Feed in, fish out: why every aquaculture design starts with a mass balance

The feed sets the loads

Ask what size biofilter, oxygen cone or drum filter a farm needs and the answer is always the same: it depends on how much feed goes in each day, what is in it, and how much of it the fish retain. Everything a treatment train has to remove was once feed. The nitrogen in the protein becomes ammonia at the gill or faecal solids in the tank; the carbon becomes carbon dioxide or sludge; the energy the fish burn to grow is paid for in dissolved oxygen. A design that starts with a tank volume and a stocking density has the arrow pointing the wrong way. The tank, and every pump, blower and reactor behind it, is a consequence of the feed plan.

The farm-scale budgets make the point plainly. Across the Norwegian Atlantic salmon (Salmo salar) industry in 2009, at a mean feed conversion ratio of 1.16, an estimated 62 per cent of the nitrogen, 70 per cent of the carbon and 70 per cent of the phosphorus in the feed entered the water, with 45 per cent of feed nitrogen excreted as dissolved inorganic nitrogen, 48 per cent of feed carbon respired as CO₂ and 44 per cent of feed phosphorus released as particles (Wang et al., 2012). A single-farm study with measured feed, fish and faeces gave a similar picture: 43 per cent of feed nitrogen retained, 39 per cent excreted as dissolved inorganic nitrogen and 15 per cent released as particles (Wang et al., 2013). Those fractions differ between species, diets and fish sizes, which is why they have to be written down before anything is sized.

Ammonia: the stoichiometry that sizes the biofilter

Total ammonia nitrogen is the load designers reach for first, because the biofilter is usually the least forgiving reactor in the system. The production term is short: feed rate, multiplied by the protein fraction of the diet, by the nitrogen content of protein (0.16 g N per g protein), and by the fraction of that nitrogen excreted. In Ebeling, Timmons and Bisogni's worked case, 1 kg of a 35 per cent protein feed with 90 per cent of the nitrogen excreted yields 50.4 g of ammonia nitrogen (Ebeling et al., 2009). That last factor is where judgement enters: the salmon farm budgets above put dissolved inorganic nitrogen at 39 to 45 per cent of feed nitrogen, roughly half the conservative figure, and the difference propagates one for one into every downstream line.

What the biofilter then does to each gram of ammonia nitrogen is not a matter of judgement at all; it is stoichiometry, worked through by the same authors from half-reactions. Autotrophic nitrification with cell synthesis consumes 4.18 g of oxygen and 7.05 g of alkalinity (as CaCO₃), and produces 5.85 g of CO₂, 0.20 g of volatile suspended solids and 0.976 g of nitrate nitrogen, per gram of ammonia nitrogen removed (Ebeling et al., 2006; Ebeling et al., 2009). Seven kilograms of alkalinity as calcium carbonate per kilogram of ammonia nitrogen nitrified, closer to twelve kilograms once converted to sodium bicarbonate on an equivalent basis, is a dosing line item, and it appears in the design the moment the ammonia load does.

The heterotrophic pathway, in which dosed carbohydrate lets bacteria assimilate ammonia directly into cell mass, trades alkalinity for sludge: per gram of ammonia nitrogen it consumes 4.71 g of oxygen, 6.07 g of carbohydrate and 3.57 g of alkalinity, and produces 9.65 g of CO₂ and 8.07 g of volatile suspended solids (Ebeling et al., 2006; Ebeling et al., 2009). Forty times the sludge of nitrification is the price of a biofloc system's small alkalinity bill.

Oxygen, carbon dioxide and solids follow the same feed

Oxygen demand has three sources: fish respiration, nitrification and the heterotrophic activity that lives on whatever organic matter solids removal did not catch. Measurements in commercial Atlantic salmon smolt tanks found an oxygen demand across the tank of 7.4 to 10.4 mg/L, and the estimated respiration rate roughly doubled, from about 0.3 kg of O₂ per kg of feed to about 0.7 kg per kg, as total suspended solids rose from 3 mg/L to 10 to 12 mg/L (Gorle et al., 2018). Add the biofilter's 4.18 g of oxygen per gram of ammonia nitrogen and the oxygen budget is a function of feed rate, diet and solids control, not of tank volume.

Carbon dioxide arrives from the same two places. Farm budgets put respired CO₂ at 40 to 48 per cent of feed carbon (Wang et al., 2012; Wang et al., 2013), and nitrification adds 5.85 g of CO₂ per gram of ammonia nitrogen removed while consuming the alkalinity that would otherwise buffer it (Ebeling et al., 2006). The two are coupled through pH, so the degasser and the bicarbonate dosing are sized from the same sheet as the biofilter.

