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The upgrading of a model sub-quality natural gas mixture containing 40 mol% CH4 and 60 mol% N2 by dual reflux-pressure swing adsorption (DR PSA) was studied numerically. A separation target of >93 mol% CH4 in the heavy product and <1 mol% CH4 in the light product was adopted for the purpose of evaluating the viability of the upgrading process. Two different CH4-selective adsorbents were considered: (i) a commercial activated carbon (AC1) and (ii) a novel ionic liquidic zeolite (ILZ), which has twice the selectivity of activated carbon. Key process parameters such as the heavy product to feed ratio, the feed step time, and the light reflux ratio were varied iteratively to maximize the separation performance and minimize the energy consumption in each of the four DR PSA cycle configurations (PL-A, PH-A, PL-B and PH-B). The simulation results showed that the separation performance of A cycles was superior to that of B cycles for both of the adsorbents studied. The ILZ adsorbent was able to achieve the separation target and in general performed substantially better under the conditions investigated than AC1, which did not meet the product specifications for any of the cycles tested. The best-performing DR PSA cycle (PL-A) with ILZ achieved 94 mol% CH4 in the heavy product and 1 mol% CH4 in the light product with a compressor duty of 19.1 kJ mol−1. The corresponding cycle with AC1 as the adsorbent only delivered 87 mol% CH4 in the heavy product and 6.1 mol% CH4 in the light product. This result shows that a DR PSA process using ILZ can effectively upgrade sub-quality natural gas while keeping associated methane emissions low.