Supermassive black holes ( SMBHs ) pair and form bound binaries after their host galaxies merge .
In a gas-rich merger , accretion discs are expected to form around the binary and its components .
These discs control the binary orbital evolution until the system is compact enough for gravitational waves to drive the SMBHs to coalescence .
In this work , we implemented a time-dependent 1D model to follow the long-term evolution of the coupled binary + discs system , from a separation of 10 ^ { 5 } down to 20 Schwarzschild radii .
We run different models changing the system parameters , including the binary mass ratio q \leq 0.3 and a factor \gamma that controls the inflow across the gap created by the secondary .
We find that our implementation yields higher residual masses and longer binary residence times than previous studies .
Our main conclusion is the non-steady-state nature of the evolution of the system : the properties the disc had when the binary was still at large separations influence its whole evolution .
To recover steady state , the binary residence time would have to be much longer than the inflow time-scale of the disc throughout their entire history , which in general is not satisfied .