If you have a closed system and your extraction rate is higher than the feeding rate, you could get into compressibility effects as the air starts to get thin. If your computational domain has opening (similar to your domain) and you are treating the fluid as incompressible, this is a strong possibility that you will get inflow from other boundaries such that your inflow rate matches your outflow.
Again, this is just a speculation based on what I can gather about your problem from the write-ups you have provided. Please feel free to run and analyse your results and let us know if you find anything amiss.
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