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Modelo matemático a travez de fórmulas químicas de  la viscosidad= en soluciones técnicas y puras  durant= e el procesamiento del azúcar  de remola= cha

 

Mathematical model through chemical formulas of viscosity in technical and pure solutions during processing of  beet sugar

 

= Javier Ignacio Briones García. [1], = Keren Esther Vásquez Martínez. [2], Diana Nereida Villa <= span class=3DSpellE>Uvidia. [3] & Teresita Jackelin Mejía Reinoso. [4]

 

Recibido: 10-02-2019 / Revisado: 15-02-209 /Aceptado: 04-03-2019/ Publicado: 14-06-2019

 

 Abstract.                     DOI: https://doi.org/10.33262/cienciadigital.v3i3.1.704

 

This research = has as a main objective to study the variation of viscosity in the technical and pure solutions in the different stages of the process of sugar using a mathematical model. The optimization of the technological systems in the process of ebullition and crystallization of sugar will improve significant= ly the technical and economic profit of the plant, in order to carry out this task, it is necessary to control and determine a series of parameters such = as: viscosity, saturation, supersaturation, purity of the = intercrystalline solution and the molasses. It was carried out through the VisSim 7.0 program, which permitted the modulation of the isobaric evaporative crystallization process to obtain 60 tons of sugar, under the equations of = S.V. Shterman, the values of the total duration of t= he crystallization do not observe pronounced divergence, even though there is a discrepancy for the values of viscosity, which cannot be more than 1500 pas= cal, for the correct functioning of the vacuum apparatus and to avoid damage. By developing new and revolutionary technologies will per= mitid to obtain the normal purity of the intercrystalline solution in the vacuum devices and exclude of the technological line the polythermic crystallization process of saccharose, re= ducing the costs of operating and expenses in electricity, the use of cooling water consumption and simplify in a great quantity the technology to obtaining su= gar.

Keywords: sugar, computer simulation, mathematical model, optimization.

 

Resumen.

 

Esta investigación tiene como objetivo estudiar la variación de la viscosidad en soluciones técnicas y puras en las diversas etapas del procesamiento del azúcar utiliz= ando un modelo matemático. La optimización del régimen tecnológico del proceso de ebullición y cristalización del azúcar mejorará significativamente el rendimiento técnico y económico de la planta, para realizar dicha  tarea, es necesario controlar y determi= nar una serie de parámetros como: viscosidad, saturación, sobresaturación, pure= za de la solución intercristalina y  m= elaza. Se llevó a cabo mediante el programa VisSim 7.0, el cual permitió la modula= ción del proceso de cristalización evaporativa isobárica para la obtención de 60 toneladas  azúcar, bajo las ecuacio= nes de S.V. Shterman,  los valores de la duración total de la cristalización no observan divergencia pronunciada, au= nque existe discrepancia  para los valor= es de viscosidad, los cuales no deben ser mayor a 1500 pascal, para el correcto funcionamiento del aparato de vacío y evitar dańos. Al desarrollar nuevas y revolucionarias tecnologías  permit= irán obtener la pureza normal de la solución intercristalina en los aparatos de vacío  y excluir de la línea tecnol= ógica el proceso de cristalización politérmica de la sacarosa, reduciendo  costos de operación, gastos en electric= idad, consumo de agua refrigerante y simplificaría en gran medida la tecnología de obtención de azúcar.

Palabras claves: azúcar, simulación computarizada, modelo matemático, optimización.

Introducción.

La remolacha azucarera es la principal fuente de obtención de azúcar en muchos países, siendo el 90% de azúcar consumida en Europa a base de remolacha azucarera y el 30% a nivel mundial, gracias a su elevado contenido de sacarosa. En la producción de es= te tipo de azúcar, intervienen procesos físicos y químicos complejos,  donde la sacarosa es extraída de las cé= lulas en difusión  por acción  química y termo-física separando los az= úcares de los no-azúcares convirtiéndolo en un producto cristalino puro.

