1
Operaciones de Transferencia De Cantidad de Movimiento-
TEMA VI
SEDIMENTA SEDIMENTACION CENTRIFUGA
rof!" In#! $or#e R! %&' A(O" )*+, 1
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6
SEPARACIONES CENTRÍFUGAS 1. Introduc Introducción: ción: Objetivos Objetivos de de la separ separación ación centrífuga centrífuga La “sedimentación centríf!a"# es $a se%aración de %artíc$as de n f$id& %&r acción de $a fer'a centríf!a( Una %artíc$a )e cae a tra*+s de n f$id& ,a-& $a acción de $a fer'a de !ra*edad. $& /ace a na *e$&cidad )e de%ende de s tama0& de s densidad( Las %artíc$as %e)e0as & $as !&tas $í)idas $& /acen a *e$&cidades ,a-as. %&r $& ca$ s se%aración se$e ser difíci$ se re)ieren e)i%&s de !randes dimensi&nes 2%es e$ tama0& de$ e)i%& est3 determinad& %&r $a *e$&cidad de sedimentación de $as %artíc$as m3s %e)e0as )e se desea se%arar4( Una f&rma de amentar $as *e$&cidades termina$es es a%$icand& na fer'a centríf!a s&,re e$ sistema( P&r $& tant&. $&s se%arad&res centríf!&s s&n mc/& m3s eficientes )e $&s se%arad&res %&r !ra*edad %ara $a se%aración de %artíc$as m %e)e0as & de !&tas finas. na *enta-a adici&na$ es )e e$ tama0& de $&s e)i%&s es mc/& men&r )e $&s de !ra*edad. %ara na ca%acidad dada de %r&dcción( 2. Principios de la separación centrífuga: centrífuga: L&s se%arad&res centríf!&s se ,asan en e$ %rinci%i& de )e# “cand& na %artíc$a es &,$i!ada a !irar en na traect&ria circ$ar en t&rn& a n %nt& & e-e centra$. a na distancia radia$ c&nstante. est3 s-eta a $a acción de na fer'a centríf!a )e act5a act5a /acia afera. en dirección radia$"( radia$"( Si e$ &,-et& )e !ira es n reci%iente ci$índric&. %&r acción de $a fer'a centríf!a e$ c&ntenid& de$ mism& es im%$sad& s&,re $as %aredes de$ reci%iente( Esta fer'a f er'a es $a )e %r&*&ca $a sedimentación de $as %artíc$as a tra*+s de$ f$id& c&ntenid& en n reci%iente en en r&tación( 6(1( Ecaci&nes %ara $a Fer'a Centríf!a( La ace$eración de $a fer'a centríf!a 2Fc4 en e$ m&*imient& circ$ar es#
ae 7 r86 9ónde# ae# ace$eración casada %&r $a fer'a centríf!a en m:s 6( r # # distancia radia$ a$ centr& de r&tación en mts( 8# *e$&cidad an!$ar en rad:s Uti$i'and& e$ SI. $a Fc )e act5a s&,re $a %artíc$a est3 dada %&r#
Fc 7 mae 7 mr86 C&m& 8 7 *t!:r siend& *t! # *e$&cidad tan!encia$ de $a %artíc$a en m:s(
( )
v tg Fc= mr r
2
Las *e$&cidades de r&tación se e;%resan en# n 2r%m4 ω=
n=
2 πn 60
60 v tg 2 πr
Sstitend& en $a ecación ecación de $a Fc. $a misma misma )eda#
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3. Métodos Métodos de separa separación ción centrífu centrífuga: ga: E;isten d&s m+t&d&s %rinci%a$es )e ti$i'an $a fer'a centríf!a %ara %r&dcir $a se%aración de %artíc$as de n f$id Separación Ciclónica: )e se $$e*a a ca,& en e)i%&s a4 La Separación e)i%&s $$amad&s “cic$&nes". “cic$&nes". en $&s ca$es $a fer'a centríf!a se !enera efect&s de r&tación de $a ss%ensión )e in!resa a$ reci%iente. e$ ca$ es estaci&nari&( L&s cic$&nes se ti$i'an %rinci%a$mente %ara se%arar %&$*&s & “nie,$as" de !ases & %artíc$as só$idas de $í)id&s( Centrifugación: )e se rea$i'a en e)i%&s $$amad&s “centríf!as". en $&s ca$es $a fer'a ,4 La Centrifugación: centríf!a se !enera %&r $a r&tación r&tación de$ reci%iente( La centrif!ación centrif!ación se ti$i'a %ara se%arar %artíc$as só$idas de n $í)id& 2c$arificación4 2c$arificación4 & %ara se%arar se%arar $í)id&s inmisci,$es(
<( entajas: C&m& $a Fc = F!. a$ amentar $a fer'a )e act5a s&,re $as %artíc$as. amentan $as *e$&cidades termina$es de $as mismas( Est& %ermite# > Se%arar %artíc$as m %e)e0as & de ,a-as densidades( > Uti$i'ar Uti$i 'ar e)i%&s m3s %e)e0&s %ara se%aración de me'c$as(
