A simple 1-1 shell-and-tube heat-exchanger model without the logarithmic-mean temperature difference DeltaT(lm) is proposed for heat-exchanger network (HEN) optimizations. The model consists of two algebraic equations and allows to determine hot and cold outlet temperatures independent of each other. HEN optimization problems are classified as feasible- and infeasible-path formulations, and compared with regard to problems originating from the use of DeltaT(lm) in exhanger energy-balance equations. The DeltaT(lm)-free model eliminates numerical failures in computing the logarithmic terms with negative arguments due to possible inconsistent initialization/progress of exchanger interconnection temperatures dining HEN optimizations. The DeltaT(lm)-free model does not require inclusion of approach-temperature inequality constraints since positive approach temperatures are guaranteed. It also eliminates iterative solution of nonlinear energy-balance equations in feasible-path formulations and is represented as linear equality constraints in infeasible-path formulations for fixed areas, heat-capacity-flow rates, and bypass flows. As demonstrated with two representative HEN optimization problems, the DeltaT(lm)-free model significantly reduces numerical difficulties and decreases computation time in the optimization phase of synthesis/design, retrofit, and flexibility-analysis of HENs. Thus, it permits handling large HEN problems.