A MODEL OF NUTRIENT FLOW IN AN AQUAPONICS SYSTEM USING DIFFUSION-ADVECTION-REACTION EQUATIONS

Posted by Jeremy Winsor on 7/12/2017

A MODEL OF NUTRIENT FLOW IN AN AQUAPONICS SYSTEM USING DIFFUSION-ADVECTION-REACTION EQUATIONS

Aquaponics is a combination of hydroponics (growing plants in a soilless environment) and aquaculture (raising fish in a tank). As a byproduct of respiration, fish excrete toxic ammonia from their gills. In an aquaponics system, the water in the fish tank is pumped to beds where plants are grown in a soilless medium. Nitrifying bacteria colonize in the medium, and convert ammonia to nitrite and then nitrate. The plants can readily absorb the nitrate as a vital nutrient, and the water, which is now free of the toxic ammonia and nitrite, is pumped back to the fish tank. In this paper, we will attempt to simulate nutrient flow in an aquaponics system with a two-dimensional model. For each of the three substances of interest: ammonia, nitrite, and nitrate; a diffusion-advection-reaction equation will be used to determine its concentration within the fish tank and plant bed as a function of time and space. Model parameters will be estimated based on empirical evidence, and we will discuss possible numerical methods that could be used to solve the equations in our model.

Mathematical Model for Nutrients in Aquaponics Article