SEDIMENTACION DE LODOS BIOLÓGICOS. Paginas 101 a 150..pptx

SEDIMENTACIÓN DE LODOS BIOLÓGICOS Procesos de sedimentación. • Diseño de sedimentadores secundarios. Calculo del área de clarificación ( ). Calculo del área de espesamiento( ). Método para obtener el flux de sólidos( ). • Ejemplo de diseño de sedimentadores secundarios. • Problemas. •

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SEDIMENTACION SEDIMENTACION DELODOSBIOLOGICOS

1

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Procesosdesedimentación: La sedimentación es un proceso utilizado para la clarificación clarificación de aguas residuales en la cual se separan los sólidos en suspensión mediante fuerzas gravitacionales. En una planta convencional para tratar aguas residuales mediante lodos activados , la sedimentación se aplica para la separar la biomasa(sólidos suspendidos)que se genera el reactor durante la degradación de los contaminantes del agua residual, para dejarla libre de sólidos suspendidos . A diferencia dela sedimentación discreta - donde la velocidad de sedimentación puede ser descrita por la ley de Stokes, debido a que las partículas conservan su tamaño de partícula y no tienen interacciones - ,en el caso de la biomasa , la concentración de partículas es muy alta (>500mg/L),si hay interacciones importantes entre los floculos suspendidos suspendidos y la velocidad de sedimentación, se considera está en función dela concentración local (véase la figura 36).

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El comportamiento del proceso de sedimentación de lodos biológicos puede ser descrito mediante el modelo de flux  de sólidos.  Al inicio de la sedimentación sedimentación

(clarificación), (clarificación), las partículas se comportan como partícula

independientes y sedimentan con velocidad constante(Vs) (figura 37). Cuando la concentración de lodos incrementa, la interacción entre los floculos aumenta y se alcanza la etapa de compactación ; por tal razón la interfase de sólidos desciende con menor velocidad. La compactación se lleva a cabo en el fondo del sedimentador. Al mismo tiempo, el agua es desplazada hacía arriba para dejar espacio al lodo biológico que sedimenta, es decir, es un fenómeno complejo de movimiento movimiento de lodos hacia el fondo y de agua hacia arriba. La presencia de microorganismos filamentosos en pequeñas concentraciones puede servir como puente para unir

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Diseño de sedimentadores secundarios: El diseño de sedimentadores secundarios es de primordial importancia para el tratamiento de aguas residuales. El diseño de estos equipos se realiza para satisfacer los requerimientos de calidad en cuanto sólidos suspendidos contenidos en el agua residual tratada, es decir, una de sus funciones es permitir que el agua tratada clarifique a los niveles deseados( véase figura 38)

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Por otra parte , debido a que en los sistemas de lodos activados se requiere obtener una alta concentración de microorganismos , es necesario reciclar lodos biológicos de los fondos del sedimentador.

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Calculo del área de clarificación (Ac) El agua residual que sale por el vertedero del sedimentador , con un caudal Qe, no debe tener una velocidad mayor a la velocidad de sedimentación (Vs); a partir de estos parámetros, se obtiene el área de clarificación mediante la ecuación (IV-2).

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Calculo del área de espesamiento: En un sedimentador que trabaja continuo ,el  flux  f lux total de sólidos (Ft) que sedimentarán esta dado por la suma del flux de sólidos que sedimentan por gravedad (FL) mas el  flux de sólidos que sedimentan el fondo del sedimentador( Ff  )por  )por la succión , con una velocidad U(m /d), / d), es decir:

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EJEMPLO DE DISEÑO DI SEÑO DE SEDIMENTADORES SEDIMENTADORES SECUNDARIOS

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% Interpolación Xfondos =input („introduzca la concentracion de lodos en el fondo del sedimentado r(mg/L)‟) Ftdiseno=interp1(x,y, Ftdiseno=interp1(x,y, fonds, „spline) Los datos de Xf se introducen en el vector x. los datos FT se introducen en el vector y. la concentración de los sólidos que se concentra en los fondos del sedimentador se denomina como xfondos, xfondos, su valor se introduce mediante el teclado utilizando el comando imput .El flux total de los sólidos para la concentración de solidos deseada (xfondos (xfondos)) se obtiene mediante interpolación (spline) utilizando el comando interpl1 asi como la indicación „spline’ (véase listado).} una vez guardado el programa programa se permite encontrar el flux total para concentración concentración de fondos deseada, se regresa al programa que permite permite encontrar el flux total para concentración concentración de fondos deseada, se regresa al programa principal (zonal (zonal,, el cual se encontraba en pausa (P ( P). Zonalinterpola, se introducen en el cuerpo zonal  zonal  las Para el programa zonal retome el cálculo realizado en Zonalinterpola, siguientes instrucciones: 

