meles Nonisothermal Reaction Engineering

7/26/2019 meles Nonisothermal Reaction Engineering

1/24

Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, Uniersity of !llinois, Ur"ana#Champaign$

L%#%

'eie() *hermochemistry for

+onisothermal 'eactor Design- .-/ 0$1

Mole "alance)

'ate la()

Stoichiometry)

-rrhenius E2uation

Need relationships: X T V

Consider an e3othermic,li2uid#phasereaction operated adia"atically in a

P' 4adia"atic operation# temperature increases do(n length of P'5)

-0

The energy balance provides this

relationship

6- B

- -

-0

d. r

d7 =

- -r 6C =

- - 0

0

- -0 -

C

C C 4% . 5

=

=

=

=

-0 --

-0 0

C 4% . 5d.

d7 C

6

E'*6 -e

=

=- -E % %

' * *%

0

%d. 4% . 5

d76 e3p

=

E % %

' * *%%6 6 e3p


2/24


L%#

'ate of accum

of energy in

system

'ate of

(or6 done

"y syst

energy added

to syst "y

massflo( in

energy leaing syst

"y massflo( out8eat

in/ # 9#

'eie() *erms in Energy Balance

:S) shaft (or6P ) pressure

lo( (or6

!nternal energy is ma;or contri"utor to energy term

Steady state)

-ccum of energy

in system

shaft

(or6

Energy &

(or6 added

"y flo( in

Energy & (or6

remoed "y flo( out

8eat

in

/0/ # 9 #

n n

i i i i sin outi % i %

: P7 P7 :

= =

= + + & &

= =

= + n nssyyss

i iin outi % i %

i i


3/24


L%#>

'eie() 'elate * to Conersion

!f .-0/0, then)

Steady state)

Total energy

balance (TEB)

0 at steady state

Multiplyout)

-ccum of energy

in system

shaft

(or6

Energy &

(or6 added

"y flo( in

Energy & (or6

remoed "y

flo( out

8eat

in/ # 9 #

( )= + +=i i0 i -0 - i -0 i i - . . i0

i-0

(here

=

= =

= + n n

s i0 i0 i

i

i

% i %

0 = : 8 8& &

( )= =

= + + n nssyyss

s i0 i -0 ii % i %

-0 i i -


4/24


L%#?

'eie() = in a CS*'

CS*' (ith a heat e3changer, perfectly mi3ed inside and outside of reactor

*, .

-0

*, .

*a*a

*he heat flo(

tothe reactor is in terms of)

@Aerall heat#transfer coefficient,

U

@8eat#e3change area,A

@Difference "et(een the am"ient temperature in the heat ;ac6et, Ta, and

r3n temperature, T

a= 4U-* *5= &


5/24


L%#

!ntegrate the heat flu3 e2uation along the length of the

reactor to o"tain the total heat added to the reactor )

8eat transfer to a perfectly mi3ed P' in a ;ac6et

a) heat#e3change area per unit olume of reactor

or a tu"ular reactor of diameter D, a / ? D

or a ;ac6eted PB' 4perfectly mi3ed in ;ac6et5)

8eat transfer to a PB'

'eie() *u"ular 'eactors 4P'PB'5)

- 7a a= U4* *5d- Ua4* *5d7= = &

ad=

Ua4* # *5d7

=&

a

" "

% d= d= Ua4* *5

d7 d: = =

& &

-a 7=


6/24


L%#

L%) +onisothermal 'eactor Design

Steadystate total energy balance (TEB):

-t a particular temperature)

or a SS nonisotherm

flo( reactor)

Goal) Use *EB to design nonisothermal steady#state reactors

+eeds to "e simplifiedF "efore (e can apply it to reactor design

Constant 4aerage5

heat capacities )

Su"stitute

48iG 8i05 / # 48iG 8i05

( ) ( )= =

= = + i0n nssyys

is

s -0 i '. -0 -i % i %


7/24Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, Uniersity of !llinois, Ur"ana#Champaign$

