Nutrient Uptake Kinetics in Hydroponic Systems
By: Octavio Gonzalez-Lugo
Tags: Mathematics, STEM, Sustainability, Analytics

Photo by Max on Unsplash

Crop nutrition is one of the most important aspects of a direct nutrition system such as the NFT hydroponic system. As there are no other sources of nutrients for the crops the nutrient solution must be monitored regularly. Conductivity and pH are the most widely used measurements used to assess the state of the nutrient solution. Although those measurements can provide information about the state of the nutrient solution, both measurements provide little information about the state of each component in the nutrient solution. The following exemplifies how to model the change in the nutrient solution composition over a hydroponic system.

Once the nutrient solution is in contact with the roots, the large surface area of the roots is used to maximize the nutrient uptake. Over the roots surface area are several transporters that take a particular nutrient from the environment to the root cell cytoplasm. Although the exact mechanism of how each nutrient is transported from the root zone environment (refers to the area that surrounds the root, soil for traditional system or nutrient solution for a hydroponic system) to the root cell cytoplasm is quite complex the key aspect that needs to be understood is that the majority of that transport is done by different proteins. If energy is used to relocate a nutrient molecule is known as active transport whereas when no energy is used is called passive transport. In each case, the nutrient uptake follows nonlinear uptake kinetics equal to a Michaelis-Menten reaction kinetics.

As the nutrient solution is the only resource available for the crops to grow many difficulties involved in nutrient uptake are removed. Some of those difficulties being the diffusion from soil to the root environment and the spatial availability of such nutrients. In a hydroponic system, the nutrients are readily available for the crop to take. Also, the content of the nutrient solution is known by the farmer as is the one that makes it, and often its the one that formulates and optimizes the nutrient solution. To model the nutrient uptake a standard commercial formulation with the most important nutrients is used as initial conditions of the model. Also, as the different uptake parameters of the nutrients are not available a change under different growing systems a simple assumption will be made, those nutrients in a higher quantity have a higher uptake rate. And only seven components of the nutrient solution will be considered for this model those are: “NO3”, “NH4”, “K”, “PO4”, “SO4”, “Ca”, “Mg”. Taking all of the above into account, the model can be defined with:

Control variables are different values that can be changed during the operation of the hydroponic system. In this model, the feeding and discharging rates are two control variables that can be modified and evaluate the effect on the nutrient solution. Under a high Feeding rate or a high discharging rate appears to not affect crop nutrition. In both cases, the total amount of nutrients in the solution is depleted around the same time. The trajectory followed by the pair NH4 and K shows a little deviation from a linear trend at low NH4 content. While the pair NO3 and Ca shows a complete non-linear behavior trough the entire process, especially at low NO3 content.