TRANSPORTATION MODELS FOR THE OPTIMAL SYNTHESIS OF HEAT EXCHANGER NETWORKS

Noting that the lowest cost heat exchanger network nearly always possesses the highest possible degree of energy recovery and comprises the least number of positive stream/stream matches, a mathematical formulation for the network design synthesis problem is proposed. The new formulation accounts for the problem thermodynamic constraints and its solution space only includes feasible networks with maximum energy recovery. Neither cyclic nor split networks have been excluded from its feasible region as long as they are thermodynamically feasible.; A much simpler mathematical relaxation of such a formulation is then solved to find a near-optimum solution which frequently already comprises a minimum number of positive matches. If not so, a modified version of the stepping stone algorithm used to solve linear transportation problems permits one to reduce it up to the minimum value. If the minimum match solution found requires a cyclic and/or split network realization, a method is proposed to draw an initial cyclic and/or split network from the information contained in the optimal solution tableau. If possible, the number of units in the initial network is then further reduced by a systematic merging of some of them.; To evaluate the amount of utilities demanded by a network with maximum energy recovery, even in the presence of restricted matches, another mathematical model is presented. It is a linear transportation problem whose optimal solution is obtained in a single iteration. Such a model with minor modifications also permits one to identify the cheapest subset of utilities available which meets the network demand as well as evaluate the least utility usage when indirect matches between process streams are allowed or the minimum approach temperature (DELTA)T(,m) is match dependent.; Another simple mathematical relaxation of the network synthesis problem formulation is defined to help search for all the other feasible networks comprising a minimum number of positive matches. Any minimum match solution which is either infeasible for that relaxation problem or demands an amount of utilities above the minimum is ignored. In this way, the number of alternatives which must be further studied to analytically verify whether they stand for feasible networks is sharply reduced.