By managing the fertilizer supplementation and adjustable combination of fresh water intake and discharge of HPS water the solution can be kept within plant specific ranges . Transpiration of the crops is the main driver of water transfer between RAS and HPS, as the water level in the HPS is kept constant. Given the fact that also the amount of water in the RAS is kept constant, the variation in transpiration results in a varying freshwater intake in the RAS. In addition to the three basic elements, as shown in Figure 1, a reverse osmosis filtration system can be implemented to further increase the difference in nutrient concentration between the RAS and HPS . As a result of the filtration process, a nutrient-rich brine is added to the HPS, while the remaining water with largely reduced nutrient concentrations is fed back to the RAS. In this study, the system has a fixed hourly flow but is deactivated when either the nitrate or phosphorus concentration in the HPS nears its upper limit, to prevent the need for dilution. The RO filtration system was not used in most of the scenarios in this study and it is specifically stated in which cases it was used. Limited seasonal variation solar radiation climate was found to be beneficial for a balanced and efficient aquaponics system by Goddek & Körner . In seasonally varied climates, a mismatch can arise between the stable nutrient flow from the RAS to the HPS and the varied nutrient demand of the HPS . Two additional strategies were tested to achieve the benefits of stable climates, using water-buffering tanks as shown in Figure 2. Both options aim to better match the supply and demand of nutrients in the HPS throughout the year.For ease of access, the model created in this study was implemented in Microsoft Excel TM and consists of various sub-models, as shown in Figure 3.
While discussed only briefly in the following sections, each is described in detail in Supplementary Materials SM 1. For more advanced aquaponics model implementations we refer to Karimanzira et al and Reyes Lastiri et al . For clarity in categorizing parameters and performance indicators, a distinction was made between the aquaponics system and the greenhouse system . Unless stated otherwise, potted blueberries the parameter values used in this study are presented in Appendix 1. Figure 3. The four sub-models of the aquaponics model and the dynamic variables that are exchanged between them. As the nutrient solution is kept within suitable bounds for the crop, it is assumed that the Water & nutrients sub-model has no further influence on the Plants sub-model. The balance equations of the four sub-models are solved numerically using the Euler forward method. A time-step of one day was found to be sufficiently accurate for the Fish production and Water & Nutrients submodels as variation in the nutrient concentration throughout the day was not considered in this study. For the Greenhouse climate and Plants sub-models, five minutes was chosen as the smallest acceptable time step in terms of computational requirements. The growth of fish in the rearing tanks is calculated using the equations from Timmons & Ebeling , as implemented by Dijkgraaf et al. . Assuming the growing environment is optimal, in terms of e.g. pH, dissolved oxygen and fish feed, the weight gain of the fish is calculated using only water temperature and several fish-specific parameters. Besides being used to calculate the fish yield, the sub-model is used to determine the feed requirements throughout the production cycle. For this, a feed conversion rate is used, which describes the ratio between feed uptake and weight gain, as explained by Dijkgraaf et al. . Staggered production of fish provides a smoother nutrient supply . As this study specifically estimates the performance over one year of operation, the start-up phase of the RAS is omitted. The Water & Nutrients sub-model calculates the flows of nutrients and water throughout the system. It is based on the work of Dijkgraaf et al. , with several corrections . The model considers nitrogen and phosphorus, for their importance in crop growth and dynamics of RAS and AD. Potassium was not considered as it makes up an insufficient fraction of the fish feed to influence the system .
In the HPS, represented by the sub-models Greenhouse climate and Plants, the concentrations of N and P were determined by the incoming flow and the nutrient uptake of the crops. Given the very complex process of nutrient uptake by plants and given the overall aim of the study to study the operation and design of a full aquaponics system, the basic assumption that the nutrient uptake by the crops is equal to the product of the crop transpiration and nutrient concentration, as in the studies of , was made. Nutrient supplementation or dilution of the HPS water was used to keep the concentrations within the suitable range for the crop. The ranges used in this study are 140 – 180 mg/L nitrate and 40 – 60 mg/L phosphate , following Resh . The main function of the Plants sub-model is to use data from the greenhouse climate to determine the transpiration of the crop, according to Stanghellini and de Jong and . Crop transpiration depends on plant-specific parameters and environment variables. In this study, the growth of the crops was not affffected by the Water & Nutrients or Fish production sub-model, as nutrient concentrations were kept within optimal bounds. In the Greenhouse climate sub-model, the temperature, humidity and light inside the greenhouse are simulated, representing the growing environment of the crops. The greenhouse climate is described by physics based, dynamic balance equations for uniform temperature and absolute humidity of the greenhouse, as done by Van Beveren et al. , see Supplementary Materials SM 1. All variables and parameters are also explained in SM 1. While the model created for this study is of relatively low complexity, the outcomes fifit within those found in the literature, as shown in Supplementary Materials SM 1.5. To ensure a suitable temperature and humidity for the crops, management and control strategies have been modelled, as well. For instance, the energy screen is deployed when solar radiation is below a threshold, as described in Kempkes & Janse . The shade screen is deployed when solar radiation exceeds a maximum or when outside temperatures are close to the maximum allowed greenhouse temperature. Artificial lighting, if used, is activated between 8 am and 8 pm if solar radiation is below a threshold and is disabled from May to October to save energy. Temperature and humidity are controlled based on the energy and vapor fluxes of the greenhouse in four steps, as displayed in Supplementary Materials SM 1.The total transpiration of the greenhouse is directly proportional to the HPS floor area. As it is assumed that nutrient uptake is proportional to the crop transpiration and the concentrations in the nutrient solution, an increase in the HPS area will increase the nutrient demand.
