Water integration techniques can be used to minimize the utility water consumption and effluent generation of process plants through the implementation of reuse or recycle networks. There are a number of graphical and mathematical programming techniques available for the synthesis of such water reuse networks. However, effective use of these methods requires the availability of reliable process data, which in reality might be difficult to acquire. This paper describes a procedure for the synthesis of robust water reuse networks from imprecise data using symmetric fuzzy linear programming (SFLP). Two model variants, one based on mass exchange units and the other on source/sink allocation, are presented. Each variant is illustrated with a numerical example.
Water is used heavily in the process industries for washing or rinsing of raw materials and process equipment. Environmental concerns pertaining to fresh water supply sustainability and effluent discharge impacts have resulted in the increased use of process integration to concurrently reduce both plant water requirements and wastewater volume. Early developments in water integration emerged from analogies with thermal pinch technology. A graphical method based on mass exchange units with water as solvent was developed by Wang and Smith (1994). This targeting method identifies the minimum water flow rate for a given set of processes. Mathematical programming techniques have also been used for water integration problems. For single-component systems the mathematical approach simultaneously yields the water target and the water reuse network configuration needed to achieve this target. Alva-Argaez, Vallianatos, and Kokossis (1999), Yang, Lou, and Huang (2000) and Bagajewicz and Savelski (2001) give examples of formulations based on the mass transfer model. A comprehensive review can be found in Bagajewicz (2000).
Subsequent work has shifted to the use of source/sink models. The graphical method developed by Dhole, Ramchandani, Tainsh, and Wasilewski (1996) is simple to use, but cannot be guaranteed to locate the global pinch point. Hallale’s water surplus diagram (2002) and Foo’s water cascade table (2003) overcome these difficulties. More recently, a simple but effective graphical technique was developed by El-Halwagi, Gabriel, and Harrel (2003) for solving source/sink problems. Formulation of the source/sink problem as a linear program is much simpler than for mass transfer-based systems (El-Halwagi et al., 2003) and results in a modified transportation problem. Compared to models based on mass exchange units, the source/sink formulation has the advantage of being able to account for non-mass transfer processes that may have water inputs with no output (e.g., boilers) or water outputs with no inputs (e.g., reactors where water is generated as a reaction byproduct).
Robustness of water reuse networks designed using imprecise data is a critical issue in the use of process integration techniques in real process plants. The principal weakness of current methods is that they assume that design data are well-defined. In practice, however, acquisition of the data needed for the use of these techniques is not a trivial task. The difficulty of obtaining process data has been cited as one of the major obstacles to the widespread use of process integration (Wenzel, Dunn, Gottrup, & Kringelum, 2002). Some process parameters such as flowrates and discharge stream concentrations can be derived from historical data or direct physical measurements, and can thus be estimated with some precision. Key sources of uncertainty differ for mass exchange unit and source/sink models:
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For mass exchange unit models, the principal source of uncertainty is the mass load, or the quantity of contaminant transferred from the product stream into the water or solvent. Typically the mass load is not directly measurable but has to be deduced from historical flowrate and concentration data (Bagajewicz, 2000).
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For source/sink problems, estimating the maximum inlet stream concentration that can be tolerated by a water-using sink without disrupting process or product quality is the main difficulty; some amount of educated guesswork is likely to be involved in arriving at a suitable value (Bagajewicz, 2000 and Wenzel et al., 2002).
Fuzzy mathematical programming offers a computationally efficient alternative to stochastic models for design problems in uncertain environments (Sahinidis, 2004 and Zimmermann, 1992).
Fuzzy linear programming models for the synthesis of robust water reuse networks for single-component retrofit problems have been developed. The formulations cover both mass exchange unit and source/sink problems. The models relax the water minimization objective to allow tolerance margins to be introduced in the mass loads of the processes or the concentration limits of the water sinks. The innovation is useful in realistic design situations wherein these design parameters are not well-defined due to absence of process data. An advantage of the fuzzy models compared to conventional robust approaches based on stochastic programming is their simplicity and computational efficiency.
Future work will focus on extending the models to hydrogen pinch and multicomponent water allocation problems. More sophisticated fuzzy models must also be developed for design problems where uncertainty is encountered in flowrates and water source concentrations.
