MNLP [i.e., MINLP] model for optimal synthesis and operation of utility plants

This paper presents a mixed-integer nonlinear programming (MINLP) model for performing structural and parameter optimization of utility plants that satisfy given electrical, mechanical and heating demands of industrial processes. In this model a nonlinear objective function that accounts for the cost of equipment and operation is minimized. The proposed approach allows for the simultaneous optimization of the configuration, and selection of flowrates, enthalpies and steam turbine efficiencies. All major conventional utility plant equipment are included in the superstructure for the MINLP model. The proposed approach is not only useful for synthesis, but also for analyzing different design alternatives. The model has been implemented in the computer package STEAM, and several applications are reported to illustrate the program capabilities, including a comparison with a simplified MILP model. Introduction Utility plants supply the required utility demands to industrial process plants, namely, electrical, mechanical and steam demands. Electrical demands come from external and internal electrical utility plant devices. Mechanical demands come from the power required to drive process units as compressors, pumps, blowers, etc. and from the power to drive utility pumps and air fans. Steam demands arise from the heat that is required from the heat exchange network and from the reaction system. The equipment that can be typically used in a utility plant include different types of boilers and steam turbines, electric motors, electric generators driven by gas turbines or steam turbines, headers at different pressures to collect and distribute steam and condensate, and other auxiliary units such as deaerators, condensers, and utility pumps. A number of feasible arrangements of these units can provide the specified utility demands. To address the problem of synthesis and design of utility plants several methods have been reported in the literature. These methods generally follow two basic approaches, those based on thermodynamic targets and heuristic rules, and those based on optimization techniques. Examples of the first group are the methods by Nishio et al. (1980), and Chou and Shih (1987). The main drawback of these methods is that even if the design with highest thermal efficiency is obtained, it may not be economically attractive because capital costs may be too high. The method by Nishio et al. (1980) relies on linear programming for the selection of drivers. The Chou and Shih (1987) design strategy allows for the inclusion of gas turbine cycles. This strategy gives preference to satisfying the heating over the power demands, and back-pressure turbines over condensing turbines. No rules are given to extend the method for the inclusion of electric motors. The first papers using mathematical optimization approaches were based on LP models such as the ones in Nishio and Johnson (1979), and Petroulas and Reklaitis (1984). Papoulias and Grossmann (1983) introduced the MILP approach. This approach consists in formulating an MDLP model to select among all the alternative units included in a proposed utility plant superstructure by minimizing linear capital costs with fixed charges and operating costs. The MILP formulation is derived from the original MINLP formulation by fixing operating conditions such as pressures and temperatures. The MILP approach has been recently used for the multiperiod optimization of utility plants (Hui and Natori (1996), Iyer and Grossmann (1996)), and for multiobjective approaches for waste minimization in utility plants, Chang and Hwang (1996). Colmenares and Seider (1989) presented a method for the design of a utility plant integrated with a chemical process using an NLP model to solve a superstructure of combined Rankine cycles. Due to the nature of the NLP model there is no option for chosing from among different steam turbine configurations, or for selecting electric motors for mechanical power demands. Existing methods based on MINLP models (Kalitventzeff (1991), Diaz and Bandoni (1996)) address the problem of optimal operation, and are not applicable to the synthesis of new utility plants. In this paper a comprehensive MINLP model for utility plants is presented. This model allows for the synthesis and design of new utility plants, and also for analyzing different design alternatives, for given electrical, mechanical and heating demands. The optimal solution is selected from a superstructure containing conventional utility plant equipment that are specified by the designer for each demand. The electrical demands can be satisfied by an electric generator driven by a gas turbine or a steam turbine. Steam can be generated in different types of boilers included in the superstructure. The mechanical power demands can be satisfied by different types of steam turbines working with inlet and outlets at different steam pressures, and at a variable efficiency depending on the working conditions and the mechanical power generated. Also the option of using an electric motor for each power demand can be considered. The design analysis of specific alternatives in utility plants is addressed by fixing some of the options available in the model to match the equipment options considered. The final solution includes the flowrates and enthalpies for steam, water and gas, and also the steam turbine efficiencies for the optimal configuration using the selected operational parameters. In the next section, the problem for the synthesis, design and optimization of utility plants is stated. It is followed by a description of the proposed MINLP model, including a presentation of the method employed to obtain the enthalpy, entropy, steam turbine efficiencies and cost functions. Next, STEAM, a user-friendly computer program implementing the proposed model is introduced. Finally, examples on synthesis, design and operation of utility plants are presented. Additional information on the data used in this study is included in an Appendix.