This work introduces new heat exchanger network (HEN) model for networks containing single phase and two phase exchangers. Rigorous simulation of HEN performance requires sequential solutions of two sets of linear equations: mass balances and energy balances which are linear in temperatures. This enables data reconciliation via QR factorization as sequential solution of linear mass and energy balances. Hence, reconciliation of energy balances can be added as a follow-on step to material balance reconciliation, thereby greatly simplifying data reconciliation in process plants. If simultaneous reconciliation of flows, temperatures and heat transfer coefficients is required, the convergence is attained in a handful of successive substitution iteration via QR factorization. Similarly, optimization of the HENs based on the proposed model converges in two three to five successive linear programming iterations. Excellent convergence of the proposed HEN model makes it suitable for use in large scale site-wide energy models.