A model is presented for the Na+ and K+ levels in the irrigation water of greenhouses, specifically those for the cultivation of tomato. The model, essentially based on mass balances, not only describes the accumulation of Na+ but includes a membrane unit for the selective removal of Na+ as well. As determined by the membrane properties, some of the K+ is removed as well. Based on real-life process parameters, the model calculates the Na+ and K+ concentration at three reference points. These process parameters include the evapotranspiration rate, the K+ uptake by the plants, the Na+ and K+ content of the fertilizer, the Na+ leaching out from the hydroponic substrate material, and the Na+ and K+ removal efficiency of the membrane unit. Using these parameters and given a constant K+ concentration of the irrigation water entering the greenhouse of 6.6 mM (resulting in the optimal K+ concentration for tomato cultivation), the composition of the solution is completely defined at all three reference points per irrigation cycle. Prime aim of this investigation is to explore the requirements for the selective membrane that currently is developed in our lab. It is found that even for a limited Na+ over K+ selectivity of 6, after a number of cycles the Na+ level reaches steady state at a level below the upper (toxic) threshold for tomato cultivation (20 mM). Economic aspects and ways of implementation of such a system are briefly discussed.
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