I. !"P#$#%I&' %I%(&'I%#: La se%aración cic$ónica es n& de $&s m+t&d&s m3s ec&nómic&s %ara se%arar %&$*&s & nie,$as de !ases & $í)id&s. sin e$ s& de fi$tr&s. ti$i'and& e$ efect& de “*órtice" %ara $a se%aración( Pede sarse %ara se%arar %artíc$as c&n di3metr&s entre 6 1??? micras. si ,ien en $a %r3ctica $as %artíc$as ma&res a 6?? micras se se%aran %referentemente %referentemente en sedimentad&res sedimentad&res de !ra*edad( !ra*edad(
#plicaciones: Aserrader&s# e$iminación de aserrín %&$*&( Refinerías de %etró$e se%aración de !ases aceites( Indstria cementera# %reca$entad&r de $&s /&rn&s( C&cinas Indstria$es & Pr&fesi&na$es# Se%aración de $a !rasa de$ f$-& de aire( Tratamient& Tratamient& de a!as resida$es# se%aración de só$id&s %resentes en $í)id&s( 2@idr&cic$&nes4( Ca,inas de Pintra# e;tracción de $a %intra resida$ en %&$*&
)escripción del e*uipo: Un cic$ón %ede ser c&nsiderad& c&m& na c3mara de sedimentación en $a ca$. $a ace$eración de,ida a $a fer'a de !ra*edad !ra*edad se reem%$a'a %&r na ace$eración ace$eración centríf!a( En est&s est&s e)i%&s. $a fer'a centríf!a %ede *ariar entre 6?? *eces $a fer'a de !ra*edad. siend& ma&r en $&s cic$&nes de di3metr& %e)e0&. $& ca$. $&s /ace a%r&%iad&s %ara $a se%aración de %artíc$as %e)e0as de ,a-as *e$&cidades *e$&cidades de sedimentación sedimentación en e$ cam%& cam%& !ra*itaci&na$( Un cic$ón tí%ic& n& c&ntiene %artes mó*i$es( C&nsiste en n ci$indr& *ertica$ c&n n f&nd& cónic&.
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Las dimensi&nes de $&s cic$&nes c&mercia$es se encentran n&rma$i'adas se e;%resan en fnción de$ di3metr& de$ cic$ón( Estdi&s e;%erimenta$es determinar&n determinar&n )e $a eficiencia de se%aración de $&s cic$&nes es m3;ima en a)e$$&s )e cm%$en c&n $as si!ientes re$aci&nes !e&m+tricas# Fi!( 1 Pr&%&rci&nes de n Se%arad&r Cic$ónic&(
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Proceso de separación en un ciclón: Cand& $a ss%ensión in!resa a$ cic$ón a tra*+s de $a entrada tan!encia$ ,icada en $a %arte s%eri&r de$ ci$indr&. ad)iere n ferte m&*imient& !irat&ri& en f&rma de /e$ic&ida$ a$reded&r /acia a,a-&. c&men'and& desde desde $& m3s a$t& 2m3s anc/&4 a $&s m3s ,a-& 2m3s estrec/&4 estrec/&4 de$ cer%& ci$índric&( E$ estrec/amient& de$ c&n& en $a %arte inferi&r. /ace )e e$ !as rea$ice n des%$a'amient& /acia arri,a en f&rma de na se!nda es%ira$. en e$ centr& de$ ci$indr&. sa$iend& fina$mente %&r e$ t,& de descar!a s%eri&r( s%eri&r( Para )e na %artíc$a se se%are de$ !as. en n tiem%& men&r & i!a$ a$ tiem%& de residencia de$ !as en e$ cic$ón. cic$ón. de,e $$e!ar a $a %ared( La fer'a centríf!a )e se &ri!ina &ri!ina c&m& c&nsecencia c&nsecencia de$ m&*imient& circ$ar de $a c&rriente !ase&sa. tiende a des%$a'ar radia$mente a $as %artíc$as /acia $a %ared. de m&d& m&d& )e a)e$$as )e a$can'an $a %ared. des$i'an des$i'an /acia a,a-& se rec&!en en e$ c&$ect&r de %&$*&s(2La sa$ida de,e ser /erm+tica %ara e*itar $a f!a de !ases a tra*+s de $a misma4( E$ !as entra a$ cic$ón a tra*+s de$ c&ndct& de a$imentación de anc/& +c. $e!& se distri,e s&,re $a %ared f&rmand& na ca%a c& es%es&r *a disminend&( En c&nsecencia. c&nsecencia. $a ma&r distancia !r )e de,en rec&rrer $as %artíc$as %ara $$e!ar a $a %ared es c 7= !r , +c Si ,ien se /an rea$i'ad& mc/&s intent&s %ara &,tener na ecación )e %ermita na %redicción teórica de$ rendimient& de n cic$ón. /asta /& n& e;isten re$aci&nes teóricas ace%tadas en !enera$( Ca$)ier %artíc$a %ede se%ararse de$ !as en e$ e)i%&. si en e$ tiem%& de residencia dis%&ni,$e. $a misma %ede $$e!ar /asta $a %ared( Sin em,ar!