Publication: MODELO MATEMÁTICO DE TIEMPO DE SECADO PRIMARIO DE PURÉ DE PAPAS EN GEOMETRÍA SEMIESFÉRICA
Date
2019
Authors
DÍAZ GARCÉS, IGNACIO ANDRÉS
Journal Title
Journal ISSN
Volume Title
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Abstract
A lo largo de los años se han implementado diversos métodos de secado de alimentos, con la finalidad de extender la vida útil. Sin embargo, actualmente dicho objetivo se ha transformado en un requisito básico, pues se descuidaban aspectos de calidad, tales como color, sabor, aroma y textura. Con la meta de minimizar la calidad organoléptica de los productos, surgió la liofilización. No obstante, este método tiene un costo energético 4 a 8 veces mayor que otros métodos convencionales de secado, debido a la presión de operación cercana al vacío, a la necesaria pre-congelación del alimento y a la sublimación del vapor de agua saliente mediante difusión. Por esta razón, a lo largo del tiempo se han creado diversos modelos matemáticos para estimar el tiempo de secado primario, con el fin de ejecutar el proceso por el tiempo justo y necesario, minimizando el impacto monetario.En base a lo anterior, se propuso el objetivo de construcción de un modelo matemático para estimar el tiempo de secado primario en geometría semiesférica, contemplando el acoplamiento de los fenómenos de transferencia de calor y de materia.La experimentación se basó en la preparación de muestras de puré de papas en geometría semiesférica de 2 [cm] de radio con una humedad inicial de 86,24%. Se programó el liofilizador a una presión de cámara de 20 [Pa], una temperatura de placa calefactora de 20 [°C], y un tiempo de 17 [h]. El tiempo experimental de duración del secado primario se estimó con el criterio de la temperatura del condensador, cuyo perfil tuvo un intervalo de estado transiente, donde el final de éste indica el fin del proceso.Empleando 100 particiones de la muestra con forma de capas semiesféricas para efectos de cálculo, se obtuvo un tiempo teórico de 14,856 horas, valor perteneciente al intervalo de confianza al 95% del tiempo experimental, de media 14,786 [h] y error muestral de 0,242 [h], lo que permitió la validación del modelo a dichas condiciones de operación, con apenas un 0,47% de error relativo, versus el 1,64% de error relativo máximo permitido. Además, las muestras tuvieron una humedad final del 16,69%, implicando una remoción de agua que alcanzó un 96,8%.Una vez validado el modelo, se procedió a variar por separado el radio de la muestra, presión de cámara y temperatura de placa calefactora, analizando los impactos en el tiempo de secado primario según el modelo propuesto, en calidad de predictor. En cuanto al radio, se obtuvo un perfil cuadrático, donde al aumentar este parámetro, el tiempo también logró la misma tendencia. Respecto a la presión de cámara, su aumento generó la elevación del tiempo, pero con una tasa de aumento decreciente. Por último, referido a la temperatura de placa calefactora, a medida que el diferencial de temperatura con la muestra disminuía, la tasa de aumento del tiempo resultó ser positiva.
Throughout the years, various methods of drying food have been implemented in order to extend the useful life. However, nowadays this objective has become a basic requirement, since aspects of quality, such as color, flavor, aroma and texture, were neglected. With the goal of minimizing the organoleptic quality of the products, lyophilization arose. However, this method has an energy cost 4 to 8 times higher than other conventional drying methods, due to the operating pressure close to the vacuum, the necessary pre-freezing of the food and the sublimation of the outgoing water vapor by diffusion. For this reason, various mathematical models have been created over time to estimate the primary drying time, in order to execute the process for the right and necessary time, minimizing the monetary impact.Based on the foregoing, the objective of constructing a mathematical model was proposed to estimate the time of primary drying in hemispherical geometry, contemplating the coupling of heat and matter transfer phenomena.The experimentation was based on the preparation of samples of mashed potatoes in semi-spherical geometry of 2 [cm] radius with an initial humidity of 86.24%. The lyophilizer was programmed to a chamber pressure of 20 [Pa], a heating plate temperature of 20 [° C], and a time of 17 [h]. The experimental time of the duration of the primary drying was estimated with the criterion of the temperature of the condenser, whose profile had a transient state interval, where the end of it indicates the end of the process.Using 100 partitions of the sample in the form of hemispherical layers for calculation purposes, a theoretical time of 14,856 hours was obtained, value belonging to the confidence interval at 95% of the experimental time, of average 14,786 [h] and sample error of 0,242 [ h], which allowed the validation of the model to these operating conditions, with barely 0.47% relative error, versus the 1.64% maximum relative error allowed. In addition, the samples had a final humidity of 16.69%, implying a water removal that reached 96.8%.Once the model was validated, the sample radius, chamber pressure and heating plate temperature were separately varied, analyzing the impacts on the primary drying time according to the proposed model, as a predictor. Regarding the radius, a quadratic profile was obtained, where by increasing this parameter, time also achieved the same trend. Regarding the chamber pressure, its increase generated the rise in time, but with a decreasing rate of increase. Finally, referring to the temperature of the heating plate, as the temperature differential with the sample decreased, the rate of increase in time turned out to be positive.
Throughout the years, various methods of drying food have been implemented in order to extend the useful life. However, nowadays this objective has become a basic requirement, since aspects of quality, such as color, flavor, aroma and texture, were neglected. With the goal of minimizing the organoleptic quality of the products, lyophilization arose. However, this method has an energy cost 4 to 8 times higher than other conventional drying methods, due to the operating pressure close to the vacuum, the necessary pre-freezing of the food and the sublimation of the outgoing water vapor by diffusion. For this reason, various mathematical models have been created over time to estimate the primary drying time, in order to execute the process for the right and necessary time, minimizing the monetary impact.Based on the foregoing, the objective of constructing a mathematical model was proposed to estimate the time of primary drying in hemispherical geometry, contemplating the coupling of heat and matter transfer phenomena.The experimentation was based on the preparation of samples of mashed potatoes in semi-spherical geometry of 2 [cm] radius with an initial humidity of 86.24%. The lyophilizer was programmed to a chamber pressure of 20 [Pa], a heating plate temperature of 20 [° C], and a time of 17 [h]. The experimental time of the duration of the primary drying was estimated with the criterion of the temperature of the condenser, whose profile had a transient state interval, where the end of it indicates the end of the process.Using 100 partitions of the sample in the form of hemispherical layers for calculation purposes, a theoretical time of 14,856 hours was obtained, value belonging to the confidence interval at 95% of the experimental time, of average 14,786 [h] and sample error of 0,242 [ h], which allowed the validation of the model to these operating conditions, with barely 0.47% relative error, versus the 1.64% maximum relative error allowed. In addition, the samples had a final humidity of 16.69%, implying a water removal that reached 96.8%.Once the model was validated, the sample radius, chamber pressure and heating plate temperature were separately varied, analyzing the impacts on the primary drying time according to the proposed model, as a predictor. Regarding the radius, a quadratic profile was obtained, where by increasing this parameter, time also achieved the same trend. Regarding the chamber pressure, its increase generated the rise in time, but with a decreasing rate of increase. Finally, referring to the temperature of the heating plate, as the temperature differential with the sample decreased, the rate of increase in time turned out to be positive.
Description
Catalogado desde la version PDF de la tesis.
Keywords
DIFUSION , GEOMETRIA SEMIESFERICA , MODELO MATEMATICO , PURE DE PAPAS , SECADO PRIMARIO , SUBLIMACION