISFIED(cond2,1e-08); |
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END values; |
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|
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END heatex; |
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|
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|
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(* |
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* heatex.a4c |
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* by Vicente Rico-Ramirez |
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* April 10, 1998 |
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* Part of the ASCEND Library |
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* $Date: 1998/06/17 19:08:03 $ |
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* $Revision: 1.3 $ |
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* $Author: mthomas $ |
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* $Source: /afs/cs.cmu.edu/project/ascend/Repository/models/heatex.a4c,v $ |
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* |
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* This file is part of the ASCEND Modeling Library. |
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* |
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* Copyright (C) 1998 Carnegie Mellon University |
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* |
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* The ASCEND Modeling Library is free software; you can redistribute |
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* it and/or modify it under the terms of the GNU General Public |
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* License as published by the Free Software Foundation; either |
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* version 2 of the License, or (at your option) any later version. |
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* |
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* The ASCEND Modeling Library is distributed in hope that it will be |
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* useful, but WITHOUT ANY WARRANTY; without even the implied |
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* warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. |
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* See the GNU General Public License for more details. |
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* |
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* You should have received a copy of the GNU General Public License |
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* along with the program; if not, write to the Free Software |
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* Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139 USA. Check |
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* the file named COPYING. |
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*) |
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