Modelling and identification of water and nutrient balances in aquaponics

Research output: Thesisinternal PhD, WU


This thesis presents the development of mathematical models of water and nutrient balances in aquaponic systems, aimed at improving our understanding of this production method towards an efficient use of resources.

Our current food production systems have large social and environmental impacts, which are commonly externalized in the context of industrial production and global trade. Aquaponics is an option for sustainable food production that combines aquatic species (aquaculture) with soilless plants (hydroponics). The main challenge in aquaponics consists of balancing optimal conditions for multiple species: aquatic organisms, plants and beneficial micro-organisms. To facilitate achieving this balance, decoupled aquaponic systems have been proposed, consisting of two separate recirculating water loops. In this way, the production loop for fish operates independently from the production loop for plants, each with their own optimal conditions. Nutrient-rich water from the fish loop can be supplied to the plants continuously or at selected times, reducing fertilizer requirements. Similarly, water from the plants loop can be recovered and supplied to the fish, reducing fresh water demand.

Managing water and nutrient exchange in aquaponic systems requires continuous information about the concentrations of chemical elements (nutrients). Some nutrients, like nitrogen and phosphorus, are excreted in abundance by fish and can be used by plants. Other nutrients, like calcium and sodium, are also present in fish water, but they can easily reach harmful levels for plants. Sensors to continuously monitor these concentrations are costly and thus uncommon in commercial applications. Therefore, mathematical models combined with available measurements (semi-physical models), are suitable to support management and control of aquaponic systems.

Mathematical models for aquaculture and hydroponic systems are widely available in literature. However, they do not describe the dynamics of nutrients. Furthermore, measurements of nutrients in the components of aquaponic systems are not always available and typically show large uncertainties.

In this context, further elaborated in Chapter 1 - General introduction, the objective of this thesis was to investigate the dynamics of water and nutrient balances in decoupled aquaponic systems and their uncertainties. The research questions formulated for this purpose aim at identifying the main challenges and opportunities in closing water and nutrient cycles, and in modelling nutrient balances under uncertainties. Chapters 2 and 3 present system-level studies. Chapters 4 and 5 focus on mathematical modelling under uncertainty, applied to biological production systems.

Chapter 2 presents a model-based study coupling a recirculating aquaculture system (RAS) for tilapia with a nutrient film technique (NFT) hydroponic system for tomato. The simulation results show that fish can provide 26% of the nitrogen requirements for plants. Furthermore, it is shown that variations in nitrate concentrations in the fish loop, can be decreased by 35%, using a water management strategy that sends water from fish to plants based on amounts proportional to the fish feed.

Chapter 3 presents a model-based study supported by a demonstration aquaponic system in Abtshagen, Germany. The model helped identifying imbalances in the system design. It predicted excess concentrations of total suspended solids (TSS) for fish, and excess sodium, calcium, magnesium, and ammonium for plants. The model was used to develop an improved management strategy, preventing excess TSS, sodium, and ammonium, decreasing fertilizer requirements, and achieving water efficiencies similar to commercial aquaculture and hydroponic systems.

Chapter 4 presents an algorithm proposed for the calibration of mathematical models applied to biological production systems. The algorithm is based on the set-membership approach, which is a suitable alternative to statistical methods in the presence of limited and uncertain experimental data. The algorithm uses Voronoi tessellation, a novel method that characterises the feasible parameter space with (hyper)spheres, quantifying deviations from experimental data.

Chapter 5 studied the dynamics and uncertainties fish growth and excretion of macronutrients. A model was developed and calibrated using the Voronoi set-membership algorithm. Uncertainty propagation was assessed using Monte Carlo simulations. The model prediction explained 84% of the literature data variability for fish growth, 75% for digestive system content, and 28% for ammonia excretion rate. The uncertainty assessment helped identifying suitable experimental conditions for future research.

Chapter 6 - General discussion, reflects on the research questions, explaining the limitations identified in each research chapter, and suggestions for future research.

From a system design perspective, closing water and nutrient cycles requires a comprehensive quantitative analysis, using indicators that reflect the trade-offs occurring when trying to balancing optimal conditions between the fish and plant loops. A list of suggested indicators for future research is provided. From a system operation perspective, several specific problems and proposed solutions were identified. Solids should be removed from fish water by combining mechanical filtration and sedimentation, to better regulate water exchange from fish to plants, and to stabilize nutrient concentrations for plants. Water storage between fish and plant loops should be aerated to prevent nitrogen loss via denitrification. Fish feed should be selected based on the mineral concentrations in local fresh water, to prevent excess of nutrients harmful for plants, which decrease the potential for nutrient reuse.

There is high multidisciplinarity involved in model development of aquaponic systems. Studies with a gradual increase in complexity are thus suggested. Future research on nutrient balances, for example, could consider the chemical form of nutrients and their bioavailability for fish and plants. Mathematical models of aquaponic systems and their components should consider simultaneously multiple variables with multiple time scales.

The discussion is extended to the more general field of modelling biological production systems, providing a framework for the development of mathematical models under uncertainty, combining set-membership calibration with uncertainty propagation assessment, to identify critical variables for future experimental measurements.

Finally, the discussion is brought back to the general socio-economic context. It is suggested to investigate whether the risks of aquaponics are most sensitive to the fish production loop. If that is the case, financial incentives for production should focus on the expansion of existing aquaculture farms to include hydroponic production. Furthermore, it is necessary to improve communication between researchers and producers.

Original languageEnglish
QualificationDoctor of Philosophy
Awarding Institution
  • Wageningen University
  • Keesman, Karel, Promotor
  • Rijnaarts, Huub, Co-promotor
  • Cappon, Hans, Co-promotor
Award date7 Sept 2021
Place of PublicationWageningen
Print ISBNs9789463958516
Publication statusPublished - 2021


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