Sizing Biofilters - Updates to Part I.

By Sergio Chaim

1.2 - Maximum Fish Weight.

Sincerely I am not exactly glad with the mismatch between the guppy growth model I proposed in Part I and Itzkovich (2002) statement that guppies raised in Israel reach market size (3.5-4 cm total length) at 2.5-3 months age. That made me take a look  at my library and to review all the data on  fancy guppy growth I found out.  I concluded  that I underestimated guppy growth curve but to design  a most reliable growth curve will demand that I get much more data and that I study a bit more, later I'll comeback with  an article restricted to this subject. Like I'd assumed in Part I I'll keep designing a system to support 2g of fishes per liter that I'm sure it is an over-estimative.

Also I redrawn the equations for lenght-weigth relationships after the addition of new data covering juvenile guppies of both genders to the data set. Now these models cover females from 0.0062 to 1.107 g body weight and from 9.6 to 45 mm total length, and males from 0.0062 to 0.285 g body weight and from 9.6 to 36.2 mm total length. So I propose:

Female Length = 43.674*(Body Weight (g))^0.2948       r² = 0.9906

Female Weight= 0.000003*(Total Length (mm)^3.3596  r² = 0.9906.

Male Length = 49.396*(Body Weight (g))^0.3231           r² = 0.9766.

Male Weight = 0.000007*(Total Length (mm)^3.0222     r² = 0.9766.

 

2 - Estimative of Waste Production. 

I found some different views of the ammonia oxidation stoichiometry than Ebeling (no date) balance I'd present in Part I.

"The stoichiometric (chemical balance) requirements of ammonia oxidation were described by Gujer and Boller (1986) as:

NH4 + 1.90 O2 + 2 HCO3  → NO3 + 1.9 CO2 + 2.9 H20 + 0.1 CH2O                  Eq.(3)

 where CH2O represents cell biomass. Equation 3 can be used to predict three stoichiometric requirements of nitrification: oxygen requirements, alkalinity consumption and biomass production. The oxidation of 1g of ammonia requires 4.34g oxygen and 7.14g alkalinity and produces 0.21g of bacterial cells, 1.98g acid and 4.43g nitrate." Hochheimer and Wheaton (no date). Just take care to understand "1g of ammonia-nitrogen" where the authors wrote "1g of ammonia".  

"According to EPA (1975), taking nitrifier synthesis together with nitrification, the overall stoichiometric relationship between the ammonium, HCO3-, and O2 consumed and the cell mass, nitrate, water, and carbonic acid (H2CO3) produced can be written

NH4+ + 1.86 O2 + 1.98 HCO3 → 0.0206 C5H7NO2 + 0.980 NO3- + 1.041 H2O + 1.88 H2CO3               (1)

The H2CO3 and CO2 are in a chemical equilibrium that strongly favors CO2, so there is approximately 600 times more dissolved CO2 than H2CO3 in water.

CO2 + H2O ↔ H2CO3  K0 =[H2CO3]/[CO3] = 1.58 x10^-3                    (2)

where K0 is the acid–base equilibrium constant that relates molar concentrations of H2CO3 and CO2.

Therefore, according to the stoichiometry shown in Eqs. (1) and (2), nitrification and nitrifier synthesis actually consume 4.6 mg/L of O2 while producing approximately 5.9 mg/L of CO2 for every 1 mg/L of TAN consumed." Summerfelt and Sharrer (in press).

This finding made I add one more item in my estimative of waste production, I mean item "2.8 - Estimated Carbon Dioxide Production by Nitrification" which is calculated multiplying "Estimated TAN Production" by 5.9. 

I would like to advance that Summerfelt and Sharrer (in press) also estimated oxygen consumption and carbon dioxide production by others bacterias living in the filter that not those evolved in nitrification (heterotrophic bacterias) but since I'm not sure about the significance of such living beings in a trickling filter I wont cover this topic for a while.  