% Mediante el siguiente archivo M se interpola para obtener flux de

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 Para continuar después de la pausa, solo se s e teclea cualquier carácter. El flux obtenido (Ftdiseno ( Ftdiseno)) se retoma para el diseño .Utilizando las ecuaciones (IV-3) Y (IVQo), el cual se introduce mediante el 4), para lo que se detiene detiene el caudal de entrada (Qo), comando input, se calcula el área de espesamiento mediante mediante la ecuación (IV-9). (IV-9).   

Qo=input (‘Introduzca el caudal de entrada del sedimentador ( m^3/d m ^3/d)’) Diasp(‘Area de speseamiento (m^2)’) Aesp= Qo*Xo/( Ftdiseno*1000) el 1000 es un factor de conversión de unidades

 A continuación, se realiza el cálculo del area de clarificación mediante la ecuación (IV-2), (IV-2), para lo que es necesario obtener el caudal que sale del sedimentador por el vertedero (Qe ( Qe); ); este se calcula mediante la ecuacion (4). Asi mismo, se requiere la concentracion de sólidos (Xe) en el agua tratada a la salida del sedimentador (vertedero). Este es el listado para el cálculo del área de clarificación: 

Xe=

input(‘Introduzca 

la

concentración

de

lodos

en

la

salida

del

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Posterior al cálculo de las dos áreas, se realizarla comparación entre ellas y asi poder utilizar la mayor para el diseño de sedimentador. Previamente habíamos introducido la la instrucción if-que nos nos permite justamente justamente esa comparación comparación entre áreas - ; en caso de que sean iguales  – para lo cual se utilizan los signos de igual(==)-, se toma el área de clarificación para el diseño. Por otra parte, si lo anterior no se cumple, se compara si el área de clarificación (AC) es mayor (>)que la de espesamiento (Aesp). Es necesario utilizar los comandos elseif y else. Caso de ser verdadero el área de clarificacion será el área de diseño ; por lo tanto, se tendrán que teclear inmediatamente inmediatamente después los siguientes comandos: 

If Ac == Aesp

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En el caso de que el área de clarificación sea la que se u tilice para el diseño, es preciso volver a calcular la concentración de los fondos, ahora con base en esta área obtenida; para esto son las instrucciones: 

% calculo de las condiciones reales de operación con



%el area de diseño (clarificacion)



Disp(‘La Ft en kg/m2d) paraestas condiciones (mg/L) que se …alcanza’)



Xfondos = interp1(y,x,Ftdiseno interp1(y,x,Ftdiseno, ‘spline’)

Como se observa se recalcula el flux con base en el area de diseño, que seria la de clarificación, y con esto se interpola el valor que se obtendrá de la concentración en los fondos; a continuación se muestran las instrucciones para volver a efectuar el cálculo de los caudales corregidos:

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Para el cálculo de las dimensiones del sedimentador, se tienen que proporcionar los datos de altura del sedimentador (con frecuencia es de alrededor de 4.0m), y el tiempo de residenciael cual no debe ser muy grande (más o menos 3 horas), ya que se puede presentar generación de gases, debido a la desnitrificacion o por condiciones de anaerosimbiosis;si fuera así; habría dificultades ; los sólidos flotarían No olvidar, olvidar, como se ha venido venido indicando, que que siempre que se utilice utilice

un if , se requiere el

correspondiente comando end al end al final (véase indicaciones ). Se utiliza el comando disp („‟) , avrias veces , para dejar varios espacios. La presentación de los datos se utiliza en la última parte del programa, para lo cual se usa el comando fprintf  ya   ya que este proporciona mejor presentación a los datos de salida.

