This paper presents a mixed-integer nonlinear programming (MINLP) model for the optimal design of mechanical counter-flow cooling towers, subjected to standard design constraints. The objective function consists of the minimization of the total annual cost, which includes the capital cost of the cooling tower (that depends on the filling material and the air flowrate) and the operating cost (that includes the costs for the water makeup and for the power consumed by the tower fan). Merkel's method is used to set the dimensions of the tower, and empirical correlations are used to estimate mass transfer coefficients for the packed section of the tower. The design variables to be optimized are the water-to-air flow ratio, the water flow rate, the water inlet and outlet temperatures, the operating temperature approach, the type of packing, the type of draft, the volume of packing material, the total pressure drop due to the air flow rate, the fan power, and the water consumption.

The MINLP model was solved with the GAMS software package using the DICOPT solver. The performance of the proposed model is shown with six examples. From the results of the examples, it can be observed that cooling towers with low temperature approaches are not suitable because driving forces become a limiting factor. On the other hand, dry-bulb temperature variations have a negligible effect on the tower size. From the set of design parameters analyzed, the temperature approach is shown to be a critical factor for the optimal design of cooling towers.