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REQUIRE "atoms.a4l"; |
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(* => atoms.a4l, measures.a4l, system.a4l, basemodel.a4l *) |
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PROVIDE "pipeline.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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* pipeline.a4s. |
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*) |
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|
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(* |
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Ascend model of the pipeline network example presented by Bullard |
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and Biegler -- Iterated Linear Programming Strategies for Nonsmooth |
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Simulation: Continuous and Mixed Integer Approaches. Comp. Chem. Eng. |
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Vol. 16, 949-961, 1992 --. The problem consists of a network of 38 pipes, |
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5 of them including a check valve (so that the flow in those pipes is |
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possible only in one direction). Each pipe is represented by a set of |
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algebraic disjunctive equations. It represent a problem |
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which we can represent as a conditional model and solve with the |
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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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(* Base model of a pipe *) |
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MODEL arc; |
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k IS_A k_constant; |
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Q IS_A volume_rate; |
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H IS_A distance; |
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METHODS |
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END arc; |
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|
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|
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(* ************************************************* *) |
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|
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(* Pipe without check valve *) |
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MODEL arc_w_no_valve REFINES arc; |
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|
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bol IS_A boolean_var; |
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|
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(* Boundary *) |
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|
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CONDITIONAL |
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cond: Q >= 0.0 {gpm}; |
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END CONDITIONAL; |
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|
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bol == SATISFIED(cond,1e-08 {gpm}); |
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|
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(* Variant Equations *) |
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|
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eq1: H = k * sqr(Q); |
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eq2: H = -k * sqr(Q); |
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|
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(* Disjunctive Statement *) |
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|
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WHEN (bol) |
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CASE TRUE: |
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USE eq1; |
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CASE FALSE: |
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USE eq2; |
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END WHEN; |
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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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k.fixed := TRUE; |
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END specify; |
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|
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METHOD bound_self; |
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Q.lower_bound := -1e50{gpm}; |
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H.lower_bound := -1e50{ft}; |
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END bound_self; |
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|
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METHOD values; |
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H := 0 {ft}; |
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bol := SATISFIED(cond,1e-08 {gpm}); |
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END values; |
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|
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END arc_w_no_valve; |
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|
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(* ************************************************* *) |
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|
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(* Pipe with check valve *) |
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MODEL arc_w_valve REFINES arc; |
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|
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bol IS_A boolean_var; |
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|
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(* Boundary *) |
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|
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CONDITIONAL |
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cond: H >= 0.0 {ft}; |
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END CONDITIONAL ; |
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|
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bol == SATISFIED(cond,1e-08{ft}); |
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|
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(* Variant Equations *) |
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|
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eq1: sqr(Q) = H/k; |
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eq2: Q = 0.0 {gpm}; |
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|
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(* Disjunctive Statement *) |
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|
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WHEN (bol) |
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CASE TRUE: |
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USE eq1; |
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CASE FALSE: |
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USE eq2; |
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END WHEN; |
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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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k.fixed := TRUE; |
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END specify; |
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|
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METHOD bound_self; |
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H.lower_bound := -1e50{ft}; |
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END bound_self; |
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|
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METHOD values; |
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H := 1.0 {ft}; |
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bol := SATISFIED(cond,1e-08{ft}); |
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END values; |
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END arc_w_valve; |
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|
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(* ************************************************* *) |
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|
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(* Pipeline Network *) |