 

Cocción del = jarabe – Es la etapa final en la producción del azúcar. El objetivo principal es la extracción de la sacarosa disuelta en el almíbar, en forma de cristales. Durante el proceso de purificación llamado carbonatación – el  líquido resultante del proceso de difus= ión se mezcla con lechada de cal  [Ca(OH)_2 ]   y gas carbónico (= CO= _2 ), produciendo carbonato de calcio (CaCO_3 )  que se precipita, arrastrando la mayor parte de las impurezas consigo, en el proce= so se elimina un tercio de los no azucares.

 <= /o:p>

Las sustanci= as restantes junto con la sacarosa son redirigidas al departamento de producci= ón, donde el jarabe pasa por el proceso de evaporación hasta que llegue a una concentración de 70-75% de contenido sólidos, después de lo cual está listo para su cristalización. El azúcar cristalino se obtiene mediante dos técnic= as:

ˇ&nb= sp;        Cristalización politérmica;

ˇ&nb= sp;        Cristalización por evaporación isobárica.<= /span>

 <= /o:p>

La separació= n de la sacarosa es realizada en dos o tres etapas, teniendo en cuenta la calida= d de la materia prima. En el caso de materias primas de baja calidad, el azúcar = es obtenida mediante  dos esquemas de = cristalización (cristalización politérmica). Por lo contrario, si la materia prima es de a= lta calidad se utilizan tres esquemas (cristalización por evaporación isobárica= ).

 <= /o:p>

Los investigadores centran cada vez más su atención en el desarrollo de nuevas tecnologías de cristalización, debido al gran contenido de impurezas acumul= adas en la solución madre, trayendo como resultado, mayor viscosidad y dificulta= d en el proceso de cristalización, disminuyendo el volumen final del producto. La reducción de la pureza de la melaza ha generado un mayor rendimiento productivo, pero ha alcanzado límites prácticos, llevando resultados indeseables.

 

Esto se debe= a la elevada viscosidad de la solución intercristalina, lo que empeora las condiciones de nucleación, crecimiento cristalino y duración del proceso de= bido a una disminución en la velocidad de cristalización. Dado que la pureza de = la melaza depende de la calidad de los productos que entran en ebullición, como del retorno y recirculación del licor madre, esto conduce a la gran acumula= ción de no-azucares, lo que afecta negativamente al rendimiento técnico y económ= ico de la planta.

 

La modelación matemática en los últimos ańos ha sido un método efectivo y comúnmente utilizado en el desarrollo y estudio de procesos tecnológicos, proporcionan= do respuestas a muchas preguntas incluso en la etapa preliminar de investigaci= ón, permitiendo determinar modos óptimos y esquemas apropiados en los procesos tecnológicos. Eliminando los gastos innecesarios de mano de obra y recursos materiales en la construcción de esquemas irracionales y en la implementaci= ón de regímenes ineficientes. El modelo matemático es una herramienta extremadamente flexible que permite reproducir cualquier situación, tanto r= eal como hipotética, ya que no está sujeta a limitaciones físicas. Esto reduce = la necesidad de sofisticados equipos de laboratorio y pruebas operacionales de los proce= sos tecnológicos que se están creando.

 

Metodologia.

El análisis del material bibliográfico permitió concluir, que la viscosidad depende ampliamente de la densidad, temperatura, composición química y asociación de las moléculas en= las distintas soluciones. Cuanto más complicada sea la separación de la solución intercristalina de los cristales de sacarosa, mayor será la concentración de no-azúcares en el licor madre, requiriendo una mayor cantidad de  equipos para su procesamiento.

 <= /o:p>

Numerosos estudios han demost= rado que la viscosidad de las soluciones técnicas de azúcar, incluyendo la melaz= a, no dependen de la velocidad de cizallamiento, es decir, estos fluidos son newtonianos. Sin embargo, estudios más detallados han demostrado el carácte= r no newtoniano de algunas melazas y que las propiedades de las soluciones de az= úcar son similares a las soluciones de polímeros y de sistemas dispersos. <= /o:p>

 <= /o:p>

Estas desviaciones se deben a= la presencia de burbujas de gas, altos polímeros y sólidos suspendidos en las soluciones. Que en comparación con  soluciones<= span style=3D'mso-spacerun:yes'>  puras de sacarosa, que contienen no-azu= cares, durante una misma concentración de sólidos tiene una viscosidad más baja. P= ero esto sólo aplicaría a soluciones que no contengan pectinas, dextranos, polímeros cuya presencia aumenta considerablemente la viscosidad.

