No replies to this topic

[Marc Kuliszer]

Hello all,

 

I am tasked with determining a WWTP digester mixing efficiency.  I am to inject a Lithium Chloride tracer slug at the input during a digester feed event then take samples from a recirculation loop to a THP process and the digester discharge during feeding according to the following schedule.

1 sample of digester discharge every 5 minutes during each feeding operation (12 hour test)

1 sample of recirculation loop every 10 minutes for the first 4 hours (12 hour test)

1 sample of recirculation loop every 30 minutes for the following 4 hours (12 hour test)

1 sample of recirculation loop every 60 minutes for the following 4 hours (12 hour test)

 

1 sample of digester discharge every day for 28 days then (Washout test)

1 sample of digester discharge every second day for another 28 days Washout test)

 

I must also record the total digester feed volume every day in order to perform the following calculations.

 

It has been quite a while since I last performed chemical reaction kinetics equations for what would be a zero order reaction as it is a non-reactive tracer that is being sampled.  I am quite sure that that I can calculate the retention time from regression analysis of the washout curve by simply substituting my sample values for the lithium concentration © and dividing it by the theoretical equilibrium concentration of the tracer (Co).  Ln(C/Co) and plotting this over time.  Fitting a linear trend line to this data will give me a negative gradient (m) that I can then apply to the following calculation I think.  Mean Residence Time (MRT) = Va/q1 = -1/m  Hence if I returned a value for ‘m’ of -0.0261 this would return a mean residence time of -1/-0.0261 = 38.3 days????

Is this correct?

My biggest question is determining the percentage dead space and short circuit volume using the following equation from chapter 9 of Chemical Reaction Engineering - Octave Levenspiel – Wiley International Edition 2 1972…. Which I can’t find anywhere hence I don’t have an example.  The equation is as follows.

 

C/Co = V/Va * [(q₁/Q)^2] * e^(-t* q₁/Va)

 

Where

C = Lithium concentration at time t

Co = Theoretical equilibrium concentration of tracer (should be 3mg/l)

V = Total volume of vessel (Design size)

Va = Actively mixed volume

q₁ = Flow entering actively mixed zone

q₂ = Short circuit flow

t = Time

 

Noting that (Q = q₁ + q₂)

 

Basically I am unsure how to calculate the short circuit flow q₂ and the dead space of the reactor and would really appreciate some help.  Would I be correct in using the regression analysis to determine the dead space. Would I use information from my SCADA/HMI to find the flow entering the actively mixed zone every day and apply that?  I do not know how to calculate Va.  If I knew the % available volume used in the reactor then I would.  Do I apply the sample data to a graph and integrate each data point using the trapezoidal method to the apex of a global maxima or second local maxima after what would be the short circuit maxima then take this volume as the short circuit volume over the total volume? Any help would be appreciated or any links or points  in the right direction would also be very much appreciated. Thank you very much.