L%#1

'elating 8'.4*5 to 8H'.4*'5 andAerall Change in 8eat Capacity

Anly considering constant 4aerage5 heat capacities)

T reaction temp Ti! initial ("eed) temp T# re"erence temp

( ) + = o *'. ' *' P'. 8 4* C d*58 *

= =nP i pi

i %

oerall heat capaci Ct Cy)

( )=

= + + o& & *n

s -0 i p,i -0 -

i %

'*

P

*i0

. *'' C8 40 = : C d* * d* .5

( ) ( )=

=o on

'. ' i i 'i %

oerall heat of reaction at reference t 8 * 8emp) *

( )= =

= +

o n

*i pi

n

i i ' *'ii % %

'. 8 4* 5 C d8 **

[ ] ( )=

= + o& &'

n

s -0 i p .,i i0 -0 -i %

' P '



L%#I

Soling *EB for Conersion

'earrange to isolate terms (ith .-on one side of e2)

Sole for .-)

Plug in = for the specific type of reactor, and

sole this e2 simultaneously (ith design e2uation

-l(ays start (ith this *EB)

[ ] ( )=

= + o& &

n

s -0 i p,i i0 '. ' P ' -0 -i %



L%#J

Soling *EB for .-for an -dia"atic '3n

'earrange)

:hich term in this e2uation is ero "ecause (ere soling for an adia"atic

reactiona5 dEsysdt

"5

c5 d5

-0e5 +one of the a"oe

:hen the reaction is adia"atic 4=/05)

[ ] ( )n

s -0 i p,i i0 '. ' P ' -0 -

i %



L%#%0

Soling *EB for .-for an -dia"atic '3n

:hen shaft (or6 can "e neglected 4/05 and the reaction is adia"atic 4=/05)

'earrange)

Sole for .-)

* / reaction temp *i0/ initial 4feed5 temperature *'/ reference temp

Sole this e2 simultaneously

(ith design e2uation

Design e2s do not change,

e3cept 6 (ill "e a function of *

[ ] ( )n

s -0 i p,i i0 '. ' P ' -0 -

i %



L%#%%

+onisothermal -dia"atic Aperation

Constant or mean heat capacities

or a system (ith no shaft (or6 4 5 & adia"atic operation 4 5)

Usually,

.energy "alance

*emperature

CS*', P', PB', Batch

Adiabatic exothermic reactions

n

s A i pi i A RX R p Ri

Q W F C ( T T ) F X H ( T ) C ( T T )=

+ = 0 0 0%0o& %&

0=sW

0=Q

n

i pi i0i %

'. ' p '

C 4* * 5

.



L%#%

+onisothermal CS*'Design e2uation 4rom mass "alance5 )

Energy "alance) Coupled

:ith the e3ception of processes inoling highly iscous materials,

the (or6 done "y the stirrer can "e neglected 4i$e$ 5:ith heat e3changer)

=-0

-

.7

r

= + =

o& & %n

-0 i pi i0 -0 '. ' p 'i %

s



L%#%>

-pplication to CS*'

a5 Sole *EB for * at the e3it 4*e3it/ *insidereactor5

"5 Calculate 6 / -e#E'*(here * (as calculated in step a

c5 Plug the 6 calculated in step " into the design e2uation to calculate 7CS*'

Case %) Nien -0, C-0, -, E, Cpi, 8O!, and .-, calculate * & 7

a5 Sole *EB for * as a function of .-"5 Sole CS*' design e2uation for .-as a function of * 4plug in 6 / -e

#E'*5

c5 Plot .-,EBs * & .-,MB s * on the same graph$ *he intersection of these

lines is the conditions 4* and .-5 that satisfies the energy & mass "alance

Case ) Nien -0, C-0, -, E, Cpi, 8O!, and 7, calculate * & .-

.-,EB / conersion determined from the *EB e2uation

.-,MB/ conersion determined using the design e2uation

.-

*

.-,EB

.-,MB

.-,e3it

*e3it

!ntersection is * and .-that

satisfies "oth e2uations

L% %?



