How was the reactor length determined here?

[hpc2016]

I've recently been reading this paper (a free version is available here).

I've been trying to work out how they came to the 128m length, but I just can't. Feel like it's been just beyond my grasp for a long time and it's been driving me mad. Any help would be appreciated.

Thanks in advance.

 

[Chestermiller]

The system is designed so that all parcels of water passing through the reactor receive the same dose of uv radiation to kill bacteria. Since the solar radiation rate is highest at mid-day, and falls off toward early morning or late afternoon, the flow rate of water through the reactor is highest at mid-day, and is less earlier in the day and later in the day. The diameter and length of the pipe are chosen so that the total dosage at any time during the day is sufficient to kill the bacteria (down to a desired level). At night, the water flow rate is, of course, zero. There are surge tanks at the exit of the reactor to allow for the variable flow rate in conjunction with the variable demand times.

 

[hpc2016]

Thanks for your reply.

I think I should have been more precise in my original question. The system makes sense to me conceptually, what I don't understand is why the length is 128m and not, for example, 200m or 100m. The maths of it is the part I'm struggling with, I think.

 

[Chestermiller]

So, your question really is "how does one go about quantitatively designing a tubular continuous flow chemical reactor to achieve a desired product concentration in the exit stream, given the flow rate through the reactor?"

 

[hpc2016]

Yes, also given the inactivation constant, the pipe diameter and the initial water quality.

 

[Chestermiller]

Yes, also given the inactivation constant, the pipe diameter and the initial water quality.

OK. I can't give you every last detail because they don't provide all the details. But, it goes something like this. Each parcel of fluid passing through the reactor has to receive a certain minimum solar UV radiation dosage. To do this, they vary the water flow rate so that, as the solar flux decreases, the flow rate also decreases in proportion. There is going to be a certain minimum value of the total pipe volume and surface area necessary to achieve the desired cumulative radiation dosage over all radiation conditions and associated flow rates. This determines the design of the reactor.