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Mass-Balance Process Model of a Decoupled Aquaponics System
Rohit Kalvakaalva2, Mollie Smith3, Emmanuel Ayipio3, Caroline Blanchard3, Stephen A. Prior1, G. Brett Runion1, Daniel Wells3, David Blersch2, Sushil Adhikari2, Rishi Prasad4, Terrill R. Hanson5, Nathan Wall2, Brendan T. Higgins2,*
Published in Journal of the ASABE 66(4): 955-967 (doi: 10.13031/ja.15468). 2023 American Society of Agricultural and Biological Engineers.
1USDA Agricultural Research Service, Washington, District of Columbia, USA.
2Biosystems Engineering Department, Auburn University, Auburn, Alabama, USA.
3Department of Horticulture, Auburn University, Auburn, Alabama, USA.
4Department of Crop, Soil, and Environmental Sciences, Auburn University, Auburn, Alabama, USA.
5School of Fisheries and Aquatic Sciences, Auburn University, Auburn, Alabama, USA.
*Correspondence: bth0023@auburn.edu
The authors have paid for open access for this article. This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License https://creative commons.org/licenses/by-nc-nd/4.0/
Submitted for review on 21 November 2022 as manuscript number NRES 15468; approved for publication as a Research Article by Associate Editor Dr. Xiaoyu (Iris) Feng and Community Editor Dr. Kati Migliaccio of the Natural Resources & Environmental Systems Community of ASABE on 27 April 2023.
Mention of company or trade names is for description only and does not imply endorsement by the USDA. The USDA is an equal opportunity provider and employer.
Highlights
Abstract. Aquaponics presents a viable solution to water pollution from aquaculture by utilizing nitrate- and phosphate-rich effluent for crop production. The objective of this study was to develop a mass-balanced process model based on a pilot-scale aquaponics facility growing Nile tilapia (Oreochromis niloticus) and cucumbers (Cucumis sativus) in Auburn, Alabama. This enabled a better understanding of how key elements partition among different downstream processes, ultimately affecting nutrients available to plants or discharged to the environment. Data were collected from a pilot scale decoupled aquaponics system for a full calendar year and included weekly water quality, direct GHG emissions, and water flows. Bio-solids, fish mass, and plant mass were also quantified and underwent elemental analysis. Together, these measurements were used to create stoichiometric equations for mass partitioning. The resulting stoichiometry was used to develop a mass-balanced process model constructed in SuperPro Designer software. Four separate variations of the model were developed, one for each season. The model showed that 21.6% of input nitrogen was assimilated by tilapia and only 2.81% by plants, while 33% of input phosphorus was assimilated by tilapia and 2.6% by plants. Modeled effluent concentrations of nitrate from the fish tank, clarifier, and plants averaged 440, 441, and 307 mg L-1, respectively, compared to average measured values of 442, 406, and 298 mg L-1. Modeled effluent phosphate concentrations from the fish tank, clarifier, and plants were 25, 27, and 20 mg L-1 of phosphate, respectively, over the course of one year, while average measured values were 30, 31, and 26 mg L-1. The model was not suitable for predicting short term system changes. The constructed model shows promise in predicting long-term changes in system outputs based on upstream operational changes and is effective for simulation and scenario analysis.
To cope with global population growth, methods of providing sufficient, nutritious food and clean water must be developed. At the same time, there is an urgent need to mitigate the negative environmental impacts of agricultural production systems. Currently, over 50 percent of the world’s fish supply comes from aquaculture production (FAO and UNICEF, 2018). Aquaculture creates environmental emissions, particularly the production of nutrient-rich wastewater, which can enter the environment through incidental runoff or routine draining (Guong and Hoa, 2012). This can result in severe cases of eutrophication, affecting preexisting ecosystems or surrounding aquaculture facilities (Cao et al., 2007).
Aquaponics presents a solution to problems associated with traditional aquaculture by repurposing nutrients from aquaculture effluent for hydroponic plant production (Love et al., 2014; Wongkiew et al., 2017). This reduces nutrient emissions while promoting sustainable food production. Aquaponics has recently grown in popularity due to its intensive production of fish and plant crops in a relatively small space and its perception of sustainability (Love et al., 2014; Palma Lampreia Dos Santos, 2018). In some cases, aquaponics has also shown promise as an economically competitive approach (Xie and Rosentrater, 2015). However, to maximize both the economic and environmental performance of aquaponics, it is important to understand the fate and flow of nutrients in these systems to ensure efficient use. For example, nitrogen can be lost to the atmosphere via denitrification, while phosphorous can be lost through precipitation and other conversion processes that reduce bioavailability to plants (Cerozi and Fitzsimmons, 2016; Eck et al., 2019; Yang and Kim, 2019). Additionally, imbalances between plant crop and fish production can lead to excess nutrients in post-plant effluent water from decoupled aquaponics systems, leading to negative downstream environmental impacts such as eutrophication (Calone et al., 2019; Maucieri et al., 2018).
