Graphene oxide (GO) is a monolayer of sp2-bonded graphene sheets decorated with abundant oxygenated functional groups, where membranes of this material formed from laminated GO sheets contain interconnected nanochannels to enable molecular or ionic solutions to pass through. Metal cations, including aluminum (Al3+), can crosslink with GO and create aluminum graphene oxide (AGO) and can alter the membrane’s properties. Current research on the behaviors and properties of these membranes help determine how to incorporate these membranes in applications regarding gas-fluid separation, purification, and fuel dehydration. The objective was to analyze the permeability and stability of GO and AGO membranes with inorganic and organic solvents in various temperature settings to determine the reliability, efficiency, sustainability, and longevity of these membranes. Results suggest that both membranes potentially possess selective permeability, which is dependent on the fluid. Both membranes displayed results of high permeability measurements with water and low permeability results were observed for organic solvents, such as ethanol, methanol, and propanol. The stability features of the GO and Al3+ modified GO membrane, which were tested with sonication, stirring, and submerging, demonstrated improvement through metal cation modification for all tested solvents, in which were elucidated through both membrane hydrophilicity change and dative bonding formation.