 <= /o:p>

Diferentes profesionales de la industria azucarera han basado sus trabajos investigativos en el estudio de= la viscosidad en las diferentes etapas que presentan las soluciones, para la obtención de los cristales de azúcar, dichas investigaciones han podido gen= erar ecuaciones que describen la dependencia de esta, desde diferentes variables formando un grupo de 17 ecuaciones, las cuales se muestran en la tabla 1. S= in embargo es imposible compararlas entre sí, ya que la literatura no cuenta c= on valores de constantes para cada ecuación.

 

Tabla 1: Ecuaciones de viscosidad de soluciones técnicas y puras de la sacarosa=

&= #8470;

A= UTORES

ECUACIÓN DE VISCOSIDAD

1=

G= . Waterman

2=

J= . Pidu

3=

Y= . Frankel

  <= /span>

4=

R= . Mishchuk, L. Belostotsky

5=

G= . Znamenskii

, μ=3D(3.5-0.025*P) <= /span>

6=

D= . Shliphake

7=

K= . Wagner

=

8=

J= . Jhonatelle

9=

N= . Lyusy

11

V. Shterman= , A. Filippov

 

1= 2

<= o:p> 

S= . Petrov

13

B. Maurandi

1= 4

V= . Shterman, G. Vovk<= /o:p>

  <= o:p>

1= 5

V. Shterman

                =

<= /span>

16

N. Silina

1= 7

A= . Gromkovsky, V. Fursov

 

Elaborado<= span lang=3DES style=3D'font-size:12.0pt;line-height:115%;font-family:"Times New= Roman",serif'>: Por los autores

 

En base a los cambios en la viscosidad de solucion= es técnicas y puras de la sacarosa en el proceso de ebullición y cristalizació= n se tomo como referencia las ecuaciones creadas por Sergey Shterman las cuales coinciden con la lín= ea investigativa del proceso planteado.

 

Primera ecuación de S. Shterm= an

 

            (1)

        = (2)

                                                   (3)                              =

                    (4)                

En donde:

 

mum =3D viscosidad  de la solución intercristalina; DBm3 =3D pureza  d= e la solución intercristalina; CVm3 =3D sólidos en la solución intercristalina; = K =3D coeficiente de impurezas sobre la viscosidad de soluciones técnicas azucara= das; Ncv3 =3D fracción molar de  sólidos= en la solución intercristalina; muy =3D viscosidad de la masa cocida; gamy =3D fracción de volumen de los cristales en la m= asa cocida; dkr =3D tamańo de los cristales.

 

Viscosidad por la segunda ecuación de S. Shterman:

 

  =      (5)              =

               (6)                          

            (7)     

 

Donde:

 

mum1 =3D viscosidad de la solución intercristalina= ; Ty3 - temperatura de la masa de cocion; Ncv3 y Nncx= 3 =3D fracción molar de las sustancias solidas y los = no azucares.

 

Por consiguiente, la viscosidad se describe median= te la ecuación:

 

     (8)

 

La investigación se implementó eficazmente utiliza= ndo el modelo matemático (VisSim 7.0), VisSim – es  = un lenguaje visual de programación, diseńado para modelar sistemas dinámicos, = así como proyecciones basadas en modelos matemáticos.

 

VisSim combina un ensamblado de la interfaz intuitiva de arrastrar y colocar los diagramas de bloques a un motor de simulación de gran alcance. El lenguaje = de programacion fue desarrollado por la compańía america= na Visual Solutions, que se encuentra en Westford (Massachusetts).