Solids are set by digestibility and feeding practice rather than by stoichiometry. Cho and Bureau's review put it directly: remove poorly digestible ingredients such as whole grains and grain by-products used as binders, reduce the digestible protein to digestible energy ratio to cut nitrogen waste, match digestible phosphorus to requirement, and control feed wastage, which can dominate all three (Cho and Bureau, 2001). In replicated low-exchange recirculating systems, rainbow trout (Oncorhynchus mykiss) on a fish meal-free grain-based diet held significantly higher concentrations of total ammonia nitrogen and suspended solids, and more fine solids of 2 to 30 µm, than fish on a fish meal diet, with less phosphorus in the effluent (Davidson et al., 2013). Screening and sedimentation on flow-through trout farms remove suspended solids carrying 7 to 32 per cent of total nitrogen and 30 to 84 per cent of total phosphorus; what passes through becomes dissolved load (Sindilariu, 2007).

The feed-to-waste mass balance. Feed sets the loads; the coefficients on the right convert ammonia removed into the oxygen, alkalinity, carbon dioxide and sludge that the rest of the plant has to handle. Original diagram, AquaBlueprint.

A worked example: a nominal 100 t/yr barramundi RAS

Take a land-based barramundi (Lates calcarifer) farm designed for 100 t per year. The inputs below are stated design assumptions, not measurements, to be replaced with the farm's own records before anything is ordered. A feed conversion ratio of 1.4 gives 140 t of feed a year, about 384 kg per day on average; the plant has to carry the peak, so the design day is taken as 480 kg of a 45 per cent protein grower diet. Feed demand can be predicted more carefully than a flat FCR allows: Glencross's factorial model, built on Australian farm and laboratory data, describes weight gain as a function of fish weight and temperature and derives feed demand from digestible energy (Glencross, 2008).

At 480 kg of feed and 45 per cent protein, the nitrogen entering the system is 480 × 0.45 × 0.16 = 34.6 kg per day. The table carries that through two bounding assumptions for the excreted fraction: 0.45, the dissolved inorganic nitrogen fraction from the Norwegian salmon budget (Wang et al., 2012), and 0.90, the conservative value in Ebeling's worked case (Ebeling et al., 2009). Nitrification coefficients are from Ebeling et al. (2006) and the tank respiration range from Gorle et al. (2018).

Two assumptions, the excreted fraction and the solids concentration the fish live in, move the total oxygen line from 209 kg to 466 kg per day, a factor of more than two, before a single piece of equipment has been chosen. The alkalinity line doubles on the excreted fraction alone. Solids can be bracketed the same way: the measured suspended solids load from flow-through rainbow trout farms was 278 kg per tonne of fish produced (Koçer et al., 2013), which for 100 t a year is 27.8 t, about 76 kg a day on average. The respired CO₂ line is left open because it needs the diet's carbon content; the farm budgets give it only as 40 to 48 per cent of feed carbon. The barramundi-specific fractions are the larger gap; no peer-reviewed waste-output budget for the species surfaced in the search behind this article, so an Australian farm's own effluent data are worth more than any number here.

Does the method hold up against real farms?

The nutritional mass balance is a model, and models earn their place by being tested. The most direct test compared it with hydrological measurement on three flow-through rainbow trout farms of 250, 750 and 2,500 t a year. The nutritional method predicted 44.3 kg of nitrogen and 8.4 kg of phosphorus per tonne of fish produced; the measured loads were 43.9 kg and 8.8 kg. For suspended solids, prediction and measurement were the same, 278 kg per tonne, and the authors concluded that the nutritional mass balance may be the method of choice for environmental assessment of land-based aquaculture (Koçer et al., 2013). A French study of twenty commercial flow-through trout farms found a high correlation between the two methods for total nitrogen and total phosphorus; given the uncertainty in both, the authors could not say which was more accurate (Aubin et al., 2011).

A review of 36 farm-scale fish models published between 1985 and 2021 found the same mass-flow models in use for precision farming, integrated multi-trophic design, spatial management and life cycle assessment (Chary et al., 2022). The mass balance is not a preliminary to the design work. It is the design work, and component sizing is bookkeeping that follows from it.

