This article investigates a novel TSA-based gas separation cycle that uses a microchannel monolith with a hollow polymer-adsorbent matrix coated along the inner walls of each microchannel. CO2 is removed from CH4 by passing impure feed gas through the microchannels, followed by a sequential flow of desorbing hot liquid, cooling liquid, and purge gas through the same microchannels. This configuration is expected to augment the heat and mass transfer to the adsorbent due to direct contact between the transfer fluid and the adsorbent layer, and also reduce the overall system size due to flow of the working and coupling fluids through the same microchannels. In this Part I of a two-part study, computational models are developed to study the relevant fluid dynamics, heat transfer, and mass transfer in each process. Parametric studies are conducted to determine the optimum microchannel geometry and adsorbent and heat transfer fluid (HTF) materials. The process is expected to purify up to two orders of magnitude greater gas throughput compared to bed-based designs. In the accompanying paper, Part II, a comprehensive process performance map and optimization of energy requirements for the process are discussed.