Few studies have attempted to construct detailed mass-balance models of aquaponics systems. Cerozi and Fitzsimmons (2017) created an empirical phosphorus mass balance model of a recirculating coupled aquaponics system to predict how various management practices can affect downstream nutrient fate. They found that over 71% of P was assimilated into fish and plant biomass in their coupled aquaponics system. Karimanzira et al. (2016) created a sophisticated dynamic mass-balance simulation model for an aquaponics system; however, their model was not calibrated using real system data. Rather, parameters from the literature were used for simulation purposes. Similarly, Dijkgraff et al. (2019) and Goddeck and Korner (2019) developed sophisticated simulation models of decoupled aquaponics systems, but these were apparently not calibrated with data from a real system. Instead, they used the simulations to aid in system design and sizing. For example, Dijkgraff et al. (2019) simulated a multi-loop decoupled aquaponics system that used anaerobic digestion of the sludge and found maximum N and P utilization efficiencies (uptake into fish and plants) of 77% and 95%, respectively, in an optimized system design. Other researchers have created experimentally-calibrated mass balance models for recirculating aquaculture systems (RAS), but these did not include aquaponics (Cerozi and Fitzsimmons, 2017; Karimanzira et al., 2016; Klas et al., 2006; Wik et al., 2009). Additional studies have examined nitrogen transformation (Wright, 2018) based on small-scale aquaponics systems. However, none of these studies has created a comprehensive mass balance model for water, nitrogen, and phosphorus in an aquaponics system based on comprehensive data collected from a large-scale system.
Herein, we present a mass-balance process engineering model based on a large (multiple greenhouse), decoupled biofloc aquaponics system located at Auburn University, Auburn, Alabama, USA. This system produces Nile tilapia (Oreochromis niloticus) and cucumbers (Cucumis sativus). The goal of this study was to utilize data from the facility, collected over the course of one year, to construct a mass-balance model that can predict nutrient transformations based solely on upstream inputs (water, feed, and season). Experimentally derived stoichiometric equations and empirical formulas of each major output of the system (e.g., tilapia, sludge, and cucumber plant components) were developed. We then used this model to run Monte Carlo simulations based on variations in inputs to capture the effects of uncertainty. Ultimately, we seek to utilize this model to aid in management and operational decisions as well as carry out scenario analyses in future life-cycle assessments.
Materials and Methods
System Description
The system of study was located at the E.W. Shell Fisheries Center in Auburn, Alabama. The system was operated in a decoupled fashion, meaning water from post-plant production was not recirculated back into the fish tank (fig. 1). The pilot system included two 279 m2 climate-controlled greenhouses. The first greenhouse housed a 150,000 L fish tank, outfitted with hapa nets for the production of Nile tilapia (O. niloticus) according to Auburn University’s Institutional Animal Care and Use Committee protocols #2019-3607 and #2021-3922. Euthanasia for fish on this project was obtained through physical means (pithing) to avoid altering the chemical composition of the fish prior to analysis. The fish tank was constantly aerated using a submerged aeration system (Wagner and Pöpel, 1998), and tilapia were fed using a combination of 3606 and 4010 aquaculture feed (Cargill, Franklinton, LA, USA) at an intensity ranging from 0-0.21 kg m-3 d-1, with operational detail provided in a previous publication (Kalvakaalva et al., 2022). The 3606 feed is 36% crude protein and 6% fat, whereas the 4010 feed is 40% crude protein and 10% fat. The fish tank was operated as a biofloc system to control ammonia concentrations (HRT of ~100 days), and water was circulated through an airlift pump to a 3-stage clarifier where solids were removed (HRT of ~3.5 days). The supernatant from the clarifier was used for plant irrigation or recirculated back into the fish tank. The second greenhouse was used for the production of Beit Alpha seedless cucumbers (C. sativus) grown in Perlite-filled 11 L “Dutch” buckets (Crop King Inc., Lodi, OH, USA). Cucumbers were irrigated using drip irrigation with the scheduling described previously (He et al., 2018; Kalvakaalva et al., 2022). Unused drained water was fed into underground sumps before being released to a drainage ditch. No micronutrient supplementation was used in this system except for the calcium associated with lime additions. Data from this system were collected over a one year period, and multiple cucumber cultivation experiments were carried out in this timeframe and are described previously (Kalvakaalva et al., 2022). Briefly, two pH experiments were conducted in the spring (8 March 2019-6 May 2019) and summer (22 May 2019-17 July 7 2019). In these studies, the irrigation water pH was adjusted to 5.5, 6, 6.5, and 7 using citric acid (spring) or sulfuric acid (summer). These pH levels did not significantly affect macronutrient uptake into plants over the course of the growth campaign (Blanchard et al., 2020). In the fall (11 September 2019-22 October 2019) and winter (9 January 2020-6 March 2020), experiments were conducted based on substrate type (pine bark vs. perlite).
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| Figure 1. Operational schematic of pilot-scale decoupled aquaponics system at Auburn University. |
Biological Material Collection and Compositional Analysis
Solid biological materials associated with the system were collected in April of 2019 and included fish feed, tilapia, sludge from the clarifiers, and cucumber roots, stems/leaves, and fruit. Both juvenile and adult fish were collected to account for any compositional variations between age groups. Cucumber stems and leaves were first dried using a forced-air industrial dryer (70°C) for three days (Grieve SC-3300) and then homogenized using a plant grinder (Thomas Scientific USA). Fish feed, tilapia, and cucumber fruit were homogenized using a kitchen blender (Ninja) and stored in 10 ml vials. Homogenized material was transferred to vials (n = 6 for fish feed and tilapia, n = 10 for cucumber materials) and then freeze dried at -45°C (Labconco). Cucumber roots were removed from the perlite root balls by hand and then cut into pieces using a kitchen knife before freeze drying. Sludge was collected from the clarifier effluent and centrifuged (4696 x g, 15 min) to concentrate solid material. The remaining material was stored in 10 ml vials and freeze dried to remove the remaining moisture (n = 3).
