**A Geometric Method to calculate the Minimum Reflux of Complex Columns Using Enthalpy-Composition Diagram**

José D. Olguín-Ángeles , Fernando Pérez-Villaseñor, Arturo Ortiz-Arroyo, Ángel Castro-Agüero.

Facultad de Ciencias Básicas Ingeniería y Tecnología, Universidad Autónoma de Tlaxcala, Apizaco, Tlaxcala, México, 90300.

Distillation is the most common process separation used to purifying homogeneous fluid mixtures, but at the same time it is the one that consume most energy in a chemical plant. Underwood design methods have been used through many years to calculate minimum reflux of conventional (Seader et al, 2010) and complex columns (Nikolaides and Malone, 1987; Triantafyllou, C. and Smith, 1992; Ramirez et al., 2010; Muralikrishna et al., 2002). The Underwood equation is used mainly for thermodynamically ideal mixtures due the assumptions considered in this equation, therefore the designs of column distillation for separations of non-ideal mixtures are not convenient.

Doherty and Malone (1987) proposed a design method for ideal multicomponent mixtures using rigorous thermodynamic models for conventional distillation columns. This methodology can be applied to non-ideal mixtures but it must deal with azeotropic points and “tangent pinch” solutions. Doherty and Malone do not considered the energy balance, so thermal effects cannot be considered. They used the “Zero Volume Method” to find the minimum reflux ratio in a stage-to-stage solution of mass equations.

The Ponchon-Savarit method for binary mixtures is the rigorous design method when acceptable thermodynamic models are used for the specified mixture. The Ponchon-Savarit method is well known for binary separation mixtures but is not utilized for ternary or multicomponent mixtures. Reyes y col. (2000) used the Enthalpy-Concentration diagram using an iterative methodology to estimate the minimum reflux. They find the minimum reflux of conventional ideal distillation columns and compare against shortcut and stage-to-stage solutions.

In this work, it is proposed a methodology to find the minimum reflux ratio of conventional and non-conventional columns (multiple feeds and multiple side-streams). The Zero Volume Method is used to determine the minimum reflux ratio, but instead of solve stage-to-stage mass balance, an adiabatic flash solution is proposed. With the adiabatic flash, the tie lines that determine the zero volume method can be found for every column section. Besides, the zero volume method incorporates the energy balance, so that thermal effects can be considered.

The main column of the Petlyuk column is presented as a result of a non-conventional distillation column, which contains two feed streams and one liquid side stream. In a complex column, besides to find the minimum reflux for each feed, it is necessary determine which of the feeds has the maximum of all minimum reflux. With this methodology, the minimum reflux ratio of the main column of Petlyuk system was calculated, the minimum reflux ratio of each feed stream and then the minimum reflux ratio of the main Petlyuk column. The estimated minimum reflux ratio of main column was compared against to a stage-to-stage simulation with ASPEN PLUS. The simulated composition profile shows that the column operates at minimum reflux, there is a composition pinch zone, and the pinch zone is located at the correct feed stream.

**References **

Doherty, M. F. y Malone, M. F., “Conceptual Design of Distillation Systems”, Editorial Mc Graw Hill, 1st Edition, (2001).

Muralikrishna, K., Madhavan, K. P. and Shah, S. S., “Development of Dividing Wall Distillation Column Design Space for a Specified Separation”, Trans IChemE., 80, p. 155-166, (2002).

Nikolaides, I. P. and Malone, M. F., “Approximate Design of Multiple-Feed/Side Stream Distillation Systems”, Ind. Eng. Chem. Res., 26, p. 1839-1845, (1987).

Ramírez, N., Jiménez, A., Castro, A. and Rico, V., “Optimum Design of Petlyuk and Divided-Wall Distillation Systems using a Shortcut Model”, Chem. Eng. Res. Des., 8, p. 1405-1418, (2010).

Reyes, J.A., Gómez, A. And Marcilla, A., “Graphical Concepts to Orient the Minimum Reflux Ratio Calculation on Ternary Mixtures Distillation”, Ind. Eng. Chem. Res., 39, 3912-3919, (2000).

Seader, J.D., Henley, E.J., and Roper, D.K., “Separation Process Principles”, John Wiley and Sons, 3th Edition, (2010).

Triantafyllou, C. and Smith, R. “The Design and Operation of Fully Thermally Coupled Distillation Columns”, Trans. Inst. Chem. Eng., p.118-132, (1992).

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