Dynamics of mixed phase CSTR

Once again I have to ask a question with incomplete information, sorry about that.
We have a continuous flow CSTR holding slurry, with a gas injected into the
base via nozzles, directly into the agitated charge. The vessel is pressure controlled via the gas flow, and the reaction consists of absorption of the gas into the slurried charge. The absorption rate is directly proportional to pressure.
There's also a relatively small scavenger flow at the top of the ractor to purge the usual noncondensibles.
My question is whether there is likely to be any significant dynamics between pressure and absorption rate. IOW, if there is a step upward in gas flow, is the pressure response likely to include an S/(1+sT) term? If so, might the value of T be estimable with typical industrial control OOM accuracy as (charge volume / gas flow rate)?
Any experience with a real scenario would be particularly useful. TIA
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