In this investigation, the conventional and advanced exergy analysis is used to obtain information about the conditions of the heat exchangers belonging to a crude oil distillation unit, previously to future studies to establish the most cost-efficient moments for the execution of maintenance activities in the exchangers. Conventional, unavoidable, avoidable, endogenous, and exogenous exergy destruction is calculated and the combinations between these last four terms. Mexogenous analysis is applied to individualize the relationships between the exchangers of the network. The results put the total exergy destruction at over 61.6 MW, being 63% avoidable. Five heat exchangers are considered critical because they concentrate the highest rates of exergy destruction, corresponding to 39% of the total exergy destruction in the network, this categorization allows focusing the improvement works on heat exchangers that will produce a substantial increase in the efficiency of the preheat train. Additionally, to evaluate the performance in a better way, the effect of unavoidable exergy destruction on performance measurement of exchangers through the exergy efficiency is studied, indicating that in some cases removing the unavoidable part can increase the second law efficiency by more than fifteen percentage points.