&. es difíci$ %redecir $a traect&ria de $as %artíc$as dentr& de$ cic$ón. %&r $& ca$. $as ecaci&nes teóricas )e se /an desarr&$$ad& se ,asan en na serie de s%&sici&nes( s%&sici&nes( )i-etro Mínio. E$ di3metr& de $a %artíc$a m3s %e)e0a. )e rec&rre na distancia Sr 7 c. teóricamente se se%ara de$ !as c&n na eficiencia ƞi 7 1?? D. & sea. )e se se%ara t&ta$mente de$ !as se $$ama diámetro mínimo( Estas %artíc$as s&n $as m3s %e)e0as )e se se%aran t&ta$mente en e$ cic$ón n& a%arecen en $a c&rriente de !as )e sa$e de$ mism&( Las %artíc$as c&n 9% 9% min. en e$ tiem%& de residencia dis%&ni,$e. rec&rren na distancia Sr c %&r $& tant& n& se se%aran c&m%$etamente c&m%$etamente de$ !as2eficiencia !as2eficiencia de se%aración se%aración ƞi 1??D4( Cas& c&ntrari& c&n 9% = 9% min. en e$ tiem%& de residencia dis%&ni,$e. rec&rren na distancia Sr = c. se se%aran t&ta$mente de $a c&rriente !ase&sa( La ecación m3s satisfact&ria es $a )e re$aci&na e$ di3metr& de %artíc$a c&n $a eficiencia de se%aración. %r&%esta %&r R&sin. Ramm$er e Inte$mann. )e %ermite ca$c$ar e$ diámetro mínimo 29%mín4. /ace Sr 7 c 7= 9% 7 9% min ( − ) √ c 7 anc/& de $a sección de entrada a$ a$ cic$ón 7 distancia distancia m3;ima )e rec&rre $a %artíc$a Dpmin =
9 μ Bc
π.ne.Vc ρ s ρ
9ónde# en dirección radia$. /asta $a %ared c 7 *e$&cidad de entrada a$ cic$ón ne 7 n5mer& efica' de *e$tas )e efect5a e$ !as dentr& de$ cic$ón( Se determina e;%erimenta$mente( Para cic$&nes c&n $as %r&%&rci&nes !e&m+tricas de $a Fi! 214# ne 7
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J
se s%&ne )e $a c&rriente de !as d3 n n5mer& determinad& de *e$tas 2 ne4. a na *e$&cidad ´ ) ( tan!encia$ c&nstante e i!a$ a $a *e$&cidad media a $a entrada de$ cic$ón ( Vc se c&nsidera *3$ida $a $e de St&Hes St&Hes de $a *e$&cidad termina$ %ara e$ m&*imient& de $as %artíc$as %artíc$as en n cam%& centríf!&( 2 2 r ω Dp ( ρs− ρ) 2m:s4 Vt R= 18 μ
9ónde# ω =
´ velocidad Vc tangencial = velocidad tangencial r posición posición radial ´ = Vc
distanci distancia a recorrida ecorrida por el gas dentrodel dentrodel ciclón ciclón 2 πrne = tiemp tiempo o de reside esidenci ncia a del del gas gas en elciclón elciclón θR
ne 7 n5mer& efecti*& de *e$tas /ec/as %&r e$ !as en e$ cic$ón( Adem3s# Vt R=
distancia distancia radial recorrida recorrida por la partícula partícula !r = tiempoue tiempoue la partícul partícula a tarda tarda enr en recorre ecorrerr esadistancia esadistancia θR
)i-etro de %orte. E$ diámetro de corte es e$ di3metr& de %artíc$a %ara $a ca$ $a eficiencia de se%aración es de$ ? D 2distancia m3;ima )e rec&rre $a %artíc$a en dirección radia$ 7 c:64( Es decir# Dpc =
Siend 9%c:9%mín 7
1
√ 2
√
4,5 μ Bc
π.ne.Vc ( ρ s− ρ )
=0,707
Si $a ecación de R&sin se e;%resa en $a f&rma !enera$# Dp c =
√
9 μ !r
π.ne.Vc ( ρ s− ρ )
9&nde Sr 7 $a distancia )e rec&rre $a %artíc$a %ara $$e!ar /asta $a %ared. %ara# Para ƞi 7 1??D# Sr 7 c. 9% 7 9%mín 9%mín Para ƞi 7 D# Sr Sr 7 ?.c Para ƞi 7 ?D# Sr 7 c:6 c:6 & Sr 7 ?.c 9% 7 9%c. etc Para ƞi 7 6D# Sr 7 ?.6c Se %ede &,tener $a cr*a teórica de “eficiencia de se%aración en fnción de$ di3metr& de %artíc$a". e;%resad& +ste c&m& $a re$ación 9%:9%c( C&m& 9%c es fnción de c. +sta a s *e' de%ende de$ di3metr& de$ cic$ón 9c. este ti%& de cr*as %ermite estdiar $a de%endencia de $a eficiencia de se%aración c&n e$ di3metr& de %artíc$a e$ di3metr& de$ cic$ón(
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"ficiencia de separación en un ciclón: 9e na manera !enera$. %ara $&s e)i%&s rec&$ect&res de %&$*&s. $a “eficiencia de se%aración" se define c&m& $a re$ación entre e$ %es& de %&$*& rec&$ectad& di*idid& %&r e$ %es& de %&$*& )e entra a$ e)i% ƞ" =
m#" m $"
100
2D4