Following methods described by Wang et al. (2020), samples were analyzed using a Vario MICRO cube Elemental Analyzer (Elementar, Langenselbold, Germany) for carbon (C), hydrogen (H), nitrogen (N), and sulfur (S) content. Samples were also analyzed for other elements such as phosphorous (P), iron (Fe), and potassium (K), using inductively coupled plasma with optical emission spectrometry (ICP-OES) analysis following methods described in Chaump et al. (2019). Ash content was determined using standard gravimetric methods (Chaump et al., 2019). Oxygen content was estimated by subtracting C, H, N, S, and ash from the total dry mass.
Water Sampling
Water samples were collected on an approximately weekly basis for one year at four locations within the aquaponics system: system influent, fish tank, clarifier effluent, and the post-plant sumps. Water samples (2 ml) were filtered using nylon syringe filters (0.2 µm) and then stored at -80? prior to analysis. At the conclusion of the sampling period, each sample was analyzed for soluble ion concentrations via high pressure liquid chromatography (HPLC; Shimadzu Prominence System, Kyoto, Japan) using an anion exchange column (Dionex AS22, ThermoFisher Scientific, USA) and ion suppressor (Dionex AERS 500, ThermoFisher Scientific, USA) per a previously-published method (Chaump et al., 2019). Compounds detected included nitrate (NO3-), nitrite (NO2-), and soluble phosphate (PO43-). Cation chromatography was also performed (Dionex CS12, ThermoFisher Scientific, USA) using an ion suppressor (Dionex CERS500, ThermoFisher Scientific, USA). The compounds detected included potassium (K+) and ammonium (NH4+) ions. Along with compositional analysis of solid materials, these data were used to develop empirical formulas and construct the mass-balance process model.
Greenhouse Gas Emissions
Direct greenhouse gas emissions were measured in the system from the summer of 2019 through the winter of 2020, as detailed in our previous work (Kalvakaalva et al., 2022). During each growing period, samples were taken on an approximate weekly basis. Gas samples were collected from the fish tank, clarifiers, and the greenhouse Dutch buckets and closely followed the sampling protocol as described in Marble et al. (2012). Using a gas chromatograph (Shimadzu GC-2014, Columbia, MD), samples were analyzed for three trace gases: carbon dioxide (CO2), methane (CH4), and nitrous oxide (N2O). Readings were then converted and presented as gas flux (kg m-2 d-1). These data assisted with establishing the stoichiometry of carbon and nitrogen transformations.
Other Data Collection
Water flows were metered and recorded daily and included fish tank makeup water and irrigation. The water recirculation rate from the clarifiers to the fish tank, and sludge removal rates were also recorded and used to generate water partitioning parameters. Based on this information, water losses due to evaporation and leakages were calculated. Fish feed type and rates were also recorded daily. Additionally, parameters such as fish tank aeration were assumed to be constant throughout the sampling period. The aeration rate for the fish tank was based on a one-time measurement of air flow through aeration manifolds with the use of an anemometer, as described in Kalvakaalva et al. (2022).
Model Construction and Calibration
Overall Model Structure
The mass balance process model was constructed in SuperPro Designer® v.8.5 (ESM 1). Due to seasonal variation of certain parameters, such as apparent denitrification and plant growth rates, a separate model was parametrized for each season. Within each seasonal model, three mass inputs drove downstream mass flows, partitioning, and transformations: feeding rate, input water to the fish tank, and influent nitrate. All model input and outputs were presented as an average kg h-1 calculated on a weekly basis (the approximate timing of water quality sampling) over the course of a year. The model was structured as a semi-steady-state system in which the system was assumed to operate at steady state based on average inputs for a given week. The model inputs were based on the average values for the seven days prior to the water sampling date. Then the steady state operation was allowed to adjust based on inputs for the subsequent week. In reality, the system was constantly in flux but modeling such a dynamic system would require a continuous stream of real-time data for all constituents (for calibration purposes) within the system. This was not practical and unlikely to add significant value when using the model for decision-making and simulation purposes over long timeframes.
Development of Fish Tank Stoichiometry
Using the methods described in Tattershall (1979), mass based macro-element quantities, derived from CHNS and ICP analysis, were used to create empirical formulas (table 1) for the different materials associated with the aquaponics system. Empirical formulas were then used to generate stoichiometric relationships among system constituents (table 2) that were balanced for all macro-elements (C, H, N, S, P, and O). Several of these reactions (e.g., feed conversion) are actually the sum of dozens of reaction steps but were combined for simplicity and because intermediates were not measured. Although fish excrete ammonia-N, this form of nitrogen was nearly undetectable in the fish tank due to the aerobic conditions in the fish tank (DO > 2.5 mg L-1), leading to rapid nitrification by biofloc bacteria.
