We modify our recently introduced bound contraction methodology for global optimization of bilinear MINLP models1 to solve the stage-wise superstructure model for heat exchanger networks.2 Because the problem has nonlinearities that are not bilinear or quadratic instead of converting the problem into a fully quadratic one, which would add much more variables and equations, we use a different relaxation approach that takes advantage of monotonicity. Aside from the original bound contraction method, we also use branch and bound combined with bound contraction at each node.