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MODEL pipeline; |
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|
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nodes IS_A set OF integer_constant; |
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arcs IS_A set OF integer_constant; |
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Pipe[arcs] IS_A arc; |
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P[nodes] IS_A distance; |
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W[nodes] IS_A volume_rate; |
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Q[arcs] IS_A volume_rate; |
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H[arcs] IS_A distance; |
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k IS_A k_constant; |
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|
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(* Sets definition *) |
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|
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nodes :== [1..22]; |
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arcs :== [1..38]; |
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|
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(* Wire up network *) |
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|
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Pipe[15],Pipe[19],Pipe[23],Pipe[32], |
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Pipe[34] IS_REFINED_TO arc_w_valve; |
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|
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FOR i IN [1..14] CREATE |
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Pipe[i] IS_REFINED_TO arc_w_no_valve; |
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END FOR; |
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FOR i IN [16..18] CREATE |
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Pipe[i] IS_REFINED_TO arc_w_no_valve; |
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END FOR; |
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FOR i IN [20..22] CREATE |
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Pipe[i] IS_REFINED_TO arc_w_no_valve; |
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END FOR ; |
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FOR i IN [24..31] CREATE |
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Pipe[i] IS_REFINED_TO arc_w_no_valve; |
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END FOR; |
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Pipe[33] IS_REFINED_TO arc_w_no_valve; |
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FOR i IN [35..38] CREATE |
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Pipe[i] IS_REFINED_TO arc_w_no_valve; |
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END FOR; |
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|
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FOR i IN arcs CREATE |
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Q[i],Pipe[i].Q ARE_THE_SAME; |
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H[i],Pipe[i].H ARE_THE_SAME; |
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k,Pipe[i].k ARE_THE_SAME; |
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END FOR; |
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|
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(* Invariant Equations *) |
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|
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(* Pressure Drops at each arc *) |
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P[1] - P[6] = H[1]; |
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P[2] - P[1] = H[2]; |
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P[2] - P[3] = H[3]; |
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P[3] - P[11] = H[4]; |
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P[13] - P[11] = H[5]; |
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P[14] - P[12] = H[6]; |
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P[12] - P[16] = H[7]; |
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P[16] - P[17] = H[8]; |
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P[19] - P[20] = H[9]; |
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P[21] - P[19] = H[10]; |
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P[7] - P[6] = H[11]; |
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P[10] - P[9] = H[12]; |
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P[7] - P[9] = H[13]; |
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P[21] - P[18] = H[14]; |
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P[14] - P[10] = H[15]; |
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P[22] - P[10] = H[16]; |
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P[21] - P[22] = H[17]; |
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P[1] - P[5] = H[18]; |
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P[5] - P[4] = H[19]; |
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P[4] - P[2] = H[20]; |
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P[3] - P[4] = H[21]; |
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P[11] - P[4] = H[22]; |
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P[11] - P[12] = H[23]; |
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P[12] - P[13] = H[24]; |
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P[13] - P[14] = H[25]; |
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P[12] - P[15] = H[26]; |
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P[16] - P[15] = H[27]; |
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P[18] - P[15] = H[28]; |
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P[17] - P[18] = H[29]; |
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P[19] - P[15] = H[30]; |
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P[15] - P[20] = H[31]; |
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P[20] - P[21] = H[32]; |
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P[9] - P[22] = H[33]; |
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P[9] - P[8] = H[34]; |
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P[5] - P[8] = H[35]; |
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P[5] - P[10] = H[36]; |
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P[8] - P[7] = H[37]; |
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P[6] - P[5] = H[38]; |
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|
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(* Flow balance around each node *) |
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|
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W[1] = Q[2] - Q[1] - Q[18]; |
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W[2] = Q[20] - Q[2] - Q[3]; |
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W[3] = Q[3] - Q[4] - Q[21]; |
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W[4] = Q[19] + Q[21] + Q[22] - Q[20]; |
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W[5] = Q[18] + Q[38] - Q[19] - Q[35] - Q[36]; |
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W[6] = Q[1] + Q[11] - Q[38]; |
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W[7] = Q[37] - Q[11] - Q[13]; |
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W[8] = Q[34] + Q[35] - Q[37]; |
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W[9] = Q[12] + Q[13] - Q[33] - Q[34]; |
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W[10] = Q[15] + Q[16] + Q[36] - Q[12]; |
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W[11] = Q[4] + Q[5] - Q[22] - Q[23]; |
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W[12] = Q[6] + Q[23] - Q[7] - Q[24] - Q[26]; |
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W[13] = Q[24] - Q[5] - Q[25]; |
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W[14] = Q[25] - Q[6] - Q[15]; |
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W[15] = Q[26] + Q[27] + Q[28] + Q[30] - Q[31]; |
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W[16] = Q[7] - Q[8] - Q[27]; |
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W[17] = Q[8] - Q[29]; |
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W[18] = Q[14] + Q[29] - Q[28]; |
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W[19] = Q[10] - Q[9] - Q[30]; |
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W[20] = Q[9] + Q[31] - Q[32]; |
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W[21] = Q[32] - Q[10] - Q[14] - Q[17]; |
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W[22] = Q[17] + Q[33] - Q[16]; |