| Table 1. Empirical formulas for biological materials utilized in a large pilot-scale, decoupled biofloc aquaponics system located at the E.W. Shell Fisheries Center, Auburn, AL. | |
| Material | Empirical Formula |
| Root | C28.2H43.4N4.4O23.8P0.1 |
| Plant (stems + leaves) | C33H48.4N2.3O16P.07 |
| Cucumber | C27.4H52.9N1.4O18.1P0.1 |
| Mixed Feed | C32.9H54N3.45O9.35P0.28 |
| Tilapia | C35.15H57.68N4.86O1.7P0.58 |
| Sludge | C27.8H53.67N3.62O14.16P0.66 |
While the reaction stoichiometry did not vary in the different seasonal models, the reaction extent was adjusted by season for various processes based on measured data (table 3). This included denitrification, gas production from sludge clarification, and plant growth rate. Distinguishing between water losses due to system leakage and evaporation proved challenging. Fish tank evaporation rates were set to not exceed total calculated water losses for the season but to also achieve a targeted, average concentration of PO4 for each season. Phosphate was used since it does not transform into volatile constituents. Following this, denitrification rates for the fish tank were set to target the average concentration of NO3 within the fish tank during a given season. In other words, N2 was the presumed form of unaccounted nitrogen losses in the system given negligible observed ammonia-N. Volatilization of ammonia-N is the other possible means of gaseous nitrogen loss. The stoichiometry of trace gas emissions (CO2, CH4, N2O) in the fish tank was based on trace gas emissions measurements and feeding rates during the summer period. This stoichiometry was built into the feed conversion stoichiometry and therefore was retained for the other seasons as well. This was suitable because the fish tank had relatively stable GHG emissions across season (Kalvakaalva et al., 2022), likely due to its large water volume and location within the greenhouse.
Development of Clarifier Stoichiometry
The stoichiometry of gases emitted from the clarifiers was modeled as an anaerobic digestion process. This was done because the methane emissions from the clarifier significantly exceeded the measured CO2 emissions (Kalvakaalva et al., 2022). Methane has lower solubility in water compared to CO2, and therefore its production is easier to capture via direct gas emission measurement from the clarifier. Consequently, CO2 was set to account for the remainder of the available carbon lost during sludge mineralization. The molar ratio (65:35) that resulted from this approach reflected a typical balance of CH4 and CO2 in an anaerobic digester (Moestedt et al., 2015). The amount of H2O consumed in this process was set to balance hydrogen in the reaction given that water is a known reactant in anaerobic acetogenesis (Kalyuzhnyi and Davlyatshina, 1997). Nitrous oxide emissions from the clarifier were integrated into the stoichiometry of sludge mineralization to partially balance N in the mineralization reaction. Typically, digesters produce reduced forms of nitrogen as either ammonia-N or nitrogen gas (Percheron et al., 1999). No ammonia-N was detected in the clarifier, so denitrification was assumed to be the predominant reductive pathway, accounting for the remainder of N lost from the clarifier during mineralization. The formation of nitrite or nitrate was not considered in the clarifier given the apparent anaerobic conditions and the fact that levels of these molecules declined in the clarifier. The extent of sludge mineralization and denitrification reactions were adjusted by season to target the average measured CH4 and N2O emissions from the clarifier. These emissions were found to vary considerably among seasons (Kalvakaalva et al., 2022), likely because they were located outdoors.
Development of Plant Stoichiometry
The stoichiometry of cucumber production was straightforward and based on photosynthesis and plant uptake of mineral nutrients. The uptake of nutrients was set to account for the growth and nutrient composition of the fruit, stems and leaves, and roots of the cucumber plants.
Model Assumptions
The model was constructed and run based on the following assumptions: (1) Inputs of feed and water drive all downstream mass flows. (2) A constant feed conversion ratio (FCR) of 1.6 was used throughout the year based on an FCR study carried out in the spring and summer of 2019. (3) A constant elemental formula was assumed for fish, sludge, cucumber fruit, and plant stems/roots/leaves based on the elemental analyses for macro-elements carried out in the spring of 2019. (4) The system operates at quasi steady-state, assuming that the fish tank water volume is constant, and that each week is treated as a steady-state operating period based on feed and water inputs for that week. (5) The fish tank is well mixed through intensive aeration (confirmed through DO measurements at different locations and depths throughout the tank). (6) The following parameters were allowed to vary by season: Growth rate of cucumber plants; water evaporation and evapotranspiration; denitrification extent; and irrigation and water recirculation rates (table 3).