Siend mCT 7 masa c&$ectada t&ta$ mET 7 masa entrante( C&m& $&s só$id&s di*idid&s n&rma$mente est3n %resentes c&n tama0&s diferentes de %artíc$as. se c&$ectan casi t&das $as %artíc$as !randes )e entran . %er& %&cas %artíc$as %e)e0as )e sa$en c&n e$ !as 2 mSi4. $a eficiencia de se%aración se%aración de,e ca$c$arse %ara cada cada tama0& c&m ƞi 2 %artíc$as !randes4 !randes4 == ƞi 2 %artíc$as %e)e0as4 %e)e0as4 siend ƞi =
m #i m $i
100
2D4
Siend& mCi 7 masa c&$ectada c&$ectada t&ta$ de %artíc$as de 9%i mEi 7 masa entrante de %artíc$as de 9%i Se %ede escri,ir na ecación !enera$# 100 ƞ" =100 % & i ƞi = % m #i 2D4 m $"
Siend & i=
m $i m $"
C&n fines %r3ctic&s. $a eficiencia de se%aración de n cic$ón de,e ser determinada e;%erimenta$mente( Para cic$&nes c&n $as %r&%&rci&nes !e&m+tricas descritas inicia$mente. $a cr*a e;%erimenta$ es re%resentada %&r $a ecación 2&,tenida %&r c&rre$ación de dat&s e;%erimenta$es4#
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K
L&s cic$&nes !randes dan $!ar a men&res eficiencias de se%aración. de,id& %rinci%a$mente a $a disminción de $a fer'a centríf!a a$ amentar e$ 9c( Est& si!nifica )e. si en n dad& %r&ces& de se%aración. se desea amentar $a eficiencia de$ %r&ces&. es necesari& ti$i'ar cic$&nes de di3metr& %e)e0&. $& ca$ %resenta $a des*enta-a de )e. %ara tratar n determinad& cada$ de a$imentación. %&dría ser necesari& ti$i'ar *arias nidades de %e)e0& di3metr& &%erand& en %ara$e$&. $& )e encarece $a insta$ación( E$ dise0& fina$ de,e im%$icar e$ $$e!ar a n t+rmin& medi& entre eficiencia c&m%$e-idad de$ e)i%& 2c&st&4( La disminción de $a eficiencia de se%aración a$ disminir e$ tama0& de $as %artíc$as es men&r )e $a %redic/a %&r $a ecación de R&sin &tr&s. de,id& %r&,a,$emente a )e %ede %r&dcirse a!$& a!$&me mera raci ción ón de $as $as %artí %artíc c$a $ass fina finass c&n c&n e$ c&ns c&nsi! i!i ien ente te ame ament nt&& de $as $as *e$& *e$&ci cida dade dess de sedimentación(
"ficiencia global de separación. Ca$)ier %&$*& & ne,$ina se c&m%&ne de %artíc$as )e c,ren na !ran *ariedad de tama0&s( La eficiencia !$&,a$ de rec&$ección es $a sma de $as eficiencias de cada tama0& de %artíc$a. m$ti%$icada %&r $a fracción de masa de ese tama0& en e$ %&$*& & nie,$a(
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La caída de %resión m3;ima %ermisi,$e en n cic$ón est3 determinada %&r $as $imitaci&nes de$ *enti$ad&r. c&rres%&nde c&rres%&nde a na *e$&cidad de entrada a$ cic$ón entre J a 61 m:se!. de m&d& )e %ara dise0ar n cic$ón se se$e esta,$ecer na *e$&cidad de entrada de 1 m:se!( En !enera$. %ara ca$c$ar $a caída de %resión en e$ cic$ón. se ti$i'a $a ecación# ´ ρ Vc ' (= ) . 2 gc
2
9ónde# P 7 caída de %resión de,ida a fricción 2M!:m 64 M 7 c&nstante c&nstante 7 K. %ara cic$&nes c&n $as %r&%&rci&nes !e&m+tricas de $a Fi! 214 7 densidad de$ !as 2M!:m B4 c 7 *e$&cidad de entrada de$ !as 2m:se!4 ´ seg2 (se! !c 7 .K m(M!: )g
II. %"'0$I/#%I&': %"'0$I/#%I&': Centrif!ación es $a se%aración de %artíc$as só$idas & !&tas $í)idas de na fase $í)ida c&ntina. %&r acción de na na fer'a centríf!a( centríf!a( T&d&s $&s c&m%&nentes de n sistema f&rmad& %&r %artíc$as ss%endidas en na fase $í)ida. encerr encerrad& ad&ss en n reci%i reci%ient entee ci$índ ci$índric ric&& !irat& !irat&ri& ri&.. est3n est3n s&meti s&metid&s d&s a $a acció acciónn de na fer'a fer'a centríf!a( Esta fer'a /ace )e t&das $as %artíc$as de ma&r densidad )e e$ $í)id& se des%$acen radia$mente /acia $as %aredes de$ reci%iente 2sedimenten4. $as %artíc$as c&n men&r densidad )e e$ $í)id& se des%$acen radia$mente /acia e$ centr& de r&tación 2f$&ten4(
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1?
