By Sergio Chaim

Now we'll really and finally see how to size a trickling biofilter itself.  Initially I'll make a brief discussion of the factors affecting nitrifying bacteria growth and later a somewhat extend discussion of factors affecting biofilter performance and so used for biofilter sizing.  

Factors Affecting Nitrifying Bacteria Growth.

Although there are several nitrifying bacteria populations and species, each one having different environmental requirements, that makes possible set a biofilter for any water condition were fishes are kept, the nitrifiers growth and/or rate of nitrification are in large extent affected by ammonia level, pH, alkalinity, temperature, dissolved oxygen, suspended solids, light and salinity. 

Ammonia. 

Ammonia is the main bacterial growth limiting factor in aquaculture biofilters. Research has shown that ammonia removal rate raises as function of  increasing TAN concentrations up to around 2-2.5 mg TAN per liter, when ammonia removal rate reaches a plateau and further increases in effluent TAN do not cause any significant increase in TAN removal rate (Greiner and Timmons, 1998; Kamstra et al. 1998). On the other hand, Zhu and Chen (1999) estimated that for 27,2ºC the mean minimum TAN concentration needed to keep nitrification biofilm at health steady-state is 0.07mg TAN per liter.     

pH.

Ebeling (no date) cites that optimum pH range for nitrification is from 6 to 9.  Hochheimer and Wheaton (no date) mentioned "In general nitrification is most efficient at pH levels ranging from about 7.5 to 9. At higher pH ranges (8.5-9), nitrification rates are fastest given sufficient ammonia. However, at the low ammonia concentrations usually found in aquacultural systems, operating at a pH of about 7 can be efficient." Both sources agree that to maintain pH near the lower end will be helpful to avoid ammonia stress on cultivated fishes. 

Alkalinity. 

The buffering capacity of an aquatic system, also named alkalinity,  is taken into account because bicarbonate ions are consumed to neutralize acids generated by oxidation of ammonia and by cell production.  A role-of-thumb is to add 0.25 kg of baking soda per kilo of feed consumed. 

"Rapid changes in pH over a few minutes of more than 0.5 to 1 unit will stress the filter and require time for adaptation to the new environmental conditions."  Ebeling (no date).

Temperature.

Nitrification is slower at lower temperatures, just like happens in most chemical and biological kinetic reactions, but as water temperature is determined by the species being cultivated there is not too much we can do. Usually nitrifiers show best growth at 20-30°C range and lethal temperatures above 30°C. 

Dissolved Oxygen.

Dissolved oxygen lower than 1 mg per liter becomes limiting for nitrification so is recommended that water entering a biofilter has at least 2 mg of dissolved oxygen per liter (Hochheimer and Wheaton, no date) or that the dissolved oxygen level of the discharge from the biofilter should be at least 2 mg per liter (Ebeling, no date). 

Suspended Solids.  

Suspended solids can be used by heterotrophic bacteria as food and support the growth of these beings that will compete with nitrifiers and fishes by the oxygen in the system. Suspended solids can clog the filter and obstruct water/ammonia/oxygen flow to nitrifying bacterias. Also particles that reside in the filter for extended periods can be used by nitrifiers for attachment and these ones can perform a significant portion of nitrification at expenses of those growing in media surface. If the system  is flushed these bacterias are removed and filter efficiency will decrease for some time.

Light.   

Light is believed to oxidize cytochrome C in nitrifiers. Like Nitrosomonas (bacterias that convert ammonia to nitrite) has more cytochrome C than Nitrobacter (bacterias that convert nitrite to nitrate) the later ones are more sensitive to light effects.

Salinity.

Hochheimer and Wheaton (no date) cited that freshwater nitrifiers are inhibited by saline water but successful transitions can be achieved. Although maximum changes of 5 ppt should not adversely affect biofilter operation a gradual change in salinity over several weeks is preferable.    

5 - Biofilter Sizing.

5.1 – Water Turnover.

This is how many times whole aquarium water content will be exchanged per unit of time, it is expressed as exchanges per hour (exchanges/h).

