Heat inleak through insulation in the storage tanks produces boil-off gas (BOG) in LNG-carrying ships. Reverse Brayton cycle (RBC) with nitrogen is often chosen as the refrigeration cycle to reliquefy BOG to prevent loss of valuable gas and environmental pollution. In this paper, parametric evaluations of a basic RBC-based reliquefaction system are done based on exergy analysis. The analyses revealed that formation of liquid at turbine exit and close minimum temperature approach/temperature pinch in the BOG condenser plateaus out the improvement of performance of the RBC based reliquefaction system. The specification of equipment and operating parameters are determined to derive the highest savings in terms of power consumption and recovery of BOG. If RBC is operated in the range of 10-50 bara, close to 93% of BOG is reliquefied. Total reliquefaction is possible only if the RBC is designed with compressor suction at 4 bara. However, it increases the sizes of pipelines, compressor and heat exchangers. All parameters are non-dimensionalized to facilitate application of the results to any capacity of LNG-carrying ship. Part 2 of this paper presents the analyses on thermodynamically improved configurations of reliquefaction systems. (C) 2019 Elsevier Ltd. All rights reserved.