Metal–organic frameworks (MOFs) hold great potential as materials for the separation of gas mixtures. To effectively use MOFs as an adsorbent for the dynamic separation of gas and liquid mixtures, they must be formulated and shaped into a mechanically stable bead or pellet form. This study focuses on the synthesis of MIL-53(Al)-FA in the form of beads and pellets. The MOF beads are produced using alginic acid as a binder and calcium chloride as a gelling agent, and pellets are formed through mechanical pressing. Different physicochemical techniques, such as powder X-ray diffraction, Fourier-transform infrared spectroscopy (FTIR), thermal gravimetric analysis, and scanning electron microscopy were used for the characterization of the synthesized beads and pellets form. The adsorption uptake capacity of CH4 and N2 gases was measured from 1 to 10 bar pressure at 298 and 313 K, respectively. The adsorption isotherm data for both adsorbates were evaluated by using the dual site Langmuir isotherm equations. Additionally, the adsorption selectivity of CH4 over N2 in a binary feed mixture was predicted using the ideal adsorbed solution theory. Breakthrough experiments were performed with beads and pellets as adsorbents using CH4/N2 feed mixtures (30:70 and 50:50 v/v). These experiments were conducted under various flow rates, pressures, and temperatures. The MIL-53(Al)-FA beads exhibited a comparable CH4/N2 selectivity (5.34) and a higher dynamic CH4 adsorption capacity (1 mmol/g) compared to those of the pellets, which showed a selectivity of 5.74 and a dynamic CH4 capacity of 0.71 mmol/g under the same conditions. The higher CH4/N2 selectivity in the pellet form was mainly due to the higher ratio of coadsorption of CH4 and N2. The lower length of the unused bed in the case of beads (7.30 cm) leads to a higher CH4 dynamic capacity than that of the pellet form (13.30 cm).