| Table 2. Stoichiometry of aquaponics mass balance (molar basis) for the large pilot-scale, decoupled biofloc aquaponics system located at the E.W. Shell Fisheries Center, Auburn, AL. | ||||||||||||||||
| Process | Feed | Tilapia | Sludge | O2 | Fruit | Stem/ Leaves | Root | NO3 | NO2 | PO4 | CO2 | CH4 | N2O | N2 | H2O | |
| Fish Tank | ||||||||||||||||
| Feed Conversion | -0.1523 | 0.0268 | 0.0385 | -4.12 | 0.252 | 0.0014 | 0.0047 | 3.00 | 0.0003 | 0.0007 | 2.3002 | |||||
| Fish Tank Denitrification | 1.5 | -1 | 0.5 | |||||||||||||
| Clarification | ||||||||||||||||
| Mineralization | -1 | 0.68 | 0.66 | 9.73 | 18.07 | 1.014 E-07 | 1.811 | -9.3 | ||||||||
| Clarifier Denitrification | 0.5 | -1 | 1.00 | |||||||||||||
| Plant House | ||||||||||||||||
| Plant Production | 2.18 | 0.0516 | 0.010 | 0.00119 | -0.1012 | -0.00704 | -1.759 | -1.64 | ||||||||
| NO2 Oxidation | -0.5 | 1 | -1 | |||||||||||||
| Plant Bed Denitrification | 1.5 | -1 | 0.5 | |||||||||||||
| Table 3. Extent of reaction (%)[a] for the different components of the large pilot-scale, decoupled biofloc aquaponics system located at the E.W. Shell Fisheries Center, Auburn AL. | |||||
| Process | Spring | Summer | Fall | Winter | |
| Fish Tank | |||||
| Feed Conversion | 100 | 100 | 100 | 100 | |
| Fish Tank Denitrification[a] | 36.0 | 73.1 | 36.0 | 80.0 | |
| Clarification | |||||
| Mineralization | 0.875 | 1.000 | 2.800 | 0.750 | |
| Clarifier Denitrification | 91.25 | 92.00 | 95.00 | 90.50 | |
| Plant House | |||||
| Plant Production | 41 | 28 | 37 | 40 | |
| NO2 Oxidation | 89.6 | 89.6 | 89.6 | 89.6 | |
| Plant Bed Denitrification | 30.5 | 12.5 | 20.5 | 28.5 | |
[a] Extent of reaction refers to the extent of reaction completion in each unit procedure in the SuperPro Designer model | |||||
Model Assessment
Predicted values were compared with measured weekly data for phosphate and nitrate from the fish tank, clarifier, and post-greenhouse sumps. The root mean squared error (RMSE) and RMSE as a percent of the measured parameter were averaged across all seasons to assess the ability of the model to predict short term changes in phosphate and nitrate. Seasons were defined as Spring (22 March 2019-15 May 2019), Summer (22 May 2019-28 August 2019), Fall (4 September 2019-30 October 2019), and Winter (8 November 2019-7 February 2020) based on when different plant production campaigns were occurring.
Monte Carlo Simulation
To better understand the effects of uncertainty on model inputs, Monte Carlo simulations were carried out using the Crystal Ball package in MS Excel. Excel was then linked to the model in SuperPro Designer using the COM linkage. Specific model inputs included in the simulation were water influx and feeding rate, as these were highly variable from week to week (fig. S1). The input mean and distribution type used in the Monte Carlo simulation were generated from the experimental data collected from the system. Table S1 shows the form of the distribution, mean, and standard deviation used for water and feed inputs to the simulation. Model outputs of particular interest were the soluble nitrate and phosphate levels within different stages of the decoupled aquaponics system.
Results and Discussion
System Production
The system model predicted approximately 455 kg of dry weight tilapia and 175 kg of dry weight cucumbers within the calendar year based on cumulative upstream inputs of feed and water. This compares to a recorded 460 kg of dry weight tilapia and 218 kg of dry weight cucumbers produced within the study period. A greater magnitude of error is expected in downstream processes (e.g., cucumber fruit production) given the potential for error propagation through the model.
Nitrogen Mass Balance
Nitrogen Mineralization and Oxidation
Measured data showed large fluctuations in soluble forms of nitrogen throughout the study period. Nitrate concentrations in the fish tank reached a high of 864 mg L-1 on the first collection date of 3/22/2019 and achieved a low of 123 mg L-1 on 1/22/2020. The average concentration was 420 mg L-1. This decline in nitrate level likely resulted from an increased water flow rate through the system in the fall and winter periods of 2020 (fig. S1). These nitrate levels compare to a peak nitrate concentration observed by Cerozi and Fitzsimmons (2017) (Cerozi and Fitzsimmons, 2017) of ~170 mg L-1 during tilapia production in a coupled aquaponics system. Decouple systems should have higher nutrient concentrations in the fish tank since no recirculation of water occurs after nutrient removal by plants. In the simulation of an optimized decoupled aquaponics system by Dijkgraaf et al. (2019), the fish tank fluctuated between 480 and 800 mg L-1 of nitrate (110-180 mg L-1 NO3-N), which is similar to our observations and model results.
On average, the model showed that 34% of nitrogen entering the system in the feed was converted into nitrate while approximately 21.6% each was integrated into sludge and tilapia (fig. 2). This compares to a range of 19.4%-24.3% for tilapia in a coupled aquaponics system (Hu et al., 2015). Only 2.81% of the nitrogen in the original feed was assimilated into plant biomass, which is higher than the 0.6% observed by Jaeger et al. (Jaeger et al., 2019) but lower than the 15%-17% observed by Hu et al. (Hu et al., 2015). Major losses of nitrogen in the system occurred in the form of N2 gas (19.5%), while 34.3% and 25.2% of the available nitrate in the system escaped via water leakage or was unused after plant production, respectively. Overall, the model had 2.72% of nitrogen unaccounted for within the entire system. These results suggest that the plant production system could be increased significantly in scale given the large fraction of remaining nitrate in the post-plant effluent.