I mean exchange rate in aquariums as linked to water flow rate in the filter. Some systems are designed with intermediary reservoirs between the rearing units, screening units and the biofilter and/or with different pumps between each component of the system. In my case due financial limitations I plan use only one pump that will drive all the system and only one small reservoir below the filter so both exchange rate in aquariums and the water flow rate in the filter will effect each other. If you'll configure your system in a way that there are independent pumps to drive water flow over aquariums and filter you would set water turnover as how many times the whole system water content will be passed by the filter per hour.

Every time that water pass through a trickling filter its  ammonia content is decreased and its oxygen content is increased, that's good, but all this circulation must to be kept in such level that do not decrease the growth of fishes due excessive expenditure of energy in swimming activity. 

Kaiser & Vine (no date) observed an "optimum" exchange rate of  3 exchanges/h for growing guppies.

Kaiser et al. (1998) studied the effect of stocking rate (2 or 20 guppies per liter) and water exchange rate (0.25, 2 or 6 exchanges/h) on diurnal water-quality fluctuations in a closed recirculating system. They found: (1) Survival rates were not effected by flow rate or stocking rate during this experiment which was carried out for 6 weeks; (2) fish kept at lower stocking rate had significantly higher average weight and length gains than fish kept at the high stocking rate; (3) at 6 turnovers per hour ammonia levels remained constant and stocking rate had no effect on average ammonia levels; (4) nitrite levels did not differ between either the time of the day or the stocking rate or water exchange rate; (5) oxygen increased significantly in the afternoon at lower exchange rates at both stocking rates, dissolved oxygen level was significantly effected by stocking rate at these lower exchange rates and there was an overall tendency for lower oxygen levels at lower exchange rates; (6) pH followed the tendencies described by oxygen levels; and (7) temperature increased at afternoon at all stocking rates and at all exchange rates.

When reading this article mentioned above I figured on my guppies like that mad laboratory mice running all the time inside wheels. Nicoletto (1996) carried out an experiment to determine if different water velocities during ontogeny affect male physical condition, male signal intensity and female mating preferences in the guppy. He raised wild-caught guppies in 20 gal aquariums containing a powerhead which pumped 1.5 or 4.5 liter per minute or like 1.19 or 3.57 exchanges/h, respectively, and always fed in excess. The observed results shown that high velocity males had longer mean displays, spent more total time displaying, had faster swimming speeds, had wider caudal peduncles and were more attractive to females than low velocity males, but there was no differences in display rates, body widths, standard lengths or copulation attempts. The author justified his findings as caused by the increased muscle development of males raised in high water velocities.   

In short, we should use exchange rates between 3 to 6 exchanges per hour. I'll set my water turnover at 3 exchanges per hour.  

5.2 - Media Specific Surface Area.

This is the amount of superficial area made available for nitrifiers to attach per unit of media volume, it is expressed as  m² of surface area per m³ of media (m² surface area/m³ media).

Here is the point were you will choose the filter media. Media specific surface area is the most important factor to be taken into account when choosing the media to be used in your filter but is not the only one. For an review on this topic I recommend you to take a look at  http://www.biofilters.com/webreview.htm.

Last years I had saw an increasing use of porous filter media in aquariums and since they provide an enormous surface area per unit of volume they were my first choice until I saw this statement by Hochheimer and Wheaton (no date): "Media in working biofilter becomes coated with a biofilm, resulting from the growing bacterial population. The two components where mass transport became important are within the biofilter (transfer of substrate(s) to the surface of the biofilm) and them within the biofilm. Getting substrate to the surface of the biofilm is associated with concentrations of the individual substrates in the culture system water and movement of the water through the biofilter. Work from Hochheimer (1990)  indicates that ammonia concentrations are too low to be influenced by diffusion in the water flowing through the biofilter. Physical mass transport of the ammonia then becomes the dominant factor in determining availability of ammonia to the nitrifying bacteria. The other substrates (oxygen and alkalinity), if kept at recommended levels, are dominated by diffusion." My intention is not to fire any manufacturer/seller of porous media, but I understood that as media becomes coated by biofilm water would no longer have a free passage through internal porous structure. Even if there were no biofilm coating the media, all porous media I already saw have so small holes that I don't think they would allow water to pass trough them to support bacterial growth in inner structure.