In general, a system with a high HPS area will require nutrient supplementation, while dilution is required for a smaller HPS, as is shown in Figure 4. While nutrients can be supplemented individually, dilution results in the loss of all nutrients in the diluted volume. At a low HPS area, the dilution resulting from one nutrient may lead to the need to increase supplementation of the other, as is the case for N with an HPS area smaller than 1500 m2. The chosen irrigation technique determines the volume of water in the HPS. While nutrient supply and demand are initially unchanged by this, the buffering capacity of high-volume systems can prevent shocks in the nutrient concentrations. Overall, a larger volume results in an increase in performance, as shown in Figure 5, with most benefits for medium and large-sized HPS areas . The discontinuity at around an HPS area of 2700 m2 for DWC is a result of the absence of any need for dilution. The remaining inefficiency is due to fixed losses from the nutrients in the waste sludge of the digester. The ratio between the phosphorus and nitrogen content in the fish feed is an important factor in balancing the nutrient supply to the crop demand. Determining the optimal ratio is complicated by the different ways through which N and P are supplied to the HPS. Most of the nitrogen flow is directly from the RAS and is linked to the transpiration rate, which varies greatly throughout the season. Phosphorus, on the other hand, mainly enters the HPS through digester effluent , with only a slight oscillation resulting from the staggered fish production . With the reference settings, the ratio between the nutrients was optimal for a low P content between 0.65% and 0.8%. However, this could be insufficient for proper fish growth. While Sugiura et al. reported no difference in the growth of tilapia between 1% and 1.4%, a decrease of 28% in overall growth was found for a P content of 0.5% by Eding et al. . The reverse osmosis system results in an additional transfer of nutrients from the RAS to the HPS, square plastic pot which also lowers the nitrate concentration in the RAS. Besides increasing the HPS area, adding RO is practically the only way of reducing NO3 in the RAS, which is especially important for more sensitive fish species. The RO system was temporarily disabled when the concentration of either N or P in the HPS was at 95% of their respective maximum, as it could otherwise result directly in dilution. This puts a limit on the desalination flow and decreased additional benefits at higher flow capacities, especially for smaller HPS areas. As the N content in the RAS and HPS are closely linked, the RO system is mainly able to transfer nutrients when demand is low, resulting in only a minor increase in performance. When demand is high in summer, the low nutrient concentrations of the RAS results in only a small additional transfer from the RO.
As shown in Figure 3, the Greenhouse climate and Plant sub-models can only influence the AP system through the transpiration rate. A large variation in crop transpiration can result in a mismatch between the relatively constant supply of nutrients and the transpiration-dependent demand. This large variation can also lead to the requirement of both supplementation and dilution of a nutrient within the same year, as is also more likely in the low-volume NFT system. The same effects of variation can be seen for the nitrate concentration in the RAS. While low variation results in lower peaks in the cold months, the higher concentration in summer also means that more nitrate is transferred to the HPS, lowering supplementation requirements.The objective of this research was to investigate and demonstrate the effect of changes in various physical and operational parameters on an on-demand coupled aquaponics system with anaerobic digester and potential use of RO filtration system. The research focused on changes that could result in energy savings, as it is one of the crucial aspects of sustainable food production in northern latitudes. While there are studies that compare the system performance at different locations, the specific influence of physical and operational parameters was not yet investigated for aquaponics systems.Goddek & Körner suggested that a plant production system with a constant nutrient demand , would result in a balanced system with better performance. This observation resulted in our hypothesized correlation between the variation in transpiration and the performance of the AP system. It has been found that the coefficient of variation of the transpiration rate, as representative for the different scenarios , was an appropriate factor that highly correlates with the chosen KPIs of the AP system , given that the HPS area is resized as shown in Appendix 3. This strong correlation also holds for the average KPI, as was demonstrated in Figure 10. While increasing variation generally results in decreasing efficiency, the sensitivity to it was not the same for different settings of the aquaponics system.