NOVELTY - Gas processing system (100) comprises: housing arrangement (110) having multiple manifolds; heat/mass transfer element (130) containing adsorbent positioned within the housing arrangement and rotatable relative to the housing arrangement about the rotation axis; and seal arrangement (150) positioned between the heat/mass transfer element and housing arrangement to expose the radial flow paths but not the axial flow paths to the entry and exit ports of one of the manifolds, and expose the axial flow paths but not the radial flow paths to the entry and exit ports of another of the manifolds.    USE - The systems are useful for processing and purifying gas such as methane gas (claimed).    ADVANTAGE - The gas processing and purification systems: can be operated at single uniform internal pressure despite large thermal transitions, thus enhancing the overall efficiency and reducing or eliminating the structural stresses on the system components, hence it is economical; utilize the heat/mass transfer element that can continuously operate to thermally regenerate the adsorbent processing medium and require less time to undergo the purge operation; and provide methane in an economical manner. The majority of the hot and cold thermal energy required for regeneration of the adsorbent is recycled through the system to significantly improve the overall thermal efficiency of the temperature swing adsorption purifier system.    DETAILED DESCRIPTION - Gas processing system (100) comprises: a housing arrangement (110) having multiple manifolds, where each manifold has an entry port and an exit port, and different circumferential locations relative to a rotation axis; a heat/mass transfer element (130) containing an adsorbent, positioned within the housing arrangement and rotatable relative to the housing arrangement above the rotation axis; and a seal arrangement (150) positioned between the heat/mass transfer element and the housing arrangement to expose the radial flow paths but not the axial flow paths to the entry and exit ports of one of the manifolds, and expose the axial flow paths but not the radial flow paths to the entry and exit ports of another of the manifolds. The heat/mass transfer element includes: multiple radial flow paths oriented transverse to the rotation axis; and multiple axial flow paths oriented transverse to the radial flow paths, where the axial flow paths are in thermal communication with the radial flow paths, and isolated from fluid communication with the radial flow paths at the heat/mass transfer element. INDEPENDENT CLAIMS are also included for:    (1) a gas purification system comprising a toroidal housing having the first manifold, the second manifold opposite the first manifold, the third manifold between the first and second manifolds, and a fourth manifold opposite the third manifold, a toroidal heat/mass transfer ring positioned within the housing and rotatable relative to the housing about a rotation axis, where the heat/mass transfer ring includes multiple radial flow paths oriented along radii extending outwardly from the rotation axis, multiple axial flow paths oriented parallel to the rotation axis, and an adsorbent material positioned within or along the radial flow paths, the seal arrangement positioned between the heat/mass transfer ring and the housing, a driver (190) operatively coupled to the heat/mass transfer ring to rotate the heat/mass transfer ring relative to the housing about the rotation axis, a process gas supply coupled to the entry port of the first manifold to direct process gas through the adsorbent, a purge gas supply coupled to the entry port of the second manifold to direct purge gas through the adsorbent, and a heat transfer loop coupled between the third and fourth manifolds to heat the adsorbent at the third manifold as the adsorbent rotates from the first manifold to the second manifold, and cool the adsorbent at the fourth manifold as the adsorbent rotates from the second manifold to the first manifold;    (2) a heat and mass transfer system, comprising the rotatable heat/mass transfer element that is symmetric about a rotation axis;    (3) a method (M1) for processing a gas, comprising directing a process gas at a first region through an adsorbent processing medium along one of a radial axis and an axial axis, rotating the adsorbent processing medium about a rotation axis from the first region to a third region and directing a heat transfer fluid along the other of the radial axis and the axial axis to be in thermal contact with the adsorbent processing medium at the third region, rotating the adsorbent processing medium about the rotation axis from the third region to a second region and directing a purge fluid through the adsorbent processing medium along the one of the radial axis and the axial axis at the second region, rotating the adsorbent processing medium about the rotation axis from the second region to a fourth region and directing the heat transfer fluid along the other of the radial axis and the axial axis to be in thermal contact with the adsorbent processing medium at the fourth region, and rotating the adsorbent processing medium about the rotation axis from the fourth region to the first;    (4) a method (M2) for processing a gas, comprising rotating an adsorbent-containing heat/mass transfer element about a rotation axis to sequentially expose a portion of the heat/mass transfer element to multiple processing regions, directing at one of the processing regions a first fluid through the portion of the heat/mass transfer element in one of an axial direction and a radial direction while preventing the first fluid from passing through the portion of heat/mass transfer element in the other of the axial direction and the radial direction at the one processing region, and directing at another of the processing regions a second fluid through the portion of heat/mass transfer element in the other of the axial direction and the radial direction while preventing the second fluid from passing through the portion of the heat/mass transfer element in the one of the axial direction and the radial direction at the other processing region; and    (5) a method (M3) for forming a heat and mass transfer apparatus, comprising connecting four elbow-shaped channels end-to-end to form a toroidal housing, positioning an adsorbent-containing heat/mass transfer element within the housing, and connecting the heat/mass transfer element to a driver to rotate the heat/mass transfer element about the rotation axis.    DESCRIPTION OF DRAWING(S) - The figure shows a partially schematic plan view of the gas processing system.    Gas processing system (100)    Housing arrangement (110)    Heat/mass transfer element (130)    Seal arrangement (150)    Driver (190)