(237g) An MINLP Formulation for the Optimal Design of Distributed Effluent-Cooling Systems
Chemical, petrochemical, petroleum refining and other process industries not only require significant quantities of freshwater for stripping, liquid-liquid extraction, and different washing operations but also discharge much wastewater. Recently, the increasing scarcity of freshwater resources has motivated process industries to maximize water reuse in order to remain competitive and support the sustainability. Furthermore, because the stricter regulations for environment protection, the chemical and thermal pollution of wastewater must be reduced to an acceptable level before being discharged into different water disposal sites. The control of chemical pollution problems of wastewater is achieved through an arrangement of chemical, physical and biological treatment processes, which traditionally is added at the end of the production line. On the other hand, when the temperatures of the effluent streams are higher than the environmental discharge limit for the effluent temperature, an effective thermal treatment system is needed to reduce such temperatures before discharge of wastewater streams directly to the receiving water. In 2001, Kim et al. introduced and solved the problem of designing optimal distributed-cooling systems for effluent temperature reduction by combining heat recovery and effluent evaporative-cooling. Their approach is based on pinch technology and comprises two sequential stages. In the first stage, targets are set which minimize flowrate for cooling tower. Then, in the second stage, distributed cooling systems are designed to achieve the flowrate target while satisfying the environmental regulation for effluent temperature. In this work, the problem of temperature reduction of aqueous effluents before discharge is formulated and solved as a mixed integer nonlinear optimization problem based on a new superstructure. The basic components of the superstructure are stream mixers, stream splitters and a wet-cooling tower. As an example, the superstructure for the representation of a cooling system for three aqueous effluents that require temperature reduction is presented in Figure 1. Each aqueous effluent has a splitting point followed by two mixing points. Thus, as shown in Figure 1, each aqueous effluent can be split into two streams, one of which is directed to the mixer at the inlet of the cooling tower while the other stream is a by-pass that is directed to the mixer prior to the final effluent discharged from the plant. Note that the superstructure model provides the degrees of freedom available through the by-passing capabilities to reduce the cooling load of the cooling tower. In this way, the superstructure features three alternative structural options which are stream mixing, splitting and by-passing. This representation, therefore, contains all the potential distributed-cooling system configurations of interest. The superstructure described above is used simultaneously with a detailed design model for the cooling tower. The Merkel's method is used for sizing the cooling tower, together with empirical correlations for the air pressure drop and overall mass transfer coefficients in the packing region of the tower. Design guidelines and constraints are incorporated to obtain practical cooling towers. The objective function is to minimize the total annualized cost, which involves the capital cost for the cooling tower and the operating cost due to power consumption of the tower fan. Solution of this mathematical formulation provides simultaneously the optimal distributed-cooling system configuration, which satisfies the specified environmental discharge limit for effluent temperature, as well as the optimal operating conditions and design parameters required for the cooling tower. Three example problems are presented to show the application of the proposed MINLP model. The results show that the MINLP model gives better or equal designs than previous procedures that solve this problem. Literature cited Kim, J.K., Savulescu, L., Smith, R. Design of cooling systems for effluent temperature reduction. Chemical Engineering Science, 2001, Vol. 56, 1811-1830.
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