FORMULARIO ABSORCION + DESORCION

Nomenclatura y conversiones de unidades de concentración en ABSORCION y DESORCION de un componente. FASE GASEOSA: Fracción molar (1): Relación molar: Fracción peso: Relación molar: Presión total: Densidad molar: Densidad total: Densidad parcial:

Densidad masa: Fracción molar (2): Fracción peso (2): %mol: %peso:

ppm

:

    =   =   =   =  [=]  .   =   =   =  [=]       ∙ [ ]  =   =  = ∙( = )∙    .    =  [=]   =  +    [=]    =  () ∙  =  ( ) ∙  =   [=] . .  . .  =  = . =  = (.∙, ⁄ ∙)∙(,) [=] . . ̅ =   ̅  = ̅ ∙  =  ∙  =  ( ∙ ) ∙  = ( ∙ ) ∙  =  ∙ ∙[=] . . ̅ =  ∙  =   ∙ [=]  .   ̅  =   ∙  =  [=] .      = . =  [=]  .  =   [=] . 10 ∙  10 ∙  10 ∙    ̅  .   ∙  .. [=] . 10 ∙  01

0 01

0

01 01

=

 ppm

:

FASE LIQUIDA: PM mezcla:

    =  ∙  + (1− (1− )∙[=]  

̅ .  ..  [=] .  = . [=]  .   =    = 1−    = ̅ .  ..    .. [=] . = ()∙ =  ∙  =  ∙ ̅  ̅ =  . ∙    [=] . = ̅̅ ∙ ̅ =  ∙   = (  ∙ )∙̅ =  ∙ ∙ ̅[=] . ̅   = ()∙    = =∙∙      =  ∙  ( = )∙  ∙  =   ∙   ∗      ==  ∙∙∗   ∗∗ == ∙∙    == ∙∙ ∗∗     ∗ =  ∙  ∗[] =  ∙  =  ∙   ppm

:

=

Fracción molar (2):

01

Densidad molar:

Densidad masa:

Densidad parcial:

:

En la interfase:

o

=

En el equilibrio:

o o



 = ∗∗  =  = 1  =   = 

Recuperaciones: Gastos:

Balance de masa:

 =    =  ∙  = ∙ = ∙(1+)  =  ∙(1+)  = (1−)∙  =  ∙(1+)  ∙ ̅ =  ∙   =  ∙ ( − ) =  ∙ (  − ) = , ∙ ( ∗ −)

Velocidades de transferencia A o flujos molares de A: Pesos moleculares:

 =  ∙ ()+ ∙ (1−)

=

 =  = , =   = ∗ [=] ∆∆

o

 = ∗ [=] ∆∆

Absorción

=

 =  =   = ∗ [=] ∆∆

o

 = ∗ [=] ∆∆

Desorción

COEFICIENTES DE TRANSFERENCIA DE MASA:

 = ( )∙ =  −   = ()∙ ∙ =  −  = (1−)(1−)  =   ∙ () =  −  =  ∙ () =   = () = ()⁄( ⁄) =   ∙ ()  = ()(1−)(1−) =   −  −   ̅  = () ̅ − ̅  = ()() =  ()∙( − )⁄(⁄)  =   =   = 

, ver definición abajo

y

∗    −     =  ∙ () = ∗ −∙()  =  ∙ ()  = ()∙(1−)(1−∗) = ( )∙( − ∗) =  ∗ −  =   ∙ () =  ∙   ≈    = ∗ − =  ()  

Para soluciones diluidas:

RESUMEN: Coeficiente de transferencia de masa local entre fases GAS

LIQUIDO

  ∙  = ( ∙ ) × 

 →  

 ∙ aloc = (G ∙ a)loc × PT  ∙  = (  ∙ ) × 

 →  

 ∙ aloc = (C ∙ a)loc × CTG

 →  

 → 

  PM × Mezcla PMA

  →  

 

(L ∙ a)loc = ( ∙ a)loc ×

PMMezcla ρL

PMMezcla PMA  (  ̅ ∙ ) = (  ∙ ) × 

 →   ̅

1 PMA  (  ∙ ) = (  ∙ ) ×   (L ∙ a)loc = (L ∙ a)loc ×

  →  

1 × PMA

(X ∙ a)loc = (X ∙ a)loc ×

  PM × GS PMA

( ∙ ) = ( ∙ ) ×

,  [=] ó    : , ,    ,,, [=] ó   

Coeficientes de transferencia de masa local entre dos fases RESISTENCIAS:

 