 

La ventaja de este modelo es que con su ayuda es posible demostrar, desarrollar y analizar efectivamente nuevas tecnologías = de ebullición y cristalización de masas cocidas, alcanzando 60 toneladas de pr= oducto final y la concentracion requerida en la masa c= ocida, independientemente de los parametros tecnologicos, fisico-quimicos y termo-tecnicos del proceso.

 

Está diseńado para estudiar, fundamentar nuevas tecnologías de cristalización sobre la base del estudio y procesamiento de = los resultados de un experimento informático durante el modelado matemático del proceso de cristalización industrial, por ejemplo, la sacarosa

 

La simulacion se llevo a cabo tomando en cuentas los siguientes parametros tecnologicos:<= o:p>

 

ˇ      =    M= odo típico de ebullición, dentro del cual se mantuvo una sobresaturación consta= nte de P =3D const y el final del proceso fue deter= minado por la materia seca de la masa cocida. En este caso, la cantidad final de la masa cocida es siempre diferente, dependiendo de los parámetros tecnológico= s y de la composición de las impurezas.

ˇ      =    M= odo de soldadura con control automático. En este caso, la cantidad final de la masa cocida y las sustancias secas permanecen inalteradas, y en cualquier caso, hasta el final del proceso de ebullición, los valores de volumen de producto final alcanzando 60 toneladas, con un coeficiente de sobresaturación dado.<= o:p>

ˇ      =    E= l modo de cristalización cuando se alcanza la frecuencia normal, que es la base del modo típico.

ˇ      =    E= l regimen de cristalización cuando se alcanza la pureza mínima.

ˇ      =    El régimen de cristalización con la selección de cristales a sobresaturación constante es P =3D const.

&nbs= p;

Resultados.<= /span>

La comparación de las ecuaciones de Sergey Shterman se llevó a cabo utilizando= el modelo matemático antes mencionado, dando como resultado que las primeras ecuaciones descritas por el autor ruso corresponden a datos referenciales de parámetros finales para la melaza, pero la viscosidad es mucho mayor que en= las ecuaciones mas recientemente creadas por este, afirmando que estas poseen datos  mucho mas precisos (Shterman, 2006).

&= nbsp;

S.V. Shterman enfatiza tomar en cuenta el efecto de los no-azúcares sobre las principales características tecnológicas de los productos de ebullición y cristalización con la ayuda  de coeficientes m, b y k. Los dos primeros coeficientes reflejan la influencia= de los no azucares sobre la solubilidad de la sacarosa, y la segunda sobre la viscosidad de las soluciones técnicas de azúcar.

&= nbsp;

Figura 1: Comparaci= ón de las ecuaciones 1, 4, 5, 8

Fuente: Los autores<= /p>

 

&= nbsp;

Con el programa informático, se llevó a cabo una serie de experimentos, para estud= iar el proceso de ebullición del licor madre por las ecuaciones de viscosidad de Shterman, para el ultimo producto con los siguientes datos:

&= nbsp;

Concen= tración de sólidos - 0,94 / 0,95 / 0,96, pureza - 0,76. El coeficiente "m" varía en el intervalo de 0,1 a 0,5; B =3D 1-m, los coeficientes "c&quo= t; y "k" se asumieron sin cambios, los datos se resumen en las tablas = 2, 3 y 4. El programa proporcionó las siguientes funciones:

&= nbsp;

El modelado y control del proceso de cristalización por evaporación isobárica = en la zona de crecimiento cristalino metaestable  manteniendo la relación calculada de la masa de agua evaporada y el producto cristalizable a ańadir. Al mismo tiempo, el control del proceso se llevó a cabo de tal manera que el producto cristalizado, como regla, necesariamente alcanza la concentración especificada y el volumen  requerido del producto cristalizado, dependiendo del tipo y diseńo del equipo utilizado.