En $a Fi!( 2a4 se mestra n reci%iente ci$índric& )e c&ntiene na ss%ensión de %artíc$as só$idas en n $í)id&( Si e$ reci%iente es estaci&nari&. $a s%erficie de$ $í)id& es /&ri'&nta$. se %r&dce e$ asentamient& de $&s só$id&s en e$ f&nd& de$ reci%iente %&r acción de $a fer'a de !ra*edad( En $a Fi!( 2,4 e$ mism& reci%iente se /ace !irar a$reded&r de s e-e *ertica$( En este cas&. s&,re e$ sistema act5an d&s fer'as# $a fer'a de !ra*edad. )e act5a /acia a,a-&. $a fer'a centríf!a. )e act5a en dirección radia$( En $&s e)i%&s indstria$es. $a ma!nitd de $a fer'a centríf!a es mc/& ma&r )e $a fer'a de !ra*edad %&r $& ca$ esta 5$tima 5$t ima se %ede des%reciar( a-& $a acción de $a fer'a centríf!a. $a ca%a de $í)id& t&ma na %&sición de e)i$i,ri& c&n s s%erficie interna casi *ertica$. mientras )e $as %artíc$as só$idas se asientan /&ri'&nta$mente. en dirección radia$. /acia e$ e;teri&r. se c&m%rimen c&ntra $as %aredes *ertica$es de$ reci%iente( Ca$)ier e)i%& !irat&ri& en e$ )e se a%$ica na fer'a centríf!a c&n %r&%ósit&s 5ti$es 2e-# %ara se%aración de fases4 se c&n&ce c&m& na centrífuga. %&r $& !enera$ c&nsta de# Fi!ra Ane;& n reci%iente ci$índric& & rotor . en e$ )e $a ss%ensión se ace$era en f&rma centríf!a( n t,& de a$imentación. a tra*+s de$ ca$ entra $a ss%ensión a$ r&t&r( n e-e de im%$s& c&-inetes( n mecanism& im%$s&r 2!enera$mente n m&t&r e$+ctric&4 %ara !irar e$ e-e e$ r&t&r( na c,ierta %ara se%arar $&s %r&dct&s de $a centrif!ación( na estrctra de s&%&rte %ara t&d&s est&s e$ement&s(
#plicaciones de la centrifugación. La se%aración %&r centrif!ación se ti$i'a en n !ran n5mer& de %r&ces&s indstria$es. en f&rma es%ecia$. en $a indstria a$imenticia( A$!nas de estas a%$icaci&nes s&n#
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11
c4 se%ara se%aració ciónn de $í)id $í)id&s &s inmis inmisci, ci,$es $es((
/undaentos de la separación centrífuga: En ca$)ier %r&ces& de se%aración centríf!a. na %artíc$a de n determinad& tama0& se se%ara de$ $í)id& si dis%&ne de sficiente tiem%& %ara $$e!ar /asta $a %ared de$ reci%iente se%arad&r( E$ tiem%& dis%&ni,$e %ara $a se%aración de $a %artíc$a es e$ tiem%& de residencia de $a ss%ensión en e$ e)i%& 2e$ tiem%& de residencia es $a re$ación entre# *&$men de $í)id& $í)id& en e$ reci%iente:cada$ a$imentad& a$ e)i%&4( C&m& $as %artíc$as se me*en a tra*+s de$ f$id& en dirección radia$ a ss *e$&cidades termina$es radia$es. es %&si,$e ca$c$ar e$ di3metr& de $as $ as %artíc$as )e se %eden se%arar c&m%$etamente en $a centríf!a 2& sea. e$ di3metr& de $as %artíc$as %ara $as ca$es $a eficiencia de se%aración sea de$ 1?? D4( En e$ es)ema se re%resenta e$ r&t&r de na centríf!a senci$$a( La a$imentación in!resa a$ reci%iente %&r $a %arte inferi&r. e$ $í)id& c$arificad& se descar!a %&r $a %arte s%eri&r( Se %ede s%&ner )e e$ $í)id& )e in!resa se me*e /acia arri,a c&n na *e$&cidad c&nstante arrastrand& c&nsi!& a $as %artíc$as só$idas. só$idas. $as ca$es. a$ mism& tiem%& s&n s&n des%$a'adas /acia $a %ared a ss *e$&cidades termina$es( E$ tiem%& de sedimentación de $a %artíc$a est3 $imitad& %&r e$ tiem%& de residencia de $a ss%ensión( Las %artíc$as )e. en e$ tiem%& de residencia de $a ss%ensión. %eden $$e!ar /asta $a %ared. s&n se%aradas de$ $í)id&. mientras )e $as )e en ese tiem%& n& $$e!an a $a %ared. s&n arrastradas arrastradas %&r e$ $í)id& )e )e sa$e de $a centríf!a( centríf!a( La se%aración se%aración & n& de $a %artíc$a de%ende de s *e$&cidad termina$ de $a %&sición inicia$ de $a %artíc$a en e$ f$id& 2& distancia radia$ )e de,e rec&rrer $a %artíc$a %ara $$e!ar /asta $a %ared4(
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16 r *
∫ ri
2
2
dr Dp ω ( ρ (− ρ ) = 18 μ r
θ R
∫ dθ 0