What this means for design

Start every design with the feed plan: daily feed on the design day, protein and phosphorus content, an explicit feed conversion ratio and an explicit assumption for the fraction of nitrogen excreted. Write the assumptions where a reviewer can see them; two of them can move the oxygen line by a factor of two. Convert feed to loads with published coefficients rather than supplier tables, and carry the alkalinity line from the start; it is the one that decides whether the biofilter holds its pH in month three. Treat solids removal as the lever that sets the oxygen and biofilter loads downstream. Then size the components, in that order, and expect to revise the balance when the first month of farm data arrives; the trout farm comparisons suggest it will land close.

This is the logic AquaBlueprint's mass balance module follows. It takes daily feed, feed conversion and diet composition and returns the daily ammonia, oxygen, carbon dioxide, alkalinity and solids loads that component sizing and feasibility work from, with every assumption visible and editable. The methods implement widely accepted industry design standards; the output is a design report summary and a bill of materials, a design aid for the professional doing the work. What it does not do is supply species-specific retention data the literature has not published, or replace measurement on the site.

References

Aubin, J., Tocqueville, A. and Kaushik, S.J. (2011). Characterisation of waste output from flow-through trout farms in France: comparison of nutrient mass-balance modelling and hydrological methods. Aquatic Living Resources 24, 63-70. https://doi.org/10.1051/alr/2011008

Chary, K., Brigolin, D. and Callier, M.D. (2022). Farm-scale models in fish aquaculture: an overview of methods and applications. Reviews in Aquaculture 14, 2122-2157. https://doi.org/10.1111/raq.12695

Cho, C.Y. and Bureau, D.P. (2001). A review of diet formulation strategies and feeding systems to reduce excretory and feed wastes in aquaculture. Aquaculture Research 32 (Suppl. 1), 349-360. https://doi.org/10.1046/j.1355-557x.2001.00027.x

Davidson, J., Good, C., Barrows, F.T., Welsh, C., Kenney, P.B. and Summerfelt, S.T. (2013). Comparing the effects of feeding a grain- or a fish meal-based diet on water quality, waste production, and rainbow trout Oncorhynchus mykiss performance within low exchange water recirculating aquaculture systems. Aquacultural Engineering 52, 45-57. https://doi.org/10.1016/j.aquaeng.2012.08.001

Ebeling, J.M., Timmons, M.B. and Bisogni, J.J. (2006). Engineering analysis of the stoichiometry of photoautotrophic, autotrophic, and heterotrophic removal of ammonia-nitrogen in aquaculture systems. Aquaculture 257, 346-358. https://doi.org/10.1016/j.aquaculture.2006.03.019

Ebeling, J.M., Timmons, M.B. and Bisogni, J.J. (2009). An engineering analysis of the stoichiometry of autotrophic, heterotrophic bacterial control of ammonia-nitrogen in zero-exchange marine shrimp production systems. International Journal of Recirculating Aquaculture 10(1), 63-89. https://doi.org/10.21061/ijra.v10i1.1336

Glencross, B.D. (2008). A factorial growth and feed utilization model for barramundi, Lates calcarifer, based on Australian production conditions. Aquaculture Nutrition 14, 360-373. https://doi.org/10.1111/j.1365-2095.2007.00543.x

Gorle, J.M.R., Terjesen, B.F., Mota, V.C. and Summerfelt, S.T. (2018). Water velocity in commercial RAS culture tanks for Atlantic salmon smolt production. Aquacultural Engineering 81, 89-100. https://doi.org/10.1016/j.aquaeng.2018.03.001

Koçer, M.A.T., Kanyılmaz, M., Yılayaz, A. and Sevgili, H. (2013). Waste loading into a regulated stream from land-based trout farms. Aquaculture Environment Interactions 3, 187-195. https://doi.org/10.3354/aei00059

Sindilariu, P.-D. (2007). Reduction in effluent nutrient loads from flow-through facilities for trout production: a review. Aquaculture Research 38, 1005-1036. https://doi.org/10.1111/j.1365-2109.2007.01751.x

Wang, X., Olsen, L.M., Reitan, K.I. and Olsen, Y. (2012). Discharge of nutrient wastes from salmon farms: environmental effects, and potential for integrated multi-trophic aquaculture. Aquaculture Environment Interactions 2, 267-283. https://doi.org/10.3354/aei00044

Wang, X., Andresen, K., Handå, A., Jensen, B., Reitan, K.I. and Olsen, Y. (2013). Chemical composition and release rate of waste discharge from an Atlantic salmon farm with an evaluation of IMTA feasibility. Aquaculture Environment Interactions 4, 147-162. https://doi.org/10.3354/aei00079