The gas-solid cyclone has been remarkably widely used among all types of industrial gas-cleaning devices. The objective of this work was to present the nonlinear optimization modeling of series and parallel cyclone arrangement for 1D3D, 2D2D and 1D2D cyclones of the Nitrogen, Phosphorus, and Potassium (NPK) fertilizer plant. The numerical solutions were carried out using the General Algebraic Modeling System (GAMS) software for different case studies. The optimal number of cyclone with the minimum total cost for two types of arrangements was obtained. From the economic point of view, the results of mathematical programming models showed that the small cyclone with a small number of the cyclone arrangement could be implemented for space-limited conditions on the field, and the pressure drop across the cyclone was directly related to the fan power requirement.
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