L%#%?

-pplication to a Steady#State P'

P'P'-0 -

distance

*.-

+egligi"le shaft (or6 4S/05 and adia"atic 4=/05

a5 Use *EB to construct a ta"le of * as a function of .-"5 Use 6 / -e#E'*to o"tain 6 as a function of .-c5 Use stoichiometry to o"tain Gr-as a function of .-d5 Calculate)

( )

.--

-0

- -.-0

d.7

r . ,*=

L% %- fi t d ti -4l5 B4l5 i t " i d t di " ti ll i CS*'



L%#%- first order reaction -4l5 B4l5 is to "e carried out adia"aticallyin a CS*'$

Nien -, E, *0, 0, C-0, and -0, find the reactor olume that produces aconersion .-$ *he heat capacities of - & B are appro3imately e2ual, & S/0$a5 Sole *EB for *)

Multiply out

actor out *

Plug in alues4QCp,

Q8O'.4*'5, Cp,i5 gien

in pro"lem statement

4loo6 them up if

necessary5 & sole

*emp (hen

specified

.-is

reached

0 0

!solate *

[ ] ( )n

-0 i p,i i0 '. ' P ' -0 -i %

C * * 8 4* 5 C * * .=

= + o

[ ] ( )n

s -0 i p,i i0 '. ' P ' -0 -i %0 = : C * * 8 4* 5 C * * .

=

= +

o& &

[ ] ( )'. ' P 'n

i p,i i0i

-%

8C * * 4* 5 C * * .=

+ = o

n

i p,i i0i

'. ' P%

i p,i P- '- -8 4* 5 C C *. .C C * .* *=

= + o

n

i p,i i

n

i p,i P - 0'. ' - P ' -i % i %

C C . 8 4* 5. C * . C* **==

+ = + + o

n

i p,i P - '. ' - P ' - p,- -0i %

C C . 8 4* 5. C * . C **

=

+ = + +

o

- -

n

'. ' P ' i p,i i0i %

n

i p,i P

%

-

i

.8 4* 5 C * C *

C

*

C

.

.

=

=

+ + =

+

o

L% %- fi t d ti -4l5 B4l5 i t " i d t di " ti ll i CS*'



L%#%- first order reaction -4l5 B4l5 is to "e carried out adia"aticallyin a CS*'$

Nien -, E, *0, 0, C-0, and -0, find the reactor olume that produces aconersion .-$ *he heat capacities of - & B are appro3imately e2ual, & S/0$a5 Sole *EB for * of reaction (hen the specified .-is reached)

"5 Calculate 6 / -e#E'*

(here * (as calculated in step 4a5 Loo6 up E in a thermo "oo6

c5 Plug the 6 calculated for the reactions temperature (hen the specified .-

is reached 4in step "5 into the design e2uation to calculate 7CS*'

n'. ' - P ' - i p,i i0

i %n

i p,i P -i %

8 4* 5. C * . C *

*

C C .

=

=

+ + =

+

o

( ) ( )-0 - -0 - -0 - -0 0 -

- - -0 - -0 - . . . C .7 7 7 7

r 6C 6C % . 6C % .

= = = =

( )0 -

-

.7

6 % .

=

L% %1



L%#%1

+o(, the first order reaction -4l5 B4l5 is carried out adia"atically(ith and

inlet temp of >00 K, CP-/0 calmolRK, and the heat of reaction / #0,000

calmol$ -ssume S/0$ *he energy "alance is)

rom thermodynamics.EB

*

rom energy "alance

0 0

( )

( )

n

i pi 0i %

EB '.

C * *

.8 *

=

=

%-

n

i pi pi %

C % C

=

= ( )

( )

-P 0

EB '.