( ∙ a)loc = ( ∙ a)loc ×

( ∙ ) ∙ ( ∙ a) (G ∙ a)loc = C loc R∙T  (  ∙ ) = (  ∙ ) × 

(Y ∙ a)loc = (Y ∙ a)loc

(  ∙ ) = (  ∙ ) ×

 →   ( ∙ ) = ( ∙ ) ×

(  ∙ ) =

(C ∙ a)loc = (C ∙ a)loc

( ∙ a)loc = (L ∙ a)loc × CTL

P CTG = R∙T ρ CTL = L PML

 →    ∙  =  ∙  ×  ∙ aloc =  ∙ aloc

(  ∙ ) = (  ∙ ) × 

 → 

 =  +  1 =  +  1  = 1  +     y

PMLS PMA

1  = 1 +     1  = 1 +     1  = 1 + 1   ∙ ()   =  +  1  = 1  + 1   ∙   1  = 1  + 1  = 1  1    ∙     1  = 1 + 1   ∙   Para la resistencia gaseosa:

1 1 1              =   =  =  ∙  =  ∙   1  1 1  = 1 =  =   ∙1() =  1   1  ∙ ()       =   =   ∙ = 1  1  1  =   =  ∙  = 1 =  1  1 

Para la resistencia líquida:

RESUMEN: ABSORCIÓN

     =   + ( ∙1)  × (1 ∙ ) ( ∙ 1) (K ∙ a)loc = m ×  ∙ aloc + ( ∙ a)loc 1 1 1 =   + (KL ∙ a)loc m   × (G ∙ a)loc (L ∙ a)loc 1 1 1 =   + (KL ∙ a)loc m  ´  × (C ∙ a)loc (L ∙ a)loc       =   + ( ∙ ) (m ∙´) ( ∙ ) 1 1  =   + K ∙ aloc ( ∙ a)loc  ∙ aloc

DESORCIÓN

     =   + ( ∙1) ( ∙1)  × (1 ∙ ) (K ∙ a)loc = ( ∙ a)loc + m ×  ∙ aloc 1 1 1 =   + (KL ∙ a)loc (L ∙ a)loc m   × (G ∙ a)loc 1 1 1 =   + (KL ∙ a)loc (L ∙ a)loc m  ´ × (C ∙ a)loc       =   + ( ∙ ) ( ∙ ) (m ∙ ´) 1 1  =   + K ∙ aloc  ∙ aloc ( ∙ a)loc

ABSORCIÓN

DESORCIÓN

1 = m´    + 1 (KG ∙ a)loc (L ∙ a)loc (G ∙ a)loc 1 = m´    + 1 (KC ∙ a)loc (L ∙ a)loc (C ∙ a)loc ( ∙ ) =   × ( ∙ ) (K ∙ a)loc = m × K ∙ aloc (KL ∙ a)loc = m   × (KG ∙ a)loc (KL ∙ a)loc = m   × (KC ∙ a)loc ¨ = − ((  ∙∙ )) m¨ = − (  ∙∙ aa)locloc m¨   = − ((GL  ∙∙ a)a)locloc m¨   = − ((LC  ∙∙ a)a)locloc

1 = 1  + m´    (KG ∙ a)loc (G ∙ a)loc (L ∙ a)loc 1 = 1  + m´   (KC ∙ a)loc (C ∙ a)loc (L ∙ a)loc ( ∙ ) =   × ( ∙ ) (K ∙ a)loc = m × K ∙ aloc (KL ∙ a)loc = m    × (KG ∙ a)loc (KL ∙ a)loc = m    × (KC ∙ a)loc ¨ = − ((  ∙∙ )) m¨ = − (  ∙∙ aa)locloc m¨   = − ((GL  ∙∙ a)a)locloc m¨   = − ((CL  ∙∙ a)a)locloc

Flujos molares específicos de A o velocidades de transferencia de masa de A,



:

ABSORCION:

 = ( − ) = ()( − ) = ()( − )∙ = ( − ∗) = () − ∗   −   = () −  = () −  = ()( − ) = ()1−  1− = ()( − ) = ()   −    = ()(∗ − ) = ()( − )

 ̅ ̅      ∗  = ( − ) = ()( − ) = () −  = () −  = ()̅ ̅ − ̅ ̅ = ( ̅ )(̅ − ̅) = ()( ∗ − ) = ()( ∗ − )  = ()( − ∗) = ()(∗ −) = ()(∗ − ) = ( − ∗) = ()( − ∗) = ()(∗ −) = ()∙ ∙ ( − ∗)=()(  − ) DESORCION: (Cambia el orden del subíndice i y el superíndice * respecto a la absorción)

