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6-21
P6-8 (d)
If the drug is taken on a full stomach most of it will not reach the wall at all. The processed food can also
drag the drug to the intestines and may limit its effectiveness. This effect can be seen in the adsorption
Concentration Profiles
6
8
0.6
CB (mg/dm3)
Ca (mg/dm3)
Cb (mg/dm3)
P6-9 (a)
Reactor selection
DBA !+
AD
rr
1
!=
BAA CCTKr )/8000exp(10
1!=
UBA !+
AU rr 2
!=
2/32/1
2)/1000exp(100 BAA CCTKr !=
B
Hence In order to maximize SDU, use higher concentrations of A and lower concentrations of B. This can be
achieved using:
6-22
P6-9 (b)
DBA !+
and
BAA CCTKr )/1000exp(100
1!=
P6-9 (c)
DBA !+
and
110exp( 8000 / )
A A B
r K T C C=!
P6-9 (d)
DA !
and
AA CTKr )/12000exp(4280
1!=
6-23
DA
D
UUD CTKCTK
CTKCTK
rr
r
S
)/10800exp(26)/15000exp(100,10
)/15000exp(100,10)/12000exp(4280
21/ !+!
!!!
=
+
=
At T = 1000K
k1 = 0.026 & k2 = 3.1 X 10-3 & k3 = 5.3 x 10-4
If we keep CA > 1000CD
P6-9 (e)
DBA !+
and
BAA CCTKr )/10000exp(109
1!=
The desired reaction lies very far to the left and CD is probably present at very low concentrations so that:
BA
DBA
UD CC
CCC
S
045.0
025.01034.3 6
/
!"
=
!
0.000334 0.000074
4.5
!=
/0
D U
S!
6-24
P6-9 (f)
DBA !+
and
110exp( 8000 / )
A A B
r K T C C!=!
We want high concentrations of B and U in the reactor. Also low temperatures will help keep the
selectivity high.
If we use pseudo equilibrium and set –rA = 0.
P6-9 (g)
DBA !+
and
0.5
1800exp( 8000 / )
A A B
r K T C C!=!
(1)
( )
( )
( )
( )
1
0.5
/0.5
800exp 8000 / 80exp 8000 /
10exp 300 / exp 300 /
A B
D U
A B A
T C C T
S
T C C T C
! !
= =
! !
At T = 300
6-25
To keep optimize the reaction, run it at a low temperature to maximized SD/U1 in a membrane reactor that
allows only D to diffuse out.
(2)
( )
( ) ( )
0.5
/ 1 2 6
800exp 8000 /
10exp 300 / 10 exp 8000 /
A B
D U U
A B D B
T C C
S
T C C T C C
!
=!+!
P6-9 (h) No solution will be given
P6-9 (i)
1/ 2
1/ 2
exp( 7000 / )
10
D A
U B
r K T C
r C
!
=
DBA !+
AD
rr
1
!=
110exp( 8000 / )
A A B
r K T C C=! !
UBA !+
AU rr 2
!=
1/ 2 3/ 2
2100exp( 1000 / )
A A B
r K T C C=! !
6-26
POLYMATH Results
Calculated values of the DEQ variables
Variable initial value minimal value maximal value final value
V 0 0 10 10
Fa 4 0.5141833 4 0.5141833
Fb 0 0 4.5141833 4.5141833
Fd 0 0 3.034E-06 3.034E-06
ODE Report (RKF45)
Differential equations as entered by the user
Explicit equations as entered by the user
[1] Cto = .4
[2] T = 600
6-27
P6-9 (j) No solution will be given
P6-10 (a)
6-28
P6-10 (b)
For CSTR,
0.5h
!