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| Figure 2. Flow of nitrogen through the aquaponics facility based on outputs from the model parametrized with spring season data. All values shown on an N basis. Leakage was due to water leakages from the system. All molecules listed are quantified on an N mass basis. The Sankey diagram was prepared using the SankeyMATIC tool. |
Denitrification
After determining water evaporation rates for each unit procedure, denitrification extent was set to hit target nitrate concentrations averaged for each season. The fish tank was the largest source of modeled N2 gas emissions with average emission rates of 20.4, 0.25, and 2.71 (g N2 kg-1 feed) from the fish tank, clarifier, and plant greenhouse respectively (fig. S2). The largest modeled denitrification rates came during the summer months, which aligns with previous studies which observed a relationship between increased temperature and denitrifying microbial activity (Dawson and Murphy, 1972; Elefsiniotis and Li, 2006). This also aligns with the increased feed and water input during this time period (fig. S1). The modeled 19.5% N loss due to denitrification in the fish tank was considerably lower than the denitrification rate reported in the study of a biofloc recirculating aquaculture system where over 64% of input N was lost to denitrification (Deng et al., 2020). This latter system did not use flow-through nor was it an aquaponics system, depriving it of two potential sinks for nitrate. This distinguishes it from the biofloc aquaponics system in the present study in which nitrate left the system via flow through and, to a lesser extent, plant uptake, thus resulting in a lower percent loss of N due to denitrification. Moreover, the initial fish stocking density used by Deng et al. was over 6-fold higher than that used in our study (22 vs 3.5 kg m-3) and they also fed the system with tapioca starch as a carbon source which can support denitrification.
Phosphorus Mass Balance
Soluble phosphate concentrations in the fish tank reached a high concentration of 52.2 mg L-1 on 9/11/2019 and a low concentration of 13.7 mg L-1 on 10/30/2019. This compares to the soluble phosphate concentrations observed by Cerozi and Fitzsimmons (2017) (Cerozi and Fitzsimmons, 2017) of 4-17 mg L-1 in a couple aquaponics system. Only 13.5% of phosphorus in the feed entering the system was converted into soluble phosphate, while 33% and 50.2% of feed was integrated into tilapia and sludge solids, respectively (fig. 3). This is similar to previous studies which modeled phosphorus mass balance flows within an aquaponics system (Cerozi and Fitzsimmons, 2017). It was also higher than the 19.9% and 43.3% of P assimilated into fish and sediment in a study by Jaeger et al. (Jaeger et al., 2019). The majority of phosphorus exited the system with tilapia and sludge, but additional losses occurred in the form of water leakages (4.51%) and post-plant production effluent (4.17%); 3.74% of phosphorous was unaccounted for in the model. Plants assimilated 2.6% of P in the original feed which is higher than the 0.7% observed by Jaeger et al. (Jaeger et al., 2019). Both of the latter research groups operated recirculating coupled aquaponics systems in contrast to the decoupled biofloc system under investigation in our study. Given phosphorus losses in the post-plant effluent, it is clear that the plant production system was undersized and was therefore not able to fully utilize the phosphate made available from the aquaculture system. High retention of phosphorus in sludge solids also suggests potential for the addition of sludge mineralization operations.
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| Figure 3. Flow of phosphorus through the aquaponics facility based on outputs from the model parametrized with spring season data. All values shown on a P basis. Leakage was due to water leakages from the system. All molecules listed are quantified on a P mass basis. The Sankey diagram was prepared using the SankeyMATIC tool. |
Carbon Mass Balance
The carbon mass balance (fig. 4) was based predominantly on the stoichiometry shown in table 2 and extents of reaction shown in table 3 for the spring season. Of the carbon entering the system with the feed, 17.4% was assimilated by the fish and 19.8% into the sludge biomass with the remainder assumed to mostly form CO2 due to fish and microbial respiration. However, previous work showed that direct CO2 emissions from the system were only 3.4-13.7% of feed carbon (Kalvakaalva et al., 2022). Just under 60% of carbon remained unaccounted for through direct measurement and was assumed to be soluble carbon forms dissolved in the water. Much of this is expected to be dissolved CO2 and bicarbonate due to fish and bacterial respiration. The fish tank pH was maintained at 7 through frequent lime addition and this likely inhibited off-gassing of generated CO2. At this pH, only 17% of dissolved inorganic carbon is expected to be in the form of dissolved CO2/carbonic acid.
Water Balance
Water flow rates through the system were driven by makeup water inputs to the fish tank. This water was then partitioned into evaporation, evapotranspiration, leakage, released sludge, recirculation, and irrigation (fig. 5). The partitioning coefficients were adjusted for each season. Evaporation rates accounted for the greatest water losses in all seasons except for the spring and were highest during the summer and fall months. This is consistent with management practices during hotter months, when greenhouse temperatures were regulated by ventilation fans. Moreover, fall is the driest season in Auburn, AL (Beck et al., 2018), with lower relative humidity driving additional water losses from the system. Water leakage from the system was considerable, with visible leakage from the tank in the late summer and early fall. Repairs were made to the fish tank liner during a temporary suspension of operation during the fall. This explains the reduction in modeled leakage between the fall and winter seasons.
 |
| Figure 4. Flow of carbon through the aquaponics facility based on outputs from the model parametrized with spring season data. All values are shown on a C basis. Leakage was due to water leakages from the system. Dissolved carbon includes both dissolved inorganic and organic fractions. All molecules listed are quantified on a C mass basis. The Sankey diagram was prepared using the SankeyMATIC tool. |
Modeled irrigation rates closely followed measured values (fig. 5). Over the entire modeled period, the model showed a root-mean square and percent error of 18.02 L hr-1 and 33.38%, respectively. The percent error was calculated per equation 1.
 |
| Figure 6. Nitrate (as NO3-) concentrations in the three main unit processes of the aquaponics system: fish tank (A), clarifier (B), and plant production (C). |
(1)
The increased irrigation rates in the late summer and fall reflect intensive campaigns of cucumber production during those periods.