For a while I chose to use 16 mm diameter corrugated PVC tubing/ducts made to protect/install electric wires inside walls , in Brazil its brand name is Conduite® and they look like Trickle Filter Media - RMP® sold by Aqua Systems Uk Ltd..  Sixteen millimeters Conduite® provides around 500 m² of surface area/m³ of media and  I plan to cut it in pieces of 1/8 to 1/10 of filter diameter. I read somewhere that filter media diameter would be 1/8 of filter diameter to allow its better placing but I could not find this reference again...

5.3 - Hydraulic Loading Rate.

This is the amount of water pumped through the filter per unit  of cross sectional area of the filter per unit of time, it is expressed as m³ of water per m² of filter cross sectional area per day (m³ water/ m² filter cross sectional area/d). Kamstra et al. (1998) named this parameter as "hydraulic surface load".

Like I already said above media surface must to be wet to becomes functional, so you must pump through the filter an amount of water enough to keep all media wet but not so much that causes biofilm scouring and/or flood the filter filling its void space with water, that should be used by air for circulation,  in a way it works like a submerged filter.

Basically minimum and maximum hydraulic loading rates required by a media type for proper biofilm growth are a function of its specific surface area, void space and shape. Usually media manufacturers will provide data on recommended minimum and maximum hydraulic loading rates. 

Hochheimer and Wheaton (no date) suggested to use for design purpose 50 and 300 m³  water/ m² filter cross sectional area/d as minimum and maximum hydraulic loading rates, respectively. On the other hand several authors had reported increases in nitrification rates due increases in hydraulic loading rates but would there be an upper limit for this correlation . 

Greiner and Timmons (1998), that is the main source I'll use to predict ammonia removal rate, observed no significant effect of hydraulic loading rates between 469 and 1231 m³ water/ m² filter cross sectional area/d on nitrification rate. They used a media they spelt as Norpak® having an specific surface area of 164 m² surface area/m³ media and 5.1cm diameter. I did a search in the web to see how this stuff looks,  but all I found was another media spelt as Nor-pac®, produced by the same company, but I don't think they have the same shape because last one when having 5.1cm or 2" diameter provides only ~125 m² surface area/m³ media. 

Kamstra et al. (1998), that is a secondary source I'll use to predict ammonia removal rate, observed that trickling filters of eel farms filled with Munter's cross-flow media (234 m² of surface area/m³ of media) achieved higher ammonia removal rates and that they were operated at higher loading rates (200-800 vs. 50-400 m³ water/ m² filter cross sectional area/d) than filters using another types of media.  

This later reference also stated that  "The effect of the filter medium configuration on nitrification has been well documented (Keümer and Rosenthal, 1993; Parker and Merrill, 1984; Richards and Reinhart, 1896; Harrison and Daigger, 1987) and it is generally concluded that cross-flow media perform better than vertical-flow and random-flow media. This effect is attributed to differences in hydraulic and wetting characteristics between media, resulting in differences in water retention time. In our study, the cross-flow media (Munter's) shows a superior performance compared to vertical-flow (Bionet) and the random-flow medium (Filterpak), which is in agreement with the literature mentioned above." Just as fast as I read it I gave up to cut Conduite® in small pieces (random-flow) but to cut it in larger pieces and to glue it meet Munter's like configuration.

I'll set a hydraulic loading rate of 500 m³ of water/ m² of filter cross sectional area/d just above minimum hydraulic loading rate estimated in item 5.3.1 just below.

5.3.1 - Minimum Hydraulic Loading Rate. 

Like I'll use a media that has 2 or 3 fold more specific area than media used in experiments I took as references and like I plan use something that is not a biofilter media itself, so I can't call the manufactures to ask it about its minimum and maximum hydraulic loading rates, I'll use this parameter to make sure that all this surface available for bacteria attachment will be in proper condition to be colonized. 

