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Page 1: 0*123-450-* !#$%&'()*+,-$./&'/&.0*. 1&2'1&+(%*.3456,+*.cevale2.uis.edu.co/~cevale2/wiki/images/EQuimicaCristianB.pdf · _3H

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r(t +#t) = r(t) + v(t)#t +12a(t)#t +…

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(+,-./0*123-450-*Catálisis #$/4'<2,*./&0.1&<2-0&9H.+2*34&9D.2&I926*/9D.2&69+,-$./&.+&2*'D.&0*J92*+,-$./&.+96J4'(J0&'.',$<K(+9'.

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Aplicaciones emergentes de las zeolitas P,0<2*+,-$./&.10969.Q&'&+*$<&'.1*2*.$4&%*'.<&+$909)5*'./&.*,2&'.*+9$/,+,9$*/9'.:2*61*'./&.B,/29+*2J429'.1*2*.$4&%9'.+9$%&2(/92&'.+*<*05(+9'.@,J&2*+,-$.+9$<290*/*./&./29)*'R.S*<&2,*0&'.91(+9&0&+<2-$,+9'.

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CONVENIO DE COOPERACIÓNCONVENIO DE COOPERACIÓNTECNOLÓGICA 005 DE 2006TECNOLÓGICA 005 DE 2006

UIS- ICPUIS- ICP

DESARROLLO DE UN MODELO MATEMÁTICODESARROLLO DE UN MODELO MATEMÁTICOY DE SIMULACIÓN DEL PROCESO DEY DE SIMULACIÓN DEL PROCESO DE

BIODEGRADACIÓN DE FENOLBIODEGRADACIÓN DE FENOL

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(+,-./0*123-450-*DESCRIPCIÓN DEL SISTEMADESCRIPCIÓN DEL SISTEMA

Variables de Estudio• Biomasa• Fenol• Amonio• Sulfuro• Hidrocarburo

• pH• Oxígeno Inyectado• Oxígeno Disuelto

!Sistema en Continuo!Utiliza un consorcio microbiano "Pool especie Pseudomonas putida"

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Balances de Materia

MODELO MATEMÁTICOMODELO MATEMÁTICO

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(+,-./0*123-450-*MODELO CINETICOMODELO CINETICO

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(+,-./0*123-450-*MODELOS DE SIMULACIONMODELOS DE SIMULACION

Diagramas de Flujo

El conjunto de ecuaciones diferenciales ordinariasse resolvió inicialmente usando diferencias f initasde primer orden por el método de restas hacia laderecha, y posteriormente se utilizó el método deRunge-Kutta (grado 4) debido a la crecientecomplejidad del modelo. Todo esto fue resueltoutilizando Matlab 6.5.

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1387B023E4*a<S3-8P/-{=>>h*k0,<C*.-*!4,/0.0*)|7-4,-*j>>ig*k0,<C*.-*10B3.0*!|7-4,-*j>?>A*[}jl>>9O8*g*n}@OO8*g*Ow}hA@\2,-]*g*cATA}?i*M</0Cg**

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!"#$%&'()*

(+,-./0*123-450-*

•  79614<&2'.,$.+B&6,'<2C.– (B0CC320B*8-2M0432C*

– 1,<2M0C52*8-,M<.C*

– #704,78*8-2M0432C*

– 1,05C520B*,M-/8<.;40832C*

Page 37: 0*123-450-* !#$%&'()*+,-$./&'/&.0*. 1&2'1&+(%*.3456,+*.cevale2.uis.edu.co/~cevale2/wiki/images/EQuimicaCristianB.pdf · _3H

!"#$%&'()*

(+,-./0*123-450-*

N}~* N}~* N}~* N}~*

!

H"n (x) = En"n (x)

En =h2n2

8mL2

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!"#$%&'()*

(+,-./0*123-450-*

T393.*T<,</*=k*

/*

O*

ZH*

>*=!"

#"

!!"

#$$%

&

'

'+

'

'(= 2

2

2

22

2 yxH

µ!

IJ

Im

rmE

EH

llm

mmm

l

lll

222

)()(222

2

22

===

!=!

!!µ

""

!!"

#$$%

&

'

'+

'

'+

'

'(= 2

2

22

22 112 )µ rrrr

H !

2

2

2

2

2 !µ dd

rH !

"=!±±±=

±=

=

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222

l

lz

l

mmJmJ!

!

Page 39: 0*123-450-* !#$%&'()*+,-$./&'/&.0*. 1&2'1&+(%*.3456,+*.cevale2.uis.edu.co/~cevale2/wiki/images/EQuimicaCristianB.pdf · _3H

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(+,-./0*123-450-*

T393.*T<,</*lk*

lllmmJ

llJllJ

l

lz

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!!!

22

2

2

2

2

2

22

22!"=##

$

%&&'

(

)

)+

)

)+

)

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µµ!!

zyxH

IJ

rllE

EH

l

ll

lll

ml

mlml

mlmlml

22)1(

),()()(),(),(),(

2

2

2

,

,,

,,,

=+

=

!="#$=%%=%

µ

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!!!"

#$$%

&'+

(

()= 2

22

22 112 r

rrr

Hµ!

!!