ρ (− ρ ) r * Dp ω ( ρ θ R = ln ri 18 μ 2
2
9ónde# R 7 7 :Q. siend& Q# cada$ de a$imentación a$imentación c&m& e$ *&$men *&$men de $í)id& $í)id& en $a centríf!a 2 2 es# 7 π+ ( r 2−r 1 ) . reem%$a'and& en $a ecación anteri&r des%e-and& 9%#
√
r* ) ri Dp = 2 ω ( ρ ( − ρ ) V / , 18 μ ln (
Esta ecación %ermite re$aci&nar re$aci&nar $a eficiencia de se%aración de na %artíc$a c&n $a distancia )e de,e rec&rrer en e$ tiem%& de residencia dis%&ni,$e(
)i-etro Mínio. Se define e$ diámetro mínimo 29%min4 c&m& e$ di3metr& de $as %artíc$as m3s c/icas )e se se%aran t&ta$mente en $a centríf!a 2 )e %&r $& tant&. tienen na eficiencia de se%aración de$ 1?? D4( Estas %artíc$as s&n $as )e. en e$ tiem%& tiem%& de residencia. %eden rec&rrer $a ma&r ma&r distancia %ara %ara $$e!ar /asta $a %ared. es decir. desde r 1 /asta r 6 & e$ es%es&r de $a ca%a $í)ida 2r 6 > r 14 P&r $& tant
Dpmin =
√
r2 ) r1 2 ω ( ρ (− ρ ) V
18 μ , ln (
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1B
> Si r 6 r 1 - estam&s ante n cas& %artic$ar. e$ es%es&r de$ $í)id& es %e)e0& c&m%arad& c&n e$ radi& de $a centríf!a. %&dem&s decir )e r 6 r 1 7 cte 9% 7 9% c. ≅
≅
Vt R= r 2− r 1 2
=vt R . θ R 7=
Dp c =
dr = cte. dθ
√
7=
Vt R=
& dθ
( )
r 2− r 1 2 r ω ( ρ (− ρ ) V / , 9 μ
%ara & =
r
≅
r 2− r 1 2
r2
Genera$i'and& $a e;%resión. se %ede e;%resar# Dpc =
√
( )
9 μ
!e
ω ( ρ (− ρ ) V / , ℜ 2
Para# Se 7 es%es&r medi& de $a ca%a $í)ida( re 7 *a$&r medi& de$ radi& de $a centríf!a( E$ cada$ Qc de a$imentación %ara %r&dcir $a se%aración de$ ?D de $as %artíc$as de 9% c es# ω Dp c ( ρ (− ρ ) . V
ℜ
9 μ
!e
2
,c=
2
alor de siga. %abio de escala. La ecación anteri&r se$e m&dificarse %ara s a%$icación a centríf!as indstria$es( $ti%$icand& di*idiend& %&r 26(!4 a!r%and& $&s t+rmin&s re$aci&nad&s c&n $a centríf!a en n !r%&. $&s re$aci&nad&s c&n $&s só$id&s e$ $í)id& en &tr& !r% 2
2
Dp V ( ( 2
)
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1<
!eparación de (í*uidos Iniscibles. La se%aración de $&s c&m%&nentes c&m%&nentes de na me'c$a me'c$a $í)id&$í)id&. en $a )e am,&s am,&s s&n inmisci,$es est3n finamente di*idid&s. c&m& es e$ cas& de $as em$si&nes. es na &%eración m c&m5n en $a indstria de $a a$imentación( Si en na centrif!a se intr&dce na me'c$a de d&s $í)id&s inmisci,$es in misci,$es A 2 A = 4. se f&rman d&s fases $í)idas. e$ $í)id& m3s dens& tiende a m&*erse /acia $a %ared de$ reci%iente f&rmar n ani$$& s&,re s s%erficie interi&r( E$ $í)id& m3s $i*ian& es des%$a'ad& /acia e$ centr& de r&tación f&rmand& n ani$$& c&nc+ntric& c&n e$ %rimer&( Am,as Am,as fases $í)idas %ermanecen se%aradas %&r na interfase $í)id&$í)id&. $$amada zona neutra( E$ %r&ces& de se%aración dentr& de $a centríf!a se c&m%$eta c&n e$ m&*imient& de !&tas /acia $a interfase 2%r&ces& simi$ar a $a c$arificación4
Fi!( Es)ema de Centríf!a de R&t&r T,$ar La fase c&ntina A es na ss%ensión de !&tas de $í)id& en $í)id& %esad& A# %&r acción de $a fer'a centríf!a estas !&tas !&tas se me*en /acia $a interfase interfase 2/acia $a ca%a de $í)id& 4( E$ di3metr&
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1
En mc/as a%$icaci&nes es im%&rtante c&n&cer $a %&sición de $a interfase $í)id&$í)id&( Para $&ca$i'ar$a se rea$i'a n ,a$ance de $as %resi&nes e;istentes en am,as ca%as( 9rante e$ %r&ces& de se%aración $a interfase de,e %ermanecer esta,$e( 9e acerd& c&n $&s %rinci%i&s de $a est3tica est3tica de f$id&s. $a interfase ser3 esta,$e esta,$e si $a diferencia de %resión en e$ $í)id& $í)id& $i*ian& entre r 1 r i es i!a$ a $a )e )e e;iste en e$ $í)id& $í)id& %esad& entre r < r i 2en e$ re,&sader& de $í)id& %esad&4( Es decir#
