Simultaneous optimization and heat integration of chemical processes

A procedure is proposed for simultaneously handling the problem of optimal heat integration while performing the optimization of process flowsheets. The method is based on including a set of constraints into the nonlinear process optimization problem so as to ensure that the minimum utility target for heat recovery networks is featured. These heat integration constraints, which do not require temperature intervals for their definition, are based on a proposed representation for locating pinch points that can vary according to every set of process stream conditions (flowrates and temperatures) selected in the optimization path. The underlying mathematical formulations correspond to nondifferentiable optimization problems, and an efficient smooth approximation method is proposed for their solution. An example problem on a chemical process is presented to illustrate the economic savings that can be obtained with the proposed simultaneous approach. The proposed method reduces to very simple models for the case of fixed flowrates and temperatures. Scope The heat recovery network synthesis problem in process design has received considerable attent ion in the literature [see Nishida et a!., 1981 ] . The most recent approaches include the pinch design method of Linnhoff and Hindmarsh [ 1 9 8 3 ] , the transportation formulat ion of Cerda et al. [ 1 9 8 3 ] , and the transshipment model of Papoulias and Grossmann [ 1 9 8 3 a ] . These methods decompose this synthesis problem into t w o successive stages: a ) prediction of minimum uti l i ty cost, and, b ) derivation of a network structure that satisf ies the minimum uti l i ty cost and involves the fewest number of heat exchange units. Since this strategy is aimed at the reduction of both operating and investment costs of the network, these methods tend to produce very good solutions. However , the def ini t ion of the synthesis problem for which these methods apply relies on the assumption that f ixed values are given for the f lowrates and temperatures of the process streams that are to be integrated in the network. Consequently, these methods for heat integration are sequential in the sense that they can only be applied after the process condit ions have been determined. In the opt imizat ion, as we l l as in the synthesis of process f lowsheets , the f lowrates and temperatures of the process streams are in general unknown since they must be determined so as to def ine an opt imal processing scheme. Since f lowrates and temperatures have an important impact in the heat recovery network, the heat integration problem should be considered simultaneously wi th the opt imizat ion and synthesis problems. This would account explicit ly for the interactions between the chemical process and the heat recovery network. However, to make this simultaneous approach possible, the heat integration problem should be formulated so as to a l low for variable f lowrates and temperatures of the process streams. Papoulias and Grossmann [ 1 9 8 3 b ] have proposed to take into account the interactions between a chemical process and a heat recovery network by including the linear constraints of their transshipment model for heat integration within a UNIVERSITY LIBRARIES CARNEGIE-MELLON UNIVERSITY PITfSBiiRGH, PENNSYLVANIA 15213 mixed-integer linear formulation for the structural optimization of the chemical process. The actual network structure is derived in a second stage with information obtained from the solution of this optimization problem. An important limitation of this procedure is that while the flowrates of the streams can be treated as variables in the optimization, the temperatures can only assume discrete values in a prespecified set. This is due to the fact that the transshipment model requires fixed temperature intervals, and that the operating conditions that give rise to nonlinearities (e.g. pressures, temperatures) are discretized in order to obtain a mixed-integer linear model for the chemical process. The objective of this paper is to present a procedure for solving nonlinear optimization and synthesis problems of chemical processes simultaneously with the minimum utility target for heat recovery networks. As will be shown in this paper, a set of constraints that are based on a pinch point location method, can be formulated for embedding the minimum utility target within the process optimization. Since no temperature intervals are required in the proposed procedure, variable flowrates and temperatures of the process streams can be handled, and thus process nonlinearities can be treated explicitly. An example problem is presented to illustrate the large economic savings that can be obtained with this procedure for simultaneous optimization and heat integration. Conclusions and Significance This paper has presented a procedure for the simultaneous optimization and heat integration of process flowsheets. It was shown that this objective can be accomplished by introducing a special set of constraints into the optimization problem so as to ensure that the flowsheet will feature the minimum utility target for heat integration. The unique characteristic in this approach is that variable flowrates and temperatures of the streams can be handled within a nonlinear optimization framework. The procedure is applicable to the optimization of fixed flowsheet structures, as well as to the simultaneous structural and parameter optimization methods for process synthesis. Also, the proposed procedure renders very simple models for the standard heat integration case of fixed flowrates and temperatures. Constraints were developed for the case when only one heating and one cooling utility is available, as well as for the case of multiple utilities. As was shown, these constraints lead to structural nondifferentiabilities which can be handled efficiently with a proposed smooth approximation procedure. The results of the example problem showed that the proposed simultaneous approach can produce considerable economic savings, because of its capability of establishing proper tradeoffs between capital investment, raw material utilization and energy consumption in integrated chemical processes.