 

Además, el programa permitió explorar a fondo la cinética y la dinámica del proceso= de cristalización, estudiar los patrones de cambios en la tecnología, la  ingeniería térmica, los indicadores físico-químicos y otros del proceso, sobre esta base justificar= y desarrollar nuevas tecnologías para la cristalización de la sacarosa.<= /o:p>

 

Figura 2: Modelo matemático por las ecuaciones de S. V. Shterman=

 

 =

Fuente: Los autor= es

 

 En las tablas 2, 3 y 4 se  muestra como resultado que el menor tiempo de cristalización proporc= iona la ecuación 2 con parámetro b=3D0.5 y m=3D0.5, el análisis de las mediciones e= n la viscosidad de la masa cocida y de la solución intercristalina durante el proceso de ebullición y cristalización con el uso del modelo matemático ha demostrado que la regularidad de la medicion en la viscosidad con la composición de impurezas depende fuertemente de los valores integrales de l= os coeficientes m, b, k, los dos primeros coeficientes reflejan la influencia = de los no azucares sobre la solubilidad de la sacarosa, y la segunda sobre la viscosidad de las soluciones técnicas de azúcar.


 <= /o:p>

Tabla 2: M= asa cocida de producto final con parámetros: Solidos =3D0,94; pureza=3D0,76; b= =3D0.9; 0.7; 0.5

 


Parámetros de investigación

m =3D 0.1

Cambios en  %

m =3D 0.3

Cambios en %

m =3D 0.5

Cambios en %

Ecuación 1

Ecuación 2

Ecuación  1

Ecuación 2

Ecuación 1

Ecuación 2

Tiempo total= de cristalización t<= /span>

7.82

7.9

+ 1%

5.75

5.65

- 1.7%

5.25

4.51

- 14%

Masa de jara= be ańadido mcd3

67692.2

67692.3

0%

66769.6

66766.7

-0.004%=

66769.2

66774.6

+ 0.008%

Masa general= de agua evaporada MviOb

27694

27694.4

0%

26771.5

26772.7

+0.004%=

26770

26772.9

+ 0.01%

Cantidad tot= al de azúcar cristalizada Mkrob3

26396.9

26403.7

+ 0.02%

16335.9

16345.4

+ 0.5%

8827.2

8834.12

+ 0.07%

Viscosidad d= e la masa cocida muy

325.5

5.56

- 98.3%

330.2

8.124

- 97.4%

1068

7.642

- 99.6%

Concentración final de solución intercristalina Cvm3

0.910758

0.910763

+ 0.005%

0.91759

0.917624

+ 0.002%

0.92966

0.929678

+ 0.001%

Pureza final= de la solución intercristalina Dbm3=

0.552993

0.552895

- 0.02%

0.66214

0.662061

- 0.01%

0.71547

0.715433

- 0.005%

Viscosidad d= e la solución intercristalina mum

25.14

3.561

- 86.5%

95.29

4.093

- 96.2%

594

4.736

- 99.8%

Tamańo final= del cristal dkp=

0.000376

0.000376

0%

0.00032

0.00032

0%

0.00026

0.000261

0%

 

Fuente: Los autor


Tabla 3: M= asa cocida de producto final con parámetros: Solidos =3D0,95; pureza =3D0,76; b= =3D0.9; 0.7; 0.5

 