There is another point related to waste production that I would like to discuss.  Basically we use diets with 50% crude protein in dry basis. Like I said in Part I around 16% of protein is nitrogen, so for every kilo of diet thrown into the system we have a potential addition of 80g  nitrogen into the system (50% crude protein in diet X 16% nitrogen in crude protein). One kilo of guppies (wet weight) contain around 24g nitrogen (30% dry weight X 50% crude protein in dry weight X 16% nitrogen in protein). Well, all the protein that is not fixed in the form of fish tissue can became waste. So to keep the TAN production at 3.5% level of feed input (35g per kilo)   we should recover 45g of nitrogen fixed in/as fish tissues for every kilo of diet thrown into the system  (80 g nitrogen input - 35g nitrogen fixed/recovered). Then we should produce almost 2kg of guppies for every kilo of feed intake (45g of nitrogen to be fixed / 24g of nitrogen fixed in each kilo of guppies). The ratio between feed consumption and weight gain  is called Feed Conversion Rate (FCR). In this case our goal would be a FCR = 0.5 (1kg of feed / 2kg of guppies).  I know that there are many more elements on this equation than I'd presented but the best feed conversion rates I ever saw for guppies are around  0.6-0.7 (Tamaru et al., 1998). Sometimes it can reach much higher FCR's like  3 or 4 as observed by Shim and Bajrai (1982) for some treatments during some periods in their study on the effects of  natural and artificial foods on the growth of guppies, or FCR's above 4 like observed by Fah and Leng (1986) for all treatments as means of two-week periods during their study on protein requirements of female guppies. All said I also would like use this freak out to justify my option for an over-estimation of  filtration requirements.  

3.1 - Oxygen Demanded by Guppies for Respiration.

Thurston and Gehrke (1990) created models to estimate oxygen consumption by fishes at different activity levels through the compilation of data from published literature on respiratory oxygen requirements of several fishes species. 

Figure 1 - Comparison of oxygen consumption estimative for  guppies based on different data sources. 

 

For a while I propose to use Thurston and Gehrke (1990) model for “active” activity level, because like we’ll see later  fishes in recycle systems are somewhat raised in a forced swimming environment, plus a 50% safety/correction factor to make this estimative closer to Teo and Chen (1993) observations that is the only study I saw until now that was performed using fancy guppies as test animals. 

Oxygen Consumption (mg O2/fish/h) = (0.4677*(Body Weight (g))^0.877)*1.5. 

I yet kept the “for a while” because  there is a study from India, Narayanan and Ramachandran (2001), that sounds to be the best reference on the respiratory metabolism of guppies but I was not able to get its copy. Not yet...

Few hours before I finished this article a received a copy of Narayanan and Ramachandran (2001) from PRAISE. Like my life is nothing but flowers this article did not enlighten my mind. Anyway I got a piece from their article: "The rate of respiration decreased with increasing biomass of Poecilia reticulata. For instance, the rate of O2 consumption decreased from 1.886 to 0.201mg O2/g/hr as the size of fish was increased from 7±0.85 mg to 1069±30.28 mg respectively (Fig 1 a)."

Figure 2 - Effect of biomass on respiratory metabolism (a) and rate of metabolism (b). >From Narayanan and Ramachandran (2001).

 

Although this article did not provided me straight useful data these three black points parked closest to Y-axis in b graph called to my mind a reference by Post and Lee, 1996. In short I mean that sound there is sudden change which happens in metabolism of guppies  when they are around a half month old and this switch is making difficult my analysis of their growth pattern and oxygen consumption, a few more time please...

Now, after changing my estimative for the amount of oxygen demanded by guppies for respiration, the total dissolved oxygen demand on feed basis was calculated as 44% that is the average between Losordo and Hobbs (2000) maximum estimative (50%) and Ebeling (no date) estimative (40%).

 

Further References.

Ebeling, J. M. No date. Biofiltration. AES Workshop: Intensive Fin-Fish Systems and Technologies. p 47-56.

EPA (US Environmental Protection Agency). 1975. Process design manual for nitrogen control. US Environmental Protection Agency, Office of Technology Transfer, Washington, DC.

Hochheimer, J. N. and F. W. Wheaton. No date. Biological filters: Trickling and RBC design. p 291-318.

Itzkovich, J. 2002. Guppy culture thrives in Israel. Infofish International 4/2002:45-47.

Narayanan, M. and Ramachandran, S. 2001. Respiratory metabolism as a function of oxygen tension in different life stages of Poecilia reticulata. Aquacult 2(2):147-152.  

Shim, K. F. and J. R. Bajrai. 1982. Growth rates and food conversion in young guppy (Poecilia reticulata Peters) fed on natural and artificial foods. Singapore Journal of  Primary  Industries 10(1):26-38.

Summerfelt, S. T. and M. J. Sharrer. 2004. Design implication of carbon dioxide production within biofilters contained in recirculating salmonid culture systems. Aquacultural Engineering (in press) .

Tamaru, C. S., H. Ako and H. Pagurigan. 1998. Growth of guppies, Poecilia reticulata,
using various commercial feeds. Makai May 1998. p 3.

Teo, L. H. and T. W. Chen. 1993. A study of metabolic rates of Poecilia reticulata Peters under different conditions. Aquaculture and Fisheries Management 24:109-117.