=
First calculate k1 and k2 :
(1) Non-linear equation solver method
POLYMATH Results
No Title 03-06-2006, Rev5.1.233
NLES Solution
Variable Value f(x) Ini Guess
Ca 0.6236527 4.693E-10 1.5
NLES Report (safenewt)
Nonlinear equations
[1] f(Ca) = tau*(-ra)-(1.6-Ca) = 0
Explicit equations
[1] tau = .5
[4] R = 1.987
(2) Differential equation solver method
POLYMATH Results
No Title 03-06-2006, Rev5.1.233
Calculated values of the DEQ variables
Variable initial value minimal value maximal value final value
t 0 0 500 500
T 200 200 700 700
tau 0.5 0.5 0.5 0.5
ODE Report (RKF45)
Differential equations as entered by the user
[1] d(T)/d(t) = 1
Explicit equations as entered by the user
[1] tau = 0.5
0.6
0.7
0.8
P6-10 (c)
6-31
P6-10 (d)
P6-10 (e)
6-32
P6-11 (a)
Intermediates (primary K-phthalates) are formed from the dissociation of K-benzoate with a CdCl2 catalyst
reacted with K-terephthalate in an autocatalytic reaction step:
POLYMATH Results
Variable initial value minimal value maximal value final value
t 0 0 1500 1500
k3 0.00159 0.00159 0.00159 0.00159
ODE Report (RKF45)
Differential equations as entered by the user
[1] d(A)/d(t) = -k1*A
Explicit equations as entered by the user
[1] k1 = 1.08e-3
P6-11 (b)
1) T = 703 K
CAO = 0.019 mol/dm3
& '
& '
6-33
POLYMATH Results
Calculated values of the DEQ variables
Variable initial value minimal value maximal value final value
t 0 0 1500 1500
A 0.019 3.622E-04 0.019 3.622E-04
ODE Report (RKF45)
Differential equations as entered by the user
Explicit equations as entered by the user
[1] k1 = 2.64e-3
2) T = 663 K
CAO = 0.19 mol/dm3
POLYMATH Results
Calculated values of the DEQ variables
Variable initial value minimal value maximal value final value
t 0 0 10000 10000
A 0.019 2.849E-04 0.019 2.849E-04
ODE Report (RKF45)
Differential equations as entered by the user
Explicit equations as entered by the user
[1] k1 = 0.42e-3
Independent variable
Maxima in R occurs around t = 2500 sec.
P6-11 (c)
Use the Polymath program from part (a) and change the limits of integration to 0 to 1200. We get:
P6-12 (a) P6-12 (b)
P6-12 (c) P6-12 (d)
P6-12 (e)
P6-12 (f) P6-12 (g)
6-35
P6-12 (h)
Mole balance:
( )
!
AAAO rCC "="
( )
!
CC rC =
( )
!
DD rC =
POLYMATH Results
NLES Solution
Variable Value f(x) Ini Guess
Ca 0.0068715 -2.904E-10 3
Cb 0.9620058 -1.332E-15 0
NLES Report (safenewt)
Nonlinear equations
[1] f(Ca) = Cao-Ca+ra*tau = 0
[4] f(Cd) = Cd-rd*tau = 0
[5] f(Ce) = Ce - re*tau = 0
Explicit equations
P6-12 (i)
For PFR and gas phase:
Mole balance:
A
Ar
dV
dF =
B
Br
dV
dF =
C
Cr
dV
dF =
D
Dr
dV
dF =
E
Er
dV
dF =
Plot of CB and CC are overlapping.
See Polymath program P6-12-i.pol.
POLYMATH Results
Calculated values of the DEQ variables
Variable initial value minimal value maximal value final value
V 0 0 100 100
Fa 20 9.147E-04 20 9.147E-04
Cc 0 0 0.0993605 0.0993325
ka 7 7 7 7
kd 3 3 3 3
ODE Report (RKF45)
Differential equations as entered by the user
Explicit equations as entered by the user
[1] Ft = Fa+Fb+Fc+Fd+Fe
[2] Cto = 0.2
P6-12 (j) Changes in equation from part (i):
P6-13 (a)
POLYMATH Results
Calculated values of the DEQ variables
Variable initial value minimal value maximal value final value
V 0 0 6000 6000
Fa 75 6.1072984 75 6.1072984
6-39
Cto 0.05 0.05 0.05 0.05
Ca 0.0375 0.0026257 0.0375 0.0026257
ODE Report (RKF45)
Differential equations as entered by the user
[1] d(Fa)/d(V) = r1+r2
Explicit equations as entered by the user
[1] Fm = Fb
[2] Fi = 25
[3] Ft = Fa+Fb+Fp+Fm+Fi
a τ = 2.8 is necessary to achieve 90% conversion
P6-13 (b)
CSTR
Mole Balances:
6-40
!
AAA rCC += 0
!
BB rC =
!
MM rC =
!
PP rC =
Rate Laws:
( ) AA Ckkr 21 +!=
AMB Ckrr 1
==
AP Ckr 2
=
Combining:
( )
!
210
CkkCC
AAA
+"=
POLYMATH Results
No Title 03-06-2006, Rev5.1.233
Calculated values of the DEQ variables
Variable initial value minimal value maximal value final value
t 0 0 9000 9000
T 500 500 1400 1400
E2 10000 10000 10000 10000