Parámetros de investigación

m =3D 0.1

Cambios en  %

m =3D 0.3

Cambios en %

m =3D 0.5

Cambios en %

Ecuación 1

Ecuación 2

Ecuación  1

Ecuación 2

Ecu= acion 1<= o:p>

Ecu= acion 2<= o:p>

Tiempo total de cristalización t

7.82

7.9

+ 1%

6.32

6.09

- 3.6%

6.35

4.92

- 22%

Masa de jarabe ańadido mc= d3

67692.2

67692.3

0%

67692.1

67689.5

- 0.003%

67692.3

67696.3

+ 0.005%

Masa general de agua evaporada MviOb

27694

27694.4

0%

27693.5

27697.9

+ 0.01%

27694

27694

0%

Cantidad total de azúcar cristalizada Mkrob3

26396.9

26403.7

+ 0.02%

18205<= /p>

18219<= /p>

+ 0.07%

10125.9

10131.9

+ 0.05%

Viscosidad de la masa cocida muy

325.5

5.56

- 98.3%

1514

8.835

- 99.8%

6191

8.872<= /p>

- 99.6%

Concentración final de solución intercristalinaCvm3

0.910758

0.910763

+ 0.005%

0.928249

0.928341

+ 0.009%

0.939866

0.939874

+ 0.008%

Pureza final de la solución intercristalinaDbm3

0.552993

0.552895

- 0.02%

0.647381

0.647249

- 0.2%

0.708158

0.708123

- 0.004%

Viscosidad de la solución intercristalinamum

25.14

3.561

- 86.5%

355.4<= /p>

4.452

- 98.6%

3104

5.194<= /p>

- 99.3%

Tamańo final del cristal dkp

0.000376

0.000376

0%

0.000332

0.000332

0%

0.000273

0.000273

0%

 

Fuente: L= os autores

 <= /o:p>

 

Tabla 4: Masa cocida de producto final con parámetros: Solidos =3D0,95; pureza =3D0,= 76; b=3D0.9; 0.7; 0.5

 

 

Parámetros de investigación

m =3D 0.1

Cambios en  %

m =3D 0.3

Cambios en %

m =3D 0.5

Cambios en %

Ecuación 1

Ecuación 2

Ecuación  1

Ecuación 2

Ecu= acion 1<= o:p>

Ecu= acion 2<= o:p>

Tiempo total de cristalización t

8.69

8.73

+ 0.5%

7.1

6.57

- 8%

8.55

5.38

- 37.4%

Masa de jarabe ańadido mc= d3

68615.4

68615.8

0%

68615.4

68615

0%

68615.4

68615.9

0%

Masa general de agua evaporada MviOb

28617.5

28617

0%

28617

28617.5

0%

28616

28616.5

0%

Cantidad total de azúcar cristalizada Mkrob3

28897.7

28891.7

- 0.02%

20083.2

20086.4

+ 0.01%

11422.5

11426.5

+ 0.03%

Viscosidad de la masa cocida muy

1565

5.26

- 99.3%

11631

9.515

- 99.7%

62784.5

10.36

- 99.9%

Concentración final de solución intercristalinaCvm3

0.92289

0.92287

- 0.002%

0.93990

0.93992

+ 0.002%

0.95960

0.95060

0%

Pureza final de la solución intercristalinaDbm3

0.51837

0.51848

+ 0.02%

0.63153

0.63149

- 0.006%

0.70063

0.70061

- 0.002%

Viscosidad de la solución intercristalinamum

79.34

3.847

- 95.4%

2169

4.91

- 99.8%

28195.9

5.77

- 99.9%

Tamańo final del cristal dkp

0.000387

0.000387

0%

0.000343

0.000343

0%

0.000284

0.000284

0%

 <= /o:p>

Fuente: L= os Autores

 <= /span>


La simulación de procesos por computadora, ha permitido optimizar las diversas etapas de los diferentes esquemas tecnológicos utilizados por las industrias, evitando gastos innecesarios en la implementación de regímenes y equipos ineficientes. Con = el paso del tiempo la industria azucarera ha evolucionado, con la finalidad de aumentar su producción y disminuir perdidas del producto, gracias a la implementación de equipos que aceleran la saturación de la melaza y permite= n el control automático de su viscosidad.

 

 La cristalización del azúcar es consider= ada una de las etapas científicas-técnicas de mayor interés durante el procesamiento de la remolacha, porque allí ocurre la principal perdida de azúcar, alcanzando un 75% de  pérdi= da total dentro de la producción. La modelación de estos procesos permite determinar los parámetros óptimos para la obtención de una melaza normal sin gastos para la empresa.

 

En el marco de solución, se proponen y justifican las siguientes variantes tecnologicas:

ˇ      =             &nb= sp; D= isminución de la viscosidad de la solución intercristalina disminuyendo la sobresatura= ción, comenzando desde el momento en que se alcanza la viscosidad máxima 50 ... 7= 0 Pa.s.

ˇ      =             &nb= sp; D= isminución de la viscosidad de la masa cocida debido a la selección de masa cristalina= , a partir del momento en que se alcanza la viscosidad máxima 50 ... 70 Pa.s.