Redictive Capability of Mass Balance Model
Although this mass balance model lacked reaction kinetics, we tested its ability to predict nitrate and phosphate concentrations in each of the major unit procedures of the aquaponics system. Nitrate and phosphate are arguably the most important macronutrients for plant production in aquaponics systems. Modeled values for nitrate followed the general trends observed in the measured values over time, but with some deviation during certain seasons (fig. 6). The largest differences occurred within the spring season and the smallest within the winter season. This could be explained by the highly variable system operation during the spring period, when water flow rates and feeding rates were rapidly ramped up as part of an intensive production campaign. This rapid ramp-up briefly destabilized the biofloc system’s nitrifying bacteria, as evinced by a sharp spike in nitrite formation (fig. S3). The weekly steady-state assumption was likely violated during this period due to the rapid pace of operational change. Over the entire modeled period, the modeled nitrate concentrations had root-mean square errors and percent errors (per eq. 1) of 275 mg L-1 (62.2%), 285 mg L-1 (70.1%), and 188 mg L-1 (63.1%) for the fish tank, clarifier, and post-plant production, respectively.
Measured soluble phosphate concentrations followed similar trends as measured nitrate concentrations, with generally
lower concentrations in the winter months when feeding rates
 |
| Figure 7. Soluble phosphate concentrations in the three main unit processes of the aquaponics system: fish tank (A), clarifier (B), and plant production (C). |
slowed and water input increased. The latter was partly due to water replacement after the completion of repairs on the fish tank. Modeled values for soluble phosphate followed broad trends in the measured values but with a noticeable deviation in the fall season (fig. 7). Over the entire year, modeled phosphate exhibited root-mean square error and percent errors of 16.9 mg L-1 (55.1%), 17.8 mg L-1 (57.7%), and 16.3 (63.3%) for the fish tank, clarifier, and post-plant production, respectively. The largest differences came within the fall season, as the model was not able to achieve the observed soluble phosphate concentrations without violating the assumption of constant tank volume. This could be the product of a change in the base elemental composition of biological materials (e.g., sludge) or a change in phosphorus stoichiometry (Guillen-Jimenez et al., 2000; Mesplé et al., 1995, 1996). In this study, stoichiometry was determined based on material composition analyses carried out during the spring of 2019 and was assumed to not vary over the study period. Moreover, tank water volume was not constant throughout the study period despite efforts to maintain a set volume. Changes in relative humidity (and therefore evaporation), leakages, and occasional operational challenges impacted our ability to sustain a constant tank volume, particularly during the fall phase of the study. Because fish mass and feeding were maintained in a smaller tank volume during the fall, this should result in higher measured nutrient concentrations than what the model predicted based on a constant tank volume.
Limitations
Based on the results of the model, there are some limitations in its use. While the model matches well to the observed nitrate and phosphate levels on a seasonal basis, the high week-to-week deviation of nitrate and phosphate levels demonstrates the limitation of this non-kinetic modeling approach. A true kinetic model based on rate-limiting nutrients would be necessary if the goal is to predict nitrate levels more accurately on a weekly rather than seasonal basis. Doing so would make the model more similar to the well-known Activated Sludge Model (Gujer et al., 1999) used for wastewater treatment.
 |
| Figure 8. Nitrate and phosphate levels predicted by Monte Carlo simulations and measured in the aquaponics system. Distribution of nitrate levels in the fish tank (A), clarifier (B), and plant effluent (C). Distribution of phosphate levels in the fish tank (D), clarifier (E), and plant effluent (F). |
The quasi-steady state operation assumption on a weekly basis also led to significant error during periods of rapid system change (an example was production ramp-up in the spring season). The model fails to capture the “memory” of the system beyond a 1-week timeframe and therefore works best when week-to-week changes are gradual. Again, incorporation of reaction kinetics into the model would help overcome this problem but would require an extensive series of controlled experiments in the aquaponics system, which is challenging in a system that is used for production. Conducting rate-limiting experiments using vertebrate animal systems like fish is also likely to present ethical problems. This may explain why several other aquaponic studies that do incorporate kinetics take a simulation approach (Dijkgraaf et al., 2019; Goddek and Körner, 2019). Because of these limitations, we recommend the use of this model only for the prediction of long-term trends rather than the short-term effects of sudden operational changes.
The model was also unable to accurately predict weekly greenhouse gas emissions from the system in relation to measured greenhouse gas data due to the multitude of parameters that affect emission rates (Czepiel et al., 1995; Dijkstra et al., 2012; Kalvakaalva et al., 2022; Marble et al., 2012). Thus, the model in this case was only used to predict the average release of CO2, CH4, and N2O emissions by season. Despite its limitations, the model was able to capture macro-level trends in system mass flow across four seasons and significant operational changes within each season. The latter included large changes in the scale of fish production and multiple cucumber production campaigns. Thus, the model is likely to be useful in making long-term operational decisions and conducting scenario analyses for life cycle assessment.
Uncertainty Analysis
Given the high time course variability of model inputs such as feed and water (Kalvakaalva et al., 2022), we ran a Monte Carlo simulation to better understand the global effects of this variability. The soluble nitrate and phosphate concentrations in the fish tank, plant irrigation water, and plant effluent were compiled from these model runs and used to generate histograms (fig. 8). Histograms of experimental data from one year of system operation were overlaid on top of the simulation data and generally show a good match to the simulation outputs from the model. On several occasions, the measured nitrate levels in the fish tank and clarifier on several occasions fell in the low probability region of the histogram from the simulation. These specific data points were obtained during the early spring season, when feeding was rapidly ramped up. The simulation shows such high nitrate concentrations to be low-probability events, and they likely would be in stable commercial (non-research) production systems. These results show that the model can be an effective tool for conducting simulations.
