We propose a general superstructure and a model for the global optimization for integrated process water networks. The superstructure consists of multiple sources of water, water-using processes, wastewater treatment, and pre-treatment operations. Unique features are that all feasible interconnections are considered between them and multiple sources of water can be used. The proposed model is formulated as a nonlinear programing (NLP) and as a mixed integer nonlinear programing (MINLP) problem for the case when 0-1 variables are included for the cost of piping and to establish optimal trade-offs between cost and network complexity. To effectively solve the NLP and MINLP models to global optimality we propose tight bounds on the variables, which are expressed as general equations. We also incorporate the cut proposed by Karuppiah and Grossmann to significantly improve the strength of the lower bound for the global optimum. The proposed model is tested on several examples. (C) 2010 American Institute of Chemical Engineers AIChE J, 57: 434-457, 2011