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El formato debe terminar con diagonal invertida(/ ) más letra (n), es decir , (/n): esto hace que cambie el renglón. El programa completo- que describe a continuacion  –  se teclea en la ventana de trabajopara archivo.m; en este caso como, zonal.m. salvarlo como archivo.m; en como , zonal. Listado para obtener el diseño de d e un sedimentador de todos biológicos(zonal): biológicos(zonal):

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%grafica de datos experimentos y linearizados Subplot (1,2,1) Plot(xi,LnVimejor,Xi,LnVi,’o’)  Xlabel (‘Xi(mg/L’))    Ylabel( ‘Vi(mg/L’))  Hold on % resultados experimentales  



FTL=Xi.*Vsz*0.024

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SEDIMENTACION SEDIMENTACION DELODOSBIOLOGICOS

1

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Para realizar realizar la grafica, se define define la función recta  ──la cual depende de los datos experimentales 1/S (inversoS ) ──  y  y se utilizan la pendiente (m ( m) así como la ordenada al origen (b ( b) de la mejor recta obtenida: recta = inversoS.*m+b; para graficar, graficar, se usa entonces el comando

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Ks)) de la siguiente manera  ──a  destacar que al final de la línea Después se calculan (qmax (qmax)) y (Ks ahora ya no se escribe el punto y coma (; (;); esto para que si aparezcan los los datos en la pantalla ── : qmax = 1/b Ks = qmax*m Finalmente se calcula el error cuadrático promedio (ecm), el cual fue definida anteriormente; al aplicarlo para estos datos se obtiene la ecuación (V - 11):

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COMPORTAMIENDO COMPORTAMIENDO DE UN REACTOR BIOLÓGICO BIOLÓGIC O POR LOTE Teniendo en cuenta los parámetros cinéticos anteriores, se pueden hacer varias simulaciones utilizando las herramientas del Matlab® para conocer los distintos comportamientos, según diferentes condiciones de operación: el de la variación del sustrato (DQO): el del crecimiento de microorganismos (SSV) así como el oxigeno disuelto (OD). En función del tiempo, en un reactor biológico airado por lote (batch), cuando remueve los contaminantes de un agua residual. También se podría varias las condiciones de operación para observar qué efecto generan en el proceso. En este caso se prueban dos condiciones (A) y (B) para evaluar su efecto en las variaciones (DQO), (SSV) y (OD) a diferentes tiempos de reacción, en un reactor por lote y utilizando una cinética tipo monod. La condición que se vario fue la concentración inicial de biomasa expresada como (SSV): en la prueba (A) se utilizó (SSV) inicial de 210mg/L. mientras que en la prueba (B), lo fue

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Para nuestro ejemplo, se resuelve el sistema de las tres ecuaciones diferenciales que se obtienen al ordenar las ecuaciones (V-12), (V-13), (V14) y obtener las ecuaciones (V-12a), (V-13a) y (V-14a) respectivamente, que nos permiten evaluar el comportamiento dinámico en el reactor de la siguiente manera: PARA CONSUMO de DBO:  

−

   ∗  

 + 

(V(V12a)

PARA CRECIMIENTO:  

  ∗

 ∗   + 

 −  ∗ 

PARA CONSUMO DE OXÍGENO: 



 ∗ 

∗

 ∗ 

 +  ∗ 

(V(V13a)

(V14a)

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PROGRAMA LOTEMONOD.M  A continuación continuación presentamos presentamos el listado del programa lotemonod.m elaborado lotemonod.m elaborado con el fin de averiguar el comportamiento de microorganismos en un reactor por lote basado en los parámetros cinéticos obtenidos: % Comportamiento en un reactor batch % Se puede obtener el comportamiento del crecimiento. % consumo de sustrato % y oxigeno en un reactor por lote (Batch) % [t,y] = ode45(„lotemonod‟, [0 20], [668 210 5]), (para correr) % plot(t,y(:,1),‟-‟,t,y(:,2),‟-‟,t,y(:,3),‟+‟)(para graficar) % format short g; poner antes para ver todo el valor que resulta % [t,y(:,1),y(:,2),t,y(:,3)] (para tener los valores) % Ecuaciones (V-12a), (V-13a), (V-14a) % sustrato en el reactor

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function dy = batchmonodo2(t,y) batchmonodo2(t,y) Kla = 17.6; %(h-1); % de aireación O2sat = 8; Y = 0.3678; Umax = 0.07937; Ks = 115.374; % mg/L kd = 0.0041166; %h-1 a = 0.302; b = 0.010079; %h-1 %sistema de ecuaciones dy = zeros(3,1); zeros( 3,1); %vector columna dy(1) = -((Umax/Y)*y(1)*y(2))/(Ks+y(1));% -((Umax/Y)*y(1)*y(2))/(Ks+y(1));%ec.(V ec.(V-12a) -12a) dy(2) = ((Umax*y(1)*y(2))/(Ks+y(1))-kd*y(2);% ((Umax*y(1)*y(2))/(Ks+y(1))-kd*y(2);%ec.(V ec.(V-13a) -13a) dy(3) = kla*(O2sat-y(3))-(((a/Y)*Umax kla*(O2sat-y(3))-(((a/Y)*Umax*y(1)*y(2))/(Ks+y(1)))-b*y(2);%Ec.( *y(1)*y(2))/(Ks+y(1)))-b*y(2);%Ec.(V-14a V-14a)) archivo-m, por lo tanto, para correrlo se requiere Recuerde que este listado se salvó como archivo-m, regresar al ambiente Matlab.

