The advent of graphene created a revolution in materials science. Because of this there is a renewed interest in other carbon-based structures. Graphene is the ultimate (just one atom thick) membrane. It has been proposed that graphene can work as impermeable membrane to standard gases, such argon and helium. Graphene-like porous membranes, but presenting larger porosity and potential selectivity would have many technological applications. Biphenylene carbon (BPC), sometimes called graphenylene, is one of these structures. BPC is a porous two-dimensional (planar) allotrope carbon, with its pores resembling typical sieve cavities and/or some kind of zeolites. In this work, we have investigated the hydrogenation dynamics of BPC membranes under different conditions (hydrogenation plasma density, temperature, etc.). We have carried out an extensive study through fully atomistic molecular dynamics (MD) simulations using the reactive force field ReaxFF, as implemented in the well-known Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) code. Our results show that the BPC hydrogenation processes exhibit very complex patterns and the formation of correlated domains (hydrogenated islands) observed in the case of graphene hydrogenation was also observed here. MD results also show that under hydrogenation BPC structure undergoes a change in its topology, the pores undergoing structural transformations and extensive hydrogenation can produce significant structural damages, with the formation of large defective areas and large structural holes, leading to structural collapse.