From data shown in  L. S. Enterprises  site,  Sizing a biofilter - item # 8, I estimated this model represented below  (y = 10.394 * x ^ 0.6143; r² =0.999) and I'll use it to suggest a minimum hydraulic loading rate, as function of media specific surface area, for the media I chose.

Figure 1 - Relationship between Media Specific Surface Area and Minimum Hydraulic Loading Rate. 

Data adapted from L. S. Enterprises .

5.4 - TAN Concentration in Biofilter Influent Water.

This  is the expected TAN concentration in water entering the filter (influent), it is expressed as milligram per liter (mg TAN/l). 

It was observed by several researchers that ammonia concentration in the influent water effect nitrification rate but to understand a scientific model for ammonia concentration forecasting (Gutierrez-Estrada et al. 2004) has proven to be a challenge for me. 

Gujer and Boller (1986) and Nijhof (1994) also developed models intended predict the behavior of biofilters but I had no access to these articles. 

In short I'll use an alternative way that was proposed by Hochheimer and Wheaton (no date). They estimated TAN concentration dividing average hourly ammonia load by the volume of water in the system and the estimated filter exchange rate. This estimative assumes  that all ammonia produced per hour is consumed in one hour by the filter, I'm not sure about it, but like I'm working with an ammonia concentration that is much lower than ones I found in literature and with higher turnover rates I think I have a good safety margin. 

5.5 - TAN Conversion Rate.

This is the amount ammonia oxidized per unit of space available for bacterias colonize per unit of time, it is expressed as grams of TAN per m² of media surface per day (g TAN/m² media surface area/d).

Here we have basically two alternatives: The first and easiest alternative is just to get a value for TAN conversion rate from the literature and type it in appropriate cell, the second way is to use models developed by scientists. If you set any number different than zero at the above mentioned cell the spreadsheet will straightly take this TAN conversion rate to size the biofilter, if you keep the zero at this cell the spreadsheet will use smaller TAN conversion rate among the two estimative models I proposed.   

5.5.1 - TAN Conversion Rate - Literature Chose Data. 

(Ebeling, no date) mentioned that for a trickling filter operated at 15 to 20ºC  we could expect a conversion rate of 0.2 to 1.0 g TAN/m² media surface area/d and for filter operating at 25-30ºC could reach 1.0 to 2.0 g TAN/m² media surface area/d. 

Hochheimer and Wheaton (no date) used data from Wortman (1990) and/or Gujer and Boller (1986) to estimate TAN conversion rates.

Greiner and Timmons (1998) observed conversions of 0.94 to 3.92  g TAN/m² media surface area/d for TAN influent concentrations between 0.81 and 4.63 mg TAN/l, Norpak® media, hydraulic loading rates between 469 to 1231 m³ water/m² media surface/d, average influent water temperature of 26.4ºC, dissolved oxygen greater than 5 mg/l, pH of 6.7, total suspended solids of 6.4 mg/l and an alkalinity of 90 mg/l. 

There are several other sources in literature where you can get experimental data on  TAN conversion rates for different water parameters and filter/system configurations. I just took three...

5.5.2 - TAN Conversion Rate - Greiner and Timmons Data. 

Greiner and Timmons (1998) calculated the linear regression below to predict ammonia removal rate.  the conditions for/from what this model was developed were mentioned just above in item # 5.5.1.

R= k1*C1  for C1 < 2.5 mg TAN/l             R² = 0.90

Where: R = ammonia-nitrogen oxidation rate (g/m²/d); C1 = ammonia-nitrogen influent concentration (mg/l) and k1 is a constant equal 1.43 for trickling biofilters (SEcoeff = 0.108; R² = 0.58 and n = 11). 

This model uses a constant that I should call "filter specific rating" and may be it would not be repeated at every filter. I understood from their work that the main factor affecting the performance of their filter was credited to the hydraulic loading rate so I advice you to be careful when estimating/setting it.  

5.5.3 - TAN Conversion Rate - Nijhof  Data. 