!!"! #

#

#

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#=$ sin

sin1

sin1

2

2

22

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2

2!"=

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µ! 0497B0/*8<8-4,78*</3-4,05<4**

0497B0/*8<8-4,78*80943,7.-*

e*

;*

H*

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k-9-4-/02;*2l+1

Page 40: 0*123-450-* !#$%&'()*+,-$./&'/&.0*. 1&2'1&+(%*.3456,+*.cevale2.uis.edu.co/~cevale2/wiki/images/EQuimicaCristianB.pdf · _3H

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(+,-./0*123-450-*

w0/8<432*`C23BB0,</*

22

22

21

2kx

dxdH +!=

µ!

)()( xExH nnn !=!

xy

eyHNx ynnn

21

22

)()(

!"

#$%

&=

=' (

!µ)

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& +=21nEn '!

N\/]*

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a<4".-9-4-/0,-*-4-/9;*C,0,-C*

!= ...2,1,0n

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20!!

=E

Page 41: 0*123-450-* !#$%&'()*+,-$./&'/&.0*. 1&2'1&+(%*.3456,+*.cevale2.uis.edu.co/~cevale2/wiki/images/EQuimicaCristianB.pdf · _3H

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T<"S3P/05<40B*8<5<4*

222

21

2krH +!"=

µ!)(

22

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)(12

12

)(2

22

2

2

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rVr

rrr

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%

&''(

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µµµ!!!

),,(),,()(12

12

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,,,,,,2

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lll

lll

mlnmlnmln

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12 ,,,,,,

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Page 42: 0*123-450-* !#$%&'()*+,-$./&'/&.0*. 1&2'1&+(%*.3456,+*.cevale2.uis.edu.co/~cevale2/wiki/images/EQuimicaCristianB.pdf · _3H

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T<"S3P/05<40B*8<5<4*

),()(),()()(2

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µ lll mllnmlnmlln rRErRrVr

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ll mlml llJ #+=# !

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If r=re

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2

2

22

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rr#=#$

%

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Page 43: 0*123-450-* !#$%&'()*+,-$./&'/&.0*. 1&2'1&+(%*.3456,+*.cevale2.uis.edu.co/~cevale2/wiki/images/EQuimicaCristianB.pdf · _3H

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(+,-./0*123-450-*

T<"S3P/05<40B*8<5<4*

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2

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Energy for ro-vibrational motion

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2

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21

emln r

llnEl µ

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/*

Page 44: 0*123-450-* !#$%&'()*+,-$./&'/&.0*. 1&2'1&+(%*.3456,+*.cevale2.uis.edu.co/~cevale2/wiki/images/EQuimicaCristianB.pdf · _3H

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Page 46: 0*123-450-* !#$%&'()*+,-$./&'/&.0*. 1&2'1&+(%*.3456,+*.cevale2.uis.edu.co/~cevale2/wiki/images/EQuimicaCristianB.pdf · _3H

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Page 47: 0*123-450-* !#$%&'()*+,-$./&'/&.0*. 1&2'1&+(%*.3456,+*.cevale2.uis.edu.co/~cevale2/wiki/images/EQuimicaCristianB.pdf · _3H

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_740:*(Ag*13-//0:*()g*80*$+9D.7E:*!"#/'01"#&'(%"#$*34*O/-CCA*

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•  N466*2C.– (<8O7,-/C*M-BO*2M-83C,*74.-/C,04.*832/<C2<O32*d</B.*

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Page 50: 0*123-450-* !#$%&'()*+,-$./&'/&.0*. 1&2'1&+(%*.3456,+*.cevale2.uis.edu.co/~cevale2/wiki/images/EQuimicaCristianB.pdf · _3H

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Page 51: 0*123-450-* !#$%&'()*+,-$./&'/&.0*. 1&2'1&+(%*.3456,+*.cevale2.uis.edu.co/~cevale2/wiki/images/EQuimicaCristianB.pdf · _3H

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•  >@Q.S!S8!=N.!C,7.304,-C*.-*.<2,</0.<^*

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–  L00B<*&</-4<*

!C,7.304,-C*.-*&0-C,/J0^*

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•  >@Q.S!S8!=N.!C,7.304,-C*.-*O/-9/0.<*

–  Z-44;*mE8-H*

–  w78P-/,<*T73H*

–  (B07.30*$BB<0*–  �</9734*N3BB0/-0B*–  k3-9<*mE8-H*

–  (-C0/*_740*–  Z</9-*#734,-/<*–  (/3CEC,<8<*60/0Q0C*

–  Z</9-*c03W-*– &0/2<*6B042<*

–  k-3C;*T<./J97-H*

Page 54: 0*123-450-* !#$%&'()*+,-$./&'/&.0*. 1&2'1&+(%*.3456,+*.cevale2.uis.edu.co/~cevale2/wiki/images/EQuimicaCristianB.pdf · _3H

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(+,-./0*123-450-*

•  A!a.S!S8!=N.!C,7.304,-C*.-*O/-9/0.<*

– &0/,M0*(M02E4*

–  1-/93<*`S0BB-*–  L0<B0*`/ÄH*–  w-/404.<*T<C0B-C*–  !.34C<4*_EO-H*–  _07/0*(0C,-BB04<C*–  (0/B<C*(-B3C*–  _-<40/.<*mE8-H*

–  Z-Å-/C<4*N0B-4230*

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!"#$%&'()*

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!1($!_)*k!*#$%&'()*

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