If the permeate side of the membrane is at vacuum, the equilibrium adsorbed concentration at the membrane interface should be zero. However, very thin membranes do not reach that condition, and the actual concentration of the adsorbed species at and near the interface with the sink control volume is not zero. The final steady state of the membrane in this case becomes dependent on the thickness of the membrane. Our study on lattice systems indicates that the membranes needs to be hundreds of fluid diameters thick to reach the size-independent regime. (See further discussion in the SI) In the full atomistic models this would translate into model membranes >100nm thick, one order of magnitude larger than the systems considered here. These systems are currently beyond realistic computational reach.