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|
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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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k.fixed := TRUE; |
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FOR i IN nodes DO |
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W[i].fixed := TRUE; |
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END FOR; |
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W[18].fixed := FALSE; |
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P[17].fixed := TRUE; |
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END specify; |
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|
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METHOD bound_self; |
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FOR i IN nodes DO |
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W[i].lower_bound := -1e50 {gpm}; |
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END FOR; |
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FOR i IN nodes DO |
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P[i].lower_bound := 0 {ft}; |
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END FOR ; |
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END bound_self; |
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|
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METHOD bound_all; |
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FOR i IN arcs DO |
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RUN Pipe[i].bound_self; |
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END FOR; |
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RUN bound_self; |
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END bound_all; |
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|
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METHOD values; |
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|
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RUN bound_all; |
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|
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FOR i IN arcs DO |
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RUN Pipe[i].values; |
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END FOR; |
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|
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(* fixed *) |
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k := 0.36412197 {s^2/ft^5}; |
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|
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FOR i IN nodes DO |
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W[i] := 0 {gpm}; |
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END FOR; |
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W[1] := -897.6 {gpm}; |
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W[7] := -1570.9 {gpm}; |
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W[11] := 897.6 {gpm}; |
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W[17] := 1795.3 {gpm}; |
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W[20] := 448.8 {gpm}; |
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W[22] := -673.2 {gpm}; |
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|
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(* Initial guess *) |
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|
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(* Pressure head *) |
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FOR i IN nodes DO |
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P[i] := 0 {ft}; |
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END FOR ; |
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P[17] := 0 {ft}; |
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|
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(* volume rates *) |
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Q[1] := -48.5 {gpm}; |
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Q[2] := -640.7 {gpm}; |
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Q[3] := 393.2 {gpm}; |
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Q[4] := 538.9 {gpm}; |
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Q[5] := -32.3 {gpm}; |
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Q[6] := 490.2 {gpm}; |
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Q[7] := 649.9 {gpm}; |
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Q[8] := 904.7 {gpm}; |
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Q[9] := 112.2 {gpm}; |
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Q[10] := 232.5 {gpm}; |
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Q[11] := 402.3 {gpm}; |
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Q[12] := -420.4 {gpm}; |
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Q[13] := 687.3 {gpm}; |
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Q[14] := 621.7 {gpm}; |
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Q[15] := -719.2 {gpm}; |
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Q[16] := 52.7 {gpm}; |
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Q[17] := 1199 {gpm}; |
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Q[18] := 305.4 {gpm}; |
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Q[19] := 582.8 {gpm}; |
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Q[20] := -247.5 {gpm}; |
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Q[21] := -145.7 {gpm}; |
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Q[22] := -684.6 {gpm}; |
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Q[23] := 293.6 {gpm}; |
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Q[24] := -261.3 {gpm}; |
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Q[25] := -229 {gpm}; |
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Q[26] := -395.1 {gpm}; |
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Q[27] := -254.8 {gpm}; |
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Q[28] := -268.9 {gpm}; |
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Q[29] := -890.6 {gpm}; |
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Q[30] := 120.3 {gpm}; |
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Q[31] := -8.1{gpm}; |
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Q[32] := -344.7 {gpm}; |
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Q[33] := 473.1 {gpm}; |
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Q[34] := -206.2 {gpm}; |
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Q[35] := -275 {gpm}; |
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Q[36] := 351.5 {gpm}; |
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Q[37] := -481.2 {gpm}; |
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Q[38] := 353.9 {gpm}; |
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END values; |
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|
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END pipeline; |
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|
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|
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(* |
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* pipeline.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 19:15:04 $ |
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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/pipeline.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 |
| 368 |
* |
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* The ASCEND Modeling Library is free software; you can redistribute |
| 370 |
* it and/or modify it under the terms of the GNU General Public |
| 371 |
* License as published by the Free Software Foundation; either |
| 372 |
* version 2 of the License, or (at your option) any later version. |
| 373 |
* |
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* The ASCEND Modeling Library is distributed in hope that it will be |
| 375 |
* useful, but WITHOUT ANY WARRANTY; without even the implied |
| 376 |
* warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. |
| 377 |
* 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 |
| 380 |
* along with the program; if not, write to the Free Software |
| 381 |
* Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139 USA. Check |
| 382 |
* the file named COPYING. |
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*) |
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