Hello all,
I'm looking for an answer to a problem that, I think, should have been solved countless times, but so far I found nothing relevant on the internet. Only the classical case of SVR (all same size, no recirculation).
Consider 2 or 3 stirred vessel reactors as a cascade. The sizes are different. A part of the throuhput is recirculated from the last to the first. The mean hydraulic retention of course is straightforward to calculate. But what is the residence time distribution?
What is the effect of recirculation on the HRT distribution? Intuition says the distribution will be broader, but how to quantify?
Is there a significant effect on the HRT distribution of a SVR cascade when the tanks have different sizes?
To give you some background: I'm in the green energy field and design biogas plants. The situation described is a very typical situation, since often substrate is pumped back into the start of the process to keep content of the first tank liquid (As the biomass is gasified, the slurry lose solid content and become more liquid and pumpable), some feeding systems mix dry substrate with slurry from the process and convey the mixture with a monopump.
As statred above, I'm sure this is a solved problem - I just haven't been able to find the solutions. Since I'm not that fluent with differential equations, I want to avoid doing the math myself. Pointers to releveant literature would be greatly appreciated.
I'm looking for an answer to a problem that, I think, should have been solved countless times, but so far I found nothing relevant on the internet. Only the classical case of SVR (all same size, no recirculation).
Consider 2 or 3 stirred vessel reactors as a cascade. The sizes are different. A part of the throuhput is recirculated from the last to the first. The mean hydraulic retention of course is straightforward to calculate. But what is the residence time distribution?
What is the effect of recirculation on the HRT distribution? Intuition says the distribution will be broader, but how to quantify?
Is there a significant effect on the HRT distribution of a SVR cascade when the tanks have different sizes?
To give you some background: I'm in the green energy field and design biogas plants. The situation described is a very typical situation, since often substrate is pumped back into the start of the process to keep content of the first tank liquid (As the biomass is gasified, the slurry lose solid content and become more liquid and pumpable), some feeding systems mix dry substrate with slurry from the process and convey the mixture with a monopump.
As statred above, I'm sure this is a solved problem - I just haven't been able to find the solutions. Since I'm not that fluent with differential equations, I want to avoid doing the math myself. Pointers to releveant literature would be greatly appreciated.