C * *.

8 *

=

( )EB

0 * >00.

0000

=

( ) ( ) + = o'. '. ' P '



L%#%I*he irreersi"le, elementary li2uid#phase reaction - B is carried out adia"atically in

a flo( reactor (ith S/0 and (ithout a pressure drop$ *he feed contains e2ual molaramounts of - and an inert li2uid 4!5$ *he feed enters the reactor at J? K (ith 0/ dm>s and C-0/ % moldm

>$ :hat (ould "e the temperature inside of a steady#state

CS*' that achieed .-/ 0$I E3tra info)

E / %0,000 calmol Cp-/ % calmol@K CpB/ >0 calmol@K Cp!/ % calmol@K

Q8-O4*'5 / #0 6calmol Q 8BO4*'5 / #0 6calmol Q8!O4*'5 / #% 6calmol

6 / 0$0 dm>mol@s at >0 KStart (ith SS EB & sole for *)

Multiply out "rac6ets & "ring

terms containing * to % side

[ ]n

s -0 i p,i i0 '. -0 -i %

0 = : C * * 8 4*5 .=

= & &

[ ]n

-0 i p,i i0 -0 -i %

'.0 0 0 C * * 8 4*5 .

=

=

[ ] ( ) ( ) ( )n

-0 i p,i i0 ' -P' 0'i

. -%

8 C * * * *C* .=

= +o

[ ] ( )n

i p,i i0 '. ' P ' -i %

C * * 8 4* 5 C * * .=

= + o

n ni p,i P - '. ' - P ' - i p,i i0

i % i %

C * C *. 8 4* 5. C * . C *= =

+ = + + o

n

'. ' - P ' - i p,i i0i %

n

i p,i P -i %

8 4* 5. C * . C *

*

C C .

=

=

+ + =

+

o

L% %J*h i i"l l t li id h ti - B i i d t di " ti ll i



L%#%J*he irreersi"le, elementary li2uid#phase reaction - B is carried out adia"atically in



CS*' that achieed .-/ 0$IE3tra info)



6 / 0$0 dm>mol@s at >0 K

Start (ith SS EB & sole for *)

n

i p,ii %

n

i p,i

- '

i %

- i0

-

' P'

P

. . * . *C

C

*

.

C

C

8 4* 5=

=

+ + =

+

o

B -

"CCp Cp pa

= C 0p =% cal cal

>0 % mol K mol K

Cp = g g

( ) ( )n

i p,i

i

B !

%

-cal cal

% 0 % / % % 9 % %

mo

calC >0

ml K mo l Kl K o=

= = = =

g g g( ) ( ) ( ) ( ) ( )

d c "8 * 8 * 8 * 8 *D ' C '8 *'. ' B ' - 'a a a

= + o o o oo

( )% cal cal

0,000 0,000 mol m

8 ' l*

o. ' =

o ( )cal

8 * 000'. ' mol =o

L% 0*h i i"l l t li id h ti - B i i d t di " ti ll i



L%#0*he irreersi"le, elementary li2uid#phase reaction - B is carried out adia"atically in



CS*' that achieed .-/ 0$I E3tra info)



6 / 0$0 dm>mol@s at >0 K

Start (ith SS EB & sole for *)

n

i p,ii %

n

i p,i

- '

i %

- i0

-

' P'

P

. . * . *C

C

*

.

C

C

8 4* 5=

=

+ + =

+

o

C 0p =n

i p,ii %

calC >0

mol K==

g ( )

cal8 * 000'. ' mol

=o

-cal

>0

mol

cal000

Kca

moll

>0mol K

. J?