Pi > P1 7 Pi > P< La Fc e-ercida s&,re e$ f$id& a na distancia r. es# Fc 7 mr86 La fer'a diferencia$ a tra*+s de n es%es&r dr de $í)id& es# dFc 7 r86dm Per dm 7 26r L4drV La *ariación de %resión en n e$ement& e$ement& diferencia$ de radi& dr $&n!itd L es# 2 2 dFc r ω dm r ω ρ ( 2 πr+dr ) ω ρrdr ¿ = = = ρrdr gc gc 2 πr+g c gc 2
dP Inte!rand
( ω ( r i −r 4 ) (B ω ( r i −r 1 ) 2
2
2 gc
W $a %&sición de $a interfase es#
2
2
=
2
2 gc
2
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1J
E;isten tres ti%&s %rinci%a$es de centríf!as )e se diferencian %&r# a4 $a fer' fer'aa centrí centríf! f!aa )e desa desarr& rr&$$a $$ann ,4 e$ rendimient& )e %ermiten &,tener c4 $a c&ncen c&ncentració traciónn de só$id& só$id&ss c&n )e %ede %edenn &%erar( &%erar( 2er Ane;&4 Este ti%& de centríf!as centríf!as se ti$i'a mc/& %ara $a %rificación de $,ricantes sad&s &tr&s aceites indstria$es. en $as indstrias de $a a$imentación. ,i&)ímica farmac+tica( S&n ,3sicamente se%arad&ras só$id&$í)id&( C&nstan de n r&t&r & c3mara ci$índrica *ertica$ )e !ira a !ran *e$&cidad dentr& de na m&ntra e;teri&r estaci&naria( La c3mara est3 ss%endida de n s&%&rte en s %arte s%eri&r es acci&nada %&r n m&t&r e$+ctric& & na tr,ina( La a$imentación 2na ss%ensión de %artíc$as só$idas en n f$id&4 entra %&r e$ f&nd& de$ r&t&r a tra*+s de na ,&)i$$a estaci&naria de a$imentación a %resión( E$ $í)id& )e entra se ace$era c&n $a *e$&cidad de$ r&t&r. asciende a $& $ar!& de$ reci%iente en f&rma de ani$$& se descar!a %&r $a %arte s%eri&r( L&s L&s só$id&s se des%$a'an /acia arri,a c&n e$ $í)id&. a$ mism& tiem%&. se me*en c&n s *e$&cidad termina$ en dirección radia$ /acia $as %aredes( Si drante s %as& %&r $a centríf!a $a %artíc$a $$e!a a $a %ared. %ared. es se%arada se%arada de$ $í)id&X de n& n& ser así. a%arece a%arece en e$ ef$ente( ef$ente( E$ es%es&r 2& %r&fndidad4 de $a ca%a $í)ida se re!$a re!$a mediante $a %&sición %&sición radia$ de$ &rifici& de de descar!a descar!a en $a %arte s%eri&r de$ reci%iente( reci%iente( Para ace$erar ace$erar mantener e$ $í)id& $í)id& a $a *e$&cidad de r&tación de$ r&t&r. r&t&r. *an %r&*istas de a$etas mec3nicas internas en e$ f&nd& de$ r&t&r( E$ $í)id& centrif!ad& sa$e %&r $a %arte s%eri&r de$ r&t&r( A$!n&s m&de$&s *ienen %r&*ist&s de d&s descar!as de $í)id& de diferente radi&. $& )e %ermite se%arar en f&rma c&ntina d&s $í)id&s inmisci,$es de diferente densidad. mientras. sim$t3neamente. se se%aran %artíc$as só$idas %resentes en $a ss%ensión( La ,icación de $a interfase dentr& de$ r&t&r entre $&s $í)id&s se%arad&s se c&ntr&$a casi siem%re. %ara n rendimient& ó%tim&. %&r medi& de$ a-ste de $a sa$ida de $a fase %esada c&n na arande$a intercam,ia,$e de di3metr& esc&!id&( 1. Centrífugas de rotor tubular
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La fina$idad de $&s disc&s es fndamenta$mente redcir $a distancia de sedimentación. %est& )e na %artíc$a de,e rec&rrer $a distancia )e e;iste entre disc&s %ara ser se%arada( E;isten m&de$&s c&n na s&$a descar!a de $í)id& 2c$arificad&ras4 & c&n d&s descar!as de $í)id& 2%ara se%aración $í)id&$í)id&4( En este cas&. e$ di3metr& de $&s %nt&s de descar!a se %ede *ariar ti$i'and& disc&s intercam,ia,$es( intercam,ia,$es( En a$!n&s m&de$&s. m&de$&s. $a descar!a de $&s só$id&s só$id&s acm$ad&s se de,e /acer en f&rma mana$. mientras )e &tr&s m&de$&s est3n %r&*ist&s de ,&)i$$as %ara $a descar!a descar!a at&m3tica at&m3tica de só$id&s( só$id&s( L&s di3metr&s de r&t&r *arían entre 6? 1?? cm desarr&$$an fer'as de$ &rden de (??? *eces $a fer'a de !ra*edad( S&n en !enera$ de ma&r tama0& )e $as centríf!as de r&t&r t,$ar !iran a *e$&cidades m3s ,a-as( 3. Cen Centri trifug fugas as de rotor rotor macizo macizo: er Ane;&4