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ode45 de Matlab se resuelve el sistema de tres ecuaciones diferenciales por Mediante el comando ode45 de el método de Runge Kutta, de 0 a 20 horas ([o 20]), 20]), con condiciones iniciales especificas. (recuerde que estas condiciones y parámetros se obtuvieron del ejemplo de las pruebas experimentales.) Inmediatamente después, para obtener la figura con los datos gráficos de las tres variables (SSV), (DQO), (O2), se debe teclear el comando subplot(2,2,2). subplot(2,2,2). Abajo, de izquierda a derecha, estará la subplot(2,2,3). subplot(2,2,3). Por último, la supolot(2,2,4). En este ejemplo obtendremos tres gráficas: cada una corresponde a los diferentes parámetros manejados. Las indicaciones se introducen en la siguiente forma. LAS DEL COMANDO QUE CORRESPONDE A LOS (SSV): >>subplot(2,2,1),plot(t,y(:,2),`.’) LAS DEL COMANDO QUE CORRESPONDE A LA DBO:

>>subplot(2,2,2),plot(t,y(:,1),`.’) ’) LAS DEL COMANDO QUE CORRESPONDE AL OXÍGENO DISUELTO: >>subplot(2,2,3),plot(t,y(:,3),`.’)

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   L    /   g   m     )     (    V

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 Ahora ahí que agregar agregar a lo especificado que es posible utilizar utilizar la siguiente instrucción: >>plot(t,y(:1),`.’,t,y(:2),`.’,t,y(:3),`+’) Después de teclear las indicaciones de los comandos que acabamos de enlistar, nos aparecen las figuras 53,54,55, donde se observa el comportamiento de los tres parámetros en el reactor, a diferentes tiempos de reacción. En este caso aparecerán las 3 líneas de datos (SSV), (DBO), (O2disuelto) en una misma figura. Sin embargo, debido a que la concentración de (O2) disuelto es de menor magnitud que la de los (SSV) y que la de la (DQO), la línea correspondiente aparecerá como la que se observa en la parte inferior de la grafica, por lo que no se podrán detectar sus variaciones. También se puede insertar en eje adicional seleccionando con el cursor Insert  Insert  en la ventana de la figura donde aparece una lista con varios rubros entre ellos Axes, y, Axes, el cual se deberá oprimir; aparecerá el cursor en forma de cruz y,

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FIGURA Variación

55. del

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Con la finalidad de evaluar y comparar los resultados que se obtienen al variar la concentración inicial de (SSV), se realiza la corrida para el mismo periodo de tiempo, pero se varían las 5], donde se especifica el condiciones iniciales, lo cual queda ahora quedará como [668 400 5], valor inicial de (SSV)=400mg/L, dado que éste es el que corresponde a la prueba  (B). Es importante que antes de obtener los resultados para esta otra prueba (B), se teclee el comando hold on: de esta forma, las gráficas anteriores permanecen y se pueden comparar con las generadas ahora; entonces, >>hold on

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Y ya los comandos de la prueba (B): >> [t,y] = ode45(‘lotemonod’, [0 20], [668 400 5]); Se puede observar que hemos cambiado la condición inicial de (SSV), la de ahora corresponde a 400mg/L. Las figuras 57,58,59 muestran los resultados obtenidos al variar las condiciones iniciales de (SSV) de 210 (condición (condición B). A) a 400mg/L (condición Vamos primero a obtener la figura; se deberá seguir el procedimiento descrito anteriormente; decíamos que usando subplot sea el plot sea el comando subplot sea el plot,, aparecería la figura correspondiente, en este caso: Es preciso recalcar el efecto que se obtiene al incrementar la concentración de microorganismos en el inoculo (SSV) al inicio del proceso: a 400mg/L (condición B), se reduce el tiempo de agotamiento del sustrato, éste se agota antes, cerca de las 10 horas de proceso  – a diferencia de lo que sucede con los 210mg/L de la condición A, pues éste se

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