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Highlights • Large-scale HEN synthesis is a first step towards Total Site synthesis. • Two-step MILP/MINLP approach was developed for larges-scale HEN synthesis. • Number of potential matches is significantly reduced, solutions are directed to global optima using MILP TransHEN model. • MINLP model HENSyn use reduced superstructure for HEN synthesis. • Problem with 173 process streams and multiple hot utilities solved. Abstract Although different methodologies for the synthesis of heat exchanger network (HEN) problems have been introduced in the last forty years, there are still significant challenges to be addressed, such as solving large-scale problems. This study focuses on synthesizing large-scale HENs using mathematical programming to achieve near globally optimal solutions based on a two-step MILP/MINLP approach. In the first step a mixed-integer linear programming (MILP) model, TransHEN, is used that obtains a globally optimal solution at selected Δ T min. By utilisation of this model, the most promising matches are selected based on feasibility and viability. The second step entails using the matches selected in the TransHEN of Step 1 in a mixed-integer nonlinear programming (MINLP) model, HENsyn, using a reduced superstructure, to generate a feasible HEN. This study presents also a simultaneous Total Site synthesis with direct heat transfer between processes, and is the first step in the wider project of synthesising an entire Total Site with direct and indirect heat transfer; and is the first step in the wider scope of synthesising an entire Total Site with direct and indirect heat transfer; however, in order to attain this goal, a tool capable of an appropriately handling large number of streams is required. The newly developed procedure has been tested on several case studies, two of which are presented in this paper. For Case study 1 the results obtained lie within the range of best solutions obtained by other authors. Case study 2, consisting of 173 process stream and involving multiple hot utilities, shows the applicability of the developed method to handle large-scale HEN problems. [ABSTRACT FROM AUTHOR]