 = ()( − ∗) = ()( ∗ − ) ()∗ −  = ()(  − ) =

RESUMEN: ABSORCIÓN

DESORCIÓN

( ∙ ) =  ∙  − ∗  =  ∙   −   = K  ∙ aloc An − A∗n  =  ∙ aloc  An − Ai  = ( ∙ ) − ∗ = ( ∙ )  −   = (KY ∙ a)loc YAn − YA∗n  = (Y ∙ a)loc YAn  − YAi  = ( ∙ ) − ∗∙ =  ( ∙ )  −  ∙ = ( ∙ ) − ∗ ∙ =  ( ∙ )  −  ∙ = (KC ∙ a)loc An − A∗n ∙ CTG n =  (C ∙ a)loc An − Ai ∙CTG n = ( ∙ )∗ − = ( ∙ )  −  = (K ∙ a)loc A∗n −An  = ( ∙ a)loc Ai  − An  = ( ∙ )∗ − = ( ∙ )  −  = (KX ∙ a)loc XA∗ n −XAn  = (X ∙ a)loc XAi  − XAn  = ( ∙ )∗ −  ∙ =  ( ∙ )  −  ∙ DESORCIÓN

´

( ∙ ) =  ( ∙ ) − ∗  = ( ∙ )  −   = (K ∙ a)loc An − A∗n  = ( ∙ a)loc An − Ai  = ( ∙ ) − ∗ = ( ∙ )  −   = (KX ∙ a)loc XAn − XA∗ n  = (X ∙ a)loc XAn − XAi  = ( ∙ ) − ∗ ∙ =  ( ∙ )  −  ∙ = (KL ∙ a)loc An  − A∗n ∙ CTL n =  (L ∙ a)loc An − Ai ∙CTL n =   ∙ ∗ −  =  ∙   −   = K  ∙ aloc A∗n −   =  ∙ aloc Ai  −    = ( ∙ )∗ −  = ( ∙ )  −   = (KY ∙ a)loc YA∗n −   = (Y ∙ a)loc YAi  −    = ( ∙ )∗ − ∙ =  ( ∙ )  −   ∙ = ( ∙ )∗ − ∙  =  ( ∙ )  −  ∙

DISEÑO BÁSICO DIFUSIONAL DE TORRES EMPACADAS PARA LA  ADSORCÓN ISOTÉRMICA E ISOBÁRICA DE UN COMPONENTE A RÉGIMEN PERMANENTE Diseño de columnas. D c, Zc.

ABSORCIÓN: FASE GAS:

∗)+(1− )   ( 1−  (1−) =  (1−∗) (1−) ∗) − ( − ∗)   (    −    ∗ ( − ) =  ( − ∗) ( − ∗)

 = () ∗ () ) ( ( ) = ( ∗ ) ∗ (1− )     1 () =  ( − ∗) + 2(−1)  (1−)  (−1)   1 (1+) () =  ( − ∗ ) + 2   (1+) FASE LIQUIDA:

 = () ∗ () ∗)   ( )−(1− 1−   (1−) =  (1−) (1−∗) ) ( () = ( ∗ ) ∗ (1− )

  1 (1−) () =  (∗ −) − 2   (1−)   1 (1−) () =  ( ∗ −) − 2   (1−) AGOTAMIENTO: FASE GAS:

 = () ∗ () ∗)   ( )−(1− 1−   (1−) =  (1−) (1−∗) ) (  ) = ( ∗ ) ∗ (1− )   1 (1+) () =  (∗ −  ) + 2   (1+)   1 (1+) () =  (∗ −  ) + 2   (1+) FASE LIQUIDA:

 = () ∗ () ∗)−(1−)   ( 1−  (1−) =  (1−∗) (1−) ) ( () = ( ∗ ) ∗ (1− ) ) () =  ( −∗ ) + 12   (1− (1−)

  1 (1+) ( ) =  (  − ∗ ) − 2   (1+) ABSORCION SOLUCIONES DILUIDAS: FASE GAS:

  ∗ ( ) =  ( − ∗) = (  − ) ∗ −(1−  )∗   ( 1− )   (1−) = 2

∗  z =  ∗ ∗(1− )(  − ) ∗) − ( − ∗)   (    −    ∗ ( −  ) =  ( − ∗) ( − ∗)

∗  z =  ( ∗)  ∗ (  −  ) () = ((∗ − −)) Donde:

∗ − ) − (∗ − )   (   ∗ ( − ) =  (∗ − ) (∗ − ) FASE LIQUIDA:

 = () ∗ ()  = ( ∗ ) ∗ (∗ − −) AGOTAMIENTO SOLUCIONES DILUIDAS:

z = ( ∗)(∗−)

∗ ) z =  ( ∗)  ∗ (∗−) = ( ∗) ∗ (∗  ( −)  = ( ∗  )∗ ( − −)∗  ∗ −(1− )∗   ( 1−  )   (1−) = 2

Ecuaciones opcionales: Absorción:

() = ( ∗ ) ∗ (1− ) AGOTAMIENTO:

 () = ( ∗ ) ∗(1− )