Chemical Engineering Chapter 13 Irreversible, first order, long tubular reactor

Type Homework Help

Pages 11

Words 883

Textbook Elements of Chemical Reaction Engineering 5th Edition

Authors H. Scott Fogler

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13-41

Maximum Mixedness

( )

( )X

+= 1

See Polymath program P13-9-b-2.pol

POLYMATH Results

Calculated values of the DEQ variables

Variable initial value minimal value maximal value final value

z 0 0 14 14

X 0 0 0.3536026 0.3536026

13-42

ODE Report (RKF45)

Differential equations as entered by the user

[1] d(X)/d(z) = -(ra/Cao+E/(1-F)*X)

[2] d(F)/d(z) = -E

Explicit equations as entered by the user

[1] Cbo = .0313

[2] k = 175

X=35.4%

P13-9 (c)

Exit time(t), internal age(α) and life expectancy

P13-9 (d)

Adiabatic reaction

Segregation model

13-43

POLYMATH Results

Calculated values of the DEQ variables

Variable initial value minimal value maximal value final value

t 0 0 14 14

xbar 0 0 0.7585435 0.7585435

ODE Report (RKF45)

Differential equations as entered by the user

Explicit equations as entered by the user

[1] cbo = 0.0313

=76%

Maximum Mixedness Model

( )

( )X

+= 1

POLYMATH Results

Calculated values of the DEQ variables

Variable initial value minimal value maximal value final value

z 0 0 14 14

X 0 0 0.7189248 0.7189248

F 0.9999 -0.1138842 0.9999 -0.1138842

ODE Report (RKF45)

Differential equations as entered by the user

[1] d(X)/d(z) = -(ra/Cao+E/(1-F)*X)

[2] d(F)/d(z) = -E

Explicit equations as entered by the user

[1] Cbo = .0313

[2] T = 320+150*X

gives X=72%

If the reaction is carried out adiabatically the conversions are more than doubled.

13-45

P13-10

Irreversible, first order, long tubular reactor, constant volume, isothermal

For

0.2865.0 =!=

For laminar flow with negligible diffusion (LFR), the mean conversion is given by:

We can apply the approximated solution due to Hilder:

( )

( ) 782.0

5.0

!++

DaeDa

XDa

where Da=kτ=2

85.0782.0 =<= PFR

P13-11 (a)

First Moment about the mean: by definition is always equal to zero.

13-46

P13-11 (b)

Second-order liquid-phase reaction Da= τkCAo=1.0,τ=2min and kCAo=0.5min-1.

CSTR

VrFF AAAo !=!

XFFF AoAAo =!

PFR

dF !=

AAo r

F!=

Liquid-phase ε = 0 and integrating

kC Ao 1

(

5.0

=Da

LFR

13-47

Evaluate for Da=1,

451.0=X

See Polymath program P13-11-b.pol

CSTR

PFR

LFR

P13-12

( )2

1AA

ACK

The criteria

The following figure shows the reaction rate as function of the concentration.

0.01

13-48

The second derivative is initially negative (Xseg<XMM), then positive (Xseg>XMM). The flex point

is for CA=8mol/dm3 (Xseg=XMM).

P13-13 No solution will be given

P13-14 (a)

Liquid phase, Segregation Model, second order, non-ideal CSTR, adiabatic:

E(t)=IF (t<=1) THEN (t) ELSE ( IF (t>=2) THEN (0) ELSE (2-t))

For a batch globule:

AAo r

C!=

AA kCr =!

13-49

0502/1002/1 =!=!="papb CCCp

T=300+150X

POLYMATH Results

Calculated values of the DEQ variables

Variable initial value minimal value maximal value final value

t 0 0 3 3

ODE Report (RKF45)

Differential equations as entered by the user

[1] d(xbar)/d(t) = E*x

[2] d(x)/d(t) = k*cao*((1-x)^2)

Explicit equations as entered by the user

[1] cao = 2

P13-14 (b)

Parallel reactions, isothermal, segregation model

Batch globules

13-50

BACAC

cCCkrr

22 =!==

Exit concentrations

E(t)=IF (t<=1) THEN (t) ELSE ( IF (t>=2) THEN (0) ELSE (2-t))

P13-15

Reactor: fluidised CSTR (V=1m3; F=10dm3/s, CC

0=2 Kmol/m3)

τ = 1000dm3s/10dm3 = 100s

The system of complex reactions for the Kentucky coal n.9 is given by

P13-15 (a)