Nijhof (1994), cited by Kamstra et al. ( 1998), developed the model below:

R1 = a * square root ([NH4-N]) - 0.01          (Eq. 1)

Where: R1 = intrinsic ammonium removal rate (g /m²/d); [NH4-N] = ammonium concentration in influent (mg/l) and a = a coefficient depending on external variables (m/d).

a = 0.000781H + 0.2

Where: a = coefficient from Eq. 1 and H = hydraulic load of the filter: flow/cross-sectional area (m/day).

I thought these units are somewhat strange but you can be sure I typed it exactly like it was published and I do not know about any errata for this article. Also, like I had no access to a full copy of Nijhof (1994), I don't know for what conditions this model was calculated but this model was tested by Kamstra et al. ( 1998) who concluded that this model "...gives an adequate prediction of these filters when the effect of the filter medium on nitrification is taken into account." I also suppose that this model was developed taking into account water temperature around 20-25°C, that is about the lower range we raise guppies. 

5.6 - Media Surface Area Needed for Biofilm Attachment.

This is the amount of biofilm surface area demanded to convert the ammonia produced in our system, it is expressed as square meter (m²).

Once we have an estimative of ammonia production and TAN conversion rate if we divide the former by the later we'll now how many meters of surface we'll need to get rid all ammonia produced in the system.  

I estimated surface area needed for biofilm attachment as ~ 28 m².

5.7 - Volume of Media.

This is the volumetric amount of  filter media we'll place in the filter to provide the media surface area need for biofilm attachment, it is expressed as liter (l).

Having an estimative of media surface area need for biofilm attachment and the amount of surface area provided per unit of media volume we divide them and we'll know how much media volume we'll need to oxidize ammonia.

I estimated volume of media as ~ 56 l, that is around the average 5-15% of system size estimated by several authors. Sincerely I expected that since we are working with relative low stocking rates (2 kg of fish/m³ of water versus up to 150-200 kg of fish/m³ of water  for most food fishes) we could use much smaller filters, I mean filters representing a smaller percentage/part of the system. But looks that our small guppies demand so many space to live that TAN concentrations in their water becomes too low, thus decreasing nitrification rates in a very large extent.   

5.8 - Biofilter Cross-Sectional Area.

This is the top cross-sectional area of our biofilter, it is expressed in our case as square centimeter (cm²).

Well, we know how much water will pass by the filter per day (total volume of water in our system X water turnover per hour X 24 hours in a day) and how much water should pass by every unit of filter top area to keep media properly wet (hydraulic loading rate), so dividing the former by the later we get an estimative of filter cross-sectional area which we can manage with a proper flow of water over media.    

I found that my filter should be ~ 806 cm² in top area.

5.9 - Biofilter Diameter.

This is the diameter of the media holding vessel, biofilter, it is expressed as centimeters (cm).

Once we know the top area of our filter (biofilter cross-sectional area) we can reach biofilter diameter using the classical formula for circumference area (area = π r²).

I estimated that my filter should have  ~ 32 cm diameter.

5.10 - Biofilter Height.

This is how tall our biofilter should be, it is expressed as centimeters (cm).

We know how much media our filter should hold (volume of media) and its top area (biofilter cross-sectional area), so dividing them we get biofilter height.

I sized a biofilter that is ~ 70 cm tall.

5.11 - Media Surface Loading Rate.

This is the amount of water loaded per unit of surface area available for bacterial growth provided by filter media, it is expressed as m³ of water per m² of media surface per day (m³ water/m² media surface/d). Sometimes filter wall area is also included in its calculation but I simply give up this, I took the nitrification  occurring in filter wall as a "safety factor". Kamstra et al. ( 1998) named this parameter as "hydraulic biofilm load".

Media surface loading rate is a parameter designed to catch the relationship between hydraulic loading rate and media specific surface area. The idea behind this number is give you an estimative of  how much water you can make pass by your filter without causing biofilm scouring based on data already reported by researchers, it could be somewhat  understood as "possible hydraulic loading rate".