*

0

0

K + + =

+g

g

-cal cal

000 . II0

mol mol*cal

>0mol K

+ =

g

( ). 0$I-

* %$1K 0$I J?K=

= +-. 0$I

* ?1$>K= =

L%#%*he irreersi"le elementary li2uid phase reaction - B is carried out adia"atically in



L%#%*he irreersi"le, elementary li2uid#phase reaction - B is carried out adia"atically in


>$ :hat (ould "e olume of the steady#state CS*' that

achiees .-/ 0$I E3tra info)



6 / 0$0 dm>mol@s at >0 K

Sole the CS*' design e2 for 7 at .-/ 0$I & * / ?1$>K)

>dm %0,000cal mol % % 0$0 e3p

mol s %$JI1cal mol K >0K+eed at ?1$>K)

?1$>6 6

=

( )>dm6 0$0 e3p $0%?mol s

=

>dm6 0$J

mol s =

-0 -

CS*'

-

.7

#r=

-

-r 6C = ( )- -0 -Stoichiometry ) C C % .= ( )

-0 0 -C

-0 -

S*'Com"ine )

C %C .7

6 .=

( )

( )

>

CS*' >&

>

dmB 0$I

s7dm mol

0$&DJD % % 0$I

mol s dm

=

>

CS*'7 >10$Jdm =

L%#*he irreersi"le elementary li2uid phase reaction - B is carried out adia"atically in


22/24


L% *he irreersi"le, elementary li2uid#phase reaction - B is carried out adia"atically in


>$ Use the $%point r&leto numerically calculate the P'

olume re2uired to achiee .-/0$I E3tra info)



6 / 0$0 dm>mol@s at >0 K@ Use the energy "alance to construct ta"le of * as a function of .-@ or each .- , calculate 6, #r-and -0#r-

@ Use numeric ealuation to calculate 7P'X' T() (dm*+mol,s) %r'(mol+dm*,s) -'!+%r'(dm*)! J?

!./ ?1$> 0$J

Calculated in CS*' portion of this pro"lem

0$00%J 0$00%J

0$0%01I?

>dm % %6 0$0& e3p B0>&$1%&DKmol s >B0K &J?

=

>dm6 0$00%&J mol s =

( )

- -0 -r 6 C % . = ( )

. 0 . 0- -

&&

- -D >

>dm mol molr 0$00%&J % % 0 r 0$00%&J

mol s dm dm s= =

= = g

( ). 0$I . 0$I- -

- - >

>dm mol molr 0$J % % 0$I r 0$0%01I?

mol s dm dm s= =

= =

g

L%#>*he irreersi"le elementary li2uid phase reaction - B is carried out adia"atically in


23/24


L% >*he irreersi"le, elementary li2uid#phase reaction - B is carried out adia"atically in







@ Use numeric ealuation to calculate 7P'X' T() (dm*+mol,s) %r'(mol+dm*,s) -'!+%r'(dm*)! J? 0$00%J 0$00%J

!./ ?1$> 0$J 0$0%01I?

>I1

?>$

-0 -0 0

C=

-

>-0

- . 0>

mol

s >I1 dmmolr

0$00%Jdm s

=

= =

g

>

-0 >

mol dm mol %

dm s s

= =

-

>-0

- . 0$I>

mol

s ?>$ dmmolr

0$0%01I?dm s

=

= =

g

L%#?*he irreersi"le elementary li2uid phase reaction - B is carried out adia"atically in


24/24

Slid t f P f M L K ft Ch i l & Bi l l E D t U i it f !lli i U " Ch i

L% ?*he irreersi"le, elementary li2uid#phase reaction - B is carried out adia"atically in







@ Use numeric ealuation to calculate 7P'X' T() (dm*+mol,s) %r'(mol+dm*,s) -'!+%r'(dm*)! J? 0$00%J 0$00%J >I1

!./ ?1$> 0$J 0$0%01I? ?>$

( ) ( ) ( )

%0 I 0 0 I

0 % % 00

= + = = =

Xh

2-point rule: ! "! X X #here h X X h $ h $X

> >0 I >I1 ?>

= + FR$

"' $ "'

>%1> =FR "'

Documents

meles Nonisothermal Reaction Engineering