6-41
ODE Report (RKF45)
Differential equations as entered by the user
[1] d(T)/d(t) = 0.1
Explicit equations as entered by the user
[1] E2 = 10000
0.025
0.03
P6-14(a)
6-42
See Polymath program P6-14-a.pol.
Calculated values of the DEQ variables
Variable initial value minimal value maximal value final value
V 0 0 50 50
Ca 1.5 0.3100061 1.5 0.3100061
Cb 2 0.3384816 2 0.3384816
Cc 0 0 0.1970387 0.105508
ODE Report (RKF45)
Differential equations as entered by the user
[1] d(Ca)/d(V) = ra/vo
Explicit equations as entered by the user
[1] vo = 10
[2] kf3 = 5
[3] ke2 = .1
[4] kd1 = 0.25
2
2.5
Ca
Cb
Cc
Cd
P6-14 (b)
P6-14 (c)
6-45
6-47
P6-14 (d)
As θB increases the outlet concentration of species D and F increase, while the outlet concentrations of
P6-14 (e)
When the appropriate changes to the Polymath code from part (a) are made we get the following.
See Polymath program P6-14-e.pol.
POLYMATH Results
Calculated values of the DEQ variables
Variable initial value minimal value maximal value final value
V 0 0 500 500
Fa 20 18.946536 20 18.946536
Fb 20 18.145647 20 18.145647
Fc 0 0 0.9342961 0.9342961
Fd 0 0 0.8454829 0.8454829
6-48
rf 0 0 8.59E-05 8.59E-05
rd 0.002 0.0014393 0.002 0.0014393
ODE Report (RKF45)
Differential equations as entered by the user
[1] d(Fa)/d(V) = ra
Explicit equations as entered by the user
[1] vo = 100
[2] Ft = Fa+Fb+Fc+Fd+Fe+Ff
[3] Cto = .4
[4] kd1 = 0.25
[5] ke2 = .1
P6-14 (f)
The only change from part (e) is:
D
D cD D
dF r k C
dV =!
See Polymath program P6-14-f.pol.
P6-14 (g)
The only change from part (e) is:
0B
B
B
F
dF r
=!
P6-15 (a)
P6-15 (b)
Add these equations to the previous program and use it to generate the desired plots.
P6-15 (c)
P6-15 (d)
P6-16 (a)
P6-16 (b)
P6-16 (c) Individualized solution
P6-17 Individualized solution
P6-18 (a)
OLYMATH Results
Example CD Solved Problems – Blood Coagulation 08-25-2005, Rev5.1.233
Calculated values of the DEQ variables
Variable initial value minimal value maximal value final value
t 0 0 700 700
TF 2.5E-11 8.24E-14 2.5E-11 8.24E-14
VII 1.0E-08 3.513E-10 1.0E-08 3.513E-10
TFVIIaIX 0 0 7.2E-14 3.568E-14
IXa 0 0 3.579E-11 3.579E-11
II 1.4E-06 -3.41E-24 1.4E-06 -1.05E-25
VIII 7.0E-10 -2.024E-28 7.0E-10 -1.026E-38
VIIIa 0 0 5.352E-10 3.366E-11
IXaVIIIa 0 0 2.988E-12 2.873E-12
IXaVIIIaX 0 0 5.372E-12 4.995E-12
VIIIa1L 0 0 6.585E-10 6.585E-10
VIIIa2 0 0 6.585E-10 6.585E-10
V 2.0E-08 -1.55E-52 2.0E-08 2.793E-90
Va 0 0 1.943E-08 5.077E-09
XaVa 0 0 1.492E-08 1.492E-08
k4 0.0031 0.0031 0.0031 0.0031
k5 4.4E+05 4.4E+05 4.4E+05 4.4E+05
k6 1.3E+07 1.3E+07 1.3E+07 1.3E+07
k7 2.3E+04 2.3E+04 2.3E+04 2.3E+04
k8 2.5E+07 2.5E+07 2.5E+07 2.5E+07
k9 1.05 1.05 1.05 1.05
k10 6 6 6 6
k11 2.2E+07 2.2E+07 2.2E+07 2.2E+07
k12 19 19 19 19