Conclusions
A mass balance process model was developed for a decoupled biofloc aquaponics system using data collected over the course of one year of operation. The model showed that 21.6% of input nitrogen was assimilated by tilapia and only 2.8% by plants, while 33% of input phosphorus was assimilated by tilapia and 2.6% by plants. The above values are comparable to observations of others in the literature but also suggest significant room for improvement regarding nutrient utilization, particularly by increasing the scale of the plant production system to better utilize nutrients available from the aquaculture system. Sludge mineralization operations could also make more nutrients available to plants. The average measured and modeled nitrate concentrations in the fish tank over the 1-year period were 442 mg L-1 and 440 mg L-1, respectively. The average measured and modeled phosphate concentrations in the fish tank over the 1-year period were 30 mg L-1 and 25 mg L-1, respectively. These concentrations of nitrate and phosphate compare closely to past simulations of nitrogen and phosphorus in decoupled aquaponics systems. The model was effective for simulating long-term effects associated with altering feed and water inputs but was not effective at predicting the short-term transient response of the system.
Supplemental Material
The supplemental materials mentioned in this article are available for download from the ASABE Figshare repository at: https://doi.org/10.13031/22788446.v1
Acknowledgments
The authors are indebted to Barry G. Dorman and Robert Icenogle for technical assistance with constructing the greenhouse gas sampling system and to Gary Foster for conducting the gas chromatograph analysis of all gas samples at the USDA-ARS National Soil Dynamics Laboratory. We are also thankful for technical assistance from Jeremiah D. Davis and for the support from the members of the Auburn aquaponics team: Nicholas Burgess, Jenny Dorick, Kyle Hensarling, Josh Marcus, Ana Gabriela Itokazu Canzian da Silva, Andrew Palmer, Allen Patillo, and Nathan Wallace-Springer. Financial support for this research was provided by the National Institute of Food and Agriculture and the Alabama Agricultural Experiment Station (ALA0HIGGINS and ALA016-1-16002).
Nomenclature
DO = Dissolved oxygen
FCR = Feed conversion ratio
GHG = Greenhouse gas
LCA = Life cycle assessment
ICP-OES = Inductively coupled plasma-optical emissions spectroscopy
RAS = Recirculating aquaculture system
RMSE = Root mean squared error
References
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Dawson, R. N., & Murphy, K. L. (1972). The temperature dependency of biological denitrification. Water Res., 6(1), 71-83. doi:https://doi.org/10.1016/0043-1354(72)90174-1
Deng, M., Li, L., Dai, Z., Senbati, Y., Song, K., & He, X. (2020). Aerobic denitrification affects gaseous nitrogen loss in biofloc-based recirculating aquaculture system. Aquaculture, 529, 735686. doi:https://doi.org/10.1016/j.aquaculture.2020.735686
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FAO, IFAD, UNICEF, WFP & WHO. (2018). The state of food security and nutrition in the world 2018: Building climate resilience for food security and nutrition. Rome, Italy: United Nations FAO.
Goddek, S., & Körner, O. (2019). A fully integrated simulation model of multi-loop aquaponics: A case study for system sizing in different environments. Agric. Syst., 171, 143-154. doi:https://doi.org/10.1016/j.agsy.2019.01.010
Guillen-Jimenez, E., Alvarez-Mateos, P., Romero-Guzman, F., & Pereda-Marin, J. (2000). Bio-mineralization of organic matter in dairy wastewater, as affected by pH. The evolution of ammonium and phosphates. Water Res., 34(4), 1215-1224. doi:https://doi.org/10.1016/S0043-1354(99)00242-0
Gujer, W., Henze, M., Mino, T., & van Loosdrecht, M. (1999). Activated sludge model no. 3. Water Sci. Technol., 39(1), 183-193. doi:https://doi.org/10.2166/wst.1999.0039
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He, J., Zhou, L., Yao, Q., Liu, B., Xu, H., & Huang, J. (2018). Greenhouse and field-based studies on the distribution of dimethoate in cotton and its effect on Tetranychus urticae by drip irrigation. Pest Manag. Sci., 74(1), 225-233. doi:https://doi.org/10.1002/ps.4704
Hu, Z., Lee, J. W., Chandran, K., Kim, S., Brotto, A. C., & Khanal, S. K. (2015). Effect of plant species on nitrogen recovery in aquaponics. Bioresour. Technol., 188, 92-98. doi:https://doi.org/10.1016/j.biortech.2015.01.013
Jaeger, C., Foucard, P., Tocqueville, A., Nahon, S., & Aubin, J. (2019). Mass balanced based LCA of a common carp-lettuce aquaponics system. Aquacult. Eng., 84, 29-41. doi:https://doi.org/10.1016/j.aquaeng.2018.11.003
Kalvakaalva, R., Prior, S. A., Smith, M., Runion, G. B., Ayipio, E., Blanchard, C., . . . Higgins, B. T. (2022). Direct greenhouse gas emissions from a pilot-scale aquaponics system. J. ASABE, 65(6), 1211-1223. doi:https://doi.org/10.13031/ja.15215
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