Optimization of mechanical draft counter flow wet-cooling towers using a rigorous model Eusiel Rubio-Castro a , Medardo Serna-González a, * , José María Ponce-Ortega a , Miguel Angel Morales-Cabrera b a Chemical Engineering Department, Universidad Michoacana de San Nicolás de Hidalgo, Ciudad Universitaria, Edificio V1, Morelia, Michoacán 58060, Mexico b Chemical Engineering Department, Universidad Veracruzana, Poza Rica, Veracruz, Mexico article info Article history: Received 26 April 2011 Accepted 17 July 2011 Available online 22 July 2011 Keywords: Counter flow cooling towers Poppe method Merkel method Rigorous optimization abstract In this paper, an optimal design algorithm for mechanical draft counter flow wet-cooling towers based on the rigorous Poppe model and mixed-integer nonlinear programming (MINLP) is presented. Unlike the widely used Merkel method, the Poppe model takes into consideration the effects of the water loss by evaporation and the nonunity of the Lewis factor. As a result, the Poppe model is able to predict the performance of wet-cooling towers very accurately compared to the Merkel method. The optimization problem is formulated as an MINLP model by considering all the mass and energy balances, equations for physical properties, and empirical correlations for the loss and overall mass transfer coefficients in the packing region of the tower, in addition to feasibility constraints. The objective function to be minimized is the total annual cost, which includes capital and operating costs. The mathematical programming problem is solved with the GAMS software. Six case studies are used to show the application of the proposed algorithm. The case studies demonstrate that there can be large differences between the optimal designs based on the Poppe method and the Merkel method. Ó 2011 Elsevier Ltd. All rights reserved. 1. Introduction Along to the industrial history, the process engineers have looked for strategies and methodologies to minimize the process costs and to increase the profits. In this area, the mass [1] and thermal water integration [2,3] have represented an important role. Regarding to the thermal water integration, several strategies have been reported around the open re-circulating cooling water systems, because they are widely used to dissipate the low-grade heat of chemical and petrochemical process industries, electric- power generating stations, refrigeration and air conditioning plants. In all these systems, water is used to cool down the hot process streams, and then this water is cooled by evaporation and direct contact with air in a wet-cooling tower and recycled to the cooling network. Therefore, the cooling towers are very important industrial components and there are many references that present the fundamentals to understand these units [4e6]. The first practical theory of counter flow cooling towers was developed by Merkel [7]. In this theory, the water loss due to evaporation and the water-film heat-transfer resistance are neglected. In addition, a Lewis factor for moist air of unity is assumed. These assumptions allow the differential equations of the rigorous model for simultaneous heat and mass transfer processes occurring in cooling towers to be reduced to a single separable differential equation in terms of air enthalpy difference as the driving force. This method gives only the exit temperature of the water stream and the exit enthalpy of the air stream when it is provided with the inlet air and water conditions. In order to obtain the temperature and humidity of the outlet air, Merkel assumed that the air leaving the cooling tower is saturated with water vapor [6]. It is possible to extend Merkel’s enthalpy theory to include a finite liquid-side film resistance to heat transfer [8e12]. For typical operating conditions, however, the local bulk temperature of the water is seldom more than 0.3 K above the temperature of the air at the airewater interface [4]. Therefore, for the purpose of cooling-tower analysis it is safe to neglect the water-film resistance [4,5]. Over the years there have been a number of contributions on the literature for cooling towers that are based upon this assump- tion. Jaber and Webb [13] developed an effectiveness-number of transfer units (e-NTU) approach by utilizing the assumption of a linearized air saturation enthalpy. The effect of nonlinearity of the * Corresponding author. Tel.: þ52 443 3273584. E-mail address: mserna@umich.mx (M. Serna-González). Contents lists available at ScienceDirect Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng 1359-4311/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2011.07.029 Applied Thermal Engineering 31 (2011) 3615e3628