A heat exchanger network (HEN), using water as a circulating medium, can recover heat from hot process streams and transfer it to cold process streams. Design optimization of such an HEN for utilization of low-temperature process heat (LTHEN) is a complex task. In this paper, three mixed-integer nonlinear programming models, namely, synthesis, retrofit, and alternate retrofit models are formulated to minimize the total annual cost (TAC), for realistic LTHEN design by considering pressure drops and costs of piping, water tanks, pumps, and heat exchangers. The synthesis model provides the best LTHEN design for complete heat recovery from hot process streams and supplying it to cold process streams via the circulating water stream. The retrofit model considers heat recovery from hot process streams to cold process streams only if it is economical by considering trade-off between the capital cost of new heat exchangers and utility cost of existing heaters/coolers. Finally, the alternate retrofit model is similar to the retrofit model except that the former considers heat exchanger costs for heat exchange between hot/cold process streams and cold/hot utilities. One detailed case study from a petroleum refinery is presented to demonstrate the potential benefits of using the proposed models, which provide realistic and industrially acceptable LTHEN design. Use of multiple LTHEN circuits is considered, and the result is compared with the single circuit solution.