k13 1.0E+07 1.0E+07 1.0E+07 1.0E+07
6-56
k14 2.4 2.4 2.4 2.4
k15 1.8 1.8 1.8 1.8
k16 7500 7500 7500 7500
k17 2.0E+07 2.0E+07 2.0E+07 2.0E+07
k18 1.0E+07 1.0E+07 1.0E+07 1.0E+07
k27 4.0E+08 4.0E+08 4.0E+08 4.0E+08
k28 0.2 0.2 0.2 0.2
k29 1.0E+08 1.0E+08 1.0E+08 1.0E+08
k30 103 103 103 103
k31 63.5 63.5 63.5 63.5
k32 1.5E+07 1.5E+07 1.5E+07 1.5E+07
k33 9.0E+05 9.0E+05 9.0E+05 9.0E+05
r4 0 0 1.042E-15 5.189E-16
r5 0 0 9.923E-16 2.696E-17
r6 0 0 1.444E-11 6.953E-12
r7 0 0 4.073E-11 1.602E-14
r8 0 0 1.318E-12 5.971E-13
r9 0 0 1.962E-13 8.896E-14
r10 0 0 1.121E-12 5.083E-13
r11 0 0 5.381E-15 5.381E-15
r12 0 0 1.078E-12 4.982E-13
r13 0 0 3.024E-13 1.506E-13
r14 0 0 1.728E-13 8.609E-14
r15 0 0 1.296E-13 6.456E-14
6-57
r35 0 0 4.492E-14 1.762E-14
r36 0 0 2.065E-15 2.065E-15
r37 0 0 3.19E-15 3.19E-15
ODE Report (STIFF)
Differential equations as entered by the user
[1] d(TF)/d(t) = r2-r1-r3+r4
[2] d(VII)/d(t) = r2-r1-r6-r7-r5
[11] d(IX)/d(t) = r14-r13
[12] d(TFVIIaIX)/d(t) = r13-r14-r15
[13] d(IXa)/d(t) = r15-r18+r19+r25-r40
[14] d(II)/d(t) = r30-r29-r16
[15] d(VIII)/d(t) = -r17
[16] d(VIIIa)/d(t) = r17-r18+r19-r23+r24
[17] d(IXaVIIIa)/d(t) = -r20+r21+r22+r18-r19
[18] d(IXaVIIIaX)/d(t) = r20-r21-r22-r25
[19] d(VIIIa1L)/d(t) = r23-r24+r25
Explicit equations as entered by the user
[1] k1 = 3.2e6
[2] k2 = 3.1e-3
[3] k3 = 2.3e7
6-58
[11] k11 = 2.2e7
[12] k12 = 19
[13] k13 = 1.0e7
[14] k14 = 2.4
[25] k25 = 1e-3
[26] k26 = 2e7
[27] k27 = 4e8
[28] k28 = 0.2
[29] k29 = 1e8
[40] k40 = 4.9e2
[41] k41 = 7.1e3
[42] k42 = 2.3e2
[43] r1 = k1*TF*VII
[44] r2 = k2*TFVII
[55] r13 = k13*TFVIIa*IX
[56] r14 = k14*TFVIIaIX
[57] r15 = k15*TFVIIaIX
[58] r16 = k16*Xa*II
[59] r17 = k17*IIa*VIII
6-59
[69] r27 = k27*Xa*Va
[70] r28 = k28*XaVa
[71] r29 = k29*XaVa*II
P6-18 (b) No solution will be given
P6-19
P6-19 (a)
Selectivity of D over CO2
D
F
F
S=
POLYMATH Results
Variable initial value minimal value maximal value final value
W 0 0 2 2
Fe 5.58E-04 1.752E-10 5.58E-04 1.752E-10
Fo 0.001116 4.066E-05 0.001116 4.066E-05
Fd 0 0 2.395E-04 2.395E-04
Fu1 1.0E-07 1.0E-07 6.372E-04 6.372E-04
Differential equations as entered by the user
[1] d(Fe)/d(W) = r1e+r2e
Explicit equations as entered by the user
[1] Finert = 0.007626
[2] Ft = Fe+Fo+Fd+Fu1+Fu2+Finert
[3] K1 = 6.5
[4] K2 = 4.33
X = 0.999 and S = 0.376(mol of ethylene oxide)/(mole of carbon dioxide)
P6-19 (b)
Changes in equation from part (a):
skg
W
From Polymath program: X = 0.71
S = 0.04 (mol of ethylene oxide)/(mole of carbon dioxide)
See Polymath program P6-19-b.pol
P6-19 (c)
Changes in equation from part (a):
From Polymath program: X = 0.96
S = 0.41(mol of ethylene oxide)/(mole of carbon dioxide)
See Polymath program P6-19-c.pol
P6-19 (d) No solution will be given.
P6-20