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Lewis-Matheson Method

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Lewis-Matheson Method
Método de Lewis-Matheson para el Diseño de Columnas de
Destilación Multicomponente

Introducción
Los métodos de cálculo para el diseño de columnas de destilación, se dividen en 3 categorías: los métodos gráficos, los métodos cortos o aproximados y los métodos rigurosos. Los métodos gráficos (como el McCabe-Thiele) y aproximados (como el método FUG) solo son validos para procesos sencillos, tal es el caso de la destilación de mezclas binarias o para estudios preliminares de una columna. El diseño final, sin embargo, requiere de una determinación rigurosa de las temperaturas, flujos y concentraciones.
En este texto de explicara de manera sencilla la aplicación del método de Lewis-Matheson, para determinar el número de etapas teóricas y el plato de alimentación.

Generalidades del método
El método Lewis-Matheson, es esencialmente la aplicación del método de Lewis-Sorel, pero adaptado a multicomponente.
Se asume que el flujo molar es constante y el balance de masa y las relaciones de equilibrio se resuelven etapa por etapa, comenzando por la parte superior e inferior de la columna.
Para definir un problema para el método, las siguientes variables tienen que ser especificadas o determinadas mediante otras variables definidas. 1. Flujo y composición de entrada 2. Distribución de los componentes clave 3. El flujo de un producto 4. Relación de reflujo 5. Presión de la columna 6. Valores supuestos para la distribución de los componentes no clave
El procedimiento usual es comenzar con el cálculo en la parte superior e inferior de la columna y proceder hacia el plato de alimentación.
Los estimados iniciales de las distribuciones de los componentes se revisan y los cálculos se repiten hasta que las composiciones de la parte superior e inferior coincidan, así como el plato de alimentación con las composiciones de alimento.
Bases teóricas
En un sistema binario, la relación entre la composición del vapor yA y del liquido xA en equilibrio puede ser expresada de

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