Greiner and Timmons (1998) stated that the nitrification rates they observed were much higher than nitrification rates reported by another authors and that it could be an effect of the high hydraulic loading rates they used in their study. They wrote: "The trickling filters in this study operated at media surface loading rates of 9-24 m³/m² of media/day ...  These high hydraulic loading rates would have eliminated any substrate feeding limitations or lack of oxygen for the biofilm in the present study."  

Kamstra et al. ( 1998) also observed that filters having Munter's media also operated at higher media surface loading rates than other filters, 1.1 to 4 and 0.1 to 0.9 m³  water/ m² media surface area/d, respectively. I found a media surface loading rate of 1.43 m³ water/m² media surface area/d  for my filter.

5.12 - TAN Loading Rate.

This is the amount of  Total Ammonia Nitrogen (TAN) loaded per unit of surface area available for bacterial growth provided by filter media, it is expressed as g of TAN per m² of media surface per day (g TAN/ m²  media surface/d). 

Gujer and Boller (1986) and Nijhof (1994) used a parameter like this one intended to catch the effects substrate load per unit of area available for bacterias growth on the nitrification rate (Kamstra et al., 1998). Most sources I consulted had strongly pointed about the substrate limiting effect on the performance of  biofilter designed for aquacultural purposes but, as far as I know, they usually did not clearly studied the effect of TAN loading rate on nitrification rates. Only  Hochheimer (1990) and Kamstra et al. ( 1998) did some studies  on this topic. I had no access to Hochheimer (1990) work. 

In a careful reading of Kamstra et al. ( 1998) I was not able to exactly determine what they called "total ammonium" and they noted as NH4-N. Here we come again with the already mentioned mess on nitrogenous compounds nomenclature... But it is not vital for the point I would like discuss. Most people performing research in this area, see that as much ammonia we make available for every space unit of biofilm higher will be its nitrification rate, up to a certain filter/system/bacteria population intrinsic value. So they see two ways we can increase nitrification rates: (1) increasing water flow through the filter, since we do not cause biofilm scouring, and/or (2) increasing waste level in the water, this is a way I do not want to think about.  

Figure 2 - Relationship between the observed Ammonium Loading Rate and the observed Ammonium Removal Rate.

From  Kamstra et al. ( 1998) .

5.13 - TAN Conversion Rate. Kamstra et al. Data. 

This parameter is calculated from equation presented in figure 2. It is being presented to help you figure about the effects of  both hydraulic loading rate and TAN concentration in the water on nitrification rate. 

Finally...

Only one last opinion... 

Like I stated since I began this is a filtration method that was not fully tested and proved for guppies so I strongly suggest you to be careful when sizing and running a biofilter, read/ask/learn as much as you can about it before you take any decision and Good Luck!!!

Further References.

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

Harrison, J .R. and G. T. Daigger.  1987. A comparison of trickling filter media. J. WPCF 59 (7), 679–685.

Hochheimer, J. N. 1990. Trickling filter model for closed system aquaculture. Unpublished Ph. D. Dissertation. University of Maryland. College Park, MD.

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

Kaiser, H., Paulet, T. G. and F. Endemann. 1998. Water quality fluctuations in a closed recirculating system for the intensive culture of the guppy, Poecilia reticulata (Peters). Aquaculture Research 19:611-615. 

Kaiser, H. and N. Vine. No date. Investigations into the growth, survival and fin quality of guppy, Poecilia reticulata, at different stocking densities. p161-168.

Nicoletto, P. F., 1996. The influence of water velocity on the display behavior of male guppies, Poecilia reticulata. Behavioral Ecology 7(3):272-278. 

Parker, D.S. and D. T. Merrill. 1984. Effect of plastic media configuration on trickling filter performance. J. WPCF 56 (8), 955–961.

Richards, T. and D. Reinhart. 1986. Evaluation of plastic media in trickling filters. J. WPCF 58 (7), 774–783.

Wortman, B. 1990. Effect of temperature on biodrum nitrification. Unpublished M. Sc. Thesis. University of Maryland. College Park, MD.