Segregation Model

See Polymath program P13-15-a.pol

POLYMATH Results

Calculated values of the DEQ variables

Variable initial value minimal value maximal value final value

t 0 0 20 20

ca 0 0 900.42918 900.42918

cp 0 0 689.61265 689.61265

ODE Report (RKF45)

Differential equations as entered by the user

[1] d(ca)/d(t) = ra

Explicit equations as entered by the user

[1] k1 = 0.012

[2] k2 = 0.046

P13-15 (b)

Maximum Mixedness model

See Polymath program P13-15-b.pol

POLYMATH Results

Calculated values of the DEQ variables

Variable initial value minimal value maximal value final value

z 0 0 20 20

Ca 0 0 875.11273 875.11273

rc 0 -47.836902 0 -47.836902

ra 92 15.190162 92 15.190162

rp 24 24 37.327161 34.677371

tau 1.667 1.667 1.667 1.667

ro 0 0 35.004509 35.004509

ODE Report (RKF45)

Differential equations as entered by the user

[1] d(Ca)/d(z) = -(-ra+(Ca-Cao)*EF)

Explicit equations as entered by the user

[1] k1 = 0.012

[2] k2 = 0.046

[3] k3 = 0.020

13-53

P13-15 (c)

The selectivities are reported in the following table:

P13-15 (d)

Normal Distribution with τ = 5min and σ = 3min

POLYMATH Results

Calculated values of the DEQ variables

Variable initial value minimal value maximal value final value

t 0 0 2 2

ca 0 0 171.75027 171.75027

cp 0 0 52.879376 52.879376

cc 2000 1991.2989 2000 1991.2989

k1 0.012 0.012 0.012 0.012

k2 0.046 0.046 0.046 0.046

k3 0.02 0.02 0.02 0.02

k4 0.034 0.034 0.034 0.034

ODE Report (RKF45)

Differential equations as entered by the user

[1] d(ca)/d(t) = ra

[2] d(cp)/d(t) = rp

13-54

Explicit equations as entered by the user

[1] k1 = 0.012

[2] k2 = 0.046

[3] k3 = 0.020

Maximum Mixedness Model

See Polymath program P13-15-d-2.pol

POLYMATH Results

POLYMATH Report 08-25-2005, Rev5.1.233

Calculated values of the DEQ variables

Variable initial value minimal value maximal value final value

z 0 0 2 2

Ca 0 0 120.77791 120.77791

Cp 0 0 35.906087 35.906087

rc 0 -5.986657 0 -5.986657

ra 92 83.563477 92 83.563477

rp 24 24 27.331698 27.331698

lam 2 0 2 0

ro 0 0 4.8311165 4.8311165

ODE Report (RKF45)

Differential equations as entered by the user

[1] d(Ca)/d(z) = -(-ra+(Ca-Cao)*EF)

13-55

Explicit equations as entered by the user

[1] k1 = 0.012

[2] k2 = 0.046

[3] k3 = 0.020

[4] k4 = 0.034

[5] k5 = 0.04

P13-16

Multiple parallel reactions, isothermal

P13-16 (a)

Segregation model

3/2

ACBABA

ACCkCCkCCk

dC !!!=

175.025.1 CBBABA

BCCkCCkCCk

dC !!!=

13-56

See Polymath program P13-16-a.pol

Exit concentrations: Selectivities:

/026.0 dmmolC A=

00196.0=

P13-16 (b)

Maximum Mixedness model

E(t)=0.0279693-0.0008527λ+1.2778e-5λ2-1.0661e-7 λ3+4.5747e-10 λ4-7.73108e-13 λ5

And λ=tf-z where z=t, tf=200min (extent of E(t)).

and so on for other species.

( ) ( )

dF "=

gives F(λ)

See Polymath program P13-16-b.pol

Exit concentrations: Selectivities:

/028.0 dmmolC A=

0009.0=

13-57

P13-16 (c)

Ideal CSTR

tm=τ and

( )

Mol balances:

and so on for the other species.

See Polymath program P13-16-c.pol

Exit concentrations: Selectivities:

/050.0 dmmolC A=

068.0=

Ideal PFR

tm=τ and RTD function

( ) ( )

#=ttE

( )

dF !=

Where

3/2

ACBABAA CCkCCkCCkr !!!=

and so on for other species.

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Chemical Engineering Chapter 13 Irreversible, first order, long tubular reactor

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Chemical Engineering Chapter 13 Irreversible, first order, long tubular reactor

Unlock document.

Trusted by Thousands ofStudents

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Anna

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Trusted by Thousands of
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