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A multistage metal hydride hydrogen compression (MHHC) system uses a combination of hydride materials in order to increase the total compression ratio, whilst maximizing the hydrogenation rate from the supply pressure at each stage. By solving the coupled heat, mass and momentum conservation equations simultaneously the performance of a MHHC system can be predicted. In the current work a numerical model is proposed to describe the operation of a complete compression cycle. Four different MHHC systems are examined in terms of maximum compression ratio, cycle time and energy consumption and it was found that the maximum compression ratio achieved was 22:1 when operating LaNi 5 (AB 5 -type) and a Zr-V-Mn-Nb (AB 2 -type intermetallic) as the first and second stage alloys respectively in the temperature range of 20 °C (hydrogenation) to 130 °C (dehydrogenation).