ˇ      =             &nb= sp; D= isminución de la viscosidad de la masa cocida debido a un cambio en la pureza del prod= ucto ańadido.

ˇ      =             &nb= sp; D= isminución de la viscosidad de la masa cocida debido a una combinación de variantes de= los métodos anteriores.

 <= /span>

Conclusiones.

ˇ&nb= sp;        El análisis bibliográfico arrojo 17 ecuaciones de diferentes autores referente= s a la viscosidad en soluciones técnicas y puras durante el proceso de ebullici= ón y cristalización de la sacarosa.

ˇ&nb= sp;        Se construye un modelo matemático que proporciona 60 toneladas de producto fin= al con las ecuaciones de S. V. Shterman, tomando en cuenta que las soluciones en el aparato de vacío no pueden superar los 1500 pascal de viscosidad para evitar dańos y perdida del producto.

ˇ&nb= sp;        L= os valores de viscosidad según las ecuaciones de Shterman= mostraron diferencia, pero los resultados de la modulación del proceso de cristalización evaporativa isobárica  en los valores de la duración total de la cristalización no observan divergenc= ia pronunciada.

ˇ&nb= sp;        La validación de la modelación computacional reduciría significativamente los costos de operación de equipos voluminosos, los gasto en electricidad, el consumo de agua refrigerante y simplificaría en gran medida la tecnología de obtención de azúcar.

 

 

Referencias bibliográficas.<= /p>

Sapronov, A. (2014). Tecnologia d= e la produccion de azucar. Kolos. 150-250.

Sherman, S. (2007). La composición y viscosidad óptimas del procesamiento del azucar de romolacha = y de la última cristalización en varias etapas de su producción. Sahar, 5. 160.<= o:p>

Sherman, V. VOVK, G. (2006). Descripción analítica de la viscosidad de las soluciones técnicas de azúcar y melaza.Sahar,3. 250.

Slavyanck= iy, A. (2006). Equipos tecnológicos de las fábricas de azúcar: clasificación, características técnicas, cálculos, diseńo. MGUPP. 60-100.

Slavyanckiy, A.Goldenberg, S. (2004). Cálculo de productos de un esquema tecnológico típ= ico y el uso de computadoras para mejorar la eficiencia de la producción de azú= car. MGUPP. 98.

Tuzhilkin, V. (2007). Cristalizacion del azucar. MGUPP. 336.

Zaet= s, A. (2014). Regularizacion del azucar: problemas metodologicos de su creacio= n. Sahar, 5. 17-20

 

 

 

 

 

 

 

 

 

 

 

 

 

PARA CITAR EL ARTÍCULO INDEXADO.=

 

 

Briones García, J., Vásquez Martínez, K., Villa Uvidia., D., & = Mejía Reinoso, T. (2019). Modelo matemático a travez = de fórmulas químicas de la viscosidad en soluciones técnicas y puras durante el procesamiento del azúcar de remolacha. Ciencia Digital3(3.1), 295-309.= https://doi.org= /10.33262/cienciadigital.v3i3.1.704

 

 

 

 

El artículo que se publica es de exclusiva responsabilidad de los autores y no necesariamente reflejan el pensamiento de la Revi= sta Ciencia Digital.

 

El artículo queda en propiedad de la revista y, por tanto, su publicación parc= ial y/o total en otro medio tiene que ser autorizado por el director de la Revista Ciencia Digital.

 

 

 

 



[1] Escuela Superior Politécnica de Chimborazo, Sede Morona Santiago. Macas, Ecuador. javier.bri= ones@espoch.edu.ec

[2]    Unidad Educativa Particular Emanuel. M= acas, Ecuador. kvasquez@emanuel.edu.ec

[3] Escuela Superior Politécnica de Chimborazo, Sede Morona Santiago. Macas, Ecu= ador. diana.villa@espoch.edu.ec

[4] Escuela Superior Politécnica de Chimborazo, Sede Morona Santiago. Macas, Ecu= ador. teresita.mejia@espoch.edu.ec

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REVISTA IN= DEXADA EL LATINDEX 2.0     =                                                    =                                              Página 10

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