**Mathematical model for heat integrated water network systems**

Anoop Jagannath, Ali Almansoori*

Department of Chemical Engineering, The Petroleum Institute, Abu Dhabi, P.O. Box 2533, United Arab Emirates

Process industries such as chemical, petroleum, petrochemical, bio-fuel, food, paper and pulp etc. consume a lot of water. Some of the primary functions of water in these industries include washing (water used as a cleansing medium to clean equipments, rinse and wash raw materials, products etc.), separation (water used as a mass separating agent in absorption, scrubbing and liquid-liquid extraction processes), product manufacture (water used as a prominent ingredient in the manufacture of chemicals, polymers etc.) and energy generation (water used in boilers to produce steam and power, water used for cooling purposes). The water used for the above purposes tends to get contaminated and this wastewater has to be treated before it is discharged into the environment. Over the recent years, due to scarcity of freshwater sources, increasing cost of freshwater, rising demand for energy and stringent environmental regulations on the quality of wastewater discharged into the environment; process industries are forced to explore and adopt strategies that ensure adept usage of water and energy within their processes. One of the significant directions in this regard is to design a Heat Integrated Water Network (HIWN) system. The aim of such a system is to study the interactions between the Water Network (WN) design and Heat Exchanger Network (HEN) design to find economically viable and environmentally sustainable solutions. This has been one of the active areas of research in the process systems engineering domain where the focus is to develop efficient mathematical models and solution strategies for minimizing freshwater usage, wastewater generation and energy consumption.

During the last 15 years, considerable research has been carried out in the area of synthesis of HIWN systems. Although the mathematical model for the HIWN system relies primarily on the combination of WN and HEN models, the solution strategies or approaches to achieve good quality solutions within tractable computational times has remained a challenge. In the synthesis of HIWN system, two solution approaches are adopted namely sequential and simultaneous. In the simultaneous approach [1-3], the overall mathematical model consisting of water network WN design and HEN design is optimized simultaneously to explore the trade-offs and interactions between WN and HEN. In sequential strategy [4-6], the generic trend is to study the WN and HEN separately. The solution obtained by the simultaneous approach is of good quality, but it causes the model to become too large and complex finally being practically impossible to solve HIWN problems within tractable computational times. In sequential approach, although solution times are relatively less, but the quality of the solution can be extremely poor due to the sequential nature of the solution strategy.

This work presents a new superstructure and mathematical model for the design of HIWN systems. In this superstructure, heat integration is considered among all the streams in the water network. The overall mathematical model is a Mixed Integer Nonlinear Program (MINLP). A two step solution strategy is also proposed to solve this HIWN mathematical model. The presented solution strategy represents a blend of sequential and simultaneous approaches. The proposed model and solution strategy is applied to certain problems in the literature. It is observed that, for these problems, good quality solutions are obtained within tractable computational times.

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* Corresponding author: aalmansoori@pi.ac.ae (Email), +971 2 607 5583 (V), +971 2 607 5200(F)

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