En $as centríf!as anteri&res. %r&*istas de c&ndct&s %ara $a descar!a at&m3tica de só$id&s. $&s só$id&s arrastran c&nsi!& na c&nsidera,$e cantidad de $í)id&( Para se%arar na ss%ensión en na fracción de $í)id& c$ar& n $&d& sec&. es necesari& des%$a'ar mec3nicamente de$ $í)id& $&s só$id&s sedimentad&s escrrir$&s mientras se encentran t&da*ía ,a-& $a acción de $a fer'a centríf!a( Para est& se ti$i'an centríf!as se%arad&ras de $&d&s. c&m& %&r e-em%$&. $a centrífuga de rotor macizo. Ysta est3 c&m%esta %&r n r&t&r en f&rma de c&n& trncad& n trans%&rtad&r de t&rni$$& intern& %ara $&s só$id&s. )e a-sta cerradamente c&n e$ c&n& de$ r&t&r( Las d&s %artes !iran
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Mecaniso: Cand& n f$id& car!ad& car!ad& de %artíc$as c/&ca c/&ca c&ntra n cer%&. e$ mism& se des*ía des*ía r&deand& a $a s%erficie. mientras )e $as %artíc$as. en *irtd de s ma&r inercia. tienden a chocar y quedar adheridas a $a s%erficie( Un se%arad&r de im%act& im%act& es n dis%&siti*& en e$ ca$ se /ace /ace f$ir $a ss%ensión# en s traect&ria se encentra c&n &,-et&s só$id&s 2%$acas & *ari$$as %er%endic$ares a $a dirección de f$-&4( La fase !ase&sa rec%era r3%idamente s dirección de f$-&. mientras )e $as %artíc$as cr'an $as $íneas de c&rriente de$ f$id& c/&cand& ad/iri+nd&se a $a s%erficie só$ida. %ermitiend& así s se%aración(
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Objetivos: (a flotación se ti$i'a %ara se%arar %artíc$as $í)idas & só$idas de na fase $í)ida( En a)e$$&s cas&s en )e $a sedimentación de %artíc$as finas se *e$*e antiec&nómica. se $as %ede /acer f$&tar /asta $a s%erficie %&r medi& de ,r,-as de aire( Tam,i+n Tam,i+n se ti$i'a %ara se%arar %artíc$as só$idas entre sí en ,ase a $a /mectación diferencia$ de $&s c&m%&nentes de na me'c$a de %artíc$as en n f$id&( Mecaniso de separación: La se%aración se $&!ra $&!ra inectand& en $a ss%ensión ss%ensión %artíc$asf$id& na c&rriente c&rriente de !as 2!enera$mente aire4 en f&rma de ,r,-as finas( Estas ,r,-as se ad/ieren a $as %artíc$as# $a fer'a de f$&tación de$ c&n-nt& %artíc$a!as /ace )e $a %artíc$a s,a a $a s%erficie( C&n esta t+cnica se $&!ra /acer f$&tar a %artíc$as de ma&r densidad )e $a de$ $í)id&( La f$&tación de%ende de $a tendencia relativa del agua y del aire a adherirse a la superficie de la partícula# e$ a!a )e se encentra s&,re $a s%erficie de $a %artíc$a de,e ser des%$a'ada %&r e$ aire( En estas c&ndici&nes. $a f$&ta,i$idad de$ aire es sficiente %ara arrastrar $a %artíc$a -nt& c&n $a ,r,-a de aire /asta /asta $a s%erficie de$ $í)id&( $í)id&( Esta tendencia tendencia re$ati*a de%ende de%ende de $as fer'as fer'as s%erficia$es de $a %artíc$a. +sta se %eden %eden m&dificar en !ran medida a!re!and& a!re!and& cantidades m
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61
E$ %r&ces& se $$e*a a ca,& en tan)es %r&*ist&s de a!itad&res mec3nic&s( Est&s a!itad&res em%-an /acia arri,a $a me'c$a. f&rmand& na es%ma. )e se se%ara %&r $a %arte s%eri&r de$ tan)e 2!enera$mente *an %r&*ist&s de n rascador de fango %ara $a e$iminación de $a es%ma( L&s tan)es est3n e)i%ad&s c&n n sistema de inección de aire( En e$ cas& m3s senci$$&. e$ aire se intr&dce intr &dce en e$ $í)id& %&r medi& de n im%$s&r !irat&ri&. & de difs&res( En &tr&s cas&s. e$ aire se inecta en la ss%ensión mientras $a misma se encentra ,a-& %resión 2f$&tación %&r aire dise$t&4# %ara e$$& se ti$i'a n tanque de retención en e$ ca$ $a ss%ensión se mantiene drante n&s mint&s %ara %ermitir $a dis&$ción de$ de$ aire. $e!& %asa %asa a$ tan)e de f$&tación f$&tación a tra*+s de na *3$*$a redct&ra redct&ra de %resión. d&nde se %r&dce $a se%aración(
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66
ANEZO CICLONES(
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